---
title: "The Spoils of War: Trade Shocks & Segmented Labor Markets in Spain during WWI"
authors: "Simon Fuchs"
date: "February 2026"
pdf: "/research/spoils_of_war.pdf"
markdown_source: "/research/markdown/spoils-of-war.md"
markdown_generated: "2026-07-20"
---
# The Spoils of War: Trade Shocks & Segmented Labor Markets in Spain during WWI
**Authors:** Simon Fuchs
**Version:** February 2026
**JEL:** D5, F11, F12, F15, F16, N9, N14, R12, R13
**Keywords:** Gains from trade; labor mobility; economic geography
[Download the paper as PDF](/research/spoils_of_war.pdf)
> This Markdown version was generated from the authors’ TeX source and checked against the PDF linked above. Figure images are omitted here; their captions and notes are retained.
## Abstract
How do large export-demand shocks propagate across connected labor markets? This paper studies the regional incidence of the WWI trade boom in Spain using newly assembled data on product-destination exports, province-sector wages and employment, and province-product consumer prices (1910–1920). Exploiting plausibly exogenous shifts in foreign demand from belligerent nations, I use a reduced-form design that decomposes exposure into direct (local) effects and spillovers across connected markets. Exposed markets experienced large increases in nominal wages and employment; within-province wage spillovers are roughly half the size of the direct effect. These nominal gains were partially offset by rising local consumer prices. To interpret these patterns, I develop a quantitative spatial equilibrium model with nested labor mobility across regions and sectors. The model implies that limited interprovincial mobility dampened worker reallocation and amplified wage and price pressures, shaping the spatial distribution of real-income gains. Counterfactuals show that spatial labor-market segmentation is an important amplifier of incidence: removing spatial migration frictions reduces cross-province dispersion in nominal wages and real income, while shifting adjustment toward reallocation rather than local wage/price pressure. Moreover, making the export-demand impulse spatially even sharply compresses inflation dispersion, implying that both the geography of the shock and domestic segmentation are first-order for the distribution of gains.
**Author note:** Acknowledgements and institutional disclaimers are preserved in the paper notes.[^1]
## Introduction
A large body of empirical research has documented the uneven effects of trade shocks on local labor markets, highlighting changes in employment, wages, and economic activity across regions and sectors ([David H. Autor et al. 2016a](#ref-doi:10.1146/annurev-economics-080315-015041); [Topalova 2010](#ref-10.1257/app.2.4.1); [Kovak 2013](#ref-10.1257/aer.103.5.1960); [Dix-Carneiro and Kovak 2017](#ref-10.1257/aer.20161214); [Jaravel and Sager 2019](#ref-RePEc:cep:cepdps:dp1642); [Adao et al. 2019](#ref-NBERw25544)). Much of this evidence focuses on trade shocks operating through the *import side*---import competition and liberalizations that increase import penetration. By contrast, we know less about the local labor-market incidence of shocks operating through the *export side*, i.e., sudden increases in foreign demand for domestic exports ([McCaig and Pavcnik 2018](#ref-10.1257/aer.20141096)). In addition, many studies implicitly treat local labor markets as isolated, overlooking the interconnected network structure through which labor mobility constraints and sectoral linkages shape the distributional effects of shocks---potentially generating localized wage pressure, inflation, and limited labor reallocation.
This paper studies the regional incidence of a large *export-demand boom* when workers face frictions moving across regions and sectors. Export booms may operate through different margins than import shocks---especially in segmented labor markets where worker inflows are limited---and their incidence may hinge on equilibrium spillovers across connected province--industry cells. We bring these elements together by combining newly assembled historical data with a reduced-form design that decomposes the impact of WWI into direct (local) exposure and indirect (spillover) exposure, and by using a quantitative spatial model with nested region--sector labor supply to interpret the estimated direct and indirect responses.
This delivers two contributions. First, we provide evidence on the *regional incidence of an export-demand shock*, a dimension of trade adjustment that is less documented than import-competition shocks in the local labor-markets literature. Second, we show that the incidence of export demand operates through an *interconnected system of province--industry labor markets*: limited mobility generates spillovers across sectors and space and shifts adjustment toward wages and consumer prices, with first-order implications for real income.
Our empirical setting is Spain during World War I (1914--1918). Although Spain remained neutral, the war generated a sharp and plausibly exogenous increase in foreign demand for Spanish goods as belligerent economies reallocated production and procurement toward wartime needs. Because Spanish provinces differed in their pre-war export specialization, the aggregate boom translated into substantial *province-by-industry* heterogeneity in exposure (Figure [1](#figure:aggregate_exports)). We compile a new spatial panel dataset that merges (i) hand-collected product--destination trade statistics, (ii) province-level employment and wage information by sector and worker type from nationwide surveys, and (iii) province-by-product consumer prices (with urban/rural coverage) from 1910 to 1920. This combination of outcomes---wages, employment, and consumer prices---lets us trace the nominal and real incidence of the export boom across space and sectors.
> **Aggregate Exports from Spain**
>
> Figure available in the [PDF](/research/spoils_of_war.pdf).
Empirically, we construct predetermined exposure measures using pre-war export shares. The baseline specification is a two-way fixed-effects event-study/difference-in-differences design at the province--sector--labor-type level (and analogously for province--product prices), where outcomes respond to (i) *direct* exposure to the WWI export-demand shock and (ii) an *indirect* exposure that captures spillovers from other locations through the connected structure of labor markets. This reduced-form decomposition mirrors the way a broad class of spatial models can be expressed in terms of direct and indirect effects via labor market linkages ([Adao et al. 2019](#ref-NBERw25544)) and provides a transparent link between the empirical estimates and the quantitative model. We assess the identifying assumption---parallel counterfactual trends---using flat pre-war patterns in exports and outcomes, and we further strengthen the demand-shock interpretation with a third-country shift-share instrument that uses destination-level import growth measured outside Spain. Throughout, we also control for contemporaneous import-side disruptions using predetermined import-exposure measures, ensuring the estimated export-demand effects are not confounded by wartime import supply shocks.
We find three main results. First, provinces and sectors more exposed to the export-demand shock experienced sizable increases in nominal wages (with within-province indirect wage spillovers being roughly half the size of the direct effect), but they also saw pronounced increases in consumer prices, implying that real-income gains were substantially muted in the most exposed places. Second, spillovers matter: indirect exposure generates economically and statistically meaningful wage and price responses outside the directly exposed cells, consistent with shock propagation through connected labor markets when spatial mobility is limited. Third, employment adjustment is comparatively more constrained and occurs primarily within provinces (across sectors and worker types) rather than through large inter-provincial reallocation (which accounts for only 24 percent of the total reallocation flow), highlighting the importance of spatial mobility frictions in shaping the incidence of the boom.
To interpret these empirical patterns, we develop a quantitative spatial equilibrium model with multiple sectors and a nested region--sector labor supply system. The model makes explicit how mobility frictions shape both (i) the local wage/employment response to an external demand shock and (ii) the spillovers to other locations. We discipline the key propagation parameters---sectoral and spatial labor supply elasticities and trade elasticities---using moments that are directly comparable to the reduced-form estimates. We then use the model to quantify the incidence of the WWI export-demand shock on wages, employment, and consumer prices across provinces and to run counterfactuals that isolate the role of spatial and sectoral mobility frictions. In line with the reduced-form evidence, the quantitative exercise shows that limited mobility amplifies nominal wage and price pressures in exposed locations and dampens reallocative adjustment, shaping the distribution of gains and losses across regions.
> **(1) Aggregate Composition of the Economy and (2) Evolution of the Spanish CPI**
>
> Figure available in the [PDF](/research/spoils_of_war.pdf).
This paper contributes to several strands of research in international trade, labor economics, and economic geography. First, it adds to the extensive literature on the impacts of trade shocks on local labor markets. While much of this literature has focused on the adverse effects of import-competition shocks---most prominently in the "China shock" tradition ([Autor et al. 2013](#ref-10.1257/aer.103.6.2121); [David H. Autor et al. 2016b](#ref-Autor2016-fa))---this paper shifts focus to the regional incidence of an export-demand expansion. In doing so, it complements a smaller but influential body of work studying how improved access to foreign markets reallocates labor and changes local outcomes ([McCaig and Pavcnik 2018](#ref-10.1257/aer.20141096); [Dauth et al. 2014](#ref-10.1111/jeea.12092)). By examining a large export boom in WWI-era Spain, the paper provides new evidence that export-demand shocks can generate uneven regional adjustments in segmented labor markets, showing up not only in wages and employment but also in local consumer prices---an incidence margin that is rarely observed in modern trade-shock settings (with one exception being ([Jaravel and Sager 2023](#ref-Jaravel2023-zb))).
Second, this paper adds to a growing empirical literature that studies how trade shocks propagate through *connected* local labor markets once general-equilibrium linkages are taken seriously. A key insight is that even when the primitive impulse is sector-level foreign demand, equilibrium outcomes in a given local market depend on both *direct* exposure and an *indirect* exposure component that aggregates shocks hitting other markets through equilibrium reallocation and goods-market linkages ([Adao et al. 2019](#ref-NBERw25544)). We adopt this organizing principle and apply it to a large export-demand expansion during WWI, using a labor-supply structure that distinguishes between sectoral reallocation frictions and spatial mobility frictions. The resulting incidence patterns are consistent with spatial frameworks in which mobility frictions and interregional trade shape whether adjustment loads onto wages versus employment and local costs of living ([Monte et al. 2018](#ref-10.1257/aer.20151507); [Caliendo et al. 2019a](#ref-Caliendo2019-gz)), while highlighting that sectoral and spatial adjustment margins can play distinct roles in the propagation of shocks across markets.
Finally, the paper contributes to the spatial trade and local labor markets literature by highlighting how incidence depends jointly on workers' ability to reallocate *across sectors within a location* and to migrate *across locations*. To capture these two margins separately, we embed a nested region--sector labor-supply system that allows the sectoral and spatial reallocation elasticities to differ. This structure implies distinct predictions for (i) direct effects in the shocked province--sector cells and (ii) indirect spillovers to other sectors within the same province and to the same sector in nearby provinces, with adjustment showing up not only in wages and employment but also in local consumer prices. The paper therefore complements the existing literature that explore the implication of labor mobility on spatial equilibria ([Caliendo et al. 2019a](#ref-Caliendo2019-gz); [Galle et al. 2017](#ref-RePEc:nbr:nberwo:23737); [Kim and Vogel 2020](#ref-RePEc:nbr:nberwo:27133); [Lee 2020](#ref-RePEc:eee:inecon:v:125:y:2020:i:c:s0022199620300283); [Adao et al. 2019](#ref-NBERw25544); [Monte et al. 2018](#ref-10.1257/aer.20151507)), but goes beyond the existing literature by highlighting the sharp distinction between spatial and sectoral labor mobility and its implication for spatial inequality, and providing sharp quantitative results on the implications of different types of labor mobility frictions on the spatial dispersion of equilibrium outcomes and specifically real income.
The remainder of the paper is structured as follows. Section [2](#sec:Data) introduces the historical background, describes the newly assembled data, and documents the export-demand shock induced by World War I. Section [3](#sec:empirical_strategy) uses these shifters to construct predetermined local exposure measures and provides reduced-form evidence on the trade shock's effect on local labor markets. Section [4](#sec:Theoretical-Model-1) describes the quantitative spatial equilibrium model and its estimation, and explores the regional incidence of the boom through counterfactuals. Finally, Section [5](#sec:Conclusion) concludes.
## Historical setting, data, and the WWI export-demand shock
This section provides the historical background, describes the data, and documents the export-demand shock induced by World War I. Spain's neutrality provides a plausibly exogenous foreign-demand shift: the onset of the war generated sharp changes in external demand in specific product groups and destinations, while the timing and primary drivers of the shock are external to Spanish local conditions. Using newly assembled product--destination trade records (1910--1919), we show that exports to belligerent destinations rise sharply at the onset of the war, with no differential pre-trends. We then summarize this variation by estimating sector-level WWI export-demand shifters, $\widehat z_s$, which capture each sector's differential export growth to belligerent destinations during WWI relative to 1910--1913. Section [3](#sec:empirical_strategy) uses these shifters to construct predetermined local exposure measures and estimate reduced-form effects on wages, employment, and prices.
> **Data at a Glance: Summary of Regional Panel Components (1910--1920)**
-------------------------- ------------------------------ ----------- ------------ ---------------------------------------
**Dataset** **Unit of Analysis** **Freq.** **Years** **Primary Source(s)**
Wages & Employment Province $\times$ Industry Annual 1908--1920 *Inst. de Reformas Sociales*
Trade (Exports/Imports) Product $\times$ Destination Annual 1910--1919 *Estadística del Comercio Exterior*
Consumer Prices Province $\times$ Product Monthly 1910--1919 *Bol. del Inst. de Reformas Sociales*
Census (Population/Mig.) Province Decennial 1910--1920 *Censos de Población de España*
Railroad Distances Province $\times$ Province Fixed 1920 *Guía de Ferrocarriles (1920)*
-------------------------- ------------------------------ ----------- ------------ ---------------------------------------
At the beginning of the 20th century, Spain remained at a relatively low level of industrial development.[^2] According to census data, in 1900 roughly 70% of the working population worked in agriculture and only 12.5% worked in manufacturing. Industrialization proceeded only slowly, with the industrial sector growing marginally in total employment by 3%, adding a little less than 40,000 jobs nationwide in the first decade of the century. At that time, the largest share of the industrial sector was made up of sectors associated with primary goods, such as the exploitation of mines or the production of construction material.
In terms of the spatial distribution of the population, most of the population was still concentrated in predominantly rural and agricultural areas such as Andalucı́a[^3] or Castilla y León.[^4] Major urban centers such as Oviedo, Valencia, Bilbao, Madrid, and Barcelona concentrated most of the industrial activity, as can be seen in Figure [3](#figure:map_manu_employment-2). These spatial clusters imply that sectoral export shocks will be geographically concentrated, increasing the scope for local labor-market tightness when mobility is limited.
> **Spatial Distribution of Manufacturing Employment**
>
> Figure available in the [PDF](/research/spoils_of_war.pdf).
>
> Notes: Spatial distribution of total manufacturing and mining employment by province in 1910. The map excludes the Canary Islands and North African territorial possessions. The data captures employment across 23 industrial sectors and mining at the provincial level. Darker shading corresponds to higher absolute employment levels. Notable industrial and mining clusters are visible in Catalonia (Barcelona), the Basque Country (Vizcaya), Asturias (Oviedo), and the capital (Madrid), alongside mining hubs in Andalusia (Huelva). Source: author’s calculations based on digitized provincial-level records from the 1910 Census of Population.
In terms of internal migration, up until the 1920s, the Spanish economy was marked by perennially low levels of internal migration, with net migration never amounting to more than 5% of the population at a decennial rate---as has been previously discussed by the literature ([Silvestre 2005](#ref-10.2307/41378422)).[^5] Finally, in terms of external markets, at the end of the 19th century, (former) colonies and other Latin American markets played a particularly important role, while after the loss of the colonies Spain's exports shifted more towards European countries with France and Great Britain taking up the biggest share of exports (compare the right-hand side in Figure [4](#figure:export_composition)). Most of the exports were raw materials or agricultural products consistent with the low developmental status of Spain at the time as depicted on the left-hand side in Figure [4](#figure:export_composition). In general, Spain ran a trade deficit for most of the beginning of the 20th century except for the short period under consideration in this paper.
> **Top Export Sectors and Destinations (1910, 1915, 1916)**
>
> Figure available in the [PDF](/research/spoils_of_war.pdf).
>
> Notes: Aggregate exports (in million pesetas) by sector; aggregate exports (in million pesetas) by destination country. Exports reported for top seven sectors and top six destinations respectively according to their rank in 1915. The source data are the digitized product-destination level trade statistics, as discussed in the online appendix.
To examine the impact of WWI on both trade flows and local labor markets, we construct a regionally disaggregated dataset for Spain. The core analysis relies on a high-frequency annual panel spanning 1908--1919 for wages and employment, and 1910--1919 for prices and trade. We supplement this panel with benchmark cross-sections for 1910, 1914, 1920, and 1925 to validate broader structural changes.[^6]
First, we digitize disaggregated information regarding wages and labor quantities across local labor markets from historical surveys by the *Instituto de Reformas Sociales* and the Ministry of Labor (e.g., [Ministerio de Trabajo 1927](#ref-spain1927estadistica)). This yields an annual panel (1908--1919) of wages and employment levels across 48 different provinces and 23 different industries. Second, we augment this industry survey with additional demographic data from the decennial censuses to impute agricultural employment and baseline internal net migration flows ([Silvestre 2005](#ref-10.2307/41378422)). Third, we digitized trade statistics for the years 1910--1919, compiling the quantity and value of both exports and imports across 383 product categories and 77 different origin and destination countries. We construct a correspondence between product-level data and industry-level labor market data using official occupational concordance publications ([Instituto Nacional de Prevision Social 1930](#ref-4185)). Fourth, we obtain detailed information on province-level consumer prices of key agricultural and non-agricultural goods at a monthly frequency (1910--1919) from the bulletins of the *Instituto de Reformas Sociales* ([Gomez-Tello et al. 2018](#ref-SpainHistPrices)).
[Table](#tab:data_glance) provides a concise overview of the regional panel components, their scope, and their archival sources.
In a first step, we document the WWI export shock using the trade records. In 1915, aggregate exports increased sharply and stayed at a high level for as long as the war lasted.[^7]
Most of the increase was due to a differential rise in exports to belligerent destinations relative to non-belligerent destinations, as shown in Figure [1](#figure:aggregate_exports). To formalize this and to assess pre-trends, we estimate the following event-study specification at the destination--product level using Poisson Pseudo-Maximum Likelihood (PPML) to accommodate zeros and heteroskedasticity ([Silva and Tenreyro 2006](#ref-RePEc:tpr:restat:v:88:y:2006:i:4:p:641-658)):[^8]
$$
\mathbb{E}[X_{d,p,t} \mid \cdot] = \exp\!\left(\sum_{t \neq 1913} \beta_{t} \times \mathbf{1}\{t\}\times \text{Belligerent}_{d} + \mu_{d,p} + \mu_{p,t}\right),
$$
where $X_{d,p,t}$ is the value of Spanish exports of product $p$ to destination $d$ in year $t$, and $\text{Belligerent}_{d}$ indicates destinations participating in WWI throughout the war. The fixed effects $\mu_{d,p}$ and $\mu_{p,t}$ absorb time-invariant destination--product differences and product-specific year shocks, respectively. The coefficients $\beta_t$ capture differential changes in exports to belligerent destinations relative to the omitted year 1913. These estimated coefficients are plotted in Figure [5](#figure:exports_event_study_destination), graphically confirming the lack of pre-trends and the sharp, sustained increase in exports to belligerent destinations starting in 1914.
> **Belligerent Export Destinations**
>
> Figure available in the [PDF](/research/spoils_of_war.pdf).
>
> Notes: Figure plots the estimated coefficient on the dummy variable that indicates that a destination country is a belligerent country. The depicted coefficient corresponds to βt from Equation ([eq:stylized_fact_1]). The red dotted lines indicate 95% confidence intervals. The blue shaded area indicates the period of WWI. The source data are the digitized product-destination level trade statistics. More information on data construction can be obtained in the online appendix.
Table [Table](#table:event_study_exports) reports the corresponding coefficients $\beta_t$ from [Equation](#eq:stylized_fact_1), quantifying the aggregate export event study. Column (3), which includes strict product--year and destination--product fixed effects, confirms that exports to belligerent nations hovered around zero differential prior to the war (with small and statistically insignificant estimates for 1910--1912). However, starting precisely in 1914, we observe a significant positive divergence, leaping to a highly significant 0.926 log-point differential by 1915. This level is sustained through the end of the war, reinforcing visually clear lack of pre-trends in Figure [5](#figure:exports_event_study_destination) with rigorous regression evidence.
To map the export shock into local labor-market exposure, we next recover sector-specific WWI export-demand shifters. The core identification challenge is to isolate foreign-demand variation rather than confounding domestic trends in Spanish production.
We therefore estimate a destination-based difference-in-differences design that compares exports to belligerent and non-belligerent destinations before vs. during the war, allowing the belligerent differential to vary by sector. Let $s(p)$ denote the sector associated with product $p$. We estimate:
$$
\mathbb{E}[X_{d,p,t} \mid \cdot] = \exp\!\left(
\mu_{d,p} + \mu_{p,t} + \sum_{s} \theta_{s}\; \mathbf{1}\{s(p)=s\}\times \text{WWI}_{t}\times \text{Belligerent}_{d}
\right),
$$
where $\text{WWI}_{t}$ indicates the war years (1914--1918) against the pre-war baseline (1910--1913). The coefficient $\theta_s$ measures the differential change in exports of sector $s$ to belligerent destinations during WWI, relative to pre-war years, net of destination--product composition effects and product-year shocks.
Because PPML is log-linear in the index, $\theta_s$ can be interpreted as a semi-elasticity of exports to belligerents during WWI; therefore, $(\exp(\theta_s)-1)$ is the implied percent differential. We treat the estimated parameter as our continuous sector-level WWI demand shifter, defining $\widehat{z}_s \equiv \widehat{\theta}_s$ to directly link the trade estimation to our subsequent spatial exposure variables.
Table [Table](#table:event_study_exports_sec_belligerent) presents the estimated coefficients $\widehat{\theta}_s$ across the different industrial sectors. Column (3) reports the preferred specification, which controls for year and destination--product fixed effects. We observe significant heterogeneity in the wartime export-demand shock across the Spanish economy. The most pronounced, statistically significant increases in exports to belligerent nations occurred in sectors critical to the war effort and basic provisions. For instance, Tobacco, Metallurgy, Leather, Garments, Paper, and Textiles all exhibit large, positive semi-elasticities, implying substantial percent differentials over pre-war levels. These sectors align historically with the spike in foreign demand for Spanish manufactured goods and uniform materials needed by combatant nations. Conversely, sectors like Public Industry and Wood faced a relative decline or stagnation. This rich, cross-sectoral variation in the external demand shock---driven explicitly by belligerent destinations during the conflict---forms the basis of our spatial exposure measures.
> **Aggregate Export Event Study**
+:-----------------------------------------------+:-----------------------:+:-----------------------:+:-----------------------:+:----------------------:+
| | Exports (Value) |
+------------------------------------------------+-----------------------------------------------------------------------------+------------------------+
| | PPML | PPML (IV-CF) |
+------------------------------------------------+-------------------------+-------------------------+-------------------------+------------------------+
| | \(1\) | \(2\) | \(3\) | \(4\) |
+------------------------------------------------+-------------------------+-------------------------+-------------------------+------------------------+
| Belligerent Destination $\times$ Year $=$ 1910 | -0.1970 (0.2652) | -0.2356 (0.2949) | -0.0144 (0.1261) | 2.180$^{**}$ (0.9960) |
+------------------------------------------------+-------------------------+-------------------------+-------------------------+------------------------+
| Belligerent Destination $\times$ Year $=$ 1911 | -0.0516 (0.3124) | -0.1605 (0.2893) | 0.1144 (0.1298) | 0.2922 (0.9451) |
+------------------------------------------------+-------------------------+-------------------------+-------------------------+------------------------+
| Belligerent Destination $\times$ Year $=$ 1912 | -0.1904 (0.2619) | -0.1997 (0.2868) | -0.1152 (0.1253) | 1.760$^{*}$ (0.9101) |
+------------------------------------------------+-------------------------+-------------------------+-------------------------+------------------------+
| Belligerent Destination $\times$ Year $=$ 1914 | 0.2649 (0.2608) | 0.3267 (0.2786) | 0.2197$^{*}$ (0.1156) | 5.409$^{***}$ (1.105) |
+------------------------------------------------+-------------------------+-------------------------+-------------------------+------------------------+
| Belligerent Destination $\times$ Year $=$ 1915 | 1.058$^{***}$ (0.2718) | 1.159$^{***}$ (0.2692) | 0.9258$^{***}$ (0.1419) | 8.571$^{***}$ (1.077) |
+------------------------------------------------+-------------------------+-------------------------+-------------------------+------------------------+
| Belligerent Destination $\times$ Year $=$ 1916 | 0.9330$^{***}$ (0.2685) | 1.022$^{***}$ (0.2751) | 0.6710$^{***}$ (0.1240) | 6.178$^{***}$ (0.9328) |
+------------------------------------------------+-------------------------+-------------------------+-------------------------+------------------------+
| Belligerent Destination $\times$ Year $=$ 1917 | 1.013$^{***}$ (0.2817) | 1.113$^{***}$ (0.2780) | 0.7110$^{***}$ (0.1576) | 6.017$^{***}$ (0.8367) |
+------------------------------------------------+-------------------------+-------------------------+-------------------------+------------------------+
| Belligerent Destination $\times$ Year $=$ 1918 | 0.6607$^{***}$ (0.2553) | 0.7338$^{***}$ (0.2652) | 0.4703$^{***}$ (0.1474) | 3.665$^{***}$ (0.9075) |
+------------------------------------------------+-------------------------+-------------------------+-------------------------+------------------------+
| Belligerent Destination $\times$ Year $=$ 1919 | 0.6684$^{***}$ (0.2577) | 0.8010$^{***}$ (0.2536) | 0.3726$^{**}$ (0.1471) | 6.557$^{***}$ (0.9034) |
+------------------------------------------------+-------------------------+-------------------------+-------------------------+------------------------+
| F-test (1st stage) | | | | CF Approach |
+------------------------------------------------+-------------------------+-------------------------+-------------------------+------------------------+
| | | | | |
+------------------------------------------------+-------------------------+-------------------------+-------------------------+------------------------+
| Observations | 80,245 | 79,830 | 78,749 | 66,185 |
+------------------------------------------------+-------------------------+-------------------------+-------------------------+------------------------+
| Pseudo R$^2$ | 0.66364 | 0.72370 | 0.92801 | 0.93938 |
+------------------------------------------------+-------------------------+-------------------------+-------------------------+------------------------+
| | | | | |
+------------------------------------------------+-------------------------+-------------------------+-------------------------+------------------------+
| Product fixed effects | $\checkmark$ | | | |
+------------------------------------------------+-------------------------+-------------------------+-------------------------+------------------------+
| Year fixed effects | $\checkmark$ | | | |
+------------------------------------------------+-------------------------+-------------------------+-------------------------+------------------------+
| Destination fixed effects | $\checkmark$ | $\checkmark$ | | |
+------------------------------------------------+-------------------------+-------------------------+-------------------------+------------------------+
| Product-Year fixed effects | | $\checkmark$ | $\checkmark$ | $\checkmark$ |
+------------------------------------------------+-------------------------+-------------------------+-------------------------+------------------------+
| Destination-Product fixed effects | | | $\checkmark$ | $\checkmark$ |
+------------------------------------------------+-------------------------+-------------------------+-------------------------+------------------------+
Our empirical strategy relies on a parallel-trends assumption: absent WWI, within a product $p$, exports to belligerent and non-belligerent destinations would have followed parallel trends. We assess this directly using the destination--product event-study in [Equation](#eq:stylized_fact_1), estimated by PPML with destination--product and product--year fixed effects. In the preferred specification (Table [Table](#table:event_study_exports), col. 3), the belligerent differential is close to zero and statistically insignificant in 1910--1912, and then breaks sharply at the onset of WWI, reaching a large and highly significant differential by 1915 and remaining elevated throughout the war years. We use column (3) as the pre-trends diagnostic; column (4) is a robustness check aimed at isolating foreign demand from potential Spanish supply responses.
A remaining concern is that Spain's wartime export expansion could partly reflect endogenous, Spain-specific supply responses correlated with the belligerent demand shock. To address this at the trade stage, Table [Table](#table:event_study_exports), col. 4 re-estimates the event study using an IV specification implemented via a PPML control-function approach, instrumenting belligerent-destination demand with third-country import growth from the TRADHIST dataset. Despite the caveat that TRADHIST only offers aggregate bilateral trade data abstracting from product and sectoral heterogeneity and the smaller sample implied by TRADHIST coverage, the post-1914 coefficients remain strongly positive and precisely estimated - albeit with slightly different coefficient stemming from the more aggregate variation in the TRADHIST data - which reinforces the interpretation that the export shock reflects external foreign-demand shifts induced by WWI rather than contemporaneous Spanish supply changes. In the next Section (specifically Section [3.3](#sec:borusyak)) we will provide additional diagnostics regarding the exogeneity of the export-demand shock specific to our empirical setting.
The estimated sector shifters $\widehat z_s$ provide the sector-specific component of foreign demand induced by WWI that we use in the local incidence analysis. In Section [3](#sec:empirical_strategy), we map $\widehat z_s$ into local labor-market exposure by decomposing the shock into direct, within-province indirect, and spatial indirect components using predetermined pre-war employment shares and a predetermined connectivity matrix.
## Empirical strategy: direct and indirect exposure in connected labor markets
### Theoretical Motivation for Spatial Spillovers
WWI generated large, plausibly exogenous shifts in sectoral export demand. In a spatial equilibrium, such shocks do not remain confined to the directly exposed market: a demand increase in one province--sector raises its wage, which reallocates workers and spending across sectors and space, and these adjustments feed back into labor demand everywhere. For our purposes, the key implication is therefore not a particular microfoundation, but a general *sufficient-statistics* characterization of how equilibrium outcomes respond to shocks. Specifically, under mild regularity conditions, log changes in wages (and other outcomes) admit a first-order representation in which each market's response can be written as the sum of a *direct* effect of its own shock exposure and an *indirect* effect of other markets' exposure transmitted through general-equilibrium linkages. Adao et al. ([2019](#ref-NBERw25544)) (henceforth AAE) state this decomposition formally for wages in Theorem 1, and show (Appendix A.3) that analogous first-order representations obtain for outcomes that are differentiable functions of the equilibrium wage/price vector (e.g. employment, population, and real income). This is the theoretical motivation for our reduced-form specifications for multiple outcomes.
Formally, let $i\in\{1,\dots,I\}$ index local labor markets. In the empirical application, a market corresponds to a province--sector cell $i\equiv(r,s)$, and we track outcomes separately by worker type $c$ (see Online Appendix D for details on data construction and sources). Let $w_i$ denote the market wage and let $y_i$ denote a generic outcome of interest (wages, employment, or prices). Let $\tau$ collect exogenous primitives (trade costs, foreign demand shifters, or other external fundamentals) that may change during WWI. An equilibrium is a wage vector $w$ that clears all local labor markets, which can be written as
$$
D_i(w\mid\tau)=0\qquad \forall i,
$$
where $D_i(\cdot)$ is excess labor demand. The specific form of $D_i(\cdot)$ depends on the environment, but the economic mechanism is common: shocks shift labor demand; wages adjust to clear markets; and because preferences, technology, mobility, and trade link markets, wage changes in one location/sector typically shift labor demand in others.
Log-linearizing the market-clearing system around the pre-war equilibrium yields a linear system that can be written schematically as
$$
\bar{\gamma}^{0}\,\widehat{\mathbf{w}}=\widehat{\boldsymbol{\eta}},
$$
where $\widehat{\mathbf{w}}$ collects log wage changes across markets, $\widehat{\boldsymbol{\eta}}$ collects the corresponding *excess labor-demand shifts* induced by the shock, and the matrix $\bar{\gamma}^{0}$ is the (pre-war) Jacobian of the market-clearing conditions with respect to wages. Economically, $\bar{\gamma}^{0}$ summarizes the strength of general-equilibrium linkages: an off-diagonal element captures how a wage change in market $j$ shifts excess labor demand in market $i$ via mobility, trade, and other cross-market interactions.
Under a stability/invertibility condition (AAE provide sufficient diagonal-dominance restrictions), the system can be inverted to obtain a reduced-form representation in which each market's wage change is a weighted sum of demand shifters across all markets:
$$
\widehat{w}_i
\;=\;
\beta_{ii}\,\widehat{\eta}_i
\;+\;
\sum_{j\neq i}\beta_{ij}\,\widehat{\eta}_j,
\qquad
\beta_{ij}\equiv \big[(\bar{\gamma}^0)^{-1}\big]_{ij}.
$$
The decomposition in [Equation](#eq:direct_indirect_formal) is the key intuition for spillovers. The first term is the *direct* effect: how market $i$ responds to its own demand shift. The second term is the *indirect* effect: how shocks in other markets move $w_i$ once equilibrium adjustments propagate through the network of linkages embedded in $(\bar{\gamma}^0)^{-1}$. AAE further show that these reduced-form elasticities admit a convergent Neumann-series expansion in a normalized spatial-links matrix, which gives a useful interpretation: shocks propagate in multiple rounds (a first round from immediately connected markets, then second-round effects through neighbors of neighbors, and so on).
Finally, AAE show that the exposure term $\widehat{\eta}_i$ has a shift--share form (their equation (16)): it aggregates sectoral shifters with predetermined pre-shock employment shares. This motivates our exposure measures, which interact sector-level WWI export-demand shifters with pre-war local employment shares. Because our unit of observation is a province--sector cell, the object $\widehat{\eta}_{r,s}$ can be interpreted as the sector-$s$ component of a province's revenue-shock exposure, with $\widehat{\eta}_{r}=\sum_{s}\widehat{\eta}_{r,s}$.
The empirical challenge is dimensionality. With $I$ markets, [Equation](#eq:direct_indirect_formal) contains $I^2$ bilateral elasticities $\{\beta_{ij}\}$, so an unrestricted estimation of the spillover kernel is infeasible. In the next subsection we impose a disciplined low-dimensional approximation that preserves the direct/indirect logic while focusing on the dominant linkages in our setting, construct the implied exposure indices, and state the reduced-form panel specifications.
### From Theory to Reduced-form
[Equation](#eq:direct_indirect_formal) motivates our empirical strategy: to first order, an outcome responds to its own exposure and to a weighted average of other markets' exposures, with weights pinned down by pre-war general-equilibrium linkages. To take this logic to the data, we (i) approximate the high-dimensional spillover kernel with a parsimonious structure that targets the main channels in province--sector markets, (ii) construct exposure indices that map exactly into those channels, and (iii) estimate difference-in-differences / event-study regressions that interact these indices with the WWI period.
We focus on two empirically-relevant sources of off-diagonal propagation in province--sector markets: (1) *within-province cross-sector* spillovers (competition for workers across sectors inside the same province), and (2) *across-province within-sector* spillovers (sector-$s$ shocks propagating spatially through pre-war connectivity). A nested labor-supply structure is one microfoundation that generates this pattern, but we interpret it more generally as a low-dimensional approximation to the Jacobian $\bar{\gamma}^0$ in [Equation](#eq:aae_system).
To make this structure explicit, index markets by province--sector cells $(r,s)$ and posit the pre-war linear system $\bar{\gamma}^0\,\widehat{\mathbf w}=\widehat{\boldsymbol\eta}$ with
$$
\bar{\gamma}^0 = dI-a_LL-a_SS,\qquad d>0,
$$
where, for any array $x$,
$$
(Lx)_{r,s}=\sum_{k\neq s}x_{r,k},
\qquad
(Sx)_{r,s}=\sum_{r'\neq r}\omega_{rr'}x_{r',s},
\qquad
\sum_{r'\neq r}\omega_{rr'}=1.
$$
Here $a_L>0$ means cross-sector wage increases tighten other sectors locally (competition for workers), and $a_S>0$ means wage increases elsewhere (same sector, nearby provinces) raise demand pressure in $r,s$ (we normalize signs so that $d>0$ and the implied multipliers in $\left(\bar{\gamma}^0\right)^{-1}$ are positive under stability). Define $A\equiv \frac{a_L}{d}L+\frac{a_S}{d}S$ and assume $\rho(A)<1$[^9]. Then the inverse admits the Neumann expansion $(\bar{\gamma}^0)^{-1}=\frac{1}{d}\sum_{m=0}^\infty A^m$, and multiplying by $\widehat{\boldsymbol\eta}$ yields
$$
\widehat{\mathbf w}
=
\frac{1}{d}\widehat{\boldsymbol\eta}
+\frac{a_L}{d^2}L\widehat{\boldsymbol\eta}
+\frac{a_S}{d^2}S\widehat{\boldsymbol\eta}
+R,
\qquad
R\equiv \frac{1}{d}\sum_{m=2}^{\infty}A^m\widehat{\boldsymbol\eta}.
$$
The first two off-diagonal terms are the *first-round* spillovers through the two channels; the remainder $R$ collects higher-order propagation (second-round-and-beyond effects through longer paths in the network).
In components, the first-round decomposition is
$$
\widehat w_{r,s}
=
\frac{1}{d}\widehat\eta_{r,s}
+\frac{a_L}{d^2}\sum_{k\neq s}\widehat\eta_{r,k}
+\frac{a_S}{d^2}\sum_{r'\neq r}\omega_{rr'}\,\widehat\eta_{r',s}
+R_{r,s}.
$$
[Equation](#eq:w_nested_first_round) provides the rationale for two indirect-exposure indices: the within-province spillover is "other sectors in the same province," and the spatial spillover is "the same sector in nearby provinces," with proximity captured by $\omega_{rr'}$. Using the sector-level shifters $\widehat z_s$ estimated in Section [Section](#sec:sector_shifters), we therefore construct exposure components that map national trade shocks into local labor-market impacts.
Let $r$ index provinces and $s$ index sectors. Let $\pi_{r,s}^{0}$ denote sector $s$'s share of total employment in province $r$, averaged over 1910--1913, so that $\sum_s \pi_{r,s}^{0}=1$ for each $r$. The overall province-level Bartik shock is $B_r \equiv \sum_s \pi_{r,s}^{0}\widehat{z}_s$. We decompose local labor-market exposure into three components. First, a market's direct exposure to its own shock is
$$
\text{DirectExposure}_{r,s} \equiv \pi_{r,s}^{0}\widehat{z}_s.
$$
Second, its within-province indirect exposure to shocks hitting other sectors in the same province is
$$
\text{WithinProvinceIndirect}_{r,s} \equiv \sum_{s'\neq s}\pi_{r,s'}^{0}\widehat{z}_{s'}
= B_r - \pi_{r,s}^{0}\widehat{z}_s.
$$
Third, its spatial indirect exposure to shocks hitting the same sector in connected provinces is
$$
\text{SpatialIndirect}_{r,s} \equiv \sum_{r'\neq r} \omega_{rr'}\,\pi^0_{r',s}\widehat{z}_s .
$$
These indices are the empirical counterparts to the first-round terms in [Equation](#eq:w_nested_first_round). In the two-channel environment, the reduced-form coefficients on these indices map to composites of equilibrium slopes (a direct-response composite $1/d$ and spillover-strength composites $a_L/d^2$ and $a_S/d^2$), while higher-order spillovers are captured by $R$ and/or absorbed by richer specifications.
Theorem 1 in AAE is stated for changes (log differences) in wages. Empirically, we observe levels in an annual (or monthly) panel. We therefore estimate difference-in-differences / event-study specifications that isolate WWI-period changes relative to pre-war years, absorbing time-invariant heterogeneity across markets with market fixed effects and aggregate shocks common to all markets with time fixed effects. For wages and employment, let $Y_{r,s,c,t}$ denote either $\log(w_{r,s,c,t})$ or $\log(\ell_{r,s,c,t})$. To avoid confusion with the bilateral reduced-form elasticities $\beta_{ij}$ in [Equation](#eq:direct_indirect_formal), we denote the estimated reduced-form coefficients by $(\delta_D,\delta_L,\delta_S)$:
$$
\begin{aligned}
Y_{r,s,c,t} =\;& \alpha_{r,s,c} + \alpha_t \nonumber \\
& + \delta_{D}\left(\text{WWI}_{t} \times \text{DirectExposure}_{r,s}\right) \nonumber \\
& + \delta_{L}\left(\text{WWI}_{t} \times \text{WithinProvinceIndirect}_{r,s}\right) \nonumber \\
& + \delta_{S}\left(\text{WWI}_{t} \times \text{SpatialIndirect}_{r,s}\right) \nonumber \\
& + \delta_{I}\left(\text{WWI}_{t} \times \text{DirectImportExposure}_{r,s}\right) \nonumber \\
& + \kappa \left(\text{WWI}_{t} \times \log\text{DistFrance}_r\right) \nonumber \\
& + \varepsilon_{r,s,c,t}.
\end{aligned}
$$
This specification is the empirical analogue of the direct/indirect decomposition in [Equation](#eq:direct_indirect_formal), specialized to the two dominant linkage dimensions highlighted in [Equation](#eq:direct_indirect_formal) and operationalized via the indices [Equation](#eq:eta_proxy)--[Equation](#eq:eta_spatial). For consumer prices, we aggregate exposure to the province level because prices are observed by province and product rather than by production sector. Define $\text{DirectExposure}_{r}\equiv \sum_{s}\text{DirectExposure}_{r,s}=B_r$ and $\text{SpatialIndirect}_{r}\equiv \sum_{r'\neq r}\omega_{rr'}\,\text{DirectExposure}_{r'}$. Because consumer price data are reported at the province-by-product level (rather than for production sectors), we aggregate the indices to the province level to estimate the consumer price response. We estimate:
$$
\begin{aligned}
\log\left(p_{r,p,u,m,t}\right) =\;&
\alpha_{r,u} + \alpha_{p,m} + \alpha_{u,p} + \alpha_t \nonumber\\
& + \pi_{D}\left(\text{WWI}_{t} \times \text{DirectExposure}_{r}\right) \\
& + \pi_{S}\left(\text{WWI}_{t} \times \text{SpatialIndirect}_{r}\right) \nonumber\\
& + \pi_{I}\left(\text{WWI}_{t} \times \text{SectoralImportShock}_{p}\right) \nonumber\\
& + \kappa \left(\text{WWI}_{t} \times \log\text{DistFrance}_r\right) \nonumber \\
& + \varepsilon_{r,p,u,m,t}. \nonumber
\end{aligned}
$$
Because consumer prices are observed by province and product, the relevant exposure object is province-level and captures local demand/cost pressure from the export boom; by contrast, wage and employment exposures are defined at the province--sector level and isolate within-province cross-sector spillovers. The fixed effects absorb permanent province--urban differences, seasonal product patterns, and common inflationary forces. To ensure our estimates of export-demand spillovers are not confounded by concurrent supply movements, all specifications include controls for sectoral import-disruption exposure.[^10] Both specifications also control for the interaction of the WWI period with the log distance to the French border ($\log\text{DistFrance}_r$) to capture secular spatial trends related to European geography. In additional saturated specifications, we replace subsets of fixed effects with higher-dimensional interactions (e.g. product--month and province--urban), as in the baseline table below. To assess pre-trends and visualize the time profile of adjustment, we also estimate event-study versions that replace $\text{WWI}_t$ with a full set of year dummies interacted with the exposure measures, normalizing 1913 to zero.
In estimating equations [Equation](#eq:stylized_fact_3) and [Equation](#eq:stylized_fact_4), we adopt a uniform two-way fixed effects design as our preferred specification. For transparency, we also report parsimonious difference-in-differences estimates for wages and employment in Table [Table](#apptab:stylized_fact_3). For wages and employment, we include unit fixed effects at the region--sector--gender level ($\alpha_{r,s,c}$) and year fixed effects ($\alpha_t$), so identification comes from within-unit changes over time comparing more- and less-exposed cells during WWI relative to pre-war years. Because the exposure measures are time-invariant, the regressions include only their interactions with the WWI period indicator (and, in the event-study specification, interactions with year dummies); level terms are absorbed by the unit fixed effects. For consumer prices, we analogously include province--capital, capital--product, and product--month interactions, alongside month and year fixed effects. These choices align the fixed effects structure across specifications to flexibly absorb aggregate time trends and unit-level differences while isolating the differential impact of the external shock.
> **Direct and Indirect Effect on Wages, Labor Allocations and Prices**
*The table layout is available in the PDF.*
Table [Table](#apptab:stylized_fact_3) reports reduced-form estimates of [Equation](#eq:stylized_fact_3) and [Equation](#eq:stylized_fact_4) for wages, employment, and consumer prices. For wages and employment, Columns (1) and (3) use a parsimonious difference-in-differences specification with a single WWI indicator and coarse fixed effects; Columns (2) and (4) absorb all time-invariant heterogeneity at the province--sector--gender level and include year fixed effects. In these saturated specifications, identification comes entirely from differential *changes* during WWI as a function of pre-war exposure. For prices, Columns (5) and (6) use the product--province--month panel and move from a baseline set of location and product controls to a highly saturated specification with rich interactions.
The wage results show a clear role for both direct exposure to the export-demand shock and indirect propagation through connected markets. In the preferred specification (Column (2)), the direct term is positive and precisely estimated: more-exposed province--sector cells experience larger WWI wage increases. Just as important, wages rise with exposure elsewhere: shocks hitting *other* sectors in the same province are associated with higher wages in a given sector, and same-sector exposure in nearby provinces also puts upward pressure on wages. These positive spillovers are consistent with the sufficient-statistics logic in AAE: when reduced-form elasticities $\beta_{ij}$ are predominantly nonnegative, external demand shifts propagate through the network in the same direction as the direct effect. In this setting, the relative strength of the within-province indirect term compared with the spatial term is also suggestive about the underlying adjustment margin: it is consistent with strong within-province general-equilibrium interactions (e.g. sectoral reallocation and local labor-market tightening) and significant cross-province adjustment, although potentially constrained by historically high mobility frictions.
Employment responds in the same direction, but with a different balance of margins. Direct exposure predicts employment expansion during WWI. Employment also comoves positively with exposure in other local sectors and with same-sector exposure in nearby provinces. Taken together with the wage results, the pattern is consistent with adjustment that is driven by both local tightened labor markets and spatial reallocation. The export boom shows up strongly in both wages and employment, suggesting that despite mobility frictions, worker reallocation was a primary margin of adjustment ([Silvestre 2005](#ref-10.2307/41378422)). The distance-to-France gradient (WWI$\times$LogDist $\approx -0.18$ in Column 2 in Appendix Table [Table](#tab:event_study_combined_full)) reinforces this interpretation: provinces farther from the border experience systematically smaller WWI wage increases, matching the geographic decay of the trade shock.
Price responses point to an additional, welfare-relevant channel. In Column (6), provinces with greater *own* exposure experience relative price increases, while exposure coming from connected provinces is associated with *higher* local prices. Furthermore, sectors with higher exposure to import disruption see significant price pressure. This highlights why indirect effects matter for welfare: the trade shock fundamentally restructured local price levels through both demand pressure and supply integration across the Spanish interior.
To ensure our export-demand estimates are not confounded by concurrent supply shocks, we explicitly control for import-disruption exposure across all outcomes. We construct these measures symmetrically to the export shocks: we leverage bilateral trade data to measure the national collapse in imports from belligerent nations and project these sectoral shifters to the province level using pre-war employment shares (*Direct Import Exposure*). By interacting these shifters with the WWI indicator, we capture the stimulative effect of the wartime "import substitution" forced upon the Spanish economy. As reported in Table [Table](#apptab:stylized_fact_3), the export-demand coefficients remain large and significant even under these stringent controls. The direct import term confirms that import disruptions acted as a complementary stimulus to local industrial labor demand, while the export boom remained the primary driver of regional economic divergence.
Our reduced-form design mirrors the central insight in AAE: when regions are connected, the incidence of trade shocks is not confined to directly exposed markets, so specifications that focus only on "own exposure" can miss economically meaningful general-equilibrium propagation. AAE study a negative trade shock (import competition) and show that nearby regions' exposure generates additional negative effects on local wages and employment, while expenditure-exposure provides little offsetting attenuation and population responses are limited. In our historical setting the shock is a positive foreign-demand shift induced by WWI, so the sign reverses: more exposed province--sector cells experience larger wage and employment gains. Importantly, these gains propagate beyond directly exposed cells. In our preferred two-way fixed-effects specification (Table [Table](#apptab:stylized_fact_3)), the within-province indirect exposure is positive and precisely estimated, amounting to roughly 44% of the direct wage effect and about 87% of the direct employment effect, whereas cross-province same-sector spillovers are positive but estimated less precisely. Together with the price evidence, this pattern suggests that the WWI boom was transmitted primarily through local cross-sector labor-market tightness and connected-market pressure, reinforcing AAE's broader message that measuring indirect exposure is essential for characterizing the distributional and welfare consequences of trade shocks.
### Shift-Share Identification and Robustness
The exposure measures in [Equation](#eq:eta_proxy)--[Equation](#eq:eta_spatial) define a shift--share (Bartik) design: sector-level WWI export-demand shifters $\widehat z_s$ (the "shifts") are interacted with predetermined pre-war province--sector employment shares $\pi^{0}_{r,s}$ (the "shares") to generate differential wartime exposure across province--sector cells. Because pre-war industrial composition is a generic predictor of exposure to many wartime changes, and the identifying variation is fundamentally at the sector level (18 shocks), we place primary weight on an *exogenous-shifts* interpretation (following [Borusyak et al. 2025](#ref-Borusyak2025-es)). Conditional on fixed effects and predetermined controls, the identifying variation comes from sector-level shifters that capture foreign-demand movements induced by WWI rather than contemporaneous local Spanish shocks.
Appendix Table [Table](#tab:robustness_main) consolidates robustness checks for wages and employment across four specifications: baseline OLS, a third-country IV strategy, an "incomplete-shares" adjustment, and a recentered-shock construction. Crucially, as in the main results, all robustness specifications symmetrically control for sectoral import disruption (*Direct Import Exposure*) to ensure that captured export effects are not confounded by the stimulative effects of wartime import substitution. We structure these checks around core threats to shift--share designs:
First, to address *mechanical exposure construction issues*, we note that because $\text{WithinProvinceIndirect}_{r,s}$ excludes sector $s$, the sum of included shares varies mechanically with $(1-\pi^{0}_{r,s})$. Following the shift--share diagnostics in Borusyak et al., we include an explicit "incomplete-shares" control $\text{WWI}_{t}\times(1-\pi^{0}_{r,s})$. The resulting estimates preserve the qualitative patterns: for wages, both direct exposure and within-province indirect exposure remain positive and significant; for employment, the within-province indirect term also retains a stable positive sign and statistical significance.
Second, to address *shifter endogeneity and contamination* by domestic sectoral shocks, we report a third-country instrumental-variable design in the spirit of Autor et al. ([2013](#ref-10.1257/aer.103.6.2121)). We leverage bilateral trade data from the TRADHIST dataset ([Fouquin and Hugot 2016](#ref-fouquin2016two)) to construct a destination-level demand shock based on the growth in total imports from the rest of the world (excluding Spain) during the WWI period. We project these destination-level shocks to the sector level using Spain's pre-war sector-by-destination export shares, and thereby construct exogenous spatial and within-province indirect instrumental variables that mirror our baseline exposure measures. As reported extensively in Online Appendix [Section](#sec:robustness), our IV estimates confirm that the baseline results are robust (see Appendix [Table](#tab:robustness_main)). The first-stage F-statistics are extremely large. The IV estimates for wages preserve the positive and significant direct and within-province indirect effects. For employment, the within-province indirect effect remains positive but loses precision. Overall, this supports the interpretation that the reduced-form responses are driven by external demand shifts rather than local supply factors.
Third, to address *finite-sample and mechanical correlation* concerns in shift--share exposure designs, we implement a recentered-shifter construction ([Borusyak and Hull 2023](#ref-BorusyakHull2023)) (weighted by shock-importance weights). The recentered specification continues to deliver a positive and statistically significant direct wage effect, and it preserves a positive and significant within-province indirect effect for employment, although precision for the wage indirect term attenuates.
Fourth, to test for *shifter predictable pre-trends*, we validate shift exogeneity at both the sector level and the panel level. Appendix Table [Table](#tab:rob_exog) reports the results of regressing the export shocks directly against pre-trend industry export growth (1910--1913). The table shows the WWI export shifters are not a continuation of pre-war growth (the relationship is negative), but they are not strictly orthogonal to pre-war growth either; therefore, we emphasize conditional shift exogeneity and robustness controlling for pre-war trends. Furthermore, Appendix Table [Table](#tab:rob_pretrends) tests for pre-trend balance in outcomes under a stringent fixed-effect structure, confirming no significant relationship between WWI exposures and pre-war wage or employment growth.
As noted, the effective identifying variation occurs at the sector-shifter level (18 sectors). We therefore cluster standard errors by sector in the panel specifications (Table [Table](#tab:robustness_main) and Table [Table](#tab:rob_pretrends)), and use robust standard errors for the sector-level shifter regression (Table [Table](#tab:rob_exog)). We acknowledge that cluster-robust asymptotics are finite with 18 clusters, and we interpret precision with this small-sample variation in mind.
Finally, across these robustness checks, evidence on spatial spillovers (the spatial indirect term) is comparatively less stable, often flipping signs or remaining statistically insignificant. We therefore treat estimates of the spatial indirect term as suggestive, while emphasizing the robust direct and within-province spillover channels. Overall, these direct and indirect effects indicate a nuanced picture of WWI-driven adjustment in local labor markets and consumer prices, with first-order implications for welfare.
Finally, we investigate the persistence of these effects by extending our analysis to the immediate post-war period (1919--1920). While pooled specifications covering 1908--1920 show attenuated coefficients, Appendix [Table](#tab:robustness_1920) reveals that this is due to the extreme intensity of the post-war treatment effect rather than a return to the pre-war mean. By separately interacting the war (1915--18) and post-war (1919--20) periods with our exposure measures, we find that the direct wage effect remains strong during the war ($\beta \approx 0.98$) and accelerates significantly in the aftermath ($\beta \approx 2.45$). This persistent divergence validates our choice of the 1908--1918 baseline while uncovering a "long shadow" of the WWI shock that continued to drive regional wage inequality well into the 1920s.
### From reduced form to quantification
Our reduced-form system treats WWI as a vector of external demand shifters that moves province--sector labor demand and estimates how these shifts propagate through connected labor markets. The quantitative model in Section 4 takes the same shock as primitive input and imposes structure on (i) goods-market adjustment, (ii) nested labor reallocation across sectors and space, and (iii) the mapping from nominal changes into real income and welfare. Before setting up our quantitative model we turn towards discussing the price and (labor) quantity responses to a demand shift in a general equilibrium model with labor market frictions. To do that we derive the response of the equilibrium to a demand shift under different degrees of labor market frictions by deriving a formal Le Chatelier type result ([Milgrom 2006](#ref-Milgrom2006-zo); [Silberberg 1971](#ref-Silberberg1971-xp)). This result will show that even in general equilibrium adding adjustment margins (more elastic mobility) weakly dampens wage responses and shifts adjustment toward quantities, i.e. labor reallocations. This result will motivate both the quantitative model as well as the counterfactuals in the next section.
To recap, in the model at the beginning of the section, each province--sector cell $(r,s)$ is a market. Labor demand is pinned down by revenues and zero profits, $\ell^{D}_{r,s}(w\mid\tau)=R_{r,s}(w\mid\tau)/w_{r,s}$, while labor supply $\ell^{S}_{r,s}(w\mid\tau)$ is implied by nested mobility across provinces and sectors. Define log excess demand
$$
D_{r,s}(w\mid\tau)\equiv \ln \ell^{D}_{r,s}(w\mid\tau)-\ln \ell^{S}_{r,s}(w\mid\tau),
$$
so equilibrium is characterized by $D_{r,s}(w\mid\tau)=0$ for all $(r,s)$. Log-linearizing around the pre-war equilibrium yields a first-order system of the form
$$
\bar\Gamma^{0}\,\widehat{\mathbf w}=\widehat{\boldsymbol\eta},
\qquad
\bar\Gamma^{0}\equiv -\left.\frac{\partial \mathbf D}{\partial \ln \mathbf w}\right|_{0},
$$
where $\widehat{\boldsymbol\eta}$ is the vector of revenue-equivalent labor-demand shifts induced by WWI. In our setting $\bar{\Gamma}^0$ is the pre-war Jacobian of the market clearing system that embeds all the information about equilibrium adjustments and determines the price and quantity responses to a demand shift. It can be decomposed into a labor-demand component and a labor-supply (reallocation) component:
$$
-\bar\Gamma^{0} \;=\; \Gamma^{D,0} + \Gamma^{S,0},
$$
where $\Gamma^{S,0}$ summarizes how labor supply in each market responds to wage differences through reallocation across sectors and space. Now index the degree of labor-market integration by $\chi$ and parameterize labor supply as a function of $\chi$:
$$
-\bar\Gamma^{0}(\chi) \;=\; \Gamma^{D,0} + \Gamma^{S,0}(\chi),
$$
with $\Gamma^{D,0}$ fixed and $\Gamma^{S,0}(\chi_2)-\Gamma^{S,0}(\chi_1)$ positive semidefinite whenever $\chi_2\ge \chi_1$ (i.e., integration increases labor-supply elasticities in every direction). It can be shown that under standard stability conditions ensuring a unique local equilibrium (so $\bar\Gamma^{0}(\chi)$ is invertible), the equilibrium multiplier is monotone:
$$
\big(\bar\Gamma^{0}(\chi_2)\big)^{-1} \;\preceq\; \big(\bar\Gamma^{0}(\chi_1)\big)^{-1}
\qquad \text{for } \chi_2\ge \chi_1,
$$
where $A\preceq B$ means $B-A$ is positive semidefinite. Thus, for a fixed exposure vector $\widehat{\boldsymbol\eta}$, the overall magnitude of wage responses $\widehat{\mathbf w}(\chi)=\big(\bar\Gamma^{0}(\chi)\big)^{-1}\widehat{\boldsymbol\eta}$ is weakly smaller as integration rises.[^11] This motivates our counterfactuals: by varying $(\nu,\gamma)$ we trace how the same WWI demand shift is absorbed by wages versus labor reallocation in a high-dimensional spatial equilibrium with network interactions.
In what follows we will introduce a two-elasticity formulation of spatio-sectoral labor supply: Our nested mobility structure delivers two curvature parameters: $\nu$ governs sector-switching within a province and $\gamma$ governs spatial relocation across provinces. Increasing $(\nu,\gamma)$ makes reallocation more elastic, which raises $\Gamma^{S,0}$ and strengthens the supply-side offset to any given partial-equilibrium demand shift. The economic implication is a matrix version of Le Chatelier: adding adjustment margins (more elastic mobility) weakly dampens equilibrium wage responses and shifts adjustment toward quantities .
Finally, before turning towards the quantitative model, it is worth noting that the reduced-form that we have estimated, has a structural interpretation. It is the first-order approximation of how labor supply linkages response to demand shocks in a network of local labor markets. That implies that the reduced-form regressions estimate GE responses, and under careful interpretation they can be used to inform our structural estimation of the quantitative model that follows. This is a point that we will return to later.
## Quantitative Model
This section develops a quantitative framework that starts from explicit preferences and production, delivers an equilibrium mapping from WWI-era foreign-demand shocks to local wages, employment, and consumer prices, and connects directly to the reduced-form exposure measures in Section [3.1](#sec:motivation_spillovers)--[3.2](#sec:baseline_specs). The economy is static within each period. The two-period structure - while not completely dynamic - is used to organize a comparative-static exercise: starting from the observed pre-war allocation (1914), we ask how a WWI-era shift in foreign demand changes the wartime equilibrium allocation, wages, and prices.
Provinces are indexed by $i, n, j \in \mathcal{D}=\{1,\dots,N_D\}$ and sectors by $s,k \in \mathcal{S}=\{1,\dots,S\}$, matching Section [3.1](#sec:motivation_spillovers). Foreign destinations are indexed by $l\in\mathcal{F}=\{1,\dots,N_F\}$. We use the same index set $\mathcal{F}$ for partner countries that are both export destinations and import origins. For any object $x$, we write $\widehat x\equiv \ln(x^1/x^0)$ for the log change from $t=0$ to $t=1$.
### Static Environment
Labor is the only factor of production. Province $i$ has an amenity shifter $A_i>0$ and a fixed housing stock $H_i$. The pre-war allocation of employment $\{\ell^0_{i,s}\}$ is observed. Throughout, workers are also the residents: local wage income is the source of local spending on tradables and housing, up to net transfers with the rest of the world introduced below.
Trade is subject to iceberg costs. The term $\tau_{n i,s}\ge 1$ is the cost of shipping one unit of sector-$s$ output from origin province $i$ to destination province $n$, and $\tau_{l i,s}$ is the iceberg cost for shipping a Spanish variety from origin $i$ to foreign destination $l$. Imported varieties enter through delivered prices, treated as exogenous objects. This corresponds to a small-open-economy interpretation that is well-suited to the episode: WWI shifts export opportunities faced by Spain and plausibly changes import conditions (shipping disruptions), while Spain does not determine world prices.
On the demand side, a representative resident of province $n$ has Cobb--Douglas preferences over a non-housing composite $C_n$ and housing services $R_n$:
$$
U_n = A_n \, C_n^{1-\delta} R_n^{\delta}, \qquad \delta\in(0,1).
$$
where $\delta$ is the housing expenditure share. The non-housing composite is Cobb--Douglas across sectors and CES across origins within each sector:
$$
\begin{aligned}
C_n &= \prod_{s\in\mathcal{S}} C_{n,s}^{\alpha_s}, \qquad \sum_{s}\alpha_s=1,
\\
C_{n,s} &=
\left(
\sum_{i\in\mathcal{D}} C_{ni,s}^{\frac{\sigma_s-1}{\sigma_s}}
+
\sum_{l\in\mathcal{F}} C_{nl,s}^{\frac{\sigma_s-1}{\sigma_s}}
\right)^{\frac{\sigma_s}{\sigma_s-1}},
\qquad \sigma_s>1.
\end{aligned}
$$
Let $p_{ni,s}$ denote the consumer price in $n$ for the variety produced in $(i,s)$, and $p_{nl,s}$ the consumer price in $n$ of the imported variety from $l$ in sector $s$. The sectoral and aggregate non-housing price indices are
$$
\begin{aligned}
P_{n,s} &= \left(
\sum_{i\in\mathcal{D}} p_{ni,s}^{1-\sigma_s}
+ \sum_{l\in\mathcal{F}} p_{nl,s}^{1-\sigma_s}
\right)^{\frac{1}{1-\sigma_s}},
\\
P_n &= \prod_{s\in\mathcal{S}} P_{n,s}^{\alpha_s}.
\end{aligned}
$$
We take foreign prices (import delivered prices $p_{nl,s}$) as the numeraire in both periods.
Let $y_i\equiv \sum_s w_{i,s}\ell_{i,s}$ be the province wage bill. To accommodate time variation in Spain's aggregate trade balance over 1910--1920, we allow a province-level transfer $T_i$ capturing net resources from (or to) the rest of the world, and define non-housing expenditure as
$$
E_n \equiv y_n + T_n.
$$
The model allows for non-zero trade imbalances. Let $D_t$ denote the net resource transfer from abroad (positive for a deficit / net borrowing). Then aggregate absorption satisfies $\sum_{i\in\mathcal{D}} E_i = \sum_{i\in\mathcal{D}} y_i + D_t$, where $D_t = \text{Imports}_t - \text{Exports}_t$. Balanced trade is the special case $D_t=0$. In the quantitative exercises, we discipline $D_t$ using the benchmark-year external position; our welfare comparisons therefore do not mechanically impose balanced trade. We set the province-specific transfer $T_i^t$ such that $\sum_{i \in \mathcal{D}} T_i^t = D_t$, allocating it according to fixed 1914 population weights $\omega_i$: $T_i^t = \omega_i \cdot D_t$, where $\omega_i = \text{Pop}_i^{1910} / \sum_m \text{Pop}_m^{1910}$.
We assume that housing is owned by immobile local landowners and rents are rebated locally to these owners (or via a lump-sum transfer fixed at baseline), so rent income does not enter the marginal mover's payoff. With Cobb--Douglas preferences and this local rebate of land rents, housing-market clearing pins down the rental rate $r_n$:
$$
r_n H_n = \frac{\delta}{1-\delta}\, (y_n + T_n).
$$
[Equation](#eq:housing_clear_quant) links labor-market outcomes to the local cost of living: a province that experiences a large wage-bill increase will also experience higher housing costs, which matters both for real outcomes and for mobility incentives.
CES demand implies expenditure on a domestic variety from origin $i$ in destination $n$ and sector $s$:
$$
X_{ni,s}
= \alpha_s \, E_n \left(\frac{p_{ni,s}}{P_{n,s}}\right)^{1-\sigma_s},
$$
and analogously for imports from $l$:
$$
X_{nl,s}
= \alpha_s \, E_n \left(\frac{p_{nl,s}}{P_{n,s}}\right)^{1-\sigma_s}.
$$
Define the domestic expenditure share on origin $i$ in destination $n$ and sector $s$ as $\lambda_{ni,s} \equiv X_{ni,s} / (\alpha_s E_n)$, and similarly for imports $\lambda_{nl,s}$. The "home share" of destination $n$ in sector $s$ is $\lambda_{nn,s}$.
Foreign markets matter only through their demand for Spanish exports. Let $E_{l,s}$ denote foreign destination $l$'s total expenditure on Spanish varieties in sector $s$. Conditional on $E_{l,s}$, foreign expenditure is allocated across Spanish origins via CES:
$$
X_{li,s}
=
s_{li,s}\, E_{l,s},
\qquad
s_{li,s}
=
\frac{p_{li,s}^{1-\sigma_s}}
{\sum_{j\in\mathcal{D}} p_{lj,s}^{1-\sigma_s}}.
$$
This formulation keeps the model focused on incidence within Spain: WWI shifts the spending envelope $\{E_{l,s}\}$, while Spanish provinces compete endogenously for that spending through prices and trade costs.
On the production side, each province--sector $(i,s)$ produces a differentiated variety with linear technology
$$
q_{i,s} = z_{i,s}\,\ell_{i,s},
$$
so marginal cost is $w_{i,s}/z_{i,s}$. Iceberg trade costs imply delivered prices
$$
p_{ni,s} = \tau_{n i,s}\frac{w_{i,s}}{z_{i,s}},
\qquad
p_{li,s} = \tau_{l i,s}\frac{w_{i,s}}{z_{i,s}}.
$$
Imported delivered prices $p_{nl,s}$ are treated as exogenous objects entering [Equation](#eq:Pnr_quant). In robustness, we allow sector-level import shifters $\widehat m_s$ such that $p_{nl,s}^{\,1}=p_{nl,s}^{\,0}\exp(\widehat m_s)$, capturing WWI-related disruptions to shipping and import supply.
Total revenue of origin $(i,s)$ equals domestic plus export expenditures on its variety:
$$
R_{i,s}
=
\sum_{n\in\mathcal{D}} X_{ni,s}
+
\sum_{l\in\mathcal{F}} X_{li,s}.
$$
With constant returns and perfect competition, zero profits imply
$$
w_{i,s}\,\ell_{i,s} = R_{i,s}.
$$
**Definition (Static equilibrium).** Given fundamentals $\{A_i, H_i, \tau_{ni,s}, z_{i,s}, E_{l,s}, T_i\}$ and an allocation $\{\ell_{i,s}\}$, a static equilibrium is a set of wages, rents, prices, and trade shares $\{w_{i,s}, r_i, P_{i,s}, \lambda_{ni,s}, \lambda_{li,s}\}$ satisfying equations [Equation](#eq:housing_clear_quant)--[Equation](#eq:labordemand_quant). When labor is mobile, equilibrium additionally requires that the allocation $\{\ell^1_{i,s}\}$ satisfies the labor-supply system [Equation](#eq:Lsupply_quant).
Workers are initially attached to a province--sector $(i,s)$ in period $0$ and may reallocate in period $1$. We use a two-stage (nested) discrete-choice structure that remains tractable with many province--sector markets and captures the idea that labor markets were segmented both geographically and occupationally during the period.[^12] If location and sector decisions were made fully jointly with richer unobserved correlation, the main qualitative GE forces would be unchanged, but the implied substitution patterns across province--sector markets would differ because the model would no longer separate the geographic and occupational elasticities.
Conditional on choosing a destination province $n$, a worker initially in sector $s$ chooses a destination sector $k$ subject to switching costs $\mu_{sk}\ge 1$ and Fréchet taste shocks with dispersion $\nu>0$. Writing the cost-adjusted wage as $\tilde w_{n,k|s}\equiv w_{n,k}/\mu_{sk}$, the sectoral option value in province $n$ is
$$
\Pi_{n,s} \equiv \left(\sum_{k\in\mathcal{S}} \tilde w_{n,k|s}^{\nu}\right)^{1/\nu},
$$
and the sectoral choice probability is
$$
\rho_{sk|n}
=
\frac{\tilde w_{n,k|s}^{\nu}}{\Pi_{n,s}^{\nu}}.
$$
Before choosing a sector, workers choose a destination province $n$ subject to bilateral migration costs $\mu_{in}\ge 1$ and Fréchet location shocks with dispersion $\gamma>0$. We assume that transfers $T_i$ and local rent rebates accrue to immobile local owners or are distributed such that they do not affect the relative migration incentives of marginal workers; thus, they do not enter the private utility in [Equation](#eq:v_quant). The deterministic component of moving from origin $i$ to $n$ is
$$
\tilde v_{i n|s}
\equiv
\frac{A_n}{\mu_{in}}
\cdot
\frac{\Pi_{n,s}}{P_n^{1-\delta} r_n^{\delta}},
$$
implying province-choice probabilities
$$
\rho_{i n|s}
=
\frac{\tilde v_{i n|s}^{\gamma}}
{\sum_{j\in\mathcal{D}} \tilde v_{i j|s}^{\gamma}}.
$$
Higher $(\gamma,\nu)$ corresponds to more elastic reallocation (a less segmented labor market): idiosyncratic location/sector tastes are less dispersed, so relative wage and cost-of-living changes induce larger worker flows. In the limit, labor markets integrate and indirect effects weaken.
The sequential structure implies multiplicative flows $\rho_{i n, s k}=\rho_{i n|s}\rho_{s k|n}$. Given the observed pre-war allocation $\{\ell^0_{i,s}\}$, period-$1$ labor supply to $(n,k)$ is
$$
\ell^1_{n,k}
=
\sum_{i\in\mathcal{D}}\sum_{s\in\mathcal{S}}
\rho_{i n, s k}\, \ell^0_{i,s}.
$$
This equation represents the propagation mechanism on the supply side. When mobility is limited, a positive demand shift in one market raises wages there and, through tighter outside options, can raise wages elsewhere as well. This is the mechanism behind the indirect exposure terms in Section [3.2](#sec:baseline_specs): other sectors in the same province and nearby provinces in the same sector matter because they affect the local availability of workers. The sequential structure implies IIA within provinces and allows separate curvature parameters for spatial versus sectoral mobility. If instead choices were joint, the model would still admit a direct/indirect decomposition, but the cross-market substitution patterns would generally not factor into separate spatial and sectoral components, changing the interpretation of $(\gamma,\nu)$ and the relative role of local versus spatial spillovers.
Given an allocation $\{\ell_{i,s}\}$, wages $\{w_{i,s}\}$ are pinned down by [Equation](#eq:labordemand_quant) together with [Equation](#eq:X_domestic)--[Equation](#eq:X_export), since revenues depend on wages through delivered prices and CES shares. Price indices follow from [Equation](#eq:Pnr_quant)--[Equation](#eq:Pn_quant), and rents from [Equation](#eq:housing_clear_quant). With endogenous mobility, the allocation must also satisfy [Equation](#eq:Lsupply_quant) evaluated at those same equilibrium wages and prices.
A two-period comparative static reallocation maps an initial pre-war allocation $\{\ell^0_{i,s}\}$ and a set of wartime foreign-demand shifters $\{E^1_{l,s}\}$ to a period-1 allocation $\{\ell^1_{i,s}\}$ and its corresponding static equilibrium. The period-1 allocation must satisfy the labor supply condition [Equation](#eq:Lsupply_quant) evaluated at the period-1 static equilibrium wages, rents, and price indices.
We implement WWI as a sector-specific shift in foreign expenditures on Spanish varieties. Let $\widehat z_s$ be the sectoral export-demand shifter estimated in Section [Section](#sec:sector_shifters). For belligerent destinations $l$, we set
$$
E_{l,s}^{1} = E_{l,s}^{0}\cdot \exp(\widehat z_s),
\qquad
E_{l,s}^{1}=E_{l,s}^{0}\ \text{ for non-belligerent } l,
$$
and solve for the period-$1$ equilibrium. In counterfactual "Spain without WWI" simulations, we set all foreign-demand shocks and shifters back to their pre-war values (setting $\widehat z_s=0$ and $\widehat m_s=0$) and solve for the spatial equilibrium endogenously.
### Quantification: calibration, estimation, and incidence
The quantification involves four groups of parameters and fundamentals, summarized in Table [Table](#tab:calibration). First, we set global parameters governing goods substitution ($\sigma$), housing expenditure ($\delta$), spatial and sectoral labor supply curvatures ($\gamma,\nu$), and the distance sensitivity of domestic trade costs ($\theta$) and migration costs ($\zeta$). Second, we recover sector-specific expenditure weights $\{\alpha_s\}$ and, in robustness, sector-level import shifters $\{\widehat m_s\}$. Third, we recover province-specific housing stocks $\{H_i\}$, amenities $\{A_i\}$, and migration-origin shifters $\{\zeta_i\}$. Finally, we recover high-dimensional fundamentals $\{z_{is}\}$ (baseline productivities) and $\{\mu_{sk}\}$ (sector-switching costs) by matching observed 1914 wage bills and 1920 reallocation patterns.
Our quantification proceeds in four sequential steps: (i) an exact inversion of the 1914 economy to recover $\{z_{is},A_i\}$, (ii) external closure and implementation of the WWI export-demand shocks $\{E_{l,s}\}$, (iii) identification of the propagation elasticities $\theta$ and $\sigma$, and (iv) disciplining mobility frictions $\{\zeta,\nu,\gamma,\mu_{sk}\}$. Together, these steps ensure that the model exactly rationalizes the pre-war spatial economy, while remaining consistent with the reduced-form evidence on spillovers and local adjustment.
We begin by ensuring that the model reproduces the pre-war spatial economy by construction. Given trade costs and elasticities, we recover baseline productivities $\{z_{i,s}\}$ (up to a sectoral normalization) so that the $t=0$ equilibrium matches observed province--sector wage bills and the implied demand system. Operationally, this involves solving the GE system at $t=0$ with observed $\ell^0_{i,s}$ fixed and treating $z_{i,s}$ as unknowns that satisfy [Equation](#eq:labordemand_quant). Amenities $\{A_i\}$ and housing stocks $\{H_i\}$ then translate wage-bill differences into differences in local costs of living through [Equation](#eq:housing_clear_quant). This inversion anchors the counterfactual on the external shock and equilibrium adjustment rather than on arbitrary fundamentals.
Because Spain's net exports change over 1910--1920, we do not impose balanced trade mechanically in quantification. Instead, we allow for an aggregate external imbalance $D_t$ and implement it via province-level transfers $\{T_i^t\}$ such that $\sum_i T_i^t = D_t$ in each period. We set $D_t$ to match the aggregate trade surplus/deficit measured in customs data, and allocate $T_i^t$ across provinces using predetermined weights (baseline population or wage-bill shares). WWI is implemented as the sectoral foreign-demand shifter in [Equation](#eq:WWI_shock_impl); in robustness, we also allow for import-side shifters $\{\widehat m_s\}$ (see [Equation](#eq:prices_quant)).
Because province-by-destination exports and annual bilateral migration flows are not directly observed, we discipline trade and migration costs using geography and the pre-war transport network. For foreign destinations, we proxy provinces' exposure to destination-specific demand using port accessibility: iceberg costs depend on inland distance to the relevant port and sea distance from that port to the destination (Appendix [3.2](#app:imputation_flows:foreign)). For domestic trade, we assume iceberg trade costs are a power function of bilateral rail distance, so that trade weights (and hence the spatial propagation of foreign demand shocks) decay with distance at rate $\theta$; we choose $\theta$ to match the distance profile of wage spillovers in the data (Appendix [3.3](#app:imputation_flows:trade) and Appendix Table [Table](#tab:distance_elasticity)). Finally, we parameterize bilateral migration costs as an exponential function of distance and estimate their distance sensitivity from gravity regressions on census birthplace-residence stocks, scaling levels to match the observed propensity to live outside one's province of birth (Appendix [3.4](#app:imputation_flows:migration) and Appendix Table [Table](#tab:mig_gravity)). The gravity estimate identifies a composite parameter $\gamma\zeta=1.45$ and yields strong distance frictions to migration and severely limits mobility across provinces.
We estimate $\sigma$ by first inverting the demand system to obtain origin-price shifters (up to normalization) as in Allen and Donaldson ([2020](#ref-allenanddonaldson)). Under marginal-cost pricing, the inverted object satisfies
$$
\log \hat{p}_{is,t}^{1-\sigma}
= \mu_{is}+\mu_{s,t} + (1-\sigma)\log w_{is,t} + u_{is,t},
$$
where $u_{is,t}\equiv-(1-\sigma)\log z_{is,t}$ collects unobserved productivity.[^13] We estimate $(1-\sigma)$ by IV: OLS is biased because wages $w_{i,s}$ co-move with unobserved productivity $z_{i,s}$. We instrument for wages using the WWI shift--share exposure measures in [Equation](#eq:exposure_index_theta), which move labor demand through external export opportunities but are orthogonal to local productivity innovations (conditional on fixed effects). As detailed in Appendix Table [Table](#tab:struct_estim_mean-1), we obtain a preferred estimate of $\sigma=3.35$ ($\text{SE}=0.71$), which sits in the standard range ($3$--$5$) used in quantitative trade models ([Head and Mayer 2014](#ref-HeadMayer2014)).
A key advantage of our natural experiment is that the empirical "direct/indirect exposure" design is not merely descriptive: it corresponds to the *first-order general-equilibrium (GE) mapping* of a multi-market model in the sense of Adao et al. ([2019](#ref-NBERw25544)). In the model, equilibrium wages clear a log excess-demand system $D_{r,s}(w\mid\tau)\equiv \ln\ell^{D}_{r,s}(w\mid\tau)-\ln\ell^{S}_{r,s}(w\mid\tau)=0$. Log-linearizing around the pre-war equilibrium implies that equilibrium wage changes are a linear function of partial-equilibrium demand shifts, $\hat w = (\bar\gamma_{0})^{-1}\hat\eta$, so the reduced-form coefficients in our event-study regressions are *entries of the inverse Jacobian* and therefore have a structural incidence interpretation.[^14] Moreover, the shock objects line up naturally: the model-consistent first-order "exposure" term is a *revenue (wage-bill) labor-demand shifter*; since this is not directly observed, both the reduced form and the quantitative model proxy for it using the employment-based shift--share exposure ([Adao et al. 2019](#ref-NBERw25544)).
To see how this yields labor-supply elasticities, let $X$ denote an exposure term that shifts labor demand in a given province--sector cell but does not directly shift labor supply (formal restrictions stated below). Under market clearing, a demand shifter moves the equilibrium *along the relevant labor-supply schedule*. Hence, for any such $X$, the implied labor-supply elasticity is identified by the ratio of reduced-form employment to wage responses:
$$
\frac{\partial \ln \ell}{\partial \ln w}
=
\frac{\partial \ln \ell/\partial X}{\partial \ln w/\partial X}.
$$
Our nested two-way structure delivers the additional separability needed to interpret these ratios *by margin*. To first order, GE transmission of the WWI demand shift operates through two indices: (i) *within-province cross-sector exposure* and (ii) *spatial within-sector exposure*. In the quantitative model these map exactly to the two margins of reallocation in the nested labor-supply system: *sector switching within a province* (governed by $\nu$) and *spatial relocation across provinces* (governed by $\gamma$). Therefore, we can read off the two structural mobility elasticities from the incidence ratios associated with the direct and spatial exposure coefficients:
$$
\nu \equiv \widehat\varepsilon^{\,\text{sector}} = \frac{\hat\delta_D^{\ell}}{\hat\delta_D^{w}},
\qquad
\gamma \equiv \widehat\varepsilon^{\,\text{space}} = \frac{\hat\delta_S^{\ell}}{\hat\delta_S^{w}}.
$$
To keep the empirical target proportional to the model-consistent revenue (wage-bill) shifter---rather than exports alone---we use a variation of our baseline regression where we furthermore adjust for the province-sector's export exposure by constructing and scaling with the export share over total revenue in a province-sector, i.e. $\frac{\mathrm{Exp}^{1914}_{rs}}{\mathrm{Rev}^{1914}_{rs}}$. The structurally scaled event study is available in Appendix Table [Table](#tab:event_study_combined_structural). Using Appendix Table [Table](#tab:event_study_combined_structural), columns (2) and (4), the relevant WWI-period coefficients are: $\hat\delta_D^{w}=2.657$, $\hat\delta_D^{\ell}=5.634$, $\hat\delta_S^{w}=17.28$, and $\hat\delta_S^{\ell}=12.75$, implying $\nu=2.12$ and $\gamma=0.74$. These values summarize the equilibrium labor-supply elasticities faced by firms in a province--sector cell along the two dominant margins of adjustment: sectoral reallocation within provinces is substantially more elastic than spatial reallocation across provinces.
*Identifying restrictions.* The interpretation of $\widehat\varepsilon^{\,\text{sector}}$ and $\widehat\varepsilon^{\,\text{space}}$ as labor-supply incidence elasticities (and their use as targets for $(\nu,\gamma)$) relies on: (i) WWI export shifters are exogenous demand shocks conditional on fixed effects and controls (including import exposure); (ii) exclusion, i.e. these shifters affect local wages/employment only through labor demand (not via unobserved productivity/amenity changes); and (iii) the AAE log-linearization provides a valid first-order approximation, so the empirical projection recovers the relevant equilibrium incidence moments implied by the two-channel Jacobian. The requirements for (i) and (ii) mirror those for the reduced-form results in Section 3 to be valid. The requirements for (iii) is basically the assumption that the (first-order approximation) of the model is an appropriate specification of the equilibrium adjustment and that higher order terms are not significant confounders.[^15]
We discipline the sector-switching costs $\{\mu_{sk}\}$ using the persistence of sectoral employment in the presence of wage differentials. Because an unrestricted $S\times S$ matrix is infeasible, we impose a parsimonious structure in the spirit of Kambourov ([2009](#ref-RePEc:oup:restud:v:76:y:2009:i:4:p:1321-1358)): destination-specific adjustment costs for all sectors, plus an origin-specific cost for leaving agriculture. This captures the reality that moving from agriculture to non-agriculture often required within-province relocation to urbanized areas, and allows us to tractably infer the parameters governing the large absolute flows out of agriculture. We choose these parameters to match 1920 province--sector employment via minimum distance:
$$
\widehat\mu
=
\arg\min_{\mu\in\mathcal{M}}
\sum_{i,s}
\left(
\ell^{\,\text{data}}_{i,s,1920}
-
\ell^{\,\text{model}}_{i,s,1920}(\mu)
\right)^2.
$$
This step imputes an otherwise missing switching-cost structure that rationalizes the observed post-war reallocation patterns under the WWI shifters. The results (Appendix Table [Table](#apptab:mobility_cost_sec)) confirm that labor is highly sticky. Agriculture, in particular, exhibits high switching costs across all provinces, meaning the large absolute numbers of workers it released were driven by massive wage differentials overcoming these frictions.
Table [Table](#tab:calibration) summarizes the calibration of the model and the moments used for each parameter.
> **Calibration and Joint Estimation**
+:-------------------------------------------------+:--------------------------:+:----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| **Parameter / Object** | **Value** | **Identification / Target** |
+--------------------------------------------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| ***Externally set from historical sources*** |
+--------------------------------------------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Housing expenditure share $\delta$ | 0.33 | Imputed from historical sources |
+--------------------------------------------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Sector expenditure weights $\{\alpha_s\}$ | --- | Imputed from historical sources |
+--------------------------------------------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Housing stock $\{H_r\}$ | --- | Census housing units |
+--------------------------------------------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| ***Auxiliary estimation (outside full model)*** |
+--------------------------------------------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Trade elasticity $\sigma$ | 3.35 | 2SLS estimation ([Table](#tab:struct_estim_mean-1)) |
+--------------------------------------------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Domestic trade-cost distance elasticity $\theta$ | 1.77 | MD on spatial decay of spillovers ([Table](#tab:distance_elasticity)) |
+--------------------------------------------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Migration distance slope $(\gamma\zeta)$ | $-$``{=html}1.45 | Gravity estimation on census data ([Table](#tab:mig_gravity)) |
+--------------------------------------------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| ***Simulation-based minimum distance / inversion (within model)*** |
+--------------------------------------------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Spatial dispersion $\gamma$ | 0.74 | Implied ([Table](#tab:event_study_combined_structural)) |
+--------------------------------------------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Sectoral dispersion $\nu$ | 2.12 | Implied ([Table](#tab:event_study_combined_structural)) |
+--------------------------------------------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Implied migration cost slope $\zeta$ | $-$``{=html}0.32 | $\zeta=(\gamma\zeta)/\gamma$ |
+--------------------------------------------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Sector-switching costs $\{\mu_{sk}\}$ | --- | MD to match 1920 province--sector employment via [Equation](#eq:md_switching) |
+--------------------------------------------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Baseline productivities $\{z_{r,s}\}$ | --- | Exact equilibrium inversion on 1914 wage bills |
+--------------------------------------------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Amenities $\{A_r\}$ | --- | Recovered via baseline exact inversion |
+--------------------------------------------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| External transfers $\{T_r^t\}$ | --- | Match aggregate trade balance, allocated by baseline shares |
+--------------------------------------------------+----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Notes: **---** indicates arrays of parameters without a single scalar value. |
+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
The domestic distance elasticity is $\theta=1.77$ (Table [Table](#tab:calibration)), and the preferred IV estimate implies $\sigma=3.35$. Spatial migration frictions are disciplined by the gravity estimates in [Equation](#eq:gravity_birthplace), while sectoral switching costs $\mu_{sk}$ are chosen to match 1920 province--sector employment levels. Throughout, mobility curvatures $\nu$ and $\gamma$ are set to match the reduced-form incidence ratios in Table [Table](#tab:calibration). With parameters in hand, we solve the model under [Equation](#eq:WWI_shock_impl) and compute implied changes in $w_{i,s}$, $\ell_{i,s}$, and $P_i$. The model translates the reduced-form exposure language into equilibrium mechanisms: direct exposure raises labor demand through export revenue; within-province indirect exposure captures within-province congestion across sectors; spatial indirect exposure captures propagation across provinces through goods-market linkages and mobility frictions. In the benchmark, the combination of estimated mobility curvatures and migration/switching cost levels implies that much of the adjustment occurs through within-province reallocation and local price/wage pressure rather than through large cross-province migration flows. Overall, the fully calibrated model matches both provincial population numbers and aggregate sectoral numbers well, as detailed in Appendix Figures [8](#figure:map_fit_prov_emp) and [9](#figure:map_fit_sec_emp).
We simulate the economy in 1920. This choice is driven by data constraints (availability/consistency of the required sectoral and trade objects) and by the fact that 1920 is a post-war year in which wartime disruptions to trade and financing had largely subsided. Trade balances around the war exhibit substantial variation; our benchmark therefore reflects a period in which trade patterns had begun to normalize, and the model allows for any remaining imbalance through $D_t$ (implemented via $\{T_i^t\}$).
Figure [6](#fig:quant_fit) presents the goodness of fit for employment visually. Panel (a) reports the cross-sectional fit in levels for 1920, and Panel (b) reports the fit for log changes between 1914 and 1920. Point sizes reflect the employment size of the sector in the baseline. The model achieves a strong fit for employment levels (correlation of $0.972$, shock-weighted $R^2$ of $0.969$) and captures the systematic variation in log changes (correlation of $0.310$, RMSE of $0.381$). A full set of diagnostic metrics including wage fit statistics is tabulated in Appendix Table [Table](#tab:gof_metrics) (see also Appendix Figure [10](#figure:map_fit_prov_wage_changes) for a visual counterpart of provincial wage log changes). For wages we have a strong fit in the baseline (correlation of 0.516, RMSE of 0.381) and a somewhat weaker correlation for wage changes (correlation of 0.122, RMSE of 0.381). We highlight that the model implied wage changes need to be interpreted cautiously. The model-implied nominal wages are generated for the 1920 (non-WWI shock) equilibrium and compared to 1920 post-WWI wages in the data. Because the model lacks nominal downward wage rigidity [^16], it predicts a flexible downward adjustment as the demand shock dissipates, while in the data that is not the case.
> **Model fit: Employment Levels and Log Changes**
>
> Figure available in the [PDF](/research/spoils_of_war.pdf).
>
> Notes: Panel (a) compares model-implied log employment against observed log employment at the province–sector level in 1920. Panel (b) compares model-implied employment log changes against observed employment log changes between 1914 and 1920. Point sizes are proportional to the absolute magnitude of the local shift–share export demand shock at the province–sector level.
### Counterfactuals: isolating the role of segmentation
The quantitative model is most useful as a laboratory for questions the reduced form cannot answer on its own. In particular, it lets us separate (i) *where the shock lands* (the spatial incidence of foreign demand across province--sector cells) from (ii) *how strongly it propagates* through the domestic economy given segmented reallocation across space and sectors.
Our baseline exercise holds fixed the pre-war domestic economy and asks how outcomes would have evolved absent the WWI export-demand shift. Concretely, we solve for the equilibrium under the WWI foreign-demand implementation in [Equation](#eq:WWI_shock_impl) and compare it to a "Spain without WWI" equilibrium in which we reset the foreign-demand and import shifters to their pre-war values (setting $\widehat z_s=0$ and $\widehat m_s=0$). In all counterfactuals, external trade quantities are external parameters calibrated consistently with the experiment that we are conducting. For the "Spain without WWI" counterfactual, we set the foreign demand shifters to their pre-war values (setting $\widehat z_s=0$ and $\widehat m_s=0$).[^17] We keep fixed the aggregate trade-balance transfer $D_t$, and we solve for equilibrium wages, allocations, and prices. To ensure that comparisons do not mechanically load on changes in the external budget constraint, we reassign the province-level transfers $\{T_i^1\}$ so that the model matches the same aggregate trade balance in each scenario.
The counterfactuals below change labor-market integration by varying mobility frictions (e.g. $\mu_{in}$ and $\mu_{sk}$). As discussed in Section [3.4](#sec:rf_to_quant) (formalized in Appendix [4.2](#app:lechatelier)), lowering segmentation raises the effective elasticity of labor supply facing each province--sector market. Holding fixed the same foreign-demand shift, this shifts adjustment away from nominal wages (and local prices via marginal costs and housing) and toward labor reallocation. Because the economy is a network, this attenuation result is most naturally stated in shock-aligned quadratic forms; it need not imply cell-by-cell monotonicity.
We implement four scenarios that isolate distinct mechanisms. First, we simulate the Baseline WWI with frictions (Panel A). This is the fully estimated model with the WWI export-demand shifters and the baseline spatial and sectoral frictions. It provides the benchmark incidence pattern: in places where foreign demand rises, limited mobility prevents rapid quantity adjustment, so the shock shows up strongly in nominal wages and local prices, with substantial heterogeneity across provinces. Second, we simulate a version of the model with more Integrated labor markets (Panel B) (specifically, we set $\zeta=0, \nu=2$). To isolate the role of spatial segmentation, we remove spatial migration frictions (setting the distance component of migration costs to zero, i.e. "no spatial frictions"). This counterfactual increases cross-province reallocation and therefore reduces the dispersion of nominal wage changes and real-income changes across provinces. Intuitively, integration makes the domestic economy a better spatial shock absorber: demand pressure can be exported through worker flows rather than being absorbed locally through wage and housing-cost increases.
Third, we simulate the economy assuming an 'even trade shock' (Panel C) (specifically halving the distance coefficient $\gamma$ in the origin-specific component of export trade costs). To isolate the role of *where* the shock lands, we remove the spatial unevenness of the export-demand impulse by eliminating the origin-specific component of export trade costs (restricting $\tau_{li,s}$ to depend only on $(l,s)$, not on $i$). This yields a counterfactual in which foreign-demand growth is "spatially even" across domestic origins within a sector, so remaining heterogeneity reflects domestic propagation under segmentation rather than the initial spatial targeting of demand.
Finally, we combine Panels B and C to strip out both sources of heterogeneity ('Even shock with integrated labor markets (Panel D).'): (i) spatial unevenness in the external impulse and (ii) spatial segmentation in worker reallocation. This benchmark clarifies how much residual dispersion is generated by within-province sectoral adjustment, housing-market effects, and goods-market linkages.
To visualize how segmentation shapes incidence, Figure [7](#fig:counterfactual_scatter) plots province--sector employment log changes between 1914 and 1920 in each counterfactual (y-axis) against the baseline fitted log changes (x-axis). Point sizes are proportional to pre-war employment, so deviations from the 45-degree line highlight economically meaningful reallocations. Panel (a) removes the WWI export-demand shifters ("No WWI"). The cloud indicates a horizontal shape, implying that the WWI shock is responsible for most of the employment changes in the baseline scenario. Providing validation for the model's ability to capture the main drivers of the Spanish economy during WWI. Panel (b) keeps the WWI shifters but lowers spatial migration frictions ("Integrated Markets"). Here the scatter tilts away from the 45-degree line: province--sectors that expand in the baseline expand more, while contracting cells contract more. This rotation captures the Le Chatelier logic in incidence space: when spatial frictions fall,adjustment shifts away from within-province wage/price pressure and toward reallocation, amplifying employment responses in the most attractive province--sectors.
Table [Table](#tab:welfare_variance) summarizes population-weighted means and variances across provinces of the main local components---nominal wages, rents, consumer prices, and implied static real income---along with spatial and sectoral reallocation measures.
Under the baseline trade shock with estimated spatial and sectoral frictions (Panel A), the average province experiences sizable nominal wage growth and price inflation, translating into a positive mean change in static real income. At the same time, dispersion is substantial: the variance of provincial real-income changes is 90.66, alongside large cross-province dispersion in nominal wages (variance 139.82).
> **Local Averages and Variances of Sub-components**
+:---------------------------------------------------------+:-------------:+:-------------:+:-------------:+:-------------:+:-------------:+:-------------:+:-------------:+:-------------:+:---------------:+:---------------:+:-------------:+:-------------:+
| | Nominal Wage | Rental Cost | Price (Inflation) | Real Income | Spat. Flow ($\Delta \ln L_n$) | Sec. Flow ($\%$ Switched) |
+----------------------------------------------------------+---------------+---------------+---------------+---------------+---------------+---------------+---------------+---------------+-----------------+-----------------+---------------+---------------+
| Welfare Changes from (in $\%$) | Mean | Var | Mean | Var | Mean | Var | Mean | Var | Mean | Var | Mean | Var |
+----------------------------------------------------------+---------------+---------------+---------------+---------------+---------------+---------------+---------------+---------------+-----------------+-----------------+---------------+---------------+
| **Panel A: Baseline Result** |
+----------------------------------------------------------+---------------+---------------+---------------+---------------+---------------+---------------+---------------+---------------+-----------------+-----------------+---------------+---------------+
| (1a) Baseline (Trade shock & Spat./Sec. Frictions) | 7.98 | 139.82 | 0.89 | 2.98 | 3.79 | 9.12 | 5.18 | 90.66 | 0.14 | 0.12 | 1.62 | 2.65 |
+----------------------------------------------------------+---------------+---------------+---------------+---------------+---------------+---------------+---------------+---------------+-----------------+-----------------+---------------+---------------+
| **Panel B: Integrated Labor Markets** |
+----------------------------------------------------------+---------------+---------------+---------------+---------------+---------------+---------------+---------------+---------------+-----------------+-----------------+---------------+---------------+
| (2a) Baseline Trade Shock without Spat. Frictions | 7.13 | 102.55 | 0.34 | 2.85 | 3.56 | 8.32 | 4.66 | 66.76 | 0.12 | 1.19 | 1.86 | 3.49 |
+----------------------------------------------------------+---------------+---------------+---------------+---------------+---------------+---------------+---------------+---------------+-----------------+-----------------+---------------+---------------+
| **Panel C: Even Trade Shock** |
+----------------------------------------------------------+---------------+---------------+---------------+---------------+---------------+---------------+---------------+---------------+-----------------+-----------------+---------------+---------------+
| (3a) Spatially Even Export Shock & Spat./Sec. Frictions | 7.79 | 93.73 | 0.78 | 2.34 | 3.45 | 1.92 | 5.24 | 78.59 | 0.13 | 0.14 | 1.73 | 2.90 |
+----------------------------------------------------------+---------------+---------------+---------------+---------------+---------------+---------------+---------------+---------------+-----------------+-----------------+---------------+---------------+
| **Panel D: Even Trade shock & Integrated Labor Market** |
+----------------------------------------------------------+---------------+---------------+---------------+---------------+---------------+---------------+---------------+---------------+-----------------+-----------------+---------------+---------------+
| (4a) Spatially Even Export Shock without Spat. Frictions | 7.34 | 68.15 | 0.10 | 2.25 | 3.61 | 2.11 | 4.93 | 59.95 | 0.13 | 1.27 | 1.92 | 3.79 |
+----------------------------------------------------------+---------------+---------------+---------------+---------------+---------------+---------------+---------------+---------------+-----------------+-----------------+---------------+---------------+
Eliminating spatial migration frictions (Panel B) substantially smooths the spatial incidence of the shock. The variance of real-income changes falls from 90.66 to 66.76, and nominal-wage dispersion falls from 139.82 to 102.55. Consistent with the mechanism, this compression in wage and real-income dispersion comes with meaningfully stronger reallocation: spatial flows become much more uneven across provinces (spatial-flow variance rises from 0.12 to 1.19), and sectoral switching increases.
Panels C and D separate "where the shock lands" from "how strongly segmentation prevents dissipation." Making the export shock spatially even while holding frictions fixed (Panel C) sharply compresses the spatial dispersion in inflation (variance moves from 9.12 to 1.92) and reduces dispersion in wages and real income as well. Combining a spatially even shock with integrated labor markets (Panel D) yields the lowest dispersion overall (real-income variance 59.95; nominal-wage variance 68.15). Together, these results show that both the geography of the export boom and domestic labor-market segmentation are quantitatively important for the cross-province distribution of gains, with the spatial unevenness of the shock playing a particularly large role in the dispersion of local inflation.[^18]
Overall, the counterfactuals line up with the model's theoretical prediction that segmentation acts as an amplifier. When mobility frictions are high, the same external demand impulse is absorbed disproportionately through local nominal-wage and cost-of-living adjustments (and thus larger cross-market dispersion), whereas lowering segmentation shifts adjustment toward quantities---worker reallocation across province--sector cells---thereby attenuating nominal responses and smoothing the spatial incidence of gains. The scatter evidence is especially consistent with this mechanism: reducing spatial frictions changes the incidence mapping in the direction implied by the Le Chatelier result, with relative adjustment occurring more through reallocation and less through within-market price pressure. Taken together, the simulations therefore provide a coherent quantitative validation of the theory: they show that the propagation of the export-demand shock depends not only on where it initially lands, but also on how strongly domestic segmentation prevents the economy from dissipating it through reallocation.
> **Counterfactual Log Changes in Employment**
>
> Figure available in the [PDF](/research/spoils_of_war.pdf).
>
> Notes: The figure compares simulated counterfactual log changes between 1914 and 1920 (y-axis) against the baseline fitted log changes (x-axis) for employment at the province–sector level. Counterfactual 1 (Panel a) removes the WWI export demand shocks. Counterfactual 2 (Panel b) maintains the WWI shocks but halves the spatial migration distance friction parameter. Point sizes are scaled by pre-war employment levels.
## Conclusion
This paper provides new reduced-form and quantitative evidence on how segmented domestic labor markets shape the welfare effects of trade. We show that when factor mobility is imperfect, an external demand shock can raise allocative efficiency. But when exposure to the shock is uneven across space and sectors, adjustment occurs primarily through localized increases in wages and consumer prices rather than through worker reallocation, limiting the potential reallocative gains from trade.
We substantiate this mechanism using a historical natural experiment: a large international trade demand shock to the Spanish economy during World War I (1914--1918), triggered by the participation of Spain's main trading partners in the war. Because belligerent countries sharply increased their demand for Spanish goods, the shock was substantial and plausibly external to Spain's domestic conditions. We document that local wages and consumer prices adjusted along a distinct spatial pattern shaped by both the direct and indirect effects of the shock, with labor-market adjustment remaining largely local.
To interpret these empirical patterns, we extend a standard economic geography framework to incorporate imperfect labor mobility. By introducing a tractable worker-reallocation mechanism with sectoral and spatial frictions, the model captures how interconnected local labor markets mediate the propagation of an external demand shock. After estimating the model, we simulate a counterfactual Spanish economy without the WWI shock. The results indicate that real income gains from the shock were highly heterogeneous across regions and that limited labor mobility transmitted these gains weakly across space. As a consequence, the economy experienced substantial labor-market congestion in high-exposure locations, which constrained the aggregate benefits from trade.
Overall, this paper underscores that understanding the welfare gains from aggregate trade shocks requires accounting for the domestic, disaggregated distribution of economic activity and the frictions governing factor reallocation across local labor markets. Our findings highlight the importance of explicitly modeling and measuring the domestic network structure connecting local labor markets in both reduced-form and quantitative analyses of trade.
## Appendix
## Figures
> **Model Fit: Provincial Employment (1920 Data vs Fitted Model)**
>
> Figure available in the [PDF](/research/spoils_of_war.pdf).
> **Model Fit: Sectoral Employment (1920 Data vs Fitted Model)**
>
> Figure available in the [PDF](/research/spoils_of_war.pdf).
> **Model Fit: Provincial Wages Log Changes (1914-1920 Data vs Fitted Model)**
>
> Figure available in the [PDF](/research/spoils_of_war.pdf).
> **No WWI Cfl: Provincial Employment (1920 Data vs Cfl)**
>
> Figure available in the [PDF](/research/spoils_of_war.pdf).
> **No WWI Cfl: Sectoral Employment (1920 Data vs Cfl)**
>
> Figure available in the [PDF](/research/spoils_of_war.pdf).
> **Sectoral Heterogeneity of the Trade Shock**
>
> Figure available in the [PDF](/research/spoils_of_war.pdf).
## Regression Tables
### Main Regression Tables
> **Regression Results: Event Study on Sectoral Imports**
------------------------------------------------------------ --------------------------
import_value
\(1\)
War Period $\times$ Sector $=$ Chemicalindustry -0.8245$^{***}$ (0.0003)
War Period $\times$ Sector $=$ Civilengineering 2.016$^{***}$ (0.0018)
War Period $\times$ Sector $=$ Construction -0.3590$^{***}$ (0.0003)
War Period $\times$ Sector $=$ Constructionmaterials -0.8941$^{***}$ (0.0005)
War Period $\times$ Sector $=$ Electricity -0.2292$^{***}$ (0.0002)
War Period $\times$ Sector $=$ Foodindustry -0.0499$^{***}$ (0.0001)
War Period $\times$ Sector $=$ Furniture -0.9317$^{***}$ (0.0004)
War Period $\times$ Sector $=$ Garmentindustry -0.2040$^{***}$ (0.0002)
War Period $\times$ Sector $=$ Gasfactory 0.6405$^{***}$ (0.0007)
War Period $\times$ Sector $=$ Glassindustry -1.079$^{***}$ (0.0005)
War Period $\times$ Sector $=$ Industriasdelaornamentacion 0.1294$^{***}$ (0.0385)
War Period $\times$ Sector $=$ Industriasdeltabaco 0.4784$^{***}$ (0.0014)
War Period $\times$ Sector $=$ Industriasvarias -0.1073$^{***}$ (0.0002)
War Period $\times$ Sector $=$ Ironworksandothermetals -0.1384$^{***}$ (0.0003)
War Period $\times$ Sector $=$ Jewellery 1.255$^{***}$ (0.0018)
War Period $\times$ Sector $=$ Leatherindustry -0.4298$^{***}$ (0.0006)
War Period $\times$ Sector $=$ Metalobjects -0.7456$^{***}$ (0.0001)
War Period $\times$ Sector $=$ Metallurgy -0.3049$^{***}$ (0.0003)
War Period $\times$ Sector $=$ Mines,Saltminesandquarries -0.0027$^{***}$ (0.0001)
War Period $\times$ Sector $=$ Paperindustry -0.3318$^{***}$ (0.0003)
War Period $\times$ Sector $=$ Potteryandceramics -0.6268$^{***}$ (0.0017)
War Period $\times$ Sector $=$ Printindustry -0.4105$^{***}$ (0.0003)
War Period $\times$ Sector $=$ PublicServices 0.3489$^{***}$ (0.0006)
War Period $\times$ Sector $=$ Shops -0.5431$^{***}$ (0.0003)
War Period $\times$ Sector $=$ SilverwareandJewelry -0.4557$^{***}$ (0.0005)
War Period $\times$ Sector $=$ Textiles -0.2915$^{***}$ (0.0002)
War Period $\times$ Sector $=$ Transportindustry -1.322$^{***}$ (0.0002)
War Period $\times$ Sector $=$ Wood -0.3438$^{***}$ (0.0001)
Observations 232
Pseudo R$^2$ 0.98626
Sector fixed effects $\checkmark$
Year fixed effects $\checkmark$
------------------------------------------------------------ --------------------------
> **Sector-Level Export Demand Shifters ($\widehat{z}_s$)**
+:-------------------------------------------------------------------+:----------------------:+:----------------------:+:-----------------------:+
| | Exports (Value) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| | \(1\) | \(2\) | \(3\) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| Belligerent | 2.049$^{***}$ (0.1689) | | |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent | 0.4035$^{*}$ (0.2428) | 0.2985 (0.1929) | 0.2461$^{*}$ (0.1356) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Books | -0.3825 (0.5973) | -0.3859 (0.5149) | -0.4341 (0.3521) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Ceramics | -0.1552 (0.5689) | -0.1794 (0.5760) | -0.1749 (0.4190) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Chemicals | 0.8262$^{*}$ (0.4303) | 0.7580$^{**}$ (0.3770) | 0.7982$^{**}$ (0.3524) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Construction | 0.2978 (0.5313) | 0.5123 (0.5009) | 0.6182$^{*}$ (0.3162) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Decoration | 1.197 (1.248) | 1.077 (1.274) | 1.155 (1.336) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Electricity | 0.0713 (0.6816) | 0.3267 (0.7208) | -0.0820 (0.6371) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Food | 0.1643 (0.3313) | 0.1417 (0.3019) | 0.1536 (0.2300) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Forrest | 0.3829 (0.8404) | 0.2847 (0.8239) | -0.0495 (0.7061) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Furniture | -0.0415 (0.4626) | -0.0963 (0.3756) | 0.0046 (0.3327) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Garments | 1.564$^{***}$ (0.5131) | 1.722$^{***}$ (0.4658) | 1.632$^{***}$ (0.4382) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Glass | 0.2927 (0.9716) | 0.4907 (0.8949) | 0.4762 (0.8873) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Gold | -0.4985 (0.6270) | -0.0315 (0.5750) | -0.2444 (0.4845) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Leather | 1.796 (1.195) | 2.106$^{*}$ (1.121) | 2.204$^{*}$ (1.136) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Metallurgy | 2.288$^{**}$ (0.9711) | 2.216$^{**}$ (0.9518) | 2.007$^{**}$ (0.9241) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ MetalWorks | 0.5281 (0.5615) | 0.7327 (0.4840) | 0.9247$^{**}$ (0.4579) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Mines | 0.3043 (0.4720) | 0.2123 (0.3517) | 0.1589 (0.2297) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Other | 0.0005 (0.4426) | -0.0126 (0.4183) | -0.1717 (0.3561) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Paper | 1.664$^{**}$ (0.7098) | 1.658$^{**}$ (0.6647) | 1.685$^{**}$ (0.6570) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ PublicIndustry | 0.6260 (1.503) | 1.185 (1.555) | -3.553$^{**}$ (1.398) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Textiles | 1.045$^{**}$ (0.4254) | 1.041$^{***}$ (0.3897) | 0.9815$^{***}$ (0.3416) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Tobacco | 3.460$^{***}$ (1.278) | 3.868$^{***}$ (1.316) | 3.907$^{***}$ (1.261) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Transport | 0.6397 (0.5999) | 0.3015 (0.5706) | 0.3076 (0.4537) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Wood | -0.3595 (0.4678) | -0.3461 (0.3309) | -0.4224$^{*}$ (0.2284) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| | | | |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| Observations | 80,143 | 80,143 | 79,914 |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| Pseudo R$^2$ | 0.49221 | 0.68012 | 0.87923 |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| | | | |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| Product fixed effects | $\checkmark$ | $\checkmark$ | |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| Year fixed effects | $\checkmark$ | $\checkmark$ | $\checkmark$ |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| Destination fixed effects | | $\checkmark$ | |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| Destination-Product fixed effects | | | $\checkmark$ |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
> **Migration Gravity**
------------------------------ ------------------------- ------------------------- ------------------------- -------------------------
Census 1920
Census 1930
Census 1920 and 1930
Census 1920
\(1\) \(2\) \(3\) \(4\)
Log Bilateral Distance -1.450$^{***}$ (0.0454) -1.455$^{***}$ (0.0476) -1.434$^{***}$ (0.0556) -1.450$^{***}$ (0.0476)
Internal Move 3.285$^{***}$ (0.0952) 3.193$^{***}$ (0.0995) 2.796$^{***}$ (0.1168) 3.380$^{***}$ (0.0891)
Observations 2,209 2,209 1,881 2,209
Pseudo R$^2$ 0.98644 0.98493 0.97488 0.67283
Dest. Province fixed effects $\checkmark$ $\checkmark$ $\checkmark$ $\checkmark$
Orig. Province fixed effects $\checkmark$ $\checkmark$ $\checkmark$ $\checkmark$
------------------------------ ------------------------- ------------------------- ------------------------- -------------------------
### Robustness Results
To address potential concerns regarding the exogeneity of the Spanish export shocks and the construction of the shift-share exposures, this section presents a series of unified robustness checks for wages and labor outcomes.
> **Wages and Labor: Consolidated Robustness Results**
*The table layout is available in the PDF.*
> **Shift Exogeneity: Direct Shocks vs Pre-War Growth**
+:----------------------------------+:------------------------------------------------:+
| Dependent Variable: | Sectoral Export Demand Shifter ($\widehat{z}_s$) |
+-----------------------------------+--------------------------------------------------+
| Model: | \(1\) |
+-----------------------------------+--------------------------------------------------+
| *Variables* | |
+-----------------------------------+--------------------------------------------------+
| Constant | 0.3637$^{**}$ |
+-----------------------------------+--------------------------------------------------+
| | (0.1425) |
+-----------------------------------+--------------------------------------------------+
| Pre-War Export Growth (1910-1913) | 0.2646 |
+-----------------------------------+--------------------------------------------------+
| | (0.4530) |
+-----------------------------------+--------------------------------------------------+
| *Fit statistics* | |
+-----------------------------------+--------------------------------------------------+
| Observations | 18 |
+-----------------------------------+--------------------------------------------------+
| R$^2$ | 0.02310 |
+-----------------------------------+--------------------------------------------------+
| Adjusted R$^2$ | -0.03796 |
+-----------------------------------+--------------------------------------------------+
| *Heteroskedasticity-robust standard-errors in parentheses* |
+--------------------------------------------------------------------------------------+
| *Signif. Codes: \*\*\*: 0.01, \*\*: 0.05, \*: 0.1* |
+--------------------------------------------------------------------------------------+
> **Pre-War Outcome Balance Test (1908-1913)**
+:------------------------------+:------------------:+:------------------:+
| | | |
+-------------------------------+--------------------+--------------------+
| (1908-1913) | | |
+-------------------------------+--------------------+--------------------+
| (1908-1913) | | |
+-------------------------------+--------------------+--------------------+
| Model: | \(1\) | \(2\) |
+-------------------------------+--------------------+--------------------+
| *Variables* | | |
+-------------------------------+--------------------+--------------------+
| WWI Direct Exposure | 2.307 | -4.759 |
+-------------------------------+--------------------+--------------------+
| | (1.675) | (7.296) |
+-------------------------------+--------------------+--------------------+
| WWI Spatial Indirect Exposure | 3.481 | -81.73 |
+-------------------------------+--------------------+--------------------+
| | (56.29) | (280.8) |
+-------------------------------+--------------------+--------------------+
| *Fixed-effects* | | |
+-------------------------------+--------------------+--------------------+
| Typef-Industryf | Yes | Yes |
+-------------------------------+--------------------+--------------------+
| Typef-Provincef | Yes | Yes |
+-------------------------------+--------------------+--------------------+
| *Fit statistics* | | |
+-------------------------------+--------------------+--------------------+
| Observations | 217 | 230 |
+-------------------------------+--------------------+--------------------+
| R$^2$ | 0.51282 | 0.34740 |
+-------------------------------+--------------------+--------------------+
| Within R$^2$ | 0.02609 | 0.00274 |
+-------------------------------+--------------------+--------------------+
| *Clustered (Industryf) standard-errors in parentheses* |
+-------------------------------------------------------------------------+
| *Signif. Codes: \*\*\*: 0.01, \*\*: 0.05, \*: 0.1* |
+-------------------------------------------------------------------------+
> **Robustness Analysis: Extended Sample (1908--1920) with Post-War Controls**
+:---------------------------------------------------------------------+:------------------------:+:------------------------:+:-----------------------:+:-----------------------:+
| | lwages | llabor |
+----------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+
| | Log Wages | Log Employment |
+----------------------------------------------------------------------+--------------------------+--------------------------+-------------------------+-------------------------+
| | \(1\) | \(2\) | \(3\) | \(4\) |
+----------------------------------------------------------------------+--------------------------+--------------------------+-------------------------+-------------------------+
| Direct Exposure | 0.2581 (0.4886) | | 14.52$^{***}$ (2.780) | |
+----------------------------------------------------------------------+--------------------------+--------------------------+-------------------------+-------------------------+
| Spatial Indirect Exposure | 5.472 (15.81) | | 46.47 (94.86) | |
+----------------------------------------------------------------------+--------------------------+--------------------------+-------------------------+-------------------------+
| WWI Period $\times$ Log Distance to France | -0.2016$^{***}$ (0.0450) | -0.1866$^{***}$ (0.0343) | -0.1330 (0.2649) | -0.1384 (0.1488) |
+----------------------------------------------------------------------+--------------------------+--------------------------+-------------------------+-------------------------+
| WWI Period $\times$ Direct Exposure | 1.918$^{***}$ (0.5266) | 1.830$^{***}$ (0.3148) | 0.2814 (3.392) | 0.9871 (0.9023) |
+----------------------------------------------------------------------+--------------------------+--------------------------+-------------------------+-------------------------+
| WWI Period $\times$ Within-Province Indirect Exposure | 1.377$^{***}$ (0.1974) | 1.272$^{***}$ (0.1658) | 1.627 (1.324) | 2.336$^{***}$ (0.6829) |
+----------------------------------------------------------------------+--------------------------+--------------------------+-------------------------+-------------------------+
| WWI Period $\times$ Spatial Indirect Exposure | 1.929 (5.468) | 3.049 (4.083) | 28.31 (37.15) | 17.58 (13.43) |
+----------------------------------------------------------------------+--------------------------+--------------------------+-------------------------+-------------------------+
| WWI Period $\times$ Provincial Import Control | 1.037$^{***}$ (0.1894) | 0.9474$^{***}$ (0.1569) | -0.1403 (1.165) | 0.1058 (0.6687) |
+----------------------------------------------------------------------+--------------------------+--------------------------+-------------------------+-------------------------+
| Log Distance to France $\times$ Post-War Period (1919-20) | -0.1558$^{***}$ (0.0600) | -0.1502$^{***}$ (0.0558) | -1.177$^{***}$ (0.3499) | -1.205$^{***}$ (0.2482) |
+----------------------------------------------------------------------+--------------------------+--------------------------+-------------------------+-------------------------+
| Direct Exposure $\times$ Post-War Period (1919-20) | 3.554$^{***}$ (0.7788) | 3.538$^{***}$ (0.5158) | 3.500 (4.343) | 2.551 (1.733) |
+----------------------------------------------------------------------+--------------------------+--------------------------+-------------------------+-------------------------+
| Within-Province Indirect Exposure $\times$ Post-War Period (1919-20) | 1.466$^{***}$ (0.2803) | 1.479$^{***}$ (0.2496) | 4.229$^{***}$ (1.612) | 4.063$^{***}$ (0.9714) |
+----------------------------------------------------------------------+--------------------------+--------------------------+-------------------------+-------------------------+
| Spatial Indirect Exposure $\times$ Post-War Period (1919-20) | -2.121 (8.057) | -1.631 (6.730) | 31.08 (45.46) | 19.01 (21.73) |
+----------------------------------------------------------------------+--------------------------+--------------------------+-------------------------+-------------------------+
| Provincial Import Control $\times$ Post-War Period (1919-20) | 1.237$^{***}$ (0.2441) | 1.224$^{***}$ (0.2244) | 4.199$^{***}$ (1.420) | 3.697$^{***}$ (0.9331) |
+----------------------------------------------------------------------+--------------------------+--------------------------+-------------------------+-------------------------+
| R$^2$ | 0.76669 | 0.84798 | 0.46690 | 0.82185 |
+----------------------------------------------------------------------+--------------------------+--------------------------+-------------------------+-------------------------+
| Observations | 3,860 | 3,853 | 3,998 | 3,988 |
+----------------------------------------------------------------------+--------------------------+--------------------------+-------------------------+-------------------------+
| Pseudo R$^2$ | 0.91829 | 1.1900 | 0.14759 | 0.40537 |
+----------------------------------------------------------------------+--------------------------+--------------------------+-------------------------+-------------------------+
| Industryf fixed effects | $\checkmark$ | | $\checkmark$ | |
+----------------------------------------------------------------------+--------------------------+--------------------------+-------------------------+-------------------------+
| Typef fixed effects | $\checkmark$ | | $\checkmark$ | |
+----------------------------------------------------------------------+--------------------------+--------------------------+-------------------------+-------------------------+
| Provincef fixed effects | $\checkmark$ | | $\checkmark$ | |
+----------------------------------------------------------------------+--------------------------+--------------------------+-------------------------+-------------------------+
| Yearf fixed effects | $\checkmark$ | $\checkmark$ | $\checkmark$ | $\checkmark$ |
+----------------------------------------------------------------------+--------------------------+--------------------------+-------------------------+-------------------------+
| Typef-Industryf-Provincef fixed effects | | $\checkmark$ | | $\checkmark$ |
+----------------------------------------------------------------------+--------------------------+--------------------------+-------------------------+-------------------------+
> **Main Regression Results: Full Output including Level Terms**
*The table layout is available in the PDF.*
### Calibration
> **Structural Calibration Regression Targets**
*The table layout is available in the PDF.*
> **Elasticity of Substitution**
*The table layout is available in the PDF.*
> **GMM Estimation of Distance Elasticity**
*The table layout is available in the PDF.*
> **Model Goodness of Fit Metrics**
------------------------ ----------------------- ---------- ---------------------------- ------------------------------------
**Model Fit Scenario** **Correlation ($r$)** **RMSE** **$R^2$ (vs 45-deg line)** **Weighted $R^2$ (by Shock Size)**
Employment Levels 0.972 0.480 0.932 0.969
Wage Levels 0.516 0.381 -0.092 -0.024
Employment Changes 0.310 0.480 -1.043 0.386
Wage Changes 0.122 0.381 -1.752 -0.168
------------------------ ----------------------- ---------- ---------------------------- ------------------------------------
## Inferring Domestic Trade and Mobility Linkages When Bilateral Flows Are Unobserved
### Motivation and data limitations
A core goal of the quantitative framework is to map a sectoral foreign-demand shifter into (i) province--sector labor-demand changes and (ii) general-equilibrium propagation across province--sector markets through goods-market linkages and labor reallocation. Implementing this mapping requires objects that are not directly observed in the historical record at the spatial and temporal granularity needed for the model.
In particular, two classes of bilateral flows are missing from the data:
1. **Foreign trade costs and port accessibility.** We do not observe shipment matrix by sector (or product) by provinces. Without such flows, we also cannot nonparametrically recover domestic trade shares or bilateral iceberg costs. Instead we parameterize the iceberg costs using the pre-war rail-distance network, and information on geolocation of ports and sea distances.
2. **Domestic trade flows across provinces.** Similarly, We do not observe an inter-province shipment matrix by sector (or product). Without such flows, we also cannot nonparametrically recover domestic trade shares or bilateral iceberg costs.
3. **Annual bilateral migration flows across provinces and sectors.** The census provides cross-sections of residents by province of birth, but not annual origin--destination flows. Likewise, we do not observe annual cross-sector switching flows at the province level.
Rather than treating these missing flows as additional data to be "filled in" ad hoc, we treat them as *latent equilibrium objects* implied by a tractable structure for trade and mobility frictions. The appendix details how we (i) parameterize domestic trade costs and bilateral migration costs using the pre-war rail-distance network, (ii) estimate/discipline the key distance sensitivities using auxiliary moments, and (iii) infer a parsimonious sector-switching cost structure by matching observed medium-run reallocation outcomes.
### Foreign iceberg trade costs and the distance elasticity
Since province-by-destination export flows are not observed, we parameterize $\tau_{li,s}$ to determine which provinces are most exposed to destination $l$'s demand using port accessibility:
$$
\tau_{li,s}
=
\exp\!\Big(
\theta^{\text{port}}\text{dist}_{i,\text{port}(l)}
+
\theta^{\text{sea}}\text{seaDist}_{\text{port}(l),l}
+
\theta_{s,\text{int}}
\Big),
$$
where $\text{port}(l)$ is the nearest major Spanish port serving destination $l$. We calibrate $(\theta^{\text{port}},\theta^{\text{sea}})$ using pre-war shipping cost data and destination-specific weights from customs records. In the benchmark, we assume the trade elasticity $\sigma$ and distance elasticity $\theta$ are common across sectors.
### Domestic iceberg trade costs and the distance elasticity $\theta$
Let $\tau_{ni,s}\ge 1$ denote the iceberg cost of shipping a sector-$s$ variety produced in province $i$ to a domestic destination province $n$. Because inter-province trade flows are not observed, we impose a standard distance-based parameterization:
$$
\tau_{ni,s} \;=\; \text{dist}_{ni}^{\kappa},
$$
where $\text{dist}_{ni}$ is the shortest-path rail distance between provinces $n$ and $i$ computed on the historical rail network, and $\kappa>0$ controls how quickly domestic trade costs rise with distance.
Under CES demand with trade elasticity $\sigma$, delivered-price terms enter expenditure shares through $\tau_{ni,s}^{1-\sigma}$. Therefore bilateral trade *weights* scale with distance as
$$
\tau_{ni,s}^{1-\sigma} \;=\; \text{dist}_{ni}^{-\theta},
\qquad \text{where } \theta \equiv \kappa(\sigma-1).
$$
In practice, $\theta$ is the key scalar that governs how strongly domestic market access and spillovers decay with distance in the model.
Under CES, this implies that trade weights scale as $\tau_{ni,s}^{1-\sigma}=\text{dist}_{ni}^{-\theta}$, where $\theta\equiv\kappa(\sigma-1)$. The model implies that the incidence of foreign demand shocks across domestic locations is summarized by the exposure index
$$
X_i(\theta)
\equiv
\sum_{l\in\mathcal{F}} \sum_{s\in\mathcal{S}} \frac{E_{l,s}}{Y_i}
\left(
\frac{\text{dist}_{li}^{-\theta}\,\pi^0_{i,s}}
{\sum_{j\in\mathcal{D}}\text{dist}_{lj}^{-\theta}\,\pi^0_{j,s}}
\right),
$$
where $\text{dist}_{li}$ denotes the (generalized) distance from province $i$ to foreign destination $l$ (constructed using port access and sea distance, consistent with [Equation](#eq:tau_foreign_ports)).
We choose $\theta$ to match the empirical distance profile of spatial spillovers. We estimate the spillover regression in Section [3.2](#sec:baseline_specs) on distance-binned spatial exposure measures, and select $\theta$ so that the model-implied spillover profile aligns with the data:
$$
\widehat\theta
=
\arg\min_{\theta}
\sum_{b}
\left(
\widehat\delta^{w,\text{data}}_{S}(b)
-
\widehat\delta^{w,\text{model}}_{S}(b;\theta)
\right)^2,
$$
where $b$ indexes distance bins along the rail network and $\widehat\delta^{w}_{S}(b)$ is the wage spillover coefficient at distance $b$. As reported in Appendix Table [Table](#tab:distance_elasticity), we estimate $\theta=1.77$ ($\text{SE}=0.21$), implying that exposure decays moderately with distance. This estimate is closely aligned with the intranational rail-distance elasticities documented in Wolf ([2009](#ref-RePEc:cup:jechis:v:69:y:2009:i:03:p:846-881_00)) for Germany during the same time period.
### Bilateral migration costs from census birthplace stocks
Let $\mu_{in}\ge 1$ denote the bilateral cost for a worker to relocate from an origin province $i$ to a destination province $n$. We parameterize migration costs as
$$
\mu_{in} \;=\; \exp\!\left(\zeta_i + \zeta\cdot \text{dist}_{in}\right),
$$
where $\zeta_i$ is an origin shifter capturing persistent push factors (and/or origin-specific barriers), and $\zeta$ governs how migration costs rise with distance.
Because we do not observe annual bilateral migration flows, we use a gravity-style regression on census *stocks* of residents by place of birth. Let $M_{in}$ denote the number of residents living in province $n$ who were born in province $i$. Under the Fréchet discrete-choice structure for province choice (with dispersion parameter $\gamma$), bilateral stocks satisfy a log-gravity relationship:
$$
\log M_{in}
\;=\;
\psi_i + \psi_n
-
(\gamma\zeta)\,\text{dist}_{in}
+
\kappa\cdot \mathbf{1}\{i=n\}
+
\varepsilon_{in},
$$
where $\psi_i$ and $\psi_n$ are origin and destination fixed effects and $\mathbf{1}\{i=n\}$ captures the mechanical home-province diagonal. This regression identifies the composite slope $\gamma\zeta$. Given $\gamma$ (disciplined separately using incidence moments in the main calibration), we invert to obtain $\zeta=(\gamma\zeta)/\gamma$.
This identifies the composite slope $\gamma\zeta$; given $\gamma$ from the incidence moments, we invert to obtain $\zeta$ and then scale levels so that the model reproduces the observed fraction of workers living outside their province of birth. The resulting gravity estimates are summarized in Appendix Table [Table](#tab:mig_gravity). Across specifications, distance is a strong deterrent to mobility, with an estimated slope $-(\gamma\zeta)\approx -1.45$ (implying a composite distance elasticity $\gamma\zeta \approx 1.45$). These high spatial frictions imply low levels of internal migration, with only about 24 percent of wartime labor reallocation taking place across province borders.
The gravity regression identifies the *distance sensitivity* of mobility frictions (and origin/destination shifters), but not the overall level of migration costs. We therefore scale the levels of $\mu_{in}$ so that the model reproduces the observed fraction of workers living outside their province of birth.
The census provides a cross-section of residents by province of birth rather than annual origin--destination flows. We use these birthplace stocks only to discipline the persistent geographic component of mobility frictions, which is plausibly stable over time because it is driven by distance, transport connectivity, and long-run spatial barriers. In the model, workers reallocate from their province of *residence* in the pre-war baseline, not from birthplace.
### What is "imputed" and why it matters for the analysis
The objects $\{\tau_{ni,s}\}$, $\{\mu_{in}\}$, and $\{\mu_{sk}\}$ should be interpreted as *reduced-form wedges* that stand in for unobserved bilateral flows in the historical record:
- Domestic trade costs summarize how geography and transport connectivity shape the strength of goods-market linkages across provinces.
- Migration costs summarize how distance and persistent barriers shape the feasibility of spatial reallocation.
- Sector-switching costs summarize occupational rigidities that govern cross-sector labor reallocation.
These frictions are introduced because the required flows are unobserved, but they are not arbitrary: the key distance sensitivities are disciplined using auxiliary moments (the spatial decay of spillovers and the gravity relationship in birthplace stocks), and the sectoral switching structure is disciplined by matching observed medium-run employment reallocation. The resulting model-implied trade and labor flows are therefore best viewed as *latent equilibrium linkages consistent with the observed data and the maintained structure*, not as directly measured historical flows.
### Sensitivity and robustness
Because these objects summarize unobserved linkages, it is useful to assess how sensitive counterfactual conclusions are to their magnitudes. We therefore (i) report alternative gravity specifications and alternative birthplace matrices where available, (ii) consider alternative values of $\theta$ within confidence intervals around the auxiliary estimate, and (iii) report counterfactuals that vary the strength of spatial mobility and sectoral switching frictions.
## Derivations
### General Theory Results
This appendix provides the algebra underlying the results in Section 3. The first part re-derives the standard linearized equilibrium system and then direct/indirect decomposition emphasized by AAE (their Theorem 1) starting from a generic market-clearing formulation. The second part shows that a two-channel (nested) restriction on the Jacobian delivers a transparent first-round decomposition into the exposure indices used in the empirical specifications, plus an explicit remainder collecting higher-round feedback effects. Finally, we state the Le Chatelier result formally and provide the proof.
Wages are strictly positive so that log changes are well-defined. Hats denote log-differentials around the baseline equilibrium, e.g. $\widehat w \equiv d\log w$. The main text uses indices $(r,s)$ (province--sector) and $(p,d)$ (product--destination); below, generic indices $(i,j)$ are sometimes used for compactness. In the appendix tables, *Direct Shock* corresponds to Direct Exposure; *Within-Province Indirect Shock* corresponds to Within-Province Indirect Exposure; and *Spatial Indirect Shock* corresponds to Spatial Indirect Exposure.
Let markets be indexed by $i\in\{1,\dots,I\}$. Write equilibrium as market clearing:
$$
D_i(w,\tau)=0\qquad \forall i,
$$
where $w=(w_1,\dots,w_I)$ is the vector of market wages and $\tau$ collects exogenous primitives (trade costs, demand shifters, amenities, mobility frictions, etc.). Interpret $D_i(\cdot)$ as excess labor demand in market $i$ (or any model-specific excess-demand object); the only requirement is that the equilibrium can be written as [Equation](#eq:mc_app) and is differentiable around a baseline $(w^0,\tau^0)$.
Define log wages $u\equiv \log w$ (elementwise), and assume the Jacobian $\partial D/\partial u$ evaluated at the baseline is invertible. By the Implicit Function Theorem, the equilibrium wage vector is locally differentiable in primitives, so small $d\tau$ imply well-defined small changes in equilibrium wages. Totally differentiating [Equation](#eq:mc_app) at $(w^0,\tau^0)$ yields, for each $i$,
$$
\sum_{j=1}^I \left.\frac{\partial D_i}{\partial \log w_j}\right|_{0}\, d\log w_j
\;+\;
\left.\frac{\partial D_i}{\partial \tau}\right|_{0}\cdot d\tau
\;=\;0,
$$
where $\left.\frac{\partial D_i}{\partial \tau}\right|_{0}$ is a row vector and $\cdot$ denotes the inner product. Stacking across $i$ gives
$$
\underbrace{\left.\frac{\partial D}{\partial \log w}\right|_{0}}_{\equiv \bar\gamma^{0}}\,
\underbrace{d\log w}_{\equiv\,\widehat w}
\;=\;
\underbrace{-\left.\frac{\partial D}{\partial \tau}\right|_{0}\, d\tau}_{\equiv\,\widehat\eta}.
$$
Thus the linearized equilibrium mapping takes the compact form
$$
\bar\gamma^{0}\,\widehat w=\widehat\eta.
$$
The matrix $\bar\gamma^{0}$ summarizes local general-equilibrium linkages: its $(i,j)$ entry is the baseline response of market $i$'s excess demand to a change in $\log w_j$. The vector $\widehat\eta$ is the partial-equilibrium shift in the market-clearing equations induced directly by the change in primitives $d\tau$, holding wages fixed at baseline values; this is the "shock exposure" object in AAE's terminology.
When $\bar\gamma^{0}$ is invertible, the unique solution is
$$
\widehat w=(\bar\gamma^{0})^{-1}\widehat\eta.
$$
Let $\beta_{ij}$ denote the $(i,j)$ entry of $(\bar\gamma^{0})^{-1}$. Then
$$
\widehat w_i=\sum_{j=1}^I \beta_{ij}\,\widehat\eta_j
=\beta_{ii}\widehat\eta_i+\sum_{j\neq i}\beta_{ij}\widehat\eta_j.
$$
This is the direct/indirect decomposition: the first term is the direct response to market $i$'s own exposure, and the second term is the indirect response to exposures in other markets transmitted through equilibrium linkages. The economics of a particular model enters through the implied objects $\bar\gamma^{0}$ and $\widehat\eta$; the decomposition itself follows mechanically from linearization and invertibility.
A useful "rounds of propagation" interpretation comes from separating diagonal adjustment from off-diagonal linkages. Let $\Gamma^{\mathrm{diag}}\equiv \mathrm{diag}(\bar\gamma^{0}_{11},\dots,\bar\gamma^{0}_{II})$ and define the off-diagonal matrix $\Gamma^{\mathrm{off}}$ by $(\Gamma^{\mathrm{off}})_{ii}=0$ and $(\Gamma^{\mathrm{off}})_{ij}\equiv -\bar\gamma^{0}_{ij}$ for $i\neq j$. Then $\bar\gamma^{0}=\Gamma^{\mathrm{diag}}-\Gamma^{\mathrm{off}}$ and
$$
\bar\gamma^{0}=\Gamma^{\mathrm{diag}}\Big(I-\underbrace{(\Gamma^{\mathrm{diag}})^{-1}\Gamma^{\mathrm{off}}}_{\equiv\,\widetilde\Gamma}\Big).
$$
If $\rho(\widetilde\Gamma)<1$ (equivalently, if $\|\widetilde\Gamma\|<1$ for some induced matrix norm), then
$$
(\bar\gamma^{0})^{-1}=(I-\widetilde\Gamma)^{-1}(\Gamma^{\mathrm{diag}})^{-1}
=\sum_{m=0}^{\infty}\widetilde\Gamma^{\,m}(\Gamma^{\mathrm{diag}})^{-1}.
$$
The $m=0$ term is the own-market adjustment holding spillovers fixed; higher powers $\widetilde\Gamma^{\,m}$ trace $m$ successive rounds of propagation through the baseline network encoded in $\widetilde\Gamma$.
In the empirical setting, it is natural to index markets by province--sector cells $i\equiv(r,s)$ with $r\in\{1,\dots,R\}$ and $s\in\{1,\dots,K\}$. The two-channel restriction behind Appendix [Section](#sec:Additional-Derivations) imposes that off-diagonal linkages operate primarily through (i) cross-sector interaction within a province and (ii) cross-province interaction within a sector. Define linear operators (equivalently, $RK\times RK$ matrices) $L$ and $S$ by
$$
(Lx)_{r,s} \equiv \sum_{k\neq s} x_{r,k},
\qquad
(Sx)_{r,s} \equiv \sum_{r'\neq r}\omega_{rr'}\,x_{r',s},
$$
where $\omega_{rr'}\ge 0$ are predetermined spatial weights satisfying $\sum_{r'\neq r}\omega_{rr'}=1$ for each $r$. The restriction is that, at the baseline equilibrium, the Jacobian can be approximated by the two-channel form
$$
\bar\gamma^{0}= d\,I-a_L\,L-a_S\,S,
$$
for scalars $d>0$, $a_L$, and $a_S$. (One microfoundation is a nested labor-supply system across space and sectors, but [Equation](#eq:gamma_nested_app) can also be interpreted as a reduced-form restriction selecting the quantitatively dominant spillover channels.)
Factor out $d$:
$$
\bar\gamma^{0}=d\Big(I-\underbrace{\frac{a_L}{d}L+\frac{a_S}{d}S}_{\equiv\,A}\Big).
$$
A sufficient condition for Neumann convergence is $\rho(A)<1$. A transparent sufficient condition follows from an induced-norm bound. Under the definitions above, each row of $L$ has $(K-1)$ ones, so $\|L\|_{\infty}=K-1$, and each row of $S$ sums to one, so $\|S\|_{\infty}=1$. Hence
$$
\|A\|_{\infty}\le \frac{|a_L|}{d}\|L\|_{\infty}+\frac{|a_S|}{d}\|S\|_{\infty}
=\frac{|a_L|}{d}(K-1)+\frac{|a_S|}{d},
$$
so a simple sufficient condition for $\|A\|_{\infty}<1$ (and therefore $\rho(A)<1$) is
$$
\frac{|a_L|}{d}(K-1)+\frac{|a_S|}{d}<1
\quad\Longleftrightarrow\quad
d>(K-1)|a_L|+|a_S|.
$$
Under $\rho(A)<1$, we have
$$
(\bar\gamma^{0})^{-1}=\frac{1}{d}(I-A)^{-1}=\frac{1}{d}\sum_{m=0}^{\infty}A^{m}.
$$
Substituting into $\widehat w=(\bar\gamma^{0})^{-1}\widehat\eta$ gives the exact identity
$$
\widehat w
=\frac{1}{d}\widehat\eta+\frac{1}{d}A\widehat\eta+\frac{1}{d}\sum_{m=2}^{\infty}A^{m}\widehat\eta.
$$
Using $A=(a_L/d)L+(a_S/d)S$, the $m=1$ term becomes
$$
\frac{1}{d}A\widehat\eta=\frac{a_L}{d^{2}}L\widehat\eta+\frac{a_S}{d^{2}}S\widehat\eta.
$$
Define the higher-round remainder
$$
R\equiv \frac{1}{d}\sum_{m=2}^{\infty}A^{m}\widehat\eta.
$$
Then [Equation](#eq:w_nested_first_round_app) implies the decomposition
$$
\widehat w=\frac{1}{d}\widehat\eta+\frac{a_L}{d^{2}}L\widehat\eta+\frac{a_S}{d^{2}}S\widehat\eta+R,
$$
or element-by-element, for each province--sector cell $(r,s)$,
$$
\widehat w_{r,s}
=\frac{1}{d}\widehat\eta_{r,s}
+\frac{a_L}{d^{2}}\sum_{k\neq s}\widehat\eta_{r,k}
+\frac{a_S}{d^{2}}\sum_{r'\neq r}\omega_{rr'}\,\widehat\eta_{r',s}
+R_{r,s}.
$$
The first term is the direct response; the next two terms are the two first-round spillover channels (within-province across sectors and within-sector across provinces); and $R$ collects all feedback effects operating through two or more rounds of equilibrium propagation.
The leading omitted component is the $m=2$ term:
$$
\frac{1}{d}A^{2}\widehat\eta
=\frac{1}{d}\left(\frac{a_L}{d}L+\frac{a_S}{d}S\right)^{2}\widehat\eta
=\frac{a_L^{2}}{d^{3}}L^{2}\widehat\eta+\frac{a_La_S}{d^{3}}(LS+SL)\widehat\eta+\frac{a_S^{2}}{d^{3}}S^{2}\widehat\eta.
$$
These correspond to distinct two-step paths: $L^{2}\widehat\eta$ is "within-province spillovers of within-province spillovers" (two sectoral steps within a province), and $S^{2}\widehat\eta$ is "neighbors-of-neighbors" propagation within a sector. The mixed component $(LS+SL)\widehat\eta$ is the first point at which *cross-province, cross-sector* exposure appears. For example,
$$
(LS\,\widehat\eta)_{r,s}=\sum_{r'\neq r}\omega_{rr'}\sum_{k\neq s}\widehat\eta_{r',k},
$$
which loads on other sectors $k\neq s$ in neighboring provinces $r'$. Given the definition of $S$ above (sector-invariant weights $\omega_{rr'}$), $L$ and $S$ commute, so $LS=SL$ and the mixed term simplifies to $2(a_La_S/d^{3})\,LS\,\widehat\eta$. Higher powers $A^{m}$ generate longer sequences of alternating within-province and across-province steps.
This makes clear why a reduced form that includes only the two first-round indices is a disciplined low-dimensional approximation: additional channels---including cross-province cross-sector terms like $LS\,\widehat\eta$, or higher-order spatial terms like $S^{2}\widehat\eta$---enter through $R$.
In the empirical analysis, the market-level excess-demand shift is proxied by the shift--share object $\widehat\eta_{r,s}\equiv \pi^{0}_{r,s}\widehat z_{s}$ (equation [Equation](#eq:eta_proxy) in the main text). Substituting into the first-round terms yields
$$
\frac{1}{d}\widehat\eta_{r,s}=\frac{1}{d}\pi^{0}_{r,s}\widehat z_{s},
\qquad
\frac{a_L}{d^{2}}(L\widehat\eta)_{r,s}
=\frac{a_L}{d^{2}}\sum_{k\neq s}\pi^{0}_{r,k}\widehat z_{k}
\equiv \frac{a_L}{d^{2}}\,\widehat\eta^{\,\mathrm{local}}_{r,s},
$$
and
$$
\frac{a_S}{d^{2}}(S\widehat\eta)_{r,s}
=\frac{a_S}{d^{2}}\sum_{r'\neq r}\omega_{rr'}\pi^{0}_{r',s}\widehat z_{s}
\equiv \frac{a_S}{d^{2}}\,\widehat\eta^{\,\mathrm{spatial}}_{r,s}.
$$
Therefore, under the two-channel Jacobian structure, the two indirect-exposure regressors in [Equation](#eq:eta_local)--[Equation](#eq:eta_spatial) coincide exactly with the model-implied *first-round* propagation terms. The corresponding regression coefficients equal $(a_L/d^{2},a_S/d^{2})$ only under additional conditions that render $R$ negligible or orthogonal to the included indices. More generally, the empirical specifications in Section 3 should be interpreted as low-dimensional projections of the full indirect component $\sum_{j\neq i}\beta_{ij}\widehat\eta_{j}$ onto the two first-round channels that can be measured cleanly in the data.
### A matrix Le Chatelier result for segmentation
**Corollary 1** (Matrix Le Chatelier: lower segmentation attenuates wage responses). *Let $\chi$ index labor-market integration (higher $\chi$ corresponds to lower segmentation). Suppose the AAE linearization can be written as
$$
\bar\gamma^{0}(\chi)\,\widehat{\mathbf w}(\chi)=\widehat{\boldsymbol\eta}^{\mathrm{orig}}.
$$
It is convenient to work with a sign-normalized ("effective") Jacobian
$$
\tilde\gamma^{0}(\chi)\equiv -\bar\gamma^{0}(\chi),
$$
and the corresponding sign-normalized shock $\widehat{\boldsymbol\eta}\equiv -\widehat{\boldsymbol\eta}^{\mathrm{orig}}$, so that the system becomes
$$
\tilde\gamma^{0}(\chi)\,\widehat{\mathbf w}(\chi)=\widehat{\boldsymbol\eta}.
$$
*
*Assume $\tilde\gamma^{0}(\chi)$ admits the decomposition
$$
\tilde\gamma^{0}(\chi)=\Gamma^{D,0}+\Gamma^{S,0}(\chi),
$$
with:*
1. *$\Gamma^{D,0}$ is symmetric positive definite and does not depend on $\chi$;*
2. *for each $\chi$, $\Gamma^{S,0}(\chi)$ is symmetric positive semidefinite; and*
3. *$\Gamma^{S,0}(\chi)$ is weakly increasing in $\chi$ in the Loewner order:
$$
\chi_2\ge \chi_1 \quad\Longrightarrow\quad
\Gamma^{S,0}(\chi_2)-\Gamma^{S,0}(\chi_1)\succeq 0.
$$
*
*Then $\tilde\gamma^{0}(\chi)\succ 0$ for all $\chi$, and for any $\chi_2\ge \chi_1$,
$$
\bigl(\tilde\gamma^{0}(\chi_2)\bigr)^{-1}\preceq \bigl(\tilde\gamma^{0}(\chi_1)\bigr)^{-1}.
$$
Equivalently, the pass-through operator from shocks to wages,
$$
\widehat{\mathbf w}(\chi)=\bigl(\tilde\gamma^{0}(\chi)\bigr)^{-1}\widehat{\boldsymbol\eta},
$$
is weakly smaller in every quadratic direction: for every $x\in\mathbb R^n$,
$$
x'\bigl(\tilde\gamma^{0}(\chi_2)\bigr)^{-1}x \le x'\bigl(\tilde\gamma^{0}(\chi_1)\bigr)^{-1}x.
$$
In particular, along the shock direction,
$$
\widehat{\boldsymbol\eta}'\widehat{\mathbf w}(\chi_2)
=
\widehat{\boldsymbol\eta}'\bigl(\tilde\gamma^{0}(\chi_2)\bigr)^{-1}\widehat{\boldsymbol\eta}
\le
\widehat{\boldsymbol\eta}'\bigl(\tilde\gamma^{0}(\chi_1)\bigr)^{-1}\widehat{\boldsymbol\eta}
=
\widehat{\boldsymbol\eta}'\widehat{\mathbf w}(\chi_1).
$$
Thus greater integration (a larger $\Gamma^{S,0}(\chi)$) attenuates equilibrium wage responses, shifting adjustment toward the margins summarized by $\Gamma^{S,0}(\chi)$ (e.g. reallocation/quantity adjustment).[^19]*
**Remark (what the Loewner comparison does and does not imply).** The conclusion
$$
(\tilde\gamma^{0}(\chi_2))^{-1}\preceq(\tilde\gamma^{0}(\chi_1))^{-1}
$$
is *exactly* a statement about monotonicity of quadratic forms $x'(\tilde\gamma^{0}(\chi))^{-1}x$ (equivalently Rayleigh quotients). It therefore delivers monotonicity for any quadratic-loss measure $\|x\|_{(\tilde\gamma^{0}(\chi))^{-1}}^2\equiv x'(\tilde\gamma^{0}(\chi))^{-1}x$. It does *not* generally imply component-by-component monotonicity of each entry of $\widehat{\mathbf w}(\chi)$ without additional structure.
A convenient sufficient condition for *entrywise* monotonicity under nonnegative shocks is: (a) each $\tilde\gamma^{0}(\chi)$ is a symmetric $M$-matrix (equivalently a Stieltjes matrix), so $(\tilde\gamma^{0}(\chi))^{-1}\ge 0$ entrywise, and (b) the increment $\Gamma^{S,0}(\chi_2)-\Gamma^{S,0}(\chi_1)\ge 0$ entrywise. Then
$$
(\tilde\gamma^{0}(\chi_1))^{-1}-(\tilde\gamma^{0}(\chi_2))^{-1}
=
(\tilde\gamma^{0}(\chi_1))^{-1}\bigl(\Gamma^{S,0}(\chi_2)-\Gamma^{S,0}(\chi_1)\bigr)(\tilde\gamma^{0}(\chi_2))^{-1}
\ge 0
$$
entrywise, which implies $\widehat{\mathbf w}(\chi_2)\le \widehat{\mathbf w}(\chi_1)$ entrywise whenever $\widehat{\boldsymbol\eta}\ge 0$.
Finally, notice that the result here is qualitative rather than quantitative.[^20]
*Proof.* Fix $\chi_2\ge \chi_1$ and define
$$
A \equiv \tilde\gamma^{0}(\chi_1)=\Gamma^{D,0}+\Gamma^{S,0}(\chi_1),\qquad
B \equiv \tilde\gamma^{0}(\chi_2)=\Gamma^{D,0}+\Gamma^{S,0}(\chi_2).
$$
By (i)--(ii), $A\succ 0$ and $B\succ 0$ are symmetric positive definite. Moreover,
$$
B-A=\Gamma^{S,0}(\chi_2)-\Gamma^{S,0}(\chi_1)\succeq 0
\quad\Longrightarrow\quad
A\preceq B.
$$
Matrix inversion is order-reversing on the SPD cone. For completeness, let $\Delta\equiv B-A\succeq 0$ and $M\equiv A^{-1/2}\Delta A^{-1/2}\succeq 0$. Then
$$
B=A+\Delta=A^{1/2}(I+M)A^{1/2}
\quad\Rightarrow\quad
B^{-1}=A^{-1/2}(I+M)^{-1}A^{-1/2}.
$$
Since $M\succeq 0$, all eigenvalues of $(I+M)^{-1}$ lie in $(0,1]$, hence $(I+M)^{-1}\preceq I$. Congruence with $A^{-1/2}$ preserves Loewner order, giving $B^{-1}\preceq A^{-1}$, i.e.
$$
\bigl(\tilde\gamma^{0}(\chi_2)\bigr)^{-1} \preceq \bigl(\tilde\gamma^{0}(\chi_1)\bigr)^{-1}.
$$
The quadratic-form statements follow immediately. ◻
### A Tractable Model of Imperfect Sectoral and Spatial Mobility
I begin by introducing a quantitative framework that can account for the direct and indirect effect of trade shocks across local labor markets. To do so, I extend an otherwise standard multi-sector economic geography model ([Allen and Arkolakis 2014](#ref-RePEc:oup:qjecon:v:129:y:2014:i:3:p:1085-1140); [Redding 2012](#ref-RePEc:nbr:nberwo:18008); [Caliendo and Parro 2015](#ref-RePEc:oup:restud:v:82:y:2015:i:1:p:1-44); [Caliendo et al. 2019b](#ref-https://doi.org/10.3982/ECTA13758)) by embedding a tractable description of imperfect labor mobility across space and sectors, as well as incorporating domestic and foreign trade. The section sets up the model and derives a tractable and decomposable expression for gains from trade in terms of spatial and sectoral labor flows.
Let there be a number of locations within a country $n,i,j,h\in\mathbb{D}=\left\{ 1,\ldots,N^{D}\right\}$. Let there also be a number of foreign locations $k,l,m\in\mathbb{F}=\left\{ 1,\ldots,N^{F}\right\}$. Domestic locations are heterogeneous in their exogenously fixed housing supply, $H_{i}$, and their geographical location relative to one another. The only factor of production is labor. In each location production occurs across multiple sectors $r,s,t\in\mathbb{S}=\left\{ 1,\ldots,S\right\}$. There are only two periods and the initial distribution of workers across locations $[\ell_{n,r}]_{\forall(n,r)\in\mathbb{D}\times\mathbb{S}}$, is given, while the distribution of workers in the second period, $[\ell_{n,r}']_{\forall(n,r)\in\mathbb{D}\times\mathbb{S}}$, is endogenously determined.
Workers residing in location $n$ and providing labor to sector $s$ consume a Cobb-Douglas aggregate of housing and a consumption bundle: $U_{n}=\left(\frac{C_{n}}{1-\delta}\right)^{1-\delta}\left(\frac{H_{n}}{\delta}\right)^{\delta}$ where $\delta$ is the expenditure share on housing. $C_{n}$ is a Cobb-Douglas aggregate of sector-specific CES aggregates of origin-differentiated goods of both domestic and foreign origin. The indirect utility and the optimal price index of this problem is given by,
$$
u_{n,r}=\frac{\rho_{n}e_{n,r}}{p_{n}^{(1-\delta)}r_{n}^{\delta}},\quad p_{n}=\prod_{r=1}^{S}\left(p_{n,r}\right)^{\alpha_{r}}\quad p_{n,r}=\left[\sum_{i=1}^{N^{D}}\left(p_{ni,r}\right)^{1-\sigma_{r}}+\sum_{l=1}^{N^{F}}\left(p_{nl,r}\right)^{1-\sigma_{r}}\right]^{\frac{1}{1-\sigma_{r}}}
$$
where, the expenditure shares add up to 1, i.e. $\sum_{r=1}^{S}\alpha_{r}=1$ and where $\sigma_{r}>1$ is the elasticity of substitution between varieties within a sector and where $v_{n,r}$ represents the disposable income of a representative worker residing in location $n$ and providing labor to sector $s$.
Households in foreign locations $l$ spend a fixed endowment $e_{l}$ across domestic locations. They consume a CES aggregate of origin-differentiated goods across domestic locations. The indirect utility and the optimal price index that households derive from consuming across domestic locations is given by,
$$
u_{l}=\frac{e_{l}}{\prod_{r=1}^{S}\left(p_{n}^{r}\right)^{\alpha_{l,r}}},\quad\sum_{r=1}^{S}\alpha_{l,r}=1\quad p_{l,r}=\left(\sum_{i=1}^{N^{D}}\left(p_{li,r}\right)^{1-\sigma_{r}}\right)^{\frac{1}{1-\sigma_{r}}}
$$
where $\sigma_{r}>1$ is again the elasticity of substitution between varieties within a sector and where $e_{l}$ represents the endowment of workers in location $l$.
Applying Roy's identity, demand in location $n$ for sector $r$ specific varieties produced in domestic locations $i$ and foreign locations $l$ are given by,
$$
q_{ni,r}\left(\boldsymbol{p}_{n,r}\right)=\frac{\left(p_{ni,r}\right)^{-\sigma_{r}}}{\sum_{j=1}^{N^{D}}\frac{1}{\bar{d}}\left(p_{nj,r}\right)^{1-\sigma_{r}}+\sum_{k=1}^{N^{F}}\left(p_{nk,r}\right)^{1-\sigma_{r}}}\left(1-\delta\right)\alpha_{r}\sum_{r=1}^{S}e_{n,r}\ell_{n,r}
$$
$$
q_{nl,r}\left(\boldsymbol{p}_{n,r}\right)=\frac{\left(p_{nl,r}\right)^{-\sigma_{r}}}{\sum_{j=1}^{N^{D}}\frac{1}{\bar{d}}\left(p_{nj,r}\right)^{1-\sigma_{r}}+\sum_{k=1}^{N^{F}}\left(p_{nk,r}\right)^{1-\sigma_{r}}}\left(1-\delta\right)\alpha_{r}\sum_{r=1}^{S}e_{n,r}\ell_{n,r}
$$
where $\boldsymbol{p}_{n}^{r}$ refers to the price vector for sector-specific $r$ goods available in location $n$and produced in all other locations.
Applying Roy's identity, demand in location $l$ for the good produced in location $i$ is given by,
$$
q_{li,r}\left(\boldsymbol{p}_{l,r}\right)=\frac{p_{li,r}^{-\sigma_{r}}}{\sum_{j=1}^{N^{D}}p_{lj,r}^{1-\sigma_{r}}}\alpha_{l,r}e_{l}
$$
where $\boldsymbol{p}_{l}$ refers to the price vector for sector-specific $r$ goods available in location $l$ of the goods produced in all other locations. We can then define expenditure shares of domestic locations for domestic and foreign varieties, which are given by,
$$
\begin{aligned}
s_{ni,r} & =\alpha_{r}\left(1-\delta\right)\frac{p_{ni,r}^{1-\sigma_{r}}}{\sum_{i=1}^{N^{D}}\left(p_{ni,r}\right)^{1-\sigma_{r}}+\sum_{l=1}^{N^{F}}\left(p_{nl,r}\right)^{1-\sigma_{r}}}
\end{aligned}
$$
$$
s_{nl,r}=\alpha_{r}\left(1-\delta\right)\frac{p_{nl,r}^{1-\sigma_{r}}}{\sum_{i=1}^{N^{D}}\left(p_{ni,r}\right)^{1-\sigma_{r}}+\sum_{l=1}^{N^{F}}\left(p_{nl,r}\right)^{1-\sigma_{r}}}
$$
And expenditure shares by foreign location on domestic varieties are given by,
$$
\begin{aligned}
s_{li,r} & =\alpha_{l,r}\frac{\left(p_{li,r}\right)^{1-\sigma_{r}}}{\sum_{j=1}^{N^{D}}\left(p_{lj,r}\right)^{1-\sigma_{r}}}
\end{aligned}
$$
Between the first and second period, workers can reallocate between domestic local labor markets to respond to changes in factor returns. Workers can both change their location and their sector. To obtain a parsimonious but flexible description of the problem, I specify reallocation in terms of a sequential stochastic choice. The initial allocation of workers across locations and sectors is given, $[\ell_{n,s}]_{\forall(n,s)\in\mathbb{D}\times\mathbb{S}}$, but workers can choose their location and sector for the second period. They first make a geographical relocation choice from location $n$ to location $i$ and subsequently a sectoral relocation choice moving from an initial sector $r$ to another sector $s$. Both the geographical reallocation choice and the sectoral reallocation choice is subject to variable geographical and sectoral migration cost, $\mu_{ni}$ and $\mu_{rs}$ respectively. The properties of the Frechet distribution and the sequencing of the reallocation choice imply that labor flows between location $n$ and location $i$ and between sector $r$ and $s$ take on a multiplicatively separable form,
$$
\sigma_{ni,rs}'=\sigma_{ni|r}'\sigma_{rs|i}'
$$
where $\sigma_{ni|r}$ is the share of workers that originate from sector $r$ in location $n$ and reallocate to location $i$, and where $\sigma_{rs|i}$ is the share of workers that conditional on having chosen location $i$ and choose to relocate from sector $r$ to sector $s.$ I present the solution to the problem by solving backwards. First, conditional on having chosen location $i$ the probability of relocating from sector $r$ to sector $s$ can be written as,
$$
\sigma_{rs|i}'=\frac{(w_{is|r}')^{\nu}}{\left(\Pi_{i,r}'\right)^{\nu}}
$$
where $\nu$ is the dispersion parameter of the sector-specific preference shock, $w_{is|r}'\equiv w_{is}'/\mu_{rs}$ represents the wage adjusted by the mobility cost, and $\Pi_{i,r}'\equiv\left(\sum_{t}(w_{it|r}')^{\nu}\right)^{1/\nu}$ represents the option value of a worker conditional on having chosen location $i$ and being initially attached to sector $r$. Prior to making the sectoral relocation choice, the worker makes a geographical choice. In a first step the worker therefore compares the different option values of the sectoral reallocation choice across geographical locations. The geographical reallocation share takes on the following closed form form expression,
$$
\sigma_{ni|r}'=\frac{\left(v_{ni|r}'\right)^{\gamma}}{\left(\Omega_{n,r}'\right)^{\gamma}}
$$
where $\gamma$ is the dispersion parameter of the location-specific preference shock, $v_{ni|r}'$ is the expected utility of location from $n$ to $i$ conditional on initial attachment to sector $r$[^21] and where finally $\left(\Omega_{n,r}'\right)^{\gamma}\equiv\sum_{j}\left(v_{nj|r}'\right)^{\gamma}$ represents the option value of the geographical choice.
Production is as before given by a constant return to scale production technology,
$$
q_{i,r}=z_{i,r}\ell_{i,r}
$$
where $z_{i,r}$ denotes a productivity shifter for sector $r$ in location $i$ and $\ell_{i,r}$ denotes the number of workers employed there. Goods can be traded between locations within and between countries, but transport is subject to iceberg variable trade costs, implying that delivering a unit of any good from location $n$ to location $i$ requires shipping $\tau_{ni}\geq1$ units of the good. Therefore, the price that a representative worker faces in location $i$ for any good from location $n$is given by,
$$
\begin{aligned}
p_{ni,r} & =\tau_{ni}mc_{i,r}=\frac{\tau_{ni}w_{i,r}}{z_{i,r}}
\end{aligned}
$$
where $z_{i}$ captures as before the productivity of a given location and iceberg variable trade costs satisfy $\tau_{ni}>1$ and $\tau_{nn}=1$, that is we normalize trade costs within a location to 1, and $mc_{i,r}=w_{i,r}/z_{i,r}$ is the marginal cost of production in location $i$ and sector $r$.
The equilibrium of the model can be formulated in terms of four market clearing conditions. First, goods market clearing implies that total factor income equals total income derived both from foreign and domestic sales,
$$
w_{i,r}\ell_{i,r}=\sum_{n=1}^{N^{D}}s_{ni,r}\left(\sum_{r=1}^{S}e_{n,r}\ell_{n,r}\right)+\sum_{l=1}^{N^{F}}s_{li,r}e_{l}
$$
Second, balanced trade implies that total disposable income in a location equals total imports of that locations both foreign and domestic,
$$
\left(\sum_{r=1}^{S}e_{n,r}\ell_{n,r}\right)=\sum_{r=1}^{S}\left(\sum_{i=1}^{N}s_{ni,r}\left(\sum_{r=1}^{S}e_{n,r}\ell_{n,r}\right)+\sum_{l=1}^{N^{F}}s_{nl,r}\left(\sum_{r=1}^{S}e_{n,r}\ell_{n,r}\right)\right)
$$
Third, total expenditure on housing services has to equal the total returns to housing,
$$
H_{n}r_{n}=\delta\left(\sum_{r=1}^{S}e_{n,r}\ell_{n,r}\right)
$$
Fourth, and finally, the above conditions hold both in the first and second period, but while labor allocations are given in the first period, in the second period there is a reallocation choice. Spatial labor market clearing implies,
$$
\ell_{i}'=\sum_{n}\sum_{r}\sigma_{ni|r}\ell_{n,r}
$$
Sector-province labor market clearing is given by,
**
$$
\ell_{i,s}^{'}=\sum_{r=1}^{S}\sum_{n=1}^{N}\sigma_{ni,rs}\ell_{n,r}
$$
**
which implies that the total number of workers in a location in the second period is equal to the total number of workers that have reallocated to that location from the previous period.
### Aggregate welfare derivation in the quantitative model
To construct a measure of aggregate welfare that takes reallocation into account, I assume that rather than the initial allocation being fixed, workers receive a location-specific extreme value distributed preference shock that gives rise to and matches the observed allocation of workers across space as in the canonical quantitative spatial equilibrium model in Redding ([2012](#ref-RePEc:nbr:nberwo:18008)). The welfare expression that corresponds to the first step, and expresses the value of being able to choose any of the domestic location by summing up over the migration value of each one location, that is,
$$
\mathcal{W}\equiv E\left(\Omega_{n,r}\right)=\delta\left[\sum_{n=1}^{N^{D}}\sum_{r=1}^{S}\left(\tilde{\rho}_{n,r}\Omega_{n,r}\right)^{\epsilon}\right]^{1/\epsilon}
$$
where $\delta=\Gamma\left(\frac{\epsilon}{\epsilon-1}\right)$ and $\Gamma(\cdot)$ is the gamma function and we impose $\epsilon>1$ to obtain a finite value for the expected utility. Additionally, $\tilde{\rho}$ corresponds to an amenity shifter that is chosen to exactly fit the distribution of the population across space. Following Redding ([2012](#ref-RePEc:nbr:nberwo:18008)), I use this measure of expected utility as a proxy for aggregate welfare. Conditional on the initial allocation, workers face a reallocation choice subject to switching costs and a new set of independently drawn extreme value distributed preferences shocks as stated above and as before $\Omega_{n}'$ corresponds to the expected utility of that choice,
$$
\Omega_{n,r}'=\tilde{\delta}\left[\sum_{j=1}^{N^{D}}\left(v_{nj|r}'\right)^{\gamma}\right]^{1/\gamma}
$$
where again $\delta=\Gamma\left(\frac{\gamma}{\gamma-1}\right)$ and $\Gamma(\cdot)$ is the gamma function and we impose $\gamma>1$ to obtain a finite value for the expected utility. Totally differentiating the welfare expression, we obtain,
$$
\begin{aligned}
\frac{d\mathcal{W}'}{\mathcal{W}'} & =\sum_{n=1}^{N^{D}}\sum_{r=1}^{S}\frac{d\Omega_{n,r}'}{\Omega_{n,r}'}\times\frac{\left(\tilde{\rho}_{n,r}\Omega_{n,r}\right)^{\epsilon}}{\sum_{n=1}^{N^{D}}\sum_{r=1}^{S}\left(\tilde{\rho}_{n,r}\Omega_{n,r}\right)^{\epsilon}}\\
& =\sum_{n=1}^{N^{D}}\sum_{r=1}^{S}\frac{d\Omega_{n,r}'}{\Omega_{n,r}'}\times\pi_{i,r}
\end{aligned}
$$
where $\pi_{i,r}=\frac{\ell_{i,r}}{\sum_{i}\sum_{r}\ell_{i,r}}$ is the population share observed in the data in the baseline period. Integrating, we obtain,
$$
\begin{aligned}\int_{\mathcal{W}^{0}}^{\mathcal{W}^{1}}\frac{\mathrm{d}\mathcal{W}'}{\mathcal{W}'} & =\sum_{n=1}^{N^{D}}\sum_{r=1}^{S}\pi_{i,r}\times\int_{\Omega_{n,r}^{0}}^{\Omega_{n,r}^{1}}\frac{d\Omega_{n,r}'}{\Omega_{n,r}'}\\
\ln\left(\frac{\mathcal{W}^{1}}{\mathcal{W}^{0}}\right) & =\sum_{n=1}^{N^{D}}\sum_{r=1}^{S}\pi_{n,r}\ln\left(\frac{\Omega_{n,r}^{1}}{\Omega_{n,r}^{0}}\right)\\
\left(\frac{\mathcal{W}^{1}}{\mathcal{W}^{0}}\right) & =\prod_{n=1}^{N^{D}}\prod_{r=1}^{S}\left(\frac{\Omega_{n,r}^{1}}{\Omega_{n,r}^{0}}\right)^{\pi_{n,r}}
\end{aligned}
$$
where $\pi_{i,r}=\frac{\ell_{i,r}}{\sum_{i}\sum_{r}\ell_{i,r}}$ is the population share observed in the data in the baseline period. From ([Equation](#eq:spatial_relocation)) we can construct an expression for changes in the option value $\Omega_{n,r}$,
$$
\hat{\Omega}_{n,r}=\hat{v}_{nn|r}\left(\hat{\sigma}_{nn|r}\right)^{-\frac{1}{\gamma}}
$$
where hatted variables, $\hat{x}=x'/x$, denote changes and where the option value only depends on the change in the expected utility from remaining and the share of workers who choose to remain in their origin province. From the definition of the exepcted utility, we can obtain,
$$
\hat{v}_{nn|r}=\hat{\delta}_{n}\hat{\Pi}_{n|r}
$$
which only depends on the change in the expected value of the sectoral relocation choice. Again, from the definition of the sectoral relocation share ([Equation](#eq:sec_relocation)) we can obtain,
$$
\hat{\Pi}_{n,r}=\hat{w}_{nr|r}\left(\hat{\sigma}_{rr|i}\right)^{-\frac{1}{\nu}}
$$
combining with the result above we obtain,
$$
\hat{\Omega}_{n,r}=\hat{u}_{nr|r}\left(\hat{\sigma}_{rr|i}\right)^{-\frac{1}{\nu}}\left(\hat{\sigma}_{nn|r}\right)^{-\frac{1}{\gamma}}
$$
and substituting back in,
$$
\left(\frac{\mathcal{W}^{1}}{\mathcal{W}^{0}}\right)=\prod_{n=1}^{N^{D}}\prod_{r=1}^{S}\left(\underbrace{\left(\frac{\sigma_{nn|r}^{1}}{\sigma_{nn|r}^{0}}\right)^{-\frac{1}{\gamma}}}_{\text{Spatial Flows}}\underbrace{\left(\frac{\sigma_{rr|n}^{1}}{\sigma_{rr|n}^{0}}\right)^{-\frac{1}{\nu}}}_{\text{Sectoral Flows}}\frac{u_{nr|r}^{1}}{u_{nr|r}^{0}}\right)^{\pi_{n,r}}
$$
where $\sigma_{nn|r}^{1}$ represents the share of workers initially located in province $n$ and working sector $r$ and deciding to remain in that province, while $\sigma_{rr|n}^{1}$ represents the share of workers who in the second period will be located in province $n$, were initially attached to sector $r$and decide to remain in sector $r$. Intuitively, if more workers decide to either change their sector or their location, then this is informative about the option value of a spatial or sectoral change to have increased, relative to the remain option. In other words, the remain share (to the power of the negative inverse of the labor supply elasticity) is proportional to changes in the option-value and therefore a sufficient statistic for welfare changes that arise due to the ability of the worker being able to reallocate. This approach is intimately related to the argument that conditional choice probabilities can be used to infer continuation values in dynamic discrete choice problems ([Hotz and Miller 1993](#ref-10.2307/2298122)). Even though, it is here stated in the context of two period model, the approach is much more general and a similar expression for welfare can be derived for multi-period or infinite horizon models. The final term represents cross-Sectional improvements in the indirect utility of workers across locations. This term can be constructed using the tools by Arkolakis et al. ([2012](#ref-RePEc:aea:aecrev:v:102:y:2012:i:1:p:94-130)) and Ossa ([2015](#ref-RePEc:eee:inecon:v:97:y:2015:i:2:p:266-277)), which gives us,
$$
\hat{u}_{n,r}=\frac{\left(\hat{w}_{n,r}\right)^{\delta}}{\left(\hat{r}_{n}\right)^{\delta}}\frac{\left(\hat{w}_{n,r}\right)^{(1-\delta)}}{\prod_{r=1}^{S}\left(\hat{w}_{n,r}\right)^{(1-\delta)\alpha_{r}}}\prod_{r=1}^{S}\left(\hat{s}_{nn,r}\right)^{\frac{(\delta-1)\alpha_{r}}{\sigma_{r}-1}}
$$
substituting into above formula gives us the expression in the main text,
$$
\left(\frac{\mathcal{W}^{1}}{\mathcal{W}^{0}}\right)=\prod_{n=1}^{N^{D}}\prod_{r=1}^{S}\left(\underbrace{\left(\frac{\sigma_{nn|r}^{1}}{\sigma_{nn|r}^{0}}\right)^{-\frac{1}{\gamma}}}_{\text{Spatial Flows}}\underbrace{\left(\frac{\sigma_{rr|n}^{1}}{\sigma_{rr|n}^{0}}\right)^{-\frac{1}{\nu}}}_{\text{Sectoral Flows}}\underbrace{\left(\frac{r_{n}^{1}}{r_{n}^{0}}\right)^{-\delta}}_{\text{Housing Cost}}\underbrace{\prod_{t=1}^{S}\left(\frac{s_{nn,t}^{1}}{s_{nn,t}^{0}}\right)^{-\frac{\left(1-\delta\right)\alpha_{t}}{\sigma_{t}-1}}}_{\text{ACR Gains}}\right)^{\pi_{n,r}}
$$
### Trade Imbalances
To reflect the change in trade deficits in the analysis, I incorporate exogenous trade imbalances as in Dekle, Eaton, and Kortum (2007) and Caliendo and Parro (2015). However, instead of an additive formulation, I instead model trade balances as a multiplicative scalar that adjusts the disposable income available to the representative agent. Furthermore, I distinguish between domestic and external trade, and while external trade might be unbalanced, domestic trade is assumed to be balanced. Consider the domestic and external trade balance condition separately. As before, trade is balanced domestically, implying that domestic income is equal to domestic expenditure,
$$
d_{1}y_{n}=\sum_{r=1}^{S}\left(\sum_{i=1}^{N}s_{ni,r}y_{n}\right)
$$
where $d_{1}$ is defined as the fraction of income that is being derived from domestic sales and $y_{n}$ denotes the disposable income, such that,
$$
y_{n}=\sum_{r=1}^{S}e_{n,r}\ell_{n,r}
$$
Externally, trade is possibly unbalanced, such that expenditures on foreign goods might be below or above income derived from foreign goods, i.e.
$$
\left(1-d_{1}\right)y_{n}=d_{2}\times\sum_{r=1}^{S}\sum_{l=1}^{N^{F}}s_{nl,r}y_{n}
$$
where the left hand side denotes income derived from foreign sales and the right hand side denotes expenditures on foreign goods. As before, $d_{1}$, is the fraction of income that is being derived domestically. On the right hand side, $d_{2}$ is the proportion of foreign income that is being expended on foreign goods. where $d_{2}$ is defined as,
$$
d_{2}=\frac{\sum_{l=1}^{N^{F}}\sum_{r=1}^{S}X_{nl.r}}{\sum_{l=1}^{N^{F}}\sum_{r=1}^{S}X_{ln,r}}
$$
To derive the total price index, combine,
$$
y_{n}=\sum_{r=1}^{S}\sum_{i=1}^{N}s_{ni,r}y_{n}+d_{2}\times\sum_{r=1}^{S}\sum_{l=1}^{N^{F}}s_{nl,r}y_{n}
$$
Dividing by income and noticing that $s_{ni,r}=\left(p_{ni,r}\right)^{1-\sigma_{r}}p_{n,r}^{\sigma_{r}-1}$, we obtain,
$$
p_{n,r}^{1-\sigma}=\sum_{i=1}^{N^{D}}p_{ni,r}^{1-\sigma}+d_{2}\sum_{l=1}^{N^{F}}p_{nl,r}^{1-\sigma}
$$
which allows us to express the price index in terms of the weighted domestic and external prices, i.e.
$$
p_{n,r}=\left(\sum_{i=1}^{N^{D}}p_{ni,r}^{1-\sigma}+d_{2}\sum_{l=1}^{N^{F}}p_{nl,r}^{1-\sigma}\right)^{\frac{1}{1-\sigma}}
$$
This implies that the indirect utility and the optimal price index of this problem is given by,
$$
u_{n,r}=\frac{\rho_{n}e_{n,r}}{p_{n}^{(1-\delta)}r_{n}^{\delta}},\quad p_{n}=\prod_{r=1}^{S}\left(p_{n,r}\right)^{\alpha_{r}}\quad p_{n,r}=\left[\sum_{i=1}^{N^{D}}\left(p_{ni,r}\right)^{1-\sigma_{r}}+d_{2}\sum_{l=1}^{N^{F}}\left(p_{nl,r}\right)^{1-\sigma_{r}}\right]^{\frac{1}{1-\sigma_{r}}}
$$
Combining and factoring out the trade imbalance term we obtain,
$$
u_{n,r}=d_{2}^{-\sum_{r}\frac{(1-\delta)\alpha_{r}}{1-\sigma_{r}}}\frac{\rho_{n}e_{n,r}}{r_{n}^{\delta}\prod_{r=1}^{S}\left(\left(\sum_{i=1}^{N^{D}}\frac{1}{d_{2}}p_{ni}^{1-\sigma_{r}}+\sum_{l=1}^{N^{F}}p_{nl}^{1-\sigma_{r}}\right)^{\frac{(1-\delta)\alpha_{r}}{1-\sigma_{r}}}\right)}
$$
Following the same derivations as before,
$$
\left(\frac{\mathcal{W}^{1}}{\mathcal{W}^{0}}\right)=\underbrace{\left(\frac{d_{2}^{1}}{d_{2}^{0}}\right)^{-\sum_{r}\frac{(1-\delta)\alpha_{r}}{1-\sigma_{r}}}}_{\text{Deficit Adjustment}}\prod_{n=1}^{N^{D}}\prod_{r=1}^{S}\left(\underbrace{\left(\frac{\sigma_{nn|r}^{1}}{\sigma_{nn|r}^{0}}\right)^{-\frac{1}{\gamma}}}_{\text{Spatial Flows}}\underbrace{\left(\frac{\sigma_{rr|n}^{1}}{\sigma_{rr|n}^{0}}\right)^{-\frac{1}{\nu}}}_{\text{Sectoral Flows}}\underbrace{\left(\frac{\tilde{r}_{n}^{1}}{\tilde{r}_{n}^{0}}\right)^{-\delta}}_{\text{Housing Cost}}\underbrace{\prod_{t=1}^{S}\left(\frac{\tilde{s}_{nn,t}^{1}}{\tilde{s}_{nn,t}^{0}}\right)^{-\frac{\left(1-\delta\right)\alpha_{t}}{\sigma_{t}-1}}}_{\text{ACR Gains}}\right)^{\pi_{n,r}}
$$
## Online Appendix
In this online appendix I provide additional information on data sources as well as additional figures, tables and derivations. In Section I I provide additional information regarding the data sources being used. In Section J I provide additional derivations, including detailed derivations for the stylized model used in the introduction, as well as derivations for the welfare formula and the extension allowing for trade imbalances. In Section K I include additional figures omitted from the main text. In Section L. Section M provides detailed derivations for the quantitative model. Finally, in Section N, I describe data construction and references for data sources.
## Data sources and data construction
### Data sources
The data used in this paper comes from the following sources:
1. All information regarding **wages and labor quantities across local labor markets and all sectors** are compiled from different national publications. Specifically:
1. Yearly reports on wages and labor quantities from the Institute for Social Reform for 1910-1920 ([Instituto de Reformas Sociales 1911](#ref-1910memoria), [1912](#ref-1911memoria), [1913](#ref-1912memoria), [1914](#ref-1913memoria), [1915](#ref-1914memoria), [1916](#ref-1915memoria), [1917](#ref-1916memoria), [1918](#ref-1917memoria), [1919](#ref-1918memoria), [1920](#ref-1919memoria), [1921](#ref-1920memoria))
2. Compilation of the reports from the Ministry of Labor for 1914, 1920 and 1925 ([Ministerio de Trabajo 1927](#ref-spain1927estadistica)).
3. Agricultural employment from census publications ([Instituto Geográfico 1912](#ref-instituto1912censo), [1932](#ref-instituto1932censo), [1922](#ref-instituto1922censo))
2. All information regarding **external trade** are provided by the Spanish customs agency. Specifically:
1. Annual Trade Statistics for 1910-1920 ([Dirección General de Aduanas 1911](#ref-estadisticaexterior1910), [1912](#ref-estadisticaexterior1911), [1913](#ref-estadisticaexterior1912), [1914](#ref-estadisticaexterior1913), [1915](#ref-estadisticaexterior1914), [1916](#ref-estadisticaexterior1915), [1917](#ref-estadisticaexterior1916), [1918](#ref-estadisticaexterior1917), [1919](#ref-estadisticaexterior1918), [1920](#ref-estadisticaexterior1919), [1921](#ref-estadisticaexterior1920))
Note: I used an additional publication that lists the official correspondence between industries and occupations ([Instituto Nacional de Prevision Social 1930](#ref-4185)), often explicitly stating the associated product as occupation name for an industry. From that I constructed a correspondence table that matches products to industries
3. All information regarding **internal migration** are drawn from a special section of the census publications as previously compiled in ([Silvestre 2005](#ref-10.2307/41378422)).
4. All information regarding **consumer prices** are obtained from the publications of the Institute for Social Reforms as previously examined by Gomez-Tello et al. ([2018](#ref-SpainHistPrices)). Specifically:
1. Consumer prices of key agricultural and non-agricultural products across Spanish provinces throughout the decade are reported in the bulletins of the Institute for Social Reforms ([Instituto de Reformas Sociales 1923](#ref-prices_data))
5. Information regarding **the housing market**, including data on the housing stock and housing expenditures is taken from the statistical yearbooks and the bulletins of the Institute for Social Reforms. Specifically:
1. Rental rates as reported in the bulletins of the Institute for Social Reforms ([Instituto de Reformas Sociales 1923](#ref-prices_data))
2. Housing stock as reported in the statistical yearbooks ([Instituto Nacional de Estadı́stica 1920](#ref-instituto1934anuario))
### Data construction: A spatial dataset for Spain between 1910-1920.
To examine the impact of WWI on both trade flows and local labor markets, I construct a regionally disaggregated dataset for Spain between 1910-1920 that covers handcollected information on wages, employment levels, prices and exports across local labor markets. This dataset allows me for the first time to analyze the impact of the trade shock taking both external trade and internal labor reallocation into account. I rely on six principal data sources that together describe manufacturing and agricultural employment, external trade, migration patterns, consumer prices, the transportation network and the housing market.
I obtain disaggregated information regarding wages and labor quantities across local labor markets. At the beginning of the 20th century, the plight of the working class and their working conditions became a more prominent political issue in Spain. In order to better understand and track the working conditions the Institute for Social Reform - an entity that would later morph into the ministry of labor - started conducting large-scale surveys on working conditions with the first annual report being released in 1907. The institute continued to publish yearly reports covering the whole period of 1910-1920. The surveys were conducted at all public firms and large private enterprises in cities that are larger than 20,000 inhabitants (Casanovas 2004). They covered 23 different industries[^22] and 48 different provinces.[^23] In the annual reports, the institution reported wages, working hours, and number of employees across local labor markets. The results are available in two different formats. On the one hand, industry-specific results are available across the more geographically aggregated unit of regions, on the other hand, provincial wages are reported but with the industry-specific results missing. Additionally, the Ministry of Labor later published a compilation that offers a more complete picture across local labor markets with employment and wages being reported across province-sector pairs for the years 1914, 1920 and 1925 ([Ministerio de Trabajo 1927](#ref-spain1927estadistica)).
I augment the industry survey with additional data from the census. While the industry survey covers a large range of the manufacturing sector, it does not give further information on the remaining economy. As mentioned before, a crucial feature of the Spanish economy was the large agricultural sector. To account for that, I digitized the occupation-province specific Section of the census for 1900, 1910, 1920, and 1930. I use the 1920 data on agricultural employment to augment the 1920 data. For the 1914 data, I use the 1910 province-specific agricultural employment data and extrapolate by calculating province-specific fertility trends until 1914. Finally, I use data contained in the official Spanish statistical yearbooks on province-specific agricultural mean wages for 1915 and 1920.
I obtained detailed data regarding exports and imports from annual trade records released by the Spanish custom agency. I digitized the trade statistics for the years 1910-1919. For those years, the quantity of exports in 383 product categories across 77 different destination countries is available. Furthermore, the border agency uses a system of product-level prices to obtain total export values. These prices do not vary throughout and can be interpreted to give the relative pre-war prices across goods. To construct a correspondence between product-level trade data and industry-level labor market data, I used an additional publication that lists the official correspondence between industries and occupations ([Instituto Nacional de Prevision Social 1930](#ref-4185)), often explicitly stating the associated product as occupation name for an industry. From that I constructed a correspondence table that matches products to industries.[^24]
I augment the data on employment stocks with additional data on migration flows. I follow Silvestre ([2005](#ref-10.2307/41378422)) and use the province level data on inhabitants that are born in another province as published in the censuses. For 1920 and 1930 additional information is available listing not only the stock of migrants which were born in another province, but the identity of their origin province as well. The difference between 1930 and 1920 in the stock of migrants - adjusted for decennial survivability rates - is informative about net migration. In order to construct net migration, I follow Silvestre ([2005](#ref-10.2307/41378422)) and use the decennial census survivability rate between 1921-1930, $S\equiv0.86$. Net internal migration can be obtained by constructing the survivability adjusted change in stock of migrants, i.e.
$$
\text{Internal migrations}_{1930,1920,i,j}=BAP_{i,j,1930}-S\times BAP_{i,j}^{1920}
$$
where $BAP_{i,j}^{1920}$ refers to the stock of residents in $i$ who were born in province $j$ in 1920.
The bulletins of the Institute for Social Reforms contain detailed information on consumer prices of key agricultural and non-agricultural products across Spanish provinces throughout the decade ([Instituto de Reformas Sociales 1923](#ref-prices_data)). The data was previously used by Gomez-Tello et al. ([2018](#ref-SpainHistPrices)) and I refer for detailed information to their paper.
I georeferenced the Spanish railroad network in 1920. Then, using Dijkstra's algorithm I obtain bilateral distances between provincial capitals along the shortest path of the railroad network. To obtain distances to Paris, I augmented the graph with the French railroad network - as can be seen in Figure [14](#figure:map_railroad) - and further added maritime linkages between important ports in France and Spain. Again using Dijkstra's algorithm, I can obtain the shortest distance along this transportation network between provincial capitals in Spain and Paris which I will use to approximate the transport distance to the French market. All other external markets will be assigned to one location that is sufficiently distant such that domestic transport distances have little impact on the overall transport cost. Mirroring the importance of Latin American destination markets I include the location of Cuba in the transportation network and assign foreign trade - except for French trade - to that location.
I compute the housing expenditure share as well as stock and rental rates from different data sources. The statistical yearbooks make available the number of buildings available in a province as well as the inhabitants and thus the effective occupancy rate, the inverse of which is the share of a building that is rented by an average resident. Additionally, average yearly rental expenditure is selectively available across provinces in the bulletins of the Institute for Social Reforms. This yearly rate can be adjusted towards an hourly rate in a province, $r_{i}$. Total expenditure on housing can be imputed by firstly multiplying the rental rate and the inverse of the occupancy rate - call this the unit rental rate - with the stock of housing. Calculating total expenditure on housing as a share of total labor income across all provinces defines the expenditure share on housing, which I will refer to as $\delta$.
## Additional derivations
This Section provides additional derivations. Subsection [Section](#sec:Additional-Derivations) provides details underlying the mapping from the structural first-order representation to the reduced-form exposure indices used in the empirical specifications. Subsection [Section](#subsec:Aggregate-welfare-in-1) derives the aggregate welfare formula. Finally, Subsection [Section](#subsec:Trade-Imbalances) derives the aggregate welfare formula incorporating trade imbalances.
### Estimation of the Domestic Distance Elasticity
To discipline the domestic distance elasticity $\theta$ (the decay parameter for iceberg trade costs), we exploit the spatial decay of the WWI export-demand shock. Intuitively, locations further from the French border experienced a less pronounced increase in labor demand and consequently wages. We estimate this spatial decay using a nonlinear estimation procedure. Let $\text{dist}_{n}$ denote the transport distance of province $n$ to the French border. Following the structure of our spatial indirect exposure measure, we model the wage in province $n$ at time $t$ as a function of its relative accessibility to the demand shock. Specifically, we estimate the parameters $(\theta, \delta)$ by matching the functional form implied by the model's indirect spillovers:
$$
w_{n,t} = \exp\left( \alpha_{n} + \gamma_{t} + \delta \times \text{WWI}_{t} \times \frac{\text{dist}_{n}^{\theta}}{\sum_{j=1}^{N_D} \text{dist}_{j}^{\theta}} \right)
$$
where $\text{WWI}_{t}$ is an indicator for the war period (1914--1918), $\alpha_{n}$ are province fixed effects, and $\gamma_{t}$ are year fixed effects.
The parameter $\theta$ governs how rapidly the influence of foreign demand decays with domestic transport distance. We estimate [Equation](#eq:gmm_distance) via a nonlinear Poisson Pseudo-Maximum Likelihood (PPML) / Minimum Distance estimator on the panel of provincial wages from 1908 to 1919. The resulting point estimate of $\theta$ is tightly identified from the spatial footprint of the shock, yielding the baseline value reported in [Table](#tab:distance_elasticity) of $\theta = -1.769$.
## Additional figures
> **Railroad Network Spain/France 1910**
>
> Figure available in the [PDF](/research/spoils_of_war.pdf).
> **Spatial Distribution of Gains from Trade: Sectoral vs Spatial Adjustments**
>
> Figure available in the [PDF](/research/spoils_of_war.pdf).
## Additional tables
> **Regression Results: Difference-in-Differences for Belligerent Sectoral Exports I**
+:-----------------------------------------------+:------------------------:+:-----------------------:+:-----------------------:+
| | Exports (Value) |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| | \(1\) | \(2\) | \(3\) |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| War Period $\times$ Sector $=$ Books | -0.0641 (0.0783) | -0.1183 (0.1666) | -0.1154 (0.1390) |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| War Period $\times$ Sector $=$ Ceramics | -0.0280 (0.1195) | -0.0519 (0.1871) | -0.0780 (0.1791) |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| War Period $\times$ Sector $=$ Chemicals | 0.5472$^{*}$ (0.3094) | 0.6098$^{***}$ (0.2269) | 0.5782$^{**}$ (0.2625) |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| War Period $\times$ Sector $=$ Construction | -0.0965 (0.2133) | -0.1724 (0.2127) | -0.0223 (0.1927) |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| War Period $\times$ Sector $=$ Decoration | 0.9878$^{***}$ (0.0718) | 1.184$^{**}$ (0.5652) | 1.245$^{***}$ (0.4558) |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| War Period $\times$ Sector $=$ Electricity | 0.3231$^{***}$ (0.0903) | 0.5665$^{***}$ (0.2091) | 0.6373$^{**}$ (0.3011) |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| War Period $\times$ Sector $=$ Food | 0.2104 (0.1414) | 0.1873$^{***}$ (0.0701) | 0.1634$^{*}$ (0.0951) |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| War Period $\times$ Sector $=$ Forest | -0.3512$^{***}$ (0.0736) | -0.1829 (0.3355) | -0.0531 (0.3673) |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| War Period $\times$ Sector $=$ Furniture | 0.1017 (0.1767) | 0.0873 (0.1525) | 0.0063 (0.1988) |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| War Period $\times$ Sector $=$ Garments | 0.9378$^{***}$ (0.3113) | 0.8903$^{**}$ (0.3804) | 0.9717$^{***}$ (0.2990) |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| War Period $\times$ Sector $=$ Glass | 0.3393$^{***}$ (0.0817) | 0.3104$^{*}$ (0.1772) | 0.3738$^{*}$ (0.1931) |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| War Period $\times$ Sector $=$ Gold | -0.4479$^{***}$ (0.0848) | -0.3956$^{*}$ (0.2117) | -0.0607 (0.1444) |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| War Period $\times$ Sector $=$ Leather | 1.482$^{***}$ (0.0732) | 1.368$^{**}$ (0.5329) | 1.536$^{***}$ (0.5491) |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| War Period $\times$ Sector $=$ Metallurgy | -0.0023 (0.5717) | 0.1213 (0.6505) | 0.1755 (0.7238) |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| War Period $\times$ Sector $=$ Metal Works | 0.0470 (0.3080) | -0.0038 (0.2332) | 0.0923 (0.2586) |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| War Period $\times$ Sector $=$ Mines | -0.2246$^{*}$ (0.1227) | -0.2188 (0.2379) | -0.2129 (0.2147) |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| War Period $\times$ Sector $=$ Other | 0.1419 (0.1660) | 0.2017 (0.1308) | 0.2319 (0.1547) |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| War Period $\times$ Sector $=$ Paper | -0.4212 (0.6106) | -0.4654 (0.3268) | -0.4700 (0.3765) |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| War Period $\times$ Sector $=$ Public Industry | -4.433$^{***}$ (0.0726) | -4.397$^{***}$ (1.255) | -1.591$^{*}$ (0.8529) |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| War Period $\times$ Sector $=$ Textiles | 0.7245$^{***}$ (0.1608) | 0.7617$^{***}$ (0.2321) | 0.7419$^{***}$ (0.1476) |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| War Period $\times$ Sector $=$ Tobacco | 2.147$^{***}$ (0.0706) | 1.723$^{**}$ (0.8450) | 1.864$^{**}$ (0.9063) |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| War Period $\times$ Sector $=$ Transport | 0.5031$^{**}$ (0.2152) | 0.1470 (0.1938) | -0.1267 (0.1046) |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| War Period $\times$ Sector $=$ Wood | -0.1806$^{*}$ (0.0924) | -0.1865$^{*}$ (0.1125) | -0.1532 (0.1379) |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| | | | |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| Standard-Errors | Product | Destination | Destination-Product |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| Observations | 80,153 | 80,150 | 79,920 |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| Pseudo R$^2$ | 0.37166 | 0.66054 | 0.87407 |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| | | | |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| Product fixed effects | $\checkmark$ | $\checkmark$ | |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| Year fixed effects | $\checkmark$ | $\checkmark$ | $\checkmark$ |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| Destination fixed effects | | $\checkmark$ | |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
| Destination-Product fixed effects | | | $\checkmark$ |
+------------------------------------------------+--------------------------+-------------------------+-------------------------+
> **Regression Results: Difference-in-Differences for Belligerent Sectoral Exports II**
+:-------------------------------------------------------------------+:----------------------:+:----------------------:+:-----------------------:+
| | Exports (Value) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| | \(1\) | \(2\) | \(3\) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| Belligerent | 2.049$^{***}$ (0.1689) | | |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent | 0.4035$^{*}$ (0.2428) | 0.2985 (0.1929) | 0.2461$^{*}$ (0.1356) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Books | -0.3825 (0.5973) | -0.3859 (0.5149) | -0.4341 (0.3521) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Ceramics | -0.1552 (0.5689) | -0.1794 (0.5760) | -0.1749 (0.4190) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Chemicals | 0.8262$^{*}$ (0.4303) | 0.7580$^{**}$ (0.3770) | 0.7982$^{**}$ (0.3524) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Construction | 0.2978 (0.5313) | 0.5123 (0.5009) | 0.6182$^{*}$ (0.3162) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Decoration | 1.197 (1.248) | 1.077 (1.274) | 1.155 (1.336) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Electricity | 0.0713 (0.6816) | 0.3267 (0.7208) | -0.0820 (0.6371) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Food | 0.1643 (0.3313) | 0.1417 (0.3019) | 0.1536 (0.2300) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Forrest | 0.3829 (0.8404) | 0.2847 (0.8239) | -0.0495 (0.7061) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Furniture | -0.0415 (0.4626) | -0.0963 (0.3756) | 0.0046 (0.3327) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Garments | 1.564$^{***}$ (0.5131) | 1.722$^{***}$ (0.4658) | 1.632$^{***}$ (0.4382) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Glass | 0.2927 (0.9716) | 0.4907 (0.8949) | 0.4762 (0.8873) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Gold | -0.4985 (0.6270) | -0.0315 (0.5750) | -0.2444 (0.4845) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Leather | 1.796 (1.195) | 2.106$^{*}$ (1.121) | 2.204$^{*}$ (1.136) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Metallurgy | 2.288$^{**}$ (0.9711) | 2.216$^{**}$ (0.9518) | 2.007$^{**}$ (0.9241) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ MetalWorks | 0.5281 (0.5615) | 0.7327 (0.4840) | 0.9247$^{**}$ (0.4579) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Mines | 0.3043 (0.4720) | 0.2123 (0.3517) | 0.1589 (0.2297) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Other | 0.0005 (0.4426) | -0.0126 (0.4183) | -0.1717 (0.3561) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Paper | 1.664$^{**}$ (0.7098) | 1.658$^{**}$ (0.6647) | 1.685$^{**}$ (0.6570) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ PublicIndustry | 0.6260 (1.503) | 1.185 (1.555) | -3.553$^{**}$ (1.398) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Textiles | 1.045$^{**}$ (0.4254) | 1.041$^{***}$ (0.3897) | 0.9815$^{***}$ (0.3416) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Tobacco | 3.460$^{***}$ (1.278) | 3.868$^{***}$ (1.316) | 3.907$^{***}$ (1.261) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Transport | 0.6397 (0.5999) | 0.3015 (0.5706) | 0.3076 (0.4537) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| War Period $\times$ Belligerent $\times$ Sector $=$ Wood | -0.3595 (0.4678) | -0.3461 (0.3309) | -0.4224$^{*}$ (0.2284) |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| | | | |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| Observations | 80,143 | 80,143 | 79,914 |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| Pseudo R$^2$ | 0.49221 | 0.68012 | 0.87923 |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| | | | |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| Product fixed effects | $\checkmark$ | $\checkmark$ | |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| Year fixed effects | $\checkmark$ | $\checkmark$ | $\checkmark$ |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| Destination fixed effects | | $\checkmark$ | |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
| Destination-Product fixed effects | | | $\checkmark$ |
+--------------------------------------------------------------------+------------------------+------------------------+-------------------------+
> **Results: Mobility Cost Estimation Sectoral Parameters**
---------------- ------------
Sector $\mu_{rs}$
Agriculture 0.1000
Books 0.0006
Ceramics 0.0010
Chemicals 0.0005
Construction 0.0007
Decoration 0.0008
Electricity 0.0012
Food 0.0004
Forrest 0.0009
Furniture 0.0005
Garments 0.0005
Glass 0.0004
Leather 0.0006
Metallurgy 0.0005
MetalWorks 0.0005
Mines 0.0011
Other 0.0014
Paper 0.0005
Public 0.0009
PublicIndustry 0.0013
Textiles 0.0006
Tobacco 0.0007
Transport 0.0006
Wood 0.0005
---------------- ------------
> **Results: Mobility Cost Estimation Geographical Parameters**
------------ ----------- ----------- --------------
Province $\beta_n$ $\zeta_n$ $\mu_{ag,n}$
Lerida 0.45 0.52 0.80
Logrono 0.09 0.41 0.22
Lugo 0.18 0.08 0.26
Madrid 0.08 1.95 0.95
Malaga 0.15 0.96 0.16
Murcia 1.11 5.04 0.00
Navarra 0.10 0.13 0.60
Orense 0.10 0.04 0.29
Oviedo 1.46 3.54 0.46
Palencia 0.14 0.27 0.24
Pontevedra 0.04 0.09 0.42
Salamanca 0.26 0.15 0.36
Santander 0.06 0.29 0.53
Segovia 0.11 0.06 0.39
Sevilla 0.31 2.86 0.36
Soria 0.18 0.08 0.01
Tarragona 0.09 0.12 0.72
Teruel 0.35 0.18 0.29
Toledo 0.56 0.59 0.00
Valencia 0.33 0.95 0.48
Valladolid 0.10 0.17 0.58
Vizcaya 0.02 0.32 0.71
Zamora 0.27 0.11 0.00
Zaragoza 0.20 0.35 0.82
------------ ----------- ----------- --------------
## Detailed Derivations for quantitative-model
In this section of the online appendix, I report detailed derivations for the quantitative model, allowing for multiple sectors, reallocation across sectors and space, as well as trade deficits.
### Setting
Let there be a number of locations within a country $n,i,j,h\in\mathbb{D}=\left\{ 1,\ldots,N^{D}\right\}$. Let there be also a number of foreign locations $k,l,m\in\mathbb{F}=\left\{ 1,\ldots,N^{F}\right\}$. Domestic locations are heterogeneous in their exogenously fixed housing supply, $H_{i}$, and their geographical location relative to one another. The only factor of production is labor. In each location production occurs across multiple sectors $r,s,t\in\mathbb{S}=\left\{ 1,\ldots,S\right\}$. There are only two periods and the initial distribution of workers across locations $[\ell_{n,r}]_{\forall(n,r)\in\mathbb{D}\times\mathbb{S}}$, is given, while the distribution of workers in the second period, $[\ell_{n,r}']_{\forall(n,r)\in\mathbb{D}\times\mathbb{S}}$, is endogenously determined.
### Domestic Preferences
Workers residing in location $i$ consume a Cobb-Douglas aggregate of housing and a consumption bundle:
$$
U_{n}=\left(C_{n}\right)^{1-\delta}\left(R_{n}\right)^{\delta}
$$
where $\delta$ is the expenditure share on housing. $C_{n}$ is a Cobb-Douglas aggregate over sector-specific CES aggregates of origin-differentiated goods of both domestic and foreign origin:
$$
C_{n}=\prod_{s=1}^{S}\left(C_{n,r}\right)^{\alpha_{r}}
$$
$$
C_{n,r}=\left(\sum_{i=1}^{N^{D}}C_{ni,r}^{\frac{\sigma_{r}-1}{\sigma_{r}}}+\sum_{l=1}^{N^{F}}C_{nl,r}^{\frac{\sigma_{r}-1}{\sigma_{r}}}\right)^{\frac{\sigma_{r}}{\sigma_{r}-1}}
$$
where $\sigma>1$ is the elasticity of substitution. The indirect utility and the optimal price index of this problem is given by,
$$
u_{n,r}=\frac{\rho_{n}e_{n,r}\bar{d}}{p_{n}^{(1-\delta)}r_{n}^{\delta}},\quad p_{n}=\prod_{r=1}^{S}\left(p_{n,r}\right)^{\alpha_{r}}\quad\sum_{r=1}^{S}\alpha_{r}=1
$$
$$
p_{n,r}=\left[\sum_{i=1}^{N^{D}}\left(p_{ni,r}\right)^{1-\sigma_{r}}+\sum_{l=1}^{N^{F}}\left(p_{nl,r}\right)^{1-\sigma_{r}}\right]^{\frac{1}{1-\sigma_{r}}}
$$
where $e_{n,r}$ represents the disposable income of a representative worker in $n$. Notice that the ideal price index is adjusted to account for the fact that trade is balanced domestically, but not externally, which induces a wedge between domestic and foreign goods in the price index. Applying Roy's identity, demand in location $n$ for the good produced in location $i$ is given by,
$$
q_{ni,r}\left(\boldsymbol{p}_{n,r}\right)=\frac{\left(p_{ni,r}\right)^{-\sigma_{r}}}{\sum_{j=1}^{N^{D}}\left(p_{nj,r}\right)^{1-\sigma_{r}}+\sum_{k=1}^{N^{F}}\left(p_{nk,r}\right)^{1-\sigma_{r}}}\left(1-\delta\right)\alpha_{r}\sum_{r=1}^{S}e_{n,r}
$$
where $\boldsymbol{p}_{n}$ refers to the vector of prices in location $n$ of the goods produced in all other locations. Similarly, demand in location $n$ for the good produced in location $l$ is given by,
$$
q_{nl,r}\left(\boldsymbol{p}_{n,r}\right)=\frac{\left(p_{nl,r}\right)^{-\sigma_{r}}}{\sum_{j=1}^{N^{D}}\left(p_{nj,r}\right)^{1-\sigma_{r}}+\sum_{k=1}^{N^{F}}\left(p_{nk,r}\right)^{1-\sigma_{r}}}\left(1-\delta\right)\alpha_{r}\sum_{r=1}^{S}e_{n,r}
$$
### Foreign Preferences
Households in foreign locations $l$ spend a fixed endowment $e_{l}$ across domestic locations. They consume a Cobb-Douglas aggregate over sector-specific CES aggregates of origin-differentiated goods across domestic locations:
$$
C_{l}=\prod_{s=1}^{S}\left(C_{l,r}\right)^{\alpha_{l,r}}
$$
$$
C_{l,r}=\left(\sum_{i=1}^{N^{D}}C_{li,r}^{\frac{\sigma_{r}-1}{\sigma_{r}}}\right)^{\frac{\sigma_{r}}{\sigma_{r}-1}}
$$
where $\sigma_{r}>1$ is the elasticity of substitution. The indirect utility and the optimal price index that households derive from consuming across domestic locations is given by
$$
u_{l}=\frac{e_{l}}{\prod_{r=1}^{S}\left(p_{n}^{r}\right)^{\alpha_{l,r}}},\quad\sum_{r=1}^{S}\alpha_{l,r}=1
$$
$$
p_{l,r}=\left(\sum_{i=1}^{N^{D}}\left(p_{li,r}\right)^{1-\sigma_{r}}\right)^{\frac{1}{1-\sigma_{r}}}
$$
where $e_{l}$ represents the endowment of workers in location $l$. Applying Roy's identity, demand in location $l$ for the good produced in location $i$ is given by,
$$
q_{li,r}\left(\boldsymbol{p}_{l,r}\right)=\frac{p_{li,r}^{-\sigma_{r}}}{\sum_{j=1}^{N^{D}}p_{lj,r}^{1-\sigma_{r}}}\alpha_{l,r}e_{l}
$$
where $\boldsymbol{p}_{l}$ refers to the vector of prices in location $l$ of the goods produced in all other locations.
### Production
Goods are produced only with labor and production is characterized by a constant returns to scale production technology, i.e.
$$
q_{i,r}=z_{i,r}\ell_{i,r}
$$
where $z_{i}$ denotes a productivity shifter in location $i$ and $\ell_{i}$ denotes the number of workers employed there. Goods can be traded between locations within and between countries, but transport is subject to iceberg variable trade costs, implying that delivering a unit of any good from location $n$ to location $i$ requires shipping $\tau_{ni}\geq1$ units of the good. Therefore, the price that a representative worker faces in location $i$ for any good from location $n$is given by,
$$
\begin{aligned}
p_{ni,r} & =\tau_{ni}mc_{i,r}=\frac{\tau_{ni}w_{i,r}}{z_{i,r}}
\end{aligned}
$$
where $z_{i}$ captures as before the productivity of a given location and iceberg variable trade costs satisfy $\tau_{ni}>1$ and $\tau_{nn}=1$, that is we normalize trade costs within a location to 1.
### Expenditure Shares
In this model we have three different types of expenditures. I first derive the expenditure shares of domestic locations on domestic varieties for a given sector $r$,
$$
\begin{aligned}
\frac{s_{ni,r}}{\left(1-\delta\right)} & =\frac{p_{ni,r}q_{ni,r}\left(\boldsymbol{p}_{n}\right)}{\sum_{s=1}^{S}\sum_{j=1}^{N^{D}}p_{nj,s}q_{nj,s}\left(\boldsymbol{p}_{n}\right)+\sum_{s=1}^{S}\sum_{k=1}^{N^{F}}p_{nk,s}q_{nk,s}\left(\boldsymbol{p}_{n}\right)}\\
& =\frac{x_{ni,r}\left(\boldsymbol{p}_{n}\right)}{\sum_{s=1}^{S}\sum_{j=1}^{N^{D}}x_{nj,s}\left(\boldsymbol{p}_{n}\right)+\sum_{s=1}^{S}\sum_{k=1}^{N^{F}}x_{nk,s}\left(\boldsymbol{p}_{n}\right)}\\
& =\frac{\frac{1}{\bar{d}}p_{ni,r}^{1-\sigma}}{\sum_{j=1}^{N^{D}}\frac{1}{\bar{d}}\left(p_{nj,r}\right)^{1-\sigma_{r}}+\sum_{k=1}^{N^{F}}\left(p_{nk,r}\right)^{1-\sigma_{r}}}\alpha_{r}
\end{aligned}
$$
where $\boldsymbol{p}_{n}$ represents the price vector across locations and sectors. We can similarly derive expenditure shares of domestic locations on foreign varieties for a given sector $r$,
$$
\begin{aligned}
\frac{s_{nl,r}}{\left(1-\delta\right)} & =\frac{p_{nl,r}q_{nl,r}\left(\boldsymbol{p}_{n}\right)}{\sum_{s=1}^{S}\sum_{j=1}^{N^{D}}p_{nj,s}q_{nj,s}\left(\boldsymbol{p}_{n}\right)+\sum_{s=1}^{S}\sum_{k=1}^{N^{F}}p_{nk,s}q_{nk,s}\left(\boldsymbol{p}_{n}\right)}\\
& =\frac{x_{nl,r}\left(\boldsymbol{p}_{n}\right)}{\sum_{s=1}^{S}\sum_{j=1}^{N^{D}}x_{nj,s}\left(\boldsymbol{p}_{n}\right)+\sum_{s=1}^{S}\sum_{k=1}^{N^{F}}x_{nk,s}\left(\boldsymbol{p}_{n}\right)}\\
& =\frac{p_{nl,r}^{1-\sigma}}{\sum_{j=1}^{N^{D}}\frac{1}{\bar{d}}\left(p_{nj,r}\right)^{1-\sigma_{r}}+\sum_{k=1}^{N^{F}}\left(p_{nk,r}\right)^{1-\sigma_{r}}}\alpha_{r}
\end{aligned}
$$
Finally, I can derive expenditure shares of foreign locations on domestic varieties,
$$
\begin{aligned}
s_{li,r} & =\frac{p_{li,r}q_{li,r}\left(\boldsymbol{p}_{n}\right)}{\sum_{j=1}^{N^{D}}p_{lj,r}q_{lj,r}\left(\boldsymbol{p}_{l}\right)}=\frac{x_{li,r}\left(\boldsymbol{p}_{l}\right)}{\sum_{j=1}^{N^{D}}x_{lj,r}\left(\boldsymbol{p}_{l}\right)}=\frac{p_{li,r}^{1-\sigma_{r}}}{\sum_{j=1}^{N^{D}}p_{lj,r}^{1-\sigma_{r}}}\alpha_{l,r}
\end{aligned}
$$
For convenience we can also define the domestic expenditure share of domestic locations and foreign expenditure share of domestic locations,
$$
\begin{aligned}
\frac{s_{nD,r}}{\left(1-\delta\right)} & =\frac{\sum_{i=1}^{N^{D}}p_{ni,r}q_{ni,r}\left(\boldsymbol{p}_{n}\right)}{\sum_{s=1}^{S}\sum_{j=1}^{N^{D}}p_{nj,s}q_{nj,s}\left(\boldsymbol{p}_{n}\right)+\sum_{s=1}^{S}\sum_{k=1}^{N^{F}}p_{nk,s}q_{nk,s}\left(\boldsymbol{p}_{n}\right)}\\
& =\frac{\sum_{i=1}^{N^{D}}x_{ni,r}\left(\boldsymbol{p}_{n}\right)}{\sum_{s=1}^{S}\sum_{j=1}^{N^{D}}x_{nj,s}\left(\boldsymbol{p}_{n}\right)+\sum_{s=1}^{S}\sum_{k=1}^{N^{F}}x_{nk,s}\left(\boldsymbol{p}_{n}\right)}\\
& =\frac{\left(p_{nD,r}\right)^{1-\sigma_{r}}}{\sum_{j=1}^{N^{D}}\frac{1}{\bar{d}}\left(p_{nj,r}\right)^{1-\sigma_{r}}+\sum_{k=1}^{N^{F}}\left(p_{nk,r}\right)^{1-\sigma_{r}}}\alpha_{r}
\end{aligned}
$$
$$
\begin{aligned}
\frac{s_{nF,r}}{\left(1-\delta\right)} & =\frac{\sum_{\ell=1}^{N^{F}}p_{nl,r}q_{nl,r}\left(\boldsymbol{p}_{n}\right)}{\sum_{s=1}^{S}\sum_{j=1}^{N^{D}}p_{nj,s}q_{nj,s}\left(\boldsymbol{p}_{n}\right)+\sum_{s=1}^{S}\sum_{k=1}^{N^{F}}p_{nk,s}q_{nk,s}\left(\boldsymbol{p}_{n}\right)}\\
& =\frac{\sum_{l=1}^{N^{F}}x_{nl,r}\left(\boldsymbol{p}_{n}\right)}{\sum_{s=1}^{S}\sum_{j=1}^{N^{D}}x_{nj,s}\left(\boldsymbol{p}_{n}\right)+\sum_{s=1}^{S}\sum_{k=1}^{N^{F}}x_{nk,s}\left(\boldsymbol{p}_{n}\right)}\\
& =\frac{\left(p_{nF,r}\right)^{1-\sigma_{r}}}{\sum_{j=1}^{N^{D}}\frac{1}{\bar{d}}\left(p_{nj,r}\right)^{1-\sigma_{r}}+\sum_{k=1}^{N^{F}}\left(p_{nk,r}\right)^{1-\sigma_{r}}}\alpha_{r}
\end{aligned}
$$
where in the final equality of both equations we have used a definition for the domestic and foreign sector specific price index respectively, i.e.
$$
\left(p_{nD,r}\right)^{1-\sigma_{r}}\equiv\sum_{i=1}^{N^{D}}p_{ni,r}^{1-\sigma_{r}}
$$
$$
\left(p_{nF,r}\right)^{1-\sigma_{r}}\equiv\sum_{l=1}^{N^{F}}p_{nl,r}^{1-\sigma_{r}}
$$
I assume that expenditure on land in each location is redistributed lump sum to the workers residing in that location. Total disposable income can then be written as,
$$
e_{n,s}\ell_{n,s}=w_{n,s}\ell_{n,s}+\delta e_{n,s}\ell_{n,s}=\frac{w_{n,s}\ell_{n,s}}{1-\delta}
$$
### Static Equilibrium
In this subsection I characterize the static equilibrium which is the equilibrium taking the labor allocations as given. This definition of the equilibrium is appropriate for the first period while for the second period labor allocations are determined endogenously and an extended equilibrium definition will be provided below that uses the static equilibrium definition as a building block.
Conditional on the measure of workers in each location, $[\ell_{n,r}]_{\forall(n,r)\in\mathbb{D}\times\mathbb{S}}$, foreign endowments, $[e_{l}]_{\forall l\in\mathbb{F}}$, the national external trade deficit $\bar{d}$, a fixed domestic housing supply, $[H_{n}]_{\forall n\in\mathbb{D}}$ , a fixed assignment of producitivities across domestic locations, $[z_{n,r}]_{\forall(n,r)\in\mathbb{D}\times\mathbb{S}}$ and marginal costs across foreign locations, $[mc_{l,r}]_{\forall(l,r)\in\mathbb{F}\times\mathbb{S}}$, as well as a specification of the domestic geography of the economy, $[\tau_{ni}]_{\forall(n,i)\in\mathbb{D}x\mathbb{D}}$ and the foreign geography of the economy, $[\tau_{nl},\tau_{ln}]_{\forall(n,l)\in\mathbb{D}x\mathbb{F},\forall(l,n)\in\mathbb{F}x\mathbb{D}}$, the equilibrium in the first period is a set of prices $[p_{ni,r},p_{nl,r}]_{\forall(n,i,r)\in\mathbb{D}x\mathbb{D}\times\mathbb{S},\forall(n,l,r)\in\mathbb{D}x\mathbb{F}\times\mathbb{S}}$, housing rental rates $[r_{n}]_{n\in\mathbb{D}}$, wages in each domestic location-sector $[w_{n,r}]_{\forall(n,r)\in\mathbb{D}\times\mathbb{S}}$, as well as the foreign and domestic expenditure shares of domestic locations, $[s_{ni,r},s_{nl,r}]_{\forall(n,i,r)\in\mathbb{D}x\mathbb{D}\times\mathbb{S},\forall(n,l,r)\in\mathbb{D}x\mathbb{F}\times\mathbb{S}}$, and the expenditure of foreign locations on domestic varieties, $[s_{ln,r}]_{\forall(l,n,r)\in\mathbb{F}x\mathbb{D}\times\mathbb{S}}$ such that
1. Given domestic and foreign prices in domestic locations, $[p_{ni,r},p_{nl,r}]_{\forall(n,i,r)\in\mathbb{D}x\mathbb{D}\times\mathbb{S},\forall(n,l,r)\in\mathbb{D}x\mathbb{F}\times\mathbb{S}}$ as well as domestic prices in foreign locations $[p_{ln,r}]_{\forall(l,n,r)\in\mathbb{F}x\mathbb{D}\times\mathbb{S}}$, wages in each domestic location $[w_{n,r}]_{\forall(n,r)\in\mathbb{D}\times\mathbb{S}}$, and the assumption that expenditure on land is locally redistributed lump sum which defines the disposable income as in ([Equation](#eq:disposable_income)), the domestic and foreign households choose expenditure shares to maximize their respective utility ([Equation](#eq:utility_function)) subject to their budget constraint, with the respective expenditure shares being given by,
$$
\begin{aligned}
s_{ni,r} & =\alpha_{r}\left(1-\delta\right)\frac{p_{ni,r}^{1-\sigma_{r}}}{\sum_{i=1}^{N^{D}}\frac{1}{\bar{d}}\left(p_{ni,r}\right)^{1-\sigma_{r}}+\sum_{l=1}^{N^{F}}\left(p_{nl,r}\right)^{1-\sigma_{r}}}
\end{aligned}
$$
$$
s_{nl,r}=\alpha_{r}\left(1-\delta\right)\frac{p_{nl,r}^{1-\sigma_{r}}}{\sum_{i=1}^{N^{D}}\frac{1}{\bar{d}}\left(p_{ni,r}\right)^{1-\sigma_{r}}+\sum_{l=1}^{N^{F}}\left(p_{nl,r}\right)^{1-\sigma_{r}}}
$$
$$
\begin{aligned}
s_{li,r} & =\alpha_{l,r}\frac{\left(p_{li,r}\right)^{1-\sigma_{r}}}{\sum_{j=1}^{N^{D}}\left(p_{lj,r}\right)^{1-\sigma_{r}}}
\end{aligned}
$$
2. Firms optimize their profits via marginal cost pricing, such that domestic and foreign prices are given by,
$$
p_{ni,r}=\frac{\tau_{ni}w_{i,r}}{z_{i,r}}
$$
$$
p_{nl,r}=\tau_{nl}mc_{nl,r}
$$
3. In each domestic location the labor income equals expenditure on goods produced in that location with expenditures originating both from domestic and foreign locations:
$$
w_{i,r}\ell_{i,r}=\sum_{n=1}^{N^{D}}s_{ni,r}\left(\sum_{r=1}^{S}e_{n,r}\ell_{n,r}\right)+\sum_{l=1}^{N^{F}}s_{li,r}e_{l}
$$
4. Trade is balanced domestically, but unbalanced externally,
$$
\bar{d}\left(\sum_{r=1}^{S}e_{n,r}\ell_{n,r}\right)=\sum_{r=1}^{S}\left(\sum_{i=1}^{N}s_{ni,r}\left(\sum_{r=1}^{S}e_{n,r}\ell_{n,r}\right)+\sum_{l=1}^{N^{F}}s_{nl,r}\left(\bar{d}e_{n}\ell_{n}\right)\right)
$$
5. Housing market clears
$$
H_{n}r_{n}=\delta\left(\sum_{r=1}^{S}e_{n,r}\right)
$$
### Labor Reallocation
Between the first and second period, workers can reallocate between domestic locations to respond to changes in factor returns. The initial allocation of workers across locations is given, $[\ell_{n,s}]_{\forall(n,s)\in\mathbb{D}\times\mathbb{S}}$, but the allocation of workers in the second period is determined by their endogenous reallocation choice across sectors and locations. Recall that the indirect utility of a worker in a given location $n$ and in a given sector is given by,
$$
u_{n,r}=\frac{\rho_{n}e_{n,r}'\bar{d}'}{\left(p_{n}'\right)^{1-\delta}\left(r_{n}'\right)^{\delta}}
$$
I specify the reallocation choice using in terms of a stochastic sequential choice. Individuals first make a geographical relocation choice from location $n$ to location $i$ and subsequently a sectoral reloction choice moving from an initial sector $r$ to another sector $s$. The introduction of extreme value distributed preference shocks allow us to write down the problem in closed form. Specifically, a worker first draws a location-specific preference shock $\kappa_{i}$, that is Frechet distributed with dispersion parameter $\gamma$. She then makes her geographical reallocation choice, forming expectations over, but prior to uncovering, the sector-specific preference shock $\iota_{s}$, that will be drawn after the geographical reallocation choice is made from a Frechet distributed with dispersion parameter $\nu$. Both the geographical reallocation choice and the sectoral reallocation choice is subject to variable geographical and sectoral migration cost, $\mu_{ni}$ and $\mu_{rs}$ respectively. The properties of the Frechet distribution and the sequencing of the reallocation choice imply that labor flows between location $n$ and location $i$ and between sector $r$ and $s$ take on a multiplicatively separable form,
$$
\sigma_{ni,rs}'=\sigma_{ni|r}'\sigma_{rs|i}'
$$
where $\sigma_{ni|r}$ is the share of workers that originate from sector $r$ in location $n$ and reallocate to location $i$, and where $\sigma_{rs|i}$ is the share of workers that conditional on having chosen location $i$ and choose to relocate from sector $r$ to sector $s.$ I present the solution to the problem by solving backwards. First, conditional on having chosen location $i$ the indirect utility relocating from sector $r$to $s$is given by,
$$
v_{rs|i}'=\frac{u_{i,s}'}{\mu_{rs}}\times\iota_{s}
$$
where I assume that the preference shocks $\iota_{s}$ are distributed identically and independently according an extreme value type II or Frechet distribution. Their cumulative distribution function is respectively given by,
$$
F_{\kappa}\left(\iota_{s}\right)=e^{\left(-\iota_{s}\right)^{-\nu}}\qquad\nu>1
$$
and where the iceberg (variable) sectoral migration costs satisfy $\mu_{rs}\geq1$ and $\mu_{rr}=1$, that is staying in your initial sector is costless. Conditional on having chosen location $i$the properties of the Frechet distribution allow us to write in closed form the probability of relocating from sector $r$ to sector $s$ as,
$$
\sigma_{rs|i}'=\frac{(w_{is|r}')^{\nu}}{\left(\Pi_{i,r}'\right)^{\nu}}
$$
where $w_{is|r}'\equiv w_{is}'/\mu_{rs}$ and $\Pi_{i,r}'\equiv\left(\sum_{t}(w_{it|r}')^{\nu}\right)^{1/\nu}$ represents the option value of a worker conditional on having chosen location $i$ and being initially attached to sector $r$. Prior to making the sectoral relocation choice, the worker makes a geographical choice. In a first step the worker therefore compares the different option values across geographical locations. The expected ex-ante utility, i.e. prior to observing and forming expectations over the sectoral preference shocks, that an individual derives from moving from location $n$ to location $i$ can be expressed in terms of the option value of being in that location-sector $\Pi_{i,r}'\equiv\left(\sum_{t}(w_{it}'/\mu_{rt})^{\nu}\right)^{1/\nu}$, multiplied by a stochastic location-specific preference shock $\kappa_{i}$, a stochastic sector-specific preference shock $\iota_{s}$, and adjusted by variable geographical migration cost, $\mu_{ni}$, i.e.
**
$$
v_{ni|r}'\equiv\frac{\delta}{\mu_{ni}}\frac{\rho_{i}\Pi_{i|r}'}{\left(p_{i}'\right)^{1-\delta}\left(r_{i}'\right)^{\delta}}\times\kappa_{i}
$$
** where I assume that the preference shocks $\iota_{s}$ are distributed identically and independently according an extreme value type II or Frechet distribution. Their cumulative distribution function is respectively given by,
$$
F_{\kappa}\left(\iota_{s}\right)=e^{\left(-\kappa_{i}\right)^{-\gamma}}\qquad\gamma>1
$$
and where the iceberg (variable) geographical migration costs satisfy $\mu_{ni}\geq1$ and $\mu_{nn}=1$, that is we assume the absence of migration costs if the worker remains in its current location. Given the properties of the Frechet distribution the geographical reallocation share takes on the following closed form form expression,
$$
\sigma_{ni|r}'=\frac{\left(v_{ni|r}'\right)^{\gamma}}{\left(\Omega_{n,r}'\right)^{\gamma}}
$$
where analogously to the option value of the sectoral choice, $\left(\Omega_{n,r}'\right)^{\gamma}\equiv\sum_{j}\left(v_{nj|r}'\right)^{\gamma}$ represents the option value of the geographical choice. The indirect utility depends on earnings, price indices and rental rates in the destination location. I assume that expenditure on land in each location is redistributed lump sum to the workers residing in that location. Total disposable income can then be written as,
$$
e_{n,s}'\ell_{n,s}'=w_{n,s}'\ell_{n,s}'+\delta e_{n,s}'\ell_{n,s}'=\frac{w_{n,s}'\ell_{n,s}'}{1-\delta}
$$
Wages are pinned down by a labor market clearing condition: In each domestic location the labor income equals expenditure on goods produced in that location with expenditures originating both from domestic and foreign locations:
$$
w_{i}'\ell_{i}'=\sum_{i=1}^{N^{D}}s_{ni}'e_{n}'\ell_{n}'+\sum_{l=1}^{N^{F}}s_{li}'e_{l}'
$$
I can then define the land market clearing condition that implies that the equilibrium land can be determined from the condition that total housing expenditure has to equal land income,
$$
r_{n}=\frac{\delta e_{n}}{H_{n}}=\frac{\delta}{1-\delta}\frac{w_{n}\ell_{n}}{H_{n}}
$$
Finally, it will be instructive to see the forces that pin down the changes in reallocation shares. Totally differentiating geographical mobility we obtain, **
$$
d\sigma_{ni|r}'=\gamma\frac{\left(v_{ni|r}'\right)^{\gamma}}{\sum_{j=1}^{N^{D}}\left(v_{nj|r}'\right)^{\gamma}}\frac{dv_{ni|r}'}{v_{ni|r}'}-\gamma\sum_{h=1}^{N^{D}}\frac{\left(v_{ni|r}'\right)^{\gamma}}{\sum_{j=1}^{N^{D}}\left(v_{nj|r}'\right)^{\gamma}}\frac{\left(v_{nh|r}'\right)^{\gamma}}{\sum_{j=1}^{N^{D}}\left(v_{nj|r}'\right)^{\gamma}}\frac{dv_{nh|r}'}{v_{nh|r}'}
$$
$$
\frac{d\sigma_{ni|r}'}{\sigma_{ni|r}'}=\gamma\frac{dv_{ni|r}'}{v_{ni|r}'}-\gamma\sum_{h=1}^{N^{D}}\frac{\left(v_{nh|r}'\right)^{\gamma}}{\sum_{j=1}^{N^{D}}\left(v_{nj|r}'\right)^{\gamma}}\frac{dv_{nh|r}'}{v_{nh|r}'}
$$
$$
\frac{d\sigma_{ni|r}'}{\sigma_{ni|r}'}=\gamma\frac{dv_{ni|r}'}{v_{ni|r}'}-\gamma\sum_{h=1}^{N^{D}}\sigma_{nh|r}'\frac{dv_{nh|r}'}{v_{nh|r}'}
$$
**
which summarizes the overall effect on labor reallocation shares as a combination between the change in the attractiveness of the destination location $i$ compared to the change in the attractiveness of all other locations. Similarly, totally differentiating sectoral flows, we obtain, **
$$
d\sigma_{rs|i}'=\nu\frac{\left(w_{is|r}'\right)^{\nu}}{\sum_{t=1}^{S}(w_{itr}')^{\nu}}\frac{dw_{is|r}'}{w_{is|r}'}-\nu\sum_{t=1}^{S}\frac{\left(w_{is|r}'\right)^{\nu}}{\sum_{t=1}^{S}(w_{itr}')^{\nu}}\frac{\left(w_{it|r}'\right)^{\nu}}{\sum_{t=1}^{S}(w_{itr}')^{\nu}}\frac{dw_{it|r}'}{w_{it|r}'}
$$
$$
\frac{d\sigma_{rs|i}'}{\sigma_{rs|i}'}=\nu\frac{dw_{is|r}'}{w_{is|r}'}-\nu\sum_{t=1}^{S}\frac{\left(w_{it|r}'\right)^{\nu}}{\sum_{t=1}^{S}(w_{itr}')^{\nu}}\frac{dw_{it|r}'}{w_{it|r}'}
$$
$$
\frac{d\sigma_{rs|i}'}{\sigma_{rs|i}'}=\nu\frac{dw_{is|r}'}{w_{is|r}'}-\nu\sum_{t=1}^{S}\sigma_{rt|i}'\frac{dw_{it|r}'}{w_{it|r}'}
$$
**
which summarizes the overall effect on sectoral labor reallocation shares as a combination between the change in the attractiveness of the destination sector $s$ compared to changes in the attractiveness of all other sectors.
### Second-period equilibrium with endogenous labor reallocation
In this subsection I characterize the general equilibrium which extends the static equilibrium above to allow for the endogenous allocation of labor across space. This definition of the equilibrium is appropriate for the second period: It extends the definition of the static equilibrium by allowing for an endogenous labor reallocation choice given the initial labor allocations in the previous period.
Conditional on the measure of workers in each location in the first period, $[\ell_{n,r}]_{\forall(n,r)\in\mathbb{D}\times\mathbb{S}}$, and for the second period, foreign endowments, $[e_{l}']_{\forall l\in\mathbb{F}}$, the national external trade deficit $\bar{d}'$, a fixed domestic housing supply, $[H_{n}']_{\forall n\in\mathbb{D}}$ , an fixed assignment of producitivities across domestic locations, $[z_{n}']_{\forall n\in\mathbb{D}}$ and marginal costs across foreign locations, $[mc_{l,r}']_{\forall(l,r)\in\mathbb{F}\times\mathbb{S}}$, as well as a specification of the domestic geography of the economy, $[\tau_{ni}']_{\forall(n,i)\in\mathbb{D}x\mathbb{D}}$ and the foreign geography of the economy, $[\tau_{nl}',\tau_{ln}']_{\forall(n,l)\in\mathbb{D}x\mathbb{F},\forall(l,n)\in\mathbb{F}x\mathbb{D}}$, the equilibrium in the first period is a set of prices $[p_{ni,r}',p_{nl,r}',p_{ln,r}']$, housing rental rates $[r_{n}']$, wages in each domestic location $[w_{n,r}']_{\forall(n,r)\in\mathbb{D}\times\mathbb{S}}$, the measure of workers in each location, $[\ell_{n}']_{\forall n\in\mathbb{D}}$, as well as the foreign and domestic expenditure shares of domestic locations, $[s_{ni,r}',s_{nl,r}']_{\forall(n,i,r)\in\mathbb{D}x\mathbb{D}\times\mathbb{S},\forall(n,l,r)\in\mathbb{D}x\mathbb{F}\times\mathbb{S}}$, and the expenditure of foreign locations on domestic varieties, $[s_{ln,r}']_{\forall(l,n,r)\in\mathbb{F}x\mathbb{D}\times\mathbb{S}}$ , and the reallocation shares of workers across the domestic economy,$[\sigma_{ni}']_{\forall(n,i)\in\mathbb{D}x\mathbb{D}}$, such that,
1. Given domestic and foreign prices in domestic locations, $[p_{ni,r}',p_{nl,r}']_{\forall(n,i,r)\in\mathbb{D}x\mathbb{D}\times\mathbb{S},\forall(n,l,r)\in\mathbb{D}x\mathbb{F}\times\mathbb{S}}$, wages in each domestic location $[w_{n,r}']_{\forall(n,r)\in\mathbb{D}\times\mathbb{S}}$, and the assumption that expenditure on land is locally redistributed lump sum which defines the disposable income as in ([Equation](#eq:disposable_income)), the domestic household chooses optimally where to relocate, such that,
$$
\sigma_{ni,rs}'=\sigma_{ni|r}'\sigma_{rs|i}'
$$
$$
\sigma_{ni|r}'=\frac{\left(v_{ni|r}'\right)^{\nu}}{\sum_{j}\left(v_{nj|r}'\right)^{\nu}}\qquad\sigma_{rs|i}'=\frac{(w_{is}'/\mu_{rs})^{\gamma}}{\sum_{t}(w_{it}'/\mu_{rt})^{\gamma}}
$$
2. Given domestic and foreign prices in domestic locations, $[p_{ni,r}',p_{nl,r}']_{\forall(n,i,r)\in\mathbb{D}x\mathbb{D}\times\mathbb{S},\forall(n,l,r)\in\mathbb{D}x\mathbb{F}\times\mathbb{S}}$ as well as domestic prices in foreign locations $[p_{ln,r}']_{\forall(l,n,r)\in\mathbb{F}x\mathbb{D}\times\mathbb{S}}$, wages in each domestic location $[w_{n,r}']_{\forall(n,r)\in\mathbb{D}\times\mathbb{S}}$, and the assumption that expenditure on land is locally redistributed lump sum which defines the disposable income as in ([Equation](#eq:disposable_income)), the domestic and foreign households choose expenditure shares to maximize their respective utility ([Equation](#eq:utility_function)) subject to their budget constraint, with the respective expenditure shares being given by,
$$
\begin{aligned}
s_{ni,r}' & =\alpha_{r}\left(1-\delta\right)\frac{\left(p_{ni,r}'\right)^{1-\sigma_{r}}}{\sum_{i=1}^{N^{D}}\frac{1}{\bar{d}}\left(p_{ni,r}'\right)^{1-\sigma_{r}}+\sum_{l=1}^{N^{F}}\left(p_{nl,r}'\right)^{1-\sigma_{r}}}
\end{aligned}
$$
$$
s_{nl,r}'=\alpha_{r}\left(1-\delta\right)\frac{\left(p_{nl,r}'\right)^{1-\sigma_{r}}}{\sum_{i=1}^{N^{D}}\frac{1}{\bar{d}}\left(p_{ni,r}'\right)^{1-\sigma_{r}}+\sum_{l=1}^{N^{F}}\left(p_{nl,r}'\right)^{1-\sigma_{r}}}
$$
$$
\begin{aligned}
s_{li,r}' & =\alpha_{l,r}\frac{\left(p_{li,r}'\right)^{1-\sigma_{r}}}{\sum_{j=1}^{N^{D}}\left(p_{lj,r}'\right)^{1-\sigma_{r}}}
\end{aligned}
$$
3. Firms optimize their profits via marginal cost pricing, such that domestic and foreign prices are given by,
$$
p_{ni,r}'=\frac{\tau_{ni}w_{i,r}'}{z_{i,r}'}
$$
$$
p_{nl,r}'=\tau_{nl}mc_{nl,r}'
$$
4. In each domestic location the labor income equals expenditure on goods produced in that location with expenditures originating both from domestic and foreign locations:
$$
w_{i,r}'\ell_{i,r}'=\sum_{n=1}^{N^{D}}s_{ni,r}'\left(\sum_{r=1}^{S}e_{n,r}'\ell_{n,r}'\right)+\sum_{l=1}^{N^{F}}s_{li,r}'e_{l}'
$$
5. Trade is balanced domestically, but unbalanced externally,
$$
\bar{d}'\left(\sum_{r=1}^{S}e_{n,r}'\ell_{n,r}'\right)=\sum_{r=1}^{S}\left(\sum_{i=1}^{N}s_{ni,r}'\left(\sum_{r=1}^{S}e_{n,r}'\ell_{n,r}'\right)+\sum_{l=1}^{N^{F}}s_{nl,r}'\left(\bar{d}'e_{n}'\ell_{n}'\right)\right)
$$
6. The labor market clearing condition requires that the measure of workers in the second period is equal to all the incoming labor flows, i.e. **
$$
\ell_{i,s}^{'}=\sum_{r=1}^{S}\sum_{n=1}^{N}\sigma_{ni,rs}\ell_{n,r}
$$
**
7. Housing market clears
$$
H_{n}r_{n}'=\delta\left(\sum_{r=1}^{S}e_{n,r}'\right)
$$
### Aggregate Welfare
In this subsection, I will derive an expression for the change in aggregate welfare **across** all domestic locations in the second period, taking into account the endogenous reallocation of workers and how the reallocation itself depends on the initial allocation of workers in the first period. In order to do so, I proceed in two steps: In a first step I will assume that rather than the initial allocation of workers in the first period being fixed, it instead by thought of as a separate allocation problem, where ex-ante homogenous household make a choice where they would like to be located in the first period. Following the convention in the literature, I stipulate this as a discrete optimization problem where households receive location-specific extreme value distributed preference shock that gives rise to and matches the observed allocation of workers across space as in Redding ([2012](#ref-RePEc:nbr:nberwo:18008)). In a second step the household then faces a second subsequent location choice problem that mirrors the re-allocation problem in section ([Section](#subsec:Labor-Reallocation)). This way of characterizing the problem allows me to derive a closed-form expression for the expected utility in the second period of a hypothetical aggregate household that incorporates the dependence of the economy on the initial allocation of labor in the first period and takes migration costs explicitly into account.
The welfare expression that corresponds to the first step, and expresses the value of being able to choose any of the domestic location by summing up over the migration value of each one location, that is,
$$
\mathcal{W}\equiv E\left(\Omega_{n,r}\right)=\delta\left[\sum_{n=1}^{N^{D}}\sum_{r=1}^{S}\left(\tilde{\rho}_{n,r}\Omega_{n,r}\right)^{\epsilon}\right]^{1/\epsilon}
$$
where $\delta=\Gamma\left(\frac{\epsilon}{\epsilon-1}\right)$ and $\Gamma(\cdot)$ is the gamma function and we impose $\epsilon>1$ to obtain a finite value for the expected utility. Additionally, $\tilde{\rho}$ corresponds to an amenity shifter that is chosen to exactly fit the distribution of the population across space. Following Redding ([2012](#ref-RePEc:nbr:nberwo:18008)), I use this measure of expected utility as a proxy for aggregate welfare. Conditional on the initial allocation, workers face a reallocation choice subject to switching costs and a new set of independently drawn extreme value distributed preferences shocks as stated above and as before $\Omega_{n}'$ corresponds to the expected utility of that choice,
$$
\Omega_{n,r}'=\tilde{\delta}\left[\sum_{j=1}^{N^{D}}\left(v_{nj|r}'\right)^{\gamma}\right]^{1/\gamma}
$$
where again $\delta=\Gamma\left(\frac{\gamma}{\gamma-1}\right)$ and $\Gamma(\cdot)$ is the gamma function and we impose $\gamma>1$ to obtain a finite value for the expected utility. Totally differentiating the welfare expression, we obtain,
$$
\begin{aligned}
\frac{d\mathcal{W}'}{\mathcal{W}'} & =\sum_{n=1}^{N^{D}}\sum_{r=1}^{S}\frac{d\Omega_{n,r}'}{\Omega_{n,r}'}\times\frac{\left(\tilde{\rho}_{n,r}\Omega_{n,r}\right)^{\epsilon}}{\sum_{n=1}^{N^{D}}\sum_{r=1}^{S}\left(\tilde{\rho}_{n,r}\Omega_{n,r}\right)^{\epsilon}}\\
& =\sum_{n=1}^{N^{D}}\sum_{r=1}^{S}\frac{d\Omega_{n,r}'}{\Omega_{n,r}'}\times\pi_{i,r}
\end{aligned}
$$
where $\pi_{i,r}=\frac{\ell_{i,r}}{\sum_{i}\sum_{r}\ell_{i,r}}$ is the population share observed in the data in the baseline period. Integrating, we obtain,
$$
\begin{aligned}\int_{\mathcal{W}^{0}}^{\mathcal{W}^{1}}\frac{\mathrm{d}\mathcal{W}'}{\mathcal{W}'} & =\sum_{n=1}^{N^{D}}\sum_{r=1}^{S}\pi_{i,r}\times\int_{\Omega_{n,r}^{0}}^{\Omega_{n,r}^{1}}\frac{d\Omega_{n,r}'}{\Omega_{n,r}'}\\
\ln\left(\frac{\mathcal{W}^{1}}{\mathcal{W}^{0}}\right) & =\sum_{n=1}^{N^{D}}\sum_{r=1}^{S}\pi_{n,r}\ln\left(\frac{\Omega_{n,r}^{1}}{\Omega_{n,r}^{0}}\right)\\
\left(\frac{\mathcal{W}^{1}}{\mathcal{W}^{0}}\right) & =\prod_{n=1}^{N^{D}}\prod_{r=1}^{S}\left(\frac{\Omega_{n,r}^{1}}{\Omega_{n,r}^{0}}\right)^{\pi_{n,r}}
\end{aligned}
$$
From we can construct an expression for changes in the option value $\Omega_{n,r}$,
$$
\hat{\Omega}_{n,r}=\hat{v}_{nn|r}\left(\hat{\sigma}_{nn|r}\right)^{-\frac{1}{\gamma}}
$$
which only depends on the
$$
\hat{v}_{nn|r}=\hat{\delta}_{n}\hat{\Pi}_{n|r}
$$
which only depends on the
$$
\hat{\Pi}_{n,r}=\hat{w}_{nr|r}\left(\hat{\sigma}_{rr|i}\right)^{-\frac{1}{\nu}}
$$
$$
\hat{\Omega}_{n,r}=\hat{u}_{nr|r}\left(\hat{\sigma}_{rr|i}\right)^{-\frac{1}{\nu}}\left(\hat{\sigma}_{nn|r}\right)^{-\frac{1}{\gamma}}
$$
$$
\left(\frac{\mathcal{W}^{1}}{\mathcal{W}^{0}}\right)=\prod_{n=1}^{N^{D}}\prod_{r=1}^{S}\left(\underbrace{\left(\frac{\sigma_{nn|r}^{1}}{\sigma_{nn|r}^{0}}\right)^{-\frac{1}{\gamma}}}_{\text{Spatial Flows}}\underbrace{\left(\frac{\sigma_{rr|n}^{1}}{\sigma_{rr|n}^{0}}\right)^{-\frac{1}{\nu}}}_{\text{Sectoral Flows}}\frac{u_{nr|r}^{1}}{u_{nr|r}^{0}}\right)^{\pi_{n,r}}
$$
where $\sigma_{nn|r}^{1}$ represents the share of workers initially located in province $n$ and working sector $r$ and deciding to remain in that province, while $\sigma_{rr|n}^{1}$ represents the share of workers who in the second period will be located in province $n$, were initially attached to sector $r$and decide to remain in sector $r$. Intuitively, if more workers decide to either change their sector or their location, then this is informative about the option value of a spatial or sectoral change to have increased, relative to the remain option. In other words, the remain share (to the power of the negative inverse of the labor supply elasticity) is proportional to changes in the option-value and therefore a sufficient statistic for welfare changes that arise due to the ability of the worker being able to reallocate. This approach is intimately related to the argument that conditional choice probabilities can be used to infer continuation values in dynamic discrete choice problems ([Hotz and Miller 1993](#ref-10.2307/2298122)). Even though, it is here stated in the context of two period model, the approach is much more general and a similar expression for welfare can be derived for multi-period or infinite horizon models. The final term represents cross-sectional improvements in the indirect utility of workers across locations. This term can be constructed using the tools by Arkolakis et al. ([2012](#ref-RePEc:aea:aecrev:v:102:y:2012:i:1:p:94-130)) and Ossa ([2015](#ref-RePEc:eee:inecon:v:97:y:2015:i:2:p:266-277)). Starting from the expenditure shares, we can solve for sectoral price indices,
$$
\begin{aligned}
p_{n,r} & =p_{ni,r}\left(\frac{s_{ni,r}}{\alpha_{r}\left(1-\delta\right)}\right)^{\frac{1}{\sigma_{r}-1}}
\end{aligned}
$$
constructing aggregate price indices,
$$
\begin{aligned}
p_{n} & =\prod_{r=1}^{S}\left(p_{n,r}\right)^{\alpha_{r}}\\
& =\prod_{r=1}^{S}\left(p_{ni,r}\left(\frac{s_{ni,r}}{\alpha_{r}\left(1-\delta\right)}\right)^{\frac{1}{\sigma_{r}-1}}\right)^{\alpha_{r}}\\
& =\prod_{r=1}^{S}\left(\left(w_{n,r}\right)^{\alpha_{r}}\left(\frac{s_{nn,r}}{\alpha_{r}\left(1-\delta\right)}\right)^{\frac{\alpha_{r}}{\sigma_{r}-1}}\right)\\
\end{aligned}
$$
rewriting this in changes,
$$
\begin{aligned}
\hat{p}_{n} & =\prod_{r=1}^{S}\left(\left(\hat{w}_{n,r}\right)^{\alpha_{r}}\left(\hat{s}_{nn,r}\right)^{\frac{\alpha_{r}}{\sigma_{r}-1}}\right)
\end{aligned}
$$
noticing that utility in changes can be written as,
$$
\hat{u}_{n,r}=\hat{e}_{n,r}\hat{\bar{d}}\hat{p}_{n}^{(\delta-1)}\hat{r}_{n}^{-\delta},
$$
and substituting, we obtain,
$$
\hat{u}_{n,r}=\hat{e}_{n,r}\hat{d}\hat{r}_{n}^{-\delta}\prod_{r=1}^{S}\left(\left(\hat{w}_{n,r}\right)^{(\delta-1)\alpha_{r}}\left(\hat{s}_{nn,r}\right)^{\frac{(\delta-1)\alpha_{r}}{\sigma_{r}-1}}\right)
$$
$$
\hat{u}_{n,r}=\hat{w}_{n,r}\hat{d}\hat{r}_{n}^{-\delta}\prod_{r=1}^{S}\left(\left(\hat{w}_{n,r}\right)^{(\delta-1)\alpha_{r}}\left(\hat{s}_{nn,r}\right)^{\frac{(\delta-1)\alpha_{r}}{\sigma_{r}-1}}\right)
$$
$$
\hat{u}_{n,r}=\frac{\left(\hat{w}_{n,r}\right)^{\delta}}{\left(\hat{r}_{n}\right)^{\delta}}\frac{\left(\hat{w}_{n,r}\right)^{(1-\delta)}}{\prod_{r=1}^{S}\left(\hat{w}_{n,r}\right)^{(1-\delta)\alpha_{r}}}\prod_{r=1}^{S}\left(\hat{s}_{nn,r}\right)^{\frac{(\delta-1)\alpha_{r}}{\sigma_{r}-1}}
$$
substituting into above formula gives us the expression in the main text,
$$
\left(\frac{\mathcal{W}^{1}}{\mathcal{W}^{0}}\right)=\prod_{n=1}^{N^{D}}\prod_{r=1}^{S}\left(\underbrace{\left(\frac{\sigma_{nn|r}^{1}}{\sigma_{nn|r}^{0}}\right)^{-\frac{1}{\gamma}}}_{\text{Spatial Flows}}\underbrace{\left(\frac{\sigma_{rr|n}^{1}}{\sigma_{rr|n}^{0}}\right)^{-\frac{1}{\nu}}}_{\text{Sectoral Flows}}\underbrace{\left(\frac{r_{n}^{1}}{r_{n}^{0}}\right)^{-\delta}}_{\text{Housing Cost}}\underbrace{\prod_{t=1}^{S}\left(\frac{s_{nn,t}^{1}}{s_{nn,t}^{0}}\right)^{-\frac{\left(1-\delta\right)\alpha_{t}}{\sigma_{t}-1}}}_{\text{ACR Gains}}\right)^{\pi_{n,r}}
$$
### Trade Imbalances
To reflect the change in trade deficits in the analysis, I incorporate exogenous trade imbalances as in Dekle, Eaton, and Kortum (2007) and Caliendo and Parro ([2015](#ref-RePEc:oup:restud:v:82:y:2015:i:1:p:1-44)). However, instead of an additive formulation, I instead model trade balances as a multiplicative scalar that adjusts the disposable income available to the representative agent. Furthermore, I distinguish between domestic and external trade, and while external trade might be unbalanced, domestic trade is assumed to be balanced. Consider the domestic and external trade balance condition separately. As before, trade is balanced domestically, implying that domestic income is equal to domestic expenditure,
$$
d_{1}y_{n}=\sum_{r=1}^{S}\left(\sum_{i=1}^{N}s_{ni,r}y_{n}\right)
$$
where $d_{1}$ is defined as the fraction of income that is being derived from domestic sales and $y_{n}$ denotes the disposable income, such that,
$$
y_{n}=\sum_{r=1}^{S}e_{n,r}\ell_{n,r}
$$
Externally, trade is possibly unbalanced, such that expenditures on foreign goods might be below or above income derived from foreign goods, i.e.
$$
\left(1-d_{1}\right)y_{n}=d_{2}\times\sum_{r=1}^{S}\sum_{l=1}^{N^{F}}s_{nl,r}y_{n}
$$
where the left hand side denotes income derived from foreign sales and the right hand side denotes expenditures on foreign goods. As before, $d_{1}$, is the fraction of income that is being derived domestically. On the right hand side, $d_{2}$ is the proportion of foreign income that is being expended on foreign goods. where $d_{2}$ is defined as,
$$
d_{2}=\frac{\sum_{l=1}^{N^{F}}\sum_{r=1}^{S}X_{nl.r}}{\sum_{l=1}^{N^{F}}\sum_{r=1}^{S}X_{ln,r}}
$$
To derive the total price index, combine,
$$
y_{n}=\sum_{r=1}^{S}\sum_{i=1}^{N}s_{ni,r}y_{n}+d_{2}\times\sum_{r=1}^{S}\sum_{l=1}^{N^{F}}s_{nl,r}y_{n}
$$
Dividing by income and noticing that $s_{ni,r}=\left(p_{ni,r}\right)^{1-\sigma_{r}}p_{n,r}^{\sigma_{r}-1}$, we obtain,
$$
p_{n,r}^{1-\sigma}=\sum_{i=1}^{N^{D}}p_{ni,r}^{1-\sigma}+d_{2}\sum_{l=1}^{N^{F}}p_{nl,r}^{1-\sigma}
$$
which allows us to express the price index in terms of the weighted domestic and external prices, i.e.
$$
p_{n,r}=\left(\sum_{i=1}^{N^{D}}p_{ni,r}^{1-\sigma}+d_{2}\sum_{l=1}^{N^{F}}p_{nl,r}^{1-\sigma}\right)^{\frac{1}{1-\sigma}}
$$
This implies that the indirect utility and the optimal price index of this problem is given by,
$$
u_{n,r}=\frac{\rho_{n}e_{n,r}}{p_{n}^{(1-\delta)}r_{n}^{\delta}},\quad p_{n}=\prod_{r=1}^{S}\left(p_{n,r}\right)^{\alpha_{r}}\quad p_{n,r}=\left[\sum_{i=1}^{N^{D}}\left(p_{ni,r}\right)^{1-\sigma_{r}}+d_{2}\sum_{l=1}^{N^{F}}\left(p_{nl,r}\right)^{1-\sigma_{r}}\right]^{\frac{1}{1-\sigma_{r}}}
$$
Combining and factoring out the trade imbalance term we obtain,
$$
u_{n,r}=d_{2}^{-\sum_{r}\frac{(1-\delta)\alpha_{r}}{1-\sigma_{r}}}\frac{\rho_{n}e_{n,r}}{r_{n}^{\delta}\prod_{r=1}^{S}\left(\left(\sum_{i=1}^{N^{D}}\frac{1}{d_{2}}p_{ni}^{1-\sigma_{r}}+\sum_{l=1}^{N^{F}}p_{nl}^{1-\sigma_{r}}\right)^{\frac{(1-\delta)\alpha_{r}}{1-\sigma_{r}}}\right)}
$$
Following the same derivations as before,
$$
\left(\frac{\mathcal{W}^{1}}{\mathcal{W}^{0}}\right)=\underbrace{\left(\frac{d_{2}^{1}}{d_{2}^{0}}\right)^{-\sum_{r}\frac{(1-\delta)\alpha_{r}}{1-\sigma_{r}}}}_{\text{Deficit Adjustment}}\prod_{n=1}^{N^{D}}\prod_{r=1}^{S}\left(\underbrace{\left(\frac{\sigma_{nn|r}^{1}}{\sigma_{nn|r}^{0}}\right)^{-\frac{1}{\gamma}}}_{\text{Spatial Flows}}\underbrace{\left(\frac{\sigma_{rr|n}^{1}}{\sigma_{rr|n}^{0}}\right)^{-\frac{1}{\nu}}}_{\text{Sectoral Flows}}\underbrace{\left(\frac{\tilde{r}_{n}^{1}}{\tilde{r}_{n}^{0}}\right)^{-\delta}}_{\text{Housing Cost}}\underbrace{\prod_{t=1}^{S}\left(\frac{\tilde{s}_{nn,t}^{1}}{\tilde{s}_{nn,t}^{0}}\right)^{-\frac{\left(1-\delta\right)\alpha_{t}}{\sigma_{t}-1}}}_{\text{ACR Gains}}\right)^{\pi_{n,r}}
$$
### Deriving an Empirical Specification to estimate the Distance Elasticity
This subsection shows how the model in this section can be used to derive an empirical specification as used in the reduced form section in the paper. Specifically, we derive the impact of an increase in foreign expenditures on domestic locations taking domestic trade cost into account. I start with the goods market clearing condition,
$$
w_{i,r}\ell_{i,r}=\sum_{n=1}^{N^{D}}s_{ni,r}\left(\sum_{r=1}^{S}e_{n,r}\ell_{n,r}\right)+\sum_{l=1}^{N^{F}}s_{li,r}e_{l}
$$
considering the case where only foreign expenditures vary, $d\ln e_{l}\neq0$, totally differentating, I obtain,
$$
\frac{dy_{i,r}}{y_{i,r}}=\sum_{l=1}^{N^{F}}\frac{s_{li,r}e_{l}}{y_{i,r}}\frac{de_{l}}{e_{l}}
$$
which represents the impcat of changes in foreign expenditures on local income as a weighted sum over percentage changes in foreign expenditures, where the weights are given by the share of revenue that is due to foreign expenditures, $\frac{s_{li}e_{l}}{y_{i,r}}$. Since data on region specific exports to foreign locations is not available, I will use the structural of the model to recover a representation of region-specific export shares that depends on the share of a location in national employment and its geographical location vis-a-vis the destination market only. In order to derive this, define the hypothetical market share of a location in the absence of domestic frictions as,
$$
\tilde{s}_{i,r}=\alpha_{r}\frac{p_{i,r}^{1-\sigma_{,r}}}{\sum_{n=1}^{N^{D}}p_{n,r}^{1-\sigma_{,r}}}
$$
Notice that I can now derive the deviation from this hypothetical market share that is due to trade costs, as,
$$
\begin{aligned}
\frac{s_{li,r}}{\tilde{s}_{i,r}} & =\left(\frac{\alpha_{l,r}}{\alpha_{r}}\right)\left(\frac{p_{li,r}}{p_{i,r}}\right)^{1-\sigma_{,r}}\times\left(\frac{\sum_{n=1}^{N^{D}}p_{ln,r}^{1-\sigma}}{\sum_{n=1}^{N^{D}}p_{n,r}^{1-\sigma}}\right)^{-1}\\
& =\left(\frac{\alpha_{l,r}}{\alpha_{r}}\right)\left(\tau_{li}\right)^{1-\sigma}\times\left(\frac{\sum_{n=1}^{N^{D}}p_{ln,r}^{1-\sigma}}{\sum_{n=1}^{N^{D}}p_{n,r}^{1-\sigma}}\right)^{-1}\\
& =\left(\frac{\alpha_{l,r}}{\alpha_{r}}\right)\left(\tau_{li}\right)^{1-\sigma}\times\left(\sum_{n=1}^{N^{D}}\frac{p_{ln,r}^{1-\sigma}}{\sum_{n=1}^{N^{D}}p_{n,r}^{1-\sigma}}\right)^{-1}\\
& =\left(\frac{\alpha_{l,r}}{\alpha_{r}}\right)\left(\tau_{li}\right)^{1-\sigma}\times\left(\sum_{n=1}^{N^{D}}\tau_{ln}^{1-\sigma}\frac{p_{n,r}^{1-\sigma}}{\sum_{n=1}^{N^{D}}p_{n,r}^{1-\sigma}}\right)^{-1}\\
& =\left(\frac{\alpha_{l,r}}{\alpha_{r}}\right)\left(\tau_{li}\right)^{1-\sigma}\times\left(\sum_{n=1}^{N^{D}}\tau_{ln}^{1-\sigma}\tilde{s}_{n,r}\right)^{-1}
\end{aligned}
$$
Returning to the expression for the differentiated market clearing condition, I have,
$$
\begin{aligned}
\frac{dy_{i,r}}{y_{i,r}} & =\sum_{l=1}^{N^{F}}\frac{s_{li,r}e_{l}}{y_{i,r}}\frac{de_{l}}{e_{l}}\\
& =\sum_{l=1}^{N^{F}}\frac{e_{l}}{y_{i,r}}\tilde{s}_{i,r}\frac{s_{li,r}}{\tilde{s}_{i,r}}\frac{de_{l}}{e_{l}}
\end{aligned}
$$
substituting from above,
$$
\begin{aligned}
\frac{dy_{i,r}}{y_{i,r}} & =\sum_{l=1}^{N^{F}}\frac{e_{l}}{y_{i,r}}\left(\left(\frac{\alpha_{l,r}}{\alpha_{r}}\right)\frac{\left(\tau_{li}\right)^{1-\sigma}\tilde{s}_{i,r}}{\sum_{n=1}^{N^{D}}\tau_{ln}^{1-\sigma}\tilde{s}_{n,r}}\right)\frac{de_{l}}{e_{l}}
\end{aligned}
$$
where we can empirically approximate the hypothetical market shares with the observed labor share of that location and trade costs are approximated with the inverse of distance along the transportation network. This gives,
$$
\begin{aligned}
d\ln y_{i,r} & \approx\sum_{l=1}^{N^{F}}\frac{e_{l}}{y_{i,r}}\left(\frac{dist_{li}^{-1}\pi_{i,r}}{\sum_{n=1}^{N^{D}}dist_{ln}^{-1}\pi_{n,r}}\right)d\ln e_{l}
\end{aligned}
$$
where $\pi_{ir}=\ell_{ir}/\bar{\ell}_{r}$ is the share of workers in a given location and where $\frac{e_{l}}{y_{i,r}}$ can be readily constructed from data. Similar in spirit to Autor et al. ([2013](#ref-10.1257/aer.103.6.2121)) I define a trade shock exposure variable,
$$
TE_{i,r}\equiv\sum_{l=1}^{N^{F}}\frac{e_{l}}{y_{i,r}}\left(\frac{dist_{li}^{-1}\pi_{i,r}}{\sum_{n=1}^{N^{D}}dist_{ln}^{-1}\pi_{n,r}}\right)\Delta\ln e_{l}
$$
As an approximation of the labor market reallocation, I will use the geographical mobility model from section [Section](#subsec:Labor-Reallocation) to derive an empirical specification that exploits observable geographical distance, but incorporating trade exposure that is driven by sectoral specialization. For this purpose we take an average across the sectoral trade exposure measures,
$$
TE_{i}\equiv\sum_{r}\pi_{r|i}TE_{i,r}
$$
## Details on Data Sources
I have assembled a unique dataset that provides disaggregated information on the distribution of economic activity across regions and sectors, consumer prices, factor reallocation and external trade for the period between 1910-1920. The dataset draws on multiple historical sources some of which were digitized specifically for this project, others (such as the migration and price data) had been previously digitized, but were matched to the other data sources to give a comprehensive view of the evolution of the Spanish economy during that period. In this section I will introduce the different data series that are contained in the dataset, present their sources, describe the digitization effort and how they were matched together into one cohesive dataset.
> **Example Page: Ministerio de Trabajo (1927)**
>
> Figure available in the [PDF](/research/spoils_of_war.pdf).
### Provincial Wage Data from Annual Reports of the Instituto para Reformes Sociales
Data on wages across provinces and sectors can be obtained at a yearly frequency from the annual publications of the Institute for Social Reforms ([Instituto de Reformas Sociales 1911](#ref-1910memoria), [1912](#ref-1911memoria), [1913](#ref-1912memoria), [1914](#ref-1913memoria), [1915](#ref-1914memoria), [1916](#ref-1915memoria), [1917](#ref-1916memoria), [1918](#ref-1917memoria), [1919](#ref-1918memoria), [1920](#ref-1919memoria), [1921](#ref-1920memoria)). The publications contain information on workplace conditions collected through a large-scale effort to collect information on manufacturing workers across all provinces and industries. At the end of the decade, in 1920, the survey employed more than 80 full time investigators who dispatched more than 18.000 documents summarizing their reports from visits across all Spanish Regions. The publications summarize work hours, infractions of labor laws, and hourly wages. They also offer disaggregated information across industries and gender. For the purpose of this study, I digitized the hourly wages of workers across regions and industries for the years between 1910-1920.
> **Summary Statistics: Provincial Wages Panel Data**
---- ------------- ----------- ----------- ------------- ------------- ---------------- ---------------- ------------------ ------------------
Province Male_1914 Male_1919 Female_1914 Female_1919 Male_Wage_1914 Male_Wage_1919 Female_Wage_1914 Female_Wage_1919
1 Madrid 10204 23409 1094 4454 2.88 4.30 1.40 2.13
2 Badajoz 630 4231 164 1412 2.75 2.98 1.00 0.90
3 Caceres 4807 3556 667 807 1.96 3.70 0.70 1.00
4 Ciudad_Real 10587 645 2.50 0.75
5 Guadalajara 703 75 2.25 0.75
6 Toledo 602 230 3.00 0.85
7 Barcelona 57323 44791 61759 41259 4.34 7.11 2.01 3.41
8 Gerona 11455 6022 17606 6212 3.21 4.86 1.75 2.56
9 Lerida 4868 1754 3.94 1.86
10 Tarragona 4136 2868 6068 3818 2.84 5.84 1.40 3.33
11 Vizcaya 20391 10328 3173 3264 3.67 4.80 1.88 2.46
12 Alava 974 464 214 58 2.94 3.87 1.39 1.89
13 Guipuzcoa 7414 2493 3.44 1.59
14 Logrono 2809 8230 3190 2342 2.40 3.87 1.42 1.85
15 Santander 4298 10687 1300 1080 3.16 5.23 1.58 2.72
16 Oviedo 14853 12421 4327 3307 3.00 6.00 1.75 2.00
17 Coruna 9388 10561 8701 9582 2.40 3.75 1.50 1.50
18 Leon 4807 3615 1029 865 2.50 3.75 1.25 1.25
19 Lugo 438 2321 14 593 2.50 3.00 0.75 1.73
20 Orense 503 360 4 22 2.50 4.00 1.50 1.50
21 Pontevedra 6006 5377 3774 2905 2.50 4.00 1.25 1.75
22 Granada 14155 7756 5626 1924 2.50 3.94 1.03 1.33
23 Almeria 1997 5279 390 1072 2.75 3.50 1.00 1.00
24 Cadiz 2448 11463 876 2042 3.00 2.88 1.87 1.55
25 Cordoba 15000 4443 890 1376 2.25 3.30 1.19 1.20
26 Huelva 24791 15138 1969 2148 2.86 3.51 1.26 1.55
27 Jaen 1437 4 2.50 1.25
28 Malaga 23801 12303 8312 3545 3.30 3.50 1.09 1.75
29 Sevilla 9997 5997 11978 2586 3.10 3.96 1.57 1.83
30 Valencia 11799 12815 12745 22541 2.70 4.26 1.45 2.07
31 Albacete 838 616 2.50 1.20
32 Alicante 12263 2388 11965 5311 2.40 4.04 1.25 1.91
33 Castellon 3280 1813 1884 3745 2.20 3.69 0.75 1.53
34 Cuenca 313 2477 8 2890 2.50 4.40 0.90 2.00
35 Murcia 10527 4785 3588 9058 2.55 3.05 1.20 1.56
36 Valladolid 3369 4568 1556 6253 3.00 4.00 1.00 1.25
37 Avila 192 1077 28 1214 2.50 3.50 0.75 1.50
38 Burgos 685 2821 133 3459 2.50 3.50 1.00 1.50
39 Palencia 1924 2849 344 3252 2.50 3.50 1.00 1.25
40 Salamanca 657 1839 67 2055 2.00 3.50 1.25 1.25
41 Segovia 4514 4470 621 4752 2.50 4.00 1.00 1.50
42 Zamora 762 1515 283 2332 2.50 3.50 1.00 1.25
43 Zaragoza 7135 9261 1865 11366 3.50 8.60 1.50 2.75
44 Huesca 1838 2841 41 3003 2.50 4.50 1.25 2.25
45 Navarra 5242 3418 1607 4162 3.00 4.00 1.10 1.50
46 Soria 438 266 1 310 2.75 3.75 1.50 1.00
47 Teruel 1589 1702 38 1786 3.00 4.00 1.00 1.50
---- ------------- ----------- ----------- ------------- ------------- ---------------- ---------------- ------------------ ------------------
### Sector-Province Data from Salarios
I obtain information regarding the labor market from two related sources: First a comprehensive industry survey that reports labor quantities and wages across province-sector pairs and covers the years 1914, 1920, 1925 ([Ministerio de Trabajo 1927](#ref-spain1927estadistica)). This industry survey was published by the Ministry for Labor and Industry and is based on surveys conducted at all public firms and large private enterprises in cities that are larger than 20,000 inhabitants (Casanovas 2004). It covers 23 different industries[^25] and 48 different provinces.
> **Summary Statistics: Salarios**
---- ------------- ---------------- ---------------- ------------ ------------
Province wage_mean_1914 wage_mean_1920 labor_1914 labor_1920
1 Alava 0.31 0.64 2774 4107
2 Albacete 0.36 0.65 7897 10057
3 Alicante 0.37 0.71 24615 28456
4 Almeria 0.45 0.69 11908 11607
5 Avila 0.40 0.70 1250 1823
6 Badajoz 0.31 0.47 18296 20664
7 Baleares 0.35 0.64 24744 29143
8 Barcelona 0.46 0.87 259736 320564
9 Burgos 0.36 0.65 1760 2715
10 Caceres 0.26 0.44 8805 11217
11 Cadiz 0.49 0.87 33026 40604
12 Castellon 0.29 0.62 7518 9553
13 Ciudad_Real 0.36 0.63 12618 17545
14 Cordoba 0.36 0.67 25916 33933
15 Coruna 0.40 0.61 29602 30939
16 Cuenca 0.30 0.56 3304 4425
17 Gerona 0.41 0.68 24944 28370
18 Granada 0.37 0.55 12001 11907
19 Guadalajara 4557 4887
20 Guipuzcoa 0.48 0.76 19210 25172
21 Huelva 0.39 0.57 21945 20166
22 Huesca 0.38 0.71 6405 5213
23 Jaen 0.42 0.64 15500 14237
24 Leon 0.43 1.02 9084 11780
25 Lerida 0.41 0.70 6767 8667
26 Logrono 0.37 0.67 8244 8662
27 Lugo 0.32 0.44 3036 4017
28 Madrid 0.44 0.85 81107 93963
29 Malaga 0.45 0.68 19326 25444
30 Murcia 0.38 0.61 27005 29872
31 Navarra 0.39 0.75 8227 10240
32 Orense 0.32 0.50 2871 3784
33 Oviedo 0.46 1.37 42732 68770
34 Palencia 0.39 0.74 5886 8048
35 Pontevedra 0.38 0.62 16057 19262
36 Salamanca 0.30 0.58 12496 13389
37 Santander 0.44 0.87 15708 22859
38 Segovia 0.33 0.60 2881 3457
39 Sevilla 0.40 0.71 44966 63816
40 Soria 0.38 0.56 1393 2211
41 Tarragona 0.51 0.83 10977 13838
42 Teruel 0.37 0.96 4631 5845
43 Toledo 0.38 0.65 5458 8623
44 Valencia 0.31 0.72 67963 71027
45 Valladolid 0.39 0.66 10476 13815
46 Vizcaya 0.41 1.06 32956 42515
47 Zamora 0.31 0.62 1821 3160
48 Zaragoza 0.45 0.96 18443 27657
---- ------------- ---------------- ---------------- ------------ ------------
### Export Data from Annual Export Statistics
Data on external trade for Spain from 1910-1920 can be obtained from the annual statistical publications of the Spanish customs agency ([Dirección General de Aduanas 1911](#ref-estadisticaexterior1910), [1912](#ref-estadisticaexterior1911), [1913](#ref-estadisticaexterior1912), [1914](#ref-estadisticaexterior1913), [1915](#ref-estadisticaexterior1914), [1916](#ref-estadisticaexterior1915), [1917](#ref-estadisticaexterior1916), [1918](#ref-estadisticaexterior1917), [1919](#ref-estadisticaexterior1918), [1920](#ref-estadisticaexterior1919), [1921](#ref-estadisticaexterior1920)). Each year the Spanish customs published two volumes, one containing information on imports and exports across all destination countries and divided by tariff groups - which can be seen as product groups - and the other containing information on imports and exports across tariff groups and reported by the processing custom location. For each observation quantities (typically in kilogram, liters or units) and values are being reported. To obtain overall export values, the Spanish customs agency employed a table of fixed unit prices that are reported alongside the export and import quantities. Overall the publications contains 383 tariff categories and 77 different destination countries.
> **Summary Statistics: Exports (Million Pts)**
---- ---------------- ------ ------ ------ ------ ------ ------ ------ ------ ------ ------
Industry 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919
1 Agriculture 324 347 347 407 303 306 391 384 270 435
2 Books 6 6 7 9 6 5 5 5 4 5
3 Ceramics 2 3 3 3 2 2 3 2 2 2
4 Chemicals 13 18 21 16 15 29 47 51 44 40
5 Construction 3 3 4 4 3 3 3 2 2 2
6 Decoration 0 0 0 0 0 0 0 0 0 0
7 Electricity 0 0 1 1 0 1 1 1 1 1
8 Food 121 128 145 128 109 141 202 194 140 250
9 Forrest 4 3 4 7 3 5 4 4 2 3
10 Furniture 3 4 3 4 3 3 5 3 4 5
11 Garments 30 32 35 31 46 162 140 119 58 91
12 Glass 2 2 4 3 2 5 7 6 5 8
13 Gold 19 18 18 28 17 18 20 16 11 10
14 Leather 0 1 0 0 0 7 2 1 1 2
15 MetalWorks 135 271 144 144 107 128 179 185 132 89
16 Metallurgy 4 4 22 1 6 15 7 5 1 0
17 Mines 181 163 165 175 123 102 116 103 84 79
18 Other 4 4 4 4 4 6 6 6 8 10
19 Paper 7 64 7 7 6 9 15 11 11 10
20 PublicIndustry 0 0 7 0 0 0 0 0 0 0
21 Textiles 48 49 53 52 66 249 165 168 186 193
22 Tobacco 0 0 0 0 0 0 0 0 1 0
23 Transport 1 1 1 1 1 1 9 14 8 9
24 Wood 62 69 66 67 60 58 48 39 33 59
25 0 0 1 1 1 1 1
---- ---------------- ------ ------ ------ ------ ------ ------ ------ ------ ------ ------
> **Summary Statistics: Exports Destinations (A-J, Million Pts)**
------------------------------------- ------ ------ ------ ------ ------ ------ ------ ------ ------ ------
dest_country 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919
Algeria 4 5 6 8 6 15 11 8 4 10
Alhucemas 0 0 0 0 0 0 0 0 0 0
Andorra 0 0 0 0 0 0 0 0 0 0
Argentina 63 82 71 72 41 68 85 95 113 66
Austria-Hungria 5 3 8 8 5 0 0 0 0 2
Belgium 33 103 49 45 21 0 0 0 1 87
Bolivia 0 0 0 0 0 0 0 0 0 0
Brazil 2 2 5 8 3 4 4 6 4 4
Bulgaria 0 0 0 0 0 0 0 0 0
Canary Islands 11 14 14 13 14 17 18 18 17 22
Ceuta 2 3 2 3 5 6 8 9 9 10
Chafarinas 0 0 0 0 0 0 0 0 0 0
Chile 8 10 15 7 6 3 6 10 8 5
China 0 0 0 0 0 0 0 0 0 0
Colombia 2 0 1 3 2 2 6 5 0 1
Costa_rica 1 0 0 1 1 0 0 0 0 0
Cuba 56 60 64 64 52 57 71 62 43 44
Denmark 8 13 4 4 4 9 15 3 3 10
Ecuador 1 1 1 1 1 2 2 0 0 0
Egypt 0 0 0 1 0 2 8 2 2 2
El Salvador 0 0 0 0 0 0 0 0 0 0
Espana 0
Estados_unidos 66 55 67 72 63 63 95 106 50 99
Fernando_poo 1 2 2 2 2 3 3 3 4 3
Finlandia 0 0 0 1 0 0 0 0 0 0
France 187 257 199 246 206 517 534 557 327 450
Germany 55 49 65 74 43 0 0 0 0 5
Gibraltar 2 2 1 1 3 5 3 8 14 8
Gran_bretana 261 299 252 229 231 263 285 202 168 205
Greece 0 0 0 0 0 1 12 2 38 33
Guatemala 0 0 0 0 0 0 0 0 0 0
Haiti 0 0 0 0 0 0 0 0 0
Holanda 55 59 65 70 40 20 8 2 1 25
Honduras 1 0 0 0 0 0 0 0 0 0
Italy 31 42 43 33 49 78 75 54 53 44
Japan 1 0 0 0 0 0 0 0 0 0
Liberia 0 0 0 0 0 0 0 0
Marruecos\_\_tanger_y_zona_internal 0 1 1 2 4 7 4
Marruecos\_\_zona_espanola 0 2 4 4 12 9 6
Marruecos\_\_zona_francesa 10 16 16 9 7 11
Melilla 3 3 5 4 4 5 5 12 13 17
Mexico 12 11 18 16 3 1 2 6 4 7
Monaco 0 0 0 0 0 0
------------------------------------- ------ ------ ------ ------ ------ ------ ------ ------ ------ ------
> **Summary Statistics: Exports Destinations (K-Z, Million Pts)**
----------------------------------- ------ ------ ------ ------ ------ ------ ------ ------ ------ ------
dest_country 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919
Montenegro 0 0 0 0 0 0
Morocco 2 6 6 9 0 0 0 0 0 0
Nicaragua 0 0 0 0 0 0 0 0 0 0
Norway 2 2 3 2 3 8 8 5 10 14
Panama 4 13 9 3 4 4 6 6 4 6
Paraguay 1 0 0 0 0 0 0
Penon_de_la_gomera 0 0 0 0 0 0 0 0 0 0
Peru 1 0 1 2 1 1 2 1 1 2
Philippines 8 8 8 7 7 6 6 4 3 1
Portugal 40 44 32 31 14 17 25 27 29 14
Posesiones_danesas_en_america 0 0 0 0 0 0 0 0 0 0
Posesiones_danesas_en_asia 0
Posesiones_danesas_en_europa 0 0 0 0 0 0
Posesiones_franceas_en_africa 0
Posesiones_franceas_en_america 0
Posesiones_francesas_en_africa 0 0 0 0 0 0 0 0 0 0
Posesiones_francesas_en_america 0 0 0 0 0 0 0 0 0 0
Posesiones_holandesas_en_america 0 0 0 0 0 0 0 0 0 0
Posesiones_holandesas_en_asia 0 0 0
Posesiones_holandesas_en_oceania 0 0 0 0 1 0 0 0 0 0
Posesiones_inglesas_en_africa 0 0 0 0 0 0 0 0 0 0
Posesiones_inglesas_en_america 2 2 2 2 2 1 1 1 1 1
Posesiones_inglesas_en_asia 1 2 1 1 1 2 2 1 0 1
Posesiones_inglesas_en_europa 0 0 0 0 0 0 0 0 0 1
Posesiones_inglesas_en_oceania 2 0 1 1 1 0 0 0 0 0
Posesiones_portueguesas_en_africa 0
Posesiones_portuguesas_en_africa 0 0 0 0 0 0 0
Puerto_rico 3 4 3 3 3 2 2 3 1 2
Rio_de_oro 0 0 0 0 0 0 0
Romania 0 0 0 0 1 1 0 0 6
Russia 7 5 7 8 6 25 14 3 0 0
Santo_domingo 1 1 0 1 0 0 0 0 0 0
Servia 0 0 0 0 0 1
Siam 0 0 0 0 0 0 0 0
Sweden 2 2 2 2 3 4 3 1 0 7
Switzerland 7 8 10 12 3 6 10 56 38 32
Tunez 0 0 0 1 0 0 0 0 0
Turkey 2 0 1 6 3 0 0 0 0 23
Uruguay 10 12 10 10 6 12 13 11 17 11
Venezuela 2 1 3 4 3 3 5 6 5 2
Zancibar 0
Zanzibar 0 0
0
----------------------------------- ------ ------ ------ ------ ------ ------ ------ ------ ------ ------
### Import Data from Annual Export Statistics
Data on external trade for Spain from 1910-1920 can be obtained from the annual statistical publications of the Spanish customs agency ([Dirección General de Aduanas 1911](#ref-estadisticaexterior1910), [1912](#ref-estadisticaexterior1911), [1913](#ref-estadisticaexterior1912), [1914](#ref-estadisticaexterior1913), [1915](#ref-estadisticaexterior1914), [1916](#ref-estadisticaexterior1915), [1917](#ref-estadisticaexterior1916), [1918](#ref-estadisticaexterior1917), [1919](#ref-estadisticaexterior1918), [1920](#ref-estadisticaexterior1919), [1921](#ref-estadisticaexterior1920)). The import data exhibits a similar structure to the export data, showing quantities and values across products over time.
> **Summary Statistics: Imports (Million Pts)**
---- -------------------------------- ------ ------ ------ ------ ------ ------ ------ ------
Industry 1912 1913 1914 1915 1916 1917 1918 1919
1 Agriculture 434 520 460 469 452 269 325 490
2 Chemical industry 14 27 11 4 7 9 7 8
3 Civil engineering 0 0 1 0 1 3 1 3
4 Construction 14 12 8 6 10 9 7 6
5 Construction materials 4 8 4 1 1 2 3 2
6 Electricity 23 27 22 15 22 16 9 20
7 Food industry 43 60 47 41 49 38 41 37
8 Furniture 7 8 4 2 2 2 1 4
9 Garment industry 21 14 16 7 10 12 12 17
10 Gas factory 2 2 2 2 3 4 2 5
11 Glass industry 7 6 2 1 2 1 1 5
12 Industrias de la ornamentacion 0 0 0 0 0 0 0 0
13 Industrias del tabaco 0 1 2 0 0 1 0 0
14 Industrias varias 39 52 36 33 46 30 15 52
15 Iron works and other metals 10 17 7 10 5 6 2 30
16 Jewellery 0 0 4 0 0 0 0 0
17 Leather industry 3 4 2 1 2 2 1 2
18 Metal objects 69 113 60 31 40 26 20 45
19 Metallurgy 9 10 1 8 9 9 2 8
20 Mines, Saltmines and quarries 95 61 113 73 89 50 28 50
21 Paper industry 13 14 10 9 8 9 4 10
22 Pottery and ceramics 0 0 0 0 0 0 0 0
23 Print industry 10 11 7 5 6 5 5 7
24 Public Services 2 2 1 1 5 5 1 3
25 Shops 14 12 14 6 6 5 4 5
26 Silverware and Jewelry 4 5 4 2 2 3 2 3
27 Textiles 41 46 30 28 33 28 21 29
28 Transport industry 21 44 19 3 4 7 5 6
29 Wood 104 125 107 91 78 48 31 62
---- -------------------------------- ------ ------ ------ ------ ------ ------ ------ ------
### Correspondence between Tariff Groups and Industry Classifications
A separate publication by the institute for social reform contains a correspondence between industries and occupations ([Instituto Nacional de Prevision Social 1930](#ref-4185)) . Since occupations can be more easily mapped to the products in the export data, this information is particularly helpful in constructing the correspondence between sectors and product-level trade data. The complete correspondence between export products and sectors is available upon request.
### Migration Data
I follow Silvestre ([2005](#ref-10.2307/41378422)) and use the province level data on inhabitants that are Born in Another Province which is contained in the censuses. For 1920 and 1930 additional information is available listing not only the stock of migrants which were born in another province, but their origin province as well. The difference between 1930 and 1920 in the stock of migrants - adjusted for decennial survivability rates - is informative about net migration. In order to construct net migration, I follow ([Silvestre 2005](#ref-10.2307/41378422)) and use the decennial census survivability rate between 1921-1930, $S\equiv0.86$. Net internal migration can be obtained by constructing the survivability adjusted change in stock of migrants, i.e.
$$
\text{Internal migrations}_{1930,1920,i,j}=BAP_{i,j,1930}-S\times BAP_{i,j}^{1920}
$$
where $BAP_{i,j}^{1920}$ refers to the stock of residents in $i$ who were born in province $j$ in 1920.
### Consumer Price Data
The Boletins of the Instituto de Reformas Sociales contain detailed information on consumer prices of key agricultural and non-agricultural products across Spanish provinces throughout the decade. The data was previously used by Gomez-Tello et al. ([2018](#ref-SpainHistPrices)) and I refer for detailed information to their paper.
### Transportation Network
I georeferenced the Spanish railroad network in 1920. Then, using MATLAB's internal shortest path function, I obtain bilateral distances between provincial capitals along the shortest path of the railroad network. In order to obtain distances to Paris, I augmented the graph with the French railroad network and further added maritime linkages between important ports in France and Spain. Again using the shortest path functionality of MATLAB I can obtain the shortest distance along this transportation network between provincial capitals in Spain and Paris.
### Census Data
I digitized data from four different census publications for 1900, 1910, 1920 and 1930 respectively Instituto Geográfico ([1912](#ref-instituto1912censo), [1932](#ref-instituto1932censo), [1922](#ref-instituto1922censo)). The census publication contain population data disaggregated by profession for each province of Spain between 1900-1930. Additionally the census publication in 1920 and 1930 contain data on the origin of residents in each province that were born in another province, which - as described before - I use to construct bilateral migration data in the spirit of ([Silvestre 2005](#ref-10.2307/41378422)).
As has been previously noted in the literature, the structure of the population censuses for Spain between 1900-1920 is not consistent, which makes it difficult to construct a consistent time series for sectoral labor shares across broadly defined categories ([Erdozain Azpilicueta and Mikelarena Pena 1999](#ref-cifras_agrarios); [Dovring 2013](#ref-dovring2013land)). Particularly troublesome is an item called "jornaleros, braceros, peones, destajistas" (day-laborers, etc.) which in the 1900 census is subsumed in the agricultural category, but in the 1910 census listed separately. This category likely contains both agricultural workers and workers in other sectors of the economy. I follow Dovring ([2013](#ref-dovring2013land)) and partition the category proportionately to agricultural and manufacturing sectors.
## Aggregate and Regional Welfare Effects
We summarize welfare using a sufficient-statistics expression that combines changes in trade shares, housing costs, and the option-value gains from reallocation implied by the nested mobility structure. Assuming that the initial allocation arises from an EV1 allocation problem equivalent to a canonical quantitative spatial equilibrium model, we can construct an aggregate welfare formula corresponding to the expected utility for a worker:
$$
\left(\frac{\mathcal{W}^{1}}{\mathcal{W}^{0}}\right)=\prod_{i\in\mathcal{D}, s\in\mathcal{S}}\left(\underbrace{\left(\frac{\rho_{ii|s}^{1}}{\rho_{ii|s}^{0}}\right)^{-\frac{1}{\gamma}}}_{\text{Spatial Flows}}\underbrace{\left(\frac{\rho_{ss|i}^{1}}{\rho_{ss|i}^{0}}\right)^{-\frac{1}{\nu}}}_{\text{Sectoral Flows}}\underbrace{\left(\frac{r_{i}^{1}}{r_{i}^{0}}\right)^{-\delta}}_{\text{Housing Cost}}\underbrace{\prod_{k\in\mathcal{S}}\left(\frac{\lambda_{ii,k}^{1}}{\lambda_{ii,k}^{0}}\right)^{-\frac{\left(1-\delta\right)\alpha_{k}}{\sigma_{k}-1}}}_{\text{ACR Gains}}\right)^{\pi_{i,s}},
$$
where $\rho_{ii|s}^{1}$ is the probability that a worker initially in province $i$ and sector $s$ remains in that province, $\rho_{ss|i}^{1}$ is the probability they remain in sector $s$, and $\lambda_{ii,k}$ is the domestic home share defined above. The weights $\pi_{i,s}$ denote the period-0 employment shares $\ell^0_{i,s}$. Intuitively, the remain share (to the power of the negative inverse of the respective labor supply elasticity) is proportional to changes in the option value and serves as a sufficient statistic for welfare changes arising from a worker's ability to reallocate across space and sectors. The final two terms capture the static gains from changes in real income across locations stemming from changes in housing costs and the consumer price index. The detailed derivation of this first-order approximation is provided in the theoretical subsections of this appendix.[^26]
**ACR benchmark and aggregation.** The ACR formula provides a sufficient statistic for changes in *real income* at a location in a canonical CES trade environment with immobile factors. In our multi-location setting, the ACR term is therefore naturally interpreted as a *location-level* benchmark component. Whenever we report a single summary number, we aggregate location-level ACR changes using baseline employment weights (1914 shares), consistent with a utilitarian average across workers. Our model-implied welfare change differs from this benchmark because endogenous spatial and sectoral reallocation generates an additional *option-value* component in expected utility, and because rents and cost-of-living change heterogeneously across provinces.
Table [Table](#tab:welfare-1) reports the decomposition of welfare gains across the different counterfactual scenarios. Relative to the counterfactual "No WWI" scenario, the baseline WWI export boom yielded an aggregate welfare gain of approximately $2.54\%$. Importantly, the ACR-style benchmark captures only the *static real-income* component; the remaining difference to model-implied welfare reflects the option-value (reallocation) terms implied by imperfect mobility and the endogenous distribution of workers across province--sector markets. Furthermore, Panel B demonstrates that as spatial migration frictions are removed, creating highly integrated labor markets, the resulting spatial reallocation lowers inflationary pressure, spreading the gains from trade more evenly and further bolstering aggregate welfare.
> **Decomposition of Welfare Gains across Counterfactual Scenarios**
+:--------------------------------------------------------------+:-----------------:+:-----------------:+:-------:+:------------------------:+:-------:+:------------------------:+:---------:+:------------------------:+
| | Reallocation (Option-Value) Gains | Static Gains | Total |
+---------------------------------------------------------------+-------------------+-------------------+---------+--------------------------+---------+--------------------------+-----------+--------------------------+
| Welfare Changes from (in $\%$) | Spatial | Sectoral | ACR | Rental | Wage | Inflation | **Total** | Deficit |
+---------------------------------------------------------------+-------------------+-------------------+---------+--------------------------+---------+--------------------------+-----------+--------------------------+
| **Panel A: Baseline Result** |
+---------------------------------------------------------------+-------------------+-------------------+---------+--------------------------+---------+--------------------------+-----------+--------------------------+
| (1a) External Trade fixed at 1914 level (rel. to WW1) | 0.06 | 0.49 | 1.49 | $-$``{=html}0.20 | 2.79 | $-$``{=html}1.73 | **2.89** | $-$``{=html}7.70 |
+---------------------------------------------------------------+-------------------+-------------------+---------+--------------------------+---------+--------------------------+-----------+--------------------------+
| (1b) External Trade fixed at 1914 level (rel. to 1920) | 0.06 | 0.49 | 1.07 | $-$``{=html}0.14 | 2.23 | $-$``{=html}1.58 | **2.13** | $-$``{=html}2.32 |
+---------------------------------------------------------------+-------------------+-------------------+---------+--------------------------+---------+--------------------------+-----------+--------------------------+
| **Panel B: Integrated Labor Markets** |
+---------------------------------------------------------------+-------------------+-------------------+---------+--------------------------+---------+--------------------------+-----------+--------------------------+
| (2a) No Spatial Mobility Cost ($\zeta=0,\nu=2$, rel. to WWI) | 0.56 | 0.42 | 1.30 | $-$``{=html}0.13 | 2.57 | $-$``{=html}1.62 | **3.11** | $-$``{=html}7.70 |
+---------------------------------------------------------------+-------------------+-------------------+---------+--------------------------+---------+--------------------------+-----------+--------------------------+
| (2b) No Spatial Mobility Cost ($\zeta=0,\nu=2$, rel. to 1920) | 0.56 | 0.42 | 1.23 | $-$``{=html}0.02 | 2.06 | $-$``{=html}1.53 | **2.72** | $-$``{=html}2.32 |
+---------------------------------------------------------------+-------------------+-------------------+---------+--------------------------+---------+--------------------------+-----------+--------------------------+
| **Panel C: Even Trade Shock** |
+---------------------------------------------------------------+-------------------+-------------------+---------+--------------------------+---------+--------------------------+-----------+--------------------------+
| (3a) Removing Spatial Bias in Trade Shock (rel. to WWI) | 0.02 | 0.56 | 1.76 | $-$``{=html}0.19 | 2.97 | $-$``{=html}1.87 | **3.25** | $-$``{=html}7.70 |
+---------------------------------------------------------------+-------------------+-------------------+---------+--------------------------+---------+--------------------------+-----------+--------------------------+
| (3b) Removing Spatial Bias in Trade Shock (rel. to 1920) | 0.02 | 0.56 | 0.73 | $-$``{=html}0.13 | 2.39 | $-$``{=html}1.90 | **1.68** | $-$``{=html}2.32 |
+---------------------------------------------------------------+-------------------+-------------------+---------+--------------------------+---------+--------------------------+-----------+--------------------------+
| **Panel D: Even Trade shock & Integrated Labor Market** |
+---------------------------------------------------------------+-------------------+-------------------+---------+--------------------------+---------+--------------------------+-----------+--------------------------+
| (4a) Even Trade Shock & No Spat. Friction (rel. to WWI) | 0.48 | 0.46 | 1.77 | $-$``{=html}0.08 | 2.95 | $-$``{=html}1.95 | **3.63** | $-$``{=html}7.70 |
+---------------------------------------------------------------+-------------------+-------------------+---------+--------------------------+---------+--------------------------+-----------+--------------------------+
| (4b) Even Trade Shock & No Spat. Friction (rel. to 1920) | 0.48 | 0.46 | 0.71 | 0.00 | 2.38 | $-$``{=html}2.01 | **2.01** | $-$``{=html}2.32 |
+---------------------------------------------------------------+-------------------+-------------------+---------+--------------------------+---------+--------------------------+-----------+--------------------------+
The aggregate gains from trade mask substantial spatial heterogeneity. As the export boom directly affected the industrial and coastal hubs, the welfare improvements concentrated heavily in the most productive and directly exposed provinces. Table [Table](#tab:welfare_prov) reports the top and bottom five province-level contributions to the aggregate welfare gains, decomposing these contributions into nominal wage, inflation, and rental cost components. We observe that welfare gains were generated most intensely in provinces like Barcelona, Valencia, and Coruna, emphasizing the highly heterogeneous, localized impact of trade shocks within national borders. Panel B reports the same decomposition under the integrated labor market counterfactual.
> **Provincial Contributions to Aggregate Welfare**
+:---------------------+:------------------------:+:------------:+:------------------------:+:------------------------:+
| Province | Total Gain (%) | Nominal Wage | Inflation | Housing Cost |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| **Panel A: Baseline Result** |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| *Top 5 Provinces* | | | | |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| Barcelona | 0.64 | 0.88 | $-$``{=html}0.26 | $-$``{=html}0.05 |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| Zaragoza | 0.28 | 0.07 | $-$``{=html}0.06 | 0.00 |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| Valencia | 0.15 | 0.23 | $-$``{=html}0.10 | 0.03 |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| Huesca | 0.12 | 0.03 | $-$``{=html}0.03 | $-$``{=html}0.00 |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| Madrid | 0.10 | 0.11 | $-$``{=html}0.04 | 0.01 |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| *Bottom 5 Provinces* | | | | |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| Jaen | $-$``{=html}0.02 | 0.00 | $-$``{=html}0.04 | 0.00 |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| Orense | $-$``{=html}0.03 | 0.01 | $-$``{=html}0.03 | 0.00 |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| Leon | $-$``{=html}0.03 | 0.02 | $-$``{=html}0.03 | $-$``{=html}0.01 |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| Oviedo | $-$``{=html}0.07 | 0.02 | $-$``{=html}0.04 | $-$``{=html}0.01 |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| Lugo | $-$``{=html}0.07 | 0.01 | $-$``{=html}0.05 | 0.00 |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| **Panel B: Integrated Labor Markets** |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| *Top 5 Provinces* | | | | |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| Barcelona | 0.58 | 0.76 | $-$``{=html}0.25 | $-$``{=html}0.02 |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| Zaragoza | 0.24 | 0.06 | $-$``{=html}0.05 | $-$``{=html}0.00 |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| Valencia | 0.16 | 0.20 | $-$``{=html}0.09 | 0.04 |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| Huesca | 0.11 | 0.03 | $-$``{=html}0.03 | $-$``{=html}0.00 |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| Madrid | 0.09 | 0.09 | $-$``{=html}0.04 | 0.00 |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| *Bottom 5 Provinces* | | | | |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| Jaen | $-$``{=html}0.02 | 0.00 | $-$``{=html}0.03 | 0.00 |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| Orense | $-$``{=html}0.02 | 0.01 | $-$``{=html}0.03 | 0.01 |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| Leon | $-$``{=html}0.02 | 0.02 | $-$``{=html}0.03 | $-$``{=html}0.01 |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| Lugo | $-$``{=html}0.05 | 0.01 | $-$``{=html}0.05 | 0.01 |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
| Oviedo | $-$``{=html}0.05 | 0.03 | $-$``{=html}0.04 | 0.00 |
+----------------------+--------------------------+--------------+--------------------------+--------------------------+
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[^1]: Contact: simon.fuchs@atl.frb.org. For their comments, I am grateful to Konrad Adler, Treb Allen, Andy Bernard, Emily Blanchard, Toni Braun, Albert Carreras, Thomas Chaney, Kerem Coşar, Klaus Desmet, Chris Edmond, Patrick Fève, Jim Feyrer, Sharat Ganapati, Christian Hellwig, Rob Johnson, Brian Kovak, Tim Lee, Thierry Mayer, Rory McGee, Martí Mestieri, Nina Pavcnik, Franck Portier, B Ravikumar, Vincent Rebeyrol, Juan Rubio-Ramírez, Mohammed Saleh, Chris Snyder, François de Soyres, Bob Staiger, Robert Ulbricht, Nikolaus Wolf as well as seminar and workshop participants in many places. I also want to thank Javier Silvestre for sharing his data on internal migration in Spain and Julio Martinez-Galarraga for sharing their data on consumer prices as well as providing helpful comments. Finally, I acknowledge financial support via ERC grant No 337272-FiNet. All remaining errors are my own. The views expressed herein are those of the author and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System.
[^2]: After missing the first wave of the industrial revolution in the first half of the 19th century ([Harrison 1978](#ref-harrison1978economic)), the Spanish economy underwent a period of rapid industrialization in the second half of the 19th century, fueled by market integration due to the expansion of the railroad network, which in turn resulted in the devolution of industrial capacity to the peripheral provinces with the cotton industry in Catalonia and metallurgy in the Basque country developing especially rapidly ([Nadal 1975](#ref-nadal1975fracaso)). However, industrialization soon came to an early halt with the census data showing little increase in industrial employment from 1887 onwards. This is also mirrored by very low GDP per head growth rates averaging 0.6 percent between 1883--1913 ([Prados de la Escosura 2017](#ref-de2017spanish)). Some authors attribute the low levels of growth to limited demand for manufacturing goods domestically as well as little capacity to compete with goods from countries such as Germany, France, and the UK that were more advanced in terms of their industrialization ([Harrison 1978](#ref-harrison1978economic)).
[^3]: Andalucı́a comprises eight provinces: Almerı́a, Cádiz, Córdoba, Granada, Huelva, Jaén, Málaga and Seville, with major industrial activity located in Seville and Mining employment in Huelva
[^4]: Castilla y León comprises nine provinces: Ávila, Burgos, León, Palencia, Salamanca, Segovia, Soria, Valladolid and Zamora with major industrial activity centered in Valladolid.
[^5]: Explanations focus mainly on an insufficient release of agricultural workers to urban areas, driven either by supply-based factors---such as low agricultural productivity and demographic dynamism---or demand-based factors---such as the lack of pull of industry and services until at least WWI. Either explanation is perfectly consistent with the point of view that substantial push or pull factors were required to overcome the economic, linguistic, or sociological barriers that impeded spatial and sectoral mobility. For a complete discussion and references of demand-based and supply-based explanation see Section 2 in Silvestre ([2005](#ref-10.2307/41378422)).
[^6]: We rely on four principal data sources covering labor, trade, migration, and prices. See the online appendix for highly granular data construction details, including auxiliary datasets like shortest-path distance computations via the 1920 railroad network and housing stock imputations.
[^7]: This increase is probably underestimated since official statistics kept the price for the calculation of values of exported goods at a constant level during the decade under consideration, while it is plausible that increased demand further increased the price.
[^8]: We define belligerent destinations as France and the UK, excluding late entrants such as the US and Italy, as well as nations where trade was mechanically disrupted by central naval blockades or frontline combat (e.g., Germany and Austria-Hungary). All results are robust to the inclusion of Italy. While the primary focus of this paper is on the exogenous export shock, imports also experienced significant disruptions. In Online Appendix Table [Table](#apptab:stylized_fact_imports_sec), we provide an analogous event study for sectoral imports, demonstrating the heterogeneous impact of the war on different import sectors relative to Agriculture. However, because import origins are not consistently reported at the product level in early years, an origin-level event study comparable to exports is not feasible.
[^9]: A sufficient condition is $d>(K-1)|a_L|+|a_S|$; see Appendix [4.1](#app:gen_theory_results) for detailed derivations for the decomposition and the sufficient condition.
[^10]: Formally, sectoral import exposure is constructed as $\text{DirectImportExposure}_{r,s} \equiv \pi_{r,s}^0 \hat{m}_s$, where $\hat{m}_s$ is a sector-level shifter estimated from the national collapse in imports from belligerent nations using newly digitized trade data from the *Estadística del Comercio Exterior de España*. For prices, $\text{SectoralImportShock}_p$ is the shifter $\hat{m}_s$ for the industry $s$ corresponding to product $p$.
[^11]: Appendix [4.2](#app:lechatelier) provides sufficient conditions and a formal proof.
[^12]: This timing assumption is a tractable way to introduce correlation in unobserved tastes across alternatives and to allow *distinct* elasticities for geographic mobility and occupational/sectoral switching. Formally, the specification is equivalent to a nested-logit / generalized extreme value (GEV) random-utility model in which *destination provinces are nests* and *sectors are alternatives within each nest*. A worker initially in sector $s$ draws a province-specific taste component (measured with Fréchet shocks with dispersion $\gamma$) and chooses a destination province $n$ based on the *inclusive value* (option value) of sectoral opportunities in that province,
$$
\Pi_{n,s} \equiv \Big( \sum_{k\in \mathcal{S}} \tilde w_{n,k|s}^{\nu} \Big)^{1/\nu},
\qquad \tilde w_{n,k|s}\equiv w_{n,k}/\mu_{sk},
$$
before subsequently drawing sector-specific shocks (dispersion $\nu$) and choosing a destination sector $k$ conditional on $n$. This delivers the convenient multiplicative factorization of joint reallocation probabilities into a province component and a conditional sector component (i.e., $\Pr\{(n,k)\}=\Pr\{n\}\Pr\{k\mid n\}$), which is what makes the model tractable with many province--sector markets and allows us to separately discipline the *spatial* and *sectoral* mobility margins.
The restriction is behavioral: conditional on the chosen province, relative sector choices satisfy the usual "IIA within the nest" property (relative probabilities across sectors depend only on sector-specific utilities within that province). If instead workers chose *province--sector bundles* in one step with i.i.d. extreme-value errors, the model would collapse to a standard multinomial logit over $(n,k)$ with a *single* dispersion parameter, mechanically tying the strength of geographic substitution to the strength of sectoral substitution. More flexible structures (e.g., cross-nested logit, mixed logit, or models with unobservables that interact between province and sector) could accommodate richer correlation patterns---for example, location--occupation match effects or comparative-advantage shocks that are jointly valued with amenities---but at the cost of additional parameters and typically losing closed-form aggregation that is useful in general equilibrium.
Our maintained two-stage structure is therefore best viewed as a parsimonious reduced-form for segmented labor markets, and it is standard in the discrete-choice literature on nested logit / GEV models (McFadden, 1978; Ben-Akiva and Lerman, 1985; Train, 2009) and in quantitative spatial/trade models that separate migration and occupational adjustment margins (e.g., Redding, 2012; Ahlfeldt, Redding, Sturm and Wolf, 2015; Caliendo, Dvorkin and Parro, 2019).
[^13]: In [Equation](#eq:structural_sigma), the "hat" on $\hat p_{is,t}$ denotes the inverted origin-price shifter (up to normalization), not a time difference.
[^14]: See Section 3.1 and Appendix C.1 for the derivation and the two-channel spillover representation.
[^15]: In principle, this can be tested either via conducting a more formal SMM estimation strategy with the structural model ([McFadden 1989](#ref-McFadden1989-zy)), or by constructing higher-order moments directly.
[^16]: For recent advancements of spatial equilibrium models that incorporate that channel see ([Rodríguez-Clare et al. 2020](#ref-Rodriguez-Clare2020-lh)).
[^17]: Formally, one can interpret changes in foreign demand as either changes in the foreign preference structure or their own domestic productivity, inducing changes in foreign demand for Spanish exports.
[^18]: As a secondary summary, we also evaluate welfare using a sufficient-statistic expression that combines static changes in real income (the standard ACR-style channel) with the option-value gains from spatial and sectoral reallocation. Because the quantitative exercise compares equilibria across two periods rather than modeling a transition path, we refer to the option-value component as reallocation (option-value) gains rather than dynamic gains. A detailed decomposition of aggregate and regional welfare across counterfactuals is provided in Online Appendix Section [Appendix](#app:welfare_results). Consistent with the incidence patterns above, accounting for imperfect mobility is central for understanding both the level and the spatial distribution of gains from the WWI export-demand shock.
[^19]: *In a one-market special case, $\widehat\eta=(\varepsilon_D+\varepsilon_S(\chi))\,\widehat w$, so $\widehat w=\widehat\eta/(\varepsilon_D+\varepsilon_S(\chi))$. As $\varepsilon_S(\chi)$ rises, the wage response shrinks, while the share of the shock absorbed by quantities, $\varepsilon_S(\chi)/(\varepsilon_D+\varepsilon_S(\chi))$, rises.*
[^20]: A simple quantitative version of the attenuation result can be developed using spectral results. Take two integration levels $\chi_2\ge \chi_1$ and write $A:=\tilde\gamma^{0}(\chi_1)$, $B:=\tilde\gamma^{0}(\chi_2)$, and $\Delta:=B-A\succeq 0$. Define the baseline-normalized increment $M:=A^{-1/2}\Delta A^{-1/2}\succeq 0$ and let $\bar\lambda:=\lambda_{\max}(M)$. Then $B=A^{1/2}(I+M)A^{1/2}$, so $B^{-1}=A^{-1/2}(I+M)^{-1}A^{-1/2}$. Because the eigenvalues of $(I+M)^{-1}$ are $1/(1+\lambda)$ for $\lambda\ge 0$, they lie in $[1/(1+\bar\lambda),\,1]$, which implies the sandwich bound
$$
\frac{1}{1+\bar\lambda}\,A^{-1}\preceq B^{-1}\preceq A^{-1}.
$$
Consequently, for any vector $x$ (in particular $x=\widehat{\eta}$), the quadratic wage-adjustment measure $x'B^{-1}x$ cannot increase relative to $x'A^{-1}x$, and it cannot fall below the fraction $\frac{1}{1+\bar\lambda}$ of $x'A^{-1}x$:
$$
\frac{1}{1+\bar\lambda}\,x'A^{-1}x \le x'B^{-1}x \le x'A^{-1}x.
$$
Economically, $\bar\lambda$ summarizes how much additional adjustment capacity integration adds, measured in units of the baseline "stiffness" $A$: if $\bar\lambda$ is small, integration has little effect on shock pass-through to wages; if $\bar\lambda$ is large, wages can be much more muted because the extra reallocation/quantity margins absorb a larger share of the shock.
[^21]: The expected ex-ante utility, i.e. prior to observing and forming expectations over the sectoral preference shocks, that an individual derives from moving from location $n$ to location $i$ can be expressed in terms of the option value of being in that location-sector $\Pi_{i,r}'\equiv\left(\sum_{t}(w_{it}'/\mu_{rt})^{\nu}\right)^{1/\nu}$, multiplied by a stochastic location-specific preference shock $\kappa_{i}$, and adjusted by variable geographical migration cost, $\mu_{ni}$, i.e. **
$$
v_{ni|r}'\equiv\frac{\delta}{\mu_{ni}}\frac{\rho_{i}\Pi_{i|r}'}{\left(p_{i}'\right)^{1-\delta}\left(r_{i}'\right)^{\delta}}\times\kappa_{i}
$$
**
[^22]: The industries included are called: Books, Ceramics, Chemicals, Construction, Decoration, Electricity, Food, Forrest, Furniture, Garments, Glass, Leather, Metal Works, Metallurgy, Mines, Paper, Public, Public Industry, Textiles, Tobacco, Transport, Varias, Wood.
[^23]: The census for 1910 lists 49 different provinces. They mostly correspond to the modern administrative units called provincias - provinces - which are in turn roughly the NUTS3 level administrative units of Spain. There are some minor differences, e.g. in how different off-continental administrative units are being treated. For my analysis I drop the Canary islands from the sample since their distance from the mainland makes it hard to argue that they are similarly integrated as other provinces.
[^24]: The correspondence table is available upon request.
[^25]: The industries included are called: Books, Ceramics, Chemicals, Construction, Decoration, Electricity, Food, Forrest, Furniture, Garments, Glass, Leather, Metal Works, Metallurgy, Mines, Paper, Public, Public Industry, Textiles, Tobacco, Transport, Varias, Wood.
[^26]: See the online appendix [Section](#subsec:Aggregate-welfare-in-1) for detailed derivations and the extension incorporating aggregate trade deficits.