ESTIMATING A DYNAMIC SPATIAL EQUILIBRIUM MODEL TO EVALUATE THE WELFARE IMPLICATIONS OF REGIONAL ADJUSTMENT PROCESSES: THE DECLINE OF THE RUST BELT

• Date: 01 May 2017
• Author: Chamna Yoon
• Published date: 01 May 2017
• DOI: http://doi.org/10.1111/iere.12224

INTERNATIONAL ECONOMIC REVIEW

Vol. 58, No. 2, May 2017

ESTIMATING A DYNAMIC SPATIAL EQUILIBRIUM MODEL TO EVALUATE THE

WELFARE IMPLICATIONS OF REGIONAL ADJUSTMENT PROCESSES: THE

DECLINE OF THE RUST BELT∗

BYCHAMNA YOON1

Sungkyunkwan University, Republic of Korea

This article develops and estimates a new dynamic spatial equilibrium model to study the regional transition

dynamics and its impact on individual and aggregate welfare. The model consists of a multiregion, multisector

economy comprised of overlapping generations of individuals with heterogeneous skills and mobility costs. The

empirical findings suggest that a large fraction of the decline of the Rust Belt can be attributed to the reduction

in its region-specific comparative advantage in the goods-producing sector. This decline generated significant

differences in welfare across regions. Policy experiments show that such inequality can be significantly reduced

through place-based policies.

1. INTRODUCTION

Changes in the aggregate economic environment typically have a differential impact on

regional economies in a country. Blanchard and Katz (1992) pointed out that the adjustment of

a regional economy to an aggregate shock is not immediate, but a time-consuming transition

process in local labor and housing markets. The purpose of this article is to study the regional

transition dynamics and its heterogeneous impact on individual and aggregate welfare along

the transition path.

The first contribution of this article is that I build and estimate a new dynamic spatial equi-

librium model by extending existing static spatial equilibrium models (Rosen, 1979; Roback,

1982) in several dimensions. First, I model a multiregion and multisector economy in which

regional economies produce different bundles of goods due to the region-specific comparative

advantages. As a consequence, regions are not symmetrically affected by changes in the ag-

gregate economic environment. Second, to capture the time-consuming adjustment process in

the regional markets, I allow for heterogeneity in regional mobility costs and sector-specific

switching costs (Kennan and Walker, 2011). In addition, I allow for regional differences in the

supply of young workers. Finally, I incorporate the adjustment of regional housing markets into

a dynamic model of sectoral choice extending Lee and Wolpin (2006) and Dix-Carneiro (2014).

I show that one needs a quantitative analysis of price and quantity adjustments in both labor

and housing markets to evaluate the welfare impact along the transition path of the economy.

The second contribution of this article is that I apply the new framework to study the recent

decline of the industrial cities in the Midwest and parts of the Northeast of the United States,

an area typically known as the Rust Belt.2In recent years, the Rust Belt has experienced a

∗Manuscript received April 2015; revised January 2016.

1I would like to thank my dissertation committee members, Holger Sieg, Xun Tang, and Kenneth I. Wolpin (chair),

for their support. I would also like to thank two anonymous referees, as well as Gilles Duranton, Hanming Fang, Tom

Holmes, Illenin Kondo, Donghoon Lee, Petra Todd, and the seminar participants and discussants at various different

universities and conferences for their comments and suggestions. This research was conducted with restricted access

to Bureau of Labor Statistics (BLS) data. The views expressed here do not necessarily reflect the views of the BLS.

This research was supported in part by the National Science Foundation through XSEDE resources provided by the

XSEDE Science Gateways program. Please address correspondence to: Chamna Yoon, Department of Economics,

25-2 Sungkyunkwan-ro, Jongno-gu, Seoul, 03063, Republic of Korea. E-mail: chamna.yoon@gmail.com.

2The Rust Belt conventionally includes Illinois, Indiana, Michigan, Ohio, Pennsylvania, and Wisconsin.

473

C

(2017) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

474 YOON

relative decline in population, wages, and housing rents compared to other areas in the United

States. In 1960, 27% of the U.S. population lived in the Rust Belt; by 2010, the proportion

had decreased to 19%. Similarly, in 1960, average wages and housing rents were higher in the

Rust Belt than in other U.S. areas by 10% and 7%, respectively. By 2010, the wage gap was

eliminated and housing rents in the Rust Belt were 13% lower than elsewhere in the United

States. The empirical findings suggest that a large fraction of the decline of the Rust Belt can be

attributed to the two-thirds reduction in its region-specific comparative advantage in the goods-

producing sector. This decline generated significant differences in welfare between individuals

residing in the Rust Belt and those residing in other areas, particularly for less-educated and

older individuals. Policy experiments show that the inequality in welfare can be significantly

reduced by subsidizing labor costs in the Rust Belt or reducing mobility costs.

In the model, there are two regions in the economy. In each region, there are three production

sectors: a goods-producing sector, a service sector, and a housing sector. Goods and services

are produced using non-college-educated labor, college-educated labor, and capital. Changes

over time in the overall productivity of these sectors in each region are affected by area-

specific technological change and sector-biased aggregate shocks. The model is comprised of

overlapping generations of heterogeneous individuals who are born in one of the two regions.

Individuals can move between regions, but face potentially significant mobility costs. Individuals

are forward looking and choose among six discrete alternatives: the two location alternatives,

each with three possible work alternatives (e.g., employed in the goods sector, employed in

the service sector, and remaining out of the labor force). Individuals also decide on their

consumption of housing services.

In each period, each individual receives a wage offer from each region and sector, which

depends on the region- and sector-specific skill rental price and the individual’s accumulated

sector-specific skill. In equilibrium, a region- and sector-specific skill rental price is determined

by equating the skill price to its marginal revenue product, evaluated at the aggregate level

of skill and capital in that region and sector. The level of an individual’s skill depends on

her accumulated work experience in each sector and on the individual’s level of education.

Transitions between sectors also involve mobility costs, which can differ across demographic

groups. I use standard, finite-horizon dynamic programming techniques to model the dynamic

behavior of individuals. To close the model, I assume that housing services are produced using

capital and land as inputs. Housing rental prices clear the market for housing services in each

region at each point of time.

I define the dynamic, nonstationary equilibrium for this model. Equilibria can only be com-

puted numerically. Computing equilibria for this model is challenging for a number of reasons.

First, I need to solve the dynamic programming problem of workers, accounting for a rich set

of state variables in a nonstationary environment. Second, I need to characterize equilibrium

beliefs that workers hold over the evolution of key state variables. Computing full rational ex-

pectation equilibria is not feasible. Therefore, I adopt a forecasting rule that approximates the

rational expectations equilibrium (Krusell and Smith, 1998). The equilibrium beliefs must be

self-fulfilling. I adopt an iterative algorithm to determine the parameters of the beliefs process,

extending the procedure developed in Lee (2005) and Lee and Wolpin (2006). Third, I need

to impose market clearing conditions for a large number of markets. I show numerically that

equilibria exist and can be computed with a high degree of accuracy.

I then develop a strategy to estimate the parameters of the model using a method of simulated

moments (MSM) estimator. I use a variety of data sources to construct moments used in the

estimation. First, I have obtained data characterizing employment and wages from the U.S.

Current Population Survey (CPS). Second, I use data on region- and sector-specific output and

capital from the National Income and Product Accounts. Third, I obtained access to restricted-

use data, which I use to calculate sector and regional transition from the National Longitudinal

Survey of Youth 1979. Finally, I use data on housing rents and migration status from the U.S.

Census. I combine all these data sources and, with them, construct a large vector of moment

conditions to identify and estimate the key parameters of the model.