FIRM DYNAMICS IN AN URBAN ECONOMY *

• Author: Jeffrey Brinkman,Holger Sieg,Daniele Coen‐Pirani
• DOI: http://doi.org/10.1111/iere.12133
• Published date: 01 November 2015
• Date: 01 November 2015

INTERNATIONAL ECONOMIC REVIEW

Vol. 56, No. 4, November 2015

FIRM DYNAMICS IN AN URBAN ECONOMY∗

BYJEFFREY BRINKMAN,DANIELE COEN-PIRANI,AND HOLGER SIEG1

Federal Reserve Bank of Philadelphia, U.S.A.; University of Pittsburgh, U.S.A.; University of

Pennsylvania, U.S.A.

We develop a new dynamic general equilibrium model to explain firm entry, exit, and relocation decisions in an urban

economy with multiple locations and agglomeration externalities. We characterize the stationary distribution of firms

that arises in equilibrium. We estimate the parameters of the model using a method of moments estimator. Using unique

panel data collected by Dun and Bradstreet, we find that agglomeration externalities increase the productivity of firms

by up to 8%. Economic policies that subsidize firm relocations to the central business district increase agglomeration

externalities in that area. They also increase economic welfare in the economy.

1. INTRODUCTION

A key insight of Marshall (1920) is that geographic proximity of economic activity increases

efficiency in production and trade. Over the past several decades, research has formalized

this idea and developed general equilibrium models to study the impact of agglomeration

externalities on firm choices and economic welfare. This article makes four contributions to this

important literature. First, we develop a dynamic model that provides strong predictions about

firm dynamics as well as entry, exit, and relocation decisions. Most previous research in urban

and regional economics has been based on static models.2Second, we provide an integrated

approach for estimating our dynamic equilibrium model of firm locational choices.3Third, we

use a novel data set and show that our empirical approach provides new empirical insights

into the sorting of firms within large metropolitan areas and the importance of agglomeration

externalities. We find that agglomeration externalities increase the productivity of firms by up

∗Manuscript received October 2013; revised June 2014.

1We would like to thank the editor of the journal, the anonymous referees, Dan Ackerberg, Patrick Bayer, Steven

Berry, Rui Castro, Gilles Duranton, Dennis Epple, Joe Gyourko, Vernon Henderson, Thomas Holmes, Matt Kahn,

Ariel Pakes, Theodore Papageorgiu, Diego Puga, Stephen Redding, Steve Ross, Esteban Rossi-Hansberg, Albert Saiz,

Kurt Schmidheiny, Frank Wolak, Jipeng Zhang, and seminar participants at numerous conferences and universities.

Sieg acknowledges financial support from the NSF (SES-0958705). The views expressed here are those of the authors

and do not necessarily represent the views of the Federal Reserve Bank of Philadelphia or the Federal Reserve System.

Please address correspondence to: Holger Sieg, 459 McNeil Building, 3718 Locust Walk, University of Pennsylvania,

Philadelphia, PA 19104. Phone: 215-898-7194. E-mail: holgers@econ.upenn.edu.

2Henderson (1974) formalized Marshall’s idea in a Muth-Mills type equilibrium model. Krugman (1991) provided

theoretical foundations for a two-location model of agglomeration in the presence of small transportation costs. Anas

and Kim (1996) and Lucas and Rossi-Hansberg (2002) have developed equilibrium models of mono- and poly-centric

urban land use with endogenous congestion and job agglomeration. Rossi-Hansberg (2004) studies optimal land use

policies. Duranton and Puga (2001) focus on the effect of agglomeration externalities in innovation and the development

of production processes. The literature of agglomeration theory is reviewed in Fujita and Thisse (2002) and Duranton

and Puga (2004). Also related to our research is work by Rossi-Hansberg and Wright (2007), who examine the

relationship of establishment scale and entry and exit dynamics.

3From a purely methodological perspective, our article is related to Davis et al. (2014), who develop a growth

model in which the total factor productivity of cities depends on the density of economic activity. They estimate the

magnitude of this external effect and evaluate its importance for the growth rate of consumption per capita in the

United States. Similarly, Holmes (2011) estimates a dynamic model to study the expansion of Walmart and to quantify

the importance of geographic proximity in designing distribution networks. Ahlfeldt et al. (2012) develop a static urban

model of residential and firm location decisions and estimate it exploiting Berlin’s division and reunification as a source

of exogenous variation in the concentration of local economic activity.

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(2015) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

1136 BRINKMAN,COEN-PIRANI,AND SIEG

to 8%. Finally, we show that economic policies that subsidize firm relocations to the central

business district (CBD) increase agglomeration externalities in that area. More importantly,

they can also increase economic welfare in the economy. Hence, our analysis suggests that

place-based policies that encourage firms to relocate to locations with high agglomeration

externalities can be beneficial.

We consider a model of an economy with two distinct locations that endogenously differ

in the magnitude of their agglomeration externalities. Following Lucas and Rossi-Hansberg

(2002), agglomeration externalities are a function of local employment density and, therefore,

depend on firm sorting. We model firm dynamics and industry equilibrium as suggested by

Hopenhayn (1992). Firms enter the economy with an initial productivity and must pay an

entry cost. Productivity then evolves according to a stochastic first-order Markov process. Each

period, firms compete in the product market, must pay a fixed cost of operating, and realize

a profit.4Agglomeration externalities affect firm dynamics and the sorting of firms in at least

three important ways. First, entry patterns depend on local land rental rates and location-

specific externalities. This gives rise to an initial sorting of new firms. Second, the productivity

of firms changes over time, which implies that growth trajectories will differ by location, thus

creating incentives to relocate within a city to exploit a better match with the agglomeration

externalities. Finally, the continuation value for a firm is location specific, which implies that

exit rates depend on location. We characterize the stationary equilibrium of the urban economy

and show that it differs from a static sorting model.

Although we can establish some properties of stationary equilibria, analytical solutions of

equilibria do not exist. Equilibria exist and are locally unique. In particular, two different

equilibria have distinctly different local land rents and agglomeration externalities. When we

estimate the model, we condition on the observed wages and land rents and solve for the unique

equilibrium conditional on these outcomes. This approach then effectively deals with potential

multiplicity problems in estimation.

We develop an algorithm that can be used to estimate the parameters of our model. We show

that a subset of the structural parameters of the model can be estimated using the observed input

and output choices without solving for the equilibrium of the model. The remaining parameters

of the model, which include the cost parameters, affect the equilibrium selection rules and

can be estimated using a nested fixed point algorithm. The estimator is a simulated method of

moments estimator that matches selected moments characterizing entry, exit, and relocation of

firms within the metropolitan area.

Our empirical analysis is based on unique panel data collected by Dun and Bradstreet. Large

U.S. cities often act as a hub for service sector industries for a larger region. We, therefore,

focus on locational choices within the service sector, excluding industries in which proximity

to the consumer is a key factor for firm location. Our analysis reveals a number of important

empirical regularities that characterize firm sorting within metropolitan areas.5Firms located

in the CBD are older and larger than firms located outside the CBD. They use more land and

labor in the production process. However, they face higher rental rates for office space, which

implies that they operate with a higher employee per land ratio. Firms entering or exiting the

4Our data set does not include any measure of investment in research and development. We, therefore, abstract from

investments and innovation, which is discussed in detail in Melitz (2003), Klette and Kortum (2004), and Duranton and

Puga (2004).

5Most previous empirical studies have focused on sorting across cities or metropolitan areas. For example, Ellison and

Glaeser (1997) argued that agglomeration externalities are important to understanding the geographic concentration

of manufacturing in the United States, and Deckle and Eaton (1999) find that the geographic scale of agglomeration

is mostly at the national level, while the financial sector is concentrated in specific metropolitan areas. Combes et al.

(2001) distinguish between selection effects and productivity externalities by estimating productivity distributions

across cities. In contrast, we focus on sorting within a metropolitan area, which is more consistent with the notion that

agglomeration occurs on a local scale. This is consistent with findings by Rosenthal and Strange (2001, 2003). They

report the level and type of agglomeration at different geographic scales and also measure the attenuation of these

externalities within metropolitan areas. Holmes and Stevens (2002) also find evidence of differences in plant scale in

areas of high concentration, suggesting that production externalities act on individual establishments.