ESTABLISHMENT DYNAMICS, VACANCIES, AND UNEMPLOYMENT: A NEOCLASSICAL APPROACH

• DOI: http://doi.org/10.1111/iere.12195
• Published date: 01 November 2016
• Date: 01 November 2016
• Author: Marcelo Veracierto

INTERNATIONAL ECONOMIC REVIEW

Vol. 57, No. 4, November 2016

ESTABLISHMENT DYNAMICS, VACANCIES, AND UNEMPLOYMENT:

A NEOCLASSICAL APPROACH∗

BYMARCELO VERACIERTO1

Federal Reserve Bank of Chicago,U.S.A.

This article introduces and analyzes a Walrasian model of worker flows, job flows, vacancies, and unemployment.

Calibrating the model to U.S. data, the article finds that all variables comove with output quite well but that they

fluctuate too little. However, the failure is not as bad as in “Shimer’s puzzle.” Interestingly, the article also finds that

introducing establishment dynamics into the model, while realistic, is irrelevant for understanding unemployment and

vacancy fluctuations: The business cycles of the model with establishment dynamics are virtually the same as those of

a version with a representative firm.

1. INTRODUCTION

The literature provides two main approaches for analyzing the cyclical behavior of unemploy-

ment and vacancies: the matching/wage-bargaining model of Mortensen and Pissarides (1994)

and the competitive-search/wage-posting model of Moen (1997). In recent years both strands

of the literature have been extended to incorporate establishment level dynamics delivering

rich business cycle models of the labor market (e.g., Cooper et al., 2007; Elsby and Michaels,

2008; Fujita and Nakajima, 2009; and Hawkins, 2011, within the Mortensen–Pissarides class of

models, and Kaas and Kircher, 2011; and Schaal, 2010, within Moen’s). Surprisingly, Walrasian

theory, which plays such a preponderant role in the rest of macroeconomics, has not been used

in this literature. The main purpose of this article is to close this gap by introducing a Walrasian

alternative for analyzing establishment dynamics, unemployment, and vacancies over the busi-

ness cycle. In the process of doing this, the article provides an important irrelevance result. It

shows that, while giving rise to a great deal of richness and realism, all the heterogeneity at the

establishment level turns out to be irrelevant for the cyclical behavior of unemployment and

vacancies.

The model used is as follows. The economy is populated by a representative household with

a continuum of members that value consumption and leisure. Output, which can be consumed

or invested, is produced by a large number of spatially separated establishments that are subject

to aggregate and idiosyncratic productivity shocks. The amount of hiring that an establishment

can undertake is constrained by the number of recruitment opportunities that it has avail-

able at the beginning of the period. Unemployed workers can become employed only if they

gain employment opportunities. Recruitment opportunities for establishments and employ-

ment opportunities for workers are jointly produced by a neoclassical recruitment technology

that uses the consumption good and unemployed workers as inputs of production. All hiring

∗Manuscript received May 2012; revised February 2014.

1This article originated in a conversation with Randall Wright and was heavily influenced by it. I have also benefited

from the comments of Bjoern Bruegemann, Marco Cozzi, Michael Elsby, Toshihiko Mukoyama, Nicolas Petrosky-

Nadeau, three anonymous referees, and the editor, Guido Menzio. All remaining errors are solely mine. The views

expressed here do not necessarily reflect the position of the Federal Reserve Bank of Chicago or the Federal Re-

serve System. Please address correspondence to: Marcelo Veracierto, Federal Reserve Bank of Chicago, Research

Department, 230 South LaSalle Street, Chicago, IL 60604. Phone: (312) 322-5695. E-mail: mveracierto@frbchi.org.

1201

C

(2016) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

1202 VERACIERTO

takes place at a central location, an assumption that is crucial for introducing Walrasian labor

markets.2

The article defines and characterizes a recursive competitive equilibrium for this economy. A

key feature of the competitive equilibrium is that workers sign complete and perfectly enforce-

able state contingent employment contracts with their employers. Another important feature

is that the recruitment technology is operated by a competitive recruitment industry. Since

the economy is convex and has no distortions, the welfare theorems apply and equilibrium

allocations can be obtained as solutions to a social planner’s problem. This planner’s problem

is intractable since the state space of an individual establishment is infinite dimensional and

the planner needs to keep track of the distribution of establishments across individual states.

However, stationary equilibrium allocations turn out to solve a simplified planner’s problem, in

which the only relevant state variables of an establishment are its previous employment level, its

current recruitment opportunities, and its current idiosyncratic productivity level. The recruit-

ment opportunities and employment decision rules of establishments in this simplified planning

problem are shown to be of the (S,s) variety. This property together with the assumption that

the idiosyncratic productivity shocks take a finite number of values imply that the distribution

over establishment types has a finite support. A consequence of this is that the simplified social

planner’s problem can be formulated in terms of a finite number of state and decision variables.

This is a crucial result: Despite the model’s complexity, simple linear-quadratic methods can be

used for computing a stationary equilibrium allocation.

The article then evaluates the empirical performance of the model. Some parameter values

are closely related to the neoclassical growth model and are calibrated to reproduce similar ob-

servations. The rest of the parameters are chosen to reproduce observations on establishment

dynamics, worker flows, and vacancies. When an aggregate productivity shock of empirically

relevant magnitude is introduced, the article finds that the model fails to reproduce the data.

In particular, unemployment, vacancies, and job flows fluctuate less than their empirical coun-

terparts. However, the failure is not as dramatic as in Shimer (2005). For instance, whereas

Shimer finds that aggregate productivity shocks generate unemployment fluctuations that are

5% as large as in the data, this article finds them to be about 30% as large. Interestingly, the

rich establishment level dynamics that the model incorporates plays no role in generating this

amplification. In fact, a representative version of the economy is found to generate identical ag-

gregate fluctuations as the economy with heterogeneous establishments. Most of the differences

with Shimer (2005) are the consequence of a different calibration strategy.

The article is closely related to a number of previous studies analyzing labor markets dynam-

ics over the business cycle.3Similarly to Veracierto (2008a), Samaniego (2008), and Lee and

Mukoyama (2008), the article constructs a real business cycle model that incorporates estab-

lishment dynamics and Walrasian markets as in Hopenhayn and Rogerson (1993). However,

it extends those studies by introducing search frictions, which are essential for analyzing un-

employment. With Gomes et al. (2001) and Veracierto (2008b), the article shares the search

frictions and Walrasian markets of Lucas and Prescott (1974), but, contrary to those studies, it

incorporates two-sided search: Not only workers, but firms, actively participate in the search

process. This allows us to define vacancies in an empirically meaningful way and analyze their

behavior.4Finally, as was already mentioned, the article is closely related to the recent litera-

ture evaluating the business cycle properties of the classes of models introduced by Mortensen

and Pissarides (1994) and Moen (1997), especially to their recent extensions incorporating

2Recruitment opportunities for establishments and employment opportunities for workers can be thought of as

“tickets” for traveling to this central market.

3The article is also closely related to a class of search models of money, first introduced by Rocheteau and Wright

(2005), where prices are determined in competitive markets despite there being matching frictions. This is possible

because, similarly to this article, matched agents travel to a centralized trading location.

4In Lucas and Prescott (1974) firms behave as if they could hire any number of workers at the competitive wage rate

that they face. As a consequence, firms have no job openings that they are seeking to fill by undertaking some type of

recruitment activity; that is, there are no vacancies.

NEOCLASSICAL LABOR MARKET DYNAMICS 1203

establishments level dynamics. However, to understand the differences with these models it will

be convenient to postpone the discussion until the benchmark economy has been described in

detail.

The article is organized as follows. Section 2 describes the benchmark economy, its recur-

sive competitive equilibrium, and its relation to alternative specifications in the literature.

Section 3 characterizes a recursive competitive equilibrium and describes how to compute

it. Section 4 calibrates the model. Section 5 presents the business cycle properties of the model.

Section 6 considers a representative firm version of the model. Finally, Section 7 concludes the

article. An online Technical Appendix provides proofs to the claims made in the article.

2. THE ECONOMY

The economy is populated by a representative household that has a continuum of members

called workers with names in the unit interval. Workers can be either employed or unemployed:

Employed workers produce the consumption good and unemployed workers specialize in leisure

activities. An employed worker can become unemployed at no cost. However, an unemployed

worker can become employed only if he succeeds in making a trip to a centralized location called

the hiring market. A successful trip to the hiring market is called an employment opportunity.

All employed workers are subject to an idiosyncratic productivity shock called a quit shock that

makes them temporarily unproductive. A worker that quits needs to spend a full period of time

unemployed before regaining his productive capacity. The probability that a worker quits is

given by π.

The preferences of the representative household are given by

E0∞



t=0

βtc1−σ

t−1

1−σ+ϕut,(1)

where ctis the consumption level of a household member, utis the total number of unemployed

household members, ϕ>0, σ>0, and 0 1. This specification implicitly assumes that

workers obtain perfect insurance within the household (as in Merz, 1995).

The consumption good is produced by a large number of establishments. Each establishment

has a production function given by

yt=eztstF(nt,kt),

where ztis an aggregate productivity shock, stis an idiosyncratic productivity shock, ntis the

number of employed workers, ktis physical capital, and Fis a continuously differentiable,

strictly increasing, strictly concave, and decreasing returns to scale production function that

satisfies the Inada conditions. The idiosyncratic productivity shock sttakes values in a finite

set Sand follows a Markov process with monotone transition matrix Q. Realizations of stare

independent across establishments, and st=0 is an absorbing state. Since there are no fixed

costs of operation, exit takes place only when the idiosyncratic productivity level becomes

zero. In every period of time a measure of new establishments is exogenously born. Their

distribution over initial productivity shocks is given by ψ. In turn, the aggregate productivity

shock follows an AR(1) process given by

zt+1=ρzt+εt+1,(2)

where 0 ≤ρ<1,and εt+1is i.i.d., normally distributed, with variance σ2

εand zero mean.

The number of employed workers ntat an establishment is given by

nt=nt−1+ht−ft,(3)