EFFICIENCY AND LABOR MARKET DYNAMICS IN A MODEL OF LABOR SELECTION

• Published date: 01 November 2016
• DOI: http://doi.org/10.1111/iere.12201
• Author: Christian Merkl,Sanjay K. Chugh
• Date: 01 November 2016

INTERNATIONAL ECONOMIC REVIEW

Vol. 57, No. 4, November 2016

EFFICIENCY AND LABOR MARKET DYNAMICS IN A MODEL OF LABOR

SELECTION∗

BYSANJAY K. CHUGH AND CHRISTIAN MERKL1

Ohio State University, U.S.A., and Kiel Institute for the World Economy, Germany;

Friedrich-Alexander-Universit¨

at Erlangen-N¨

urnberg (FAU).Germany, Kiel Institutefor the

World Economy, Germany,and IZA Institute, Germany

This article characterizes efficient labor market allocations in a labor selection model. The model’s crucial aspect is

cross-sectional heterogeneity for new job contacts, which leads to an endogenous selection threshold for new hires. With

cross-sectional dispersion calibrated to microeconomic data, 40% of empirically relevant fluctuations in the job-finding

rate arise, which contrasts with results in an efficient search and matching economy. The efficient selection model’s

results hold in partial and general equilibrium, as well as with sequential search.

1. INTRODUCTION

This article uses microeconomic data on heterogeneity in training costs (or, more generally,

idiosyncratic productivity for new matches) to show that a labor selection model displays large

fluctuations in aggregate labor markets. Based on our microcalibration, the main result is that,

conditional on productivity shocks, roughly 40% of empirically relevant fluctuations in the

U.S. job-finding rate can be described by an efcient labor selection mechanism. These results

are several times larger than in an efficient search and matching model, and the efficient

selection model’s results hold in both partial equilibrium fluctuations and in general equilibrium

fluctuations.

Selection as an important margin of adjustment in firms’ hiring decisions is a long-standing

realistic idea, but has not been much emphasized in macro-labor analysis. An early important

empirical firm-level contribution was Barron et al. (1985, p. 50), who adopt and find strong

evidence for the view that “ . .. most employment is the outcome of an employer selecting from

a pool of job applicants ...”duetocross-sectional heterogeneity in the pool of applicants. Davis

et al. (2013) add further evidence to the view that, in their terminology, “hiring standards” play

an important role among the many margins of labor adjustment. Selection issues seemingly

would be an important component of hiring standards.

Our model’s analysis revolves around one critical microeconomic parameter, which is

the cross-sectional dispersion of new hires’ idiosyncratic training costs (or, more generally,

∗Manuscript received April 2013; revised July 2015.

1We thank Sushant Acharya, Susanto Basu, Matteo Cacciatore, Ryan Chahrour, Timothy Fuerst, Simon Gilchrist,

Veronica Guerrieri, Joseph Kaboski, Wolfgang Lechthaler, Guido Lorenzoni, Steven Lugauer, Michael Pries, Federico

Ravenna, Claire Reicher, Aysegul Sahin, Nicolas Vincent, and Henning Weber for useful feedback at various stages of

the project. Sanjay K. Chugh thanks the “Sch¨

oller Forschungszentrum” for financial support. Christian Merkl thanks

the Fritz Thyssen foundation for financial support during his visit at the National Bureau of Economic Research, where

the project was initiated, and the German Science Foundation (SPP 1764). Ana Lariau, Verena Maier, and Kilian

Ruppert have provided brilliant research assistance. We received helpful comments at presentations at the Federal

Reserve Board, the Federal Reserve Bank of New York, the 2011 SED Meetings, the German Economic Association,

Sveriges Riksbank, the Federal Reserve Bank of Cleveland, the Ifo Macro Seminar, the Boston College Macro Lunch

Workshop, the University of Notre Dame, the Kiel Institute, and HEC Montr´

eal.

Please address correspondence to: Christian Merkl, Friedrich-Alexander-Universit¨

at Erlangen-N¨

urnberg,

Lange Gasse 20, 90403 N ¨

urnberg, Germany. Phone: +49-911-5302-337. Fax: +49-911-5302-345. E-mail:

christian.merkl@fau.de.

1371

C

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

and Economic Research Association

1372 CHUGH AND MERKL

idiosyncratic productivity for new workers). Taking this cross-sectional dispersion as an ex-

ogenous primitive, the model economy delivers an endogenous selection threshold for new

employees. The primary data source used to discipline this cross-sectional dispersion is the 1982

U.S. Employer Opportunity Pilot Project (EOPP), which many researchers continue to use to

this day. Our focus, unlike many others who use the rich EOPP data, is on the cross section

of new hires’ training costs; to that effect, we use the cross-sectional moments calculated by

Barron et al. (1989, table 1).

The social planner framework we construct intentionally says nothing about decentralization

via wages. However, we show in Appendix D that efficiency can be decentralized. For the sake

of robustness, we also use a second, independent, data source to discipline the cross section,

which are micro-level wage data for newly hired employees constructed by Haefke et al. (2013).

We show in two different model-based ways that the wage dispersion for newly hired employees

is a very useful information to discipline our calibration exercise. Regardless of which micro

data source is used, macro-level volatility in labor markets is an order of magnitude larger than

in an efficient search and matching framework.

We show analytically that the outside option plays a different role in efficient selection models

compared to efficient search and matching models. In the selection model, the outside option

has zero first-order effect on the steady-state elasticity of the job-finding rate with respect

to productivity. In contrast, the outside option appears directly in the search and matching

model’s steady-state elasticity of the job-finding rate with respect to productivity. In the selection

framework, the driving force for amplification is the shape of the idiosyncratic distribution at

the endogenous selection threshold.

The selection model’s results depend on a distributional assumption about heterogeneous

training characteristics (which could be interpreted as “match quality” characteristics), and, in

turn, how large the mass of individuals is that moves across the endogenously time-varying

selection threshold conditional on aggregate productivity shocks. We thus consider several

different distributions. We also allow for sequential search (`

a la McCall, 1970; Mortensen,

1970) to permit an arbitrary number of “job arrivals” or “interviews” (and hence an arbitrary

number of “match-quality” realizations) during a given time period. The quantitative results,

of course, differ slightly as we vary distributions and vary the number of per-period contacts

(also known as the job arrival rate) via sequential search within an empirically plausible range,

but the main result remains the same: An efficient labor selection model provides powerful

amplification effects on job-finding rates and unemployment rates in response to productivity

shocks.

Focusing the model on selection effects and efficiency allows us to highlight that no other

frictions are needed to deliver sharp fluctuations in the labor market, which makes the intuition

easy to understand.2,3This focus on selection does not deny that other frictions, be they on

quantities or on prices, do not or cannot play an important role in macro-labor dynamics.

Rather, our focus on efficient selection is meant as a first step.

Extensively studied in the literature is the role of search and matching frictions, along with

frameworks such as the involuntary unemployment framework of Christiano et al. (2010), the

rigid-wage class of models as in Gali (2011) and Gali et al. (2012), as well as earlier versions

of the labor selection model incorporating New Keynesian pricing frictions and wage-setting

frictions, such as Lechthaler et al. (2010). These various models, based on different primitives

and distortions, do not disentangle the amplification effects that are due to efficient surplus

splitting versus inefficient surplus splitting. The point of our work is to analytically and quan-

titatively analyze efficient allocations in a tractable dynamic selection model, in a way that

2Carlsson et al. (2013) find that the market tightness of local labor markets in Sweden does not affect job creation.

This suggests that other margins such as labor selection may be at work.

3Although this focus on one margin of the labor market (namely, selection) may seem extreme at first sight, it is

similar to many search and matching papers that assume that all workers who make a contact with a firm get matched.

This is the case if the matching function is interpreted as a contact function (i.e., contact is endogenous, whereas

selection is exogenous). For a further discussion of this issue, see Brown et al. (2015).

EFFICIENT LABOR SELECTION DYNAMICS 1373

can be traced all the way back to the early indivisible (and efficient) labor models of Hansen

(1985) and Rogerson (1988). Our model and its workings has interpretations in terms of the

indivisible labor models of Hansen (1985) and Rogerson (1988), and it has connections with

their generalization in terms of heterogeneity developed in Mulligan (2001).

The rest of the article is organized as follows: Section 2 describes the details of the selection

model, derives analytical results for the efficient partial equilibrium version, and provides

some intuition. Section 3 shows quantitative results in partial equilibrium and checks for the

robustness of these results. Section 4 enlarges the model to general equilibrium by including

endogenous labor force participation (LFP) and an aggregate goods resource constraint, in

which the labor market results carry through. Section 5 concludes.

2. LABOR MARKETS I:ANALYTICS

This section defines the basic labor market setup and notation that will be used throughout

the article. To focus on the main results of the model, both Sections 2 and 3 abstract from

consumption markets and hence could be thought of “partial equilibrium.”

2.1. Structure of Labor Market. There are two central features of the model. First, each

newly selected worker imposes training costs on his employer (or, more generally, he draws a

match-specific idiosyncratic shock).4The training costs consist of a fixed component, γh>0,

and an idiosyncratic component, εi

t, for newly hired individual i. The idiosyncratic component is

revealed only when a potential worker makes contact with a firm, as shown in Figure 1, below.

The idiosyncratic component of training is the “match quality” cost in our analysis.5There is a

continuum of production units, each of which is constant-returns-to-scale and homogenous in

all other respects.

This is the second central feature of the model: Depending on his training costs realized at

a specific production unit, the potential new worker may or may not be hired. If not hired,

the individual makes finitely many more “meetings with” or “contacts with” (we use the terms

“meeting,” “contact,” “job arrival,” and“job offer” synonymously) another firm, at which he

may have had a lower contact-specific training cost, during the same period. This latter aspect of

the model is the well-known sequential search model. Until we incorporate sequential search in

Section 3, suppose that each individual available to be selected for work in a given time period

makes contact with one arbitrary production unit with probability 1. The one-contact-per-period

framework conveys virtually all of the economic intuition of the article.

From a planning perspective, it is thus efficient to hire only those individuals with sufficiently

attractive characteristics. Sufficiency is characterized by an endogenous state-contingent selec-

tion threshold, ˜εt. Because individual i’s idiosyncratic characteristics are defined as a cost,heis

hired only if εi

t≤˜εt. Training costs are i.i.d. across worker–firm pairs within any given period and

across time periods, with probability density function f(εt). Selection occurs with endogenous

probability η(˜εt), which is the cumulative distribution function of ε; all searching individuals

being considered for a job draw from the same distribution.

Both the fixed component of training costs γhand the idiosyncratic component of training

costs εi

tare measured in units of output, and they are incurred in only the rst period of a

new employment relationship.6In contrast, each incumbent worker has zero training costs and

produces stochastic output ztin period t. Newly hired worker iproduces output net of training

costs zt−εi

t−γh.

4We will interchangeably refer to “firms” and “production units” in what follows because of the linearity of the

production technology and the fact that we study only efficient allocations, so the manner in which employment

surpluses are split via wages in a decentralized economy does not affect the results.

5There is no traditional matching function in the model as in the Pissarides (1985) framework. One could suppose

that a simple matching, or “contact,” function exists in which the measure of contacts equals the number of searching

individuals.

6Individuals who have been employed for more than one period are identical in their characteristics.