Unobserved Heterogeneity, Exit Rates, and Re‐Employment Wages

• DOI: http://doi.org/10.1111/sjoe.12173
• Author: Pedro Gomes,Javier Fernández‐Blanco
• Published date: 01 April 2017
• Date: 01 April 2017

Scand. J. of Economics 119(2), 375–404, 2017

DOI: 10.1111/sjoe.12173

Unobserved Heterogeneity, Exit Rates,

and Re-Employment Wages∗

Javier Fern´

andez-Blanco

Universitat Aut`

onoma de Barcelona and Barcelona GSE, 08193 Bellaterra, Spain

javier.fernandez@uab.cat

Pedro Gomes

Universidad Carlos III, 28903 Getafe, Spain

pgomes@eco.uc3m.es

Abstract

Exit rates from unemployment and re-employment wages decline over a period of unemploy-

ment, after controlling for worker observable characteristics. We study the role of unobserved

heterogeneity in an economy with asymmetric information and directed search. We show that

the unique equilibrium is separating and that skilled workers have more job opportunities

and higher wages. The composition of the unemployed varies with the duration of unem-

ployment, so average exit rates and wages fall with time. The separating equilibrium relies

on performance-related pay schemes and the ability of firms to commit to renting an input

that is complementary to worker skills.

Keywords: Asymmetric information; directed search; unemployment duration

JEL classification:J01; J21; J42; J64

I. Introduction

It is well documented that exit rates from unemployment and wages from

re-employment decline with the duration of unemployment, after control-

ling for worker observable characteristics. Since Lancaster (1979) and

Heckman and Singer (1984), the empirical literature has emphasized that

ex ante unobserved heterogeneity (or sorting) accounts for a large part of

the decline in exit rates. According to this explanation, workers differ in

terms of certain time-invariant characteristics, which are unobservable to

the econometrician and potentially to recruiting firms, and this translates

into differences in employment prospects. As a result, the average exit

rates fall with the duration of unemployment because of variation in the

composition of the unemployed. Despite its quantitative importance, very

∗A previous version was circulated under the title “Composition effects in the labor market”.

We thank Jan Eeckhout, Bel´

en Jerez, Claudio Michelacci, and Edgar Preugschat for their

valuable feedback. J. Fern´

andez-Blanco acknowledges financial support from the Spanish

Ministry of Science and Technology under Grant Nos. ECO2010-19357 and EC02013-46395.

CThe editors of The Scandinavian Journal of Economics 2016.

376 Unobserved heterogeneity, exit rates, and re-employment wages

little theoretical research has been performed to address this explanation.

Lockwood (1991) was a remarkable early exception, but re-employment

wages were assumed to be constant in this study. Gonzalez and Shi (2010)

and Fern´

andez-Blanco and Preugschat (2014) provided theoretical explana-

tions of the duration dynamics of one of these two variables, but they were

not conclusive about the other variable. Furthermore, the explanation of

sorting in these three studies was somewhat circular because worker het-

erogeneity was modeled based on exogenous differences in the likelihood

of obtaining a job.

We consider a sorting mechanism based on productivity differences

across workers, which is consistent with falling exit rates and wages. We

analyze a frictional labor market in which workers are informed privately

about skills and search is directed. These skills are treated as abilities that

recruiters cannot grasp either from a CV or an interview, but they can be

assessed on the job. An adverse selection problem arises if unskilled work-

ers crowd out skilled applicants. Thus, firms design self-selection schemes

in equilibrium to separate worker types in different submarkets. The sort-

ing mechanism relies on two ingredients. First, in the absence of screening

devices, performance-contingent compensation plans are a central feature

of these sorting schemes, as noted in the literature regarding personnel eco-

nomics (e.g., Lazear and Shaw, 2007). In our study, performance-related

pay is derived from the assumption that rents generated by a job–worker

pair are split according to some exogenous rule. Second, firms have the

ability to commit to renting an input that is complementary in terms of

production to the skills of workers. We refer to that production input as

capital or machine quality.1These linear renting costs together with the

concavity of the production technology mean that the surplus generated by

a firm–worker pair is hump-shaped in capital.

Firms ar e ex ante identical. In equilibrium, a mass of firms commits

to renting the machine quality that maximizes the surplus derived from a

match with an unskilled worker. Likewise, a continuum of firms commits

to machines with higher quality because they and skilled workers anticipate

that their match would produce a larger surplus, and thus higher wages and

profits. Higher expected profits attract a relatively higher number of fir ms,

so they are associated with higher exit rates from unemployment. Therefore,

the average exit rate from unemployment and the average re-employment

wage fall with duration because of the variation in the composition of the

unemployment pool.

1We interpret machine quality in a generic manner as any set of inputs that are comple-

mentary in terms of production to unobservable skills. For example, this set could contain

co-workers, physical capital, and software (to the extent that the documented complementari-

ties with the observable characteristics of the labor input, mainly education, can be extended

to the unobservable characteristics), or intermediate goods.

CThe editors of The Scandinavian Journal of Economics 2016.