9-Search1.pdf

Equilibrium Search Models

and The Transition from School to Work

Audra J. Bowlus

Nicholas M. Kiefer

George R. Neumann *

Date:

June 4, 1997

Abstract

This paper applies an equilibrium search to study the transition from schooling to work of

U.S. high school graduates. We consider the case where there is heterogeneity in firm

productivity and the number of firm types is discrete. For this case the estimation problem

is non-standard and the likelihood function is non-differentiable. This paper provides a

computational method to obtain the MLE and, through several Monte Carlo studies,

characterizes the behavior of the estimator. Applying these methods to the transition

from school to work, our results show that nonemployed blacks receive fewer offers than

whites and employed blacks are more likely to lose their jobs. Importantly, employed

blacks and whites receive job offers at the same rate. However, the difference in job

destruction rates is so great that it accounts for three-quarters of the black-white wage

differential.

Keywords: Labor market transitions; duration models; simulated annealing;discrete non -

parametric heterogeneity; black-white earnings differential.

JEL Classification: J64, J3, C41.

Editorial Communications: Prof. George R. Neumann, Dept. of Economics, Univ. of Iowa,

Iowa City, IA, 52242-1000, USA

* Department of Economics, University of Western Ontario, London, Ontario Canada N6A 5C2; CLS Aarhus, Department of

Economics, University of Aarhus and Department of Economics, Cornell University, Ithaca NY 14853; and Department of Economics,

University of Iowa, Iowa City IA 52242. We have benefited from comments made by colleagues and participants in seminars at Aarhus,

Berkeley, Cornell, Iowa, the Free University of Amsterdam and the University of Western Ontario. This work was supported in part by

NSF grant SES-9122253.

1. Introduction

The essential idea of equilibrium search models of labor market behavior is that

wage policy matters. In contrast, the stylized neoclassical competitive model predicts that

firms paying a wage above the competitive equilibrium will disappear; those offering less

will attract no workers. The search approach introduces "friction" via information

asymmetries. Here, firms that offer high wages are more attractive to workers, obtaining

and retaining employees more readily than firms offering lower wages. Other things

equal high wage firms generate lower profit per worker but make it up on volume. These

simple ideas about wage policy have been stated in informal ways by several scholars.

Hicks (1932, [1966]) discusses the 'Gospel of High Wages' whereby unusually successful

employers pay high wages to have the "pick of the market" (p.36). Kerr (1954) initiated a

long-surviving, although never mainstream, line of research on empirical correlates of

wage policy that has since become known as "Dual Labor Market" theory. While these

early discussions of wage policy are often colorful, formal content has been given to the

ideas only recently in equilibrium search models by Albrecht and Axell (1984), Burdett

(1990), Burdett and Mortensen (1995), and Mortensen (1990). In competitive models

wage policy doesn't matter because by definition in equilibrium the law of one price holds:

all workers of a given type receive the same wage. Even in simple monopsony models

of the labor market (Card and Krueger (1995)) wage policy does not matter because the

law of one price still holds, albeit at lower than the competitive level. In contrast, search

models generate dynamic monopsony power for employers due to the presence of trade

frictions such as the length of time it takes to find a new job. A firm's wage policy is

important in such models because it directly affects the distribution of income in an

economy. Moreover, in such dynamic monopsony models public policy experiments such

as introducing or changing a minimum wage can have employment effects that are quite

different from those expected in the standard competitive case.

Because equilibrium search models provide a natural interpretation of interesting

labor market phenomena, the estimation of such models has attracted considerable

attention. Eckstein and Wolpin (1990) estimate a version of Albrecht and Axell's (1984)

model; van den Berg and Ridder (1993a,1993b), and Kiefer and Neumann (1993), and

Bowlus, Kiefer, and Neumann (1995) estimate a version of Mortensen's (1990) model.

Although these models differ in the forces of competition generated by firms, each

predicts a disperse price equilibrium to exist. In the Albrecht and Axell model the

equilibrium wage distribution is determined by heterogeneity in reservation wages of

workers. In Mortensen's approach the equilibrium wage distribution is determined by the

technology that matches workers to jobs. This is a pure search equilibrium model, in that

heterogeneity in workers or firms is not required for the existence of a dispersed

equilibrium. To date, efforts at fitting these models to data have not been completely

successful. The tight theoretical structure needed to generate simple estimation

strategies results in a poor match between theory and evidence. “Evidence” in this

context consists of data on the search time to find employment, the wage accepted, and

the duration of the job. While the duration data are in reasonable agreement with the

predictions of the theory, the distribution of earnings is not. This is to be expected: when

wage policy matters, higher wages bring forth greater labor supply to firms, and since

workers prefer higher wages, the distribution function of wages is predicted to have a

thick right tail. However, empirical wage distributions typically have thin right tails, looking

much like income distributions for which Pareto distributions are frequently used to

characterize the upper tail. One explanation for this mismatch between theory and

evidence is that unmeasured differences across workers and jobs can not be ignored. Of

course, unobserved heterogeneity, like dummy variables in a regression, can explain any

divergence between fact and theory. We adopt the approach of introducing

heterogeneity in small doses - so that the essential information basis for wage dispersion

is not completely absorbed into "heterogeneity."

In this paper we provide methods for estimating equilibrium search models using a

non-parametric estimator of heterogeneity. In Section 2 we describe the basic equilibrium

search model due to Mortensen (1990) and Burdett and Mortensen (1995) and we

develop the likelihood function appropriate to data generated by this model. For the case

that we consider, namely a discrete number of firm types having different productivity

levels P j , j=1,..,J, the estimation problem is non-standard, and the likelihood function is

not differentiable. We characterize the MLE for this problem and provide a means of

computing it. The computational method we employ exploits the special structure of the

problem. In the first part of the algorithm we calculate the points of support of the wage

distribution in the presence of heterogeneity; in the second part the profile likelihood

function, conditioned on the points of support of the wage distribution, is maximized with

respect to the remaining parameters in the usual manner. Asymptotic independence of

these parameter blocks guarantees that the stepwise maximum is a global maximum.

The third section contains a Monte Carlo study of the properties of the estimators

we propose using all the data from the search model - unemployment duration, accepted

wages, job spell duration and job transitions. In Sections 4 and 5 we apply this

technology to study the transition between school and work for black and white male high

school graduates using the National Longitudinal Survey of Youth (NLSY). This

application has been of considerable policy interest in recent years, so we use it to

examine how well the search framework can explain empirical patterns found in the data.

The model provides a satisfactory fit to the nonemployment durations following

graduation and the wage offer distribution for the first full-time job for both groups. It has

more difficulty matching the job duration data. Longer nonemployment spells and lower

wages for blacks are captured in the model through a lower arrival rate of offers while

nonemployed and a higher job destruction rate while employed. Three quarters of the

black-white wage differential is explained by differences in the search parameters

highlighting the important role labor market mechanisms can play in explaining wage

differentials. Our conclusions are given in the sixth and final section of the paper.

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