Semi‐Nonparametric Estimation of an Equilibrium Search Model
| Author | Pierre Koning,Gerard J. Van Den Berg,Geert Ridder |
| Published date | 01 July 2000 |
| Date | 01 July 2000 |
| DOI | http://doi.org/10.1111/1468-0084.00175 |
SEMI-NONPARAMETRIC ESTIMATION OF AN
EQUILIBRIUM SEARCH MODELy
Pierre Koning, Gerard J. van den Berg, Geert Ridder
I. INTRODUCTION
Most studies on the impact of minimum wages on employment and wages
exploit the fact that minimum wages vary over time or across labor market
segments.1As an alternative, Meyer and Wise (1983a,b) propose a method
in which the employment effect of minimum wages can be inferred using
data on the cross-sectional distribution of wages only, and without any
variation in minimum wages at all. This method rests upon two assump-
tions. First, in the absence of a mandatory minimum wage, the wage
earnings distribution of individual workers has a functional form that is
recoverable (see Flinn and Heckman, 1982). This means that the distribu-
tion belongs to a family of distributions that is not closed under truncation.
Thus the untruncated distribution can be fully identi®ed from its truncated
version (for example, the lognormal distribution belongs to this family of
distributions). Second, above a certain level (close to the minimum wage)
the wage earnings distribution is unaffected by the imposition of a minimum
wage. With these two assumptions it is possible to deduce the number of
workers who should be earning a wage at or below the minimum from the
estimated truncated wage earnings distribution.
The Meyer and Wise technique has been used by e.g. Albñk and Madsen
(1987) and Van Soest (1989). Obviously, the fundamental drawback is that
the estimated effect of the minimum wage is sensitive to functional form
assumptions on the distribution of wage earnings. In particular, the prob-
ability mass below the minimum wage is obtained by extrapolation of a
distribution to a region where there are no observations, and alternative
assumptions on the distribution of wages can result in different estimates of
the effect of (changes in) minimum wages.2In contrast to this, Koning,
Ridder and Van den Berg (1995) present a model in which the effect of
minimum wages can be identi®ed without making untestable distributional
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 62, 3 (2000)
0305-9049
327
#Blackwell Publishers Ltd, 2000. Published by Blackwell Publishers, 108 Cowley Road, Oxford
OX4 1JF,UK and 350 Main Street, Malden, MA 02148, USA.
yThe Organization for Strategic Labor Market Research (OSA) allowed us to use the OSA labor
supply panel data. We thank Aico van Vuuren, Ruud Koning and a referee for many valuable
suggestions.
1See Card and Krueger (1995) and Dolado et al. (1996) for recent surveys of the literature.
2See Dickens, Machin and Manning (1994) for an evaluation of the Meyer and Wiseapproach.
assumptions. They specify and estimate an equilibrium search model which
allows for two types of unemployment: unemployment due to search
frictions (frictional unemployment) and unemployment due to minimum
wages (structural unemployment). This is an interesting distinction, as it
allows one to infer the group of individuals that also would be unemployed
in the absence of minimum wages. Due to the structural setup of the model,
it is possible to identify the rate of structural unemployment with data on
(censored) unemployment durations and/or the fraction of unemployment.
In addition, the rate of structural unemployment is also equal to the
probability mass of the individual productivity distribution below the mini-
mum wage. This can be used as a check on the speci®cation of the
productivity distribution.
In this paper we relax the distribution assumptions made by Koning,
Ridder and Van den Berg (1995) with respect to the productivity distribution
of individual workers. For this we follow the so called `semi-nonparametric'
(SNP) estimation method developed by Gallant and Nychka (1987). The
basic idea of this estimation method is that any proper density can be
approximated by a Hermite series. Within the context of the model, the
advantages of the SNP approach are twofold. First, it allows us to estimate
the truncated productivity density more accurately, resulting in better
estimates of e.g. the elasticity of the rate of structural unemployment with
respect to the minimum wage. Second, it reduces the impact of misspeci®-
cation of the productivity distribution on the implied rate of structural
unemployment. This rate is overidenti®ed, and a more ¯exible functional
form may help us to reduce the biasing impact of this on the parameter
estimates of the model.
The organization of this paper will be as follows. Section II discusses the
Burdett-Mortensen model and the extension to heterogeneous agents. Sec-
tion III describes the data we use in the empirical analysis, and the
likelihood function is derived in Section IV. Section V discusses the
identi®cation of the model, as well as the SNP estimation method. In
Section VI we conduct two simulation experiments in order to test for the
accuracy of the SNP method, as well as to examine the impact of
misspeci®cation on the parameter estimates of the model. In Section VII we
present the estimation results of the equilibrium search model. Section VIII
concludes. Most of the exposition in Sections II± IV will be kept brief, as
the same material is discussed more extensively in Koning, Ridder and Van
den Berg (1995).
II. THE EQUILIBRIUM SEARCH MODEL
(i) Equilibrium search with identical agents
Consider a labour market with identical agents, i.e. a market in which all
workers are equally productive at all ®rms. Even in this case, the
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