Kenneth Burdett

Wage Differentials, Employer Size, and Unemployment

The unique equilibrium solution to a game in which a continuum of individual employers choose permanent wage offers and a continuum of workers search by sequentially sampling from the set of offers is characterized. Wage dispersion is a robust outcome provided that workers search while employed as well as when unemployed. The unique nondegenerate equilibrium distribution of wage offers is constructed for three cases: (1) identical workers and employers, (2) identical employers and an atomless distribution of worker supply prices, and (3) identical workers and an atomless distribution of job productivities. Copyright 1998 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Marriage and Class

Here we consider a matching model where agents are heterogeneous and utilities nontransferable. We utilize this framework to study how equilibrium sorting takes place in marriage markets. We impose conditions that guarantee the existence of a steady state equihbrium and then characterize it. Several examples are developed to illustrate the richness of equilibria. The model reveals an interesting sorting externality that can support multiple steady state equilibria, even with constant returns to matching.

Pricing and Matching with Frictions

Suppose that n buyers each want one unit and m sellers each have one or more units of a good. Sellers post prices, and then buyers choose sellers. In symmetric equilibrium, similar sellers all post one price, and buyers randomize. Hence, more or fewer buyers may arrive than a seller can accommodate. We call this frictions. We solve for prices and the endogenous matching function for finite n and m and consider the limit as n and m grow. The matching function displays decreasing returns but converges to constant returns. We argue that the standard matching function in the literature is misspecified and discuss implications for the Beveridge curve.

LONG-TERM PARTNERSHIP FORMATION: MARRIAGE AND EMPLOYMENT*

Of course, marriage and employment are different. Nevertheless, a worker looking for a job, a ®rm looking for worker, or a single person looking for a marriage partner face similar problems as all are seeking a long-term partner. Indeed, forming long-term partnerships is a common occurrence in life. There are many other examples ± business people search for other business people to form a pro®table relationship, bridge players seek to ®nd a suitable partners, students search for a good university, we would all like to ®nd a good friend, etc. The problem becomes signi®cant if there are substantial differences in the return obtained from forming a partnership with different partners. For example, employers differ in the wages they offer, or in the work environment they provide. In such a situation a worker may reject some job offers. Similarly, as many have learned to their cost, some make better marriage partners than others. The problem is two-sided. While a worker is evaluating a potential employer, the employer is also evaluating the worker. It is this two-sided aspect of the problem that generates a signi®cant interest. A workers willingness to accept employment at a ®rm depends not only on the characteristics of the ®rm but also the other possible options open to the worker. The better an individuals opportunities elsewhere, the more selective he or she will be in evaluating a potential partnership. An academic who believes Harvard may make an offer in the near future, will be more selective in evaluating offers from lesser universities. In this way expectations play a role. If a single man believes that few, if any, women will ®nd him an acceptable marriage partner, then he may accept the ®rst opportunity that presents itself. Partnership formation, typically, does not comply with a classic market situation, where all participants know everything and all trades take place at zero cost. Finding a job, ®nding a husband or wife, or ®nding a business partner is a time consuming activity where opportunities typically arrive over time at uncertain intervals of time. Of course, we can act in ways that in uence the arrival rate of potential partner. Workers go to employment agencies, or read help wanted advertisements in newspapers, singles of a certain age go to discos, or join tennis clubs. The literature on search and matching (SM) (see Mortensen (1982), and Pissarides (1990) for early examples)1 provides an excellent framework for The Economic Journal, 109 ( June), F307±F334. # Royal Economic Society 1999. Published by Blackwell Publishers, 108 Cowley Road, Oxford OX4 1JF, UK and 350 Main Street, Malden, MA 02148, USA.

Equilibrium Wage-Tenure Contracts

In this study we consider a labor market matching model where firms post wage-tenure contracts and workers, both employed and unemployed, search for new job opportunities. Given workers are risk averse, we establish there is a unique equilibrium in the environment considered. Although firms in the market make different offers in equilibrium, all post a wage-tenure contract that implies a workers wage increases smoothly with tenure at the firm. As firms make different offers, there is job turnover, as employed workers move jobs as the opportunity arises. This implies the increase in a workers wage can be due to job-to-job movements as well as wage-tenure effects. Further, there is a nondegenerate equilibrium distribution of initial wage offers that is differentiable on its support except for a mass point at the lowest initial wage. We also show that relevant characteristics of the equilibrium can be written as explicit functions of preferences and the other market parameters.

Crime, Inequality, and Unemployment

There has been much discussion of the relationships between crime, inequality and unemployment. We construct a model where all three are endogenous. Introducing crime into otherwise standard models affects the labor market in several interesting ways. For example, we show how the crime rate affects the unemployment rate and vice-versa; how the possibility of criminal activity can lead to wage inequality among homogeneous workers; and how the possibility of crime can generate multiple equilibria in natural but previously unexplored ways. In particular, two fundamentally identical neighborhoods may easily end up with different levels of unemployment, inequality, and crime. The model can be used to study the equilibrium effects of anti-crime policies, such as changes in apprehension rates or jail sentences, as well as more traditional labor market policies such as unemployment insurance.

Search, Layoffs, and Labor Market Equilibrium

The paper has two purposes: (1) to extend the theory of job search to include the case in which job prospects are characterized by layoff risk as well as the wage and (2) to synthesize the search and implicit-contract approaches by using the former to model the supply side and the latter to model the demand side of a labor market. The result is a simple and consistent theory of labor market equilibrium under conditions of imperfect information and uncertain derived demand. The theory purports to explain both search and layoff unemployment as market equilibrium phenomena.

AN ON‐THE‐JOB SEARCH MODEL OF CRIME, INEQUALITY, AND UNEMPLOYMENT*

We extend simple search models of crime, unemployment, and inequality to incorporate on-the-job search. This is valuable because, although simple models are useful, on-the-job search models are more interesting theoretically and more relevant empirically. We characterize the wage distribution, unemployment rate, and crime rate theoretically, and use quantitative methods to illustrate key results. For example, we find that increasing the unemployment insurance replacement rate from 53 to 65 percent increases unemployment and crime rates from 10 and 2.7 percent to 14 and 5.2 percent. We show multiple equilibria arise for some fairly reasonable parameters; in one case, unemployment can be 6 or 23 percent, and crime 0 or 10 percent, depending on the equilibrium.

The low skill trap

Recently, it has become popular to argue that certain workers have fallen into a trap in which they have poor skills, few job opportunities and a low return on training, while others have not. This paper demonstrates how such a trap can occur within a simple matching model with rent sharing. Rent sharing diminishes the workers incentive to acquire skills; however, since firms also benefit from training, rent sharing likewise induces job creation. The subsequent improved matching prospects may offset the initial disincentive to invest. However, for this mechanism to be effective, firms and workers must coordinate their actions. If they do not, the trap occurs.

HUMAN CAPITAL ACCUMULATION AND LABOR MARKET EQUILIBRIUM

The objective of this paper is to analyse an equilibrium search model with on-the-job search and human capital accumulation. In our model wages are disperse because firms pay workers of the same productivity different wages and workers of different productivies earn different wages. New entrants to the labour market increase their wages mainly through on-the-job search. As workers gain more experience and move up the offer distribution, job-to-job transitions become less frequent and human capital accumulation dominates wage growth. This interaction generates a wage distribution that exhibits a density with a unique mode and a long and decreasing right tail as observed in the data.