Empirical Search Models

This chapter discusses various methods that have been used to estimate structural models of search and survival models. Most of the focus is on using available data, usually on unemployment spell lengths and accepted wage o¤ers, to estimate the parameters of speci...c search models. In particular, we focus on estimating the parameters of the wage o¤er distribution, the reservation wage or reservation wage function, the cost of search, o¤er arrival rate, and discount rate. There is an added section on survival models because survival models have been used so extensively to look at unemployment spell data. Throughout we describe actual models, estimation procedures, and issues associated with identi...cation and estimation. There is not as much of an emphasis on results because we view the literature as still developing methodology. The frontier of the methodology for structural models involves estimating equilibrium search models and allowing for heterogeneity and interesting dynamics. We also think identi...cation issues should receive more attention. This chapter is divided up into sections. The next section presents the classical search model and how to estimate its parameters. We begin by presenting early ”semi-structural” attempts to estimate the model. Next, there is a discussion on estimating a basic structural search model. We build on the basic model by allowing for measurement error in wages, observed and unobserved heterogeneity, right censoring, continuous time, and observed rejected o¤ers. Next, there is a discussion of models with changing reservation wages. The third section deals with survival analysis. We construct the basic Cox proportional hazards model with unobserved heterogeneity and discuss how to estimate the e¤ects of observed covariates, the parameters of the baseline hazard function and the parameters of the unobserved heterogeneity density function. Then we discuss semiparametric approaches associated with estimating the baseline hazard and unobserved heterogeneity density function. The next section discusses empirical equilibrium search models. A few theoretical models are presented. Then we discuss how to estimate their structural parameters and to deal with special problems associated with such models. Given present data, identi...cation is an important issue. A conclusion ends the paper.