Estimating Models with Sample Selection Bias: A Survey

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. University of Wisconsin Press andThe Board of Regents of the University of Wisconsin System are collaborating with JSTOR to digitize, preserve and extend access to The Journal of Human Resources. ABSTRACT This paper surveys the available methods for estimating models with sample selection bias. I initially examine the fully parameterized model proposed by Heckman (1979) before investigating departures in two directions. First, I consider the relaxation of distributional assumptions. In doing so I present the available semi-parametric procedures. Second, I investigate the ability to tackle different selection rules generating the selection bias. Finally, I discuss how the estimation procedures applied in the cross-sectional case can be extended to panel data. Symposium: Vella 129 be similar to the average characteristics of the population. Now consider where the decision to work is no longer random and consequently the working and nonworking samples potentially have different characteristics. Sample selection bias arises when some component of the work decision is relevant to the wage determining process. That is, when some of the determinants of the work decision are also influencing the wage. When the relationship between the work decision and the wage is purely through the observables, however, one can control for this by including the appropriate conditioning variables in the wage equation. Thus, sample selection bias will not arise purely because of differences in observable characteristics.If I now assume the unobservable characteristics affecting the work decision are correlated with the unobservable characteristics affecting the wage, however, I generate a relationship between the work decision and the process determining wages. Controlling for the observable characteristics when explaining wages is insufficient, as some additional process is influencing the wage, namely, the process determining whether an individual works. If these unobservable characteristics are correlated with the observables then the failure to include an estimate of the unobservables will lead to incorrect inference regarding the impact of the observables on wages. Thus, a bias will be induced due to the sample selection.This discussion highlights that sample selectivity operates through unobservable elements and their correlation with observed variables, although often one can be alerted to its possible presence through differences in observables across the two samples. However, this latter condition is by no means necessary, or even indicative, of selection bias. Although this example is only illustrative, it highlights the generality of the issues and their relevance to many economic examples. The...

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