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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.
I. Introduction
The ability to estimate and test econometric models over nonrandomly chosen subsamples is unquestionably one of the more significant innovations in microeconometrics. Since James Heckman's seminal work on sample selection bias, the economics literature has abounded with empirical applications employing his proposed methodology. Although Heckman's ideas initially had a more significant impact on empirical studies, the recent interest in semi- and nonparametric estimation of econometric models has revitalized the theoretical interest in the sample selection model. Despite its wide applicability the model initially considered by Heckman had a rather limited structure and was highly parameterized. Subsequent papers, however, have extended it in two important directions. First, although the original model accounted for a selection process captured by a dichotomous outcome subsequent approaches have incorporated different censoring rules in the selection equation. Second, the popularity of semi- and nonparametric econometrics has seen the relaxation of many of the model's assumptions. Given the prominence of the sample selection model in microeconometrics, it is useful to survey the literature motivated by Heckman's initial investigations.
The primary objective of this paper is to provide an intuitive discussion of the ideas underlying the various estimators available for models contaminated with selection bias. I attempt to cover a wide range of estimators and provide insight into how they eliminate selection bias. I do not, however, provide a detailed discussion of their properties nor do I provide efficiency comparisons for different estimators suitable for the same model. This decision does not reflect any opinion regarding the importance of these issues but is based on the length of the discussion that would be required.
Some of the following discussion can be found in existing surveys on subsections of the literature I cover (see, for example, Maddala 1983, Verbeek and Nijman...