Models for Sample Selection Bias

When observations in social research are selected so that they are not independent of the outcome variables in a study, sample selection leads to biased inferences about social processes. Nonrandom selection is both a source of bias in empirical research and a fundamental aspect of many social processes. This chapter reviews models that attempt to take account of sample selection and their applications in research on labor markets, schooling, legal processes, social mobility, and social networks. Variants of these models apply to outcome variables that are censored or truncated--whether explicitly or incidentally--and include the tobit model, the standard selection model, models for treatment effects in quasi-experimental designs, and endogenous switching models. Heckman's two-stage estimator is the most widely used approach to selection bias, but its results may be sensitive to violations of its assumptions about the way that selection occurs. Recent econometric research has developed a wide variety of promising approaches to selection bias that rely on considerably weaker assumptions. These include a number of semi- and nonparametric approaches to estimating selection models, the use of panel data, and the analyses of bounds of estimates. The large number of available methods and the difficulty of modelling selection indicate that researchers should be explicit about the assumptions behind their methods and should present results that derive from a variety of methods.