Chapter 12 Attrition, Selection Bias and Censored Regressions Bo Honor´ e, Francis Vella and Marno Verbeek 12.1 Introduction In micro-econometric applications issues related to attrition, censoring and non- random sample selection frequently arise. For example, it is quite common in em- pirical work that the variables of interest are partially observed or only observed when some other data requirement is satisfied. These forms of censoring and selec- tivity frequently cause problems in estimation and can lead to unreliable inference if they are ignored. Consider, for example, the problems which may arise if one is interested in estimating the parameters from a labor supply equation based on the examination of a panel data set and where one’s objective is to make inferences for the whole population rather than only the sample of workers. The first difficulty that arises is that hours are generally only observed for individuals that work. In this way the hours measure is generally censored at zero and this causes difficulties for estimation as straightforward least squares methods, either over the entire sample or only the subsample of workers, are not generally applicable. Second, many of the explanatory variables of interest, such as wages, are also censored in that they are only observed for workers. Moreover, in these instances many of these variables may also be endogenous to labor supply and this may also create complications in estimation. While panel data are frequently seen as a way to overcome issues re- lated to endogeneity as the availability of repeated observations on the same unit can allow the use of various data transformations to eliminate the cause of the endogene- ity, in many instances the use of panel data can complicate matters. For example, Bo Honor´ e Department of Economics, Princeton University, Princeton, NJ 08544-1021, USA, e-mail: honore@Princeton.EDU Francis Vella Department of Economics, Georgetown University, Washington DC, USA, e-mail: fgv@georgetown.edu Marno Verbeek Department of Financial Management, RSM Erasmus University, Burg. Oudlaan 50, 3062 PA Rotterdam, The Netherlands, e-mail: mverbeek@rsm.nl L. M´ aty´ as, P. Sevestre (eds.), The Econometrics of Panel Data, 385 c  Springer-Verlag Berlin Heidelberg 2008