Sample Attrition in Panel Data: The Role of Selection on Observables

The traditional formulation of the attrition problem in econometrics treats it as a special case of the partial-population section bias model in which selection (attrition) is based on model unobservables. This paper considers instead the treatment of attrition as a special case of selection on observables. The analysis compares and contrasts the identification assumptions and estimation procedures for this case with those of the usual case of selection on unobservables. Selection on observables case has rarely been considered in the econometric literature on the problem and hence the framing of the problem in these terms, as presented here, is apparently new. The selection on observables problem is made nontrivial by the assumption that selection occurs on endogenous observables; leading examples are lagged dependent variables from earlier periods in the panel. Among other things, it is shown in the paper that (i) weighted least squares using estimated attrition equations to construct the weights is one method of consistent estimation in thise case; (ii) simply conditioning on the observables does not, by itself, generate consistent estimates; and (iii) that the model is closely related to the choice-based sampling model.