Inference in panel data models under attrition caused by unobservables

This paper concerns identification and estimation of a finite-dimensional parameter in a panel data-model under nonignorable sample attrition. Attrition can depend on second period variables which are unobserved for the attritors but an independent refreshment sample from the marginal distribution of the second period values is available. This paper shows that under a quasi-separability assumption, the model implies a set of conditional moment restrictions where the moments contain the attrition function as an unknown parameter. This formulation leads to (i) a simple proof of identification under strictly weaker conditions than those in the existing literature and, more importantly, (ii) a sieve-based root-n$n$ consistent estimate of the finite-dimensional parameter of interest. These methods are applicable to both linear and nonlinear panel data models with endogenous attrition and analogous methods are applicable to situations of endogenously missing data in a single cross-section. The theory is illustrated with a simulation exercise, using Current Population Survey data where a panel structure is introduced by the rotation group feature of the sampling process.