Sensitivity Analysis in Semiparametric Likelihood Models

Abstract

We provide methods for inference on a finite dimensional parameter of interest, � 2 < d�, in a semiparametric probability model when an infinite dimensional nuisance parameter, g, is present. We depart from the semiparametric literature in that we do not require that the pair (�,g) is point identified and so we construct confidence regions forthat are robust to non-point identification. This allows practitioners to examine the sensitivity of their estimates ofto specification of g in a likelihood setup. To construct these confidence regions for �, we invert a profiled sieve likelihood ratio (LR) statistic. We derive the asymptotic null distribution of this profiled sieve LR, which is nonstandard whenis not point identified (but is � 2 distributed under point identifica- tion). We show that a simple weighted bootstrap procedure consistently estimates this complicated distribution's quantiles. Monte Carlo studies of a semiparametric dynamic binary response panel data model indicate that our weighted bootstrap procedures per- forms adequately in finite samples. We provide three empirical illustrations where we compare our results to the ones obtained using standard (less robust) methods.