Sensitivity Analysis in Semiparametric Likelihood Models

We provide methods for inference on a finite dimensional parameter of interest, θ in Re^{d_θ}, 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 (θ,g) is point identified and so we construct confidence regions for θ that are robust to non-point identification. This allows practitioners to examine the sensitivity of their estimates of θ to specification of g in a likelihood setup. To construct these confidence regions for θ, we invert a profiled sieve likelihood ratio (LR) statistic. We derive the asymptotic null distribution of this profiled sieve LR, which is nonstandard when θ is not point identified (but is χ2 distributed under point identification). 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 performs adequately in finite samples. We provide three empirical illustrations to contrast our procedure to the ones obtained using standard (less robust) methods.