MacMillan-CSAP Workshop on Quantitative Research Methods: Xiaohong Chen, “Sensitivity Analysis in Semiparametric Likelihood Models”

“Sensitivity Analysis in Semiparametric Likelihood Models”
By X. Chen (Yale), E. Tamer (Harvard, Northwestern) and A. Torgovitsky (Northwestern)

Speaker: Xiaohong Chen, Malcolm K. Brachman Professor of Economics, Yale University

Abstract: We provide methods for inference on a finite dimensional parameter of interest, θ∈ℜ^{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 (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 Chi-square 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 an empirical illustration where we compare our results to the ones obtained using standard (less robust) methods. LINK TO PAPER