COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1836 "Sensitivity Analysis in Semiparametric Likelihood Models" Xiaohong Chen, Elie Tamer, and Alexander Torgovitsky November 2011 We provide methods for inference on a finite dimensional parameter of
interest, theta in Re^{d_theta}, 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 (theta, g) is point identified and so
we construct confidence regions for theta that are robust to non-point identification.
This allows practitioners to examine the sensitivity of their estimates of theta to
specification of g in a likelihood setup. To construct these confidence regions for theta,
we invert a profiled sieve likelihood ratio (LR) statistic. We derive the asymptotic null
distribution of this profiled sieve LR, which is nonstandard when theta is not point
identified (but is chi^2 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. |
