Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals

<p><p>This paper considers semiparametric efficient estimation of conditional moment models with possibly nonsmooth residuals in unknown parametric components (Θ) and unknown functions (h)of endogenous variables. We show that: (1) the penalized sieve minimum distance(PSMD) estimator (ˆΘ, ˆh) can simultaneously achieve root-n asymptotic normality of ˆΘ and nonparametric optimal convergence rate of ˆh, allowing for noncompact function parameter spaces; (2) a simple weighted bootstrap procedure consistently estimates the limiting distribution of the PSMD ˆΘ; (3) the semiparametric efficiency bound formula of Ai and Chen (2003) remains valid for conditional models with nonsmooth residuals, and the optimally weighted PSMD estimator achieves the bound; (4) the centered, profiled optimally weighted PSMD criterion is asymptotically chi-square distributed. We illustrate our theories using a partially linear quantile instrumental variables (IV) regression, a Monte Carlo study, and an empirical estimation of the shape-invariant quantile IV Engel curves. <p>This is an updated version of CWP09/08.