Publication Date: February 2008
Revision Date: July 2009
This paper considers semiparametric eﬀicient estimation of conditional moment models with possibly nonsmooth residuals in unknown parametric components (theta) and unknown functions (h) of endogenous variables. We show that: (1) the penalized sieve minimum distance (PSMD) estimator (theta\hat,h\hat) can simultaneously achieve root-n asymptotic normality of theta\hat and nonparametric optimal convergence rate of h\hat, allowing for noncompact function parameter spaces; (2) a simple weighted bootstrap procedure consistently estimates the limiting distribution of the PSMD theta\hat; (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.
Penalized sieve minimum distance, Nonsmooth generalized residuals, Nonlinear nonparametric endogeneity, Weighted bootstrap, Semiparametric eﬀiciency, Conﬁdence region, Partially linear quantile IV regression, Shape-invariant quantile IV Engel curves
JEL Classification Codes: C14; C22
See CFP: 1277