COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1640 Efficient Estimation of Semiparametric Conditional Moment Models Xiaohong Chen and Demian Pouzo February 2008 For semi/nonparametric conditional moment models containing unknown parametric
components (theta) and unknown functions of endogenous variables (h),
Newey and Powell (2003) and Ai and Chen (2003) propose sieve minimum distance (SMD)
estimation of (theta, h) and derive the large sample properties. This paper
greatly extends their results by establishing the followings: (1) The penalized SMD (PSMD)
estimator (hat{theta}, hat{h}) can simultaneously achieve root-n asymptotic
normality of theta hat and nonparametric optimal convergence rate of hat{h},
allowing for models with possibly nonsmooth residuals and/or noncompact infinite
dimensional parameter spaces. (2) A simple weighted bootstrap procedure can consistently
estimate the limiting distribution of the PSMD hat{theta}. (3) The semiparametric
efficiency bound results of Ai and Chen (2003) remain valid for conditional models with
nonsmooth residuals, and the optimally weighted PSMD estimator achieves the bounds. (4)
The profiled optimally weighted PSMD criterion is asymptotically Chi-square distributed,
which implies an alternative consistent estimation of confidence region of the efficient
PSMD estimator of theta. All the theoretical results are stated in terms of any
consistent nonparametric estimator of conditional mean functions. We illustrate our
general theories using a partially linear quantile instrumental variables regression, a
Monte Carlo study, and an empirical estimation of the shape-invariant quantile Engel
curves with endogenous total expenditure. |
