Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals |
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Authors: | Xiaohong Chen Demian Pouzo |
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Institution: | aCowles Foundation for Research in Economics, Yale University, Box 208281, New Haven, CT 06520, USA;bDepartment of Economics, New York University, 19 West 4th Street, New York, NY 10012, USA |
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Abstract: | 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 can simultaneously achieve root-n asymptotic normality of and nonparametric optimal convergence rate of , allowing for noncompact function parameter spaces; (2) a simple weighted bootstrap procedure consistently estimates the limiting distribution of the PSMD ; (3) the semiparametric efficiency bound formula of Ai, C., Chen, X., 2003. Efficient estimation of models with conditional moment restrictions containing unknown functions. Econometrica, 71, 1795–1843] 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. |
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Keywords: | 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 |
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