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87
Efficient Estimation of Semiparametric Conditional Moment Models with Possibly Nonsmooth Residuals
 FORTHCOMING IN JOURNAL OF ECONOMETRICS
, 2008
"... For semi/nonparametric conditional moment models containing unknown parametric components (θ) and unknown functions of endogenous variables (h), Newey and Powell (2003) and Ai and Chen (2003) propose sieve minimum distance (SMD) estimation of (θ, h) and derive the large sample properties. This paper ..."
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Cited by 21 (4 self)
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For semi/nonparametric conditional moment models containing unknown parametric components (θ) and unknown functions of endogenous variables (h), Newey and Powell (2003) and Ai and Chen (2003) propose sieve minimum distance (SMD) estimation of (θ, h) and derive the large sample properties. This paper greatly extends their results by establishing the followings: (1) The penalized SMD (PSMD) estimator ( ˆ θ, ˆ h) can simultaneously achieve rootn asymptotic normality of ˆ θ and nonparametric optimal convergence rate of ˆ 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 ˆ θ. (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 Chisquare distributed, which implies an alternative consistent estimation of confidence region of the efficient PSMD estimator of θ. 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
Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals
, 2009
"... This paper studies nonparametric estimation of conditional moment models in which the generalized residual functions can be nonsmooth in the unknown functions of endogenous variables. This is a nonparametric nonlinear instrumental variables (IV) problem. We propose a class of penalized sieve minimum ..."
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Cited by 20 (6 self)
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This paper studies nonparametric estimation of conditional moment models in which the generalized residual functions can be nonsmooth in the unknown functions of endogenous variables. This is a nonparametric nonlinear instrumental variables (IV) problem. We propose a class of penalized sieve minimum distance (PSMD) estimators which are minimizers of a penalized empirical minimum distance criterion over a collection of sieve spaces that are dense in the infinite dimensional function parameter space. Some of the PSMD procedures use slowly growing finite dimensional sieves with flexible penalties or without any penalty; some use large dimensional sieves with lower semicompact and/or convex penalties. We establish their consistency and the convergence rates in Banach space norms (such as a supnorm or a root mean squared norm), allowing for possibly noncompact infinite dimensional parameter spaces. For both mildly and severely illposed nonlinear inverse problems, our convergence rates in Hilbert space norms (such as a root mean squared norm) achieve the known minimax optimal rate for the nonparametric mean IV regression. We illustrate the theory with a nonparametric additive quantile IV regression. We present a simulation study and an empirical application of estimating nonparametric quantile IV Engel curves.
An Estimation of Economic Models with Recursive Preferences. Working paper
, 2008
"... Annette VissingJorgensen for help with the stockholder consumption data. Any errors or omissions are the responsibility of the authors, and do not necessarily re‡ect the views of the National Science Foundation. An Estimation of Economic Models with Recursive Preferences This paper presents estimat ..."
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Cited by 11 (1 self)
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Annette VissingJorgensen for help with the stockholder consumption data. Any errors or omissions are the responsibility of the authors, and do not necessarily re‡ect the views of the National Science Foundation. An Estimation of Economic Models with Recursive Preferences This paper presents estimates of key preference parameters of the Epstein and Zin (1989, 1991) and Weil (1989) (EZW) recursive utility model, evaluates the model’s ability to …t asset return data relative to other asset pricing models, and investigates the implications of such estimates for the unobservable aggregate wealth return. Our empirical results indicate that the estimated relative risk aversion parameter ranges from 1760, with higher values for aggregate consumption than for stockholder consumption, while the estimated elasticity of intertemporal substitution is above one. In addition, the estimated modelimplied aggregate wealth return is found to be weakly correlated with the CRSP valueweighted stock market return, suggesting that the return to human wealth is negatively correlated with the
A Practical Asymptotic Variance Estimator for TwoStep Semiparametric Estimators
 REVIEW OF ECONOMICS AND STATISTICS, FORTHCOMING
, 2011
"... The goal of this paper is to develop techniques to simplify semiparametric inference. We do this by deriving a number of numerical equivalence results. These illustrate that in many cases, one can obtain estimates of semiparametric variances using standard formulas derived in the alreadywellknown ..."
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Cited by 10 (2 self)
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The goal of this paper is to develop techniques to simplify semiparametric inference. We do this by deriving a number of numerical equivalence results. These illustrate that in many cases, one can obtain estimates of semiparametric variances using standard formulas derived in the alreadywellknown parametric literature. This means that for computational purposes, an empirical researcher can ignore the semiparametric nature of the problem and do all calculations “as if” it were a parametric situation. We hope that this simplicity will promote the use of semiparametric procedures.
Semiparametric efficiency in GMM models of nonclassical measurement error, missing data and treatment effects
, 2004
"... We study semiparametric efficiency bounds and efficient estimation of parameters defined through general nonlinear, possibly nonsmooth and overidentified moment restrictions, where the sampling information consists of a primary sample and an auxiliary sample. The variables of interest in the momen ..."
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Cited by 10 (0 self)
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We study semiparametric efficiency bounds and efficient estimation of parameters defined through general nonlinear, possibly nonsmooth and overidentified moment restrictions, where the sampling information consists of a primary sample and an auxiliary sample. The variables of interest in the moment conditions are not directly observable in the primary data set, but the primary data set contains proxy variables which are correlated with the variables of interest. The auxiliary data set contains information about the conditional distribution of the variables of interest given the proxy variables. Identification is achieved by the assumption that this conditional distribution is the same in both the primary and auxiliary data sets. We provide semiparametric efficiency bounds for both the “verifyoutofsample” case, where the two samples are independent, and the “verifyinsample ” case, where the auxiliary sample is a subset of the primary sample; and the bounds are derived when the propensity score is unknown, or known, or belongs to a correctly specified parametric family. These efficiency variance bounds indicate that the propensity score is ancillary for the “verifyinsample ” case, but is not ancillary for the “verifyoutofsample ” case. We show that sieve conditional expectation projection based GMM estimators achieve the semiparametric efficiency bounds for all the above mentioned cases, and establish
A Simple Nonparametric Estimator for the Distribution of Random Coefficients in Discrete Choice Models
, 2008
"... We propose an estimator for discrete choice models, such as the logit, with a nonparametric distribution of random coefficients. The estimator is linear regression subject to linear inequality constraints and is robust, simple to program and quick to compute compared to alternative estimators for mi ..."
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Cited by 9 (3 self)
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We propose an estimator for discrete choice models, such as the logit, with a nonparametric distribution of random coefficients. The estimator is linear regression subject to linear inequality constraints and is robust, simple to program and quick to compute compared to alternative estimators for mixture models. We discuss three methods for proving identification of the distribution of heterogeneity for any given economic model. We prove the identification of the logit mixtures model, which, surprisingly given the wide use of this model over the last 30 years, is a new result. We also derive our estimator’s nonstandard asymptotic distribution and demonstrate its excellent small sample properties in a Monte Carlo. The estimator we propose can be extended to allow for endogenous prices. The estimator can also be used to reduce the computational burden of nested fixed point methods for complex models like dynamic programming discrete choice.
Time series estimation of the effects of natural experiments
 Journal of Econometrics
, 2006
"... Abstract This paper investigates methods for estimating the effects of natural experiments, especially those created by an intervention or structural change occurring at a specific point in time, such as a government policy intervention, a merger, or the formation or disintegration of a cartel. We d ..."
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Cited by 7 (6 self)
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Abstract This paper investigates methods for estimating the effects of natural experiments, especially those created by an intervention or structural change occurring at a specific point in time, such as a government policy intervention, a merger, or the formation or disintegration of a cartel. We draw on the extensive literature of
SemiNonparametric IntervalCensored Mixed Proportional Hazard Models: Identification and Consistency Results”, Econometric Theory 24
, 2008
"... In this paper I propose to estimate distributions on the unit interval seminonparametrically using orthonormal Legendre polynomials. This approach will be applied to the interval censored mixed proportional hazard (ICMPH) model, where the distribution of the unobserved heterogeneity is modeled semi ..."
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Cited by 7 (5 self)
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In this paper I propose to estimate distributions on the unit interval seminonparametrically using orthonormal Legendre polynomials. This approach will be applied to the interval censored mixed proportional hazard (ICMPH) model, where the distribution of the unobserved heterogeneity is modeled seminonparametrically. Various conditions for the nonparametric identification of the ICMPH model are derived. I will prove general consistency results for M estimators of (partly) nonEuclidean parameters under weak and easytoverify conditions, and specialize these results to sieve estimators. Special attention is paid to the case where the support of the covariates is finite.