A new class of asymptotically efficient estimators for moment condition models

In this paper, we propose a new class of asymptotically efficient estimators for moment condition models. These estimators share the same higher order bias properties as the generalized empirical likelihood estimators and once bias corrected, have the same higher order efficiency properties as the bias corrected generalized empirical likelihood estimators. Unlike the generalized empirical likelihood estimators, our new estimators are much easier to compute. A simulation study finds that our estimators have better finite sample performance than the two-step GMM, and compare well to several potential alternatives in terms of both computational stability and overall performance.

[1]  G. Imbens,et al.  Information Theoretic Approaches to Inference in Moment Condition Models , 1995 .

[2]  Frank Kleibergen,et al.  Testing Parameters in GMM without Assuming that they are identified , 2005 .

[3]  D. Anderson,et al.  Algorithms for minimization without derivatives , 1974 .

[4]  Joseph G. Altonji,et al.  Small Sample Bias in GMM Estimation of Covariance Structures , 1994 .

[5]  S. Pastorello,et al.  Iterative and Recursive Estimation in Structural Non-Adaptive Models * , 2003 .

[6]  Whitney K. Newey,et al.  EFFICIENT INSTRUMENTAL VARIABLES ESTIMATION OF NONLINEAR MODELS , 1990 .

[7]  A. Owen Empirical likelihood ratio confidence intervals for a single functional , 1988 .

[8]  Joaquim J. S. Ramalho,et al.  Goodness of Fit Tests for Moment Condition Models , 2005 .

[9]  Donald W. K. Andrews,et al.  Identification and Inference for Econometric Models , 2005 .

[10]  Finite Sample Evidence Suggesting a Heavy Tail Problem of the Generalized Empirical Likelihood Estimator , 2006 .

[11]  Shane M. Sherlund,et al.  Quasi Empirical Likelihood Estimation of Moment Condition Models , 2004 .

[12]  N. Kunitomo,et al.  On Finite Sample Distributions of the Empirical Likelihood Estimator and the GMM Estimator , 2003 .

[13]  Yuichi Kitamura,et al.  Empirical Likelihood Methods in Econometrics: Theory and Practice , 2006 .

[14]  L. Hansen Large Sample Properties of Generalized Method of Moments Estimators , 1982 .

[15]  D. Andrews EQUIVALENCE OF THE HIGHER ORDER ASYMPTOTIC EFFICIENCY OF k-STEP AND EXTREMUM STATISTICS , 2002, Econometric Theory.

[16]  P. Robinson,et al.  The stochastic difference between econometric statistics , 1988 .

[17]  Stephen G. Donald,et al.  A jackknife interpretation of the continuous updating estimator , 2000 .

[18]  Xiaohong Chen,et al.  Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions , 2003 .

[19]  G. Phillips,et al.  The refinement of econometric estimation and test procedures : finite sample and asymptotic analysis , 2007 .

[20]  É. Renault,et al.  On the Efficient Use of the Informational Content of Estimating Equations: Implied Probabilities and Euclidean Empirical Likelihood , 2004 .

[21]  Timothy R. C. Read,et al.  Multinomial goodness-of-fit tests , 1984 .

[22]  Yuichi Kitamura,et al.  Empirical Likelihood Based Inference in Conditional Moment Restriction Models , 2004 .

[23]  Y. Kitamura,et al.  Robustness, Infinitesimal Neighborhoods, and Moment Restrictions , 2009 .

[24]  Guido W. Imbens,et al.  One-step estimators for over-identified generalized method of moments models , 1997 .

[25]  J. Kalbfleisch,et al.  Maximization by Parts in Likelihood Inference , 2005 .

[26]  Whitney K. Newey,et al.  Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators , 2003 .

[27]  Yukitoshi,et al.  Finite Sample Distributions of the Empirical Likelihood Estimator and the GMM Estimator Naoto , 2003 .

[28]  Richard J. Smith Efficient information theoretic inference for conditional moment restrictions , 2005 .

[29]  Monte-carlo evidence suggesting a no moment problem of the continuous updating estimator , 2005 .

[30]  J. Hahn,et al.  Finite Sample Properties of the Two-Step Empirical Likelihood Estimator , 2005 .

[31]  F. Kleibergen,et al.  Inference on subsets of parameters in GMM without assuming identification , 2009 .

[32]  Robustness, Infinitesimal Neighborhoods, and Moment Restrictions , 2009 .

[33]  Bryan W. Brown,et al.  Efficient Semiparametric Estimation of Expectations , 1998 .

[34]  Yuichi Kitamura,et al.  An Information-Theoretic Alternative to Generalized Method of Moments Estimation , 1997 .

[35]  Michael A. Malcolm,et al.  Computer methods for mathematical computations , 1977 .

[36]  Jinyong Hahn,et al.  A New Specification Test for the Validity of Instrumental Variables , 2000 .

[37]  Richard J. Smith Alternative Semi-parametric Likelihood Approaches to Generalised Method of Moments Estimation , 1997 .

[38]  J. Lawless,et al.  Empirical Likelihood and General Estimating Equations , 1994 .

[39]  G. Judge,et al.  Empirical Evidence Concerning the Finite Sample Performance of EL-Type Structural Equation Estimation and Inference Methods , 2003 .