An Alternative Way of Computing Efficient Instrumental Variable Estimators

A new way of constructing efficient semiparametric instrumental variable estimators is proposed. The method involves the combination of a large number of possibly inefficient estimators rather than combining the instruments into an optimal instrument function. The consistency and asymptotic normality is established for a class of estimators that are linear combinations of a set of√�� �� consistent estimators whose cardinality increases with sample size. It is shown that the semiparametrically efficient estimator lies in this class. The proofs do not rely on smoothness of underlying criterion functions. Potential use of the estimator can overcome the undersized sample problem. in simultaneous equation system estimation.

[1]  Aman Ullah,et al.  The second-order bias and mean squared error of nonlinear estimators , 1996 .

[2]  D. Pollard,et al.  Simulation and the Asymptotics of Optimization Estimators , 1989 .

[3]  Victoria Zinde-Walsh,et al.  Robust kernel estimator for densities of unknown smoothness , 2007 .

[4]  W. Newey,et al.  16 Efficient estimation of models with conditional moment restrictions , 1993 .

[5]  Jonathan H. Wright,et al.  Forecasting Inflation , 2011 .

[6]  H. Bierens.  Advances in Econometrics: Kernel estimators of regression functions , 1987 .

[7]  James L. Powell,et al.  Efficient Estimation of Linear and Type I Censored Regression Models Under Conditional Quantile Restrictions , 1990, Econometric Theory.

[8]  D. McFadden.  A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration , 1989 .

[9]  K. Marwah.  THE TREATMENT OF UNDERSIZED SAMPLES IN ECONOMETRICS , 1997 .

[10]  Leo Breiman,et al.  Bagging Predictors , 1996, Machine Learning.

[11]  T. Andersen.  THE ECONOMETRICS OF FINANCIAL MARKETS , 1998, Econometric Theory.

[12]  R. Koenker,et al.  GMM inference when the number of moment conditions is large , 1999 .

[13]  W. Newey,et al.  The asymptotic variance of semiparametric estimators , 1994 .

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

[15]  R. Koenker,et al.  Regression Quantiles , 2007 .

[16]  P. J. Huber.  The behavior of maximum likelihood estimates under nonstandard conditions , 1967 .

[17]  Thomas J. Rothenberg,et al.  Efficient estimation with a priori information , 1974 .

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

[19]  Mark W. Watson,et al.  Advances in Economics and Econometrics: Macroeconomic Forecasting Using Many Predictors , 2003 .

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

[21]  Victoria Zinde-Walsh,et al.  NON AND SEMI-PARAMETRIC ESTIMATION IN MODELS WITH UNKNOWN SMOOTHNESS , 2006 .

[22]  D. Andrews.  Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models , 1991 .

[23]  G. Chamberlain.  Asymptotic efficiency in estimation with conditional moment restrictions , 1987 .

[24]  L. Breiman.  USING ADAPTIVE BAGGING TO DEBIAS REGRESSIONS , 1999 .

[25]  Takeshi Amemiya,et al.  The nonlinear two-stage least-squares estimator , 1974 .

[26]  Whitney K. Newey,et al.  EFFICIENT SEMIPARAMETRIC ESTIMATION VIA MOMENT RESTRICTIONS , 2004 .

[27]  Peter M. Robinson.  Best nonlinear three-stage least squares estimation of certain econometric models , 1991 .

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

[29]  D. Turkington.  A Note on Two-Stage Least Squares, Three-Stage Least Squares, and Maximum Likelihood Estimation in an Expectations Model , 1985 .

[30]  Robust Average Derivative Estimation , 2007 .

[31]  A. Pakes,et al.  The Dynamics of Productivity in the Telecommunications Equipment Industry , 1992 .

[32]  S. Portnoy.  Asymptotic behavior of M-estimators of p regression parameters when p , 1985 .

[33]  W. Newey,et al.  Large sample estimation and hypothesis testing , 1986 .

[34]  L. Hansen.  A method for calculating bounds on the asymptotic covariance matrices of generalized method of moments estimators , 1985 .

[35]  T. Sawa.  Almost Unbiased Estimator in Simultaneous Equations Systems , 1973 .