Combining Empirical Likelihood and Generalized Method of Moments Estimators: Asymptotics and Higher Order Bias

2013 ◽  
Author(s):  
Roni Israelov ◽  
Steven Lugauer
Keyword(s):  
Empirical Likelihood ◽  
Method Of Moments ◽  
Generalized Method Of Moments ◽  
Higher Order ◽  
Moments Estimators

scholarly journals Higher Order Mean Squared Error of Generalized Method of Moments Estimators for Nonlinear Models

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yi Hu ◽  
Xiaohua Xia ◽  
Ying Deng ◽  
Dongmei Guo
Keyword(s):  
Method Of Moments ◽  
Mean Squared Error ◽  
Nonlinear Models ◽  
Generalized Method Of Moments ◽  
Higher Order ◽  
Mean Square ◽  
Finite Sample ◽  
Squared Error ◽  
Moments Estimators ◽  
Moment Restriction

Generalized method of moments (GMM) has been widely applied for estimation of nonlinear models in economics and finance. Although generalized method of moments has good asymptotic properties under fairly moderate regularity conditions, its finite sample performance is not very well. In order to improve the finite sample performance of generalized method of moments estimators, this paper studies higher-order mean squared error of two-step efficient generalized method of moments estimators for nonlinear models. Specially, we consider a general nonlinear regression model with endogeneity and derive the higher-order asymptotic mean square error for two-step efficient generalized method of moments estimator for this model using iterative techniques and higher-order asymptotic theories. Our theoretical results allow the number of moments to grow with sample size, and are suitable for general moment restriction models, which contains conditional moment restriction models as special cases. The higher-order mean square error can be used to compare different estimators and to construct the selection criteria for improving estimator’s finite sample performance.

scholarly journals GEL METHODS FOR NONSMOOTH MOMENT INDICATORS

2010 ◽  
Vol 27 (1) ◽  
pp. 74-113 ◽  
Author(s):  
Paulo M.D.C. Parente ◽  
Richard J. Smith
Keyword(s):  
Empirical Likelihood ◽  
Method Of Moments ◽  
Jacobian Matrix ◽  
Generalized Method Of Moments ◽  
Gmm Estimator ◽  
First Order ◽  
Generalized Empirical Likelihood ◽  
Finite Samples ◽  
Class Of Estimators ◽  
Validity Of Tests

This paper considers the first-order large sample properties of the generalized empirical likelihood (GEL) class of estimators for models specified by nonsmooth indicators. The GEL class includes a number of estimators recently introduced as alternatives to the efficient generalized method of moments (GMM) estimator that may suffer from substantial biases in finite samples. These include empirical likelihood (EL), exponential tilting (ET), and the continuous updating estimator (CUE). This paper also establishes the validity of tests suggested in the smooth moment indicators case for overidentifying restrictions and specification. In particular, a number of these tests avoid the necessity of providing an estimator for the Jacobian matrix that may be problematic for the sample sizes typically encountered in practice.

Book Reviews

2013 ◽  
Vol 51 (3) ◽  
pp. 886-888
Keyword(s):  
Inverse Problem ◽  
Empirical Likelihood ◽  
Method Of Moments ◽  
Linear Models ◽  
Choice Model ◽  
Generalized Method Of Moments ◽  
Problem Formulation ◽  
Distribution Functions ◽  
Binary Response ◽  
Quadratic Loss

Provides a conceptual and empirical understanding of basic information theoretic econometric models and methods. Discusses formulation and analysis of parametric and semiparametric linear models; method of moments, generalized method of moments, and estimating equations; a stochastic-empirical likelihood inverse problem—formulation and estimation; a stochastic empirical likelihood inverse problem—estimation and inference; Kullback–Leibler information and the maximum empirical exponential likelihood; the Cressie–Read family of divergence measures and empirical maximum likelihood functions; Cressie–Read minimum power divergence (MPD) type estimators in practice—Monte Carlo evidence of estimation and inference sampling performance; family of MPD distribution functions for the binary response-choice model; estimation and inference for the binary response model based on the MPD family of distributions; and choosing the optimal divergence under quadratic loss. Judge is a professor at the University of California, Berkeley. Mittelhammer is Regents Professor of Economic Sciences and Statistics at Washington State University.

Sign in / Sign up

Export Citation Format

Share Document