Computing Generalized Method of Moments and Generalized Empirical Likelihood withR

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.

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EFFICIENT TWO-STEP GENERALIZED EMPIRICAL LIKELIHOOD ESTIMATION AND TESTS WITH MARTINGALE DIFFERENCES

Econometric Theory ◽

10.1017/s0266466620000249 ◽

2020 ◽

pp. 1-40 ◽

Cited By ~ 1

Author(s):

Fei Jin ◽

Lung-fei Lee

Keyword(s):

Empirical Likelihood ◽

Generalized Method Of Moments ◽

Likelihood Estimation ◽

Nuisance Parameters ◽

Martingale Differences ◽

Generalized Empirical Likelihood ◽

Moment Functions ◽

The Impact ◽

Bias Terms ◽

Parameters Of Interest

This paper considers two-step generalized empirical likelihood (GEL) estimation and tests with martingale differences when there is a computationally simple $\sqrt n-$ consistent estimator of nuisance parameters or the nuisance parameters can be eliminated with an estimating function of parameters of interest. As an initial estimate might have asymptotic impact on final estimates, we propose general C(α)-type transformed moments to eliminate the impact, and use them in the GEL framework to construct estimation and tests robust to initial estimates. This two-step approach can save computational burden as the numbers of moments and parameters are reduced. A properly constructed two-step GEL (TGEL) estimator of parameters of interest is asymptotically as efficient as the corresponding joint GEL estimator. TGEL removes several higher-order bias terms of a corresponding two-step generalized method of moments. Our moment functions at the true parameters are martingales, thus they cover some spatial and time series models. We investigate tests for parameter restrictions in the TGEL framework, which are locally as powerful as those in the joint GEL framework when the two-step estimator is efficient.

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Book Reviews

Journal of Economic Literature ◽

10.1257/jel.51.3.883.r3 ◽

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.

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