Recent Developments in Empirical Likelihood and Related Methods

Abstract

This article reviews a number of recent contributions to estimation and inference for models de ned by moment condition restrictions. The particular emphasis is on the generalised empirical likelihood class of estimators as an alternative to generalised method of moments. Estimation methods for parameters de ned through moment restrictions and their properties are described with tests of overidentifying moment restrictions and parametric hypotheses. Computational issues are discussed together with some proposals for their amelioration. Higher order and other properties are also addressed in some detail. Models speci ed by conditional moment restriction models are considered and a discussion of the adaptation of these methods to weakly dependent data is given.

Econometricians Have Their Moments: GMM at 32

“…While the info‐metric perspective is intuitively appealing, it is often more convenient for the purposes of developing the statistical theory to take the GEL perspective, which is essentially the dual of the info‐metric approach, although it was derived by Smith () via a different route (for further discussion, see Newey and Smith (); Kitamura (); Parente & Smith, ). Smith () defines the GEL estimator of to bewhere ρ ( a ) is a continuous, twice differentiable and concave function on its domain , an open interval containing 0, , and λ is an auxiliary parameter vector restricted so that, with probability approaching 1, , for all and t = 1,…, T .…”

“…50 This info-metric approach emphasises the idea of economic models placing restrictions on the data generation process. 51 While the info-metric perspective is intuitively appealing, it is often more convenient for the purposes of developing the statistical theory to take the GEL perspective, which is essentially the dual of the info-metric approach, although it was derived by Smith (1997) via a different route (for further discussion, see Newey and Smith (2004); Kitamura (2007); Parente & Smith, 2014). Smith (1997) defines the GEL estimator of h 0 to bẽ…”

“…We concentrate here on estimation based on population moment conditions. See Parente and Smith () for a recent review of GEL based on conditional moment conditions.…”

Improved density and distribution function estimation

“…This paper focuses on the class of generalised (G) empirical likelihood (EL) estimators, which has attractive large sample properties; see, e.g., , Smith (1997Smith ( , 2011, and Parente and Smith (2014) for a recent review. Special cases of GEL include EL, (Owen, 1988), Qin and Lawless (1994), exponentially tilting (ET), Corcoran (1998), Kitamura and Stutzer (1997), Imbens et al (1998), and continuous-updating (GMM) estimators (CUE), Hansen et al (1996); see also Euclidean EL, Antoine et al (2007).…”

Methods for Nonparametric and Semiparametric Regressions with Endogeneity: A Gentle Guide

“…n . SeeSmith (1997),Donald, Imbens and Newey (2003) andParente and Smith (2014) for various choices of ψ() and other related criteria for unconditional moment restrictions (2.18) with increasing dimension.2.2.3 Computation and Heuristic choices of regularization parametersAlthough many different criteria could be used in PSE (2.9) to estimate α 0 = (θ 0 , h 0 ) for the model (2.1), some criterion functions are much easier to compute than others in the presence of unknown functions (h) with endogeneity. Without unkown h, theoretical statistics and econometrics papers recommend EL and GEL over MD and GMM for better asymptotic second-order properties in efficient estimation of θ, although MD and GMM are easier to compute with commonly used sample size in empirical work in economics.…”