ABSTRACT
Until recently, nonparametric and parametric maximum likelihood, instrumental variables and robust estimation have been treated as di¤erent frameworks, with their own advantages and drawbacks, for estimating unknown model parameters. The generalized method of moments (GMM) provided the …rst uni…ed estimation framework by demonstrating that most of the existing estimators can be expressed as solutions to an estimating equation derived from particular moment restrictions. Even after the invention of the GMM, however, the distinction between likelihood-based and moment-based estimation still remained. Since the beginning of the 1990s, a class of nonparametric likelihood estimators such as the empirical likelihood, seemingly unrelated to GMM, has been established to possess appealing asymptotic and …nite sample properties in a wide range of applications. More recently, Newey and Smith (2004) have shown that this class of nonparametric likelihood-based estimators for moment condition models, called generalized empirical likelihood (GEL) estimators, is much more general than it was initially thought, and that it can be used as a convenient analytical, estimation and inference framework. The development and analysis of the class of GEL estimators is arguably one of the most in‡uential recent contributions to the econometric literature. This class of e¢ cient estimators includes the celebrated empirical likelihood, exponential tilting and continuously updated GMM estimators. The GEL framework leads to a better understanding of the properties of the moment-based estimators and allows for more powerful test procedures, more e¢ cient estimation of density and distribution functions and improved bootstrap methods. In this chapter, we review the construction of nonparametric likelihood and
discuss its relation to e¢ cient estimation of density and distribution functions. Then, we extend this method to models de…ned by moment restrictions and develop the generalized empirical likelihood framework. The …rst-and higher-order asymptotic properties of the GEL estimators are illustrated. We also discuss extensions to models with dependent data, GEL-based tests and con…dence intervals as well as the relation of GEL to power divergence and
Kullback–Leibler information criteria. The results in this chapter are developed for unconditional moment restriction models. The extension of GEL estimators to models de…ned by conditional moment restrictions is discussed in the next chapter. Other reviews of some of the topics discussed below include Owen (2001), Kitamura (2007) and Mittelhammer, Judge and Miller (2000).
