The aim of this thesis is to investigate Generalised Empirical Likelihood (GEL) and related informational theoretical methods for estimation and inference of parameters of models that satisfy unconditional and conditional moment restrictions. Three topics in this field are studied. Firstly, the first order asymptotic theory of the GEL class of estimators for the parameters of non-smooth moment restrictions is analysed and test statistics in this framework are introduced. It is shown that, in random samples, all the estimators in the GEL class have the same asymptotic distribution of the Generalised Method of Moments (GMM) estimator in this set-up under the same assumptions. The test statistics proposed are particularly useful to perform inference in quantile regression models as they to not require the estimation of the asymptotic covariance matrix of the estimator. Secondly, definitions of exogeneity in models defined by conditional moment restrictions are introduced and test statistics for this hypothesis are proposed based on the GMM and GEL estimators. These tests are based on the equivalence between a finite number of conditional moment restrictions and a countably infinite number of unconditional restrictions. These definitions are important when the researcher is interested in estimating the parameters of functions that satisfy conditional moment restrictions as in the case of mean regression. Lastly, encompassing tests are introduced to compare a model defined by conditional moment restrictions with a parametric model. Researchers usually use parametric models as they are easier to apply, even though the assumptions of the semiparametric model may be more reasonable. Test statistics that check if models defined by conditional moment restrictions can be explained by parametric models are introduced. Tests statistics that examine if the former explain the latter are also proposed. A by-product of this analysis is the formal derivation of the asymptotic distribution of the conditional empirical likelihood estimator under misspecification
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