Generalized empirical likelihood testing in semiparametric conditional moment restrictions models

2012 ◽  
Vol 15 (1) ◽  
pp. 1-31 ◽  
Author(s):  
Francesco Bravo
Keyword(s):  
Empirical Likelihood ◽  
Conditional Moment ◽  
Generalized Empirical Likelihood ◽  
Moment Restrictions

TESTING FOR NONNESTED CONDITIONAL MOMENT RESTRICTIONS VIA CONDITIONAL EMPIRICAL LIKELIHOOD

2010 ◽  
Vol 27 (1) ◽  
pp. 114-153 ◽  
Author(s):  
Taisuke Otsu ◽  
Yoon-Jae Whang
Keyword(s):  
Empirical Likelihood ◽  
Finite Sample ◽  
Conditional Moment ◽  
Null Distributions ◽  
Finite Dimensional ◽  
Global Power ◽  
Finite Sample Properties ◽  
The Moment ◽  
Moment Restrictions ◽  
Power Properties

We propose nonnested tests for competing conditional moment restriction models using the method of conditional empirical likelihood, recently developed by Kitamura, Tripathi, and Ahn (2004) and Zhang and Gijbels (2003). To define the test statistics, we use the implied conditional probabilities from conditional empirical likelihood, which take into account the full implications of conditional moment restrictions. We propose three types of nonnested tests: the moment-encompassing, Cox-type, and efficient score-encompassing tests. We derive the asymptotic null distributions and investigate their power properties against a sequence of local alternatives and a fixed global alternative. Our tests have distinct global power properties from some of the existing tests based on finite-dimensional unconditional moment restrictions. Simulation experiments show that our tests have reasonable finite sample properties and dominate some of the existing nonnested tests in terms of size-corrected powers.

Testing conditional moment restriction models using empirical likelihood

2021 ◽  
Author(s):  
Yves G Berger
Keyword(s):  
Empirical Likelihood ◽  
Model Specification ◽  
Ratio Test ◽  
Conditional Moment ◽  
Nominal Level ◽  
Empirical Likelihood Ratio Test ◽  
Likelihood Model ◽  
Heteroscedastic Errors ◽  
Endogenous Covariates ◽  
The Relationship

Abstract An empirical likelihood test is proposed for parameters of models defined by conditional moment restrictions, such as models with non-linear endogenous covariates, with or without heteroscedastic errors or non-separable transformation models. The number of empirical likelihood constraints is given by the size of the parameter, unlike alternative semi-parametric approaches. We show that the empirical likelihood ratio test is asymptotically pivotal, without explicit studentisation. A simulation study shows that the observed size is close to the nominal level, unlike alternative empirical likelihood approaches. It also offers a major advantages over two-stage least-squares, because the relationship between the endogenous and instrumental variables does not need to be known. An empirical likelihood model specification test is also proposed.

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