Open Access. Powered by Scholars. Published by Universities.®
Social and Behavioral Sciences Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 9 of 9
Full-Text Articles in Social and Behavioral Sciences
Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure, Donald W.K. Andrews, Xu Cheng
Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure, Donald W.K. Andrews, Xu Cheng
Cowles Foundation Discussion Papers
This paper determines the properties of standard generalized method of moments (GMM) estimators, tests, and confidence sets (CS’s) in moment condition models in which some parameters are unidentified or weakly identified in part of the parameter space. The asymptotic distributions of GMM estimators are established under a full range of drifting sequences of true parameters and distributions. The asymptotic sizes (in a uniform sense) of standard GMM tests and CS’s are established. The paper also establishes the correct asymptotic sizes of “robust” GMM-based Wald, t , and quasi-likelihood ratio tests and CS’s whose critical values are designed to yield robustness …
Maximum Likelihood Estimation And Uniform Inference With Sporadic Identification Failure, Donald W.K. Andrews, Xu Cheng
Maximum Likelihood Estimation And Uniform Inference With Sporadic Identification Failure, Donald W.K. Andrews, Xu Cheng
Cowles Foundation Discussion Papers
This paper analyzes the properties of a class of estimators, tests, and confidence sets (CS’s) when the parameters are not identified in parts of the parameter space. Specifically, we consider estimator criterion functions that are sample averages and are smooth functions of a parameter theta. This includes log likelihood, quasi-log likelihood, and least squares criterion functions. We determine the asymptotic distributions of estimators under lack of identification and under weak, semi-strong, and strong identification. We determine the asymptotic size (in a uniform sense) of standard t and quasi-likelihood ratio (QLR) tests and CS’s. We provide methods of constructing QLR tests …
Maximum Likelihood Estimation And Uniform Inference With Sporadic Identification Failure, Donald W.K. Andrews, Xu Cheng
Maximum Likelihood Estimation And Uniform Inference With Sporadic Identification Failure, Donald W.K. Andrews, Xu Cheng
Cowles Foundation Discussion Papers
This paper analyzes the properties of a class of estimators, tests, and confidence sets (CS’s) when the parameters are not identified in parts of the parameter space. Specifically, we consider estimator criterion functions that are sample averages and are smooth functions of a parameter theta. This includes log likelihood, quasi-log likelihood, and least squares criterion functions. We determine the asymptotic distributions of estimators under lack of identification and under weak, semi-strong, and strong identification. We determine the asymptotic size (in a uniform sense) of standard t and quasi-likelihood ratio (QLR) tests and CS’s. We provide methods of constructing QLR tests …
Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure, Donald W.K. Andrews, Xu Cheng
Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure, Donald W.K. Andrews, Xu Cheng
Cowles Foundation Discussion Papers
This paper determines the properties of standard generalized method of moments (GMM) estimators, tests, and confidence sets (CS’s) in moment condition models in which some parameters are unidentified or weakly identified in part of the parameter space. The asymptotic distributions of GMM estimators are established under a full range of drifting sequences of true parameters and distributions. The asymptotic sizes (in a uniform sense) of standard GMM tests and CS’s are established. The paper also establishes the correct asymptotic sizes of “robust” GMM-based Wald, t; and quasi-likelihood ratio tests and CS’s whose critical values are designed to yield robustness to …
Generic Results For Establishing The Asymptotic Size Of Confidence Sets And Tests, Donald W.K. Andrews, Xu Cheng, Patrik Guggenberger
Generic Results For Establishing The Asymptotic Size Of Confidence Sets And Tests, Donald W.K. Andrews, Xu Cheng, Patrik Guggenberger
Cowles Foundation Discussion Papers
This paper provides a set of results that can be used to establish the asymptotic size and/or similarity in a uniform sense of confidence sets and tests. The results are generic in that they can be applied to a broad range of problems. They are most useful in scenarios where the pointwise asymptotic distribution of a test statistic has a discontinuity in its limit distribution. The results are illustrated in three examples. These are: (i) the conditional likelihood ratio test of Moreira (2003) for linear instrumental variables models with instruments that may be weak, extended to the case of heteroskedastic …
Similar-On-The-Boundary Tests For Moment Inequalities Exist, But Have Poor Power, Donald W.K. Andrews
Similar-On-The-Boundary Tests For Moment Inequalities Exist, But Have Poor Power, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper shows that moment inequality tests that are asymptotically similar on the boundary of the null hypothesis exist, but have very poor power. Hence, existing tests in the literature, which are asymptotically non-similar on the boundary, are not deficient. The results are obtained by first establishing results for the finite-sample multivariate normal one-sided testing problem. Then, these results are shown to have implications for more general moment inequality tests that are used in the literature on partial identification.
Similar-On-The-Boundary Tests For Moment Inequalities Exist, But Have Poor Power, Donald W.K. Andrews
Similar-On-The-Boundary Tests For Moment Inequalities Exist, But Have Poor Power, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper shows that moment inequality tests that are asymptotically similar on the boundary of the null hypothesis exist, but have poor power. Hence, existing tests in the literature, which are asymptotically non-similar on the boundary, are not deficient. The results are obtained by first establishing results for the finite-sample multivariate normal one-sided testing problem. Then, these results are shown to have implications for more general moment inequality tests that are used in the literature on partial identification.
Identification- And Singularity-Robust Inference For Moment Condition Models, Donald W.K. Andrews, Patrik Guggenberger
Identification- And Singularity-Robust Inference For Moment Condition Models, Donald W.K. Andrews, Patrik Guggenberger
Cowles Foundation Discussion Papers
This paper introduces two new identification- and singularity-robust conditional quasi-likelihood ratio (SR-CQLR) tests and a new identification- and singularity-robust Anderson and Rubin (1949) (SR-AR) test for linear and nonlinear moment condition models. The paper shows that the tests have correct asymptotic size and are asymptotically similar (in a uniform sense) under very weak conditions. For two of the three tests, all that is required is that the moment functions and their derivatives have 2 + γ bounded moments for some γ > 0 in i.i.d. scenarios. In stationary strong mixing time series cases, the same condition suffices, but the magnitude of …
Identification- And Singularity-Robust Inference For Moment Condition Models, Donald W.K. Andrews, Patrik Guggenberger
Identification- And Singularity-Robust Inference For Moment Condition Models, Donald W.K. Andrews, Patrik Guggenberger
Cowles Foundation Discussion Papers
This paper introduces a new identification- and singularity-robust conditional quasi-likelihood ratio (SR-CQLR) test and a new identification- and singularity-robust Anderson and Rubin (1949) (SR-AR) test for linear and nonlinear moment condition models. Both tests are very fast to compute. The paper shows that the tests have correct asymptotic size and are asymptotically similar (in a uniform sense) under very weak conditions. For example, in i.i.d. scenarios, all that is required is that the moment functions and their derivatives have 2+γ bounded moments for some γ>0. No conditions are placed on the expected Jacobian of the moment functions, on the …