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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 …
Robust Predictions In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Robust Predictions In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
We analyze games of incomplete information and offer equilibrium predictions which are valid for all possible private information structures that the agents may have. Our characterization of these robust predictions relies on an epistemic result which establishes a relationship between the set of Bayes Nash equilibria and the set of Bayes correlated equilibria. We completely characterize the set of Bayes correlated equilibria in a class of games with quadratic payoffs and normally distributed uncertainty in terms of restrictions on the first and second moments of the equilibrium action-state distribution. We derive exact bounds on how prior information of the analyst …
Robust Predictions In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Robust Predictions In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
We analyze games of incomplete information and offer equilibrium predictions which are valid for, and in this sense robust to, all possible private information structures that the agents may have. The set of outcomes that can arise in equilibrium for some information structure is equal to the set of Bayes correlated equilibria. We completely characterize the set of Bayes correlated equilibria in a class of games with quadratic payoffs and normally distributed uncertainty in terms of restrictions on the first and second moments of the equilibrium action-state distribution. We derive exact bounds on how prior knowledge about the private information …
Robust Predictions In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Robust Predictions In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
We analyze games of incomplete information and offer equilibrium predictions which are valid for, and in this sense robust to, all possible private information structures that the agents may have. We completely characterize the set of Bayes correlated equilibria in a class of games with quadratic payoffs and normally distributed uncertainty in terms of restrictions on the first and second moments of the equilibrium action-state distribution. We derive exact bounds on how prior knowledge about the private information refines the set of equilibrium predictions. We consider information sharing among firms under demand uncertainty and find newly optimal information policies via …
Robust Predictions In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Robust Predictions In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
We analyze games of incomplete information and offer equilibrium predictions which are valid for, and in this sense robust to, all possible private information structures that the agents may have. We completely characterize the set of Bayes correlated equilibria in a class of games with quadratic payoffs and normally distributed uncertainty in terms of restrictions on the first and second moments of the equilibrium action-state distribution. We derive exact bounds on how prior knowledge about the private information refines the set of equilibrium predictions. We consider information sharing among firms under demand uncertainty and find newly optimal information policies via …
Examples Of L 2 -Complete And Boundedly-Complete Distributions, Donald W.K. Andrews
Examples Of L 2 -Complete And Boundedly-Complete Distributions, Donald W.K. Andrews
Cowles Foundation Discussion Papers
Completeness and bounded-completeness conditions are used increasingly in econometrics to obtain nonparametric identification in a variety of models from nonparametric instrumental variable regression to non-classical measurement error models. However, distributions that are known to be complete or boundedly complete are somewhat scarce. In this paper, we consider an L 2 -completeness condition that lies between completeness and bounded completeness. We construct broad (nonparametric) classes of distributions that are L 2 -complete and boundedly complete. The distributions can have any marginal distributions and a wide range of strengths of dependence. Examples of L 2 -incomplete distributions also are provided.
Local Identification Of Nonparametric And Semiparametric Models, Xiaohong Chen, Victor Chernozhukov, Sokbae Lee, Whitney Newey
Local Identification Of Nonparametric And Semiparametric Models, Xiaohong Chen, Victor Chernozhukov, Sokbae Lee, Whitney Newey
Cowles Foundation Discussion Papers
In parametric models a sufficient condition for local identification is that the vector of moment conditions is differentiable at the true parameter with full rank derivative matrix. We show that additional conditions are often needed in nonlinear, nonparametric models to avoid nonlinearities overwhelming linear effects. We give restrictions on a neighborhood of the true value that are sufficient for local identification. We apply these results to obtain new, primitive identification conditions in several important models, including nonseparable quantile instrumental variable (IV) models, single-index IV models, and semiparametric consumption-based asset pricing models.
Local Identification Of Nonparametric And Semiparametric Models, Xiaohong Chen, Victor Chernozhukov, Sokbae Lee, Whitney Newey
Local Identification Of Nonparametric And Semiparametric Models, Xiaohong Chen, Victor Chernozhukov, Sokbae Lee, Whitney Newey
Cowles Foundation Discussion Papers
In parametric models a sufficient condition for local identification is that the vector of moment conditions is differentiable at the true parameter with full rank derivative matrix. We show that there are corresponding sufficient conditions for nonparametric models. A nonparametric rank condition and differentiability of the moment conditions with respect to a certain norm imply local identification. It turns out these conditions are slightly stronger than needed and are hard to check, so we provide weaker and more primitive conditions. We extend the results to semiparametric models. We illustrate the sufficient conditions with endogenous quantile and single index examples. We …
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 …