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Nonparametric Inference Based On Conditional Moment Inequalities, Donald W.K. Andrews, Xiaoxia Shi
Nonparametric Inference Based On Conditional Moment Inequalities, Donald W.K. Andrews, Xiaoxia Shi
Cowles Foundation Discussion Papers
This paper develops methods of inference for nonparametric and semiparametric parameters defined by conditional moment inequalities and/or equalities. The parameters need not be identified. Confidence sets and tests are introduced. The correct uniform asymptotic size of these procedures is established. The false coverage probabilities and power of the CS’s and tests are established for fixed alternatives and some local alternatives. Finite-sample simulation results are given for a nonparametric conditional quantile model with censoring and a nonparametric conditional treatment effect model. The recommended CS/test uses a Cramér-von-Mises-type test statistic and employs a generalized moment selection critical value.
Nonparametric Inference Based On Conditional Moment Inequalities, Donald W.K. Andrews, Xiaoxia Shi
Nonparametric Inference Based On Conditional Moment Inequalities, Donald W.K. Andrews, Xiaoxia Shi
Cowles Foundation Discussion Papers
This paper develops methods of inference for nonparametric and semiparametric parameters defined by conditional moment inequalities and/or equalities. The parameters need not be identified. Confidence sets and tests are introduced. The correct uniform asymptotic size of these procedures is established. The false coverage probabilities and power of the CS’s and tests are established for fixed alternatives and some local alternatives. Finite-sample simulation results are given for a nonparametric conditional quantile model with censoring and a nonparametric conditional treatment effect model. The recommended CS/test uses a Cramér-von-Mises-type test statistic and employs a generalized moment selection critical value.
Nonparametric Inference Based On Conditional Moment Inequalities, Donald W.K. Andrews, Xiaoxia Shi
Nonparametric Inference Based On Conditional Moment Inequalities, Donald W.K. Andrews, Xiaoxia Shi
Cowles Foundation Discussion Papers
This paper develops methods of inference for nonparametric and semiparametric parameters defined by conditional moment inequalities and/or equalities. The parameters need not be identified. Confidence sets and tests are introduced. The correct uniform asymptotic size of these procedures is established. The false coverage probabilities and power of the CS’s and tests are established for fixed alternatives and some local alternatives. Finite-sample simulation results are given for a nonparametric conditional quantile model with censoring and a nonparametric conditional treatment effect model. The recommended CS/test uses a Cramér-von-Mises-type test statistic and employs a generalized moment selection critical value.
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 …
A Conditional-Heteroskedasticity-Robust Confidence Interval For The Autoregressive Parameter, Donald W.K. Andrews, Patrik Guggenberger
A Conditional-Heteroskedasticity-Robust Confidence Interval For The Autoregressive Parameter, Donald W.K. Andrews, Patrik Guggenberger
Cowles Foundation Discussion Papers
This paper introduces a new confidence interval (CI) for the autoregressive parameter (AR) in an AR(1) model that allows for conditional heteroskedasticity of general form and AR parameters that are less than or equal to unity. The CI is a modification of Mikusheva’s (2007a) modification of Stock’s (1991) CI that employs the least squares estimator and a heteroskedasticity-robust variance estimator. The CI is shown to have correct asymptotic size and to be asymptotically similar (in a uniform sense). It does not require any tuning parameters. No existing procedures have these properties. Monte Carlo simulations show that the CI performs well …
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 …
A Conditional-Heteroskedasticity-Robust Confidence Interval For The Autoregressive Parameter, Donald W.K. Andrews, Patrik Guggenberger
A Conditional-Heteroskedasticity-Robust Confidence Interval For The Autoregressive Parameter, Donald W.K. Andrews, Patrik Guggenberger
Cowles Foundation Discussion Papers
This paper introduces a new confidence interval (CI) for the autoregressive parameter (AR) in an AR(1) model that allows for conditional heteroskedasticity of general form and AR parameters that are less than or equal to unity. The CI is a modification of Mikusheva’s (2007a) modification of Stock’s (1991) CI that employs the least squares estimator and a heteroskedasticity-robust variance estimator. The CI is shown to have correct asymptotic size and to be asymptotically similar (in a uniform sense). It does not require any tuning parameters. No existing procedures have these properties. Monte Carlo simulations show that the CI performs well …