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Full-Text Articles in Social and Behavioral Sciences
Structural Inference From Reduced Forms With Many Instruments, Peter C.B. Phillips, Wayne Yuan Gao
Structural Inference From Reduced Forms With Many Instruments, Peter C.B. Phillips, Wayne Yuan Gao
Cowles Foundation Discussion Papers
This paper develops exact finite sample and asymptotic distributions for structural equation tests based on partially restricted reduced form estimates. Particular attention is given to models with large numbers of instruments, wherein the use of partially restricted reduced form estimates is shown to be especially advantageous in statistical testing even in cases of uniformly weak instruments and reduced forms. Comparisons are made with methods based on unrestricted reduced forms, and numerical computations showing finite sample performance of the tests are reported. Some new results are obtained on inequalities between noncentral chi-squared distributions with different degrees of freedom that assist in …
Inference Based On Many Conditional Moment Inequalities, Donald W.K. Andrews, Xiaoxia Shi
Inference Based On Many Conditional Moment Inequalities, Donald W.K. Andrews, Xiaoxia Shi
Cowles Foundation Discussion Papers
In this paper, we construct confidence sets for models defined by many conditional moment inequalities/equalities. The conditional moment restrictions in the models can be finite, countably infinite, or uncountably infinite. To deal with the complication brought about by the vast number of moment restrictions, we exploit the manageability (Pollard (1990)) of the class of moment functions. We verify the manageability condition in five examples from the recent partial identification literature. The proposed confidence sets are shown to have correct asymptotic size in a uniform sense and to exclude parameter values outside the identified set with probability approaching one. Monte Carlo …
Inference Based On Many Conditional Moment Inequalities, Donald W.K. Andrews, Xiaoxia Shi
Inference Based On Many Conditional Moment Inequalities, Donald W.K. Andrews, Xiaoxia Shi
Cowles Foundation Discussion Papers
In this paper, we construct confidence sets for models defined by many conditional moment inequalities/equalities. The conditional moment restrictions in the models can be finite, countably in finite, or uncountably in finite. To deal with the complication brought about by the vast number of moment restrictions, we exploit the manageability (Pollard (1990)) of the class of moment functions. We verify the manageability condition in five examples from the recent partial identification literature. The proposed confidence sets are shown to have correct asymptotic size in a uniform sense and to exclude parameter values outside the identified set with probability approaching one. …
Likelihood Inference In Some Finite Mixture Models, Xiaohong Chen, Maria Ponomareva, Elie Tamer
Likelihood Inference In Some Finite Mixture Models, Xiaohong Chen, Maria Ponomareva, Elie Tamer
Cowles Foundation Discussion Papers
Parametric mixture models are commonly used in applied work, especially empirical economics, where these models are often employed to learn for example about the proportions of various types in a given population. This paper examines the inference question on the proportions (mixing probability) in a simple mixture model in the presence of nuisance parameters when sample size is large. It is well known that likelihood inference in mixture models is complicated due to 1) lack of point identification, and 2) parameters (for example, mixing probabilities) whose true value may lie on the boundary of the parameter space. These issues cause …
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.
Sensitivity Analysis In Semiparametric Likelihood Models, Xiaohong Chen, Elie Tamer, Alexander Torgovitsky
Sensitivity Analysis In Semiparametric Likelihood Models, Xiaohong Chen, Elie Tamer, Alexander Torgovitsky
Cowles Foundation Discussion Papers
We provide methods for inference on a finite dimensional parameter of interest, θ in Re ^{ d _θ}, in a semiparametric probability model when an infinite dimensional nuisance parameter, g , is present. We depart from the semiparametric literature in that we do not require that the pair (θ, g ) is point identified and so we construct confidence regions for θ that are robust to non-point identification. This allows practitioners to examine the sensitivity of their estimates of θ to specification of g in a likelihood setup. To construct these confidence regions for θ, we invert a profiled sieve …
Inference For Parameters Defined By Moment Inequalities: A Recommended Moment Selection Procedure, Donald W.K. Andrews, Panle Jai Barwick
Inference For Parameters Defined By Moment Inequalities: A Recommended Moment Selection Procedure, Donald W.K. Andrews, Panle Jai Barwick
Cowles Foundation Discussion Papers
This paper is concerned with tests and confidence intervals for parameters that are not necessarily identified and are defined by moment inequalities. In the literature, different test statistics, critical value methods, and implementation methods (i.e., the asymptotic distribution versus the bootstrap) have been proposed. In this paper, we compare these methods. We provide a recommended test statistic, moment selection critical value method, and implementation method. We provide data-dependent procedures for choosing the key moment selection tuning parameter kappa and a size-correction factor eta.
Inference For Parameters Defined By Moment Inequalities: A Recommended Moment Selection Procedure, Donald W.K. Andrews, Panle Jai Barwick
Inference For Parameters Defined By Moment Inequalities: A Recommended Moment Selection Procedure, Donald W.K. Andrews, Panle Jai Barwick
Cowles Foundation Discussion Papers
This paper is concerned with tests and confidence intervals for partially-identified parameters that are defined by moment inequalities and equalities. In the literature, different test statistics, critical value methods, and implementation methods (i.e., asymptotic distribution versus the bootstrap) have been proposed. In this paper, we compare a wide variety of these methods. We provide a recommended test statistic, moment selection critical value method, and implementation method. In addition, we provide a data-dependent procedure for choosing the key moment selection tuning parameter and a data-dependent size-correction factor.
Bootstrap For Interval Endpoints Defined By Moment Inequalities, Donald W.K. Andrews, Sukjin Han
Bootstrap For Interval Endpoints Defined By Moment Inequalities, Donald W.K. Andrews, Sukjin Han
Cowles Foundation Discussion Papers
This paper analyzes the finite-sample and asymptotic properties of several bootstrap and m out of n bootstrap methods for constructing confidence interval (CI) endpoints in models defined by moment inequalities. In particular, we consider using these methods directly to construct CI endpoints. By considering two very simple models, the paper shows that neither the bootstrap nor the m out of n bootstrap is valid in finite samples or in a uniform asymptotic sense in general when applied directly to construct CI endpoints. In contrast, other results in the literature show that other ways of applying the bootstrap, m out of …