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Full-Text Articles in Economics
Inference In Moment Inequality Models That Is Robust To Spurious Precision Under Model Misspecification, Donald W.K. Andrews, Soonwoo Kwon
Inference In Moment Inequality Models That Is Robust To Spurious Precision Under Model Misspecification, Donald W.K. Andrews, Soonwoo Kwon
Cowles Foundation Discussion Papers
Standard tests and confidence sets in the moment inequality literature are not robust to model misspecification in the sense that they exhibit spurious precision when the identified set is empty. This paper introduces tests and confidence sets that provide correct asymptotic inference for a pseudo-true parameter in such scenarios, and hence, do not suffer from spurious precision.
Inference In Moment Inequality Models That Is Robust To Spurious Precision Under Model Misspecification, Donald W.K. Andrews, Soonwoo Kwon
Inference In Moment Inequality Models That Is Robust To Spurious Precision Under Model Misspecification, Donald W.K. Andrews, Soonwoo Kwon
Cowles Foundation Discussion Papers
Standard tests and confidence sets in the moment inequality literature are not robust to model misspecification in the sense that they exhibit spurious precision when the identified set is empty. This paper introduces tests and confidence sets that provide correct asymptotic inference for a pseudo-true parameter in such scenarios, and hence, do not suffer from spurious precision.
Misspecified Moment Inequality Models: Inference And Diagnostics, Donald W.K. Andrews, Soonwoo Kwon
Misspecified Moment Inequality Models: Inference And Diagnostics, Donald W.K. Andrews, Soonwoo Kwon
Cowles Foundation Discussion Papers
This paper is concerned with possible model misspecification in moment inequality models. Two issues are addressed. First, standard tests and confidence sets for the true parameter in the moment inequality literature are not robust to model misspecification in the sense that they exhibit spurious precision when the identified set is empty. This paper introduces tests and confidence sets that provide correct asymptotic inference for a pseudo-true parameter in such scenarios, and hence, do not suffer from spurious precision. Second, specification tests have relatively low power against a range of misspecified models. Thus, failure to reject the null of correct specification …
Asymptotic Theory For Near Integrated Process Driven By Tempered Linear Process, Farzad Sabzikar, Qiying Wang, Peter C.B. Phillips
Asymptotic Theory For Near Integrated Process Driven By Tempered Linear Process, Farzad Sabzikar, Qiying Wang, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper develops an asymptotic theory for near-integrated random processes and some associated regressions when the errors are tempered linear processes. Tempered processes are stationary time series that have a semi-long memory property in the sense that the autocovariogram of the process resembles that of a long memory model for moderate lags but eventually diminishes exponentially fast according to the presence of a decay factor governed by a tempering parameter. When the tempering parameter is sample size dependent, the resulting class of processes admits a wide range of behavior that includes both long memory, semi-long memory, and short memory processes. …
Identification-Robust Subvector Inference, Donald W.K. Andrews
Identification-Robust Subvector Inference, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper introduces identification-robust subvector tests and confidence sets (CS’s) that have asymptotic size equal to their nominal size and are asymptotically efficient under strong identification. Hence, inference is as good asymptotically as standard methods under standard regularity conditions, but also is identification robust. The results do not require special structure on the models under consideration, or strong identification of the nuisance parameters, as many existing methods do. We provide general results under high-level conditions that can be applied to moment condition, likelihood, and minimum distance models, among others. We verify these conditions under primitive conditions for moment condition models. …
Misspecified Moment Inequality Models: Inference And Diagnostics, Donald W.K. Andrews, Soonwoo Kwon
Misspecified Moment Inequality Models: Inference And Diagnostics, Donald W.K. Andrews, Soonwoo Kwon
Cowles Foundation Discussion Papers
This paper is concerned with possible model misspecification in moment inequality models. Two issues are addressed. First, standard tests and confidence sets for the true parameter in the moment inequality literature are not robust to model misspecification in the sense that they exhibit spurious precision when the identified set is empty. This paper introduces tests and confidence sets that provide correct asymptotic inference for a pseudo-true parameter in such scenarios, and hence, do not suffer from spurious precision. Second, specification tests have relatively low power against a range of misspecified models. Thus, failure to reject the null of correct specification …
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, …
Asymptotic Size Of Kleibergen's Lm And Conditional Lr Tests For Moment Condition Models, Donald W.K. Andrews, Patrik Guggenberger
Asymptotic Size Of Kleibergen's Lm And Conditional Lr Tests For Moment Condition Models, Donald W.K. Andrews, Patrik Guggenberger
Cowles Foundation Discussion Papers
An influential paper by Kleibergen (2005) introduces Lagrange multiplier (LM) and conditional likelihood ratio-like (CLR) tests for nonlinear moment condition models. These procedures aim to have good size performance even when the parameters are unidentified or poorly identified. However, the asymptotic size and similarity (in a uniform sense) of these procedures has not been determined in the literature. This paper does so. This paper shows that the LM test has correct asymptotic size and is asymptotically similar for a suitably chosen parameter space of null distributions. It shows that the CLR tests also have these properties when the dimension p …
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 …
Asymptotics For Stationary Very Nearly Unit Root Processes, Donald W.K. Andrews, Patrik Guggenberger
Asymptotics For Stationary Very Nearly Unit Root Processes, Donald W.K. Andrews, Patrik Guggenberger
Cowles Foundation Discussion Papers
This paper considers a mean zero stationary first-order autoregressive (AR) model. It is shown that the least squares estimator and t statistic have Cauchy and standard normal asymptotic distributions, respectively, when the AR parameter ρ n is very near to one in the sense that 1 – ρ n = ( n –1 ).
Cross-Section Regression With Common Shocks, Donald W.K. Andrews
Cross-Section Regression With Common Shocks, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper considers regression models for cross-section data that exhibit cross-section dependence due to common shocks, such as macroeconomic shocks. The paper analyzes the properties of least squares (LS) and instrumental variables (IV) estimators in this context. The results of the paper allow for any form of cross-section dependence and heterogeneity across population units. The probability limits of the LS and IV estimators are determined and necessary and sufficient conditions are given for consistency. The asymptotic distributions of the estimators are found to be mixed normal after re-centering and scaling. t , Wald, and F statistics are found to have …
Higher-Order Improvements Of The Parametric Bootstrap For Long-Memory Gaussian Processes, Donald W.K. Andrews, Offer Lieberman
Higher-Order Improvements Of The Parametric Bootstrap For Long-Memory Gaussian Processes, Donald W.K. Andrews, Offer Lieberman
Cowles Foundation Discussion Papers
This paper determines coverage probability errors of both delta method and parametric bootstrap confidence intervals (CIs) for the covariance parameters of stationary long-memory Gaussian time series. CIs for the long-memory parameter d 0 are included. The results establish that the bootstrap provides higher-order improvements over the delta method. Analogous results are given for tests. The CIs and tests are based on one or other of two approximate maximum likelihood estimators. The first estimator solves the first-order conditions with respect to the covariance parameters of a “plug-in” log-likelihood function that has the unknown mean replaced by the sample mean. The second …
The Block-Block Bootstrap: Improved Asymptotic Refinements, Donald W.K. Andrews
The Block-Block Bootstrap: Improved Asymptotic Refinements, Donald W.K. Andrews
Cowles Foundation Discussion Papers
The asymptotic refinements attributable to the block bootstrap for time series are not as large as those of the nonparametric iid bootstrap or the parametric bootstrap. One reason is that the independence between the blocks in the block bootstrap sample does not mimic the dependence structure of the original sample. This is the join-point problem. In this paper, we propose a method of solving this problem. The idea is not to alter the block bootstrap. Instead, we alter the original sample statistics to which the block bootstrap is applied. We introduce block statistics that possess join-point features that are similar …
Higher-Order Improvements Of The Parametric Bootstrap For Markov Processes, Donald W.K. Andrews
Higher-Order Improvements Of The Parametric Bootstrap For Markov Processes, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper provides bounds on the errors in coverage probabilities of maximum likelihood-based, percentile- t , parametric bootstrap confidence intervals for Markov time series processes. These bounds show that the parametric bootstrap for Markov time series provides higher-order improvements (over confidence intervals based on first order asymptotics) that are comparable to those obtained by the parametric and nonparametric bootstrap for iid data and are better than those obtained by the block bootstrap for time series. Additional results are given for Wald-based confidence regions. The paper also shows that k -step parametric bootstrap confidence intervals achieve the same higher-order improvements as …
Equivalence Of The Higher-Order Asymptotic Efficiency Of K-Step And Extremum Statistics, Donald W.K. Andrews
Equivalence Of The Higher-Order Asymptotic Efficiency Of K-Step And Extremum Statistics, Donald W.K. Andrews
Cowles Foundation Discussion Papers
It is well known that a one-step scoring estimator that starts from any N 1 /2 -consistent estimator has the same first-order asymptotic efficiency as the maximum likelihood estimator. This paper extends this result to k -step estimators and test statistics for k > 1, higher-order asymptotic efficiency, and general extremum estimators and test statistics. The paper shows that a k -step estimator has the same higher-order asymptotic efficiency, to any given order, as the extremum estimator towards which it is stepping, provided (i) k is sufficiently large, (ii) some smoothness and moment conditions hold, and (iii) a condition on the …
Higher-Order Improvements Of A Computationally Attractive K-Step Bootstrap For Extremum Estimators, Donald W.K. Andrews
Higher-Order Improvements Of A Computationally Attractive K-Step Bootstrap For Extremum Estimators, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper establishes the higher-order equivalence of the k -step bootstrap, introduced recently by Davidson and MacKinnon (1999a), and the standard bootstrap. The k -step bootstrap is a very attractive alternative computationally to the standard bootstrap for statistics based on nonlinear extremum estimators, such as generalized method of moment and maximum likelihood estimators. The paper also extends results of Hall and Horowitz (1996) to provide new results regarding the higher-order improvements of the standard bootstrap and the k -step bootstrap for extremum estimators (compared to procedures based on first-order asymptotics). The results of the paper apply to Newton-Raphson (NR), default …
Higher-Order Improvements Of A Computationally Attractive K-Step Bootstrap For Extremum Estimators, Donald W.K. Andrews
Higher-Order Improvements Of A Computationally Attractive K-Step Bootstrap For Extremum Estimators, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper establishes the higher-order equivalence of the k -step bootstrap, introduced recently by Davidson and MacKinnon (1999a), and the standard bootstrap. The k -step bootstrap is a very attractive alternative computationally to the standard bootstrap for statistics based on nonlinear extremum estimators, such as generalized method of moment and maximum likelihood estimators. The paper also extends results of Hall and Horowitz (1996) to provide new results regarding the higher-order improvements of the standard bootstrap and the k -step bootstrap for extremum estimators (compared to procedures based on first-order asymptotics). The results of the paper apply to Newton-Raphson (NR), default …
Nonlinear Econometric Models With Deterministically Trending Variables, Donald W.K. Andrews, John Mcdermott
Nonlinear Econometric Models With Deterministically Trending Variables, Donald W.K. Andrews, John Mcdermott
Cowles Foundation Discussion Papers
This paper considers an alternative asymptotic framework to standard sequential asymptotics for nonlinear models with deterministically trending variables. The asymptotic distributions of generalized method of moments estimators and corresponding test statistics are derived using this framework. The asymptotic distributions are shown to be the same with deterministically trending variables as with non-trending variables. That is, the distributions are normal and chi-squared respectively. The asymptotic covariance matrices of the estimators, however, are found to depend on the form of the trends. These findings provide a justification for the use of standard asymptotic approximations in nonlinear models even when the variables have …
Optimal Tests When A Nuisance Parameter Is Present Only Under The Alternative, Donald W.K. Andrews, Werner Ploberger
Optimal Tests When A Nuisance Parameter Is Present Only Under The Alternative, Donald W.K. Andrews, Werner Ploberger
Cowles Foundation Discussion Papers
This paper derives asymptotically optimal tests for testing problems in which a nuisance parameter exists under the alternative hypothesis but not under the null. The results of the paper are of interest, because the testing problem considered in non-standard and the classical asymptotic optimality results for the Wald, Lagrange multiplier (LM), and likelihood ratio (LR) tests do not apply. In the non-standard cases of main interest, new optimal tests are obtained and the LR test is not found to be an optimal test.
Asymptotic Results For Generalized Wald Tests, Donald W.K. Andrews
Asymptotic Results For Generalized Wald Tests, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This note presents conditions under which a quadratic form based on a g-inverted weighting matrix converges to a chi-square distribution as the sample size goes to infinity. Subject to fairly weak underlying conditions, a necessary and sufficient condition is given for this result. The result is of interest, because it is needed to establish asymptotic significance levels and local power properties of generalized Wald tests (i.e., Wald tests with singular limiting covariance matrices). Included in this class of tests are Hausman specification tests and various goodness of fit tests, among others. The necessary and sufficient condition is relevant to procedures …