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Full-Text Articles in Social and Behavioral Sciences
A Note On Optimal Inference In The Linear Iv Model, Donald W.K. Andrews, Vadim Marmer, Zhengfei Yu
A Note On Optimal Inference In The Linear Iv Model, Donald W.K. Andrews, Vadim Marmer, Zhengfei Yu
Cowles Foundation Discussion Papers
This paper considers tests and confidence sets (CS’s) concerning the coefficient on the endogenous variable in the linear IV regression model with homoskedastic normal errors and one right-hand side endogenous variable. The paper derives a finite-sample lower bound function for the probability that a CS constructed using a two-sided invariant similar test has infinite length and shows numerically that the conditional likelihood ratio (CLR) CS of Moreira (2003) is not always very close to this lower bound function. This implies that the CLR test is not always very close to the two-sided asymptotically-efficient (AE) power envelope for invariant similar tests …
Uniform Inference In Panel Autoregression, John C. Chao, Peter C.B. Phillips
Uniform Inference In Panel Autoregression, John C. Chao, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper considers estimation and inference concerning the autoregressive coefficient (ρ) in a panel autoregression for which the degree of persistence in the time dimension is unknown. The main objective is to construct confidence intervals for ρ that are asymptotically valid, having asymptotic coverage probability at least that of the nominal level uniformly over the parameter space. It is shown that a properly normalized statistic based on the Anderson-Hsiao IV procedure, which we call the M statistic, is uniformly convergent and can be inverted to obtain asymptotically valid interval estimates. In the unit root case confidence intervals based on this …
On Confidence Intervals For Autoregressive Roots And Predictive Regression, Peter C.B. Phillips
On Confidence Intervals For Autoregressive Roots And Predictive Regression, Peter C.B. Phillips
Cowles Foundation Discussion Papers
A prominent use of local to unity limit theory in applied work is the construction of confidence intervals for autogressive roots through inversion of the ADF t statistic associated with a unit root test, as suggested in Stock (1991). Such confidence intervals are valid when the true model has an autoregressive root that is local to unity (τ = 1 + ( c/n )) but are invalid at the limits of the domain of definition of the localizing coefficient c because of a failure in tightness and the escape of probability mass. Consideration of the boundary case shows that these …
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 …
Optimal Bandwidth Choice For Interval Estimation In Gmm Regression, Yixiao Sun, Peter C.B. Phillips
Optimal Bandwidth Choice For Interval Estimation In Gmm Regression, Yixiao Sun, Peter C.B. Phillips
Cowles Foundation Discussion Papers
In time series regression with nonparametrically autocorrelated errors, it is now standard empirical practice to construct confidence intervals for regression coefficients on the basis of nonparametrically studentized t -statistics. The standard error used in the studentization is typically estimated by a kernel method that involves some smoothing process over the sample autocovariances. The underlying parameter ( M ) that controls this tuning process is a bandwidth or truncation lag and it plays a key role in the finite sample properties of tests and the actual coverage properties of the associated confidence intervals. The present paper develops a bandwidth choice rule …
Exactly Unbiased Estimation Of First Order Autoregressive/Unit Root Models, Donald W.K. Andrews
Exactly Unbiased Estimation Of First Order Autoregressive/Unit Root Models, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper is concerned with the estimation of first-order autoregressive/unit root models with independent identically distributed normal errors. The models considered include those without an intercept, those with an intercept, and those with an intercept and time trend. The autoregressive (AR) parameter alpha is allowed to lie in the interval (-1,1], which includes the case of a unit root. Exactly median-unbiased estimators of the AR parameter alpha are proposed. Exact confidence intervals for this parameter are introduced. Corresponding exactly median-unbiased estimators and exact confidence intervals are also provided for the impulse response function and the cumulative impulse response. An unbiased …