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Semiparametric Testing with Highly Persistent Predictors

Werker, B. and Zhou, B. (2022) 'Semiparametric Testing with Highly Persistent Predictors.', Journal of econometrics., 227 (2). pp. 347-370.

Abstract

We address the issue of semiparametric efficiency in the bivariate regression problem with a highly persistent predictor, where the joint distribution of the innovations is regarded an infinite-dimensional nuisance parameter. Using a structural representation of the limit experiment and exploiting invariance relationships therein, we construct invariant point-optimal tests for the regression coefficient of interest. This approach naturally leads to a family of feasible tests based on the component-wise ranks of the innovations that can gain considerable power relative to existing tests under non-Gaussian innovation distributions, while behaving equivalently under Gaussianity. When an i.i.d. assumption on the innovations is appropriate for the data at hand, our tests exploit the efficiency gains possible. Moreover, we show by simulation that our test remains well behaved under some forms of conditional heteroskedasticity.

Item Type:Article
Full text:Publisher-imposed embargo until 19 June 2023.
(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives 4.0.
File format - PDF
(544Kb)
Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1016/j.jeconom.2021.03.016
Publisher statement:© 2021 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Date accepted:04 March 2021
Date deposited:09 March 2021
Date of first online publication:19 June 2021
Date first made open access:19 June 2023

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