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Pitfalls of Two-Step Testing for Changes in the Error Variance and Coefficients of a Linear Regression Model

1
Department of Economics, Boston University, Boston, MA 02215, USA
2
Department of Economics, Hitotsubashi University, Kunitachi, Tokyo 186-8601, Japan
*
Author to whom correspondence should be addressed.
Econometrics 2019, 7(2), 22; https://doi.org/10.3390/econometrics7020022
Received: 20 April 2019 / Revised: 15 May 2019 / Accepted: 15 May 2019 / Published: 21 May 2019
In empirical applications based on linear regression models, structural changes often occur in both the error variance and regression coefficients, possibly at different dates. A commonly applied method is to first test for changes in the coefficients (or in the error variance) and, conditional on the break dates found, test for changes in the variance (or in the coefficients). In this note, we provide evidence that such procedures have poor finite sample properties when the changes in the first step are not correctly accounted for. In doing so, we show that testing for changes in the coefficients (or in the variance) ignoring changes in the variance (or in the coefficients) induces size distortions and loss of power. Our results illustrate a need for a joint approach to test for structural changes in both the coefficients and the variance of the errors. We provide some evidence that the procedures suggested by Perron et al. (2019) provide tests with good size and power. View Full-Text
Keywords: structural change; variance shifts; CUSQ tests; hypothesis testing; sup-LR test structural change; variance shifts; CUSQ tests; hypothesis testing; sup-LR test
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Perron, P.; Yamamoto, Y. Pitfalls of Two-Step Testing for Changes in the Error Variance and Coefficients of a Linear Regression Model. Econometrics 2019, 7, 22.

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