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Hypothesis testing with error correction models

Published online by Cambridge University Press:  21 July 2021

Patrick W. Kraft ,
Ellen M. Key  and
Matthew J. Lebo Open the ORCID record for Matthew J. Lebo [Opens in a new window]
Patrick W. Kraft
Affiliation:
University of Wisconsin-Milwaukee, Milwaukee, WI, USA
Ellen M. Key
Affiliation:
Appalachian State University, Boone, NC, USA
Matthew J. Lebo*
Affiliation:
University of Western Ontario, London, ON, Canada
*
*Corresponding author. Email: matthew.lebo@uwo.ca
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Abstract

Grant and Lebo (2016) and Keele et al. (2016) clarify the conditions under which the popular general error correction model (GECM) can be used and interpreted easily: In a bivariate GECM the data must be integrated in order to rely on the error correction coefficient, $\alpha _1^\ast$, to test cointegration and measure the rate of error correction between a single exogenous x and a dependent variable, y. Here we demonstrate that even if the data are all integrated, the test on $\alpha _1^\ast$ is misunderstood when there is more than a single independent variable. The null hypothesis is that there is no cointegration between y and any x but the correct alternative hypothesis is that y is cointegrated with at least one—but not necessarily more than one—of the x's. A significant $\alpha _1^\ast$ can occur when some I(1) regressors are not cointegrated and the equation is not balanced. Thus, the correct limiting distributions of the right-hand-side long-run coefficients may be unknown. We use simulations to demonstrate the problem and then discuss implications for applied examples.

Keywords

Time series models
Type
Research Note
Information
Political Science Research and Methods , Volume 10 , Issue 4 , October 2022 , pp. 870 - 878
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of the European Political Science Association

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