Hypothesis testing with error correction models

Patrick W. Kraft, Ellen M. Key and Matthew J. Lebo

Political Science Research and Methods, 2022, vol. 10, issue 4, 870-878

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.

Date: 2022
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