Replication Data for: Hypothesis Testing with Error Correction Models

Grant and Lebo (2016) and Keele, Linn, and Webb (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, α*, 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 α* 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 α* 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.

Grant、Lebo（2016）以及Keele、Linn与Webb（2016）阐明了广受欢迎的广义误差修正模型（general error correction model, GECM）的规范使用与合理解读条件：在二元广义误差修正模型中，若要依托误差修正系数α*开展协整检验，并衡量单一外生变量x与被解释变量y之间的误差修正速率，则所有数据必须为单整序列。本文研究表明，即便所有数据均为单整序列，当自变量个数多于一个时，针对α*的检验会存在解读偏差。此时原假设为y与任意x变量均不存在协整关系，而正确的备择假设应为：y与至少一个（但未必多于一个）x变量存在协整关系。当部分I(1)回归变量未形成协整关系且方程非均衡时，仍可能得到显著的α*估计结果。由此，模型右侧长期回归系数的准确极限分布可能尚未被学界探明。本文通过模拟实验验证了该问题，并随后讨论了其在实证研究中的应用启示。