Hypothesis testing with error correction models Articles uri icon

publication date

  • October 2022

start page

  • 870

end page

  • 878


  • 4


  • 10

International Standard Serial Number (ISSN)

  • 2049-8470

Electronic International Standard Serial Number (EISSN)

  • 2049-8489


  • 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, , 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 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 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.


  • Mathematics
  • Politics
  • Sociology


  • time series models