Low Frequency Cointegrating Regression with Local to Unity Regressors and Unknown Form of Serial Dependence

This article develops new t and F tests in a low-frequency transformed triangular cointegrating regression when one may not be certain that the economic variables are exact unit root processes. We first show that the low-frequency transformed and augmented OLS (TA-OLS) method exhibits an asymptotic bias term in its limiting distribution. As a result, the test for the cointegration vector can have substantially large size distortion, even with minor deviations from the unit root regressors. To correct the asymptotic bias of the TA-OLS statistics for the cointegration vector, we develop modified TA-OLS statistics that adjust the bias and take account of the estimation uncertainty of the long-run endogeneity arising from the bias correction. Based on the modified test statistics, we provide Bonferroni-based tests of the cointegration vector using standard t and F critical values. Monte Carlo results show that our approach has the correct size and reasonable power for a wide range of local-to-unity parameters. Additionally, our method has advantages over the IVX approach when the serial dependence and the long-run endogeneity in the cointegration system are important.