Low Frequency Cointegrating Regression in the Presence of Local to Unity Regressors and Unknown Form of Serial Dependence

This paper develops new t and F inferences in a low frequency transformed triangular cointegrating regression when one may not be sure the economic variables are exact unit root processes. We first show that the low frequency transformed and augmented OLS (TA-OLS) regression exhibits an asymptotic bias term in the limiting distribution. As a result, the size distortion of the testing cointegration vector can be extremely large for even small deviations from the unit root regressors. We develop a method to correct the asymptotic bias for the cointegration vector. Our modified statistics adjust the locational bias and fully reflect the estimation uncertainty of the long-run endogeneity parameter in the bias correction term, which leads to standard t and F critical values. Based on our modified TA-OLS test statistics, a simple Bonferroni method is provided to test for the cointegration vector. Monte Carlo results show that our method has advantages to the IVX approach when the serial dependence and the long-run endogeneity in the cointegration system are important.