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

Abstract

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 substantially large for even minor deviations from the unit root regressors. We develop a method to correct the asymptotic bias for the cointegration vector. Our modified TA-OLS statistics adjust the locational bias and reflect the estimation uncertainty of the long-run endogeneity parameter in the bias correction term and lead to standard t and F critical values. Based on the modified test statistics, we provide Bonferroni-based inferences to test the cointegration vector. Monte Carlo results show that our approach has the correct size and appealing power for a wide range of local to unity parameters. Also, we find that our method has advantages to the IVX approach when the serial dependence and the long-run endogeneity in the cointegration system are important.