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

Abstract

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.

KEYWORD:

• Cointegration
• Heteroscedasticity and autocorrelation-robust (HAR) inference
• Low-frequency transformation
• t test and F tests
• Trasformed and augmented OLS (TA-OLS)

Acknowledgments

We thank coeditor Christian Hansen, an anonymous associate editor, and an anonymous referee for valuable comments. We also thank Yixiao Sun for the conversations in the early stage of this project. Special thanks to David Kaplan for many helpful comments and suggestions to the earlier version of this article.

Additional information

Funding

Jungbin Hwang acknowledges the research support from the Department of Economics at the University of Connecticut, United States of America. Gonzalo Valdés acknowledges financial support from ANID Chile Fondecyt Iniciación, 11220125.