TESTING THE NULL OF NO COINTEGRATION WHEN COVARIATES ARE KNOWN TO HAVE A UNIT ROOT

Econometric Theory, 25, 2009, 18291850. Printed in the United States of America. doi:10.1017/S026646660999034X

GRAHAM ELLIOTT University of California, San Diego

ELENA PESAVENTO Emory University

A number of tests have been suggested for the test of the null of no cointegration. Under this null, correlations are spurious in the sense of Granger and Newbold (1974) and Phillips (1986). We examine a set of models local to the null of no cointegration and derive tests with optimality properties in order to examine the efciency of available tests. We nd that, for a sufciently tight weighting over potential cointe-grating vectors, commonly employed full system tests have power that can, in some situations, be quite far from the power bounds for the models examined.

1. INTRODUCTION

Given that many economic time series display trending, it is important to distinguish spurious correlation (as in Granger and Newbold, 1974; Phillips, 1986) from meaningful economic relationships. When trending is due to unit roots in the data, correlations between the levels of the data are cointegrating relationships. In their seminal paper, Engle and Granger (1987) proposed tests for the null hypothesis of no cointegration that amounted to testing for a unit root in the estimated least squares cointegrating residuals. Their contribution triggered a wave of alternative tests for this null hypothesis. Whenever there is a variety of tests for a given hypothesis, it is natural to ask which one should be employed in practice. This questions rests, in large samples, on power considerations and, in smaller samples, on size control and power. Understanding which of the tests, if any, is best, is only a rst step as relative power comparisons leave open the question of whether or not there exists a test, yet to be derived, that has even better power properties.

The authors would like to thank participants at the Conference in Honour of Paul Newbold, as well as the editor and referees for comments. All errors remain ours. Address correspondence to Elena Pesavento, Emory University, 1602 Fishburne Dr., Atlanta, GA 30322; e-mail: [email protected].

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2009 Cambridge University Press 0266-4666/09 $15.00 1829

TESTING THE NULL OF NO COINTEGRATION WHEN COVARIATES ARE KNOWN

TO HAVE A UNIT ROOT

1830 GRAHAM ELLIOTT AND ELENA PESAVENTO

This paper attempts to provide numerical bounds as to...