Testing for Cointegration When Some of The
EconometricTheory, 11, 1995, 984-1014. Printed in the United States of America. TESTINGFOR COINTEGRATION WHEN SOME OF THE COINTEGRATINGVECTORS ARE PRESPECIFIED MICHAELT.K. HORVATH Stanford University MARKW. WATSON Princeton University Manyeconomic models imply that ratios, simpledifferences, or "spreads"of variablesare I(O).In these models, cointegratingvectors are composedof l's, O's,and - l's and containno unknownparameters. In this paper,we develop tests for cointegrationthat can be appliedwhen some of the cointegratingvec- tors are prespecifiedunder the null or underthe alternativehypotheses. These tests are constructedin a vectorerror correction model and are motivatedas Waldtests from a Gaussianversion of the model. Whenall of the cointegrat- ing vectorsare prespecifiedunder the alternative,the tests correspondto the standardWald tests for the inclusionof errorcorrection terms in the VAR. Modificationsof this basictest are developedwhen a subsetof the cointegrat- ing vectorscontain unknown parameters. The asymptoticnull distributionsof the statisticsare derived,critical values are determined,and the local power propertiesof the test are studied.Finally, the test is appliedto data on for- eign exchangefuture and spot pricesto test the stabilityof the forward-spot premium. 1. INTRODUCTION Economic models often imply that variables are cointegrated with simple and known cointegrating vectors. Examples include the neoclassical growth model, which implies that income, consumption, investment, and the capi- tal stock will grow in a balanced way, so that any stochastic growth in one of the series must be matched by corresponding growth in the others. Asset This paper has benefited from helpful comments by Neil Ericsson, Gordon Kemp, Andrew Levin, Soren Johansen, John McDermott, Pierre Perron, Peter Phillips, James Stock, and three referees.
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