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Estimation and inference in cointegrated models is examined in the presence of deterministic trends in the data. It is suggested that trends be excluded in the levels regression for maximal efficiency. Fully modified test statistics are asymptotically chi-square. A chi-square test for the validity of trend exclusion is presented. The asymptotic distributions of standard cointegration test statistics are shown to depend both upon regressor trends and estimation detrending methods.
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Bruce E. Hansen (1992) studied this question.
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