This paper analyses the properties of Dickey-Fuller (1979) (DF) unit root tests in the presence of trend mis-specification. It is shown that while the performance of the DF coefficient test is as expected, the DF test in its t-ratio form exhibits unusual behaviour. In particular it is found that the power of the test increases as the autoregressive parameter approaches 1. Interestingly, this increased power is not accompanied by oversizing.DF test
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