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Many researchers have used a cointegration approach to test for the Fisher effect. This note argues that the cointegration of the nominal interest rate and the inflation rate is consistent with any theory implying a stationary ex post real interest rate and so is not a sufficient condition for the Fisher effect to hold. The sufficient condition is the unpredictability of the inflation forecast error implied by the nominal interest rate and this condition may be tested using the signal extraction framework of Durlauf and Hall (1988 Durlauf, SN and Hall, RE. 1988. “Bounds on the variances of specification errors in models with expectations”. In mimeo, Stanford University. [Google Scholar], 1989 Durlauf, SN and Hall, RE. 1989. “A signal extraction approach to recovering noise in expectations based models”. In mimeo, Stanford University. [Google Scholar]).
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