Is it really the Fisher effect?

Abstract

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, 1989).

Acknowledgements

I thank Márcio Garcia, Christopher Kilby, Joy Lei and a referee for comments on an earlier draft. Lisa Wong and Ilian Georgiev provided efficient research assistance. Financial support from the Salmon Fund at Vassar College is gratefully acknowledged. All errors are mine.

Notes

¹ Examples from other journals include Mishkin (1992), Wallace and Warner (1993), Mishkin and Simon (1995), Peláez (1995), Crowder and Hoffman (1996), Crowder (1997), Koustas and Serletis (1999) and Fahmy and Kandil (2003).

² Using data sets ending in 1986, from the USA, Belgium, Canada, and the UK, MacDonald and Murphy (1989) find little evidence that inflation rates and nominal interest rates are cointegrated. Employing subsequent advances in the econometrics of cointegrated time series, Dutt and Ghosh (1995) confirm this finding for the Canadian case. Bonham (1991) extends the work of MacDonald and Murphy (1989) by allowing for the possibility of an integrated ex ante real interest rate. He does so by proxying for the ex ante real interest rate using Huizinga and Mishkin's (1986) expected real interest rate variable and the earnings/price ratio, finding that both of these proxies and the inflation and nominal interest rates are cointegrated. Using quarterly US data from 1957 to 1992, Daniels et al. (1996) find that inflation rates and nominal interest rates are cointegrated. They also find that there is a long-run, one-to-one relationship between the two variables with unidirectional causality from the former to the latter. These results are consistent with those of Lee et al. (1998) who use Mishkin's (1992) monthly data set, which ends in December 1990. Using data from the UK over the last century, Granville and Mallick (2004) find evidence that the inflation rate is not integrated while the nominal interest rate is integrated of order one. Nonetheless, they find that a linear combination of the two variables is not integrated which they interpret as evidence in favour of the Fisher hypothesis.

³ Miron (1991) makes the same point in the context of testing the expectations theory of the term structure.

⁴ See also Rapach and Weber (2004).

⁵ Cochrane's view alone renders the results of cointegration tests of the Fisher effect meaningless as, absent integration, the concept of cointegration is vacuous. Johnson (1994b) also tests the integration and cointegration properties of interest rate data but the issue is not further discussed here.

⁶ As is the risk-free rate in the version of Fisher's theory discussed here so any role played by risk aversion in determining i_t will be reflected in the model noise.

⁷ Durlauf and Hall (1988, 1989) show that all other linear tests are special cases of this approach. Garcia (1993) and Johnson (1994a) demonstrate this proposition for some of the tests of Fisher's theory in the literature by reinterpreting them in the signal extraction framework.

⁸ If ρ _t were observable, Fisher's theory could be tested by projecting on to any .