Silvapulle ( 1992) used cointegration methods to test if the Fisher effect
applies in Australia. One question related to this is whether nominal interest rates
and inflation are cointegrated. Consider the equation
it = β0 + β1πt + ut (39)
where it is the nominal interest rate and πt is the inflation rate. Inder and Silvapulle ( 1992) treat (39) as a long-run relationship which implies that the interest rate and the inflation rate are cointegrated. They use the augmented Dickey-Fuller test to test for cointegration between the series as represented by the change in the log of CPI for inflation and the bank accepted bill rate for interest rates. The estimated parameters for equation (37) were β + ̂0 = 7.2275 and β + ̂1 = -0.4387, and the Dickey- Fullert statistic was -2.5921. Compared with a 10% critical value of -2.84, it can be seen that the null hypothesis of no cointegration could not be rejected.
However, it is possible that the failure to reject the null hypothesis was due only to lack of power of the Dickey-Fuller test, rather than true non-cointegration. To check this, we computedto test the null hypothesis of cointegration. We chose the lag length l by following Inder ( 1991), who suggested choosing the largest significant lag in the autocorrelation function of the OLS residuals. For this application, this gave a choice of l = 4. We obtained , which when compared to the 1% critical value of 0.5497 allows rejection of the null hypothesis of cointegration. This provides further evidence for the results of Inder and Silvapulle ( 1992) rejecting the cointegration hypothesis.
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