Appendix A: Power Calculations | RDP 9410: An Empirical Examination of the Fisher Effect in Australia

RDP 9410: An Empirical Examination of the Fisher Effect in Australia Appendix A: Power Calculations

Frederic S. Mishkin, John Simon

December 1994

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The power calculations found in Table A1 are obtained from Monte Carlo simulations using the same procedure that was described in Section 3.1.1, however, the data generating process is estimated from ARIMA models estimated in levels rather than first differences, that is, ARMA models. The power calculation for each test statistic in the table is the probability obtained from this Monte Carlo simulation of rejecting the null of a unit root given the alternative of no unit root using the size-corrected 5% critical value for the test statistic.

Table A1: Power of Integration Test Statistics in Table 2
Sample period	Test statistics for π_t			Test statistic for i_t
	DF	*Z_t*	*Z_α*	DF	*Z_t*	*Z_α*
1962 III–1993 IV	0.093	0.094	0.090	0.053	0.032	0.029
1962 III–1979 III	0.095	0.098	0.107	0.162	0.166	0.178
1979 IV–1993 IV	0.057	0.059	0.044	0.112	0.119	0.142

Tables A2 and A3 contains the power calculations for test statistics from the Engle Granger two step method and the ECM equations reported in Table 3 using similar Monte Carlo simulations to those used in Table A1. The data generating process for the cointegration tests for a unit root in π_t − i_t is an error correction model in which the error correction term is π_t − i_t. Similarly, the data generating process used for the tests of a unit root in π_t − i_t is an error correction model in which the error correction term is π_t − i_t. The test statistics in Table A2 are the same as those reported in Table 2 and Table A1, that is, Dickey-Fuller t-tests and Phillips Z_t and Z_α tests.

Table A2: Power of Engle Granger Co-Integration Test Statistics
Sample period	Test statistics for unit root in π_t − i_t			Test statistic for unit root in π_t − i_t
	DF	*Z_t*	*Z_α*	DF	*Z_t*	*Z_α*
1962 III–1993 IV	0.076	0.086	0.096	0.188	0.192	0.196
1962 III–1979 III	0.449	0.503	0.606	0.461	0.507	0.573
1979 IV–1993 IV	0.030	0.027	0.021	0.417	0.363	0.275

Table A3: Power of ECM Co-Integration Tests in Table 3
Sample period	Test statistics for unit root in π_t − i_t		Test statistic for unit root in π_t − i_t
	γ	δ	γ	δ
1962 III–1993 IV	0.012	0.081	0.012	0.634
1962 III–1979 III	0.034	0.358	0.072	0.750
1979 IV–1993 IV	0.019	0.284	0.690	0.523

In most cases the power of tests in Table A1, A2 and A3 are very low. This stems from both the low power of the tests themselves and the low number of observations we have to work with.