RDP 8808: Consumption and Permanent Income: The Australian Case Appendix A: Time Series Properties of the Data

Warwick J. McKibbin and Anthony J. Richards

October 1988

To test if the consumption and disposable income series are stationary we used the method of Dickey and Fuller (1979) and regressed:

where X is consumption in Table A1 and disposable income in Table A2.

Table A1: Augmented Dicky-Fuller Test for Consumption
ΔC6 = α1 + α2Ct−1 + α3ΔCt−1 + α4ΔCt−2 + α5ΔCt−3 + α6ΔCt−4
Parameter Value t-statistic
α1 0.0602 2.665
α2 −0.0054 −2.403
α3 −0.0761 −0.795
α4 −0.0886 −0.919
α5 0.0712 0.737
α6 0.2029 2.109
Table A2: Augmented Dicky-Fuller Test for Disposable Income
ΔYt = β1 + β2Yt−1 + β3ΔYt−1 + β4ΔYt−2 + β5ΔYt−3 + β6ΔYt−4
Parameter Value t-statistic
β1 0.1132 1.985
β2 −0.0105 −1.800
β3 −0.1871 −1.931
β4 −0.0394 −0.390
β5 −0.0440 −0.435
β6 0.0026 0.025

The distribution of the t-statistics on α2 are non-standard. We, therefore, use the critical values tabulated by Fuller (1976). The critical value for the significance of the coefficients is 2.6 at the 1 per cent level of significance and 1.95 at the 5 per cent level. There is some ambiguity about the results for consumption which implies that consumption is I(1) at the 1 per cent level, but not at the 5 per cent level. The results for income are a little clearer.

These results indicate that consumption and income are apparently non-stationary, although there are problems with the power of these tests. Rather than undertake a further battery of tests for non-stationarity of the individual series, we will use the properties of the residuals from the alternative models in the paper to check for possible problems.

We next test to see if consumption and income are cointegrated. The results are:

The residuals from this cointegrating equation were tested for non-stationarity using the Augmented Dickey-Fuller test as in equation (Al). These results are:

Again, we have non-standard t-statistics. In this case, we use the critial values in Table II in Engle and Granger (1987). These are 3.17 at the 95 per cent level of significance. These results show no significant co-efficient. It, therefore, appears that consumption and income are not co-integrated.