RDP 9511: Superannuation and Saving Appendix C: Unit Root Tests

Steven Morling and Robert Subbaraman

December 1995

The unit root tests are based on the testing strategy recommended by Perron (1988). Since unit root tests are widely recognised as having low power, we use both the Augmented Dickey-Fuller test (ADF) (Said and Dickey 1984) and the Phillips and Perron (1988) Zt test.[32]

Both tests are conducted over the estimation period 1960–1994. The tests share the same critical values, which is 2.96 at the five per cent significance level, and in both cases, the null hypothesis is non-stationarity. Table C1 presents the test results for the level of each series where both test procedures show that all the variables are I(1) with no drift. Subsequent tests confirmed that none of the series are I(2).

Table C1: Series in Levels
Series Level of: Φ3 Φ2 Φ1 ADF lags Zt Result
Non-super saving (/Y) 1.92 1.28 1.13 1.50 0 1.67 I(1)
Super. saving (/Y) 5.50 3.74 3.93 2.76 6 1.88 I(1)
Net contributions (/Y) 2.04 1.52 4.41 2.80 3 1.89 I(1)
Interest earnings (/Y) 0.72 0.73 1.99 1.98 1 1.46 I(1)
Super. profit (/Y) 5.04 3.42 1.62 1.72 1 2.22 I(1)
Human wealth (/Y) 2.22 1.49 2.31 2.14 0 2.22 I(1)
Non-human wealth (/Y) 1.19 1.24 0.65 0.16 0 0.33 I(1)
Population ratio 45–64 2.65 1.97 2.67 2.17 1 1.43 I(1)
Inflation 1.12 0.76 1.72 1.84 1 1.72 I(1)
Real bond rate 1.89 1.39 1.04 1.30 0 1.39 I(1)
Unemployment rate 3.21 3.04 1.25 0.06 2 0.05 I(1)
Income volatility 11.26**     4.71** 1 2.93 I(0)

Notes: **(*) denotes significance at the one (five) per cent levels. The critical values for the Φ tests are from Dickey and Fuller (1981). The critical values for the ADF and Zt tests are from MacKinnon (1991).

Footnote

This test involves making non-parametric corrections to the Dickey-Fuller test. Five lags of the residual auto-covariance were chosen. [32]