RDP 9511: Superannuation and Saving Appendix D: Diagnostic Tests

Steven Morling and Robert Subbaraman

December 1995

The equations appear to be well specified passing a host of diagnostic tests. The LM test for up to second order serial correlation, Jarque-Bera's normality test, the ARCH test and Breusch-Pagan's heteroscedasticity test are all insignificant at the 5 per cent level. The Chow predictive test is also used. For this test, the equation was estimated up to 1989/90 and the results used to do an in-sample prediction out to 1993/94. The prediction errors were then tested for a zero mean. In all three equations, the null hypothesis of parameter stability is accepted.

We tested for the possibility that the specification of the estimating equation in ratio form may have introduced spurious correlation between the superannuation and non-superannuation saving terms, by also including the denominator (income) in level terms in the final equation. The term was insignificant and the coefficients on the superannuation terms were largely unchanged.

Table D1: Diagnostic Tests
  (1) (2) (3)
Serial correlation χ2 (2) 0.39 0.30 0.20
Normality χ2 (2) 0.79 0.88 0.89
ARCH χ2 (2) 0.21 0.12 0.10
Heteroscedasticityχ2 (k) 0.26 0.38 0.39
Chow test F(4, n-k-1) 0.78 0.77 0.75

Notes: Marginal significance levels (p-values) are reported and **(*) denotes significance at the one (five) per cent levels. Serial correlation is the LM test for up to 2nd order serial correlation, Normality is the Jarque-Bera (1980) test, ARCH is Engle's (1982) test, heteroscedasticity is the Breusch-Pagan (1979) test and Chow's (1960) predictive test is employed to test the stability of the parameters.