RDP 2001-01: The Decline in Australian Output Volatility Appendix A: Data

The data used are quarterly domestic final demand plus net exports, the unemployment rate, and the terms of trade on goods and services. The output data are measured in constant chain-linked prices while the terms of trade is an index and the unemployment rate is in percentage points. The unemployment rate for a quarter is calculated as the average of the three monthly observations in that quarter. While it is not strictly necessary for the correct estimation of the VAR that the variables be stationary it is useful to have an idea of their general properties. The following table presents the results from ADF tests on the order of integration of the variables across the samples used and across the entire sample period. y is the log of output and Δy is the change in the log.

Table A1: ADF Test Statistics
  Full sample 1960s 1970s 1980s 1990s
y 2.73 0.72 2.97 0.90 2.43
Δy 7.48*** 11.13*** 6.01*** 5.82*** 7.69***
ue 2.82 3.64*** 3.25* −1.01 2.18
Δue 7.23*** 8.33*** 2.63 1.69 3.41*
TOT 5.57*** 4.63*** 2.21 2.93 1.84
ΔTOT 11.97*** 6.87*** 6.64*** 2.12 4.04**

Notes: The tests are conducted by regressing the variable (x) on its own lag (x+1), a time trend and constant, and enough lags of Δx to remove autocorrelation. The statistics reported are (1 − ρ)/σ where ρ is the coefficient on the lagged dependent variable and σ is the standard deviation of the estimate. Critical values are found in Table B.6 in the back of Hamilton (1994).
*, **, and *** indicate significance at the 10%, 5% and 1% levels.

So we see that while output growth is unquestionably stationary the unemployment rate and terms of trade seem non-stationary. Indeed, if we took these results at face value, it suggests that unemployment is I(2) in the seventies and eighties and the terms of trade is I(2) in the eighties. This is sufficiently beyond the realms of possibility that I discount these findings. The results for unemployment and the terms of trade are most likely a result of the small sample sizes involved in these decade long samples and the low overall power of the tests. Over samples including the 1960s and 1970s, and 1980s and 1990s the terms of trade is found to be stationary, however, it is still not possible to reject the null of integration for unemployment. I appeal to common sense to argue that the terms of trade and unemployment rate, while persistent, are unlikely to be integrated. The terms of trade should be stationary if even a weak form of purchasing power parity holds while the unemployment rate is bounded by definition. As such, I include them in the VAR in levels rather than differences. There is little change in the results if the change in the unemployment rate is included instead of the level, however, results change more if the change in the terms of trade is used.