RDP 2007-09: Private Business Investment in Australia Appendix C: Unit Root Tests

This Appendix shows unit root test results for the main series used in the modelling work. Two tests have a null hypothesis of a unit root (Augmented Dickey-Fuller (ADF) and Phillips-Perron tests) while an alternative has the null hypothesis of no unit root (the Kwiatkowski, Phillips, Schmidt, and Shin (KPSS) test).

These tests suggest either the presence of a unit root or provide ambiguous evidence of a unit root for all variables except the cost of capital for structures. The clearest evidence of a unit root is found for the capital-to-output ratios for equipment and structures, the investment-to-output ratio for engineering and building and the cost-of-capital measures for equipment and engineering. The results are more ambiguous for the investment-to-output ratio for equipment and the cost-of-capital measure for building.

Many of these series are highly persistent, and these tests for a unit root may be picking up some form of non-stationarity rather than a unit root per se. An inspection of many of these series – particularly the investment-to-output ratios – seems to indicate some mean-reverting characteristics, bringing into doubt some of the conclusions drawn from the results above. As is typical with these tests, their low power limits the strength of conclusions that can be drawn.

Table C1: Unit Root Tests
ADF Phillips-Perron KPSS
Equipment investment
Capital-to-output ratio −0.63 −0.90 0.42*
Investment-to-output ratio −2.54 −2.50 0.13
Cost of capital −0.92 −0.87 0.93***
Structures investment
Capital-to-output ratio 1.17 1.06 0.98***
Cost of capital −3.46** −3.19** 0.27
Building investment
Investment-to-output ratio −1.37 −1.77 0.40*
Cost of capital −4.27*** −2.12 0.15
Engineering investment
Investment-to-output ratio −0.87 −0.91 0.59**
Cost of capital −2.25 −2.40 0.60**
Notes: ***, ** and * denote significance at the 1, 5 and 10 per cent levels respectively. All variables are in logs. The capital-to-output ratios and cost-of-capital measures for equipment and structures are tested over 1975:Q2–2003:Q4. All other tests correspond with the samples used in the error-correction models shown in Table 2, namely 1974:Q2–2006:Q2 for equipment, 1986:Q3–2006:Q2 for building and 1979:Q2–2006:Q2 for engineering.