RDP 9509: Australian Wage and Price Inflation: 1971–1994 Appendix b: Integration Tests of the Data

Lynne Cockerell and Bill Russell

November 1995

The following tables present tests of the time series characteristics of the data. Table B1 shows the standard augmented Dickey Fuller (Said and Dickey (1984)) (ADF) test where a unit root null hypothesis is tested against a stationary alternative. These result are compared with Kwiatkowski, Phillips, Schmidt and Shin (1992) (KPSS) tests in Table B2 for which the null hypothesis of stationarity is tested against the unit root alternative.

Table B1: Augmented Dickey – Fuller Tests
Variable> Φ1 Φ2 Φ3 Inline Equation Inline Equation Inline Equation
pricesfc 5.56# 3.71 5.31 0.05 −3.26* −0.28
Δ pricesfc 10.37** 8.50** 12.69** −2.39* −4.54** −4.81**
prices 5.11 3.71 4.85 0.02 −3.13* −0.73
Δ prices 2.27 12.09** 18.11** −0.99 −2.12 −5.87**
wages 111.73** 74.45** 14.79** 1.16 −5.39** −0.27
Δ wages 19.12** 19.88** 29.81** −3.49** −6.18** −7.72**
unit labour costs 49.04** 32.79** 9.12** 0.98 −4.20** −0.13
Δ unit labour costs 25.55** 23.46** 35.17** −4.96** −7.15** −8.38**
import prices 22.14** 14.73** 3.56 3.20 −2.63# −0.15
Δ import prices 24.60** 18.33** 27.49** −5.65** −7.01** −7.41**
petrol prices 8.79** 5.84* 1.38 3.45 −1.63 −0.75
Δ petrol prices 60.49** 42.29** 63.43** −9.46** −11.00** −11.26**
output gap 7.48** 5.37* 8.05* −0.01 −3.87** −3.97*
Δ output gap 51.36** 33.88** 50.79** −10.19** −10.13** −10.08**
inside unemployment 7.54** 4.99* 7.48* −0.81 −3.88** −3.87*
Δ inside unemployment 21.90** 14.68** 21.92** −6.66** −6.60** −6.61**
strikes 30.59** 20.42** 30.63** −7.86** −7.82** −7.82**
Δ strikes 16.98** 11.37** 17.05** −5.87** −5.83** −5.84**
rer 1.95 1.55 2.33 −0.05 −1.97 −2.15
Δ rer 42.95** 28.36** 42.54** −9.32** −9.27** −9.22**
income share 2.04 4.38# 6.57# −0.21 −2.02 −3.58*
Δ income share 15.48** 10.39** 15.43** −5.60** −5.56** −5.55**

Notes: The likelihood ratio tests are:
Inline Equation
The ‘t-tests’ are ρ = 1 for
Inline Equation
**, * and #, denotes significance at the 1%, 5% and 10% levels respectively. The critical values for the likelihood ratio tests are from Dickey and Fuller (1981) and the critical values for the ‘t-tests’ are from Fuller (1976).
The shaded box indicates the form of the model used for inference in testing for non-stationarity.
The sample size for most cases in levels is 1971:Q1–1994:Q3 and in differences is 1971:Q2–1994:Q3.
Exceptions to this are inside unemployment and strikes which end in 1994:Q2.
All variables are in logs except inside unemployment, strikes and labour's income share.
Strikes are adjusted for a break in mean in the first quarter of 1983.
Table B2: Kwiatkowski, Phillips, Schmidt and Shin Tests
  Constant Constant and trend
  Lag Lag
Variable 0 4 8 0 4 8
pricesfc 9.33** 1.96** 1.13** 2.07** 0.45** 0.28**
Δ pricesfc 3.67** 1.15** 0.74** 0.29** 0.13# 0.10
prices 9.33** 1.96** 1.13** 2.09** 0.46** 0.28**
Δ prices 4.22** 1.15** 0.73** 0.37** 0.13# 0.10
wages 9.16** 1.93** 1.13** 2.11** 0.46** 0.28**
Δ wages 2.46** 1.04** 0.71* 0.07 0.05 0.04
unit labour costs 9.07** 1.91** 1.11** 1.93** 0.43** 0.26**
Δ unit labour costs 1.64** 0.79** 0.60* 0.06 0.04 0.04
import prices 9.06** 1.90** 1.11** 1.88** 0.41** 0.25**
Δ import prices 0.83** 0.45# 0.40# 0.09 0.06 0.07
petrol prices 9.14** 1.91** 1.10** 1.96** 0.43** 0.26**
Δ petrol prices 0.33 0.40# 0.35# 0.07 0.10 0.11
output gap 1.45 0.38# 0.29 0.33** 0.09 0.07
Δ output gap 0.04 0.04 0.05 0.04 0.04 0.05
inside unemployment 0.25 0.07 0.06 0.24** 0.07 0.06
Δ inside unemployment 0.05 0.03 0.05 0.05 0.03 0.04
strikes 0.10 0.08 0.08 0.05 0.04 0.05
Δ strikes 0.01 0.04 0.06 0.01 0.03 0.05
rer 1.51** 0.35# 0.23 0.44** 0.11 0.07
Δ rer 0.07 0.06 0.05 0.07 0.06 0.05
income share 2.06** 0.51* 0.36# 0.61** 0.16* 0.12#
Δ income share 0.07 0.05 0.06 0.05 0.03 0.04

Notes: For this test the series, yt, is expressed as yt = ξt + rt + εt, where rt = rt−1 + ut and Inline Equation. Then the null hypothesis of stationarity is the test that Inline Equation. The critical values, with the inclusion of a constant at the 1%, 5%, and 10% levels of significance, are 0.739, 0.463 and 0.347 respectively. The critical values, with the inclusion of a constant and trend at the 1%, 5%, and 10% levels of significance, are 0.216, 0.146 and 0.119 respectively.
The lag length refers to the value of l chosen when calculating the estimate of the error variance,Inline Equation, used in the testing procedure. A lag length of 8 is chosen for inference following the approach of KPSS.
**, * and # denotes significance at the 1%, 5% and 10% levels respectively.
The sample size for most cases in levels is 1971:Q1–1994:03 and in differences is 1971:Q2–1994:Q3.
Exceptions to this are inside unemployment and strikes which end in 1994:Q2.
All variables are in logs except inside unemployment, strikes and labour's income share.
Strikes are adjusted for a break in mean in the first quarter of 1983.

Using the augmented Dickey Fuller tests and a 5% level of significance, the level of market prices, prices at factor costs, import prices and petrol prices all accept the null hypothesis of non-stationarity. The first difference of these series reject the null hypothesis in favour of the stationary alternative. The level of the output gap, inside unemployment, and strike terms are all, as expected, found to be stationary. For each of these series, the results of the KPSS tests for a lag length of 8 accord with the above conclusions using a 5% level of significance (see notes for Table B2).

There are, however, four contentious results. While the ADF tests suggest wages and unit labour costs are stationary around a drift term, the null hypothesis of stationarity is rejected using the KPSS tests. Both these series are treated as non-stationary in the estimation. Of particular interest is the characterisation of the real exchange rate and labour's income share. In the paper both these series are characterised as stationary. However, the statistical tests produce conflicting results. In the ADF tests, both series do not reject the unit root hypothesis. The stationary null hypothesis in the KPSS tests is also not rejected at the 5% significance level. While the statistical results are ambiguous, the conclusion of stationarity follows from the graphical analysis and can be supported theoretically.