RDP 9407: Explaining Import Price Inflation: A Recent History of Second Stage Pass-through Appendix 2: Time Series Properties of the Data

Each of the series used in estimating cointegrating relationships was tested for non-stationarity using the Augmented Dickey-Fuller test (Said and Fuller 1984). The null hypothesis of this test is non-stationarity. The following procedure was adopted. Initially equation A2.1 was estimated for each time series yt.

Eight lags of the dependent variable were included to eliminate autocorrelation; the lags were then sequentially removed until the minimum number of lags required to avoid autocorrelation was reached.

The joint hypothesis, β = 0,ρ −1 = 0, was then tested. The results of this test are shown in the first column of table A2.1. Where the hypothesis was rejected, a test was conducted to see whether the series is integrated around a deterministic trend; thus the hypothesis ρ −1 = 0 was tested. These results are shown in the second column below.

Table A2.1: Results of Unit Root Tests
Null hypothesis:
(a) Unit root
& no trend
(b) Unit root
given trend
(a) Unit root
& no drift
(b) Unit root
given drift
First stage
p 2.579 ~ 4.673 ~
e 4.640 ~ 2.202 ~
w 11.763** −2.392 ~ ~
Δp 8.211* −3.841* ~ ~
Δe 7.400* −3.601* ~ ~
Δw 16.219** −5.455** ~ ~
Second stage
r 6.873* −2.669 ~ ~
pl 2.380 ~ 4.351 ~
c 4.098 ~ 6.775* −2.797
Δr 9.854** −4.157** ~ ~
Δpl 10.607** −4.315** ~ ~
Δc 12.422** −4.689** ~ ~
Notes: * indicates significance at the 5 per cent level and ** at the 1 per cent level.
(a) Critical values are tabled in Perron (1988).
(b) Critical values from Fuller (1976).

If the initial joint hypothesis was accepted, equation A2.1 was re-estimated with a constant but no trend. The null of a unit root and no drift was then tested (α = 0,ρ −1= 0). If this hypothesis was rejected, we tested whether the rejection was due to a significant drift term, stationarity, or both. This was done by testing for a unit root given a drift. The results, reported in Tables A2.1, suggest that the series are all integrated of order one.