RDP 9607: Towards an Understanding of Australia's Co-Movement with Foreign Business Cycles Appendix B: Estimates of the ‘Gruen and Shuetrim Model Using Detrended Variables

Nicolas de Roos and Bill Russell

November 1996

While in this paper we characterise the domestic and foreign activity variables as I(1), there is some chance that the variables follow a trend stationary process.[30] Therefore, the Gruen and Shuetrim (1994) model was re-estimated using logged activity variables detrended using a linear trend. The results are reported in Table B1. Models (1), (2) and (3) are estimated using US, OECD and export-markets GDP. As in the original results reported in Table 2 and for the ‘benchmark’ model reported in Table 7, we find foreign activity has a large impact on the cycle in domestic GDP in the contemporaneous period. For example, in the US-based model (1), a 1 percentage point increase in US GDP is associated with a 0.57 of a percentage point increase in Australian GDP in the contemporaneous period and a 1.36 percentage point increase in the long run. These are similar to the short and long-run coefficients from the ‘benchmark’ model in Table 7 of 0.45 and 1.20.

Also reported in Table B1 as model (1′) is a US-based model which includes the Australian real share price variable. The results can be compared with model (1) in Table 7. The cash rate is now jointly insignificant, but otherwise the results are similar. The lag structure associated with US GDP has been altered but the total short-run impact on domestic activity remains largely unchanged. We also see that the impact of the share market is very similar. A permanent 1 standard deviation increase in the real share price (17 per cent) leads to a 0.34 percentage point increase in Australian GDP in the short-run and a 0.90 percentage point increase in GDP in the long-run. This compares with estimates of 0.32 and 1.26 percentage points for model (1) in Table 7.

Table B1: The ‘Gruen and Shuetrim Model’ Using Detrended Variables(a)
(1981:Q3–1995:Q3)
Dependent variable: Australian GDP gap
  Lag
 		 United
States		 United
States		 OECD
 		 Export
markets
    (1) (1′) (2) (3)
Constant   0.004*
(2.26)		 0.006**
(3.52)		 0.008**
(3.45)		 0.004#
(1.85)
Australian GDP 1
 		 0.869**
(6.22)		 0.644**
(9.59)		 0.556**
(6.30)		 0.935**
(6.04)
  2
 		 −0.246#
(−1.88)		     −0.236
(−1.21)
  3
 		       −0.221#
(−1.74)
Foreign GDP 0
 		 0.565**
(3.81)		 0.377**
(5.04)		 0.907**
(4.70)		 0.320
(1.53)
  1
 		 −0.449#
(−1.95)		     −0.309
(−1.25)
  2
 		 0.395*
(2.39)		     −0.171
(−0.68)
  3
 		   0.719**
(2.90)
Real cash rate(b) 2 to 6
 		 −0.070
{0.335}		 −0.097**
{0.001}		 −0.121**
{0.010}		 −0.051
{0.158}
Real share price 1
 		   0.020**
(2.98)		    
Terms of trade log change 1 to 4
 		     0.043
{0.366}		 0.122*
{0.027}
Real exchange rate log change 1 to 4
 		     −0.085* {0.049} −0.142**
{0.002}
Joint significance of terms of trade and real exchange rate   {0.019}*
 		 {0.002}**
 
Diagnostics of residuals
Inline Equation   0.887 0.894 0.884 0.879
LM(1)(c)   1.323
{0.250}		 0.773
{0.379}		 3.299#
{0.069}		 1.878
{0.171}
Standard error of equation   0.006 0.006 0.006 0.006
DW   2.08 1.79 1.62 2.09

Notes: (a) With the exception of the real cash rate, all variables are detrended logged levels. Numbers in parentheses () are t-statistics; and numbers in brackets {} are probability values for the joint test that all the lags can be excluded. **, *, and # denote significance at the 1%, 5%, and 10% levels respectively.
(b) Real cash rate reported as the sum of the coefficients multiplied by 100.
(c) LM (1) is a Lagrange multiplier test for first order autocorrelation.

Footnote

Nelson and Plosser (1982) argue that standard unit root tests have low power in rejecting the null hypothesis of non-stationarity. The Kwiatkowski, Phillips, Schmidt and Shin (1992) tests in Appendix E, based on the null hypothesis of stationarity, provide additional evidence that these series are non-stationary. [30]