RDP 2000-05: A Small Model of the Australian Macroeconomy Appendix A: Covariance-correlation Matrix of the Equation Residuals

Meredith Beechey, Nargis Bharucha, Adam Cagliarini, David Gruen and Christopher Thompson

June 2000

This appendix reports the variance-covariance and correlation matrices of the equations' estimated residuals. The upper triangle of Table A1 shows the correlation coefficients, the main diagonal the variances, and the lower triangle the covariances of the residuals.

Table A1: Covariance-correlation Matrix of Residuals
  Output Real exchange rate Import prices Unit labour cosst Consumer prices
Output 0.2384 −0.0390 0.0860 −0.2873 −0.1025
Real exchange rate −0.0513 7.2714 0.1292 −0.2372 −0.1388
Import prices 0.0365 0.3027 0.7545 0.0252 0.0898
Unit labour costs −0.1198 −0.5460 0.0187 0.7287 −0.0485
Consumer prices −0.0114 −0.0851 0.0177 −0.0094 0.0518

Examining the diagonal of the table, the estimated residuals from the real exchange rate equation are by far the largest on average, while those from the consumer price equation are by far the smallest. The largest (absolute) correlation coefficient between estimated residuals across equations is that between the residuals from the output and unit labour cost equations, with a correlation coefficient of −0.29. This high (absolute) correlation occurs because output is used to construct unit labour costs. When fitted values from the output equation are used instead of actual output to generate the unit labour cost series, the resulting correlation coefficient between estimated residuals from the two equations is +0.25. Most of the other cross-equation correlations are very small.