RSQE 1.26 1.40 1.37 0.59 VAR1 1.27 1.88 2.24 0.90 VAR2 1.25 1.55 2.23 0.86 VAR3 1.37 1.77 2.29 0.89 VAR4 1.90 2.11 2.47 0.92 VAR5 1.88 1.98 2.46 0.92 VAR6 2.14 1.94 2.59 0.98 VAR7 2.22 1.95 2.70 1.07 VAR8 2.71 2.23 2.95 1.16
The RSQE forecasts are better on average than the best of the VAR forecasts for three of the four variables.
Over this period, RSQE forecasts of the real growth rate exhibit a small but statistically significant upward bias, and the inflation rate forecasts exhibit a small but statistically significant downward bias.
With the exception of the Treasury bill rate, the differences in root mean squared errors of the RSQE and VAR2 forecasts are small.
TABLE 4 Test Statistics for Equality of RSQE and VAR Forecast Error Variances
Turning now to the question of the conditional efficiency of RSQE forecasts, in order to determine if RSQE forecasts are efficient, one asks if they could be improved by combining them with VAR forecasts.(7) For each variable, the actual value is regressed on the RSQE forecast and the VAR forecast.
The first equation in each of these tables represents the baseline case in which the actual value of the variable is regressed on the RSQE forecast only.
The results shown in Table 5 for GNP indicate that both the RSQE and the low-order ([less than or equal to] 3) VAR forecasts are significant.
The results for the GNP deflator shown in Table 6 indicate that RSQE forecasts are efficient relative to low-order ([less than or equal to] 3) VAR forecasts, but are not efficient relative to higher-order VAR forecasts.
Table 7 shows that the RSQE forecasts of the Treasury Bill Rate uniformly dominate the VAR forecasts.
The results of the internal consistency tests for RSQE and VAR2 forecasts are shown in Table 9.
Not surprisingly, given the univariate test results in Tables 5-8, the multivariate test results indicate that except for the RSQE interest rate forecasts, neither the RSQE nor the VAR forecasts are efficient.