Page 147 - Contributed Paper Session (CPS) - Volume 5

CPS1159 Philip Hans Franses et al.
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Table 4 is the same as Table 3, but now = 0.5 is replaced by =

̂
2.0. Overall this means that deviates more from when the variance
2

increases. The differences across the deviations of ̂ versus are relatively
small.
Table 5 is the same as Table 3, but now = 20 is replaced by = 100.
Clearly, a larger sample size entails less bias in the estimates, and also much
smaller bootstrapped standard errors. But still, we see that ̂ is closer to
̂
then is to .
Table 6 is similar to Table 4, but now for = 100. A larger sample can
offset the effects of increased variance , as the standard errors are
2

reasonably small.

Analysis of forecasts
We now turn to an illustration of the Symbolic MZ regression. We choose
to consider the forecasts for annual growth rates of real GDP in the USA, for
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the years 1996 to and including 2013. This makes = 18. Our data source
gives annual growth rates per quarter. As there are no vintages of true annual
growth data available, we decide to further consider the averages of each time
these four quarterly growth rates. The data intervals are presented in Table 2.
The right-hand side columns of Table 2 concern the forecasts created in May
of year t, which means the case where = 17. This implies that we can
consider 24 Symbolic MZ regressions, each for each of the 24 months.
Table 7 presents the estimation results, the bootstrapped standard errors
and the p value of the Wald test for the null hypothesis that = 0, = 1. We
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see from the last column that a p value > 0.05 appears for the forecasts quoted
in May in year t-1, and that after that the p value stays in excess of 0.05.
However, if we look at the individual parameter estimates, we see that = 0
1
is with the 95% confidence interval until September, year t-1. So, Table 7
basically tells us that unbiased forecasts seem to appear from October, year t-
1 onwards.
Let us now turn to the MZ regression in its standard format, that is, the
explanatory variable is the mean of the forecasts and the variable to be
explained in one of the vintages of the data. Table 8 presents the results for
the first (flash) release real GDP annual growth rates, whereas Table 9 presents
the results for the currently available vintage. We also have the results of all
vintages in between, but these do not add much to the conclusions that can
be drawn from Tables 8 and 9.
First, we see that the standard errors in Table 8 and 9 are much smaller
than the bootstrapped standard errors for the Symbolic MZ Regression. This
of course does not come as a surprise as we have point data instead of

3 http://www.oecd.org/sdd/na/revisions-of-quarterly-gdp-in-selected-oecd-countries.htm
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