Page 148 - Contributed Paper Session (CPS) - Volume 5

CPS1159 Philip Hans Franses et al.
intervals. For the first vintage of data in Table 8, we see from the p values for
the Wald test in the last column that only since March, year t, the null
hypothesis of no bias can be rejected (p value is 0.485). One month earlier, the
p value is 0.071, but for that month we see that = 1 is not in 95% confidence
1
interval (0.787 with a SE of 0.098). Note by the way that the forecasts created
in the very last month of the current year (December, year t) are biased (p
value of 0.012), at least for the first release data.
Table 9 delivers quite intriguing results for the forecasts concerning the
most recent vintage of data. The p value of the Wald test becomes > 0.05 (that
is, 0.083) for the quotes in May, year t, but note that = 1 is not in 95%
1
confidence interval for 23 of the 24 months. Only for the forecasts in
December, year t, the forecasts do not seem biased (p value of 0.115, and =
1
1 is in the 95% confidence interval (0.820 with SE of 0.088).
In sum, it seems that individual MZ regressions for vintages of data deliver
confusing outcomes, which seem hard to interpret. Let alone that we
effectively do not know who of the forecasters is targeting at which vintage.
Moreover, it seems that outcomes of the Symbolic MZ Regression are much
more coherent and straightforward to interpret. Of course, due to the very
nature of the data, that is, intervals versus points, statistical precision in the
Symbolic Regression is smaller, but the results seem to have much more face
value and interpretability than the standard MZ regressions.

Conclusion and discussion
Forecasts created by professional forecasters can show substantial
dispersion. Such dispersion can change over time, but can also concern the
forecast horizon. The relevant literature has suggested various sources for
dispersion. A recent contribution to this literature by Clements (2017) adds
another potential source of heterogeneity, and this is that forecasters may
target different vintages of the macroeconomic data. Naturally, the link
between targets and forecasts is unknown to the analyst.
To alleviate this problem, we proposed an alternative version of the Mincer
Zarnowitz(MZ) regression to examine forecast bias. This version adopts the
notion that the vintages of the macroeconomic data can perhaps best be
interpreted as interval data, where at the same time, the forecasts also have
upper and lower bounds. Taking the data as intervals makes the standard MZ
regression a so-called Symbolic MZ Regression. Simulations showed that
reliable inference can be drawn from this auxiliary regression. An illustration
for annual USA GDP growth rates showed its merits.
A limitation to the interval-based data analysis is the potential size of the
intervals. More dispersion leads to less precision, and statistical inference
becomes less reliable. Also, the sample size for a Symbolic Regression should

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