Page 144 - Contributed Paper Session (CPS) - Volume 5

CPS1159 Philip Hans Franses et al.
Setting

Consider the I vintages of data for a macroeconomic variable , where =

1,2, . . , and = 1,2, … , . In our illustration below we will have = 7 and =
1996, 1997, … . , 2013, so = 18.
Professional forecasters, like the ones united in Consensus Economics
forecasts, give quotes during the months m, where = 1,2, … , . For the
Consensus Economics forecasters = 24, and the months span January in
year t-1, February in year t-1, …, December in year t-1, January in year t, until
and including December in year t. An example of the data appears in Table 1,
where the quotes are presented for May 13, 2013, for the years 2013 and 2014.
The forecasts can be denoted as
̂ ,| with = 1,2,…,
,

The number of forecasters can change per month and per forecast target,
hence we write , . In Table 1 this number is 29. For 2013, and in our notation,
Table 1 considers 2013,5 and for 2014 it is 2014,17 .
A key issue to bear in mind for later, and as indicated in the previous section,
is that we do not observe

̂ ,| with = 1,2, … , , ,
that is, we do not know who of the forecasters is targeting which vintages of
the data.
To run a Mincer Zarnowitz (MZ) regression, the forecasts per month are
usually summarized by taking the median, by using a variance measure, or by
the mean (“the consensus”), that is, by considering

,
1
̂ , = ∑ ̂ ,|
,
=1

The MZ regression then considered in practice is

= + ̂ +
1 ,
0

for = 1,2, … , , and this regression can be run for each = 1,2, … , . Under
the usual assumptions, parameter estimation can be done by Ordinary Least
Squares. Next, one computes the Wald test for the joint null hypothesis =
0
0, = 1.
1
Now, one can run this MZ test for each vintage of the data, but then still it
is unknown what the estimated parameters in the MZ regression actually
reflect. Therefore, we propose an alternative approach. We propose to
consider, for = 1,2, … , , the interval

(min ; max )

as the dependent variable, instead of , and to consider

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