trimmed mean tend to display similar properties as our measures of inflation sen-
timent.
[Table 2: about here]
3. Estimation and forecast evaluation
In our empirical analysis, we forecast the difference between the actual inflation
rate and the average inflation rate over the next h periods ( πth+ h - πt ), where πt is
observed at time t and πth+ h is not.5 Starting point of our analyses is the conven-
tional Phillips curve, which constructs a relation between future inflation on the
left hand side, a current and lagged first-differenced output variable x which repre-
sents the inflation pressure coming from the real part of the economy, and current
and lagged inflation differences on the right hand side, 6
πth+h -πt =φ+β(L)∆xt +δ(L)∆πt +εt+h. (3.1)
Relations of this type are widely used to forecast inflation. Stock and Watson
(1999), evaluate the forecasting power of various specifications of xt. In our paper
we concentrate instead on evaluating alternative specifications of the inflation
measure on the right hand side. While the standard Phillips curve specification
uses the output or the employment gap, we capture influences from the real econ-
omy by first differences of the unemployment rate or real GDP. 7
Concerning the inflation measure on the right hand side, we test one baseline and
five alternative specifications. The first follows the standard Phillips curve litera-
ture and employs past inflation rates. The success of this approach serves as a
benchmark for the other five specifications. Subsequently, we replace the current
and lagged differences in inflation one by one by current and lagged values of our
5 ∏ι = 4/h ɪog I /p I is the h period inflation rate in the price level Pt reported at an annual
/h [/Pt-h j
rate.
6 ∆ and L represent the difference- and the lag-operator, respectively. Though modelling infla-
tion as I(1) is standard, it is, however, not always consistent with unit-root tests of the inflation
series. Unit root-tests for all variables can be found in the appendix.
7 According to our analyses, first differences of real variables generally perform better than
deviations from HP-filtered variables. Two-sided filters additionally violate the out-of-sample
assumptions because information is utilized which was not available at the point where the
forecast is made. Alternatively, one might use one-sided filters or calculate quasi real-time
output gaps by forecasting x first and applying a two-sided filter afterwards. Because of the
poor results for the HP-filtered gaps we do not follow this route.