The year ahead forecasts published in the Bank of England’s quarterly Inflation Report seem
to be over-estimating the chances of relatively high rates of inflation. That is one of the
conclusions of new research by Michael Clements. His study, which investigates a number of
ways of evaluating the Bank of England’s expected probability distributions of inflation, is
published in the October 2004 Economic Journal.
Every quarter since 1997, the Bank of England Inflation Report has carried density forecasts of
inflation. That is, it has published the probabilities that it assigns to inflation taking on any
particular value. Forecasts of this sort are published for the following quarter, for half a year
ahead, and so on up to two years ahead.
Clements’ research asks: how good are these forecasts? From the density forecasts, it is
possible to calculate the outcome thought to be the most likely, and compare this with the
actual rate. This is the traditional way of evaluating forecasts. But it ignores the probabilities
assigned by the Bank to all the possible rates of inflation, and the degree of confidence
attributed to that central projection.
If we take all the forecasts stating that the probability that inflation will exceed say 3% is, say,
10%, then on approximately 10% of these, the actual rate of inflation should exceed 3%.
Similarly, for forecasts that the probability is 20%, for a fifth of these the actual inflation rate
should exceed 3%. And so on.
Evaluated in this way, the year ahead probability forecasts of the Bank appear to over-estimate
the chances of relatively high rates of inflation occurring, in line with the findings of others
using similar techniques.
Instead of looking at the whole range of forecast probabilities, statistical techniques are
developed to test the quality of the forecast probabilities of inflation falling in ranges of especial
interest to policy-makers.
The results suggest that the probabilities attached to inflation being in the range 2% to 3% in
the current quarter may not be well-calibrated, although the relatively short sample on which
the analyses are based counts against drawing firm conclusions.
Finally, forecasts are often used to guide decisions. Actions are taken today that will have
implications in the future. Whether those actions prove beneficial ex post (after the fact) will
depend on which of a number of uncertain futures materialises.
Ex ante (before the fact), it is at least possible conceptually to calculate the expected value of
a forecast. In each of those futures, we calculate the value of having used that forecast to
guide actions. We then weight those values by the true probabilities of those futures occurring,
to derive an average economic value for that forecast.
This research discusses the problems that arise in applying this sort of approach to the Bank’s
forecasts.
ENDS
Note for Editors: ‘Evaluating the Bank of England Density Forecasts of Inflation’ by Michael
Clements is published in the October 2004 issue of the Economic Journal.
Clements is in the Department of Economics at the University of Warwick.
For Further Information: contact Michael Clements on 024-76-522990 (email:
m.p.clements@warwick.ac.uk); or RES Media Consultant Romesh Vaitilingam on 0117-983-
9770 or 07768-661095 (email: romesh@compuserve.com).