Forecasting inflation;
The Fan Chart
CCBS/HKMA May 2004
Why do central banks need to
have a forecast?
• Monetary policy decisions made today
affect inflation and output in the future.
• The Central Bank needs a view on what is
going to happen in the future, to set policy
today.
Forecasts can explain policy and
gain credibility
• Forecasts are used
– to explain the process
– And acquire credibility
Exchange rate targeting
• For fixed exchange rate regimes, the central
banks’ credibility depends on its success in
defending the rate
• A credibly fixed exchange rate means that
inflationary price rises erode
competitiveness
– but this needs to be explained to price setters,
government and so on
Other targets
• Harder to judge success and therefore
credibility of money supply targeters and
inflation targeters
• Credibility related to inflation outcomes
Aim is to affect expectations
• Consider a model in which inflation is a
function of expected inflation which, in
turn, is a function of the target
• If we can anchor expectations close to the
target much of our job is done
• So we use the forecast to explain policy and
acquire credibility
Forecasting is difficult
• We don’t know the past (Estimation
uncertainty)
– errors and uncertainty in the data
• We don’t know the initial condition
– lags in data availability; revisions to data
• We don’t have a perfect model (Model misspecification)
• The past is not necessarily a good guide to
the future. (Structural breaks)
How policy is not made
• Model  Forecast  Policy
The forecast process
CORE MODEL
ASSUMPTIONS
AND
JUDGMENTS
FORECAST
OTHER
MODELS
OTHER ISSUES AND
POLICY
JUDGMENTS
POLICY
Forecasts
•
•
•
•
Inflation targeting requires forecast
Forecast made each quarter
Baseline on unchanged interest rates
Explicit recognition of uncertainty
Current CPI inflation projection based on
constant nominal interest rates at 4.0%
Current RPIX inflation projection based on
constant nominal interest rates at 4.0%
RPIX and CPI
3.5
3.0
RPIX
2.5
2.0
CPI
1.5
1.0
0.5
0.0
1997
1998
1999
2000
2001
2002
2003
RPIX and CPI
• CPI and RPIX calculated from same raw
data. But…
• Different formulae
– CPI geometric mean; RPIX arithmetic mean.
• Different coverage
– RPIX includes housing costs (9.5%weight)
Current CPI inflation projection based on
constant nominal interest rates at 4.0%
Current CPI inflation projection based
on market interest rate expectations
Current GDP projection based on constant
nominal interest rates at 4.0%
Fan chart shows uncertainty
• We cannot predict the future accurately.
• There are considerable uncertainties
surrounding any forecast.
• The fan chart shows these uncertainties.
– Fan chart shows range of outcomes
– And risks
What is the fan chart?
• The fan chart is a probability distribution
• It shows more information than a simple
point forecast
• The width of the fans measures the overall
degree of uncertainty
Advantages of the fan chart
• Describes all outcomes - not just the central
estimate
• Shows that policy is made in an uncertain
world
• Shows risks to the outlook
• Allows policy makers to talk about
probability
The fan chart; a definition
• A subjective probability distribution of
likely outcomes for inflation (and output
growth)
Constructing the fan chart
• a) Agree on the most likely outcomes for
key variables
• b) Agree on the degree of uncertainty over
the forecast horizon
• c) Agree on the balance of risks around the
most likely outcome
• Combine this information in a Fan Chart
Most likely outcome is the
MODE
• Mode - most likely behavioural assumption
• Mean - average of all possible behavioural
assumptions
MODE, MEAN, MEDIAN
Mode
Median
Mean
MODE is single most
likely outcome
MEAN is average
outcome
MEDIAN is where
there is an even chance
of higher and lower
inflation
MODE, MEAN, MEDIAN
Mode
Median
Mean
Central projection
(mode) is always in the
darkest band
Mean and median may
not be in the same
darkest band
Upside skew:
mean > median > mode
The shaded bands
• Each band shows the probability of inflation
falling within a particular range
• There is a 10% chance of inflation falling
within the central band (dark red)
• This is the narrowest range of outcomes
The shaded bands
• Each successive pair of bands adds another
10% of the probability.
• So there are an equal number of bands on
each side
• Only 90% bands shown
Calculating the bands
Median
Mode
{
Mean
10%
MODE, MEAN, MEDIAN
Mode
Median
Increase in prices on a year earlier
6
Mean
5
4
3
2
1
0
1994
95
96
97
98
99
2000 2001
The forecast process
• b) Agree on the degree of uncertainty over
the forecast horizon
How uncertain is the future?
• We use forecast errors from the previous 10
years
• Errors are adjusted if the MPC thinks future
uncertainty may be different from past.
Why use past forecast errors?
• Past forecast errors are a ‘catch all’
– We don’t have to know where the errors came
from (models, shocks, judgments)
• Generally past forecast errors suggest less
uncertain than stochastic simulations
Risks
• The decision to include risks is entirely
judgmental
• Follows from discussion of the ‘most likely
outcome’
• Key Question: If our central view is wrong,
is the outcome more likely to be on the
upside or the downside?
Examples
“International imbalances pose a downside risk to the
world outlook.”
“The longer house price inflation continues to exceed
growth in average household incomes, the greater the
additional upward pressure on spending and inflation…”
“There are upside risks to inflation from earnings growth”
November 2003 Inflation Report
2 ways to calculate risk
• 1 Balance of probability of all outcomes
either side of the central case
– e.g. 60:40 downside
• 2 Relative probability of being equal
distance above or below central case
Balance of probability
Mean estimate (2.1%)
60%
downside
Central case
- mode (2.5%)
40%
upside
Size of the skew
Two Alternative Scenarios
Mean estimate
(2.1%)
Central case
- mode (2.5%)
Downside
scenario
Upside
scenario
30%
10%
Size of the skew
Probability assessments
• Probability of recession
• Chance of having to write a letter
– +/- 1pp from central target of 2.5%
Forecast process:
summary
• Three key steps:
– Decide on the central assumptions and
outcomes
– Make a judgment about the degree of
uncertainty relative to the past
– Make a judgment about the balance of risks
around the central assumption
Summary of philosophy
• A transparent framework; publish target and
forecast
• Show uncertainty of projections
• And risks to the outlook