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 mis- specification) 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 OTHER MODELS FORECAST 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

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

Mean Mode Median MODE, MEAN, MEDIAN MODE is single most likely outcome MEAN is average outcome MEDIAN is where there is an even chance of higher and lower inflation

Mean Mode Median MODE, MEAN, MEDIAN 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

Mean Mode Median { 10% Calculating the bands

Increase in prices on a year earlier Mean Mode Median MODE, MEAN, MEDIAN

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

60% downside 40% upside Central case - mode (2.5%) Mean estimate (2.1%) { Size of the skew Balance of probability

30% 10% Central case - mode (2.5%) Mean estimate (2.1%) { Size of the skew Upside scenario Downside scenario Two Alternative Scenarios

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