Forecasting with an economic model and the role of adjustments
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Forecasting with an Economic Model and the Role of Adjustments. Andrew P. Blake CCBS/HKMA May 2004. What is a forecast?. An assessment of the unknown Usually of variables only known in the future Often probabilistic Forecast could be just a series of numbers

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Forecasting with an Economic Model and the Role of Adjustments

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Forecasting with an Economic Model and the Role of Adjustments

Andrew P. Blake

CCBS/HKMA May 2004


What is a forecast?

  • An assessment of the unknown

    • Usually of variables only known in the future

    • Often probabilistic

  • Forecast could be just a series of numbers

  • Could be a forecast of the distribution of possible outcomes

  • Forecasters therefore produce point, interval and density forecasts

    • Bank of England fan chart is a density forecast


What are adjustments?

  • Adjustments are needed because we use judgement

  • This may be imposed using information from outside the model

    • It may reflect model inadequacy

    • It may reflect data inadequacy

    • It may reflect expert opinion


Forecasting framework

  • How could we make forecasts?

    • ‘Make them up’

      • Assess (a subset of) available data and judgement to produce forecast

    • Use a (statistical) model

  • Forecast horizons

    • ‘Nowcasting’: forecasting current or past but unknown data

    • Otherwise one minute to a hundred years

      • Hundred year horizon unlikely to be very accurate


Modeling framework

  • What kinds of models are relevant?

    • Statistical and econometric

    • Univariate and multivariate

    • Structural and reduced form

  • Tools

    • Spreadsheets

    • Eviews, TSP, PcGive

    • Gauss, Matlab, Ox

    • WinSolve, Troll, Dynare


The process of forecasting

  • Where do you start?

    • Previous forecast:

      • Existing data, existing model

      • New data, new model?

    • ‘From scratch’

  • What has changed since the last time?

    • Impact of ‘news’

      • Sources of shocks


The process of forecasting (cont.)

  • How do we incorporate news?

    • Updates to historical data

    • Previously unavailable data

    • Revisions to the model

      • Previous failures may need correcting

    • ‘Adjustments’ to the forecast

      • From non-model data

      • Judgement


Simple forecasting

  • Univariate models

    • ARIMA modeling

    • Exponential smoothing (more weight on recent observations)

  • Clements and Hendry suggest that

    fits economic data well. For forecasting use:


Simple forecasting (cont.)

  • Simple multivariate models

    • VAR widely used

    • Easy to re-estimate/update

    • Models have straightforward interpretation

  • Minimum intervention needed

    • Properties depend on few choice variables

    • Benchmark forecast


VAR forecast

Data

Residuals

Forecast

Interest rate

Inflation rate


What do the residuals tell us?

  • Tell us about the goodness-of-fit of the model

  • Very useful over the recent past which may not be used in model estimation

    • May be going ‘off-track’

  • Use in determining adjustments for a forecast


More sophisticated forecasting

  • Structural Economic Model (SEM)

    • Multiple equations (2 to 5000)

    • Estimated/calibrated/imposed coefficients

    • Rich dynamics

    • Expectations

    • Complex accounting structures

  • Complicated to use

    • Institutional and technical considerations


A ‘quarterly’ forecast round

Revise assumptions

Existing model, existing data, old forecast

Final forecast

National accounts, other data release

Other data releases (prices, exchange rates)

Run forecast on new data

‘Tuning’

Assumptions:exogenous, residuals, define ragged edge

Examine residuals, re-estimate model, revise assumptions

Forecast evaluation

‘Issues’ meetings

Scenario analysis, risk assessment

Create database


‘Week 0’


New data, same old problems

  • ‘Issues’ meetings

    • Where have previous forecast failed?

    • Where has the forecast model failed?

  • New data

    • Start of forecast often determined by release dates, e.g. National Accounts

    • Create model database (transforms etc)

    • Make ‘first quarter’ assumptions

      • Expert analysis

      • Partial information


The ‘ragged edge’

Forecast date

Time

New/revised data

Assumptions

Old data


Dealing with the ragged edge

  • Exogenise all past true data values

    • Incorporate historical add factors

  • Exogenise ‘first quarter’ assumed data

  • Exogenise future assumptions

  • Solve the model from far enough back


News: data revisions

  • The past isn’t always what it used to be

    • ‘Real time’ data sets show significant changes

      • Eggington, Pick & Vahey, 2002

      • Castle & Ellis, 2002, Band of England QB

  • Question of what you wish to forecast

    • Do you wish to forecast the first outturn or final estimate?

    • Markets may react less strongly to revised data than ‘new’ data


Data revisions


‘Week 1’


Old model, same old problems

  • Exogenous variable assumptions

    • All things exogenous to the model

    • Rest of the world, policy variables, fiscal authorities

  • ‘Residuals’

    • Adjustments or add-factors

    • Constant values, future profiles

    • Helps robustify to structural breaks (Clements and Hendry)

      • ECMs helpful in this respect


Adjustments

  • What does the model tell us about how our forecast may be failing?

  • Need to look at the implicit residuals

  • We need to ensure that any adjustments are consistent with the model – or have a good reason why not


Residual profiles

Ideal

Possible break

Over-prediction


Evaluating the model forecast

  • Check performance of individual equations

    • Implicit residuals a guide to how well equations track the recent past

    • Forecast residuals may be averages of last one or two years, may fade back

  • Alternate/revised equations

    • Models may have alternate equations, perhaps on a trial basis

    • Equations may need to be re-estimated if data sufficiently revised or latest data inconsistent


Evaluating the forecast (cont.)

  • Check assumptions

    • Are the exogenous variables consistent with the forecast?

      • i.e. are productivity trends consistent with growth

  • Does the forecaster like the forecast?

  • Does the MPC like the forecast?

    • Question of ownership

  • Iterate


‘Week 2’


More news

  • For any lengthy forecast process will usually need to incorporate additional data

    • More data on exogenous variables may be available

      • Perhaps the world forecast updated

    • Perhaps non-National Accounts data becomes available

      • Price, wage and production indices

      • Monthly data

    • Financial market data needs updating


More news (cont.)

  • Impacts on:

    • Exogenous variables

    • Adjustment/residual settings

    • Equation fit

  • Do everything you did in Week 1 (again)

  • Iterate

    • Incorporate new data

    • New or different judgments


‘Week n’


Finalise forecast

  • Agree on final numbers

  • Assess impact of news

  • Decide main risks to the forecast

    • Part of the whole forecast process: the forecaster learns what drives the forecast

    • Scenario analysis

    • Perhaps present results using formal density forecast or provide standard errors


A ‘quarterly’ forecast round

Revise assumptions

Existing model, existing data, old forecast

Final forecast

National accounts, other data release

Other data releases (prices, exchange rates)

Run forecast on new data

‘Tuning’

Assumptions:exogenous, residuals, define ragged edge

Examine residuals, re-estimate model, revise assumptions

Forecast evaluation

‘Issues’ meetings

Scenario analysis, risk assessment

Create database


Forecasting with rational expectations

  • Models such as the new BEQM

  • Expectations may be structurally important

    • Exchange rates

    • Consumption Euler equations, etc.

  • Forecast values affect current behaviour

    • Any updates to path of exogenous variables become news and affect ‘jump variables’

    • No news no jumps


Forecasting with rational expectations (cont.)

  • How does the forecasting process change?

    • Variables ‘jump about’ more

    • Seemingly trivial changes have big effects

    • Residual adjustments need to be made much more carefully

      • Future residuals affect current behaviour

    • Up-to-the-minute data may incorporate the news already

      • Jumps adjusted to where you are now


Forecasting with leading indicators

  • Nothing essentially different

    • Indicator variables often available at different frequency to main forecast

    • Used as alternative ‘satellite’ models

  • Dynamic factor modeling

    (unobserved components)

    • Stock and Watson (2002)

    • Camba-Medez et al. (2001)


Forecast post mortem

  • Part of the process is to see what went wrong

    • Informal judgement when the model is deficient

    • Tests of forecast accuracy

      • Diebold and Mariano (1995)

  • Does the forecaster add value?


  • Camba-Mendez, G. et al. (2001) ‘An Automatic Leading Indicator of Economic Activity: Forecasting GDP Growth for European Countries’, Econometrics Journal 4(1), S56-90.

  • Clements, M.P and D. Hendry (1995) ‘Macro-economic Forecasting and Modelling’, Economic Journal 105(431), 1001-1013.

  • Diebold, F.X and R. Mariano (1995) ‘Comparing Predictive Accuracy’, Journal of Business and Economic Statistics 13(3), 253-63

  • Egginton, D., A. Pick and S.P. Vahey (2002) ‘‘Keep It Real!’: A Real-Time UK Macro Data Set’, Economics Letters 77(1), 15-22.

  • Stock, J.H and M. Watson (2002) ‘Macroeconomic Forecasting Using Diffusion Indexes’, Journal of Business and Economic Statistics 20(2), 147-162


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