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Empirical Economics

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01.03.2006 | Original Paper

Evaluating the survey of professional forecasters probability distributions of expected inflation based on derived event probability forecasts

verfasst von: Michael P. Clements

Erschienen in: Empirical Economics | Ausgabe 1/2006

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Abstract

Techniques are proposed for evaluating forecast probabilities of events. The tools are especially useful when, as in the case of the Survey of Professional Forecasters (SPF) expected probability distributions of inflation, recourse cannot be made to the method of construction in the evaluation of the forecasts. The tests of efficiency and conditional efficiency are applied to the forecast probabilities of events of interest derived from the SPF distributions, and supplement a whole-density evaluation of the SPF distributions based on the probability integral transform approach.

Vorheriger Artikel Measurement of technical and allocative efficiencies using a CES cost frontier: a benchmarking study of Japanese transmission-distribution electricity

Nächster Artikel An econometric analysis of the effects of market liberalization on price dynamics and price volatility

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Since the Spring of 1997, the Monetary Policy Committee in the UK has been charged with delivering an inflation rate of ±1 percentage points around a target of of 2.5%. Whether formalised or not, considerations of this type are an integral part of most Western countries’ macroeconomic stabilisation policies.

See Lopez (1996) for a discussion of the relationship between VaR analysis and interval forecasting.

See Holden and Peel (1990).

From Eq. 2 with W _t−1=1:

$$ {\left( {I_{t} - p_{t} } \right)} = {\left( {\gamma - 1} \right)}p_{t} + \beta + \varepsilon _{t} $$

and so:

$$ E{\left[ {{\left( {I_{t} - p_{t} } \right)}p_{t} } \right]} = {\left( {\gamma - 1} \right)}E{\left( {p^{2}_{t} } \right)} + \beta E{\left( {p_{t} } \right)}. $$

(3)

When the events cover all possible outcomes the adequacy of the event probability forecasts can be assessed using the multinomial logit model for unordered multi-responses, as described by Patton (2002) working within a similar framework.

There is an extensive literature on forecast encompassing: see Diebold and Lopez (1996); Newbold and Harvey (2002) for recent surveys, and Chong and Hendry (1986), Clemen (1989), Newbold and Granger (1974) and Stock and Watson (1999) inter alia. Forecast encompassing is formally equivalent to the notion of conditional efficiency introduced by Nelson (1972) and Granger and Newbold (1973).

But see for example Clements and Hendry (1993).

See e.g., Engle (1982).

West (2001) considers the effects of parameter estimation uncertainty on tests for forecast encompassing: see West (1996), West and McCracken (1998) and West and McCracken (2002) on the impact of parameter estimation uncertainty on other tests of predictive accuracy. As this issue is not relevant to the evaluation of the SPF probability distributions (which are not based on simple estimated models), we also sidestep this issue in the Monte Carlo.

The ‘no-change’ model may be a reasonable approximation to the autoregressive dynamics of the actual process, as may the moving-average variance process to the ARCH conditional variance process.

Detailed information on the survey as well as the survey results are available at the URL http://www.phil.frb.org/econ/spf. An academic bibliography of articles that either discuss or use data generated by the SPF is also maintained online.

The series were taken from the Federal Reserve Bank of St Louis database (FRED), available at the URL http://www.stls.frb.org/fred/data/ and have the codes GNPDEF, GDPDEF and GDPCTPI.

As an example, suppose we wish to calculate the forecast probability of observing a value less than Y=3.5. Suppose Pr(Y<2) is 0.5, and the bin defined by [2, 4) has a probability of 0.2. Then:

$$ \Pr {\left( {Y < 3.5} \right)} = \Pr {\left( {Y < 2} \right)} + \frac{{1.5}} {2}\Pr {\left( {Y \in \left[ {2,4} \right)} \right)} = 0.5 + \frac{{1.5}} {2}0.2 = 0.65. $$

Linear interpolation follows the assumption implicit in the histogram – that probability mass is uniform within a bin. If a bin is bordered by a high probability bin and a relatively low probability bin, it might be desirable to attach higher probabilities to points near the boundary with the high probability bin. See Giordani and Söderlind (2003) on normal approximations to the histograms.

Berkowitz (2001) also suggests a censored likelihood test of the {z _t}'s in the tail of the distribution, ‘to ignore model failures that are limited to the interior of the distribution’ (p. 469). This is motivated by the interest in VaR in the financial literature.

That is, an evaluation of the forecast densities in terms of the expected ‘economic value’ from basing decisions/actions on those forecasts.

For example, “Unfortunately the complexity of situations prevents a single definitive cost measure being formulated. Thus a range of simple statistical measures have been developed to measure various aspects of forecast quality” (Encyclopaedia of Statistical Sciences, entry on Forecasting).

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Brier GW (1950) Verification of forecasts expressed in terms of probability. Mon Weather Rev 75:1–3CrossRef

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Chong YY, Hendry DF (1986) Econometric evaluation of linear macro-economic models. Rev Econ Stud 53:671–690 (Reprinted in Granger CWJ (ed) (1990) Modelling Economic Series. Clarendon, Oxford)CrossRef

Christoffersen PF (1998) Evaluating interval forecasts. Int Econ Rev 39:841–862CrossRef

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Titel: Evaluating the survey of professional forecasters probability distributions of expected inflation based on derived event probability forecasts
verfasst von: Michael P. Clements
Publikationsdatum: 01.03.2006
Verlag: Springer-Verlag
Erschienen in: Empirical Economics / Ausgabe 1/2006
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-005-0014-9

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