TERM STRUCTURE OF INFLATION FORECAST UNCERTAINTIES AND SKEW NORMAL DISTRIBUTION ISF Rotterdam, June 29 July

Transcription

1 Term structure of forecast uncertainties TERM STRUCTURE OF INFLATION FORECAST UNCERTAINTIES AND SKEW NORMAL DISTRIBUTION Wojciech Charemza, Carlos Díaz, Svetlana Makarova, University of Leicester University of Leicester University College London ISF 2014 Rotterdam, June 29 July 014 ESRC/ORA project RES Probabilistic Approach to Assessing Macroeconomic Uncertainties Full version is available as the University of Leicester Working paper 14/01 at W. Charemza, C. Díaz, S. Makarova

2 Term structure of forecast uncertainties 2 Aim: To improve on the analysis of inflation uncertainty by applying a new statistical distribution to modelling forecast errors. In brief: This distribution reflects monetary policy actions. Purely unpredictable (ontological) and imperfect-knowledge (epistemic) elements of uncertainty can be retrieved. It fits better than two-piece normal to inflationary forecast errors for most of 38 countries. The prevalence of either anti-inflationary or output-stimulating policy can be identified.

3 Term structure of forecast uncertainties 3 Two main ways of identifying macroeconomic non-knightian uncertainty By using surveys (pools) of point and/or probabilistic forecasts (e.g. Lahiri, Peng & Sheng, 2014, Todd, Krüger & Ravazzolo, 2014). By using past forecast errors (common practice at central banks). Pros and cons of using the surveys Pros: Precise timing. Use of disaggregated information. Convincing intuition (uncertainty by disagreement, etc.). Cons: Possible dependence within the pools. Possible psychological bias of probabilistic and interval forecasts (Clements, 2014, Hansson, Juslin & Winman, 2008, Soll & Klayman, 2004).

4 Term structure of forecast uncertainties 4 Pros and cons of using forecast errors Pros: Easy to compute, disaggregated data is not required. Free from political, emotional and sociological bias of individual forecasters. Interpretation is straightforward. Cons: Uncertainty is assumed to be invariant in time (Clements Hendry critique). Estimation of underlying distributions requires large data sets.

5 Term structure of forecast uncertainties 5 Weighted Skew Normal distribution of uncertainty: definition h-period ahead ex-post uncertainty shock at time t (h = 1,2,,H, t = 1,..,T): where u t, h th t th t E, h = 1,2,,H, t = 1,..,T, t is publicly available information about t. s s u th, is a realisation of a random variable U h such that: 0 Uh U X Y IY m Y I, ( X, Y) N, Yk 0 m, k,,, 1 1 and I is an indicator of set The distribution of U is called the Weighed Skew Normal, WSN, distribution. ;

6 Term structure of forecast uncertainties 6 Weighted Skew Normal: interpretation U U X Y I Y I, h Y m Yk 0 ( X, Y) N, 0 There is some sort of inflation-controlling or output-stimulating monetary policy which affects uncertainty. The monetary policy body (central bank, CB) has its own forecasters (CB forecasters), who formulate their forecasts (corrections to public forecast E t t h t ) using private, not publicly available, information. X is public uncertainty, containing both epistemic and ontological elements if there were no CB action. Y is a random variable representing corrections of CB forecasters who formulate their forecasts relatively to the core (econometric, public) forecast.

7 Term structure of forecast uncertainties 7 Weighted Skew Normal: interpretation (cont.) U U X Y I Y I, h Y m Yk 0 ( X, Y) N, 0 is correlation coefficient between X and Y. It reflects: degree of experts competence contribution of common epistemic element of X and Y. if 1: all uncertainty in X is epistemic and experts are perfect if 0: either there is no epistemic element in X or experts are fully incompetent.

8 Term structure of forecast uncertainties 8 Weighted Skew Normal: interpretation (cont.) U U X Y I Y I, h Y m Yk m and k are the thresholds; and β are policy parameters: if the CB forecaster predicts an increase of inflation above the upper threshold (Y m), an antiinflationary action of strength is taken ( m 0, 0) a decrease of inflation below the lower threshold (Y k ), an output-stimulation action of strength is taken ( k 0, 0). Removing epistemic uncertainty from U Rationale: learning from U and its parameters about the existence of relevant monetary policy information. V-uncertainties: V U E( X Y) U Y What would have been the distribution of uncertainty if the entire X was unpredictable from Y? That is, if the effects of monetary policy were in fact external to X?

9 Term structure of forecast uncertainties 9 Interpretation of U and V U E( X Y) U Y U-uncertainty incorporates possible effects of forecast-induced monetary policy (including epistemic uncertainty). In V-uncertainty the presence of information which is relevant for CB forecasters is reduced. var V ( ) VRUV( ) var U ( ) Fully symmetric case: 2 0, 1, m k 1 If the CB forecasters are effective in explaining the epistemic element in X, but the monetary decisions are of a weak strength, variance of U increases in relation to the variance of V. In order to achieve a reduction in uncertainty, coordination between the forecasters and decision-makers is needed (policy should not be too strong or too weak).

10 Term structure of forecast uncertainties 10 Empirical analysis 1. Measurement of uncertainties Computing SARIMA inflation forecast errors (1 to 12-steps ahead, monthly data) recursively for 38 countries; that is for 32 OECD countries and Brazil, China, India, Indonesia, South Africa and the Russian Federation. 2. Fitting distributions to uncertainties 1: WSN with 3 free parameters:, β and. Fixed parameters: m m / k k / 1 ; = 0.75, 2: Two-piece skew normal distribution, TPN. Aexp ( t ) / 2 1 if t ftpn () t, Aexp ( t ) / if t where A 2 ( ) / 2 1 ; estimated parameters: 1 2 1, 2 and. Estimation method: simulated minimum distance estimation (Charemza, Makarova, Fan and Yuan (2012).

11 Term structure of forecast uncertainties 11 WSN and TPN Hellinger distances 1-step ahead forecasts 4-steps ahead forecasts The 45 degree line marks the points for which the Hellinger distances for the WSN and TPN distribution would be identical. If the dot representing a particular country is below this line, WSN distribution has a better fit (that is, smaller distance measure) than TPN distribution and vice versa.

12 Term structure of forecast uncertainties 12 Estimated and β parameters 1-step ahead forecasts 4-steps ahead forecasts Deviations from the 45 degree line downwards denote the dominance of the forecast-induced anti-inflationary effects on uncertainty (that is ) and vice versa. Outlier: Japan, with output-stimulating and pro-inflationary policy.

13 Term structure of forecast uncertainties 13 CONCLUSIONS WSN reveals interesting stories about outcomes of vaguely defined monetary actions. WSN fits better than TPN to the inflationary forecast errors for most countries. Two types of inflationary term structure for different end users can be derived: (i) (ii) based on U-uncertainties by direct fitting of WSN to historical forecast errors; for end users, who do not have the direct influence on monetary policy; based on V-uncertainties; for central bankers and other monetary policy decision makers. The small print: Only CB forecast affects monetary policy. The public forecast does not contain any information relevant for the policy makers (too much of a neoclassical flavour)? So that, the public forecast is really a core inflation forecast.

14 Term structure of forecast uncertainties 14 REFERENCES Charemza, W., Fan, Z., Makarova S. and Y. Wang (2012), Simulated minimum distance estimators in macroeconomics, paper presented at the conference Computational and Financial Econometrics, Oviedo. Clark, T.E., Krüger, F. and F. Ravazzolo (2014), Combining survey and Bayesian VAR forecasts of US macro variables: evidence from entropic tilting, paper presented at the workshop Uncertainty and Economic Forecasting, London. Clements, M.P. (2014), Forecast uncertainty ex ante and ex post: US inflation and output growth, Journal of Business and Economic Statistics, 32, Hansson, P., Juslin, P. and A. Winman (2008), The role of short-term memory capacity and task experience for overconfidence in judgment under uncertainty, Journal of Experimental Psychology: Learning, Memory and Cognition, 34, Lahiri, K. Peng, H. and X. Sheng (2014), Measuring uncertainty of a combined forecast, paper presented at the workshop Uncertainty and Economic Forecasting, London. Soll, J. B. and J. Klayman (2004), Overconfidence in interval estimates. Journal of Experimental Psychology: Learning, Memory and Cognition, 30,