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Empirical Economics

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22-08-2016

Forecast performance, disagreement, and heterogeneous signal-to-noise ratios

Authors: Jonas Dovern, Matthias Hartmann

Published in: Empirical Economics | Issue 1/2017

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Abstract

We propose an imperfect information model for the expectations of macroeconomic forecasters that explains differences in average disagreement levels across forecasters by means of cross-sectional heterogeneity in the variance of private noise signals. We show that the forecaster-specific signal-to-noise ratios determine both the average individual disagreement level and an individuals’ forecast performance: Forecasters with very noisy signals deviate strongly from the average forecasts and report forecasts with low accuracy. We take the model to the data by empirically testing for this implied correlation. Evidence based on data from the Surveys of Professional Forecasters for the USA and for the Euro Area supports the model for short- and medium-run forecasts but rejects it based on its implications for long-run forecasts.

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In general, Kajal Lahiri has paid much attention to the heterogeneity of forecasters in many of his papers (Davies and Lahiri 1995; Lahiri and Liu 2006; Lahiri and Sheng 2010b; Lahiri et al. 2015).

The alternative “sticky” information model of Mankiw and Reis (2002) has been empirically rejected as an appropriate model to describe the behavior of professional forecasters mainly due to the fact that the observed frequency of forecast updates is much higher than implied by this model (Dovern 2013; Andrade and Le Bihan 2013; Dovern et al. 2015).

We thank an anonymous referee for pointing this out.

Note that, in addition, they also allow for a forecaster-specific bias term that influences forecast performances and individual disagreement levels.

For simplicity, we ignore anticipated shocks and bias terms at this point.

In the simulation, \(\alpha \) takes values from 0 to 0.95 and \(\sigma ^2_{\varepsilon }/\sigma ^2_{\eta }\) ranges from 0.1 to 2.

By ensuring that the factors are on average equal to 1, we can simulate cases which are comparable to the homogeneous case in the sense that the average signal-to-noise ratio is equal to that in the model with symmetric forecasters.

Note that the scaling ensures that the mean is equal to 1. Results are the same qualitatively for other parameterizations of the beta distribution or other distributional assumptions.

The simulation is based on \(T=5000\) to ensure a good approximation of the expected moments.

We set \(\sigma ^2_\mu =0.5\).

Survey waves before 1992q1 refer to gross national product (GNP) rather than GDP.

Strictly speaking, the 5-years-ahead forecasts are fixed-event forecasts made for the annual average of the forecast variables in a particular target year. This target year is changing in such a way that the forecast horizon varies between 21 and 18 quarters. Given the very long forecast horizon, it is unlikely that forecasts are affected by changes in the target year or small variations in the forecast horizon.

Results are robust against selecting a higher required number of observations.

To limit the influence of outlier observations, we use the square root of \(\widehat{ MSFE}_{i,h}\) as the dependent variable in (4.1). The results based directly on \(\widehat{ MSFE}_{i,h}\) are qualitatively equivalent to those reported in the paper and are available from the authors upon request.

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Title: Forecast performance, disagreement, and heterogeneous signal-to-noise ratios
Authors: Jonas Dovern
Matthias Hartmann
Publication date: 22-08-2016
Publisher: Springer Berlin Heidelberg
Published in: Empirical Economics / Issue 1/2017
Print ISSN: 0377-7332
Electronic ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-016-1137-x

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