Measuring Forecast Uncertainty by Disagreement: The Missing Link

Using a standard decomposition of forecasts errors into common and idiosyncratic shocks, we show that aggregate forecast uncertainty can be expressed as the disagreement among the forecasters plus the perceived variability of future aggregate shocks. Thus, the reliability of disagreement as a proxy for uncertainty will be determined by the stability of the forecasting environment, and the length of the forecast horizon. Using density forecasts from the Survey of Professional Forecasters, we find direct evidence in support of our hypothesis. Our results support the use of GARCH-type models, rather than the ex post squared errors in consensus forecasts, to estimate the ex ante variability of aggregate shocks as a component of aggregate uncertainty.

Learning and heterogeneity in GDP and inflation forecasts

We estimate a Bayesian learning model with heterogeneity aimed at explaining the evolution of expert disagreement in forecasting real GDP growth and inflation over 24 monthly horizons for G7 countries during 1990-2007. Professional forecasters are found to begin and have relatively more success in predicting inflation than real GDP at significantly longer horizons; forecasts for real GDP contain little information beyond 6 quarters, but forecasts for inflation have predictive value beyond 24 months and even 36 months for some countries. Forecast disagreement arises from two primary sources in our model: differences in the initial prior beliefs of experts, and differences in the interpretation of new public information. Estimated model parameters, together with two separate case studies on (i) the dynamics of forecast disagreement in the aftermath of the 9/11 terrorist attack in the U.S. and (ii) the successful inflation targeting experience in Italy after 1997, firmly establish the importance of these two pathways to expert disagreement.Bayesian learning, Public information, Panel data, Forecast disagreement, Forecast horizon; Content function; Forecast efficiency; GDP; Inflation targeting

Learning and Heterogeneity in GDP and Inflation Forecasts

Using a Bayesian learning model with heterogeneity across agents, our study aims to identify the relative importance of alternative pathways through which professional forecasters disagree and reach consensus on the term structure of inflation and real GDP forecasts, resulting in different patterns of forecast accuracy. Forecast disagreement arises from two primary sources in our model: differences in the initial prior beliefs, and differences in the interpretation of new public information. Estimated model parameters, together with two separate case studies on (i) the dynamics of forecast disagreement in the aftermath of the 9/11 terrorist attack in the U.S. and (ii) the successful inflation targeting experience in Italy after 1997, firmly establish the importance of these two pathways to expert disagreement, and help to explain the relative forecasting accuracy of these two macroeconomic variables.

Measuring Forecast Uncertainty by Disagreement: The Missing Link

Using a standard decomposition of forecasts errors into common and idiosyncratic shocks, we show that aggregate forecast uncertainty can be expressed as the disagreement among the forecasters plus the perceived variability of future aggregate shocks. Thus, the reliability of disagreement as a proxy for uncertainty will be determined by the stability of the forecasting environment, and the length of the forecast horizon. Using density forecasts from the Survey of Professional Forecasters, we find direct evidence in support of our hypothesis. Our results support the use of GARCH-type models, rather than the ex post squared error in consensus forecasts, to estimate the ex ante variability of aggregate shocks as a component of aggregate uncertainty.Aggregate shocks, public information, forecast disagreement, forecast horizon, forecast uncertainty, panel data, private information

Analyzing Three-Dimensional Panel Data of Forecasts

With the proliferation of quality multi-dimensional surveys, it becomes increasingly important for researchers to employ an econometric framework in which these data can be properly analyzed and put to their maximum use. In this chapter we have summarized such a framework developed in Davies and Lahiri (1995, 1999), and illustrated some of the uses of these multi-dimensional panel data. In particular, we have characterized the adaptive expectations mechanism in the context of broader rational and implicit expectations hypotheses, and suggested ways of testing one hypothesis over the others. We find that, under the adaptive expectations model, a forecaster who fully adapts to new information is equivalent to a forecaster whose forecast bias increases linearly with the forecast horizon. A multi-dimensional forecast panel also provides the means to distinguish between anticipated and unanticipated changes in the forecast target as well as volatilities associated with the anticipated and unanticipated changes. We show that a proper identification of anticipated changes and their perceived volatilities are critical to the correct understanding and estimation of forecast uncertainty. In the absence of such rich forecast data, researchers have typically used the variance of forecast errors as proxies for shocks. It is the perceived volatility of the anticipated change and not the (subsequently-observed) volatility of the target variable or the unanticipated change that should condition forecast uncertainty. This is because forecast uncertainty is formed when a forecast is made, and hence anything that was unknown to the forecaster when the forecast was made should not be a factor in determining forecast uncertainty. This finding has important implications on how to estimate forecast uncertainty in real time and how to construct a measure of average historical uncertainty, cf. Lahiri and Sheng (2010a). Finally, we show how the Rational Expectations hypothesis should be tested by constructing an appropriate variance-covariance matrix of the forecast errors when a specific type of multidimensional panel data is available.

Kinetic energy operator approach to the quantum three-body problem with Coulomb interactions

We present a non-variational, kinetic energy operator approach to the solution of quantum three-body problem with Coulomb interactions, based on the utilization of symmetries intrinsic to the kinetic energy operator, i.e., the three-body Laplacian operator with the respective masses. Through a four-step reduction process, the nine dimensional problem is reduced to a one dimensional coupled system of ordinary differential equations, amenable to accurate numerical solution as an infinite-dimensional algebraic eigenvalue problem. A key observation in this reduction process is that in the functional subspace of the kinetic energy operator where all the rotational degrees of freedom have been projected out, there is an intrinsic symmetry which can be made explicit through the introduction of Jacobi-spherical coordinates. A numerical scheme is presented whereby the Coulomb matrix elements are calculated to a high degree of accuracy with minimal effort, and the truncation of the linear equations is carried out through a systematic procedureComment: 56 pages, 11 figure

Measuring Forecast Uncertainty by Disagreement: The Missing Link

Using a standard decomposition of forecasts errors into common and idiosyncratic shocks, we show that aggregate forecast uncertainty can be expressed as the disagreement among the forecasters plus the perceived variability of future aggregate shocks. Thus, the reliability of disagreement as a proxy for uncertainty will be determined by the stability of the forecasting environment, and the length of the forecast horizon. Using density forecasts from the Survey of Professional Forecasters, we find direct evidence in support of our hypothesis. Our results support the use of GARCH-type models, rather than the ex post squared error in consensus forecasts, to estimate the ex ante variability of aggregate shocks as a component of aggregate uncertainty

Measuring Uncertainty of a Combined Forecast and Some Tests for Forecaster Heterogeneity

We have argued that from the standpoint of a policy maker, the uncertainty of using the average forecast is not the variance of the average, but rather the average of the variances of the individual forecasts that incorporate idiosyncratic risks. With a slight reformulation of the loss function and a standard factor decomposition of a panel of forecasts, we show that the uncertainty of the average forecast can be expressed as the disagreement among the forecasters plus the volatility of the common shock. Using new statistics to test for the homogeneity of idiosyncratic errors under the joint limits with both T and n approaching infinity simultaneously, we show that some previously used measures significantly underestimate the conceptually correct benchmark forecast uncertainty

Learning and heterogeneity in GDP and inflation forecasts

We estimate a Bayesian learning model with heterogeneity aimed at explaining the evolution of expert disagreement in forecasting real GDP growth and inflation over 24 monthly horizons for G7 countries during 1990-2007. Professional forecasters are found to begin and have relatively more success in predicting inflation than real GDP at significantly longer horizons; forecasts for real GDP contain little information beyond 6 quarters, but forecasts for inflation have predictive value beyond 24 months and even 36 months for some countries. Forecast disagreement arises from two primary sources in our model: differences in the initial prior beliefs of experts, and differences in the interpretation of new public information. Estimated model parameters, together with two separate case studies on (i) the dynamics of forecast disagreement in the aftermath of the 9/11 terrorist attack in the U.S. and (ii) the successful inflation targeting experience in Italy after 1997, firmly establish the importance of these two pathways to expert disagreement

Learning and heterogeneity in GDP and inflation forecasts

We estimate a Bayesian learning model with heterogeneity aimed at explaining the evolution of expert disagreement in forecasting real GDP growth and inflation over 24 monthly horizons for G7 countries during 1990-2007. Professional forecasters are found to begin and have relatively more success in predicting inflation than real GDP at significantly longer horizons; forecasts for real GDP contain little information beyond 6 quarters, but forecasts for inflation have predictive value beyond 24 months and even 36 months for some countries. Forecast disagreement arises from two primary sources in our model: differences in the initial prior beliefs of experts, and differences in the interpretation of new public information. Estimated model parameters, together with two separate case studies on (i) the dynamics of forecast disagreement in the aftermath of the 9/11 terrorist attack in the U.S. and (ii) the successful inflation targeting experience in Italy after 1997, firmly establish the importance of these two pathways to expert disagreement