Estimation and testing of forecast rationality under flexible loss
In situations where a sequence of forecasts is observed, a common strategy is to examine "rationality" conditional on a given loss function. We examine this from a different perspective— supposing that we have a family of loss functions indexed by unknown shape parameters, then given the forecasts can we back out the loss function parameters consistent with the forecasts being rational even when we do not observe the underlying forecasting model? We establish identification of the parameters of a general class of loss functions that nest popular loss functions as special cases and provide estimation methods and asymptotic distributional results for these parameters. This allows us to construct new tests of forecast rationality that allow for asymmetric loss. The methods are applied in an empirical analysis of IMF and OECD forecasts of budget deficits for the G7 countries. We find that allowing for asymmetric loss can significantly change the outcome of empirical tests of forecast rationality.
© 2005 The Review of Economic Studies Limited. First version received February 2003; final version accepted December 2004 (Eds.) We thank two anonymous referees, the editors, Hidehiko Ichimura and Bernard Salanié, as well as Max Auffhammer, Peter Bossaerts and seminar participants at Atlanta Fed, Bocconi, CentrA (Seville), Duke, St Louis Fed, Stanford, UCLA, UTS, UNSW, UT-Austin, Rice, Texas A&M, Caltech-UCLA-USC workshop on forecasting and the NBER-NSF-Penn conference on time-series in September 2002. Graham Elliott and Allan Timmermann are grateful to the NSF for financial assistance under grant SES 0111238. Carlos Capistran provided excellent research assistance.