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— that we have a family of loss functions indexed by unknown shape parameters, then given forecasts can we back out the loss function parameters consistent with the forecasts being rational when we do not observe the underlying forecasting model? We establish identification of the of a general class of loss functions that nest popular loss functions as special cases and estimation methods and asymptotic distributional results for these parameters. This allows us construct new tests of forecast rationality that allow for asymmetric loss. The methods are applied an empirical analysis of IMF and OECD forecasts of budget deficits for the G7 countries. We find allowing for asymmetric loss can significantly change the outcome of empirical tests of forecast .