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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. Copyright The Review of Economic Studies Limited, 2005.

This paper examines regression tests of whether x forecasts y when the largest autoregressive root of the regressor is unknown. It is shown that previously proposed two-step procedures, with first stages that consistently classify x as I(1) or I(0), exhibit large size distortions when regressors have local-to-unit roots, because of asymptotic dependence on a nuisance parameter that cannot be estimated consistently. Several alternative procedures, based on Bonferroni and Scheffe methods, are therefore proposed and investigated. For many parameter values, the power loss from using these conservative tests is small.

Researchers desire powerful tests for unit roots. This paper derives the family of asymptotically most powerful tests for unit roots when the initial condition is drawn from its unconditional distribution under the alternative. This enables both the examination of previously proposed statistics and the construction of powerful tests against this alternative model.