Testing Forecast Optimality Under Unknown Loss

Empirical tests of forecast optimality have traditionally been conducted under the assumption of mean squared error loss or some other known loss function. In this article we establish new testable properties that hold when the forecaster's loss function is unknown but testable restrictions can be imposed on the data-generating process, trading off conditions on the data-generating process against conditions on the loss function. We propose flexible estimation of the forecaster's loss function in situations where the loss depends not only on the forecast error, but also on other state variables, such as the level of the target variable. We apply our results to the problem of evaluating the Federal Reserve's forecasts of output growth. Forecast optimality is rejected if the Fed's loss depends only on the forecast error. However, the empirical findings are consistent with forecast optimality provided that overpredictions of output growth are costlier to the Fed than underpredictions, particularly during periods of low economic growth.