Forecaster’s utility and forecasts coherence

I provide general frequentist framework to elicit the forecaster’s expected utility based on a Lagrange Multiplier-type test for the null of locality of the scoring rules associated to the probabilistic forecast. These are assumed to be observed transition variables in a nonlinear autoregressive model to ease the statistical inference. A simulation study reveals that the test behaves consistently with the requirements of the theoretical literature. The locality of the scoring rule is fundamental to set dating algorithms to measure and forecast probability of recession in US business cycle. An investigation of Bank of Norway’s forecasts on output growth leads us to conclude that forecasts are often suboptimal with respect to some simplistic benchmark if forecaster’s reward is not properly evaluated.