The Predictive Content of the Output Gap for Inflation: Resolving In-Sample and Out-of-Sample Evidence

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Abstract
This paper sifts through explanations for the weakness of the out-of-sample evidence on the Phillips curve relative to the in-sample evidence, focusing on the output gap-based models. One explanation could be that, even when the model are stable, out-of-sample metrics are less powerful than in-sample Granger tests. The weakness of the out-of-sample evidence could also be due to model instability. This paper evaluates these explanations on the basis of comparisons of the sample forecasting results to results from Monte Carlo simulations of DGPs that either assume stability or allow breaks in the DGP. This analysis shows that most of the relative weakness in the out-of-sample evidence is attributable to model instabilities, particularly in the output gap coefficients. Theoretical analysis, based on a local alternatives framework, confirms that breaks in the output gap coefficients can lead to a breakdown in the power of tests of equal forecast accuracy and forecast encompassing.