The predictive content of the output gap for inflation : resolving in-sample and out-of-sample evidence

This paper sifts through potential explanations for the weakness of the existing out-of-sample evidence on the Phillips curve relative to the in-sample evidence, focusing on models relating inflation to the output gap. The out-of-sample evidence could be weaker because, even when the models are stable over time, out-of-sample metrics are less powerful than the usual in-sample Granger causality tests. The weakness of the out-of-sample evidence could also be due to model instability—shifts in the coefficients or residual variance of the inflation-output gap model. 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 empirically-identified breaks in the coefficients of the DGP. This analysis shows that most of the weakness of the out-of-sample evidence relative to the in-sample evidence is attributable to instabilities in the model, particularly in the coefficients on the output gap. Theoretical analysis, based on a local alternatives framework, confirms that breaks in the output gap coefficients, but not breaks in residual variances or AR coefficients, can lead to a breakdown in the power of tests of equal forecast accuracy and forecast encompassing.