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Decomposing the Output Gap with Inflation Learning

We incorporate adaptive learning-based inflation expectations in an Unobserved Components model in order to study the link between inflation and the output gap. A modification of the hybrid New Keynesian Phillips curve serves as the backbone for modeling inflation dynamics. We find that learning based inflation forecasts not only shadow survey expectations in the pre-Volcker era, they also track inflation closely during the financial crisis and do not exhibit persistent overshooting. Our model also has good out of sample predictive performance both when compared with models that use survey expectations and when compared to an Unobserved Components Model without learning. We find evidence in favor of a relatively flat but significant Phillips curve relationship. The resulting output gap from our model has a lower amplitude than gaps obtained using proxy measures of expectations and other commonly used measures of the cycle. Furthermore, our results indicate that several recessions, including the Great Recession, were at least partially driven by large drops in the trend component of output.