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

By Todd E. Clark and Michael W. McCracken
August 2003 
RWP 03-06
Research Division 
Federal Reserve Bank of Kansas City 

Abstract

      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.

Keywords: Phillips curve, forecasts, causality, break test

JEL Codes: E37, E31, C53, C52

Todd Clark is vice president and economist at the Federal Reserve Bank of Kansas City and Michael McCracken is an assistant professor of economics at the University of Missouri-Columbia. The authors gratefully acknowledge the helpful comments of: Lutz Kilian; David Rapach; participants at the 2003 Missouri Economics Conference and 2003 meetings of the Society for Computational Economics; and seminar participants at Brown University and the Federal Reserve Bank of Kansas City. Jushan Bai kindly provided computer programs for computing the Bai-Perron break tests. The views expressed here are those of the authors and not necessarily those of the Federal Reserve Bank of Kansas City or the Federal Reserve System.

Clark e-mail:  todd.e.clark@kc.frb.org
McCracken e-mail:  mccrackenm@missouri.edu

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