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Atlanta Fed Working Papers

Quantifying the Half-Life of Deviations from PPP: The Role of Economic Priors

Lutz Kilian and Tao Zha
Federal Reserve Bank of Atlanta
Working Paper 99-21
December 1999

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The half-life of deviations from purchasing power parity (PPP) plays a central role in the ongoing debate about the ability of macroeconomic models to account for the time series behavior of the real exchange rate. The main contribution of this paper is a general framework in which alternative priors for the half-life of deviations from PPP can be examined. We show how to incorporate formally the prior views of economists about the half-life. In our empirical analysis we provide two examples of such priors. One example is a consensus prior consistent with widely held views among economists with a professional interest in the PPP debate. The other example is a relatively diffuse prior designed to capture a large degree of uncertainty about the half-life. Our methodology allows us to make explicit probability statements about the half-life and to assess the likelihood that the half-life exceeds a given number of years, without taking a stand on whether or not the data have a unit root. We find only very limited support for the common view in the PPP literature that the half-life is between three and five years.

JEL classification: F41, C11

Key words: purchasing power parity, half-life, mean reversion, persistence, likelihood

The authors gratefully acknowledge helpful comments from Bob Barsky, Kathryn Dominguez, Charlie Evans, John Geweke, Gordon Hanson, Jan Kmenta, Chris Sims, Linda Tesar, Harald Uhlig, Dan Waggoner, Chuck Whiteman, and seminar participants at the 1999 NBER Summer Institute in Boston. They also thank Dave Backus, Dick Baillie, Bob Barsky, Menzie Chinn, Alan Deardorff, Kathryn Dominguez, Sebastian Edwards, Charles Engel, Jürgen von Hagen, Gordon Hanson, Miles Kimball, Ken Kletzer, Bob Lippens, Nelson Mark, Mike Melvin, David Papell, Ken Rogoff, Andrew Rose, Matthew Shapiro, Chris Sims, Linda Tesar, and Jaume Ventura for participating in the survey. The views expressed here are the authors' and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors' responsibility.

Please address questions regarding content to Lutz Kilian, Department of Economics, University of Michigan, Ann Arbor, Michigan 48109-1220, 734/764-2320, 734/764-2769 (fax),; or Tao Zha, Research Department, Federal Reserve Bank of Atlanta, 104 Marietta Street, NW, Atlanta, Georgia 30303-2713, 404/498-8353, 404/498-8956 (fax),

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