Empirical Economics

, Volume 47, Issue 2, pp 495–522 | Cite as

Measuring the natural rates, gaps, and deviation cycles

Article

Abstract

One definition of the natural rate is the (time-varying) steady state equilibrium rate. Then the gap is the difference between the actual and natural rates, or the forecastable movement. Although modern business cycle theories study deviation cycles (cycles in the gap), the NBER business cycle reference dates measure classical cycles (cycles in the actual rate) in the US. Measuring deviation cycles requires detrending, and this motivated the invention of the Beveridge–Nelson (B–N) decomposition. This paper considers multivariate detrending, and proposes a Bayesian approach to the multivariate B–N decomposition. An application of the method to US data gives (i) a joint estimate of the natural rates and gaps of output, inflation, interest, and unemployment with reliable error bands, and (ii) the posterior probabilities of positive gap, recession, and revival. These results may help us to identify the four phases of deviation cycles: expansion, recession, contraction, and revival.

Keywords

Beveridge–Nelson decomposition Bayesian Business cycle  Growth cycle Turning point 

JEL classification

C11 C32 C53 C82 E32 

Notes

Acknowledgments

I thank Andrew Harvey, Chengsi Zhang, and two referees for useful comments. This work was supported by KAKENHI (16730113, 19530185, 23530255).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.School of EconomicsOsaka Prefecture UniversitySakaiJapan

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