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Measuring the natural rates, gaps, and deviation cycles

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  • Yasutomo Murasawa

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. Copyright Springer-Verlag Berlin Heidelberg 2014

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  • Yasutomo Murasawa, 2014. "Measuring the natural rates, gaps, and deviation cycles," Empirical Economics, Springer, vol. 47(2), pages 495-522, September.
    • Handle: RePEc:spr:empeco:v:47:y:2014:i:2:p:495-522
    DOI: 10.1007/s00181-013-0747-9
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    Cited by:

    1. Chalmovianský, Jakub & Němec, Daniel, 2022. "Assessing uncertainty of output gap estimates: Evidence from Visegrad countries," Economic Modelling, Elsevier, vol. 116(C).
    2. Yasutomo Murasawa, 2016. "The Beveridge–Nelson decomposition of mixed-frequency series," Empirical Economics, Springer, vol. 51(4), pages 1415-1441, December.
    3. Marcin Błażejowski, 2024. "Which C compiler and BLAS/LAPACK library should I use: gretl’s numerical efficiency in different configurations," Computational Statistics, Springer, vol. 39(7), pages 3497-3522, December.
    4. Murasawa, Yasutomo, 2015. "The multivariate Beveridge–Nelson decomposition with I(1) and I(2) series," Economics Letters, Elsevier, vol. 137(C), pages 157-162.
    5. Murasawa Yasutomo, 2022. "Bayesian multivariate Beveridge–Nelson decomposition of I(1) and I(2) series with cointegration," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 26(3), pages 387-415, June.

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    More about this item

    Keywords

    Beveridge–Nelson decomposition; Bayesian; Business cycle; Growth cycle; Turning point; C11; C32; C53; C82; E32;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C82 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Macroeconomic Data; Data Access
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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