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The multivariate Beveridge–Nelson decomposition with I(1) and I(2) series

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  • Murasawa, Yasutomo

Abstract

The consumption Euler equation implies that the output growth rate and the real interest rate are of the same order of integration; i.e., if the real interest rate is I(1), then so is the output growth rate and hence log output is I(2). To estimate the natural rates and gaps of macroeconomic variables jointly, this paper develops the multivariate Beveridge–Nelson decomposition when some series are I(1) and others are I(2). The paper applies the method to Japanese data during 1980Q1–2013Q3 to estimate the natural rates and gaps of output, inflation, interest, and unemployment jointly.

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  • Murasawa, Yasutomo, 2015. "The multivariate Beveridge–Nelson decomposition with I(1) and I(2) series," Economics Letters, Elsevier, vol. 137(C), pages 157-162.
    • Handle: RePEc:eee:ecolet:v:137:y:2015:i:c:p:157-162
    DOI: 10.1016/j.econlet.2015.11.001
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    References listed on IDEAS

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    1. Kiley, Michael T., 2013. "Output gaps," Journal of Macroeconomics, Elsevier, vol. 37(C), pages 1-18.
    2. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
    3. Donald Robertson & Anthony Garratt & Stephen Wright, 2006. "Permanent vs transitory components and economic fundamentals," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(4), pages 521-542.
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    6. Yasutomo Murasawa, 2014. "Measuring the natural rates, gaps, and deviation cycles," Empirical Economics, Springer, vol. 47(2), pages 495-522, September.
    7. Evans, George & Reichlin, Lucrezia, 1994. "Information, forecasts, and measurement of the business cycle," Journal of Monetary Economics, Elsevier, vol. 33(2), pages 233-254, April.
    8. Oh, Kum Hwa & Zivot, Eric & Creal, Drew, 2008. "The relationship between the Beveridge-Nelson decomposition and other permanent-transitory decompositions that are popular in economics," Journal of Econometrics, Elsevier, vol. 146(2), pages 207-219, October.
    9. Sbrana, Giacomo, 2013. "The exact linkage between the Beveridge–Nelson decomposition and other permanent-transitory decompositions," Economic Modelling, Elsevier, vol. 30(C), pages 311-316.
    10. Perron, Pierre & Qu, Zhongjun, 2007. "A simple modification to improve the finite sample properties of Ng and Perron's unit root tests," Economics Letters, Elsevier, vol. 94(1), pages 12-19, January.
    11. Kum Hwa Oh & Eric Zivot, 2006. "The Clark Model with Correlated Components," Working Papers UWEC-2006-06, University of Washington, Department of Economics.
    12. Shigeru Iwata & Han Li, 2015. "What are the Differences in Trend Cycle Decompositions by Beveridge and Nelson and by Unobserved Component Models?," Econometric Reviews, Taylor & Francis Journals, vol. 34(1-2), pages 146-173, February.
    13. Thomas Laubach & John C. Williams, 2003. "Measuring the Natural Rate of Interest," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 1063-1070, November.
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    Cited by:

    1. 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.
    2. Xu, Jia & Tan, Xiujie & He, Gang & Liu, Yu, 2019. "Disentangling the drivers of carbon prices in China's ETS pilots — An EEMD approach," Technological Forecasting and Social Change, Elsevier, vol. 139(C), pages 1-9.

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    More about this item

    Keywords

    Gap; Natural rate; Trend–cycle decomposition; Unit root;
    All these keywords.

    JEL classification:

    • 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
    • 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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