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When Can Trend-Cycle Decompositions Be Trusted?



In this paper, we examine the results of GDP trend-cycle decompositions from the estimation of bivariate unobserved components models that allow for correlated trend and cycle innovations. Three competing variables are considered in the bivariate setup along with GDP: the unemployment rate, the inflation rate, and gross domestic income. We find that the unemployment rate is the best variable to accompany GDP in the bivariate setup to obtain accurate estimates of its trend-cycle correlation coefficient and the cycle. We show that the key feature of unemployment that allows for precise estimates of the cycle of GDP is that its nonstationary component is \"small\" relative to its cyclical component. Using quarterly GDP and unemployment rate data from 1948:Q1 to 2015:Q4, we obtain the trend-cycle decomposition of GDP and find evidence of correlated trend and cycle components and an estimated cycle that is about 2 percent below its trend at the end of the sample.

Suggested Citation

  • Manuel P. Gonzalez-Astudillo & John M. Roberts, 2016. "When Can Trend-Cycle Decompositions Be Trusted?," Finance and Economics Discussion Series 2016-099, Board of Governors of the Federal Reserve System (U.S.).
  • Handle: RePEc:fip:fedgfe:2016-99
    DOI: 10.17016/FEDS.2016.099

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    References listed on IDEAS

    1. Arabinda Basistha, 2007. "Trend‐cycle correlation, drift break and the estimation of trend and cycle in Canadian GDP," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 40(2), pages 584-606, May.
    2. Tara M. Sinclair, 2009. "The Relationships between Permanent and Transitory Movements in U.S. Output and the Unemployment Rate," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(2-3), pages 529-542, March.
    3. Basistha, Arabinda & Nelson, Charles R., 2007. "New measures of the output gap based on the forward-looking new Keynesian Phillips curve," Journal of Monetary Economics, Elsevier, vol. 54(2), pages 498-511, March.
    4. Arabinda Basistha, 2009. "Hours per capita and productivity: evidence from correlated unobserved components models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(1), pages 187-206.
    5. Dave Reifschneider & William Wascher & David Wilcox, 2015. "Aggregate Supply in the United States: Recent Developments and Implications for the Conduct of Monetary Policy," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 63(1), pages 71-109, May.
    6. Dennis J. Fixler & Jeremy J. Nalewaik, 2007. "News, noise, and estimates of the \"true\" unobserved state of the economy," Finance and Economics Discussion Series 2007-34, Board of Governors of the Federal Reserve System (U.S.).
    7. James C. Morley & Charles R. Nelson & Eric Zivot, 2003. "Why Are the Beveridge-Nelson and Unobserved-Components Decompositions of GDP So Different?," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 235-243, May.
    8. Andrea Stella & James H. Stock, 2012. "A state-dependent model for inflation forecasting," International Finance Discussion Papers 1062, Board of Governors of the Federal Reserve System (U.S.).
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    Cited by:

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    2. Deryugina, Elena & Ponomarenko, Alexey & Rozhkova, Anna, 2020. "When are credit gap estimates reliable?," Economic Analysis and Policy, Elsevier, vol. 67(C), pages 221-238.
    3. Manuel P. Gonzalez-Astudillo & Jean-Philippe Laforte, 2020. "Estimates of r* Consistent with a Supply-Side Structure and a Monetary Policy Rule for the U.S. Economy," Finance and Economics Discussion Series 2020-085, Board of Governors of the Federal Reserve System (U.S.).
    4. Max Soloschenko & Enzo Weber, 2021. "Trend-Cycle Interactions and the Subprime Crisis: Analysis of US and Canadian Output," Journal of Business Cycle Research, Springer;Centre for International Research on Economic Tendency Surveys (CIRET), vol. 17(2), pages 109-128, November.
    5. Agbeyegbe, Terence D., 2020. "Bayesian analysis of output gap in Barbados," Latin American Journal of Central Banking (previously Monetaria), Elsevier, vol. 1(1).
    6. Constantinescu, Mihnea & Nguyen, Anh D.M., 2018. "Unemployment or credit: Which one holds the potential? Results for a small open economy with a low degree of financialization," Economic Systems, Elsevier, vol. 42(4), pages 649-664.
    7. Julien Champagne & Guillaume Poulin‐Bellisle & Rodrigo Sekkel, 2018. "The Real‐Time Properties of the Bank of Canada's Staff Output Gap Estimates," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 50(6), pages 1167-1188, September.
    8. Canova, Fabio & Ferroni, Filippo, 2020. "A hitchhiker guide to empirical macro models," CEPR Discussion Papers 15446, C.E.P.R. Discussion Papers.
    9. Alessandro Barbarino & Travis J. Berge & Han Chen & Andrea Stella, 2020. "Which Output Gap Estimates Are Stable in Real Time and Why?," Finance and Economics Discussion Series 2020-102, Board of Governors of the Federal Reserve System (U.S.).
    10. Casey, Eddie, 2020. "Do macroeconomic forecasters use macroeconomics to forecast?," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1439-1453.

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    More about this item


    unobserved component model; Trend-cycle decomposition; Trend-cycle correlation;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: 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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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