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When are trend–cycle decompositions of GDP reliable?

Author

Listed:
  • Manuel González-Astudillo

    (Federal Reserve Board
    Escuela Superior Politécnica del Litoral, ESPOL)

  • John M. Roberts

    (Federal Reserve Board)

Abstract

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 preferred 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 the unemployment rate that allows for reliable 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 2019:Q1, we obtain a trend–cycle decomposition of GDP that resembles the conventional CBO estimates; we find positively correlated trend and cycle components.

Suggested Citation

  • Manuel González-Astudillo & John M. Roberts, 2022. "When are trend–cycle decompositions of GDP reliable?," Empirical Economics, Springer, vol. 62(5), pages 2417-2460, May.
    • Handle: RePEc:spr:empeco:v:62:y:2022:i:5:d:10.1007_s00181-021-02105-4
    DOI: 10.1007/s00181-021-02105-4
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    as
    1. Perron, Pierre & Wada, Tatsuma, 2009. "Let's take a break: Trends and cycles in US real GDP," Journal of Monetary Economics, Elsevier, vol. 56(6), pages 749-765, September.
    2. Stock, James H. & Watson, Mark W., 1999. "Business cycle fluctuations in us macroeconomic time series," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 1, pages 3-64, Elsevier.
    3. 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.
    4. Kuttner, Kenneth N, 1994. "Estimating Potential Output as a Latent Variable," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 361-368, July.
    5. 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.
    6. 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.
    7. Angelia L. Grant & Joshua C.C. Chan, 2017. "A Bayesian Model Comparison for Trend‐Cycle Decompositions of Output," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 49(2-3), pages 525-552, March.
    8. James Morley & Benjamin Wong, 2020. "Estimating and accounting for the output gap with large Bayesian vector autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(1), pages 1-18, January.
    9. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    10. 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.
    11. Laurence Ball, 2014. "Long-term damage from the Great Recession in OECD countries," European Journal of Economics and Economic Policies: Intervention, Edward Elgar Publishing, vol. 11(2), pages 149-160, September.
    12. Luo, Sui & Startz, Richard, 2014. "Is it one break or ongoing permanent shocks that explains U.S. real GDP?," Journal of Monetary Economics, Elsevier, vol. 66(C), pages 155-163.
    13. 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.
    14. James H. Stock & Mark W. Watson, 2007. "Why Has U.S. Inflation Become Harder to Forecast?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 3-33, February.
    15. Wada, Tatsuma, 2012. "On the correlations of trend–cycle errors," Economics Letters, Elsevier, vol. 116(3), pages 396-400.
    16. Arabinda Basistha & Richard Startz, 2008. "Measuring the NAIRU with Reduced Uncertainty: A Multiple-Indicator Common-Cycle Approach," The Review of Economics and Statistics, MIT Press, vol. 90(4), pages 805-811, November.
    17. Joshua C C Chan & Angelia L Grant, 2017. "Measuring the output gap using stochastic model specification search," CAMA Working Papers 2017-02, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    18. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, vol. 18(1), pages 49-75, July.
    19. Peter K. Clark, 1987. "The Cyclical Component of U. S. Economic Activity," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(4), pages 797-814.
    20. Jaeho Kim & Sora Chon, 2020. "Why are Bayesian trend-cycle decompositions of US real GDP so different?," Empirical Economics, Springer, vol. 58(3), pages 1339-1354, March.
    21. Roberts John M., 2001. "Estimates of the Productivity Trend Using Time-Varying Parameter Techniques," The B.E. Journal of Macroeconomics, De Gruyter, vol. 1(1), pages 1-32, July.
    22. Clark, Peter K., 1989. "Trend reversion in real output and unemployment," Journal of Econometrics, Elsevier, vol. 40(1), pages 15-32, January.
    23. Wang, Jiahui & Zivot, Eric, 2000. "A Bayesian Time Series Model of Multiple Structural Changes in Level, Trend, and Variance," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 374-386, July.
    24. 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.
    25. Berger, Tino & Everaert, Gerdie & Vierke, Hauke, 2016. "Testing for time variation in an unobserved components model for the U.S. economy," Journal of Economic Dynamics and Control, Elsevier, vol. 69(C), pages 179-208.
    26. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    27. Zellner, Arnold & Ando, Tomohiro, 2010. "A direct Monte Carlo approach for Bayesian analysis of the seemingly unrelated regression model," Journal of Econometrics, Elsevier, vol. 159(1), pages 33-45, November.
    28. James H. Stock & Mark W. Watson, 2007. "Why Has U.S. Inflation Become Harder to Forecast?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 3-33, February.
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    More about this item

    Keywords

    Unobserved components model; Trend–cycle decomposition; Trend–cycle correlation; Bayesian estimation;
    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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