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Estimating and Accounting for the Output Gap with Large Bayesian Vector Autoregressions

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  • Morley, James
  • Wong, Benjamin

Abstract

We consider how to estimate the trend and cycle of a time series, such as real GDP, given a large information set. Our approach makes use of the Beveridge-Nelson decom- position based on a vector autoregression, but with two practical considerations. First, we show how to determine which conditioning variables span the relevant information by directly accounting for the Beveridge-Nelson trend and cycle in terms of contributions from different forecast errors. Second, we employ Bayesian shrinkage to avoid over fitting in finite samples when estimating models that are large enough to include many possible sources of information. An empirical application with up to 138 variables covering vari- ous aspects of the U.S. economy reveals that the unemployment rate, inflation, and, to a lesser extent, housing starts, aggregate consumption, stock prices, real money balances, and the federal funds rate contain relevant information beyond that in output growth for estimating the output gap, with estimates largely robust to substituting some of these variables or incorporating additional variables.

Suggested Citation

  • Morley, James & Wong, Benjamin, 2018. "Estimating and Accounting for the Output Gap with Large Bayesian Vector Autoregressions," Working Papers 2018-04, University of Sydney, School of Economics, revised Feb 2019.
    • Handle: RePEc:syd:wpaper:2018-04
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    3. Constantinescu, Mihnea & Nguyen, Anh Dinh Minh, 2021. "A century of gaps: Untangling business cycles from secular trends," Economic Modelling, Elsevier, vol. 100(C).
    4. Francesco Furlanetto & Kåre Hagelund & Frank Hansen & Ørjan Robstad, 2020. "Norges Bank Output Gap Estimates: Forecasting Properties, Reliability and Cyclical Sensitivity," Working Paper 2020/7, Norges Bank.
    5. Matteo Barigozzi & Matteo Luciani, 2017. "Common Factors, Trends, and Cycles in Large Datasets," Finance and Economics Discussion Series 2017-111, Board of Governors of the Federal Reserve System (U.S.).
    6. Dubbert, Tore & Kempa, Bernd, 2024. "Nowcasting the output gap with shadow rates," Economics Letters, Elsevier, vol. 236(C).
    7. Tino Berger & Tore Dubbert, 2022. "Government spending effects on the business cycle in times of crisis," CQE Working Papers 10022, Center for Quantitative Economics (CQE), University of Muenster.
    8. Chalmovianský, Jakub & Němec, Daniel, 2022. "Assessing uncertainty of output gap estimates: Evidence from Visegrad countries," Economic Modelling, Elsevier, vol. 116(C).
    9. Tino Berger & Lorenzo Pozzi, 2023. "Cyclical consumption," Tinbergen Institute Discussion Papers 23-064/VI, Tinbergen Institute.
    10. Kamber, Güneş & Wong, Benjamin, 2020. "Global factors and trend inflation," Journal of International Economics, Elsevier, vol. 122(C).
    11. Berger, Tino & Morley, James & Wong, Benjamin, 2023. "Nowcasting the output gap," Journal of Econometrics, Elsevier, vol. 232(1), pages 18-34.
      • Tino Berger & James Morley & Benjamin Wong, 2020. "Nowcasting the output gap," CAMA Working Papers 2020-78, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    12. Morley, James & Rodríguez-Palenzuela, Diego & Sun, Yiqiao & Wong, Benjamin, 2023. "Estimating the euro area output gap using multivariate information and addressing the COVID-19 pandemic," European Economic Review, Elsevier, vol. 153(C).
    13. Fu, Bowen, 2023. "Measuring the trend real interest rate in a data-rich environment," Journal of Economic Dynamics and Control, Elsevier, vol. 147(C).
    14. Josefine Quast & Maik H. Wolters, 2023. "The Federal Reserve's output gap: The unreliability of real‐time reliability tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(7), pages 1101-1111, November.
    15. Saeed Zaman, 2021. "A Unified Framework to Estimate Macroeconomic Stars," Working Papers 21-23R2, Federal Reserve Bank of Cleveland, revised 31 May 2024.
    16. G. Cubadda & S. Grassi & B. Guardabascio, 2022. "The Time-Varying Multivariate Autoregressive Index Model," Papers 2201.07069, arXiv.org.
    17. Ochsner, Christian & Other, Lars & Thiel, Esther & Zuber, Christopher, 2024. "Demographic aging and long-run economic growth in Germany," Working Papers 02/2024, German Council of Economic Experts / Sachverständigenrat zur Begutachtung der gesamtwirtschaftlichen Entwicklung.
    18. 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.
    19. 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.
    20. Christian Ochsner & Christopher Zuber, 2022. "Die Konjunkturbereinigung der Schuldenbremse: ein Plädoyer für methodische Reformen [The Cyclical Adjustment Procedure of the German Debt Brake: a Plea for Methodical Reforms]," Wirtschaftsdienst, Springer;ZBW - Leibniz Information Centre for Economics, vol. 102(11), pages 822-825, November.
    21. Francesco Furlanetto & Kåre Hagelund & Frank Hansen & Ørjan Robstad, 2023. "Norges Bank Output Gap Estimates: Forecasting Properties, Reliability, Cyclical Sensitivity and Hysteresis," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 85(1), pages 238-267, February.
    22. 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.).
    23. Nataliia Ostapenko, 2022. "Do output gap estimates improve inflation forecasts in Slovakia?," Working and Discussion Papers WP 4/2022, Research Department, National Bank of Slovakia.
    24. Ioannis D. Vrontos & John Galakis & Ekaterini Panopoulou & Spyridon D. Vrontos, 2024. "Forecasting GDP growth: The economic impact of COVID‐19 pandemic," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(4), pages 1042-1086, July.

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    More about this item

    Keywords

    Beveridge-Nelson decomposition; output gap; Bayesian estimation; multi- variate information;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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