IDEAS home Printed from https://ideas.repec.org/p/fip/fedgfe/2017-111.html
   My bibliography  Save this paper

Common Factors, Trends, and Cycles in Large Datasets

Author

Listed:
  • Matteo Barigozzi
  • Matteo Luciani

Abstract

This paper considers a non-stationary dynamic factor model for large datasets to disentangle long-run from short-run co-movements. We first propose a new Quasi Maximum Likelihood estimator of the model based on the Kalman Smoother and the Expectation Maximisation algorithm. The asymptotic properties of the estimator are discussed. Then, we show how to separate trends and cycles in the factors by mean of eigenanalysis of the estimated non-stationary factors. Finally, we employ our methodology on a panel of US quarterly macroeconomic indicators to estimate aggregate real output, or Gross Domestic Output, and the output gap.

Suggested Citation

  • 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 (US).
  • Handle: RePEc:fip:fedgfe:2017-111
    DOI: 10.17016/FEDS.2017.111
    as

    Download full text from publisher

    File URL: https://www.federalreserve.gov/econres/feds/files/2017111pap.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Roberto S. Mariano & Yasutomo Murasawa, 2003. "A new coincident index of business cycles based on monthly and quarterly series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(4), pages 427-443.
    2. Choi, In, 2012. "Efficient Estimation Of Factor Models," Econometric Theory, Cambridge University Press, vol. 28(02), pages 274-308, April.
    3. Kiley, Michael T., 2013. "Output gaps," Journal of Macroeconomics, Elsevier, vol. 37(C), pages 1-18.
    4. 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.
    5. Juan Antolin-Diaz & Thomas Drechsel & Ivan Petrella, 2017. "Tracking the Slowdown in Long-Run GDP Growth," The Review of Economics and Statistics, MIT Press, vol. 99(2), pages 343-356, May.
    6. Vahid, F & Engle, Robert F, 1993. "Common Trends and Common Cycles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(4), pages 341-360, Oct.-Dec..
    7. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
    8. Giannone, Domenico & Reichlin, Lucrezia & Small, David, 2008. "Nowcasting: The real-time informational content of macroeconomic data," Journal of Monetary Economics, Elsevier, vol. 55(4), pages 665-676, May.
    9. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(06), pages 1113-1141, December.
    10. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
    11. Athanasios Orphanides & Simon van Norden, 2002. "The Unreliability of Output-Gap Estimates in Real Time," The Review of Economics and Statistics, MIT Press, vol. 84(4), pages 569-583, November.
    12. Aruoba, S. Borağan & Diebold, Francis X. & Nalewaik, Jeremy & Schorfheide, Frank & Song, Dongho, 2016. "Improving GDP measurement: A measurement-error perspective," Journal of Econometrics, Elsevier, vol. 191(2), pages 384-397.
    13. Kasa, Kenneth, 1992. "Common stochastic trends in international stock markets," Journal of Monetary Economics, Elsevier, vol. 29(1), pages 95-124, February.
    14. James Morley & Benjamin Wong, 2017. "Estimating and accounting for the output gap with large Bayesian vector autoregressions," CAMA Working Papers 2017-46, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    15. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    16. Gonzalo, Jesus & Ng, Serena, 2001. "A systematic framework for analyzing the dynamic effects of permanent and transitory shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1527-1546, October.
    17. 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.
    18. Laura Coroneo & Domenico Giannone & Michele Modugno, 2016. "Unspanned Macroeconomic Factors in the Yield Curve," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 472-485, July.
    19. James H. Stock & Mark W. Watson, 2005. "Implications of Dynamic Factor Models for VAR Analysis," NBER Working Papers 11467, National Bureau of Economic Research, Inc.
    20. Bańbura, Marta & Giannone, Domenico & Lenza, Michele, 2015. "Conditional forecasts and scenario analysis with vector autoregressions for large cross-sections," International Journal of Forecasting, Elsevier, vol. 31(3), pages 739-756.
    21. Forni, Mario & Giannone, Domenico & Lippi, Marco & Reichlin, Lucrezia, 2009. "Opening The Black Box: Structural Factor Models With Large Cross Sections," Econometric Theory, Cambridge University Press, vol. 25(05), pages 1319-1347, October.
    22. Catherine Doz & Domenico Giannone & Lucrezia Reichlin, 2012. "A Quasi–Maximum Likelihood Approach for Large, Approximate Dynamic Factor Models," The Review of Economics and Statistics, MIT Press, vol. 94(4), pages 1014-1024, November.
    23. Matteo Luciani, 2015. "Monetary Policy and the Housing Market: A Structural Factor Analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(2), pages 199-218, March.
    24. Lippi, Marco & Reichlin, Lucrezia, 1994. "Common and uncommon trends and cycles," European Economic Review, Elsevier, vol. 38(3-4), pages 624-635, April.
    25. Gonzalo, Jesus & Granger, Clive W J, 1995. "Estimation of Common Long-Memory Components in Cointegrated Systems," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 27-35, January.
    26. Byeongchan Seong & Sung K. Ahn & Peter A. Zadrozny, 2013. "Estimation of vector error correction models with mixed-frequency data," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(2), pages 194-205, March.
    27. Luciana Juvenal & Ivan Petrella, 2015. "Speculation in the Oil Market," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(4), pages 621-649, June.
    28. Jushan Bai & Serena Ng, 2004. "A PANIC Attack on Unit Roots and Cointegration," Econometrica, Econometric Society, vol. 72(4), pages 1127-1177, July.
    29. Antonello D’ Agostino & Domenico Giannone, 2012. "Comparing Alternative Predictors Based on Large‐Panel Factor Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 74(2), pages 306-326, April.
    30. repec:wly:jmoncb:v:50:y:2018:i:6:p:1189-1224 is not listed on IDEAS
    31. Aastveit, Knut Are & Trovik, Tørres, 2014. "Estimating the output gap in real time: A factor model approach," The Quarterly Review of Economics and Finance, Elsevier, vol. 54(2), pages 180-193.
    32. Proietti, Tommaso, 1997. "Short-Run Dynamics in Cointegrated Systems," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 59(3), pages 405-422, August.
    33. Lunsford, Kurt Graden, 2017. "Lingering Residual Seasonality in GDP Growth," Economic Commentary, Federal Reserve Bank of Cleveland, issue March.
    34. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, vol. 18(1), pages 49-75, July.
    35. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    36. Michael E. Tipping & Christopher M. Bishop, 1999. "Probabilistic Principal Component Analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 611-622.
    37. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    38. Doz, Catherine & Giannone, Domenico & Reichlin, Lucrezia, 2011. "A two-step estimator for large approximate dynamic factor models based on Kalman filtering," Journal of Econometrics, Elsevier, vol. 164(1), pages 188-205, September.
    39. Massimo Franchi, 2017. "On the structure of state space systems with unit roots," DSS Empirical Economics and Econometrics Working Papers Series 2017/4, Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome.
    40. Jungbacker, B. & Koopman, S.J. & van der Wel, M., 2011. "Maximum likelihood estimation for dynamic factor models with missing data," Journal of Economic Dynamics and Control, Elsevier, vol. 35(8), pages 1358-1368, August.
    41. repec:hal:journl:peer-00844811 is not listed on IDEAS
    42. Bai, Jushan, 2004. "Estimating cross-section common stochastic trends in nonstationary panel data," Journal of Econometrics, Elsevier, vol. 122(1), pages 137-183, September.
    43. Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737, December.
    44. Alexei Onatski, 2009. "Testing Hypotheses About the Number of Factors in Large Factor Models," Econometrica, Econometric Society, vol. 77(5), pages 1447-1479, September.
    45. Engle, Robert F. & Issler, João Victor, 1993. "Common trends and common cycles in Latin America," Revista Brasileira de Economia - RBE, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil), vol. 47(2), April.
    46. Del Negro, Marco & Schorfheide, Frank & Smets, Frank & Wouters, Rafael, 2007. "On the Fit of New Keynesian Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 123-143, April.
    47. Marco Lippi & Lucrezia Reichlin, 1994. "Diffusion of Technical Change and the Decomposition of Output into Trend and Cycle," Review of Economic Studies, Oxford University Press, vol. 61(1), pages 19-30.
    48. Marta Bańbura & Michele Modugno, 2014. "Maximum Likelihood Estimation Of Factor Models On Datasets With Arbitrary Pattern Of Missing Data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(1), pages 133-160, January.
    49. Jeremy J. Nalewaik, 2012. "Estimating Probabilities of Recession in Real Time Using GDP and GDI," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 44(1), pages 235-253, February.
    50. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    51. Ricardo Reis & Mark W. Watson, 2010. "Relative Goods' Prices, Pure Inflation, and the Phillips Correlation," American Economic Journal: Macroeconomics, American Economic Association, vol. 2(3), pages 128-157, July.
    52. Bai, Jushan & Liao, Yuan, 2016. "Efficient estimation of approximate factor models via penalized maximum likelihood," Journal of Econometrics, Elsevier, vol. 191(1), pages 1-18.
    53. Rudebusch, Glenn D. & Wilson, Daniel J. & Mahedy, Tim, 2015. "The puzzle of weak first-quarter GDP growth," FRBSF Economic Letter, Federal Reserve Bank of San Francisco.
    54. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
    55. Marek Jarociński & Michele Lenza, 2018. "An Inflation‐Predicting Measure of the Output Gap in the Euro Area," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 50(6), pages 1189-1224, September.
    56. Giannone, Domenico & Reichlin, Lucrezia & Small, David, 2005. "Nowcasting GDP and Inflation: The Real Time Informational Content of Macroeconomic Data Releases," CEPR Discussion Papers 5178, C.E.P.R. Discussion Papers.
    57. repec:hal:journl:hal-00638009 is not listed on IDEAS
    58. Dungey, Mardi & Jacobs, Jan P.A.M. & Tian, Jing & van Norden, Simon, 2015. "Trend In Cycle Or Cycle In Trend? New Structural Identifications For Unobserved-Components Models Of U.S. Real Gdp," Macroeconomic Dynamics, Cambridge University Press, vol. 19(04), pages 776-790, June.
    59. Hallin, Marc & Liska, Roman, 2007. "Determining the Number of Factors in the General Dynamic Factor Model," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 603-617, June.
    60. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-144, January.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    EM Algorithm ; Gross Domestic Output ; Kalman Smoother ; Non-stationary Approximate Dynamic Factor Model ; Output Gap ; Quasi Maximum Likelihood ; Trend-Cycle Decomposition;

    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
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • E00 - Macroeconomics and Monetary Economics - - General - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:fip:fedgfe:2017-111. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (FRB Librarian). General contact details of provider: http://edirc.repec.org/data/frbgvus.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.