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Infinite-dimensional VARs and factor models

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Author Info
Alexander Chudik () (European Central Bank, Kaiserstrasse 29, 60311 Frankfurt am Main, Germany.)
M. Hashem Pesaran () (University of Cambridge, CIMF and USC; Faculty of Economics, Austin Robinson Building, Sidgwick Avenue, Cambridge, CB3 9DD, United Kingdom.)

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Abstract

This paper introduces a novel approach for dealing with the 'curse of dimensionality' in the case of large linear dynamic systems. Restrictions on the coefficients of an unrestricted VAR are proposed that are binding only in a limit as the number of endogenous variables tends to infinity. It is shown that under such restrictions, an infinite-dimensional VAR (or IVAR) can be arbitrarily well characterized by a large number of finite-dimensional models in the spirit of the global VAR model proposed in Pesaran et al. (JBES, 2004). The paper also considers IVAR models with dominant individual units and shows that this will lead to a dynamic factor model with the dominant unit acting as the factor. The problems of estimation and inference in a stationary IVAR with unknown number of unobserved common factors are also investigated. A cross section augmented least squares estimator is proposed and its asymptotic distribution is derived. Satisfactory small sample properties are documented by Monte Carlo experiments. JEL Classification: C10, C33, C51.

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Paper provided by European Central Bank in its series Working Paper Series with number 998.

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Length: 63 pages
Date of creation: Jan 2009
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Handle: RePEc:ecb:ecbwps:20090998

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Related research
Keywords: Large N and T Panels; Weak and Strong Cross Section Dependence; VAR; Global VAR; Factor Models.;

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. M. Hashem Pesaran & Til Schuermann & Björn-Jakob Treutler, 2005. "Global Business Cycles and Credit Risk," NBER Working Papers 11493, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  2. Conley, T. G., 1999. "GMM estimation with cross sectional dependence," Journal of Econometrics, Elsevier, vol. 92(1), pages 1-45, September. [Downloadable!] (restricted)
  3. Robert B. Litterman, 1985. "Forecasting with Bayesian vector autoregressions five years of experience," Working Papers 274, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  4. Bond, Steve & Leblebicioglu, Asli & Schiantarelli, Fabio, 2004. "Capital Accumulation and Growth: A New Look at the Empirical Evidence," IZA Discussion Papers 1174, Institute for the Study of Labor (IZA). [Downloadable!]
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  5. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January. [Downloadable!] (restricted)
  6. Binder, M. & Pesaran, H., 1996. "Multivariate Linear Rational Expectations Models: Characterisation of the Nature of the Solutions and Their Fully Recursive Computation," Cambridge Working Papers in Economics 9619, Faculty of Economics, University of Cambridge.
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  7. M. Hashem Pesaran & Ron Smith, 2006. "Macroeconometric Modelling With A Global Perspective," Manchester School, University of Manchester, vol. 74(s1), pages 24-49, 09. [Downloadable!] (restricted)
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  8. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2004. "The generalized dynamic factor model consistency and rates," Journal of Econometrics, Elsevier, vol. 119(2), pages 231-255, April. [Downloadable!] (restricted)
  9. M. Hashem Pesaran, 2006. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," Econometrica, Econometric Society, vol. 74(4), pages 967-1012, 07. [Downloadable!] (restricted)
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  10. M. Hashem Pesaran & Til Schuermann & Scott M. Weiner, 2001. "Modelling regional interdependencies using a global error-correcting macroeconometric model," 10th International Conference on Panel Data, Berlin, July 5-6, 2002 B4-1, International Conferences on Panel Data. [Downloadable!]
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  11. Filippo di Mauro & L. Vanessa Smith & Stephane Dees & M. Hashem Pesaran, 2007. "Exploring the international linkages of the euro area: a global VAR analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(1), pages 1-38. [Downloadable!]
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  12. Conley, T.G. & Topa, G., 1999. "Socio-Economic Distance and Spatial Patterns in Unemployment," Working Papers 99-04, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
  13. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(06), pages 1113-1141, December. [Downloadable!]
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  14. De Mol, Christine & Giannone, Domenico & Reichlin, Lucrezia, 2006. "Forecasting using a large number of predictors: is Bayesian regression a valid alternative to principal components?," Discussion Paper Series 1: Economic Studies 2006,32, Deutsche Bundesbank, Research Centre. [Downloadable!]
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  15. M. Hashem Pesaran & Elisa Tosetti, 2007. "Large Panels with Common Factors and Spatial Correlations," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
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  16. Giannone, Domenico & Reichlin, Lucrezia & Sala, Luca, 2005. "Monetary Policy in Real Time," CEPR Discussion Papers 4981, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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    • Domenico Giannone & Lucrezia Reichlin & Luca Sala, 2005. "Monetary Policy in Real Time," Working Papers 284, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University. [Downloadable!]
    • Domenico Giannone & Lucrezia Reichlin & Luca Sala, 2005. "Monetary Policy in Real Time," NBER Chapters, in: NBER Macroeconomics Annual 2004, Volume 19, pages 161-224 National Bureau of Economic Research, Inc. [Downloadable!]
  17. Stock, James H. & Watson, Mark W., 1999. "Forecasting inflation," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 293-335, October. [Downloadable!] (restricted)
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  18. Pesaran, M. Hashem & Schuermann, Til & Treutler, Bjorn-Jakob & Weiner, Scott M., 2006. "Macroeconomic Dynamics and Credit Risk: A Global Perspective," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 38(5), pages 1211-1261, August. [Downloadable!] (restricted)
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  19. Thomas Doan & Robert Litterman & Christopher Sims, 1984. "Forecasting and conditional projection using realistic prior distributions," Econometric Reviews, Taylor and Francis Journals, vol. 3(1), pages 1-100. [Downloadable!] (restricted)
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  20. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November. [Downloadable!] (restricted)
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  21. Marco Del Negro & Frank Schorfheide, 2004. "Priors from General Equilibrium Models for VARS," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(2), pages 643-673, 05. [Downloadable!] (restricted)
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  22. Thomas J. Sargent & Christopher A. Sims, 1977. "Business cycle modeling without pretending to have too much a priori economic theory," Working Papers 55, Federal Reserve Bank of Minneapolis. [Downloadable!]
  23. 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. [Downloadable!] (restricted)
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  24. Ben Bernanke & Jean Boivin & Piotr S. Eliasz, 2005. "Measuring the Effects of Monetary Policy: A Factor-augmented Vector Autoregressive (FAVAR) Approach," The Quarterly Journal of Economics, MIT Press, vol. 120(1), pages 387-422, January.
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  25. Bai, Jushan & Ng, Serena, 2007. "Determining the Number of Primitive Shocks in Factor Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 52-60, January. [Downloadable!] (restricted)
  26. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-62, April.
  27. 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. [Downloadable!] (restricted)
  28. repec:cup:etheor:v:13:y:1997:i:6:p:877-88 is not listed on IDEAS
  29. M. Hashem Pesaran & L. Vanessa Smith & Ron P. Smith, 2007. "What if the UK or Sweden had joined the euro in 1999? An empirical evaluation using a Global VAR," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 12(1), pages 55-87. [Downloadable!]
  30. M. Hashem Pesaran, 2007. "A simple panel unit root test in the presence of cross-section dependence," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(2), pages 265-312. [Downloadable!]
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  31. Eric M. Leeper & Christopher A. Sims & Tao Zha, 1996. "What Does Monetary Policy Do?," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 27(1996-2), pages 1-78. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. M. Hashem Pesaran & Til Schuermann & L. Vanessa Smith, 2008. "Forecasting economic and financial variables with global VARs," Staff Reports 317, Federal Reserve Bank of New York. [Downloadable!]
    Other versions:
  2. Stephane Dees & M. Hashem Pesaran & L. Vanessa Smith & Ron P. Smith, 2008. "Identification of New Keynesian Phillips Curves from a Global Perspective," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
    Other versions:
  3. Matthieu Bussière & Alexander Chudik & Giulia Sestieri, 2009. "Modelling Global Trade Flows: Results from a GVAR Model," Working Paper Series 1087, European Central Bank. [Downloadable!]
  4. Stéphane Dées & Arthur Saint-Guilhem, 2009. "The role of the United States in the global economy and its evolution over time," Working Paper Series 1034, European Central Bank. [Downloadable!]
  5. Alexander Chudik & M. Hashem Pesaran & Elisa Tosetti, 2009. "Weak and Strong Cross Section Dependence and Estimation of Large Panels," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
    Other versions:
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