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Infinite Dimensional VARs and Factor Models

  • Chudik , A.
  • Pesaran, M.H.

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. An empirical application to modelling of real GDP growth and investment-output ratios provides an illustration of the proposed approach. Considerable heterogeneities across countries and signi.cant presence of dominant effects are found. The results also suggest that increase in investment as a share of GDP predict higher growth rate of GDP per capita for non-negligible fraction of countries and vice versa.

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File URL: http://www.econ.cam.ac.uk/research/repec/cam/pdf/cwpe0757.pdf
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Paper provided by Faculty of Economics, University of Cambridge in its series Cambridge Working Papers in Economics with number 0757.

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Length: 24
Date of creation: Nov 2007
Date of revision:
Handle: RePEc:cam:camdae:0757
Contact details of provider: Web page: http://www.econ.cam.ac.uk/index.htm

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  7. 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.
  8. 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.
  9. Chudik, Alexander & Pesaran, Hashem & Tosetti, Elisa, 2009. "Weak and strong cross section dependence and estimation of large panels," Working Paper Series 1100, European Central Bank.
  10. Mario Forni & Marc Hallin & Lucrezia Reichlin & Marco Lippi, 2000. "The generalised dynamic factor model: identification and estimation," ULB Institutional Repository 2013/10143, ULB -- Universite Libre de Bruxelles.
  11. 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.
  12. Stephane Dees & Filippo di Mauro & M. Hashem Pesaran & L. Vanessa Smith, 2005. "Exploring the International Linkages of the Euro Area: a Global VAR Analysis," CESifo Working Paper Series 1425, CESifo Group Munich.
  13. 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.
  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.
  15. M. Hashem Pesaran & Til Schuermann & Bjorn-Jakob Treutler, 2007. "Global Business Cycles and Credit Risk," NBER Chapters, in: The Risks of Financial Institutions, pages 419-474 National Bureau of Economic Research, Inc.
  16. Ingersoll, Jonathan E, Jr, 1984. " Some Results in the Theory of Arbitrage Pricing," Journal of Finance, American Finance Association, vol. 39(4), pages 1021-39, September.
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  18. M. Hashem Pesaran & Ron Smith, 2006. "Macroeconometric Modelling with a Global Perspective," IEPR Working Papers 06.43, Institute of Economic Policy Research (IEPR).
  19. 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(2), pages 1-78.
  20. James H. Stock & Mark W. Watson, 1999. "Forecasting Inflation," NBER Working Papers 7023, National Bureau of Economic Research, Inc.
  21. 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.
  22. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November.
  23. Garratt, Anthony & Lee, Kevin & Pesaran, M. Hashem & Shin, Yongcheol, 2006. "Global and National Macroeconometric Modelling: A Long-Run Structural Approach," OUP Catalogue, Oxford University Press, number 9780199296859, March.
  24. Huberman, Gur, 1982. "A simple approach to arbitrage pricing theory," Journal of Economic Theory, Elsevier, vol. 28(1), pages 183-191, October.
  25. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(06), pages 1113-1141, December.
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  27. Thomas Doan & Robert B. Litterman & Christopher A. Sims, 1986. "Forecasting and conditional projection using realistic prior distribution," Staff Report 93, Federal Reserve Bank of Minneapolis.
  28. Holly, Sean & Pesaran, M. Hashem & Yamagata, Takashi, 2006. "A Spatio-Temporal Model of House Prices in the US," IZA Discussion Papers 2338, Institute for the Study of Labor (IZA).
  29. 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.
  30. 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.
  31. M. Hashem Pesaran & Alexander Chudik, 2010. "Econometric Analysis of High Dimensional VARs Featuring a Dominant Unit," CESifo Working Paper Series 3055, CESifo Group Munich.
  32. Conley, T. G., 1999. "GMM estimation with cross sectional dependence," Journal of Econometrics, Elsevier, vol. 92(1), pages 1-45, September.
  33. 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.
  34. 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.
  35. Robert B. Litterman, 1985. "Forecasting with Bayesian vector autoregressions five years of experience," Working Papers 274, Federal Reserve Bank of Minneapolis.
  36. repec:cup:etheor:v:13:y:1997:i:6:p:877-88 is not listed on IDEAS
  37. 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.
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