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Infinite Dimensional VARs and Factor Models

  • Alexander Chudik
  • M. Hashem Pesaran

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 significant 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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Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 2176.

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Date of creation: 2007
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Handle: RePEc:ces:ceswps:_2176
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  4. Alexander Chudik & M. Hashem Pesaran & Elisa Tosetti, 2009. "Weak and Strong Cross Section Dependence and Estimation of Large Panels," CESifo Working Paper Series 2689, CESifo Group Munich.
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  7. Sean Holly & M. Hashem Pesaran & Takashi Yamagata, 2006. "A Spatio-Temporal Model of House Prices in the US," CESifo Working Paper Series 1826, CESifo Group Munich.
  8. M. Hashem Pesaran & Til Schuermann & Björn-Jakob Treutler & Scott M. Weiner & April, . "Macroeconomic Dynamics and Credit Risk: A Global Perspective," Center for Financial Institutions Working Papers 03-13, Wharton School Center for Financial Institutions, University of Pennsylvania.
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  10. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(06), pages 1113-1141, December.
  11. 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.
  12. James H. Stock & Mark W. Watson, 1999. "Forecasting Inflation," NBER Working Papers 7023, National Bureau of Economic Research, Inc.
  13. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
  14. Giannone, Domenico & Reichlin, Lucrezia & Sala, Luca, 2005. "Monetary Policy in Real Time," CEPR Discussion Papers 4981, C.E.P.R. Discussion Papers.
    • 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.
  15. Alexander Chudik & M. Hashem Pesaran, 2013. "Econometric Analysis of High Dimensional VARs Featuring a Dominant Unit," Econometric Reviews, Taylor & Francis Journals, vol. 32(5-6), pages 592-649, August.
  16. 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.
  17. M. Hashem Pesaran & Elisa Tosetti, 2007. "Large Panels with Common Factors and Spatial Correlations," CESifo Working Paper Series 2103, CESifo Group Munich.
  18. Steve Bond & Asli Leblebicioglu & Fabio Schiantarelli, 2004. "Capital Accumulation and Growth: A New Look at the Empirical Evidence," Boston College Working Papers in Economics 591, Boston College Department of Economics, revised 02 Aug 2007.
  19. M. Hashem Pesaran & Til Schuermann & Scott M. Weiner, 2002. "Modeling Regional Interdependencies Using a Global Error-Correcting Macroeconometric Model," Center for Financial Institutions Working Papers 01-38, Wharton School Center for Financial Institutions, University of Pennsylvania.
  20. 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.
  21. Stephane Dees & Filippo di Mauro & M. Hashem Pesaran & L. Vanessa Smith, 2004. "Exploring the International Linkages of the Euro Area: A Global VAR Analysis," IEPR Working Papers 04.6, Institute of Economic Policy Research (IEPR).
  22. 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.
  23. De Mol, Christine & Giannone, Domenico & Reichlin, Lucrezia, 2006. "Forecasting using a large number of predictors: Is Bayesian regression a valid alternative to principal components?," Working Paper Series 0700, European Central Bank.
  24. 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.
  25. 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.
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  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.
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