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Infinite Dimensional VARs and Factor Models

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  • Chudik, Alexander

    ()
    (University of Cambridge)

  • Pesaran, M. Hashem

    ()
    (University of Cambridge)

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. 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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Bibliographic Info

Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 3206.

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Length: 66 pages
Date of creation: Dec 2007
Date of revision:
Publication status: published in: Journal of Econometrics, 2011, 163 (1), 4-22
Handle: RePEc:iza:izadps:dp3206

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Keywords: growth; global VAR; factor models; capital accumulation; large N and T panels; weak and strong cross section dependence; VAR;

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References

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  3. Steve Bond & Asli Leblebicioglu & Fabio Schiantarelli, 2004. "Capital Accumulation and Growth: A New Look at the Empirical Evidence," Economics Papers 2004-W08, Economics Group, Nuffield College, University of Oxford.
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  6. Christine De Mol & Domenico Giannone & Lucrezia Reichlin, 2008. "Forecasting using a large number of predictors: is Bayesian shrinkage a valid alternative to principal components?," ULB Institutional Repository 2013/6411, ULB -- Universite Libre de Bruxelles.
  7. 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.
  8. James H. Stock & Mark W. Watson, 1999. "Forecasting Inflation," NBER Working Papers 7023, National Bureau of Economic Research, Inc.
  9. Garratt, Anthony & Lee, Kevin & Pesaran, M. Hashem & Shin, Yongcheol, 2012. "Global and National Macroeconometric Modelling: A Long-Run Structural Approach," OUP Catalogue, Oxford University Press, number 9780199650460.
  10. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November.
  11. Litterman, Robert B, 1986. "Forecasting with Bayesian Vector Autoregressions-Five Years of Experience," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(1), pages 25-38, January.
  12. M. Hashem Pesaran & Alexander Chudik, 2010. "Econometric Analysis of High Dimensional VARs Featuring a Dominant Unit," CESifo Working Paper Series 3055, CESifo Group Munich.
  13. 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.
  14. 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.
  15. Pesaran, M.H. & Smith, R., 2006. "Macroeconometric Modelling with a Global Perspective," Cambridge Working Papers in Economics 0604, Faculty of Economics, University of Cambridge.
  16. 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.
  17. Pesaran, M. Hashem & Tosetti, Elisa, 2011. "Large panels with common factors and spatial correlation," Journal of Econometrics, Elsevier, vol. 161(2), pages 182-202, April.
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  19. Holly, Sean & Pesaran, M. Hashem & Yamagata, Takashi, 2010. "A spatio-temporal model of house prices in the USA," Journal of Econometrics, Elsevier, vol. 158(1), pages 160-173, September.
  20. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2004. "The generalised dynamic factor model: consistency and rates," ULB Institutional Repository 2013/10133, ULB -- Universite Libre de Bruxelles.
  21. Forni, Mario & Lippi, Marco, 2000. "The Generalized Dynamic Factor Model: Representation Theory," CEPR Discussion Papers 2509, C.E.P.R. Discussion Papers.
  22. Pesaran M.H. & Schuermann T. & Weiner S.M., 2004. "Modeling Regional Interdependencies Using a Global Error-Correcting Macroeconometric Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 129-162, April.
  23. Pesaran, M.H., 2003. "A Simple Panel Unit Root Test in the Presence of Cross Section Dependence," Cambridge Working Papers in Economics 0346, Faculty of Economics, University of Cambridge.
  24. 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.
  25. 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.
  26. 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.
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  30. 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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  34. 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.
  35. 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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