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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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  1. 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.
  2. 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, Oxford University Press, number 9780199650460, October.
  3. Pesaran, M.H., 2003. "A Simple Panel Unit Root Test in the Presence of Cross Section Dependence," Cambridge Working Papers in Economics, Faculty of Economics, University of Cambridge 0346, Faculty of Economics, University of Cambridge.
  4. Holly, S. & Pesaran, M.H. & Yamagata. T., 2006. "A Spatio-Temporal Model of House Prices in the US," Cambridge Working Papers in Economics, Faculty of Economics, University of Cambridge 0654, Faculty of Economics, University of Cambridge.
  5. Stephane Dees & Filippo di Mauro & M. Hashem Pesaran & L. Vanessa Smith, 2006. "Exploring the International Linkages of the Euro Area: a Global VAR Analysis," Computing in Economics and Finance 2006, Society for Computational Economics 47, Society for Computational Economics.
  6. M. Hashem Pesaran & Alexander Chudik, 2010. "Econometric Analysis of High Dimensional VARs Featuring a Dominant Unit," CESifo Working Paper Series 3055, CESifo Group Munich.
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  15. M. Hashem Pesaran & Til Schuermann & Björn-Jakob Treutler, 2005. "Global Business Cycles and Credit Risk," CESifo Working Paper Series 1548, CESifo Group Munich.
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