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Infinite Dimensional VARs and Factor Models

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  • Alexander Chudik
  • M. Hashem Pesaran

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.

Suggested Citation

  • Alexander Chudik & M. Hashem Pesaran, 2007. "Infinite Dimensional VARs and Factor Models," CESifo Working Paper Series 2176, CESifo.
  • Handle: RePEc:ces:ceswps:_2176
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    Cited by:

    1. Bonhomme, Stphane & Robin, Jean-Marc, 2009. "Consistent noisy independent component analysis," Journal of Econometrics, Elsevier, vol. 149(1), pages 12-25, April.
    2. Stephane Dees & M. Hashem Pesaran & L. Vanessa Smith & Ron P. Smith, 2009. "Identification of New Keynesian Phillips Curves from a Global Perspective," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(7), pages 1481-1502, October.
    3. Alexander Chudik & Roland Straub, 2017. "Size, Openness, And Macroeconomic Interdependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 58, pages 33-55, February.
    4. Holly, Sean & Hashem Pesaran, M. & Yamagata, Takashi, 2011. "The spatial and temporal diffusion of house prices in the UK," Journal of Urban Economics, Elsevier, vol. 69(1), pages 2-23, January.
    5. 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.
    6. Pesaran, M. Hashem & Schuermann, Til & Smith, L. Vanessa, 2009. "Forecasting economic and financial variables with global VARs," International Journal of Forecasting, Elsevier, vol. 25(4), pages 642-675, October.
    7. Sean Holly & Ivan Petrella, 2012. "Factor Demand Linkages, Technology Shocks, and the Business Cycle," The Review of Economics and Statistics, MIT Press, vol. 94(4), pages 948-963, November.
    8. Song Song & Peter J. Bickel, 2011. "Large Vector Auto Regressions," Papers 1106.3915, arXiv.org.
    9. Stephane Dees & Arthur Saint-Guilhem, 2011. "The role of the United States in the global economy and its evolution over time," Empirical Economics, Springer, vol. 41(3), pages 573-591, December.
    10. Alexander Chudik & M. Hashem Pesaran & Elisa Tosetti, 2011. "Weak and strong cross‐section dependence and estimation of large panels," Econometrics Journal, Royal Economic Society, vol. 14(1), pages 45-90, February.
    11. Yulia Vymyatnina, 2014. "Spillover Effects in the Customs Union of Russia, Kazakhstan and Belarus," EcoMod2014 7160, EcoMod.
    12. Stephane Dees & M. Hashem Pesaran & L. Vanessa Smith & Ron P. Smith, 2009. "Identification of New Keynesian Phillips Curves from a Global Perspective," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(7), pages 1481-1502, October.
    13. Consolo, Agostino & Favero, Carlo A. & Paccagnini, Alessia, 2009. "On the statistical identification of DSGE models," Journal of Econometrics, Elsevier, vol. 150(1), pages 99-115, May.
    14. Sean Holly & Ivan Petrella, 2008. "Factor demand linkages and the business cycle: interpreting aggregate fluctuations as sectoral fluctuations," CDMA Conference Paper Series 0809, Centre for Dynamic Macroeconomic Analysis.
    15. Elizabeth Bucacos, 2015. "Impact of international monetary policy in Uruguay: a FAVAR approach," Documentos de trabajo 2015003, Banco Central del Uruguay.
    16. Kappler Marcus, 2011. "Business Cycle Co-movement and Trade Intensity in the Euro Area: is there a Dynamic Link?," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 231(2), pages 247-265, April.
    17. Song, Song & Zhu, Lixing, 2016. "Group-wise semiparametric modeling: A SCSE approach," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 1-14.
    18. Pesaran, M. Hashem & Schuermann, Til & Smith, L. Vanessa, 2009. "Forecasting economic and financial variables with global VARs," International Journal of Forecasting, Elsevier, vol. 25(4), pages 642-675, October.
    19. Bussière, Matthieu & Ca' Zorzi, Michele & Chudik, Alexander & Dieppe, Alistair, 2010. "Methodological advances in the assessment of equilibrium exchange rates," Working Paper Series 1151, European Central Bank.

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    More about this item

    Keywords

    large N and T panels; weak and strong cross section dependence; VAR; global VAR; factor models; capital accumulation and growth;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General

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