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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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  2. 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.
  3. 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, December.
  4. Raffaella Giacomini & Halbert White, 2003. "Tests of Conditional Predictive Ability," Econometrics 0308001, EconWPA.
  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 47, Society for Computational Economics.
  6. M. Hashem Pesaran & Ron P. Smith, 2006. "Macroeconometric Modelling with a Global Perspective," CESifo Working Paper Series 1659, CESifo Group Munich.
  7. 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.
  8. M. Hashem Pesaran & Alexander Chudik, 2010. "Econometric Analysis of High Dimensional VARs Featuring a Dominant Unit," CESifo Working Paper Series 3055, CESifo Group Munich.
  9. 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.
  10. 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.
  11. Ben S. Bernanke & Jean Boivin & Piotr Eliasz, 2005. "Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach," The Quarterly Journal of Economics, Oxford University Press, vol. 120(1), pages 387-422.
  12. Forni, Mario & Lippi, Marco, 2000. "The Generalized Dynamic Factor Model: Representation Theory," CEPR Discussion Papers 2509, C.E.P.R. Discussion Papers.
  13. 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.
  14. Chudik, A. & Pesaran, M.H. & Tosetti, E., 2009. "Weak and Strong Cross Section Dependence and Estimation of Large Panels," Cambridge Working Papers in Economics 0924, Faculty of Economics, University of Cambridge.
  15. Pesaran, M.H. & Tosetti, E., 2007. "Large Panels with Common Factors and Spatial Correlations," Cambridge Working Papers in Economics 0743, Faculty of Economics, University of Cambridge.
  16. 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.
  17. Marco Del Negro & Frank Schorfheide, 2002. "Priors from general equilibrium models for VARs," FRB Atlanta Working Paper 2002-14, Federal Reserve Bank of Atlanta.
  18. 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.
  19. 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.
  20. Pesaran, M.H. & Schuermann, T. & Treutler, B-J. & Weiner, S.M., 2003. "Macroeconomic Dynamics and Credit Risk: A Global Perspective," Cambridge Working Papers in Economics 0330, Faculty of Economics, University of Cambridge.
  21. James H. Stock & Mark W. Watson, 1999. "Forecasting Inflation," NBER Working Papers 7023, National Bureau of Economic Research, Inc.
  22. 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.
  23. M. Hashem Pesaran & Til Schuermann & Björn-Jakob Treutler, 2005. "Global Business Cycles and Credit Risk," CESifo Working Paper Series 1548, CESifo Group Munich.
  24. M. Hashem Pesaran, 2004. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," CESifo Working Paper Series 1331, CESifo Group Munich.
  25. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
  26. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
  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. 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.
  29. 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.
  30. 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.
  31. Conley, T. G., 1999. "GMM estimation with cross sectional dependence," Journal of Econometrics, Elsevier, vol. 92(1), pages 1-45, September.
  32. 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.
  33. 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.
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  35. repec:cup:etheor:v:13:y:1997:i:6:p:877-88 is not listed on IDEAS
  36. 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.
  37. 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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