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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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  1. Forni, Mario & Lippi, Marco, 2000. "The Generalized Dynamic Factor Model: Representation Theory," CEPR Discussion Papers 2509, C.E.P.R. Discussion Papers.
  2. Pesaran, Hashem & Chudik, Alexander, 2010. "Econometric analysis of high dimensional VARs featuring a dominant unit," Working Paper Series 1194, European Central Bank.
  3. 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.
  4. Stock, James H. & Watson, Mark W., 1999. "Forecasting inflation," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 293-335, October.
  5. Domenico Giannone & Lucrezia Reichlin & Luca Sala, 2005. "Monetary Policy in Real Time," Working Papers 284, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    • 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.
  6. Pesaran, M. Hashem & Tosetti, Elisa, 2007. "Large Panels with Common Factors and Spatial Correlations," IZA Discussion Papers 3032, Institute for the Study of Labor (IZA).
  7. 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.
  8. 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.
  9. M. Hashem Pesaran & Til Schuermann & Bjorn-Jakob Treutler, 2007. "Global Business Cycles and Credit Risk," NBER Chapters, in: The Risks of Financial Institutions, pages 419-474 National Bureau of Economic Research, Inc.
  10. 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.
  11. 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.
  12. Huberman, Gur, 1982. "A simple approach to arbitrage pricing theory," Journal of Economic Theory, Elsevier, vol. 28(1), pages 183-191, October.
  13. 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, pages C45-C90, 02.
  14. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 1999. "The Generalized Dynamic Factor Model: Identification and Estimation," CEPR Discussion Papers 2338, C.E.P.R. Discussion Papers.
  15. 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.
  16. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
  17. De Mol, Christine & Giannone, Domenico & Reichlin, Lucrezia, 2008. "Forecasting using a large number of predictors: Is Bayesian shrinkage a valid alternative to principal components?," Journal of Econometrics, Elsevier, vol. 146(2), pages 318-328, October.
  18. 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.
  19. 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.
  20. 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.
  21. Pesaran, M.H. & Smith, R., 2006. "Macroeconometric Modelling with a Global Perspective," Cambridge Working Papers in Economics 0604, Faculty of Economics, University of Cambridge.
  22. Conley, T. G., 1999. "GMM estimation with cross sectional dependence," Journal of Econometrics, Elsevier, vol. 92(1), pages 1-45, September.
  23. 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.
  24. 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.
  25. 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.
  26. Marco Del Negro & Frank Schorfheide, 2002. "Priors from general equilibrium models for VARs," Working Paper 2002-14, Federal Reserve Bank of Atlanta.
  27. repec:cup:etheor:v:13:y:1997:i:6:p:877-88 is not listed on IDEAS
  28. 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.
  29. 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.
  30. Garratt, Anthony & Lee, Kevin & Pesaran, M. Hashem & Shin, Yongcheol, 2006. "Global and National Macroeconometric Modelling: A Long-Run Structural Approach," OUP Catalogue, Oxford University Press, number 9780199296859, March.
  31. M. Hashem Pesaran, 2006. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," Econometrica, Econometric Society, vol. 74(4), pages 967-1012, 07.
  32. 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.
  33. Raffaella Giacomini & Halbert White, 2003. "Tests of Conditional Predictive Ability," Econometrics 0308001, EconWPA.
  34. Stephen Bond & Asli Leblebicioglu, 2004. "Capital Accumulation and Growth: A New Look at the Empirical Evidence," Economics Series Working Papers 2004-W08, University of Oxford, Department of Economics.
  35. 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.
  36. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
  37. Holly, Sean & Pesaran, M. Hashem & Yamagata, Takashi, 2006. "A Spatio-Temporal Model of House Prices in the US," IZA Discussion Papers 2338, Institute for the Study of Labor (IZA).
  38. 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.
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