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Structural vector autoregressions: theory of identification and algorithms for inference

  • Juan F. Rubio-Ramírez
  • Daniel F. Waggoner
  • Tao Zha

Structural vector autoregressions (SVARs) are widely used for policy analysis and to provide stylized facts for dynamic general equilibrium models. Yet there have been no workable rank conditions to ascertain whether an SVAR is globally identified. When identifying restrictions such as long-run restrictions are imposed on impulse responses, there have been no efficient algorithms for small-sample estimation and inference. To fill these important gaps in the literature, this paper makes four contributions. First, we establish general rank conditions for global identification of both overidentified and exactly identified models. Second, we show that these conditions can be checked as a simple matrix-filling exercise and that they apply to a wide class of identifying restrictions, including linear and certain nonlinear restrictions. Third, we establish a very simple rank condition for exactly identified models that amounts to a straightforward counting exercise. Fourth, we develop a number of efficient algorithms for small-sample estimation and inference.

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Paper provided by Federal Reserve Bank of Atlanta in its series FRB Atlanta Working Paper with number 2008-18.

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Date of creation: 2008
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Handle: RePEc:fip:fedawp:2008-18
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  1. Gordon, David B & Leeper, Eric M, 1994. "The Dynamic Impacts of Monetary Policy: An Exercise in Tentative Identification," Journal of Political Economy, University of Chicago Press, vol. 102(6), pages 1228-47, December.
  2. Martin Eichenbaum & Charles L. Evans, 1995. "Some Empirical Evidence on the Effects of Shocks to Monetary Policy on Exchange Rates," The Quarterly Journal of Economics, Oxford University Press, vol. 110(4), pages 975-1009.
  3. Hsiao, Cheng, 2001. "Identification And Dichotomization Of Long- And Short-Run Relations Of Cointegrated Vector Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 17(05), pages 889-912, October.
  4. Fernandez-Villaverde, Jesus & Francisco Rubio-Ramirez, Juan, 2004. "Comparing dynamic equilibrium models to data: a Bayesian approach," Journal of Econometrics, Elsevier, vol. 123(1), pages 153-187, November.
  5. Sims, Christopher A & Zha, Tao, 1998. "Bayesian Methods for Dynamic Multivariate Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 949-68, November.
  6. Uhlig, H.F.H.V.S., 1999. "What are the Effects of Monetary Policy on Output? Results from an Agnostic Identification Procedure," Discussion Paper 1999-28, Tilburg University, Center for Economic Research.
  7. Eric M. Leeper & Tao Zha, 2003. "Modest policy interventions," FRB Atlanta Working Paper 2003-24, Federal Reserve Bank of Atlanta.
  8. Juan Francisco Rubio-Ramírez & Daniel F. Waggoner & Tao Zha, 2005. "Markov-switching structural vector autoregressions: theory and application," FRB Atlanta Working Paper 2005-27, Federal Reserve Bank of Atlanta.
  9. King, Robert G. & Plosser, Charles I. & Stock, James H. & Watson, Mark W., 1991. "Stochastic Trends and Economic Fluctuations," American Economic Review, American Economic Association, vol. 81(4), pages 819-40, September.
  10. Peersman, Gert & Smets, Frank, 2001. "The monetary transmission mechanism in the euro area: more evidence from VAR analysis," Working Paper Series 0091, European Central Bank.
  11. Harald Uhlig, 1997. "Bayesian Vector Autoregressions with Stochastic Volatility," Econometrica, Econometric Society, vol. 65(1), pages 59-74, January.
  12. James D. Hamilton & Daniel F. Waggoner & Tao Zha, 2007. "Normalization in Econometrics," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 221-252.
  13. Lawrence J. Christiano & Martin Eichenbaum & Charles Evans, 2001. "Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy," NBER Working Papers 8403, National Bureau of Economic Research, Inc.
  14. David O. Cushman & Tao Zha, 1995. "Identifying monetary policy in a small open economy under flexible exchange rates," FRB Atlanta Working Paper 95-7, Federal Reserve Bank of Atlanta.
  15. Pesavento, Elena & Rossi, Barbara, 2004. "Small Sample Confidence Intervals for Multivariate Impulse Response Functions at Long Horizons," CEPR Discussion Papers 4536, C.E.P.R. Discussion Papers.
  16. Hausman, Jerry A & Taylor, William E, 1983. "Identification in Linear Simultaneous Equations Models with Covariance Restrictions: An Instrumental Variables Interpretation," Econometrica, Econometric Society, vol. 51(5), pages 1527-49, September.
  17. Gali, J., 1996. "Technology, Employment, and the Business Cycle: Do Technology Shocks Explain Aggregate Fluctuations?," Working Papers 96-28, C.V. Starr Center for Applied Economics, New York University.
  18. Waggoner, Daniel F. & Zha, Tao, 2003. "Likelihood preserving normalization in multiple equation models," Journal of Econometrics, Elsevier, vol. 114(2), pages 329-347, June.
  19. Christopher A. Sims & Tao Zha, 1999. "Error Bands for Impulse Responses," Econometrica, Econometric Society, vol. 67(5), pages 1113-1156, September.
  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. Ben S. Bernanke & Ilian Mihov, 1998. "Measuring Monetary Policy," The Quarterly Journal of Economics, Oxford University Press, vol. 113(3), pages 869-902.
  22. Lawrence J. Christiano & Martin Eichenbaum & Charles Evans, 1994. "The effects of monetary policy shocks: evidence from the flow of funds," Proceedings, Federal Reserve Bank of Dallas, issue Apr.
  23. Lutz Kilian, 1998. "Small-Sample Confidence Intervals For Impulse Response Functions," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 218-230, May.
  24. Timothy Cogley & Thomas Sargent, . "Drifts and Volatilities: Monetary Policies and Outcomes in the Post WWII US," Working Papers 2133503, Department of Economics, W. P. Carey School of Business, Arizona State University.
  25. Bekker, Paul A. & Pollock, D. S. G., 1986. "Identification of linear stochastic models with covariance restrictions," Journal of Econometrics, Elsevier, vol. 31(2), pages 179-208, March.
  26. Sims, Christopher A. & Zha, Tao, 2006. "Does Monetary Policy Generate Recessions?," Macroeconomic Dynamics, Cambridge University Press, vol. 10(02), pages 231-272, April.
  27. Christopher A. Sims, 1986. "Are forecasting models usable for policy analysis?," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Win, pages 2-16.
  28. Thomas J. Sargent, 1975. "The observational equivalence of natural and unnatural rate theories of macroeconomics," Working Papers 48, Federal Reserve Bank of Minneapolis.
  29. Canova, Fabio & Nicolo, Gianni De, 2002. "Monetary disturbances matter for business fluctuations in the G-7," Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1131-1159, September.
  30. Blanchard, Olivier Jean & Quah, Danny, 1993. "The Dynamic Effects of Aggregate Demand and Supply Disturbances: Reply," American Economic Review, American Economic Association, vol. 83(3), pages 653-58, June.
  31. Canova, Fabio & Gambetti, Luca, 2006. "Structural Changes in the US Economy: Bad Luck or Bad Policy?," CEPR Discussion Papers 5457, C.E.P.R. Discussion Papers.
  32. Jon Faust, 1998. "The robustness of identified VAR conclusions about money," International Finance Discussion Papers 610, Board of Governors of the Federal Reserve System (U.S.).
  33. Benati, Luca & Mumtaz, Haroon, 2007. "U.S. evolving macroeconomic dynamics: a structural investigation," Working Paper Series 0746, European Central Bank.
  34. Atsushi Inoue & Lutz Kilian, 2000. "Bootstrapping Autoregressive Processes with Possible Unit Roots," Econometric Society World Congress 2000 Contributed Papers 0401, Econometric Society.
  35. Kim, Soyoung & Roubini, Nouriel, 2000. "Exchange rate anomalies in the industrial countries: A solution with a structural VAR approach," Journal of Monetary Economics, Elsevier, vol. 45(3), pages 561-586, June.
  36. Renee Fry & Adrian Pagan, 2007. "Some Issues in Using Sign Restrictions for Identifying Structural VARs," NCER Working Paper Series 14, National Centre for Econometric Research.
  37. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-91, May.
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