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Likelihood-preserving normalization in multiple equation models

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Author Info
Daniel F. Waggoner
Tao Zha

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Abstract

Causal analysis in multiple equation models often revolves around the evaluation of the effects of an exogenous shift in a structural equation. When taking into account the uncertainty implied by the shape of the likelihood, we argue that how normalization is implemented matters for inferential conclusions around the maximum likelihood (ML) estimates of such effects. We develop a general method that eliminates the distortion of finite-sample inferences about these ML estimates after normalization. We show that our likelihood-preserving normalization always maintains coherent economic interpretations while an arbitrary implementation of normalization can lead to ill-determined inferential results.

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Paper provided by Federal Reserve Bank of Atlanta in its series Working Paper with number 2000-8.

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Date of creation: 2000
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Handle: RePEc:fip:fedawp:2000-8

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Keywords: Time-series analysis Supply and demand Demand for money Money supply

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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  3. Tobin, James, 1970. "Money and Income: Post Hoc Ergo Propter Hoc?," The Quarterly Journal of Economics, MIT Press, vol. 84(2), pages 301-17, May. [Downloadable!] (restricted)
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  4. Christopher A. Sims, 1986. "Are forecasting models usable for policy analysis?," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Win, pages 2-16. [Downloadable!]
  5. Robert G. King & Charles I. Plosser & James H. Stock & Mark W. Watson, 1991. "Stochastic trends and economic fluctuations," Working Paper Series, Macroeconomic Issues 91-4, Federal Reserve Bank of Chicago.
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  6. Sargent, Thomas J & Wallace, Neil, 1975. ""Rational" Expectations, the Optimal Monetary Instrument, and the Optimal Money Supply Rule," Journal of Political Economy, University of Chicago Press, vol. 83(2), pages 241-54, April. [Downloadable!] (restricted)
  7. Leeper, Eric M. & Gordon, David B., 1992. "In search of the liquidity effect," Journal of Monetary Economics, Elsevier, vol. 29(3), pages 341-369, June. [Downloadable!] (restricted)
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  8. Cushman, David O. & Zha, Tao, 1997. "Identifying monetary policy in a small open economy under flexible exchange rates," Journal of Monetary Economics, Elsevier, vol. 39(3), pages 433-448, August. [Downloadable!] (restricted)
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  9. Christopher A. Sims & Tao Zha, 1999. "Error Bands for Impulse Responses," Econometrica, Econometric Society, vol. 67(5), pages 1113-1156, September.
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  10. Lawrence J. Christiano & Martin Eichenbaum & Charles L. Evans, 1998. "Monetary Policy Shocks: What Have We Learned and to What End?," NBER Working Papers 6400, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  11. William Poole, 1970. "Optimal choice of monetary policy instruments in a simple stochastic macro model," Staff Studies 57, Board of Governors of the Federal Reserve System (U.S.).
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  12. Adrian R. Pagan & John C. Robertson, 1995. "Resolving the liquidity effect," Proceedings, Federal Reserve Bank of St. Louis, issue May, pages 33-54. [Downloadable!]
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  13. Barro, Robert J, 1977. "Unanticipated Money Growth and Unemployment in the United States," American Economic Review, American Economic Association, vol. 67(2), pages 101-15, March.
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  14. Stiglitz, Joseph E & Weiss, Andrew, 1981. "Credit Rationing in Markets with Imperfect Information," American Economic Review, American Economic Association, vol. 71(3), pages 393-410, June. [Downloadable!] (restricted)
  15. John Geweke, 1995. "Monte Carlo simulation and numerical integration," Staff Report 192, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  16. Nason, J.M. & Cogley, T., 1994. "Testing the Implications of Long Run Neutrality for Monetary Business Cycle Models," UBC Departmental Archives 94-26, UBC Department of Economics.
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  17. 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.
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  18. Zha, Tao, 1999. "Block recursion and structural vector autoregressions," Journal of Econometrics, Elsevier, vol. 90(2), pages 291-316, June. [Downloadable!] (restricted)
  19. 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(1996-2), pages 1-78. [Downloadable!]
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. John Keating, 2004. "Interpreting Permanent and Transitory Shocks to Output When Aggregate Demand May Not Be Neutral in the Long-run," Econometric Society 2004 North American Summer Meetings 608, Econometric Society. [Downloadable!]
  2. Villani, Mattias & Warne, Anders, 2003. "Monetary Policy Analysis in a Small Open Economy using Bayesian Cointegrated Structural VARs," Working Paper Series 156, Sveriges Riksbank (Central Bank of Sweden). [Downloadable!]
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  3. Christopher A. Sims & Daniel F. Waggoner & Tao Zha, 2006. "Methods for inference in large multiple-equation Markov-switching models," Working Paper 2006-22, Federal Reserve Bank of Atlanta. [Downloadable!]
  4. Christopher A. Sims & Tao Zha, 2006. "Were There Regime Switches in U.S. Monetary Policy?," American Economic Review, American Economic Association, vol. 96(1), pages 54-81, March. [Downloadable!] (restricted)
    Other versions:
  5. Penelope A. Smith & Peter M. Summers, 2004. "Identification and normalization in Markov switching models of "business cycles"," Research Working Paper RWP 04-09, Federal Reserve Bank of Kansas City. [Downloadable!]
  6. James D. Hamilton & Daniel F. Waggoner & Tao Zha, 2004. "Normalization in econometrics," Working Paper 2004-13, Federal Reserve Bank of Atlanta. [Downloadable!]
    Other versions:
  7. Cyriac Guillaumin, 2007. "(A)symétrie et convergence des chocs macroéconomiques en Asie de l'Est: une analyse dynamique," Post-Print hal-00192626_v1, HAL. [Downloadable!]
  8. Adolfson, Malin & Andersson, Michael K. & Lindé, Jesper & Villani, Mattias & Vredin, Anders, 2005. "Modern Forecasting Models in Action: Improving Macroeconomic Analyses at Central Banks," Working Paper Series 188, Sveriges Riksbank (Central Bank of Sweden), revised 01 Jun 2006. [Downloadable!]
    Other versions:
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