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Likelihood-preserving normalization in multiple equation models

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  • Daniel F. Waggoner
  • Tao Zha

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.

Suggested Citation

  • Daniel F. Waggoner & Tao Zha, 2000. "Likelihood-preserving normalization in multiple equation models," FRB Atlanta Working Paper 2000-8, Federal Reserve Bank of Atlanta.
  • Handle: RePEc:fip:fedawp:2000-8
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    1. Uhlig, Harald, 2005. "What are the effects of monetary policy on output? Results from an agnostic identification procedure," Journal of Monetary Economics, Elsevier, vol. 52(2), pages 381-419, March.
    2. Christopher A. Sims, 1986. "Are forecasting models usable for policy analysis?," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 10(Win), pages 2-16.
    3. Waggoner, Daniel F. & Zha, Tao, 2003. "A Gibbs sampler for structural vector autoregressions," Journal of Economic Dynamics and Control, Elsevier, vol. 28(2), pages 349-366, November.
    4. Eric M. Leeper & Tao Zha, 2001. "Assessing simple policy rules: A view from a complete macroeconomic model," Economic Review, Federal Reserve Bank of Atlanta, vol. 86(Q4), pages 35-58.
    5. Christiano, Lawrence J. & Eichenbaum, Martin & Evans, Charles L., 1999. "Monetary policy shocks: What have we learned and to what end?," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 2, pages 65-148, Elsevier.
    6. Christopher A. Sims & Tao Zha, 1999. "Error Bands for Impulse Responses," Econometrica, Econometric Society, vol. 67(5), pages 1113-1156, September.
    7. William Poole, 1969. "Optimal choice of monetary policy instruments in a simple stochastic macro model," Special Studies Papers 2, Board of Governors of the Federal Reserve System (U.S.).
    8. Barro, Robert J, 1977. "Unanticipated Money Growth and Unemployment in the United States," American Economic Review, American Economic Association, vol. 67(2), pages 101-115, March.
    9. Ben S. Bernanke & Ilian Mihov, 1998. "Measuring Monetary Policy," The Quarterly Journal of Economics, Oxford University Press, vol. 113(3), pages 869-902.
    10. 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.
    11. Adrian R. Pagan & John C. Robertson, 1995. "Resolving the liquidity effect," Proceedings, Federal Reserve Bank of St. Louis, issue May, pages 33-54.
    12. 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.
    13. Nason, James M & Cogley, Timothy, 1994. "Testing the Implications of Long-Run Neutrality for Monetary Business Cycle Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 9(S), pages 37-70, Suppl. De.
    14. Lawrence J. Christiano & Martin Eichenbaum & Charles L. Evans, 2005. "Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy," Journal of Political Economy, University of Chicago Press, vol. 113(1), pages 1-45, February.
    15. J. B. Taylor & M. Woodford (ed.), 1999. "Handbook of Macroeconomics," Handbook of Macroeconomics, Elsevier, edition 1, volume 1, number 1, December.
    16. Aurélie Charles, 2012. "Introduction," Perspectives from Social Economics, in: Exchange Entitlement Mapping, pages 1-7, Palgrave Macmillan.
    17. 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.).
    18. 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.
    19. Geweke, John, 1996. "Monte carlo simulation and numerical integration," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 15, pages 731-800, Elsevier.
    20. 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 241-254, April.
    21. Sims, Christopher A. & Zha, Tao, 2006. "Does Monetary Policy Generate Recessions?," Macroeconomic Dynamics, Cambridge University Press, vol. 10(2), pages 231-272, April.
    22. 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 819-840, September.
    23. 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 949-968, November.
    24. James D. Hamilton & Daniel F. Waggoner & Tao Zha, 2007. "Normalization in Econometrics," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 221-252.
    25. William Poole, 1970. "Optimal Choice of Monetary Policy Instruments in a Simple Stochastic Macro Model," The Quarterly Journal of Economics, Oxford University Press, vol. 84(2), pages 197-216.
    26. Faust, Jon, 1998. "The robustness of identified VAR conclusions about money," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 49(1), pages 207-244, December.
    27. Warren Dent & John Geweke, 1980. "On Specification in Simultaneous Equation Models," NBER Chapters, in: Evaluation of Econometric Models, pages 169-196, National Bureau of Economic Research, Inc.
    28. Lieberman, Charles, 1979. "Structural and Technological Change in Money Demand," American Economic Review, American Economic Association, vol. 69(2), pages 324-329, May.
    29. 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.
    30. Wilson, Charles A, 1979. "Equilibrium and Adverse Selection," American Economic Review, American Economic Association, vol. 69(2), pages 313-317, May.
    31. James Tobin, 1970. "Money and Income: Post Hoc Ergo Propter Hoc?," The Quarterly Journal of Economics, Oxford University Press, vol. 84(2), pages 301-317.
    32. Daniel F. Waggoner & Tao Zha, 1997. "Normalization, probability distribution, and impulse responses," FRB Atlanta Working Paper 97-11, Federal Reserve Bank of Atlanta.
    33. Eric M. Leeper, 1995. "Reducing our ignorance about monetary policy effects," Economic Review, Federal Reserve Bank of Atlanta, vol. 80(Jul), pages 1-38.
    34. Jan Kmenta & James B. Ramsey, 1980. "Evaluation of Econometric Models," NBER Books, National Bureau of Economic Research, Inc, number kmen80-1, December.
    35. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1.
    36. Zha, Tao, 1999. "Block recursion and structural vector autoregressions," Journal of Econometrics, Elsevier, vol. 90(2), pages 291-316, June.
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    Keywords

    time series analysis; Supply and demand; Demand for money; Money supply;
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