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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.

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Bibliographic Info

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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  2. Eric M. Leeper & David B. Gordon, 1991. "In search of the liquidity effect," Working Paper 91-17, Federal Reserve Bank of Atlanta.
  3. Daniel F. Waggoner & Tao Zha, 1997. "Normalization, probability distribution, and impulse responses," Working Paper 97-11, Federal Reserve Bank of Atlanta.
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  21. James D. Hamilton & Daniel F. Waggoner & Tao Zha, 2007. "Normalization in Econometrics," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 221-252.
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