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Likelihood-preserving normalization in multiple equation models

Author

Listed:
  • 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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    Keywords

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