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Federal Reserve Bank of Atlanta
FRB Atlanta Working Paper
Likelihood-preserving normalization in multiple equation models
Daniel F. Waggoner
Tao Zha

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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Daniel F. Waggoner & Tao Zha, Likelihood-preserving normalization in multiple equation models, Federal Reserve Bank of Atlanta, FRB Atlanta Working Paper 2000-8, 2000.
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Keywords: Time-series analysis ; Supply and demand ; Demand for money ; Money supply
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