Bayesian Simultaneous Equations Analysis using Reduced Rank Structures

Frank Kleibergen and Herman van Dijk

No EI 9714/A, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

Abstract: Diffuse priors lead to pathological posterior behavior when used in Bayesian analyses of Simultaneous Equation Models (SEMs). This results from the local nonidentification of certain parameters in SEMs. When this, a priori known, feature is not captured appropriately, an a posteriori favor for certain specific parameter values results which is not the consequence of strong data information but of local nonidentification. We show that a proper consistent Bayesian analysis of a SEM explicitly has to consider the reduced form of the SEM as a standard linear model on which nonlinear (reduced rank) restrictions are imposed, which result from a singular value decomposition. The priors/posteriors of the parameters of the SEM are therefore proportional to the priors/posteriors of the parameters of the linear model under the condition that the restrictions hold. This leads to a framework for constructing priors and posteriors for the parameters of SEMs. The framework is used to construct priors and posteriors for one, two and three structural equation SEMs. These examples jointly with a theorem, which states that the reduced forms of SEMs accord with sets of reduced rank restrictions on standard linear models, show how Bayesian analyses of generally specified SEMs are conducted.

Keywords: Bayesian simultaneous equations analysis; simultaneous equation models (search for similar items in EconPapers)
Date: 1997-01-01
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Citations: View citations in EconPapers (2)

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Related works:
Journal Article: BAYESIAN SIMULTANEOUS EQUATIONS ANALYSIS USING REDUCED RANK STRUCTURES (1998)
Working Paper: Bayesian Simultaneous Equations Analysis using Reduced Rank Structures (1998)
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