Bayesian Simultaneous Equations Analysis using Reduced Rank Structures
AbstractDiffuse 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.
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Bibliographic InfoPaper provided by Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute in its series Econometric Institute Research Papers with number EI 9714/A.
Date of creation: 01 Jan 1997
Date of revision:
Bayesian simultaneous equations analysis; simultaneous equation models;
Other versions of this item:
- Kleibergen, Frank & van Dijk, Herman K., 1998. "Bayesian Simultaneous Equations Analysis Using Reduced Rank Structures," Econometric Theory, Cambridge University Press, vol. 14(06), pages 701-743, December.
- Frank Kleibergen & Herman K. van Dijk, 1998. "Bayesian Simultaneous Equations Analysis using Reduced Rank Structures," Tinbergen Institute Discussion Papers 98-025/4, Tinbergen Institute.
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