Bayesian Simultaneous Equations Analysis Using Reduced Rank Structures
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.
(This abstract was borrowed from another version of this item.)
Volume (Year): 14 (1998)
Issue (Month): 06 (December)
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References listed on IDEAS
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- Maddala, G S, 1976. "Weak Priors and Sharp Posteriors in Simultaneous Equation Models," Econometrica, Econometric Society, vol. 44(2), pages 345-351, March.
- Geweke, John, 1996.
"Bayesian reduced rank regression in econometrics,"
Journal of Econometrics,
Elsevier, vol. 75(1), pages 121-146, November.
- John F. Geweke, 1995. "Bayesian reduced rank regression in econometrics," Working Papers 540, Federal Reserve Bank of Minneapolis.
- Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
- Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, vol. 46(1), pages 1-19, January.
- Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(02), pages 181-240, August.
- Peter C.B. Phillips, 1987. "Partially Identified Econometric Models," Cowles Foundation Discussion Papers 845R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1988.
- Richard, J. -F. & Tompa, H., 1980. "On the evaluation of poly-t density functions," Journal of Econometrics, Elsevier, vol. 12(3), pages 335-351, April.
- RICHARD, Jean-François & TOMPA, Hans, "undated". "On the evaluation of poly-t density functions," CORE Discussion Papers RP 395, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Kleibergen, Frank & van Dijk, Herman K., 1994. "On the Shape of the Likelihood/Posterior in Cointegration Models," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 514-551, August.
- Roberts, G. O. & Smith, A. F. M., 1994. "Simple conditions for the convergence of the Gibbs sampler and Metropolis-Hastings algorithms," Stochastic Processes and their Applications, Elsevier, vol. 49(2), pages 207-216, February. Full references (including those not matched with items on IDEAS)
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