This paper studies the use of the Jeffreys prior in Bayesian analysis of the simultaneous equations model (SEM). Exact representations are obtained for the posterior density of the structural coefficient β in canonical SEMs with two endogenous variables. For the general case with m endogenous variables and an unknown covariance matrix, the Laplace approximation is used to derive an analytic formula for the same posterior density.
Posterior Distributions in Limited Information Analysis of the Simultaneous Equations Model Using the Jeffreys PriorJ.C. Chao and P. C. B. Phillips ,
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Journal of Econometrics
Posterior Distributions in Limited Information Analysis of the Simultaneous Equations Model Using the Jeffreys Prior