Jeffreys Prior Analysis of the Simultaneous Equations Model in the Case with n + 1 Endogenous Variables
This paper analyzes the behavior of posterior distributions under the Jeﬀreys prior in a simultaneous equations model. The case under study is that of a general limited information setup with n +1 endogenous variables. The Jeﬀreys prior is shown to give rise to a marginal posterior density which has Cauchy-like tails similar to that exhibited by the exact ﬁnite sample distribution of the corresponding LIML estimator. A stronger correspondence is established in the special case of a just-identiﬁed orthonormal canonical model, where the posterior density under the Jeﬀreys prior is shown to have the same functional form as the density of the ﬁnite sample distribution of the LIML estimator. The work here generalizes that of Chao and Phillips (1997), which gives analogous results for the special case of two endogenous variables.
Chao, John C. and Phillips, Peter C.B., "Jeffreys Prior Analysis of the Simultaneous Equations Model in the Case with n + 1 Endogenous Variables" (1998). Cowles Foundation Discussion Papers. 1446.