Bounded variance priors in simultaneous equations: Theory and applications to the political economy of nontariff barriers to trade

In Chapter 1, bounds for the posterior mean vector of structural parameters in a simultaneous equations model are determined in a limited information setting under the two assumptions that the prior location of the parameters is given but that their prior covariance matrix V is (i) free, and (ii) bounded above and below. The aim of the paper is to reduce the cost and effort required to specify the prior covariances of structural and reduced form parameters with precision. For this reason, upper and lower bounds of the mapping from a range of priors into posteriors are determined. Computation of these robust bounds is done in two stages. In the first stage, the structural parameter bounds are determined conditionally on the prior covariance matrix of the vector of reduced form parameters. In the second stage the unconditional bounds are determined as a computational solution to a constrained nonlinear programming problem.;In Chapter 2 this theory is applied to the computation of extreme bounds for a simultaneous model of the joint determination of the level of import penetration and the level of trade protection through nontariff barrier to trade. A cross-sectional study of the U.S. in 1983, the limited information analysis of the nontariff barrier equation reveals that import penetration net of exports is probably the single most significant determinant of the level of protection through nontariff barriers in U.S. manufacturing. The validity of some theories of political economy are also investigated. The Special Interest theory of protection is validated in the case of Price-oriented nontariff barriers, while the Status Quo model is more relevant in the formation of quotas. The results highlight the difference between the extreme bounds which are based on the sample and prior information and the commonly reported two-stage least-squares estimates for simultaneous equations, which have only a large-sample justification.