Some aspects of bivariate regression subject to linear constraints

This paper considers a two-equation linear model when a subset of the parameters in one of the equations is subject to zero constraints. Inference procedures are presented both in the Bayesian and sampling theory framework. Specifically, posterior distributions and confidence distributions of the parameters, as well as various test procedures, are derived and illustrated with examples. The effect of the zero constraints on these procedures are discussed, and a comparison of the Bayesian with the sampling results is given.