On the construction of bounds confidence regions

We modify the procedure for constructing exact bounds confidence regions introduced by Dufour (1990, Econometrica 58, 475-494) so as to drop the requirement that the confidence regions for the nuisance parameters are marginal with respect to the parameters of interest, i.e., that they are the same for all values of the parameters of interest. We illustrate this modified procedure with an application to a dependent variable heteroskedasticity model and, using a Monte Carlo study, compare the confidence regions constructed by this procedure with asymptotically justified regions.