Experimental designs in triangular simultaneous equations models

Optimal experimental designs are considered for models with simultaneous equations. In particular, a model with two equations is assumed where one of the explanatory variables (exogenous) of the first equation is then the response variable (endogenous) of the second equation. In both equations there is a control variable, which is being designed through the celebrated D-optimality criterion. This work is based on a more restricted approach using just the first equation and assuming the distribution of the exogenous/endogenous variable completely known. Then a conditionally restricted optimal design was computed afterwards. In this paper the conditional model is assumed partially known but it has to be fitted as well. Although both approaches identify different prior knowledge a comparison of the optimal designs for both approaches is made. Since the model is not linear in the usual sense the optimal designs will depend on the parameters and a sensitivity analysis against its choice is performed. Copyright Springer-Verlag Berlin Heidelberg 2015