Optimal designs subject to cost constraints in simultaneous equations models
A procedure based on a multiplicative algorithm for computing optimal experimental designs subject to cost constraints in simultaneous equations models is presented. A convex criterion function based on a usual criterion function and an appropriate cost function is considered. A specific L-optimal design problem and a numerical example are taken from Conlisk (J Econ 11:63¿76, 1979) to compare the procedure. The problem would need integer nonlinear programming to obtain exact designs. To avoid this, he solves a continuous nonlinear programming problem and then he rounds off the number of replicates of each experiment. The procedure provided in this paper reduces dramatically the computational efforts in computing optimal approximate designs. It is based on a specific formulation of the asymptotic covariance matrix of the full-information maximum likelihood estimators, which simplifies the calculations. The design obtained for estimating the structural parameters of the numerical example by this procedure is not only easier to compute, but also more efficient than the design provided by Conlisk.