Optimal Control of General Equilibrium Models: Discussion

Computable general equilibrium (CGE) models are rapidly becoming a dominant methodology in the economic analysis of developing countries and some developed economies. The value of optimal control approaches depends on the relative importance of dynamic equilibrium paths versus static equilibria in these models. Decaluw6 and Martens survey the characteristics of fifty-six applications of CGE models to national economies; forty-five of these applications have been published in the past five years, showing the rapid development of the method. Decaluw6 and Martens classify 51% (29) of these as containing some dynamic relationships. Most of the models derive their dynamic properties from systematic changes in factor endowments and parameters rather than intertemporal objective functions. Given the large proportion of CGE models that are dynamic, the advantages of calculating the optimal control path are substantial if a meaningful objective function and control costs can be specified. Given the size and problems of convergence of static CGE models, the absence of control applications is probably due to perceived computational difficulties rather than the absence of dynamic variables. Technical progress, changing factor endowments, capital formation, and changes in the labor force all point to dynamic rather than static solutions. Derpanopoulos, in his paper, shows how one method of optimal control solution, the successive approximation method, can be combined with an iterative solution of the intraperiod general equilibrium. The results of this innovative paper are more encouraging for the iterative solution of intraperiod equilibria than for the interperiod dynamic paths from optimal control. This paper discusses why Derpanopoulos's control results may be unduly pessimistic for the linear quadratic solution, and suggests alternative control approaches that may be applied to CGE models. Tailoring the control solution procedure to the CGE model characteristics may lead to more encouraging results from controlling what is essentially a dynamic system. Derpanopoulos's paper combines the linearized updating of general equilibrium models originated by Johansen with the successive linear approximation (Kendrick) approach to solving nonlinear control models. As is noted in the paper, the analytical control solution that results from the linearization is easily computed, even for large models. This adva tage makes the successive approximation approach promising for dynamic general equilibrium solutions. Three questions are raised by Derpanopoulos's analysis. First to what extent are the linear quadratic controls suboptimal when subject to binding inequality constraints on states and controls? Second, si ce the linear gain matrix determines the expected change in states over a period, what i accuracies are introduced by decoupling the gain matrix and the updating of the linearized parameters that enter into the gain matrix? Third, are the empirical solution difficulties with unstable controls reported by Derpanopoulos a general result of this approach or an empirical problem induced by the parameters used in the analysis? Constraints on policy variables for general equilibrium models such as government invest ent, tariffs, and exchange rates are intuitive. The recursive solution of the Riccatti equation, however, assumes that controls can be set at any positive or negative level. Modification of control when constraints are encountered still leads to suboptimality, since the backward recursive solution implies that the policy actions prior to the binding constraint are nonoptimal. The inequality constraint problem has been Richard E. Howitt is a professor, Department of Agricultural Economics, University of California, Davis.