A NOTE ON UNcER'rAIN'lms iN CONTROL APPLICATI ONS

Walsh and Cruz [10] have tackled an interesting subject in applying the Kalman filter technique to a constrained optimization problem in macroeconomics, using as the constraint system the familiar linear inacroeconometric model estimated by Pindyck [61. The motivation for using a Kalman filter is that, unlike the deter-ministic control applications which Pindyck [6, 7] or I [2, 3] presented, the Walsh-Cruz application includes a wide variety of uncertainties. En addition to following the procedure of Kendrick and Majors [5] for taking account of stochastic parameters of the constraint system (i.e., the macroeconometric model), the problem addressed by Walsh and Cruz includes (1) additive distur-bances (i.e., pure noise) in the system equations, (2) errors of measurement of both the state variables and the system parameters, and (3) uncertain initial conditions. In using their Kalman filter procedure in the macroeconomic application, however, Walsh and Cruz treated these uncertainties in a way which is inconsis-tent with the underlying raison d'etre of stochastic optimization in economics. I