On robust estimation in certainty equivalence control

Abstract

There are increasing indications that residuals of econometric models (uni-relational as well as systems) often present distributional characteristics different from those of normal distributions. The residuals are then preferably assumed to be distributed according to some non-normal symmetric stable distribution, and estimation based onL1 -norm is often found to be better than least squares estimation in such cases. The analysis of the relative properties of these two estimation approaches is, however, so far mainly given in the framework of structural analysis and prediction. In this paper the L1 -norm and least squares estimators are compared in cases where the ultimate purpose of econometric modelling is economic policy planning, i.e. when the estimated econometric model will be the basic restnetion in optimal control. The control strategy here applied is certainty equivalence control, and the structural model is a multiple regression model with regressors being instruments as well as purely exogenous variables. The analysis of relative estimation properties is based on simulations, and basically done for short control period lengths. The L1 -norm based control śtrategy is found to be more robust against heavy-tailed residual distributions, although least squares estimation will be more easily accepted, if allowing the first instrumental variable values to be chosen from wider intervals. When observed residuals are especially extreme, both estimation approaches will hardly display acceptable qualities.