Risk Sensitivity, Adjustment of Control and Estimation

Abstract

Risk sensitivity of optimal control rules in a dynamic model is a generic term for all types of responses to various shocks due to errors and uncertainties. The economic agent’s response is to build elements of caution into his objective function e.g., the mean-variance approach in dynamic portfolio theory. The statistician’s response to random shocks is to model the dynamic system such that the sample estimates of the random parameters are robust in some sense i.e. less sensitive to random fluctuations in equational errors. Two other situations are most important in applied economic models. One arises in dynamic or differential games, where one player’s optimal control rules depend among other things on the control rules or strategies adopted by the other player or players. Mutual consistency of control or decision rules is thus an essential prerequisite e.g., Cournot-Nash equilibrium solutions explicitly allow for such mutual consistency. To estimate the optimal decision rule for each player in such a framework, one has to postulate the side condition specifying the second player’s reaction function. Thus the method of maximizing the likelihood function subject to each player’s reaction functions has to be adopted in the estimation process. Adjustment costs play a key role here. Finally, the economic agents tend to learn over time, when the observed data on the state variables become sequentially available, this learning process also exhibits a cautious risk attitude, which is strongly emphasized in current developments in control theory.