Robust Control: A Note on the Response of the Control to Changes in the ?Free? Parameter Conditional on the Character of Nature

Abstract

In this paper an analytical framework similar to a robust control problem was developed for the one-state, one-control variable model to examine the response of the control to changes in the "free" parameter. However, in contrast to Gonzalez and Rodriguez (2003), the sign multiplying the "free" parameter in the criterion function of the min-max problem is positive. We find that this set up corresponds to the case where nature is benevolent while the problem posed by Gonzalez and Rodriguez (2003) corresponds to a malevolent nature. We show that for the benevolent case, the solution is a minimum giving way to an ordinary control problem. In addition, the left side of the discontinuity in Gonzalez and Rodriguez (2003) corresponds to the benevolent case.

Optimal Policy Response with Control Parameter and Intercept Covariance

“…Following the general methodology of Mercado and Kendrick (2000), Gonzalez and Rodriguez (2004) and Rodriguez (2004), I use the feedback matrices to characterize the policy maker's optimal response to changes in each of three covariance components: standard deviation of the control parameter, correlation coefficient and standard deviation of the intercept. The advantage of using an analytical model comes at the cost of reducing the number of control and state variables to one.…”