Robust and Risk-Neutral Optimization with Linear Dynamic Perfect Foresight Models : A Field Manual

This paper outlines several optimization techniques useful for deriving optimal monetary and fiscal policy rules in linear dynamic perfect foresight models. Two broad categories, differing in the treatment of risk, are presented. The first group comprises certainty-equivalent optimization, based on risk neutrality, and includes closed-loop optimal control, time-consistent dynamic programming, and restricted open-loop optimization. The techniques in this category are appropriate when the underlying model's specification is true. The second group, which is receiving growing attention by economists, addresses model uncertainty and falls under the heading of risksensitive or robust optimization. The two types of robust control treated here are (1) minimum entropy and (2) disturbance attennuation, better known as H-infinity-control. Robust techniques are applicable when the underlying model is viewed as no more than an approximation to a true but unknown model. Several illustrative examples are presented, based on calculations using MATLAB software especially developed or adapted for this purpose. The examples include fiscal policy in a multiplier-accelerator model by Caravani (1995), an MCI rule for an open-economy model by Ball (1998), and an interest rate rule for a closed-economy model by Tetlow and von zur Muehlen (1998). The calculations suggest that, compared with certainty equivalent rules, optimal risk-sensitive policies lead neither to attenuation of feedback nor to increased auto-regressivity of the control variable (interest rate smoothing in the case of monetary policy). The effects of discounting is to attenuate feedback responses in certainty-equivalent policies, but for robust control, the outcome is model dependent