Preliminary and Incomplete Risk and Robustness in General Equilibrium

A ‘robust decision maker’ suspects that his model is misspecified and makes decisions that work well over a restricted range of specification errors around a base or ‘reference’ model. In the context of a discrete time linear-quadratic permanent income model, Hansen, Sargent and Tallarini (1997) (HST) used a single parameter – taken from a version of Jacobson and Whittle’s ‘risk-sensitivity’ correction – to index the class of relevant model misspecifications from which the decision maker seeks protection. In that setting, HST showed how robust decision making would generate behavior that looks like risk aversion. HST calculated how much ‘preference for robustness’ – interpreted as a form of aversion to a particular kind of Knightian uncertainty – it takes to put ‘market prices of risk’ into empirically plausible regions. This paper extends the analysis of HST to economies with equilibrium allocations that solve continuous time optimal resource allocation problems. Most of our results exploit the analytical convenience of continuous-time diffusions. Working in continuous time lets us leave the confines of a linear-quadratic framework: objective functions can be nonquadratic and state evolution equations can be nonlinear. Leaving the linearquadratic framework makes it easier to link our robustness parameter to commonly used measures of risk aversion both in decision problems and in security market data. It also