The Effect of Uncertainty on Optimal Control Models in the Neighbourhood of a Steady State

For both discrete and continuous time this paper derives the Taylor approximation to the effect of uncertainty (in the simple sense of risk, not Knightian uncertainty) on expected utility and optimal behaviour in stochastic control models when the uncertainty is small enough that one can focus on only the first term that involves uncertainty. There is a close and illuminating relationship between the discrete-time and continuous-time results. The analysis makes it possible to spell out a tight connection between the behaviour of a dynamic stochastic general equilibrium model and the corresponding perfect foresight model. However, the quantitative analytics of the stochastic model local to a certainty model calls for a more thorough investigation of the nearby certainty model than is typically undertaken.”