A Generalization of Hall's Specification of the Consumption function

This paper deals with optimal consumption over time. The starting point is a dynamic utility function which is exponential where the exponent is quadratic in the observable consumption outlays. The approach is shown to be a generalization of Hall's formulation of the consumption relation. While Hall's structural form of consumption is independent of the income process, we show that this no longer holds. On the contrary, parameters of the income process are shown to affect the parameters of the consumption process in an essential way. The paper also argues for a stochastic maximum principle. In addition to generating the optimal current decisions, this principle produces simultaneously optimal estimates of the future values of the decision variables. This interplay of optimization and prediction is interesting. The paper terminates with statistical testing procedures which compare the testing of hypotheses deduced by Hall with testing of those derived in the present paper.