Approach Paths to the Steady State: A Performance Test of Current Period Decision Rule Solution Methods for Models of Renewable Resource Management

Abstract

This paper compares the perfor- mance of approximately optimal current period analytical solution methods for models of re- newable resource management. Focus is placed on linear-quadratic analytical dynamic pro- gramming and on steady-state based current period decision rules based on Taylor's series approximation of the value function. These are compared against an intertemporal decision rule used with backward induction in the context of a discrete-time stylized model of the Northern Anchovy Fishery of California. Decision rules based on Taylor's series track the optimal ap- proach path very well with social surplus less than one percent below the optimum surplus. In comparison, the linear-quadratic formulation failed to track the optimal path as well, with social surplus of more than seven percent below the optimum. These results are interesting in light of the common conviction that approximat- ing the value function with a Taylor's series is not appropriate for discrete-time renewable re- source modeling.