Efficient Computation with Taste Shocks

Abstract

Taste shocks result in nondegenerate choice probabilities, smooth policy functions, continuous demand correspondences, and reduced computational errors. They also cause significant computational cost when the number of choices is large. However, I show that, in many economic models, a numerically equivalent approximation may be obtained extremely efficiently. If the objective function has increasing differences (a condition closely tied to policy function monotonicity) or is concave in a discrete sense, the proposed algorithms are O(n log n) for n states and n choice--a drastic improvement over the naive algorithm's O(n2) cost. If both hold, the cost can be further reduced to O(n). Additionally, with increasing differences in two state variables, I propose an algorithm that in some cases is O(n2) even without concavity (in contrast to the O(n3) naive algorithm). I illustrate the usefulness of the proposed approach in an incomplete markets economy and a long-term sovereign debt model, the latter requiring taste shocks for convergence. For grid sizes of 500 points, the algorithms are up to 200 times faster than the naive approach.