A Divide and Conquer Algorithm for Exploiting Policy Function Monotonicity

A divide-and-conquer algorithm for exploiting policy function monotonicity is proposed and analyzed. To compute a discrete problem with n states and n choices, the algorithm requires at most 5n + log2(n)n function evaluations and so is O(n log2 n). In contrast, existing methods for non-concave problems require n^2 evaluations in the worst-case and so are O(n^2). The algorithm holds great promise for discrete choice models where non-concavities naturally arise. In one such example, the sovereign default model of Arellano (2008), the algorithm is six times faster than the best existing method when n=100 and 50 times faster when n=1000. Moreover, if concavity is assumed, the algorithm combined with Heer and Maußner (2005)'s method requires fewer than 18n evaluations and so is O(n).