Envelope Condition Method versus Endogenous Grid Method for Solving Dynamic Programming Problems

We introduce an envelope condition method (ECM) for solving dynamic programming problems. ECM iterates on the Bellman equation forward and is much faster than conventional value function methods that iterate backward. In the studied examples, ECM is comparable in accuracy and cost to Carroll's (2005) endogenous grid method (EGM). We also construct versions of the EGM and ECM methods that approximate derivatives of value function instead of value function itself. We demonstrate that ECM is tractable in problems with high dimensionality: in one example, we solve a multicountry model of international trade with up to 16 state variables