We introduce an envelope condition method (ECM) for solving dynamic programming problems. The ECM method is simple to implement, dominates conventional value function iteration and is comparable in accuracy and cost to Carroll’s (2005) endogenous grid method. Codes are available.

Numerical methods for dynamic programming often use value function iteration and interpolation. We present a novel shape-preserving rational spline approximation method that improves value function iteration in terms of both stability and accuracy compared to more common methods.