A General Endogenous Grid Method for Multi-Dimensional Models with Non-Convexities and Constraints

The endogenous grid method (EGM) significantly speeds up the solution of stochastic dynamic programming problems by simplifying or completely eliminating rootfinding. We propose a general and parsimonious EGM extended to handle 1) multiple continuous states and choices, 2) multiple occasionally binding constraints, and 3) non-convexities such as discrete choices. Our method enjoys the speed gains of the original one-dimensional EGM, while avoiding expensive interpolation on multi-dimensional irregular endogenous grids. We explicitly define a broad class of models for which our solution method is applicable, and illustrate its speed and accuracy using a consumption-saving model with both liquid assets and illiquid pension assets and a discrete retirement choice.