Solving models with jump discontinuities in policy functions

We show that the Value Function Iteration (VFI) algorithm has difficulties approximating models with jump discontinuities in policy functions. We find that VFI fails to accurately identify both the location and size of jump discontinuities while the Endogenous Grid Method (EGM) and the Finite Element Method (FEM) are much better at approximating this class of models. We further show that combining value function iteration with a local interpolation step (VFI-INT) is sufficient to obtain accurate approximations. Differences between policy functions generated by VFI and these alternative methods are economically significant. We highlight that these differences across methods cannot be identified using Euler equation errors as these are not a sufficient measure of accuracy for models with jump discontinuities in policy functions. As a result, speed comparisons across methods that rely on Euler equation errors as a measure for accuracy can be misleading. The combination of computational speed, relatively easy implementation and adaptability make VFI-INT especially suitable for approximating models with jump discontinuities in policy functions.