Multigrid techniques in economics

I present a self-contained introduction to multigrid methods with an emphasis on techniques relevant to dynamic programming and related problems. A probabilistic interpretation of the numerical principles is highlighted. Multigrid solvers are shown to be naturally matched to the challenges posed by intractable structural dynamic models routinely encountered in applied economics. I argue that multigrid techniques have potential to substantially extend the scale and complexity of models under consideration. Multigrid also provides a unified computational framework to extend model solvers to perform sensitivity analysis, calibration, estimation, and counterfactual policy experiments.