One-node Quadrature Beats Monte Carlo: A Generalized Stochastic Simulation Algorithm
In conventional stochastic simulation algorithms, Monte Carlo integration and curve fitting are merged together and implemented by means of regression. We perform a decomposition of the solution error and show that regression does a good job in curve fitting but a poor job in integration, which leads to low accuracy of solutions. We propose a generalized notion of stochastic simulation approach in which integration and curve fitting are separated. We specifically allow for the use of deterministic (quadrature and monomial) integration methods which are more accurate than the conventional Monte Carlo method. We achieve accuracy of solutions that is orders of magnitude higher than that of the conventional stochastic simulation algorithms.
Lilia Maliar and Serguei Maliar acknowledge support from the Hoover Institution at Stanford University, the Ivie, the Ministerio de Ciencia e Innovación and FEDER funds under the project SEJ-2007-62656. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.
Kenneth L. Judd, Lilia Maliar and Serguei Maliar, (2011). “Numerically Stable and Accurate Stochastic Simulation Methods for Solving Dynamic Models" and "Supplement", Quantitative Economics 2, 173-210.