A Scrambled Method of Moments

TL;DR

This paper investigates the use of scrambled Quasi-Monte Carlo methods in simulation-based estimation, demonstrating their advantages in reducing noise and improving accuracy in various settings, including cross-sections, panels, and time series.

Contribution

It introduces a novel application of Owen's scramble in the Method of Moments and proposes algorithms to address dimensionality issues in time series estimation.

Findings

Scrambled methods reduce simulation noise in cross-section and panel data.

New algorithms effectively handle high-dimensional time series estimation.

Finite sample simulations show improved accuracy with scrambled Quasi-Monte Carlo methods.

Abstract

Quasi-Monte Carlo (qMC) methods are a powerful alternative to classical Monte-Carlo (MC) integration. Under certain conditions, they can approximate the desired integral at a faster rate than the usual Central Limit Theorem, resulting in more accurate estimates. This paper explores these methods in a simulation-based estimation setting with an emphasis on the scramble of Owen (1995). For cross-sections and short-panels, the resulting Scrambled Method of Moments simply replaces the random number generator with the scramble (available in most softwares) to reduce simulation noise. Scrambled Indirect Inference estimation is also considered. For time series, qMC may not apply directly because of a curse of dimensionality on the time dimension. A simple algorithm and a class of moments which circumvent this issue are described. Asymptotic results are given for each algorithm. Monte-Carlo examples illustrate these results in finite samples, including an income process with "lots of heterogeneity."