Monte Carlo simulation methods are widely used to analyze a wide range of econometric models involving integrals for which no analytical solutions exist. The objective of this project is integrating within a unified framework the two major Monte Carlo integration techniques currently available to econometricians: Efficient Importance Sampling (EIS) and Markov Chain Monte Carlo (MCMC). There are several important reasons for doing so. First, none of these two methods dominate the other for all purposes. Actually, they are highly complementary to one another. Loosely speaking EIS is very effective for the numerical integration of high-dimensional latent processes, which are increasingly key components of modern econometric models (examples are stochastic volatility in financial series and unobserved heterogeneity in panels) all situations for which there exist natural sequential factorizations which EIS fully exploits. On the other hand MCMC is at its best when such factorizations are not trivially available, e.g. when dealing with posterior densities of the parameters of highly non-linear models. Secondly, and even more fundamentally, both methods critically rely upon efficient samplers for their low-dimensional (typically univariate) components. EIS relies upon individual "efficient" importance samplers. MCMC, which requires exact draws from the individual component distributions relies upon Metropolis-Hastings (MH). The two methods are very closely related. The common criticism that the Monte Carlo variance of an EIS estimate might not exist also applies to MH.
Broader Impacts: This proposal will develop and disseminate new tools for econometric analysis. More specifically, the investigator will provide detailed templates for the construction of efficient mixed EIS-MCMC procedures taking full advantage of the comparative advantages of both methods. The project will develop a fully integrated and flexible toolbox for the construction of efficient individual EIS and MH samplers. Specifically, the investigator will show that by the application of a simple EIS auxiliary technique he can fully automate the selection of optimized MH samplers.These auxiliary EIS techniques are currently fully operational for distributions from the exponential family, in which case they amount to trivial auxiliary OLS regressions. The investigator will extend the technique beyond that class by using techniques inspired from the pseudo Maximum Likelihood and non-parametric literatures. The project will provide operational diagnostic tests for the validation of these component samplers. All technical papers, source codes, documentation, applications, and datasets related to this proposal will be made available through a website dedicated to the proposal.
