Computing Densities: A Conditional Monte Carlo Estimator

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The authors propose a generalized conditional Monte Carlo technique for computing densities in economic models. Global consistency and functional asymptotic normality are established under ergodicity assumptions on the simulated process. The asymptotic normality result allows them to characterize the asymptotic distribution of the error in density space, and implies faster convergence than nonparametric kernel density estimators. They show that the results nest several other well-known density estimators, and illustrate potential applications. The Monte Carlo method is routinely used by economists and econometricians to extract information on probabilities from their models. In some cases, the random variables of interest have distributions that can be described by densities, and the researcher seeks to recover, via simulation, an approximation to these densities.