Bayesian Inference in Econometric Models Using Monte Carlo Integration

Abstract

BAYESIAN INFERENCE IN ECONOMETRIC MODELS USING MONTE CARLO INTEGRATION BY JOHN GEWEKE1 Methods for the systematic application of Monte Carlo integration with importance sampling to Bayesian inference in econometric models are developed. Conditions under which the numerical approximation of a posterior moment converges almost surely to the true value as the number of Monte Carlo replications increases, and the numerical accuracy of this approximation may be assessed reliably, are set forth. Methods for the analytical verification of these conditions are discussed. Importance sampling densities are derived from multivariate normal or Student t approximations to local behavior of the posterior density at its mode. These densities are modified by automatic rescaling along each axis. The concept of relative numerical efficiency is introduced to evaluate the adequacy of a chosen importance sampling density. The practical procedures based on these innovations are illustrated in two different models.

Short-Term Borrowing for Long-Term Projects: Are Family Businesses More Susceptible to 'Irrational' Financing Choices?

“…It can be evaluated numerically through simulation techniques. We employ the Maximum Simulated Likelihood Method using the GHK simulator (Geweke 1989, Hajivassiliou and McFadden 1998, and Keane 1994; see also Train 2009) that is implemented in the user-written command cmp in Stata to estimate the multivariate probit model (see Roodman 2009). Table 12 in the Appendix depicts the differences in marginal effects between the single probit and the 7-equation multivariate probit estimates for our two main variables of interest.…”

Systemic Risk Diagnostics: Coincident Indicators and Early Warning Signals

“…is numerically efficient, see Kloek and van Dijk (1978), Geweke (1989) and Durbin and Koopman (2001).…”

Échantillonnage de Gibbs et autres applications économétriques des chaînes markoviennes

“…Notons aussi que la faisabilité de cette approche n'est pas affectée par la dimension de z s'il est possible de tirer des aléas de la loi p(z). Geweke (1989) montre comment l'analyste peut évaluer la précision de cet estimateur afin de choisir N.…”

“…Geweke (1989) note que la convergence est plus rapide si /(G) est de forme similaire à p(<d\x) et si I(Q)>p(Q\x) pour les valeurs extrêmes de 0. Pour les modèles complexes, il est parfois très difficile d'identifier une fonction d'importance efficace.…”