Improving MCMC Using Efficient Importance Sampling

This paper develops a systematic Markov Chain Monte Carlo (MCMC) framework based upon Efficient Importance Sampling (EIS) which can be used for the analysis of a wide range of econometric models involving integrals without an analytical solution. EIS is a simple, generic and yet accurate Monte-Carlo integration procedure based on sampling densities which are chosen to be global approximations to the integrand. By embedding EIS within MCMC procedures based on Metropolis-Hastings (MH) one can significantly improve their numerical properties, essentially by providing a fully automated selection of critical MCMC components such as auxiliary sampling densities, normalizing constants and starting values. The potential of this integrated MCMC- EIS approach is illustrated with simple univariate integration problems and with the Bayesian posterior analysis of stochastic volatility models and stationary autoregressive processes. --Autoregressive models,Bayesian posterior analysis,Dynamic latent variables,Gibbs sampling,Metropolis Hastings,Stochastic volatility

The Multinomial Multiperiod Probit Model: Identification and Efficient Estimation

In this paper we discuss parameter identification and likelihood evaluation for multinomial multiperiod Probit models. It is shown in particular that the standard autoregressive specification used in the literature can be interpreted as a latent common factor model. However, this specification is not invariant with respect to the selection of the baseline category. Hence, we propose an alternative specification which is invariant with respect to such a selection and identifies coefficients characterizing the stationary covariance matrix which are not identified in the standard approach. For likelihood evaluation requiring high-dimensional truncated integration we propose to use a generic procedure known as Efficient Importance Sampling (EIS). A special case of our proposed EIS algorithm is the standard GHK probability simulator. To illustrate the relative performance of both procedures we perform a set Monte-Carlo experiments. Our results indicate substantial numerical e?ciency gains of the ML estimates based on GHK-EIS relative to ML estimates obtained by using GHK. --Discrete choice,Importance sampling,Monte-Carlo integration,Panel data,Parameter identification,Simulated maximum likelihood

Classical and Bayesian Analysis of Univariate and Multivariate Stochastic Volatility Models

In this paper Efficient Importance Sampling (EIS) is used to perform a classical and Bayesian analysis of univariate and multivariate Stochastic Volatility (SV) models for financial return series. EIS provides a highly generic and very accurate procedure for the Monte Carlo (MC) evaluation of high-dimensional interdependent integrals. It can be used to carry out ML-estimation of SV models as well as simulation smoothing where the latent volatilities are sampled at once. Based on this EIS simulation smoother a Bayesian Markov Chain Monte Carlo (MCMC) posterior analysis of the parameters of SV models can be performed. --Dynamic Latent Variables,Markov Chain Monte Carlo,Maximum likelihood,Simulation Smoother

Conférence François-Albert Angers (1999). Enchères : théorie économique et réalité

Cet article présente une synthèse de travaux relatifs aux modèles empiriques de la théorie des jeux. Les principaux sujets abordés sont : modèles structurels, identification, solutions d’équilibre, résolution par simulation de Monte-Carlo, estimation et applications.This article presents a synthesis of contributions relative to empirical game theoretic models. The main topics which are discussed are: structural models, identification, equilibrium solutions, resolution by Monte-Carlo simulation, estimation and applications

Dynamic Factor Models for Multivariate Count Data: An Application to Stock-Market Trading Activity

We propose a dynamic factor model for the analysis of multivariate time series count data. Our model allows for idiosyncratic as well as common serially correlated latent factors in order to account for potentially complex dynamic interdependence between series of counts. The model is estimated under alternative count distributions (Poisson and negative binomial). Maximum Likelihood estimation requires high-dimensional numerical integration in order to marginalize the joint distribution with respect to the unobserved dynamic factors. We rely upon the Monte-Carlo integration procedure known as Efficient Importance Sampling which produces fast and numerically accurate estimates of the likelihood function. The model is applied to time series data consisting of numbers of trades in 5 minutes intervals for five NYSE stocks from two industrial sectors. The estimated model accounts for all key dynamic and distributional features of the data. We find strong evidence of a common factor which we interpret as reflecting market-wide news. In contrast, sector-specific factors are found to be statistically insignifficant. --Dynamic latent variables,Importance sampling,Mixture of distribution models,Poisson distribution,Simulated Maximum Likelihood

Tax interaction dynamics among Belgian municipalities, 1984-1997

The purpose of this paper is to test econometrically the existence of fiscal interactions between Belgian municipalities. At the time of writing, the motivation was to provide scientific support to the lively debate on fiscal competition that took place among Belgian politicians in the late nineties. Two types of taxes are considered, for which Belgian municipalities have the decision power as to rates : the “centimes additionnels” on the personal income tax and the “précompte immobilier” which is a property tax. A dynamic adjustment model is specified and estimated using panel data for 598 municipalities over 15 years. The empirical results obtained bear upon two main points : (i) Some interaction definitely has prevailed between the municipalities’ fiscal choices made during the observation period, for both taxes; (ii) However, the adjustment reactions to the other municipalities’ fiscal choices have occured over time at the very low yearly pace of 6% and 10% respectively, of the discrepancy between the actual rates and the preferred rates.

The COBRAS/SAMBA CMB Project

COBRAS/SAMBA is a second generation satelitte dedicated to mapping at high resolution and sensitivity the anisotropies of the Cosmic Microwave Background (CMB). This mission is in the assessment study phase (A) at ESA, with a decision expected mid 1996, for a launch around 2003.Comment: PostScript, 4 pages, 4 figures in text, to appear in the Proceedings of the 1995 Moriond Meeting on ``Clustering in the Universe'