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

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

Dynamic Panel Probit Models for Current Account Reversals and their Efficient Estimation

We use panel probit models with unobserved heterogeneity and serially correlated errors in order to analyze the determinants and the dynamics of current-account reversals for a panel of developing and emerging countries. The likelihood evaluation of these models requires high-dimensional integration for which we use a generic procedure known as Efficient Importance Sampling (EIS). Our empirical results suggest that current account balance, terms of trades, foreign reserves and concessional debt are important determinants of the probability of current-account reversal. Furthermore we find under all specifications evidence for serially correlated error components and weak evidence for state dependence. --Panel data,Dynamic discrete choice,Current account reversals,Importance Sampling,Monte Carlo integration,State dependence

Determinants and dynamics of current account reversals: an empirical analysis

We use panel probit models with unobserved heterogeneity, state-dependence and serially correlated errors in order to analyze the determinants and the dynamics of current-account reversals for a panel of developing and emerging countries. The likelihood-based inference of these models requires high-dimensional integration for which we use Efficient Importance Sampling (EIS). Our results suggest that current account balance, terms of trades, foreign reserves and concessional debt are important determinants of current-account reversal. Furthermore, we find strong evidence for serial dependence in the occurrence of reversals. While the likelihood criterion suggest that state-dependence and serially correlated errors are essentially observationally equivalent, measures of predictive performance provide support for the hypothesis that the serial dependence is mainly due to serially correlated country-specific shocks related to local political or macroeconomic events. --Panel data,dynamic discrete choice,importance sampling,Monte Carlo integration,state dependence,spillover effects

An Efficient Filtering Approach to Likelihood Approximation for State-Space Representations

We develop a numerical filtering procedure that facilitates efficient likelihood evaluation in applications involving non-linear and non-gaussian state-space models. The procedure approximates necessary integrals using continuous or piecewise-continuous approximations of target densities. Construction is achieved via efficient importance sampling, and approximating densities are adapted to fully incorporate current information. --particle filter,adaption,efficient importance sampling,kernel density approximation

Dynamic invariant multinomial probit model: identification, pretesting and estimation

"We present a new specification for the multinomial multiperiod Probit model with autocorrelated errors. In sharp contrast with commonly used specifications, ours is invariant with respect to the choice of a baseline alternative for utility differencing. It also nests these standard models as special cases, allowing for data based selection of the baseline alternatives for the latter. Likelihood evaluation is achieved under an Efficient Importance Sampling (EIS) version of the standard GHK algorithm. Several simulation experiments highlight identification, estimation and pretesting within the new class of multinomial multiperiod Probit models." [author's abstract