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Empirical studies in Marketing have typically characterized a household's purchase incidence decision, i.e. the household's decision of whether or not to buy a product on a given shopping visit, as being independent of the household's purchase incidence decisions in other product categories. These decisions, however, tend to be related both because product categories serve as complements (e.g. bacon and eggs) or substitutes (e.g. colas and orange juices) in addressing the household's consumption needs, and because product categories vie with each other in attracting the household's limited shopping budget. Existing empirical studies have either ignored such inter-relationships altogether or have accounted for them in a limited way by modeling household purchases in pairs of complementary product categories. Given the recent availability of IRI market basket data, which tracks purchases of panelists in several product categories over time, and the new computational Bayesian methods developed in Albert and Chib (1993) and Chib and Greenberg (1998), estimating high-dimensional multi-category models is now possible. This paper exploits these developments to fit an appropriate panel data multivariate probit model to household-level contemporaneous purchases in twelve product categories, with the descriptive goal of isolating correlations amongst various product categories within the household's shopping basket. We provide an empirical scheme to endogenously determine the degree of complementarity and substitutability among product categories within a household's shopping basket, providing full details of the methodology. Our main findings are that existing purchase incidence models underestimate the magnitude of cross-category correlations and overestimate the effectiveness of the marketing mix, and that ignoring unobserved heterogeneity across households overestimates cross-category correlations and underestimate the effectiveness of the marketing mix.

In empirical research, panel (and multinomial) probit models are leading examples for the use of maximum simulated likelihood estimators. The Geweke–Hajivassiliou–Keane (GHK) simulator is the most widely used technique for this type of problem. This chapter suggests an algorithm that is based on GHK but uses an adaptive version of sparse-grids integration (SGI) instead of simulation. It is adaptive in the sense that it uses an automated change-of-variables to make the integration problem numerically better behaved along the lines of efficient importance sampling (EIS) and adaptive univariate quadrature. The resulting integral is approximated using SGI that generalizes Gaussian quadrature in a way such that the computational costs do not grow exponentially with the number of dimensions. Monte Carlo experiments show an impressive performance compared to the original GHK algorithm, especially in difficult cases such as models with high intertemporal correlations.

For over three decades, vector autoregressions have played a central role in empirical macroeconomics. These models are general, can capture sophisticated dynamic behavior, and can be extended to include features such as structural instability, time-varying parameters, dynamic factors, threshold-crossing behavior, and discrete outcomes. Building upon growing evidence that the assumption of linearity may be undesirable in modeling certain macroeconomic relationships, this article seeks to add to recent advances in VAR modeling by proposing a nonparametric dynamic model for multivariate time series. In this model, the problems of modeling and estimation are approached from a hierarchical Bayesian perspective. The article considers the issues of identification, estimation, and model comparison, enabling nonparametric VAR (or NPVAR) models to be fit efficiently by Markov chain Monte Carlo (MCMC) algorithms and compared to parametric and semiparametric alternatives by marginal likelihoods and Bayes factors. Among other benefits, the methodology allows for a more careful study of structural instability while guarding against the possibility of unaccounted nonlinearity in otherwise stable economic relationships. Extensions of the proposed nonparametric model to settings with heteroskedasticity and other important modeling features are also considered. The techniques are employed to study the postwar U.S. economy, confirming the presence of distinct volatility regimes and supporting the contention that certain nonlinear relationships in the data can remain undetected by standard models.

This chapter reviews graphical modeling techniques for estimating large covariance matrices and their inverse. The chapter provides a selective survey of different models and estimators proposed by the graphical modeling literature and offers some practical examples where these methods could be applied in the area of health economics.

This paper analyzes the effect of dental insurance on utilization of general dentist services by adult US population aged from 25 to 64 years using the ordered probit model with endogenous selection. Our econometric framework accommodates endogeneity of insurance and the ordered nature of the measure of dental utilization. The study finds strong evidence of endogeneity of dental insurance to utilization and identifies interesting patterns of nonlinear dependencies between the dental insurance status and individual's age and income. The calculated average treatment effect supports the claim of adverse selection into the treated (insured) state and indicates a strong positive incentives effect of dental insurance.

The latest financial crisis has stressed the need of understanding the world financial system as a network of interconnected institutions, where financial linkages play a fundamental role in the spread of systemic risks. In this paper we propose to enrich the topological perspective of network models with a more structured statistical framework, that of Bayesian Gaussian graphical models. From a statistical viewpoint, we propose a new class of hierarchical Bayesian graphical models that can split correlations between institutions into country specific and idiosyncratic ones, in a way that parallels the decomposition of returns in the well-known Capital Asset Pricing Model. From a financial economics viewpoint, we suggest a way to model systemic risk that can explicitly take into account frictions between different financial markets, particularly suited to study the ongoing banking union process in Europe. From a computational viewpoint, we develop a novel Markov chain Monte Carlo algorithm based on Bayes factor thresholding.

Heterogeneity in choice models is typically assumed to have a normal distribution in both Bayesian and classical setups. In this paper, we propose a semiparametric Bayesian framework for the analysis of random coefficients discrete choice models that can be applied to both individual as well as aggregate data. Heterogeneity is modeled using a Dirichlet process, which varies with consumers’ characteristics through covariates. We develop a Markov Chain Monte Carlo algorithm for fitting such model, and illustrate the methodology using two different datasets: a household-level panel dataset of peanut butter purchases, and supermarket chain-level data for 31 ready-to-eat breakfast cereal brands.

We consider a semiparametric panel stochastic frontier model where one-sided firm effects representing inefficiencies are correlated with the regressors. A form of the Chamberlain-Mundlak device is used to relate the logarithm of the effects to the regressors resulting in a lognormal distribution for the effects. The function describing the technology is modeled nonparametrically using penalized splines. Both Bayesian and non-Bayesian approaches to estimation are considered, with an emphasis on Bayesian estimation. A Monte Carlo experiment is used to investigate the consequences of ignoring correlation between the effects and the regressors, and choosing the wrong functional form for the technology.

This chapter proposes an approach toward the estimation of cross-sectional sample selection models, where the shocks on the units of observation feature some interdependence through spatial or network autocorrelation. In particular, this chapter improves on prior Bayesian work on this subject by proposing a modified approach toward sampling the multivariate-truncated, cross-sectionally dependent latent variable of the selection equation. This chapter outlines the model and implementation approach and provides simulation results documenting the better performance of the proposed approach relative to existing ones.