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Bayesian Econometrics is a volume in the series Advances in Econometrics that illustrates the scope and diversity of modern Bayesian econometric applications, reviews some recent advances in Bayesian econometrics, and highlights many of the characteristics of Bayesian inference and computations. This first paper in the volume is the Editors’ introduction in which we summarize the contributions of each of the papers.

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.

Hypothesis tests for dominance in income distributions has received considerable attention in recent literature. See, for example, Barrett and Donald (2003a, b), Davidson and Duclos (2000) and references therein. Such tests are useful for assessing progress towards eliminating poverty and for evaluating the effectiveness of various policy initiatives directed towards welfare improvement. To date the focus in the literature has been on sampling theory tests. Such tests can be set up in various ways, with dominance as the null or alternative hypothesis, and with dominance in either direction (X dominates Y or Y dominates X). The result of a test is expressed as rejection of, or failure to reject, a null hypothesis. In this paper, we develop and apply Bayesian methods of inference to problems of Lorenz and stochastic dominance. The result from a comparison of two income distributions is reported in terms of the posterior probabilities for each of the three possible outcomes: (a) X dominates Y, (b) Y dominates X, and (c) neither X nor Y is dominant. Reporting results about uncertain outcomes in terms of probabilities has the advantage of being more informative than a simple reject/do-not-reject outcome. Whether a probability is sufficiently high or low for a policy maker to take a particular action is then a decision for that policy maker.

The methodology is applied to data for Canada from the Family Expenditure Survey for the years 1978 and 1986. We assess the likelihood of dominance from one time period to the next. Two alternative assumptions are made about the income distributions – Dagum and Singh-Maddala – and in each case the posterior probability of dominance is given by the proportion of times a relevant parameter inequality is satisfied by the posterior observations generated by Markov chain Monte Carlo.

Time-varying proportions arise frequently in economics. Market shares show the relative importance of firms in a market. Labor economists divide populations into different labor market segments. Expenditure shares describe how consumers and firms allocate total expenditure to various categories. We introduce a state space model where unobserved states are Gaussian and observations are conditionally Dirichlet. Markov chain Monte Carlo techniques allow inference for unknown parameters and states. We draw states as a block using a multivariate Gaussian proposal distribution based on a quadratic approximation of the log conditional density of states given parameters and data. Repeated draws from the proposal distribution are particularly efficient. We illustrate using automobile production data.

In this paper, we expand Kleibergen and Zivot's (2003) Bayesian two-stage (B2S) model by allowing for unequal variances. Our choice for modeling heteroscedasticity is a fully Bayesian parametric approach. As an application, we present a cross-country Cobb–Douglas production function estimation.