In this lecture we look at Bayesian inference. Although in the statistics literature explicitly Bayesian papers take up a large proportion of journal pages these days, Bayesian methods have had very little impact in economics. This seems to be largely for historial reasons. In many empirical settings in economics Bayesian methods appear statistically more

We investigate the relationship between living standards and fertility, using a three-wave panel dataset from Indonesia to provide information on women’s fertility histories and the levels of consumption expenditure in the households to which they belong. We adopt a Bayesian approach to estimation and exploit the dynamically recursive structure implied by gestation lags to identify causal effects of living standards on fertility and vice versa.

Appointments arranged by e-mail One year of mathematical statistics required First-year graduate theory, applied econometrics recommended

This paper develops new econometric methods to infer hospital quality in a model with discrete dependent variables and non-random selection. Mortality rates in patient discharge records are widely used to infer hospital quality. However, hospital admission is not random and some hospitals may attract patients with greater unobserved severity of illness than others. In this situation the assumption of random admission leads to spurious inference about hospital quality. This study controls for hospital selection using a model in which distance between the patient’s residence and alternative hospitals are key exogenous variables. Bayesian inference in this model is feasible using a Markov chain Monte Carlo posterior simulator, and attaches posterior probabilities to quality comparisons between individual hospitals and groups of hospitals. The study uses data on 74,848 Medicare patients admitted to 114 hospitals in Los Angeles County from 1989 through 1992 with a diagnosis of pneumonia. It finds the smallest and largest hospitals to be of high quality and public hospitals to be of low quality. There is strong evidence of dependence between the unobserved severity of illness and the assignment of patients to hospitals. Consequently a conventional probit model leads to inferences about quality markedly different than those in this study’s selection

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argues that the gain from eliminating aggregate fluctuations is trivial. Following Lucas, a number of researchers have altered assumptions on preferences and found that the gain from eliminating business cycles are potentially very large. However, in these exercises little discipline is placed on preference parameters. This paper estimates the welfare cost of business cycles, allowing for potential time-non-separabilities in preferences, where discipline is placed on the choice of preference parameters by requiring that the preferences be consistent with observed fluctuations in a model of business cycles. That is, a theoretical real business cycle world is constructed and the representative agent is then placed in this world. The agent responds optimally to exogenous shocks, given the frictions in the economy. The agent's preference parameters, along with other structural parameters, are estimated using a Bayesian procedure involving Markov Chain Monte Carlo methods. Two main results emerge from the paper. First, the form for the time-non-separability estimated in this paper is very different than the forms suggested and used elsewhere in the literature. Second, the welfare cost of business cycles is close to Lucas's estimate. 1

A density forecast of the realization of a random variable at some future time is an estimate of the probability distribution of the possible future values of that variable. This article presents a selective survey of applications of density forecasting in macroeconomics and finance, and discusses some issues concerning the production, presentation and evaluation of density forecasts. 1 The helpful comments and suggestions of Frank Diebold, Stewart Hodges and two anonymous referees are gratefully acknowledged. Responsibility for errors remains with the authors

This paper surveys recently developed approaches to analyzing panel data with nonlinear models. We summarize a number of results on estimation of fixed and random effects models in nonlinear modeling frameworks such as discrete choice, count data, duration, censored data, sample selection, stochastic frontier and, generally, models that are nonlinear both in parameters and variables. We show that notwithstanding their methodological shortcomings, fixed effects are much more practical than heretofore reflected in the literature. For random effects models, we develop an extension of a random parameters model that has been used extensively, but only in the discrete choice literature. This model subsumes the random effects model, but is far more flexible and general, and overcomes some of the familiar shortcomings of the simple additive random effects model as usually formulated. Once again, the range of applications is extended beyond the familiar discrete choice setting. Finally, we draw together several strands of applications of a model that has taken a semiparametric approach to individual heterogeneity in panel data, the latent class model. A fairly straightforward extension is suggested that should make this more widely useable by practitioners. Many of the underlying results already appear in the literature, but, once again, the range of applications is smaller than it could be.