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This paper develops new econometric methods to infer hospital quality in a model with discrete dependent variables and nonrandom 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 the highest quality. There is strong evidence of dependence between the unobserved severity of illness and the assignment of patients to hospitals, whereby patients with a high unobserved severity of illness are disproportionately admitted to high quality hospitals. Consequently a conventional probit model leads to inferences about quality that are markedly different from those in this study's selection model. KEYWORDS: Bayesian inference, hospital quality, simultaneous equations, MCMC, Medicare, pneumonia, mortality.

Inference modeled on the likelihood principle remains the same regardless of the data generated by a unit root process or by a stationary process. The asymptotic posterior normality is acquired in a linear time series model with unit roots. Moreover, the Bayesian statistical decision theory can be generalized in terms of possible nonstationarity based on the criterion for asymptotic posterior normality.

A one-agent Bayesian model of learning by doing and technological choice is analyzed. The model is based on the premise that technology use provides learning which improves decision making and productivity while productivity growth is dependent on the continuous shift to better technologies. The ability to transfer previously acquired knowledge to new activities is also determined by similarities between the new and old activities.

While technically p-values should not be interpreted as probabilities, they often are, and their usual asymptotic equivalence to Bayesian posterior tail probabilities provides an approximate justification for doing so. In inference about possibly nonstationary dynamic models the usual asymptotic equivalence fails, however. We show with three-dimensional graphs how it is possible that in autoregressive models the distribution of the estimator is skewed asymptotically, while the likelihood and hence the posterior pdf remains symmetric. We show that no single prior can rationalize treating p-values as probabilities in these models, and we display examples of the sample-dependent 'priors' that would do so. We argue that these results imply at a minimum that the usual test statistics and covariance matrices for autoregressions, which characterize the likelihood shape in dynamic models just as in static regression models, should be reported without any corrections for the special unit root distribution theory, even if the corrected classical p-values are reported as well.

A Bayesian analysis of the linear regression model with only parts of the prior distribution specified or a robust Bayesian analysis lead to sets of posterior distributions. The so-called feasible ellipsoid of Leamer (1978) describes the region of posterior means if for conjugate priors the prior covariance matrix is varying in the set of symmetric positive-definite matrices. As an extension to Bayesian confidence sets (HPD regions, i.e. regions of highest posterior probability) we introduce the concept of HiFi (high fiduciary) regions. The HiFi region is a union of HPD regions, and is a tool for describing the dependence of the posterior distribution on the prior covariance. In this paper we assume that the prior covariance matrix varies in an interval of positive definite matrices.