Methods for the systematic application of Monte Carlo integration with importance sampling to Bayesian inference are developed. Conditions under which the numerical approximation converges almost surely to the true value with the number of Monte Carlo replications, and its numerical accuracy may be assessed reliably, are given. Importance sampling densities are derived from multivariate normal or student approximations to the posterior density. These densities are modified by automatic rescaling along each axis. The concept of relative numerical efficiency is introduced to evaluate the adequacy of a chosen importance sampling density. Applications in two illustrative models are presented.

[Structural and stochastic neutrality have refutable implications for aggregate economic time series only in conjunction with other maintained hypotheses. Simple and commonly employed maintained hypotheses lead to restrictions on measures of feedback and their decomposition by frequency. These restrictions also suggest an empirical interpretation of the notional long and short runs. It is found that a century of annual U.S. data, and postwar monthly data, consistently support structural superneutrality of money with respect to output and the real rate of return and consistently reject its superneutrality with respect to velocity. A quantitative characterization of the long run is suggested.]

In this paper the concept of approximate slope, introduced by R. R. Bahadur, is used to make asymptotic global power comparisons of econometric tests. The approximate slope of a test is the rate at which the logarithm of the asymptotic marginal significance level of the test decreases as sample size increases, under a given alternative. A test with greater approximate slope may therefore be expected to reject the null hypothesis more frequently under that alternative than one with smaller approximate slope. Two theorems, which facilitate the computation and interpretation of the approximate slopes of most econometric tests, are established. These results are used to undertake some illustrative comparisons. Sampling experiments and an empirical illustration suggest that the comparison of approximate slopes may provide an adequate basis for evaluating the actual performance of alternative tests of the same hypothesis.

[The regression relation between regularly sampled Y(t) and X"19t),..., X"N(t) implied by an underlying model in which time enters more generally is studied. The underlying model includes continuous distributed lags, discrete models, and stochastic differential equations as special cases. The relation between parameters identified by regular samplings of Y and X"j and those of the underlying model is characterized. Sufficient conditions for identification of the underlying model in the limit as disaggregation over time proceeds are set forth. Empirical evidence presented suggests that important gains can be realized from temporal disaggregation in the range of conventional measurement frequencies for macroeconomic data.]

We show by counterexample that Proposition 2 in Fernández-Villaverde, Rubio-Ramírez, and Santos (Econometrica (2006), 74, 93–119) is false. We also show that even if their Proposition 2 were corrected, it would be irrelevant for parameter estimates. As a more constructive contribution, we consider the effects of approximation error on parameter estimation, and conclude that second order approximation errors in the policy function have at most second order effects on parameter estimates.

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.

[The axiomatic derivation of mobility indices for first-order Markov chain models in discrete time is extended to continuous-time models. Many of the logical inconsistencies among axioms noted in the literature for the discrete time models do not arise for continuous time models. It is shown how mobility indices in continuous time Markov chains may be estimated from observations at two points in time. Specific attention is given to the case in which the states are fractiles, and an empirical example is presented.]