We establish methods that improve the predictions of macroeconometric models—dynamic factor models, dynamic stochastic general equilibrium models, and vector autoregressions—using a quarterly U.S. data set. We measure prediction quality with one-step-ahead probability densities assigned in real time. Two steps lead to substantial improvements: (a) the use of full Bayesian predictive distributions rather than conditioning on the posterior mode for parameters and (b) the use of an equally weighted pool.

The validity of the rational-expectations hypothesis as applied to prices in active auction markets has been extensively tested. Numerous investigators have analyzed an enormous amount of data using many different statistical techniques, and no serious departure from the predictions of the hypothesis has been found. Thus, there is very strong evidence in favor of the hypothesis. (Poole, 1976, p. 467)

The assumption that one of a set of prediction models is a literal description of reality formally underlies many formal econometric methods, including Bayesian model averaging and most approaches to model selection. Prediction pooling does not invoke this assumption and leads to predictions that improve on those based on Bayesian model averaging, as assessed by the log predictive score. The paper shows that the improvement is substantial using a pool consisting of a dynamic stochastic general equilibrium model, a vector autoregression, and a dynamic factor model, in conjunction with standard US postwar quarterly macroeconomic time series.

This article provides an exact Bayesian framework for analyzing the arbitrage pricing theory (APT). Based on the Gibbs sampler, we show how to obtain the exact posterior distributions for functions of interest in the factor model. In particular, we propose a measure of the APT pricing deviations and obtain its exact posterior distribution. Using monthly portfolio returns grouped by industry and market capitalization, we find that there is little improvement in reducing the pricing errors by including more factors beyond the first one.

Christoffersen, Jacobs, and Ornthanalai (2012) (CJO) propose an interesting and useful class of generalized autoregressive conditional heteroskedasticity (GARCH)-like models with dynamic jump intensity, and find evidence that the models not only fit returns data better than some commonly used benchmarks but also provide substantial improvements in option pricing performance. While such models pose difficulties for estimation and analysis, CJO propose an innovative approach to filtering intended to addresses them. However, some statistical issues arise that their approach leaves unresolved, with implications for the option pricing results. This note proposes a solution based on using the filter and estimator proposed by CJO but interpreted in the context of an alternative model. With respect to this model, the estimator is consistent, and likelihood-based model comparisons and hypothesis tests are valid.

This research compares several approaches to inference in the multinomial probit model, based on two Monte Carlo experiments for a seven choice model.The methods compared are the simulated maximum likelihood estimator using the GHK recursive probability,simulator, the method of simulated moments estimator using the GHK recursive simulator and kernel-smoothed frequency simulators, and posterior means using a Gibbs sampling-data augmentation algorithm.Overall, the Gibbs sampling algorithm has a slight edge, with the relative performance of MSM and SML based on the GHK simulator being difficult to evaluate.The MSM estimator with the kernel-smoothed frequency simulator is clearly inferior.I. Introduction T HE multinomial probit is an appealing model of choice behavior because it allows a flexible pattern of conditional covariance among the latent utilities of alternatives.Nevertheless, multinomial probit applications have been limited because the required integrations of the multivariate normal density over subsets of Euclidean space are computationally burdensome.The computational simplicity of the multinomial logit has made it the model of choice for applied work.However, because the multinomial probit model relaxes the assumption of independence of irrelevant alternatives, it is generally preferred in principle to the multinomial logit model (McFadden, 1984, pp.1395-1458).Recently the method of simulated moments (McFadden, 1989; Pakes and Pollard, 1989) and Gibbs sampling with data augmentation (Albert and Chib, 1993; McCulloch and Rossi, 1994) have shown promise of making the required computations in the multinomial probit model practical.The development of the highly accurate GHK probability simulator (see Geweke, 1991; Hajivassiliou and McFadden, 1990; and Keane, 1990, 1994a) has also led to renewed interest in simulated maximum likelihood (Albright, Lerman, and Manski, 1977) as a method for estimating multinomial probit models.The objective of the research reported here is to provide a systematic comparison of the numerical properties of different simulation-based methods of inference in the multinomial probit model.Rather than considering the performance of these methods on a single model for a single data set, we attempt to control for a number of features of the inference problem, such as the number and nature of the unknown parameters of interest and the information content of the data on which inference is based.Also, we investigate for the first time how the performance of MSM estimation is affected by the type of probability simulator employed (i.e., GHK vs. kernel smoothing).While some investigators have examined the performance of particular estimators and computational techniques, Borsch-Supan and Hajivassiliou (1993), Hajivassiliou (1992), and Hajivassiliou, McFadden, and Ruud (1992) have made systematic comparison of alternative probability simulators, we are aware of only one systematic comparison of different estimators per se: Keane (1994a) compares method of simulated moments and simulated maximum likelihood estimators for an eight period binomial probit model in a Monte Carlo study.This paper is the first to compare performance of alternative methods of inference for the multinomial probit model and the first to examine how the relative performance of alternative methods differs across model specifications and across different data sets.In addition to addressing this main objective, this work introduces a new factor structure for the disturbances that may help to alleviate the proliferation of covariance matrix parameter problems in MNP models.We also illustrate Bayesian inference in a multinomial probit model with a factor structure for the first time.(See Elrod and Keane (forthcoming) for a discussion of factor structures for probit models.)

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.

Methods for exact Bayesian inference under a uniform diffuse prior are set forth for the continuous time homogeneous Markov chain model. It is shown how the exact posterior distribution of any function of interest may be computed using Monte Carlo integration. The solution handles the problems of embeddability in a very natural way, and provides (to our knowledge) the only solution that systematically takes this problem into account. The methods are illustrated using several sets of data.

[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.]