A decision theoretic analysis of the unit root hypothesis using mixtures of elliptical models

This paper develops a formal decision theoretic approach to testing for a unit root in economic time series. The approach is empirically implemented by specifying a loss function based on predictive variances; models are chosen so as to minimize expected loss. In addition, the paper broadens the class of likelihood functions traditionally considered in the Bayesian unit root literature by: i) Allowing for departures from normality via the specification of a likelihood based on general elliptical densities; ii) allowing for structural breaks to occur; iii) allowing for moving average errors; and iv) using mixtures of various submodels to create a very flexible overall likelihood. Empirical results indicate that, while the posterior probability of trend-stationarity is quite high for most of the series considered, the unit root model is often selected in the decision theoretic analysis

Alternative efficiency measures for multiple-output production

This paper has two main purposes. Firstly, we develop various ways of defining efficiency in the case of multiple-output production. Our framework extends a previous model by allowing for nonseparability of inputs and outputs. We also specifically consider the case where some of the outputs are undesirable, such as pollutants. We investigate how these efficiency definitions relate to one another and to other approaches proposed in the literature. Secondly, we examine the behavior of these definitions in two examples of practically relevant size and complexity. One of these involves banking and the other agricultural data. Our main findings can be summarized as follows. For a given efficiency definition, efficiency rankings are found to be informative, despite the considerable uncertainty in the inference on efficiencies. It is, however, important for the researcher to select an efficiency concept appropriate to the particular issue under study, since different efficiency definitions can lead to quite different conclusions

Posterior analysis of stochastic frontier models using Gibbs sampling

In this paper we describe the use of Gibbs sampling methods for making posterior inferences in stochastic frontier models with composed error. We show how the Gibbs sampler can greatly reduce the computational difficulties involved in analyzing such models. Our fidings are illustrated in an empirical example

Posterior inference on long-run impulse responses

This paper describes a Bayesian analysis of impulse response functions. We show how many common priors imply that posterior densities for impulse responses at long horizons have no moments. Our results suggest that impulse responses should be assessed on the basis of their full posterior densities, and that standard estimates such as posterior means, variances or modes may be very misleading

Bayesian long-run prediction in time series models

This paper considers Bayesian long-run prediction in time series models. We allow time series to exhibit stationary or non-stationary behavior and show how differences between prior structures which have little effect on posterior inferences can have a large effect in a prediction exercise. In particular, the Jeffreys' prior given in Phillips (1991) is seen to prevent the existence of one-period ahead predictive moments. A Bayesian counterpart is provided to Sampson (1991) who takes parameter uncertainty into account in a classical framework. An empirical example illustrates our results

Bayesian efficiency analysis with a flexible cost function

In this paper we describe the use of Gibbs sampling methods for drawing posterior inferences in a model with an asymptotically ideal price aggregator, non-constant returns to scale and composed error. An empirical example illustrates the sensitivity of efficiency measures to assumptions made about the functional form of the frontier

Bayesian long-run prediction in time series models.

This paper considers Bayesian long-run prediction in time series models. We allow time series to exhibit stationary or non-stationary behavior and show how differences between prior structures which have little effect on posterior inferences can have a large effect in a prediction exercise. In particular, the Jeffreys' prior given in Phillips (1991) is seen to prevent the existence of one-period ahead predictive moments. A Bayesian counterpart is provided to Sampson (1991) who takes parameter uncertainty into account in a classical framework. An empirical example illustrates our results.Forecasting; Predictive moments; Unit root; Parameter uncertainty;

Posterior inference on long-run impulse responses.

This paper describes a Bayesian analysis of impulse response functions. We show how many common priors imply that posterior densities for impulse responses at long horizons have no moments. Our results suggest that impulse responses should be assessed on the basis of their full posterior densities, and that standard estimates such as posterior means, variances or modes may be very misleading.Persistence of shocks; Prior sensitivity; ARIMA models; Invertibility; Existence of moments;

Stochastic frontier models: a bayesian perspective

A Bayesian approach to estimation, prediction and model comparison in composed error production models is presented. A broad range of distributions on the inefficiency term define the contending models, which can either be treated separately or pooled. Posterior results are derived for the individual efficiencies as well as for the parameters, and the differences with the usual sampling-theory approach are highlighted. The required numerical integrations are handled by Monte Carlo methods with Importance Sampling, and an empirical example illustrates the procedures

Stochastic frontier models: a bayesian perspective.

A Bayesian approach to estimation, prediction and model comparison in composed error production models is presented. A broad range of distributions on the inefficiency term define the contending models, which can either be treated separately or pooled. Posterior results are derived for the individual efficiencies as well as for the parameters, and the differences with the usual sampling-theory approach are highlighted. The required numerical integrations are handled by Monte Carlo methods with Importance Sampling, and an empirical example illustrates the procedures.Efficiency; Composed error models; Production frontier; Prior elicitation;