Mark F. J. Steel

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.

Order-Based Dependent Dirichlet Processes

In this article we propose a new framework for Bayesian nonparametric modeling with continuous covariates. In particular, we allow the nonparametric distribution to depend on covariates through ordering the random variables building the weights in the stick-breaking representation. We focus mostly on the class of random distributions that induces a Dirichlet process at each covariate value. We derive the correlation between distributions at different covariate values and use a point process to implement a practically useful type of ordering. Two main constructions with analytically known correlation structures are proposed. Practical and efficient computational methods are introduced. We apply our framework, through mixtures of these processes, to regression modeling, the modeling of stochastic volatility in time series data, and spatial geostatistical modeling.

Bayesian efficiency analysis through individual effects: Hospital cost frontiers

Abstract This paper develops Bayesian tools for making inferences about firm-specific inefficiencies in panel data models. We begin by establishing a Bayesian setting in which fixed and random effects models are defined. What distinguishes these classes of models is the marginal prior independence of the effects. We show how such models can be analyzed using Monte Carlo integration or Gibbs sampling. These techniques are applied to a panel of U.S. hospitals. Our empirical findings illustrate the different characteristics of both types of models, as well as the influence of the particular priors used on the firm effects.

On the use of panel data in stochastic frontier models with improper priors

Abstract We consider a Bayesian analysis of the stochastic frontier model with composed error. Under a commonly used class of (partly) noninformative prior distributions, the existence of the posterior distribution and of posterior moments is examined. Viewing this model as a Normal linear regression model with regression parameters corresponding to both the frontier and the inefficiency terms, generates the insights used to derived results in a very wide framework. It is found that in pure cross-section models posterior inference is precluded under this ‘usual’ class of priors. Existence of a well-defined posterior distribution then crucially hinges upon the structure imposed on the inefficiency terms. Exploiting panel data naturally suggests the use of more structured models, where Bayesian inference can be conducted.

The components of output growth : A stochastic frontier analysis

This paper uses Bayesian stochastic frontier methods to decompose output change into technical, efficiency and input changes. In the context of macroeconomic growth exercises, which typically involve small and noisy data sets, we argue that stochastic frontier methods are useful since they incorporate measurement error and assume a (flexible) parametric form for the production relationship. These properties enable us to calculate measures of uncertainty associated with the decomposition and minimize the risk of overfitting the noise in the data. Tools for Bayesian inference in such models are developed. An empirical investigation using data from 17 OECD countries for 10 years illustrates the practicality and usefulness of our approach. Copyright 1999 by Blackwell Publishing Ltd

A Constructive Representation of Univariate Skewed Distributions

We introduce a general perspective on the introduction of skewness into symmetric distributions. Through inverse probability integral transformations we provide a constructive representation of skewed distributions, where the skewing mechanism and the original symmetric distributions are specified separately. We study the effects of the skewing mechanism on, e.g., modality, tail behavior and the amount of skewness generated. The representation is used to introduce novel classes of skewed distributions, where we induce certain prespecified characteristics through particular choices of the skewing mechanism. Finally, we use a Bayesian linear regression framework to compare the new classes with some existing distributions in the context of two empirical examples.

Multiple output production with undesirable outputs: an application to nitrogen surplus in agriculture

Many production processes yield both good outputs and undesirable ones (e.g., pollutants). In this article we develop a generalization of a stochastic frontier model that is appropriate for such technologies. We discuss efficiency analysis and, in particular, define technical and environmental efficiency in the context of our model. We develop methods for carrying out Bayesian inference and apply them to a panel data set of Dutch dairy farms, where excess nitrogen production constitutes an important environmental problem.

Modeling the Sources of Output Growth in a Panel of Countries

This article seeks to improve understanding of cross-country patterns of economic growth. It adopts a stochastic production-frontier model that allows for the decomposition of output change into input, efficiency, and technical change. The production frontier is assumed to depend on effective inputs rather than measured inputs. We develop a model in which effective inputs depend on observed factor use and a correction term that depends on variables such as education. A further extension over related work is our use of a production frontier that varies over regional country groups. Empirical results indicate that both these extensions are very important.

Modeling and Inference with υ-Spherical Distributions

Abstract A new class of continuous multivariate distributions on × ∈ ℜ n is proposed. We define these so-called υ-spherical distributions through properties of the density function in a location-scale context. We derive conditions for properness of υ-spherical distributions and discuss how to generate them in practice. The name “υ-spherical” is motivated by the fact that these distributions generalize the classes of spherical (when υ(·) is the l 2 norm) and l q -spherical (when υ(·) is the l q norm) distributions. Isodensity sets are still always situated around the location parameter μ, but exchangeability and axial symmetry are no longer imposed, as is illustrated in some examples. As an important special case, we define a class of distributions suggested by independent sampling from a generalization of exponential power distributions. This allows us to model skewness. Interestingly, all the robustness results found previously for spherical and l q -spherical models carry over directly to υ-spherical mo...

Bayesian Efficiency Analysis With a Flexible Form: The AIM Cost Function

In this article, the authors describe the use of Gibbs sampling methods for drawing posterior inferences in a cost frontier model with an asymptotically ideal price aggregator, nonconstant 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. The authors also examine the consequences of imposing regularity through parametric restrictions alone.