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

Welfare Measures and Mandatory Regulation for Transgenic Food in the European Union: A Theoretical Framework for the Analysis

This paper presents an analytical framework for studying the impact of mandatory labelling regulation for transgenic food. We compare Genetically Modified (GM) and conventional crop markets and identify gains for food processors prior to mandatory labelling and losses after this measure for the GM market. Nevertheless, food processors could obtain gains for conventional products after market disgregation. Finally, consumers will be worse off both for conventional and GM foods unless qualities other than changes to prices are considered.welfare, mandatory labelling, transgenic, genetically modified organism, European Union policy, Agricultural and Food Policy, Q18, K32, D62,

Model uncertainty in cross-country growth regressions

We investigate the issue of model uncertainty in cross-country growth regressions using Bayesian Model Averaging (BMA). We find that the posterior probability is very spread among many models suggesting the superiority of BMA over choosing any single model. Out-of-sample predictive results support this claim. In contrast with Levine and Renelt (1992), our results broadly support the more "optimistic'' conclusion of Sala-i-Martin (1997b), namely that some variables are important regressors for explaining cross-country growth patterns. However, care should be taken in the methodology employed. The approach proposed here is firmly grounded in statistical theory and immediately leads to posterior and predictive inference.Bayesian Model Averaging, Choice of Regressors, Economic Growth, Markov chain Monte Carlo, Prediction

Bayesian Modelling of Catch in a Northwest Atlantic Fishery

We model daily catches of fishing boats in the Grand Bank fishing grounds. We use data on catches per species for a number of vessels collected by the European Union in the context of the Northwest Atlantic Fisheries Organization. Many variables can be thought to influence the amount caught: a number of ship characteristics (such as the size of the ship, the fishing technique used, the mesh size of the nets, etc.), are obvious candidates, but one can also consider the season or the actual location of the catch. Our database leads to 28 possible regressors (arising from six continuous variables and four categorical variables, whose 22 levels are treated separately), resulting in a set of 177 million possible linear regression models for the log of catch. Zero observations are modelled separately through a probit model. Inference is based on Bayesian model averaging, using a Markov chain Monte Carlo approach. Particular attention is paid to prediction of catch for single and aggregated ships.Bayesian Model Averaging, Choice of Regressors, Bayesian model averaging; Categorical variables; Grand Bank fishery; Modelling Fish Catch; Predictive inference; Probit model

Model uncertainty in cross-country growth regressions

We investigate the issue of model uncertainty in cross-country growth regressions using Bayesian Model Averaging (BMA). We find that the posterior probability is very spread among many models suggesting the superiority of BMA over choosing any single model. Out-of-sample predictive results support this claim. In contrast with Levine and Renelt (1992), our results broadly support the more "optimistic'' conclusion of Sala-i-Martin (1997b), namely that some variables are important regressors for explaining cross-country growth patterns. However, care should be taken in the methodology employed. The approach proposed here is firmly grounded in statistical theory and immediately leads to posterior and predictive inference.Bayesian Model Averaging, Choice of Regressors, Economic Growth, Markov chain Monte Carlo, Prediction

Benchmark Priors for Bayesian Model Averaging

In contrast to a posterior analysis given a particular sampling model, posterior model probabilities in the context of model uncertainty are typically rather sensitive to the specification of the prior. In particular, "diffuse'' priors on model-specific parameters can lead to quite unexpected consequences. Here we focus on the practically relevant situation where we need to entertain a (large) number of sampling models and we have (or wish to use) little or no subjective prior information. We aim at providing an ``automatic'' or ``benchmark'' prior structure that can be used in such cases. We focus on the Normal linear regression model with uncertainty in the choice of regressors. We propose a partly noninformative prior structure related to a Natural Conjugate $g$-prior specification, where the amount of subjective information requested from the user is limited to the choice of a single scalar hyperparameter $g_{0j}$. The consequences of different choices for $g_{0j}$ are examined. We investigate theoretical properties, such as consistency of the implied Bayesian procedure. Links with classical information criteria are provided. More importantly, we examine the finite sample implications of several choices of $g_{0j}$ in a simulation study. The use of the MC$^3$ algorithm of Madigan and York (1995), combined with efficient coding in Fortran, makes it feasible to conduct large simulations. In addition to posterior criteria, we shall also compare the predictive performance of different priors. A classic example concerning the economics of crime will also be provided and contrasted with results in the literature. The main findings of the paper will lead us to propose a "benchmark'' prior specification in a linear regression context with model uncertainty.Bayes Factors, Markov chain Monte Carlo, Posterior odds, Prior elicitation

Benchmark priors for Bayesian models averaging

In contrast to a posterior analysis given a particular sampling model, posterior model probabilities in the context of model uncertainty are typically rather sensitive to the specification of the prior. In particular, 'diffuse' priors on model-specific parameters can lead to quite unexpected consequences. Here we focus on the practically relevant situation where we need to entertain a (large) number of sampling models and we have (or wish to use) little or no subjective prior information. We aim at providing an 'automatic' or 'benchmark' prior structure that can be used in such cases. We focus on the Normal linear regression model with uncertainty in the choice of regressors. We propose a partly noninformative prior structure related to a Natural Conjugate $g$-prior specification, where the amount of subjective information requested from the user is limited to the choice of a single scalar hyperparameter $g_{0j}$. The consequences of different choices for $g_{0j}$ are examined. We investigate theoretical properties, such as consistency of the implied Bayesian procedure. Links with classical information criteria are provided. In addition, we examine the finite sample implications of several choices of $g_{0j}$ in a simulation study. The use of the MC$^3$ algorithm of Madigan and York (1995), combined with efficient coding in Fortran, makes it feasible to conduct large simulations. In addition to posterior criteria, we shall also compare the predictive performance of different priors. A classic example concerning the economics of crime will also be provided and contrasted with results in the literature. The main findings of the paper will lead us to propose a 'benchmark' prior specification in a linear regression context with model uncertainty.Bayes factors, Markov chain, Monte Carlo, Posterior odds, Prior elicitation

Characterizations of a class of Pilipovi{\'c} spaces by powers of harmonic oscillator

We show that a smooth function $f$ on $\mathbf R^d$ belongs to the Pilipovi{\'c} space $\mathcal H_{\flat _\sigma}(\mathbf R^d)$ or the Pilipovi{\'c} space $\mathcal H_{0,\flat _\sigma}(\mathbf R^d)$, if and only if the $L^p$ norm of $H_d^Nf$ for $N\ge 0$, satisfy certain types of estimates. Here $H_d=|x|^2-\Delta _x$ is the harmonic oscillator.Comment: 13 pages. This is the third version. Some mathematical details have been clarified in this version compared to earlier version