We consider mostly Bayesian estimation of stochastic frontier models where one-sided inefficiencies and/or the idiosyncratic error term are correlated with the regressors. We begin with a model where ...a Chamberlain–Mundlak device is used to relate a transformation of time-invariant effects to the regressors. This basic model is then extended in two directions: first an extra one-sided error term is added to allow for time-varying efficiencies. Second, a model with an equation for instrumental variables and a more general error covariance structure is introduced to accommodate correlations between both error terms and the regressors. An application of the first and second models to Philippines rice data is provided.
Mathematical modelling of physical and chemical systems is used extensively throughout science, engineering, and applied mathematics. To use mathematical models, one needs solutions to the model ...equations; this generally requires numerical methods. This book presents numerical methods and associated computer code in Matlab for the solution of a spectrum of models expressed as partial differential equations (PDEs). The authors focus on the method of lines (MOL), a well-established procedure for all major classes of PDEs, where the boundary value partial derivatives are approximated algebraically by finite differences. This reduces the PDEs to ordinary differential equations (ODEs) and makes the computer code easy to understand, implement, and modify. Also, the ODEs (via MOL) can be combined with any other ODEs that are part of the model (so that MOL naturally accommodates ODE/PDE models). This book uniquely includes a detailed line-by-line discussion of computer code related to the associated PDE model.
Abstract
A low-quality patent system threatens to slow the pace of technological progress. Concerns about low patent quality are supported by estimates from litigation studies suggesting that most US ...patents granted should not have been issued. We propose a new model for measuring patent quality, based on equivalent patent applications submitted to multiple offices. Our method allows us to distinguish whether low-quality patents are issued because an office implements a low standard or because it violates its own standard. The results suggest that quality in patent systems is higher than previously thought. Specifically, the percentage of granted patents that are below each office’s own standard is under 10% for all offices. The Japanese patent office has a higher percentage of granted patents below its own standard than those from Europe, the USA, Korea, and China. This result arises from the fact that Japan has a higher standard than other offices. (JEL O34, K2, L4, F42)
Using Household, Income and Labour Dynamics in Australia (HILDA) data for 2001, 2006, 2010, 2014 and 2017, we compute posterior probabilities for dominance for all pairwise comparisons of income ...distributions in these years. The dominance criteria considered are Lorenz dominance and first‐ and second‐order stochastic dominance. The income distributions are estimated using an infinite mixture of gamma density functions, with posterior probabilities computed as the proportion of Markov chain Monte Carlo draws that satisfy the inequalities that define the dominance criteria. We find welfare improvements from 2001 to 2006 and qualified improvements from 2006 to the later three years. Evidence of an ordering between 2010, 2014 and 2017 cannot be established.
The Lorenz curve, introduced more than 100 years ago, remains as one of the main tools for analysis of inequality. International institutions such as the World Bank collect and publish grouped income ...data in the form of population and income shares for a large number of countries. These data are often used for estimation of parametric Lorenz curves which in turn form the basis for most inequality analyses. Despite the prevalence of parametric estimation of Lorenz curves from grouped data, and the existence of well-developed nonparametric methods, a formal description of rigorous methodology for estimating parametric Lorenz curves from grouped data is lacking. We fill this gap. Building on two data generating mechanisms, efficient methods of estimation and inference are described; several results useful for comparing the two methods of inference, and aiding computation, are derived. Simulations are used to assess the estimators, and curves are estimated for some example countries. We also show how the proposed methods improve upon World Bank methods and make recommendations for improving current practices.
We improve students' understanding of the F-test for linear hypotheses in a linear model by explaining elements that affect the power of the test. Including true restrictions in a joint null ...hypothesis affects test power in a way that is not generally known. Asking a student whether including the true restrictions in the null hypothesis will increase or decrease power, the student is likely to say: "I don't know." The student's answer is not bad because the power depends on the noncentrality parameter and the degrees of freedom. We show that adding true restrictions to a linear hypothesis cannot decrease the noncentrality parameter of the F-statistic, a result many will find counterintuitive. Adding true restrictions can increase or decrease F-test power depending on the offsetting negative effect of reducing the numerator degrees of freedom. We provide illustrative examples of these results and prove them for the general case.
Summary
Bayesian non‐parametric estimates of Australian distributions of mental health scores are obtained to assess how the mental health status of the population has changed over time, and to ...compare the mental health status of female/male and Aboriginal/non‐Aboriginal population subgroups. First‐order and second‐order stochastic dominance are used to compare distributions, with results presented in terms of the posterior probability of dominance and the posterior probability of no dominance. If a criterion for dominance is satisfied, then, in terms of that criterion, the mental health status of the dominant population is superior to that of the dominated population. If neither distribution is dominant, then the mental health status of neither population is superior in the same sense. Our results suggest mental health has deteriorated in recent years, that males' mental health status is better than that of females, and that non‐Aboriginal health status is better than that of the Aboriginal population.
Graphite is a candidate material for Generation IV concepts and is used as a moderator in Advanced Gas-cooled Reactors (AGR) in the UK. Spatial material variability is present within billets causing ...different material property values between different components. Variations in material properties and irradiation effects can produce stress concentrations and diverse mechanical responses in a nuclear reactor graphite core. In order to characterise the material variability, geostatistical techniques called variography and random field theory were adapted for studying the density and Young's modulus of a billet of Gilsocarbon and NBG-18 graphite grades. Variography is a technique for estimating the distance over which material property values have significant spatial correlation, known as the scale of fluctuation or spatial correlation length. The paper uses random field theory to create models that mimic the original spatial and statistical distributions of the original data set. This study found different values of correlation length for density and Young's modulus around the edges of a Gilsocarbon billet, while in the case of NBG-18, similar correlation lengths where found across the billet. Examples of several random fields are given to reproduce the spatial patterns and values found in the original data.
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We show how a wide range of stochastic frontier models can be estimated relatively easily using variational Bayes. We derive approximate posterior distributions and point estimates for parameters and ...inefficiency effects for (a) time invariant models with several alternative inefficiency distributions, (b) models with time varying effects, (c) models incorporating environmental effects, and (d) models with more flexible forms for the regression function and error terms. Despite the abundance of stochastic frontier models, there have been few attempts to test the various models against each other, probably due to the difficulty of performing such tests. One advantage of the variational Bayes approximation is that it facilitates the computation of marginal likelihoods that can be used to compare models. We apply this idea to test stochastic frontier models with different inefficiency distributions. Estimation and testing is illustrated using three examples.
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