323,314 research outputs found
Averaging Lorenz Curves
No full textA large number of functional forms have been suggested in the literature for estimating Lorenz curves that describe the relationship between income and population shares. One way of choosing a particular functional form is to pick the one that best fits the data in some sense. Another approach, and the one followed here, is to use Bayesian model averaging to average the alternative functional forms. In this averaging process, the different Lorenz curves are weighted by their posterior probabilities of being correct. Unlike a strategy of picking the best-fitting function, Bayesian model averaging gives posterior standard deviations that reflect the functional form uncertainty. Building on our earlier work (Chotikapanich and Griffiths 2002), we construct likelihood functions using the Dirichlet distribution and estimate a number of Lorenz functions for Australian income units. Prior information is formulated in terms of the Gini coefficient and the income shares of the poorest 10% and poorest 90% of the population. Posterior density functions for these quantities are derived for each Lorenz function and are averaged over all the Lorenz functions.Gini coefficient; Bayesian inference; Dirichlet distribution.
Estimating Lorenz Curves Using a Dirichlet Distribution
No full textThe Lorenz curve relates the cumulative proportion of income to the cumulative proportion of population. When a particular functional form of the Lorenz curve is specified it is typically estimated by linear or nonlinear least squares assuming that the error terms are independently and normally distributed. Observations on cumulative proportions are clearly neither independent nor normally distributed. This paper proposes and applies a new methodology which recognizes the cumulative proportional nature of the Lorenz curve data by assuming that the proportion of income is distributed as a Dirichlet distribution. Five Lorenz-curve specifications were used to demonstrate the technique. Once a likelihood function and the posterior probability density function for each specification are derived we can use maximum likelihood or Bayesian estimation to estimate the parameters. Maximum likelihood estimates and Bayesian posterior probability density functions for the Gini coefficient are also obtained for each Lorenz-curve specification.
The Lorenz curve in economics and econometrics
No full textThis paper surveys selected applications of the Lorenz curve and related stochastic orders in economics and econometrics, with a bias towards problems in statistical distribution theory. These include characterizations of income distributions in terms of families of inequality measures, Lorenz ordering of multiparameter distributions in terms of their parameters, probability inequalities for distributions of quadratic forms, and Condorcet jury theorems.Lorenz curve, Lorenz order, majorization, income distribution, income inequality, statistical distributions, characterizations, Condorcet jury theorem.
REVISITING THE ORDERED FAMILY OF LORENZ CURVES
No full textLorenz curve; Gini index Abstract: Sarabia et al. (1999) present a basic model to create ordered families of Lorenz curves, along with basic theorems that describe the conditions for the models to satisfy the definition of the Lorenz curve. Using these basic models, they suggest a family which includes several well-known Lorenz models as special cases. This paper first shows that their basic theorems can be generalized. The paper then proceeds to propose additional families of Lorenz models. Finally the performance of some of the models is compared and it is shown that more efficient Lorenz models are possible with the assistance of our generalized result of the Sarabia et al. (1999) basic model.
Estimating Lorenz Curves Using a Dirichlet Distribution.
No full textThe Lorenz curve relates the cumulative proportion of income to the cumulative proportion of population. When a particular functional form of the Lorenz curve is specified it is typically estimated by linear or nonlinear least squares, estimation techniques that have good properties when the error terms are independently and normally distributed. Observations on cumulative proportions are clearly neither independent nor normally distributed. This paper proposes and applies a new methodology that recognises the cumulative proportional nature of the Lorenz curve data by assuming that the income proportions are distributed as a Dirichlet distribution. Five Lorenz-curve specifications are used to demonstrate the technique. Maximum likelihood estimates under the Dirichlet distribution assumption provide better-fitting Lorenz curves than nonlinear least squares and another estimation technique that has appeared in the literature.Gini coefficient; maximum likelihood estimation
Ranking Intersecting Lorenz Curves
No full textThis paper is concerned with the problem of ranking Lorenz curves in situations where the Lorenz curves intersect and no unambiguous ranking can be attained without introducing weaker ranking criteria than first-degree Lorenz dominance. To deal with such situations two alternative sequences of nested dominance criteria between Lorenz curves are introduced. At the limit the systems of dominance criteria appear to depend solely on the income share of either the worst-off or the best-off income recipient. This result suggests two alternative strategies for increasing the number of Lorenz curves that can be strictly ordered; one that places more emphasis on changes that occur in the lower part of the income distribution and the other that places more emphasis on changes that occur in the upper part of the income distribution. Both strategies turn out to depart from the Gini coefficient; one requires higher degree of downside and the other higher degree of upside inequality aversion than what is exhibited by the Gini coefficient. Furthermore, it is demonstrated that the sequences of dominance criteria characterize two separate systems of nested subfamilies of inequality measures and thus provide a method for identifying the least restrictive social preferences required to reach an unambiguous ranking of a given set of Lorenz curves. Moreover, it is demonstrated that the introduction of successively more general transfer principles than the Pigou-Dalton principle of transfers forms a helpful basis for judging the normative significance of higher degrees of Lorenz dominance. The dominance results for Lorenz curves do also apply to generalized Lorenz curves and thus provide convenient characterizations of the corresponding social welfare orderings.generalized Gini families of inequality measures, rank-dependent measures of inequality, Gini coefficient, partial orderings, Lorenz dominance, Lorenz curve, general principles of transfers
TWO NEW EXPONENTIAL FAMILIES OF LORENZ CURVES
No full textWe present two new Lorenz curve families by using the basic model proposed by Sarabia, Castillo and Slottje (1999). We present estimations which show that the models in our new families are very efficient when applied to data on income distribution for a range of countries from Shorrocks (1983).Lorenz curve
Una nueva visión Konradista
No full textEsta investigación se concentró en la percepción de satisfacción de los graduados de la Fundación Universitaria Konrad Lorenz en aspectos de su vida universitaria y laboral.This research focused on the perceived satisfaction of Konrad Lorenz University Foundation graduates with aspects of their university and work life.Profesional en MercadeoPregradoMarketin
Bayesian Assessment of Lorenz and Stochastic Dominance in Income Distributions
No full textHypothesis tests for dominance in income distributions has received considerable attention in recent literature. See, for example, Barrett and Donald (2003), Davidson and Duclos (2000) and references therein. Such tests are useful for assessing progress towards eliminating poverty and for evaluating the effectiveness of various policy initiatives directed towards welfare improvement. To date the focus in the literature has been on sampling theory tests. Such tests can be set up in various ways, with dominance as the null or alternative hypothesis, and with dominance in either direction (X dominates Y or Y dominates X). The result of a test is expressed as rejection of, or failure to reject, a null hypothesis. In this paper we develop and apply Bayesian methods of inference to problems of Lorenz and stochastic dominance. The result from a comparison of two income distributions is reported in terms of the posterior probabilities for each of the three possible outcomes: (a) X dominates Y, (b) Y dominates X, and (c) neither X nor Y is dominant. Reporting results about uncertain outcomes in terms of probabilities has the advantage of being more informative than a simple reject / do-not-reject outcome. Whether a probability is sufficiently high or low for a policy maker to take a particular action is then a decision for that policy maker. The methodology is applied to data for Canada from the Family Expenditure Survey for the years 1978 and 1986. We assess the likelihood of dominance from one time period to the next. Two alternative assumptions are made about the income distributions –Dagum and Singh-Maddala – and in each case the posterior probability of dominance is given by the proportion of times a relevant parameter inequality is satisfied by the posterior observations generated by Markov chain Monte Carlo.Bayesian, Income Distributions, Lorenz
Gedanken über das gegenwärtige Schicksal der Pfarrer in Bünden, und seinen Einfluss auf Religion und Vaterland
No full textvon Lorenz F. AllieschAuf Titelbl.: Mit Approbation des 1788 zu Jenins gehaltenen hochwürdigen Synodus dem Druck übergebenOnline-Zugriff (E-Rara
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