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Hypothesis tests for dominance in income distributions has received considerable attention in recent literature. See, for example, Barrett and Donald (2003a, b), 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.

The tax evasion phenomenon affects the economic systems of European countries in different ways. The literature shows that individuals provide biased information both to administrative agencies and household surveys. The effects of tax evasion could thus influence the income inequality computed in official statistics.

In this paper, I investigate whether tax evasion generates a bias when inequality indices are computed using household survey data. To achieve this, I apply a parametric model of the Dagum type (three parameters) on the gross personal income of 27 European countries, distinguishing between the self-employed and employees. Subsequently, the parameters computed in the model are used as dependent variables in seemingly unrelated regressions.

I find that for the self-employed, tax evasion tends to reduce inequality as measured by regular wage statistics. Thus, the results reveal that tax evasion distorts inequality indices, generating an underground inequality.

This paper examines the gender differences of expenditure distribution within the last decade in Spain. In particular, the Lorenz dominance is tested using expenditure distributions as approximated by the Dagum model. The sensitivity of the results to some conceptual choices, such as the equivalence scale or the gender reference, is also analysed.

This chapter studies trends in income distributions and inequality in the European Union using data from the European Union Statistics on Income and Living Conditions. The author models the income distribution for each country under a Dagum distribution assumption and using maximum likelihood techniques. The author uses parameter estimates to form distributions for regions defined as finite mixtures of the country distributions. Specifically, the author studies the groups of ‘new’ and ‘old’ countries depending on the year they joined the European Union. The author provides formulae and estimates for the regional Gini coefficients and Lorenz curves and their decomposition for all the survey years from 2007 through 2011. The estimates of this study show that the ‘new’ European Union countries have become richer and less unequal over the observed years, while the ‘old’ ones have undergone a slight increase in inequality which is however not significant at conventional levels.

This paper aims to estimate the global income distribution during the nineties using limited information. In a first stage, we obtain national income distributions considering a model with two parameters. In particular, we propose to use the so-called Lamé distributions, which are curved versions of the Sigh-Maddala and Dagum distributions. The main feature of this family is that they represent parsimonious models which can fit income data adequately with just two parameters and whose Lorenz curves are characterized by only one parameter. In a second stage, global and regional distributions are derived from a finite mixture of these families using population shares. We test the validity of the model, comparing it with other two-parameter families. Our estimates of different inequality measures suggest that global inequality presents a decreasing pattern mainly driven by the fall of the differences across countries during the course of the study period that offsets the increase in disparities within countries.

This paper considers a parametric model for the joint distribution of income and wealth. The model is used to analyze income and wealth inequality in five OECD countries using comparable household-level survey data. We focus on the dependence parameter between the two variables and study whether accounting for wealth and income jointly reveals a different pattern of social inequality than the traditional “income only” approach. We find that cross-country variations in the dependence parameter effectively account only for a small fraction of cross-country differences in a bivariate measure of inequality. The index appears primarily driven by differences in inequality in the wealth distribution.

The purpose of this paper is to examine the level of cardinal welfare based on Sen’s index using both Pareto and non-Pareto states besides evaluating the effective factors on the welfare changes according to a fuzzy least-squares regression model.

The social welfare functions express the optimal social allocations in the public economics. Therefore, they can be applied as a tool to represent the difference of utility allocations among consumers. There are various criteria on the literature pertaining to the social welfare functions such as those of Dasgupta et al. (1970), Sheshinski (1972), Sen (1974), Yitzhaki (1979), Shorrocks (1983), Kakwani (1984), Dagum (1990, 1993), Mukhopadhaya (2003), and Mukhopadhaya and Rao (2001). The Sen’s welfare function because of strong theoretical basis and enjoying the welfare axioms is more celebrated among others so that it is a function of individual utilities resulting from the individual’s social positions.

The findings indicate that the welfare level has increased by about 4.8 percent during the period 2002-2007; by nearly 3.1 percent during 1997-2001 and mature to 2.7 percent from 1992 to 1996 such that the period 1997-2007 has had the highest level of social welfare improvement in Iran. The results obtained from the fuzzy regression show that the unemployment rate, inflation rate and Gini coefficient variables have an adverse relation with the cardinal welfare in both Pareto and non-Pareto cases, while the literacy rate and government expenditures have a positive relation with the welfare index. The findings also imply that there is a positive relationship between economic growth and welfare level in Iran.

I verify that this manuscript is an original study.

This study aims to propose a refined dynamic network slacks-based measure (DNSBM) to evaluate the efficiency of China's regional green innovation system which consists of basic research, applied research and commercialization stages and explore the influencing factors of the stage efficiency.

A two-step procedure is employed. The first step proposes an improved DNSBM model with flexible settings of stages' input or output efficiency and uses second order cone programming (SOCP) to solve the non-linear problem. In the second step, least absolute shrinkage and selection operator (LASSO) and Tobit models are used to explore the influencing factors of the stage efficiency. Global Dynamic Malmquist Productivity Index (GDMPI) and Dagum Gini coefficient decomposition method are introduced for further discussion of the productivity change and regional differences.

On average, Chinese provincial green innovation efficiency should be improved by 24.11% to become efficient. The commercialization stage outperforms the stages of basic research and applied research. Comparisons between the proposed model and input-oriented, output-oriented and non-oriented DNSBM models show that the proposed model is more advanced because it allows some stages to have output-oriented model characteristics while the other stages have input-oriented model characteristics. The examination of the influencing factors reveals that the three stages of the green innovation system have quite diverse influencing factors. Further discussion reveals that Chinese green innovation productivity has increased by 39.85%, which is driven mainly by technology progress, and the increasing tendency of regional differences between northern and southern China should be paid attention to.

This study proposes an improved dynamic three-stage slacks-based measure (SBM) model that allows calculating output efficiency in some stages and input efficiency in the other stages with the application of SOCP approach. In order to capture productivity change, this study develops a GDMPI based on the DNSBM model. In practice, the efficiency of regional green innovation in China and the factors that influence each stage are examined.

This paper compares two alternative methods for measuring multidimensional poverty. This question has become extremely important in recent years, both in the scientific literature and in social policy. We propose to use latent class analysis to evaluate poverty in Spain. We make use of the “fuzzy set” approach, and compare the results achieved from these two methodologies.