Zenga Distribution and Inequality Ordering

The aim of this article is to establish an ordering related to the inequality for the recently introduced Zenga distribution. In addition to the well-known order based on the Lorenz curve, the order based on I(p) curve is considered. Since the Zenga distribution seems to be suitable to model wealth, financial, actuarial, and, especially, income distributions, these findings are fundamental in the understanding of how parameter values are related to inequality. This investigation shows that for the Zenga distribution, two of the three parameters are inequality indicators.     

Tasks and Types: An Application of Mechanism Design to Self-Selection in Labour Markets

The Baron–Myerson (1982) regulatory mechanism is applied to the screening activity of a monopolist, who hires workers differentiated by quality and assigns them to different tasks. The employer charges a price to the workers for the screening service: necessary and sufficient conditions are provided for a self-selective price function to exist. It is shown that under the optimal price function tasks are assigned in such a way that workers' effort is increasing in workers' quality. It is not necessarily true, however, that the price function must be increasing in workers' quality. A simple two-types model is provided, showing the same results. Also the extension of the model to a dynamic context and, particularly, the requirements of a credible pre-commitment available to the screener are discussed.     

Decomposition by subpopulations of the Zenga-84 inequality curve and the related index $$\zeta $$: an application to 2014 Bank of Italy survey

Statistical Methods & Applications - This paper describes an innovative procedure to decompose by subpopulations the values assumed by the Zenga-84 inequality curve Z(p). This decomposition...     

Temporary Agency Workers in Italy: Alternative Techniques of Classification

Abstract. Cluster analysis and the classification tree technique are applied to investigate the relationship between the individual characteristics of Italian temporary help agency (THA) workers and their probability of achieving a temporary job. The application aims to show some advantages of these techniques with respect to traditional econometric tools. Sketches of the most common profiles among Italian THA workers are obtained as a result. Besides the typical THA worker pointed out by previous studies (young male workers, with a medium–high level of education, living in the Northern regions), two new profiles have been identified: the first comprising male manual workers with previous job experience, whose average age is over 30 and whose educational level is low; the second comprising young female workers with a medium–high level of education, working in the service sector or in the public sector. The results are compared with the more usual logit analysis and show their robustness.     

Decompositions by sources and by subpopulations of the Pietra index: two applications to professional football teams in Italy

In this paper two innovative procedures for the decomposition of the Pietra index are proposed. The first one allows the decomposition by sources, while the second one provides the decomposition by subpopulations. As special case of the latter procedure, the “classical” decomposition in two components (within and between) can be easily obtained. A remarkable feature of both the proposed procedures is that they permit the assessment of the contribution to the Pietra index at the smallest possible level: each source for the first one and each subpopulation for the second one. To highlight the usefulness of these procedures, two applications are provided regarding Italian professional football (soccer) teams.

     

On the parameters of Zenga distribution

In 2010 Zenga introduced a new three-parameter model for distributions by size that can be used to represent income, wealth, financial and actuarial variables. This paper proposes a summary of its main properties, followed by a focus on the interpretation of the parameters in terms of inequality. The scale parameter μ is equal to the expectation, and it does not affect the inequality, while the two shape parameters α and θ are inverse and direct inequality indicators respectively. This result is obtained through stochastic orders based on inequality curves. A procedure to generate a random sample from Zenga distribution is also proposed. The second part of this article looks at the parameter estimation. Analytical solution of method of moments is obtained. This result is used as a starting point of numerical procedures to obtain maximum likelihood estimates both on ungrouped and grouped data. In the application, three empirical income distributions are considered and the aforementioned estimates are evaluated. A comparison with other well-known models is provided, by the evaluation of three goodness-of-fit indexes.