The derivation of normative criteria for ranking distributions is at the core of welfare economics as these criteria are widely adopted to evaluate the performances of societies and, in particular, to evaluate the welfare and distributional implications of the introduction of new public policies and fiscal reforms. However, the existing frameworks impose a focus (on inequality at) the bottom of the distribution that in some cases can arise to be arbitrary and their informational content is confined to a short run perspective. This project will contribute to the existing literature by providing new normative criteria, within a self-contained and unifying framework, that will not suffer from these restrictions and by applying such criteria to real data through estimation techniques recently introduced in the econometrics literature.
The first part of the project will be aimed at developing the theoretical model to rank distributions in the short run that will account for the whole profile of inequality. The second part of the project will be aimed at extending such framework for the assessment of mobility processes so to obtain an evaluation of distributions in the long run. Differently from the existing contributions that incorporate aversion to inequality at the bottom of the distribution, our model will incorporate alternative attitudes toward inequality ¿ namely aversion to inequality at the top and middle part of the distribution - by imposing different restrictions on the set of social preferences and will make them coexist by introducing new prioritarian principles. The third part of the project will be aimed at proposing estimation methods for the empirical implementability of these criteria. In particular, a generalization of the smooth transition regression will be developed. Such generalization, being characterized by multilevel asymmetry, will be able to account for a different behaviour at the tails of the distribution both in the short and long run.
Concerning the first part of the project, the existing literature proposes measurement models that reflect concerns for inequality at the bottom of the distribution; we enrich this literature by introducing concerns for inequality at the top and middle part of the distribution and their mathematical formalization, together the introduction and formalization of new prioritarian principle. Therefore, we will be able to obtain new dominance conditions and related indexes. We will offer an explanation of how these new results relate and/or differ from those previously produced in the literature. Indeed, we expect that our framework will represent a generalization of the existing models in the literature; in which case, it will provide a unifying framework for making normative judgements. Moreover, we expect that our model will be general enough to be applied to evaluate and compare distributions of different variables. For instance, letting the non-monetary variable be represented by time, the framework could be used for the assessment of intertemporal distributions of income, hence allowing for an intertemporal evaluation of societies. Alternatively, our model could be implemented for the normative evaluation of growth processes by letting the non-monetary variable referring to the position of individuals in the reference distribution (i.e. normalized rank either in the pre-growth income distribution or in the post-growth distribution or in both) and the monetary variable referring to individual income growth. Last, this framework will arise to be suitable to make comparisons across distributions when the researcher adopts an opportunity egalitarian perspective (Roemer and Trannoy 2015, Ramos and Van de Gaer 2015). For instance the ¿need group¿ would encompass all those individuals characterized by the same set of exogenous factors that affect their outcome. In this case, the imposition of prioritarianism will correspond to whether priority is given for inequality of outcome or for inequality of opportunity.
Concerning the second part of the project, our methodology will have at least the following advantages with respect to the existing literature. It will enable assessing if and how mobility differs at different points of the distribution and to disentangle upward and downward mobility from the overall mobility process. This is important if the aim is the assessment of the social progresses made by a society. It can be used to compare the mobility of subgroups of the population; such comparisons will be particularly useful if for instance a gender or regional perspective is adopted. In addition, we aim at developing a model that, differently from existing one, can be used interchangeably to evaluate mobility with cardinal and ordinal variables, which is relevant if the researcher is interested in measuring income and educational mobility and understanding whether they follow a similar path. Last, we will show how our framework can be used to provide a normative and robust support for estimating intergenerational mobility in presence of coarse data (typically the case of developing countries).
Concerning the third part of the project, we innovate the methodology commonly adopted in the literature of Income Inequality and Social Choice. In facts, all the existing literature based on regression models (Hertz 2005; Narayan et al. 2018; Van der Weide et al. 2019) adopts nonlinear-type of functions that assumes only one slope parameter ¿ and, in any case, do not take in account the Dynamic Asymmetry as a joint coexistence of asymmetry in levels and in the distribution. In turn, this makes the investigator to conclude, at the best, that the estimated density is multimodal. Thus, if a difference in the tails of a (multimodal) distribution exists, it cannot be quantitatively assessed in phase of parameter estimation, unless adopting specific non-parametric methods for density estimation. Our GSTR model allows to identify the asymmetry in the distribution directly when estimating the two slope parameters maintaining a simple parametric approach. In particular, we adapt for multivariate regression the recent statistical models by Zanetti Chini (2018) and apply it to dataset on Income and Fiscal Policy where Dynamic Asymmetry has never been investigated. While Dynamic Asymmetry is found being a non negligible feature of this data and properly measured, policy makers would be able to identify a feasible and effective policy to reduce the spread of income distribution or mobility among people in lower and higher-tails.