# Lubrano

## Publications

This paper analyses the problems linked to the implementation of the Equal Labour Income Equalisation (ELIE) scheme proposed by [Kolm, 2005]. It successively studies the influence of uncertainty in the information about individual incomes, the impact of equivalence scales and finally the consequences of capital accumulation. If uncertainty does not modify fundamentally the equity properties of ELIE, equivalence scales can have non trivial consequences depending on the relation between income and fertility. Finally, capital accumulation introduces strong inequalities in the income distribution which are not removed by taxation. The paper relies on simulations of the income distribution, calibrated on French data and on the use of taxation indices.

[Simula and Trannoy, 2011] have shown that ELIE is confronted with implementation issues when the policymaker cannot observe the time worked by every individual. This paper tries to fix this problem. To this aim, we characterise the second-best allocations which are the closest to ELIE first in terms of welfare and then in terms of transfers. In the former perspective, we consider a welfarist setting in which the social weights are those required by ELIE to be generated as a first-best allocation. These weights are defined by the tangent hyperplane to the first-best Pareto set at the ELIE allocation. We show that, in the absence of income effect on labour supply, the closest solution to ELIE is the laissez-faire. In addition, simulations for a Cobb–Douglas economy show that the second-best transfers may then be substantially different from ELIE. This is why, in the latter perspective, we construct second-best allocations which are both incentive-compatible and generate net transfers coinciding with the first-best ELIE transfers. We show that the unique solution is Pareto-efficient in the constraint set.

In this introductory chapter, we give a subjective account of the content of Kolm’s book Macrojustice (2005) that gave rise to the idea of organising in 2006 a round table where this book was discussed by different authors coming from a large variety of horizons: philosophers, economists, econometricians. We leave Serge-Christophe Kolm the task of presenting his theory in the first part of this book. Macrojustice is concerned about social justice proposing a comprehensive redistributive scheme. Of course, any distributive proposal always raises questions at the ethical, theoretical and practical levels. These questions are at the core of the discussions that are presented in this book, which is designed as a forum for multidisciplinary exchange.

In this introductory chapter, we give a subjective account of the content of Kolm’s book Macrojustice (2005) that gave rise to the idea of organising in 2006 a round table where this book was discussed by different authors coming from a large variety of horizons: philosophers, economists, econometricians. We leave Serge-Christophe Kolm the task of presenting his theory in the first part of this book. Macrojustice is concerned about social justice proposing a comprehensive redistributive scheme. Of course, any distributive proposal always raises questions at the ethical, theoretical and practical levels. These questions are at the core of the discussions that are presented in this book, which is designed as a forum for multidisciplinary exchange.

We propose a new approach for modeling nonlinear multivariate interest rate processes based on time-varying copulas and reducible stochastic differential equations (SDEs). In the modeling of the marginal processes, we consider a class of nonlinear SDEs that are reducible to Ornstein–Uhlenbeck (OU) process or Cox, Ingersoll, and Ross (1985) (CIR) process. The reducibility is achieved via a nonlinear transformation function. The main advantage of this approach is that these SDEs can account for nonlinear features, observed in short-term interest rate series, while at the same time leading to exact discretization and closed-form likelihood functions. Although a rich set of specifications may be entertained, our exposition focuses on a couple of nonlinear constant elasticity volatility (CEV) processes, denoted as OU-CEV and CIR-CEV, respectively. These two processes encompass a number of existing models that have closed-form likelihood functions. The transition density, the conditional distribution function, and the steady-state density function are derived in closed form as well as the conditional and unconditional moments for both processes. In order to obtain a more flexible functional form over time, we allow the transformation function to be time varying. Results from our study of U.S. and UK short-term interest rates suggest that the new models outperform existing parametric models with closed-form likelihood functions. We also find the time-varying effects in the transformation functions statistically significant. To examine the joint behavior of interest rate series, we propose flexible nonlinear multivariate models by joining univariate nonlinear processes via appropriate copulas. We study the conditional dependence structure of the two rates using Patton (2006a) time-varying symmetrized Joe–Clayton copula. We find evidence of asymmetric dependence between the two rates, and that the level of dependence is positively related to the level of the two rates. (J

The basic, core theory of overall distributive justice in macrojustice is presented in this chapter. The basic facts are the following. (1) General opinion rejects differences in tastes and hedonic capacities as relevant for macrojustice in a society in a normal situation. (2) Experience shows the possibility of transfers based on given capacities with practically no disincentive effect (exemption of overtime labour earnings from the income tax). (3) Pareto efficiency is desired and a condition of stability. (4) Social liberty from given resources is desired and necessary. (5) Equal real liberty (for different domains of choice) is a priori desired and rational. The result is a simple distributive scheme rich of some twenty meaningful equivalent properties, including free exchange and labour from a given equal-labour income equalisation; general balanced labour reciprocity; basic income financed by an equal labour of each (or according to capacity); a “concentration” of total income; etc. The issues of the determination of the degree of redistribution and equalisation, and the relations with the rest of public finance are briefly recalled.

This chapter presents an axiomatic analysis of the allocation rules that assigns each economy with its set of ELIE (Equal Labour Income Equalisation) allocations. Two fairness properties, directly inspired by Serge Kolm’s theory of macrojustice are defined. Then, minimal lists of axioms are identified that, when combined to those two fairness properties, characterise the ELIE allocation rules. Finally, other fairness properties are defined that are not satisfied by the ELIE allocation rules.

This chapter is a general summarised presentation of the problem of defining the best possible choice of the overall income distribution in macrojustice (as opposed to microjustice and mesojustice concerned with allocations directly of specific goods or in particular instances). The three classical polar principles advocate respectively self-ownership and transfers motivated by comparisons of individuals’ incomes and welfares. They are synthesised by people’s general ethical views in the society that has to implement the policy. Actual policies show the material possibilities (for instance the exemption of overtime labour earnings from the income tax that amounts to basing transfers on capacities). The result is a simple and richly meaningful distributive structure that means, jointly, equal real liberty; adding an egalitarian and a classical liberal parts of income; reciprocity by providing each other with the product of the same labour; and an equal basic income financed by an equal partial labour of each. This core principle is then applied taking all the actual economic and social phenomena into account. The questions this may raise are analysed and answered in the various chapters of this volume.

Does the ELIE system of redistribution always lead to positive social emotions and improve social recognition? Receiving a transfer in ELIE could be a sign that your social status is that of the less talented: even if you make the sacrifice of working more in order to contribute to the transfer, your productive capacities may have no market value. This could decrease the strength of the social bond. In order to avoid this, we need to be able to attach social recognition to the passive sacrifice implied in being less talented. One way is to relate this situation to the value for collective adaptability of a level of randomness in the distribution of talents. The redistribution procedure – the sacrifices of the more talented people – leaves the less talented people free to contribute or not by their work to their community, and their passive sacrifice is thereby changed into an active one. Social recognition can thus become mutual.