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 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.