Advances in growth and macroeconomic dynamics - In memory of Carine Nourry

This special issue of Mathematical Social Sciences (MSS) compiles a selection of twelve original papers in four sections covering different topics in growth and macroeconomic theories, and key related normative and positive themes. It is published in memory of Carine Nourry, who was a close friend of many of the contributors.

A central question is the financing of firms’ investments when financial markets are incomplete. The contribution by Léon-Ledesma and Orrillo studies an extension of the incomplete markets’ general equilibrium model in which firms can default and therefore bankruptcy is possible. Their setting is characterized by endogenous production, and collateral constraints involve all the commodities available for consumption and production in the economy. Lenders have a portfolio of assets issued by producers but cannot anticipate the identity of the firm defaulting. Thus, lenders anticipate a default rate that depends on the average level of production and is therefore counter-cyclical. In this framework, the financial decisions of firms and their owners cannot be separated out, which implies that the real and financial spheres of the economy are not disconnected. Finally, because of an insurance premium, the equilibrium is constrained efficient.

Recursive utility describes classes of intertemporal utility functions that are tractable and extensively used in macro-dynamic models. When the model considered is sufficiently general, a relevant challenge is to find a class of utility functions that solves the Koopmans equation for a given aggregator. In their contribution to this special issue, Becker and RinconZapatero develop a computationally-motivated methodology which offers a selection principle for numerical solutions of recursive macrodynamic models where theory suggests that there are multiple fixed points. They obtain a constructive result. They show that extremal fixed points exist, using successive approximations as soon as the conditions of the Tarski-Kantorovich fixed-point theorem are met.

The last section of this special issue is specifically devoted to the analysis of inequalities.

Benhabib and Hager propose a simple and appealing theory of income distributions with “revenue diversion”, which they further: i) connect to the historical debate, and ii) illustrate with some rough quantitative exercises. A key aspect of the theory is the allocation of talents across occupations, “talent” being interpreted broadly. If the distribution of talents were fully observable, the earnings distribution could be inferred from a given mapping of talents into earnings. However, the authors point out that talents are not fully observable: there is room for “revenue diversion”, in other words, revenue gains not strictly remunerating talents but diverted by a certain class of employees called “managers” (as opposed to “workers”). Benhabib and Hager’s allocation of talent theory makes it possible to obtain that, with or without revenue diversion, the overall distribution of income is hump-shaped and is given by a Pareto distribution above the median.

Inequalities can be addressed in terms of the effects of pollution. By increasing absenteeism or affecting learning skills, the health effects of pollution have consequences on human capital and income when individuals become adults. Children with lower socioeconomic status are more vulnerable and exposed to the health consequences of pollution. Constant and Davin develop an overlapping generations model where individuals have heterogeneous human capital.

Children suffer from air pollution, but their parents can mitigate this effect by investing in health. If the production is highly polluting, inequalities will persist over time and the economy can even be relegated into an inequality trap. Indeed, pollution has a greater effect on poorer children, who will accumulate less and less human capital. Constant and Davin also study environmental and health policies that could reduce inequalities. Environmental maintenance financed by polluters can be a good tool when the initial inequality and the pollution emissions are not too high. Otherwise, adding a health policy consisting of health subsidies could be a relevant option.

Boucekkine, Desbordes and Melindi-Ghidi rely on the important work by political scientists who point out that a significant fraction of democracies is substantially departing from what is usually associated with the very concept of democracy, e.g. inclusiveness, income redistribution from rich to poor, strong welfare states. Boucekkine, Desbordes and Melindi-Ghidi identify conditions under which elite-biased democracies tend to arise as an economic-political equilibrium. The population is split into two groups, a minority and a majority, with the additional crucial ingredient that the minority enjoys preferential treatment or benefits from distinctive fiscal treatment under autocracy. As a result, the preferred tax rate of the majority member is likely to be significantly higher than under one source of income discrimination. Elite-biased democracies may then arise if one source of discrimination, distinctive fiscal treatment, is officially removed and replaced by a more acceptable coalition, even though the ensuing redistribution to majority members is lower than its counterpart under pure democracy. The optimal population-size problem is an old normative problem that has been the subject of numerous contributions and approaches since the late 60’s. A key issue arising in the standard welfarist approaches is that they ultimately involve evaluating the welfare of nonexistent people, because some people only exist in certain allocations. De la Croix and Doepke advocate a “soul’s view” approach with introspection as the accompanying method for comparison of populations. The key to the problem is to find an interpretation “where being alive and being unborn are not mutually exclusive, but merely different states which are experienced by one and the same being over time”. This can even be made operational: all it takes is to assume that the world is endowed with a fixed supply of souls who get reincarnated from time to time in different human bodies. De la Croix and Doepke elaborate on this conceptual approach, deriving a rich theoretical analysis, and discuss some applications to concrete problems involving long-term environmental risks.