By Raouf Boucekkine, Thomas Seegmuller & Alain Venditti
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.
MACROECONOMIC STABILITY AND FLUCTUATIONS
Barinci, Cho and Drugeon consider general two-sector overlapping generations with a pure consumption good and an investment good. Preferences over a two period life-cycle are based on endogenous leisure in the first period and consumption in the second period. Two stationary equilibria are shown to exist: a Wealth-to Capital equilibrium where total private wealth is equal to the value of the stock of capital, and the Golden Rule. Both equilibria can be characterized by monotone convergence or endogenous fluctuations through the existence of local indeterminacy and quasi-periodic cycles.
Human capital has been established as a major driver of economic growth. Increasingly, studies in sociology show that human capital affects welfare. Bettereducated agents have a greater demand for health and are more in control of their lives, as they live in healthier conditions. In line with this stream of research, Bosi, Loyd-Braga and Nishimura explore the implications of introducing different types of human capital externalities into the utility function, the production function, and the human capital accumulation of a Lucas-type model without physical capital. Growth no longer has to be balanced and the equilibrium can be globally indeterminate. A taxation policy based on constant tax rate may speed up the accumulation of human capital.
The last financial crisis and the recent Covid crisis generated dramatic increases in debt levels in most countries, raising the problem of debt financing. Yet the co-existence of varying experiences across countries suggests that debt financing is a complex question. Modesto et al. provide a theoretical exploration of these latter interconnected issues. They consider a small open economy with a credit constraint and a preference for domestic public bonds. Whatever the level of the debt-output ratio, there always exists a high growth balanced growth path (BGP) which features expectation-driven fluctuations. Moreover, if the debt-output ratio is low enough, global indeterminacy arises, as there is also a second BGP with a lower growth rate. But if the share of public debt held by domestic households is high enough, this second BGP is ruled out and global indeterminacy does not occur.
EXISTENCE OF EQUILIBRIA
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.
MIGRATION AND NETWORKS
A fundamental nexus between human migrations and economic growth is human capital accumulation, in particular via the inherent brain drain. In their contribution, Destrée, Gente and Nourry consider an endogenous growth model based on human capital accumulation where agents face an endogenous debt constraint to finance their education in the home country while they receive remittances from their emigrant children. Destrée, Gente and Nourry assume a non-commitment setting where individuals may choose to default on their debt and be excluded from the asset market. They show that remittances tend to tighten the borrowing constraints for a given level of interest rate, but may enhance growth at the equilibrium. Based on the existence of multiple equilibria, the model can replicate both negative and positive impacts of migration and remittances on economic growth.
The crucial role of social networks has been highlighted to explain behaviors in the labor market and migratory patterns. However, the interplay between immigrants’ informational network, job search activities, migration, and concentration in some specific industry has not yet been analytically addressed. In Domingues Dos Santos and Taugourdeau, social networks are considered in a matching model to illustrate the longstanding situation of Portuguese immigrants in the French labor market. The paper develops an original matching model revealing that the employment concentration of the Portuguese community can mainly be explained by their social network. Hence, the model explains the two main features of the Portuguese labor force in the French labor market: a low unemployment rate and high sector-concentration. It also highlights the intergenerational persistence of both these features.
The urban economics literature typically assumes that interactions are global. Augeraud-Véron, Marhuenda and Picard is the first theoretical attempt to cope with local interactions. Due to travel costs, economic agents may not find it optimal to interact with all the others, and interactions remain local. In their spatial model, they study how a given mass of identical individuals locate in a given space assuming that utility in any location depends on consumption of both a composite good and land space, plus the so-called social surplus. The key finding of the study is that changes in population density at any urban location depend on the density at some specific distance to the left and right of this location.
INEQUALITIES AND INCOME DISTRIBUTION
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.
Advances in growth and macroeconomic stability, eds. Raouf Boucekkine, Thomas Seegmuller, Alain Venditti, Mathematical Social Sciences vol.112, Elsevier, 2021.
Carine Nourry was Director of the School of Economics of Aix-Marseille, and Professor at Aix-Marseille University,specialising in the topic «growth and fluctuations».
→ This article was issued in AMSE Newletter, Winter 2021.