This paper is an introduction to the special issue of Mathematical Social Sciences on Advances in growth and macroeconomic dynamics in memory of Carine Nourry.

The relationship between public debt, growth and volatility is investigated in a Barro-type (1990) endogenous growth model, with three main features: we consider a small open economy, international borrowing is constrained and households have taste for domestic public debt. Therefore, capital, public debt and the international asset are not perfect substitutes and the economy is characterized by an investment multiplier. Whatever the level of the debt-output ratio, the existing BGP features expectation-driven fluctuations. If the debt-output ratio is low enough, there is also a second BGP with a lower growth rate. Hence, a lower debt does not stabilize the economy with credit market imperfections. However, a high enough taste for domestic public debt may rule out the BGP with lower growth. This means that if the share of public debt held by domestic households is high enough, global indeterminacy does not occur.

We consider an overlapping generations economy in which agents differ through their ability to procreate. Ex-ante infertile households may incur health expenditure to increase their chances of parenthood. This health heterogeneity generates welfare inequalities that deserve to be ruled out. We explore three different criteria of social evaluation in the long-run: the utilitarian approach, the ex-ante egalitarian criterion and the ex-post egalitarian one. We propose a set of economic instruments to decentralize each solution. To correct for the externalities and health inequalities, both a preventive (a taxation of capital) and a redistributive policy are required. We show that a more egalitarian allocation is associated with higher productive investment but reduced health expenditure and thus, lower population growth.

The aim of this paper is to study the interplay between long term productive investments and more short term and liquid speculative ones. A three-period lived overlapping generations model allows us to make this distinction. Agents have a portfolio decision. When young, they can invest in human capital that is a productive long term investment that provides a return during the following two periods. When young or in the middle age, they can invest in a bubble. Young individuals can also borrow on a credit market to finance the productive investment. However, the amount borrowed is limited by a credit constraint. We show that the existence of a stationary bubble raises productive investment and production when the bubleless economy is credit constrained and dynamically efficient. Indeed, young agents sell short the bubble to increase productive investments, whereas traders at middle age transfer wealth to old age. The bubble allows to relax the credit constraint. We outline that a permanent technological shock inducing either a larger return of capital in the short term or a similar increase in the return of capital in both periods raises productive capital, production and the bubble size. We use our framework to discuss the effect on the occurrence of bubbles of financial regulation and fiscal policy.