Medium term dynamics and inequalities under epidemics

We are concerned by the dynamic demographic and economic consequences of epidemics, and to this end, we consider a general overlapping generations model which allows for several epidemic configurations. People live for three periods, successively as children, junior adults and senior adults. A junior adult has an exogenous number of children and is perfectly altruistic in that is he only cares for the survival of his children and the social position they will get. He invests in his own health and education, and in the health and education of his children. Because we take into account both child and adult mortality, we are in principle able to investigate the implications of epidemics for any age-mortality profile. First, we fully analytically characterise the short run and long run economic and demographic properties of the model, which allows us to do the same for the distributions of human capital and thus income. Second, we analyse the consequences of one-period long epidemics in two polar cases: an epidemic hitting only children Vs an epidemic only killing adults. Both are shown to have permanent demographic and economic effects. In contrast to epidemics only killing children, ‘adult’ epidemics are additionally shown to distort the income distribution in the medium run, creating more poverty. Such distributional effects vanish in the long run. To analyse the medium term effects of HIV/AIDS, we assume that the epidemic hit junior adults, increase the number of deaths among children and reduces fertility. Then, we show that the size of the total population will decrease in the medium term, and that the share of the active population in the total population will also lower. In the active population, the proportion of people with a high level of human capital will decrease and the proportion holding a low level of human capital will increase. Finally output per worker and per capita will decrease.Epidemic, hysteresis, echo effect, overlapping generation model

Terminal conditions as efficent instruments for numerical detection of the saddlepoint paths: a linear algebra non-robustness argument

In this paper, we address a criticism against the usual prescriptions on the introduction of terminal conditions as the principal numerical instruments for detecting the saddlepoint solutions of consistent expectations models. The argumentation is purely theoretical and it is conducted on a canonical linear infinite-time horizon model, approximated by the means of an elementary fixed-value terminal condition. Considering two equivalent algebraic representations of the model, we show that the asymptotic behavior of a backward solution method, associated to the fixed-value terminal condition, depends crucially on the selected algebraic formulation of the model