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

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.Consistent expectations; Numerical solutions; Saddlepoint paths;

Liquidity constraints and time non-separable preferences: simulating models with large state spaces

This paper presents an alternative method for the stochastic simulation of nonlinear and possibly non-differentiable models with large state spaces. We compare our method to other existing methods, and show that the accuracy is satisfactory. We then use the method to analyze the features of an intertemporal optimizing consumption-saving model, when the utility function is time non-separable and when liquidity constraints are imposed. Two non-separabilities are studied, habit persistence and durability of the commodity. As the model has no closed-form solution, we compute deterministic and stochastic solution paths. It enables us to compare income and consumption volatility, and to describe the density of consumption under the different hypotheses on the utility function

Sustainability, optimality, and viability in the Ramsey model

The Ramsey model of economic growth is revisited from the point of view of viability compared to optimality. A viable state is a state from which there exists at least one trajectory in capital, consumption, and reproduction that remains in the set of constraints of minimal consumption and positive wealth. There exists a largest set of viable states, including all others, called the viability kernel. This concept is an interesting addition to those of equilibria and optimal paths. Viability is first presented with a constraint of minimal consumption, then with an additional criterion of economic sustainability in the sense of the Brundtland commission, which amounts to requiring a non-decreasing social welfare. The comparison of viability kernels with or without sustainability shows how much consumption should be reduced and when. One strong mathematical result is that the viable-optimal solution in the sense of inter-temporal consumption is obtained on the viability boundary of an auxiliary system. Varying preference, technological, and demographic parameters randomly over simulated viability kernels with and without the Brundtland criterion help identify the determinants of the non-emptiness of the viability kernel and of its volume: technological progress works against population growth to favor the possibility for a given state of being viable or viable-sustainable.Viability theory, Optimization, Sustainability, Ramsey model

Optimal Capital Accumulation, Energy Cost and the Nature of Technological Progress

This paper derives the optimal pace of capital accumulation at the firm level and the corresponding investment dynamics in the presence of an energy-saving technological progress. Energy and capital are complementary. When technical progress is disembodied, the firm invests once at the first period and never invests again. The optimal capital stock is a decreasing function of the energy price. When technical progress is embodied, the optimal scrapping time of capital goods is constant and investment is periodic. The optimal effective capital stock is shown to be lower than the optimal capital stock under disembodied technical change. A striking outcome of the paper is that under embodiment, the optimal effective capital stock is an increasing function of the energy cost, in contrast to the disembodiment caseInvestment theory;Embodied technological progress;Energy;Investment dynamics

Catching-up with the "locomotive": a simple theory

This paper extends the standard neoclassical model by considering a technology sector through which an economy with limited human capital attempts to catch up with a given "locomotive" pushing exogenously technical progress. In periods of technological stagnation, economies close enough to the frontier may find it optimal to not catch up, which reinforces worldwide technological sclerosis. Under sustainable technological growth, all the other economies will sooner or later engage in imitation. Such a phase of technology adoption may be delayed depending on certain deep characteristics of the followers.

Sustainability, optimality, and viability in the Ramsey model

The Ramsey model of economic growth is revisited from the point of view of viability. A viable state is a state from which there exists at least one tra jectory that remains in the set of constraints of minimal consumption and positive wealth. Viability is presented with a constraint of minimal consumption, then with an additional criterion of economic sustainability. The comparison of viability kernels with or without sustainability shows how much consumption should be reduced and when. The viable-optimal solution in the sense of inter-temporal consumption is obtained on the viability boundary of an auxiliary system. Technological progress works against population growth to favor the possibility for a given state of being viable or viable-sustainable.viability theory, optimization, sustainability, Ramsey model

Differential-difference equations in economics: on the numerical solution of vintage capital growth models

In this papel, we examine techniques for the analytical and numerical solution of statedependent differential-difference equations. Such equations occur in the continuous time modelling of vintage capital growth models, which form a particularly important class of models in modern economic growth theory. The theoretical treatment of non-statedependent differential-difference equations in economics has already been discussed by Benhabib and Rustichini (1991). In general, though, the state-dependence of a model prevents its analytical solution in all but the simplest of cases. We review a numerical method for solving state-dependent models, using sorne simple examples to illustrate our discussion. In addition, we analyse the Solow vintage capital growth model. We conclude by mentioning a crucial unresolved issue related to this topic

Solving recent RBC models using linearization: further reserves

Through a simple example, we show that the successive sophistications introduced in the early RBC models in order to improve their internal propagation mechanisms have actually increased their non-linearities, even locally. Accordingly, linearization-based resolution methods become much more disputableı than they were for early RBC models. Simple comparative studies ofı impulse-response functions are used to illustrate this point. We conclude by pointing at sorne alternative resolution techniques that allow the model builder to take non-linearities into account and/or to handle with the presence of large state spaces