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

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 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

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

Impacts of emission reduction policies in a multi-regional multi-sectoral small open economy with endogenous growth

The burden sharing of pollution abatement costs raises the issue of how to share the costs between entities (country, region or industry) and how the pollution permits should be distributed between the parties involved. This paper explores this issue in the framework of a dynamic endogenous growth 2 sectors - 2 regions - 2 inputs Heckscher-Ohlin model of a small open multi-regional economy with an international tradable permits market. Given an "emission-based grand-fathering" sharing rule, capital accumulation is more negatively affected by the environmental policy in the energy intensive sector. We show that such a property does not necessarily hold with a "production-based grand-fathering" sharing rule. We also show that the impact on capital is likely to translate into the sectoral added value level after some time, specially if the economy is submitted to an increasingly constraining environmental policy driving up the ratio price of permits to price of energy. Finally, we show that the impact of environmental policy at the regional level depends crucially on the specialization of the region along the baseline.pollution permits, grand-fathering, sectoral spillovers, multi- regional economy, endogenous growth

Assessing the Parfit's Repugnant Conclusion within a canonical endogenous growth set-up

Parfit's Repugnant Conclusion stipulates that under total utilitar- ianism, it might be optimal to choose increasing population size while consumption per capita goes to zero. We evaluate this claim within a canonical AK model with endogenous fertility and a reduced form re- lationship between demographic growth and economic growth. While in the traditional linear dilution model, the Parfit Repugnant Conclu- sion can never occur for realistic values of intertemporal substitution, we show that it occurs when population growth is linked to economic growth via an inverted U-shaped relationship. Finally, we find moving from the Benthamite to the Millian social welfare function may not only cause optimal population size to go up and consumption to go down, it may also favor the realization of the Repugnant Conclusion.Parfit's Repugnant Conclusion, AK models, endogenous fertility, intertemporal altruism