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

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

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

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

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

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.Stochastic simulations; Liquidity constraints; Habit formation; Durability;

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

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

Parfit's Repugnant Conclusion stipulates that under total utilitarianism, 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 relationship between demographic growth and economic growth. While in the traditional linear dilution model, the Parfit Repugnant Conclusion 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

Machine Replacement, Technology Adoption and Convergence

In this paper, we introduce adoption costs in a canonical vintage capital model. Adoption costs take the form of a direct loss in production during a fixed period of time. We explicitly characterize the optimal machine replacement policy as a function of the adoption period. Using an explicit numerical method, we study the dynamics of the model. In particular, we find that while an increase in the adoption costs lowers the long run level of output, it also rises the magnitude of short run fluctuations and decreases the convergence speed to the steady states.Machine replacement; Technology adoption; Optimal scrapping; Fluctuations; Convergence

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.