Optimal investment with vintage capital: Equilibrium distributions

The paper concerns the study of equilibrium points, or steady states, of economic systems arising in modeling optimal investment with vintage capital, namely, systems where all key variables (capitals, investments, prices) are indexed not only by time but also by age. Capital accumulation is hence described as a partial differential equation (briefly, PDE), and equilibrium points are in fact equilibrium distributions in the variable of ages. A general method is developed to compute and study equilibrium points of a wide range of infinite dimensional, infinite horizon, optimal control problems. We apply the method to optimal investment with vintage capital, for a variety of data, deriving existence and uniqueness of equilibrium distribution, as well as analytic formulas for optimal controls and trajectories in the long run. The examples suggest that the same method can be applied to other economic problems displaying heterogeneity. This shows how effective the theoretical machinery of optimal control in infinite dimension is in computing explicitly equilibrium distributions. To this extent, the results of this work constitute a first crucial step towards a thorough understanding of the behavior of optimal paths in the long run.     

Environmental taxes with heterogeneous consumers: an application to energy consumption in France

This paper constructs a model with four groups of households who have preferences over labor supply, consumption of polluting (energy related) and non-polluting (non-energy) goods, and emissions. It quantifies the model for the French economy and computes its optimal tax equilibria under nine second-best tax regimes. We find that the redistributive role of environmental taxes requires the polluting goods to be taxed at a rate much below their marginal social damage. These goods may even require an outright subsidy if the society values equality ‘a lot’. Secondly, if environmental taxes that have an exclusively externality-correcting role, they benefit all types—although the gains are rather modest. The gains and losses become more substantial when environmental taxes have a redistributive role as well. Third, setting the environmental tax at its Pigouvian level, rather than its optimal externality-correcting-cum-redistributive level, benefits the high-income group at the expense of the low-income groups. Fourth, nonlinear taxation of polluting goods, and nonlinear commodity taxation in general, is a powerful redistributive mechanism. Fifth, introducing environmental taxes in the current French tax system, with its suboptimal income taxes, results in substantial welfare gains for the highest income group and a sizable loss for the least well-off persons.     

Is the Optimal Labor Income Tax Progressive in a Unionized Economy?*

This paper concerns optimal nonlinear labor income taxation in an economy with union wage setting and endogenous hours of work. The purpose is to study the determinants of tax progression. We show that the optimal degree of progression of the labor income tax depends on the extent to which the government can influence the wage rate via tax policy as well as on its ability to redistribute income across individuals. In addition, the argument for progressive labor income taxation depends on whether hours of work are chosen by the employed themselves or the union.     

Political Measures for Strategic Environmental Policy with External Effects

This paper investigates an environmental policy designed to reduce the emission of pollutants under uncertainty, with the agent problem as an optimal stopping problem. We first analyze the two cases in which there are one agent and two competing agents by following Ohyama and Tsujimura (2005). When we consider a model of strategic agents, we need to analyze the external economic effect that is peculiar to an agent’s environmental policy implementation. Then, to improve and resolve these external effects, we examine three alternative political measures, comprising an environmental subsidy, an environmental tax and an emission trading system. The results of the analysis indicate that the environmental subsidy and environmental tax promote environmental policy. However, they do not create an incentive to be the leader. On the other hand, an emissions trading system not only promotes environmental policy but also creates an incentive for leadership.This paper was previously circulated under the title “Political Measures for Strategic Environmental Policy with Induced Effects”. The authors would like to thank Masaaki Kijima for helpful comments. The authors would also like to thank Alistair Munro and two anonymous referees providing detailed comments and suggestions. This research was partially supported by Daiwa Securities Group Inc. The second-named author was partially supported by the Ministry of Education, Culture, Sports, Science and Technology, Grant-in-Aid for Scientific Research (B) (2), 16310118.     

Public finance and the optimal speed of transition*

We develop a general equilibrium model that jointly considers the influence of capital accumulation constraints and of labour market frictions on the process of transition. We endogenize the economic and budgetary costs of different government policies and show that, early in transition, governments ought to subsidize state firms. Provided that intertemporal commitment is feasible, this policy limits the initial output fall, which relaxes capital accumulation constraints, accelerates transition, and increases welfare. Moreover, by resorting to indirect – instead of direct – taxes, governments can bring the path of transition closer to the first best. Yet, political pressures may induce a policy of suboptimal subsidization.     

财政补贴改革刍论

财政补贴是国家宏观调控的杠杆之一,但是,目前补贴不规范,财政补贴数额大、项目繁杂,补贴效果‘异化’,加大了社会不公。为了强化财政补贴杠杆功能,提高财政补贴效益,必须按照建立公共财政的要求,本着满足公共需要原则、弹性补贴制度原则和补贴方式间接化原则,改变“一刀切”和补贴刚性的局面,确保采暖费收支合理化,取消肉食、副食品、粮食等价格补贴,改革国有企业的亏损补贴制度。     

矫枉何须过正--评美国《2000年持续性倾销与补贴补偿法》

2000年底，美国国会通过了《持续性倾销与补贴补偿法》(CDSOA)，依据该法，海关征收的反倾销、反补贴税将以补偿的形式分配给受影响的国内生产者。CDSOA借维护公平贸易之名，行保护主义之实，不但缺乏经济上的合理性，也违背了美国依WT0协定承担的国际义务，从而引起了各国的声讨。     

On the smoothness of optimal paths II: some local turnpike results

We study the local turnpike property for two classes of infinite-horizon discrete-time deterministic maximization problems which have common applications, e.g., optimal growth theory. We follow a functional-analytic approach and rely on an implicit function theorem for the space of the sequences which converge to zero. We shall assume the existence of an optimal path which is not necessarily a steady-state. Relying on material developped in Blot and Crettez (Decis Econo Finance 27:1–34, 2004), “On the smoothness of optimal paths” Decis Econ Finance, 21:1–34, 2004), we provide conditions under which a variation in the initial conditions (i.e., capital stock and discount rate) yields an optimal solution which converges toward a reference solution when time becomes infinite. We also provide new results on bounded solutions of difference equations. We gratefully thank the editor, Silvano Holzer, and two anonymous referees for remarks and advices on a previous version of this paper.