The hopf bifurcation and the existence and stability of closed orbits in multisector models of optimal economic growth

It is shown that under very general circumstances, the standard optimal growth model with two or more capital goods can give rise to optimal trajectories that are limit cycles. An example with a nonjoint production Cobb-Douglass technology giving rise to closed cycles around a unique steady state is constructed. The stability of orbits is also studied.     

Effect of social security on fertility and savings: an overlapping generations model

Old-age pension schemes do not exist in most developing countries, so adults bear children as security investments for the future. This phenomenon leads to unduly high rates of population growth. It has been hypothesized that introducing social security programs in such countries would increase savings rates and reduce the number of children born over the long term. The author studies the general equilibrium effects of some social security programs on rates of population growth and capital accumulation within an overlapping generations framework with endogenous fertility and savings. Specifically, Raul's overlapping generations growth model is extended to study the general equilibrium effects of payroll-tax-financed and child-tax-financed social security programs. It is shown that if the rate of intergenerational income transfers from young to old or child care cost is low, competitive equilibrium leads toward overpopulation and capital accumulation in a modified Pareto optimal sense; a social security program in such a case is therefore Pareto improving. A fully-funded system is not neutral when financed by child taxes. Finally, it is also shown that unlike in the case of exogenous fertility where competitive equilibrium attains steady state only asymptotically, fertility, when endogenous, may attain a unique globally steady state in finite time.     

关税、货币政策与中国实际均衡汇率

加入WTO后 ,降低进口品关税等措施将影响人民币均衡汇率水平 ,同时开放经济下国内货币政策、财政政策等宏观经济政策调整也会改变均衡汇率水平。本文运用动态一般均衡的方法 ,探讨中国在加入世界贸易组织之后 ,关税税率调整、货币供应量增长率改变、财政政策调整等措施对实际均衡汇率的长期效应。把货币引入生产函数和消费者的效用函数 ,我们扩展了由Turnovsky提出的两商品资本积累模型 ,利用参数赋值(calibration)的方法进行了均衡状态下的比较静态分析。研究发现降低进口品关税使人民币面临贬值压力 ,而政府增加税收 ,减少对贸易品的消费则有利于人民币的保值和升值。实证研究结果表明 :国外实际利率水平下降 ,实际货币供应量增长率降低都将引起人民币均衡汇率贬值。     

Public Expenditure,Environment, and Economic Growth

This paper attempts to develop a model of endogenous growth with special consideration to the role of productive public expenditure in the presence of congestion effect of private capital and environmental pollution. We analyze the properties of the optimal fiscal policy in the steady‐state equilibrium when the level of production of the final good is the source of emission. Government allocates its income tax revenue between pollution abatement expenditure and productive public expenditure. In the steady‐state equilibrium, optimum ratio of productive public expenditure to national income is less than the competitive output share of the public input; and this ratio varies inversely with the magnitude of the emission‐output coefficient. The steady‐state equilibrium appears to be a saddle point; and the market economy growth rate is not necessarily less than the socially efficient growth rate in the steady‐state equilibrium.     

Does Real Exchange Rate Depreciation Boost Capital Accumulation? An Intertemporal Analysis

This paper examines the investment‐enhancing effect of real exchange rate (RER) depreciation in a two‐sector small open economy model where a representative firm in the tradable sector maximises its discounted profit over an infinite planning period. In this framework, a one‐time, permanent, unanticipated depreciation in the RER leads to a higher steady‐state level of capital stock and investment. This consequently increases the optimal investment rate associated with an arbitrary level of capital stock as the saddle path shifts upwards. In the benchmark calibration, the investment‐enhancing effect of RER depreciation is sizeable. One per cent depreciation in the RER leads to an increase of 0.4444 per cent in the rate of capital accumulation.     

FOREIGN CAPITAL AND ECONOMIC GROWTH

This paper examines the economic implications of institutional arrangements by which foreign investors are required to reinvest a certain percentage of their capital within the host country. Our analysis shows that foreign capital inflow can produce long-lasting economic benefits to the host country only when the foreign capital reinvestment rate is sufficiently greater than the host country's saving rate. In this case, the economy evolves into a unique steady state equilibrium, which is also asymptotically stable. The paper also presents several comparative static results regarding the responses of steady state capital-labour ratio and the proportion of foreign capital in total capital to changes in the population growth rate, the rate of capital depreciation, the host country's saving rate and the foreign capital reinvestment rate.     

Capital income taxation,depreciation allowances and economic growth: A perfect-foresight general equilibrium model

Conclusions The results indicated in Table 1 show that incomplete depreciation allowances reinforce the distortions in the equilibrium growth path brought about by an ideal capital income tax. A reduction in the deductible share of economic depreciation, like an increase in the tax rate, raises the current level of consumption, but reduces the steady state levels of consumption and capital per efficiency unit of labour.The reason for these distortions is that the tax law is able to drive wedges both between the rate of time preference and the market rate of interest, and between the latter and the marginal productivity of capital. The first wedge is created through capital income taxation as such and its size is directly related to the tax rate. The second wedge is created by the incomplete deductibility of depreciation. Its size is directly related to the tax rate and inversely to the deductible share of depreciation. For the distortion in the growth path of the economy it is the sum of the two wedges that counts. Therefore it is plausible that incomplete depreciation allowances reinforce the effects of capital income taxation.Knowing the determinants of the two wedges one can easily derive the influence of a tax reform on the marginal productivity of capital, the market rate of interest and the rate of time preference (cf. Table 2). In the short run, the system of these three interest rates is anchored by the marginal productivity of capital, and hence any measure that widens a wedge is translated into a reduction in the rate or those rates below the wedge. In the long run the system is anchored by the rate of time preference and an increase in the width of a wedge is translated into an increase in those rates or that rate above this wedge.The paper was written in association with the Sonderforschungsbereich 5 (Staatliche Allokationspolitik im marktwirtschaftlichen System).     

Walrasian General Equilibrium Allocations and Dynamics in Two-Sector Growth Models

This paper analyzes and solves miniature Walrasian general equilibrium systems of momentary and moving equilibria. The Walrasian framework encompasses the fundamental neoclassical and classical two‐sector growth models; the families of solutions of steady‐state and persistent growth per capita in various competitive two‐sector economies are parametrically characterized. Moreover, the endogenous behavior of relative prices and the sectoral allocation of primary factors are analyzed in detail. The technology parameters of the capital good industry are decisive for obtaining long‐run per capita growth in closed (global) economies. A review of the literature complements the theorems on the general equilibrium allocations, dynamic systems, and the time paths of Walrasian two‐sector economies.     

ENDOGENOUS FLUCTUATIONS IN TWO‐COUNTRY MODELS*

This paper investigates the interlinkage in the business cycles of large‐country economies in a free‐trade equilibrium. We consider a two‐country, two‐good, two‐factor general equilibrium model with Cobb‐Douglas technologies and linear preferences. We also assume decreasing returns to scale in the consumption good sector. We first identify the determinants of each country's global accumulation pattern in autarky equilibrium, and secondly we show how a country's business cycles may spread throughout the world once trade opens. We thus give capital intensity conditions for local and global stability of competitive equilibrium paths.     

Growth and welfare effects of stabilizing innovation cycles

We consider a simple model of innovation where equilibrium cycles may arise and show that, whenever actual capital accumulation falls below its balanced growth path, subsidizing innovators by taxing consumers has stabilizing effects, promotes sustained growth and increases welfare. Further, if the steady state is unstable under laissez faire, the introduction of the subsidy can make the steady state stable. Such a policy has beneficial effects as it fosters output growth along the transitional adjustment path, and increases the welfare of current and future generations.     

Fiscal policies, environmental pollution and economic growth

This paper develops a model of endogenous economic growth with special consideration to the role of productive public expenditure and environmental pollution; and analyses the properties of optimal fiscal policy in the steady state growth equilibrium. We consider the level of consumption as the source of pollution. Government allocates its tax revenue between pollution abatement expenditure and productive public expenditure. Optimum ratio of productive public expenditure to national income is equal to the competitive output share of the public input, when productive public expenditure is depicted as tax revenue minus abatement expenditure. However, the proportional income tax rate exceeds the competitive output share of the public input. There is no conflict between the social welfare maximizing solution and the growth rate maximizing solution in the steady state growth equilibrium. The unique steady state growth equilibrium appears to be a saddle-point when the growth rate is above a critical level and the steady state equilibrium growth rate in the market economy is not necessarily lower than the socially efficient growth rate.     

Implementing Steady State Efficiency in Overlapping Generations Economies with Environmental Externalities

We consider in this paper overlapping generations economies with pollution resulting from both consumption and production. The competitive equilibrium steady state is compared to the optimal steady state from the social planner's viewpoint. We show that the dynamical inefficiency of a competitive equilibrium steady state with capital–labor ratio exceeding the golden rule ratio still holds. Moreover, the range of dynamically efficient steady state capital ratios increases with the effectiveness of the environment maintenance technology, and decreases for more polluting production technologies. We characterize some tax and transfer policies that decentralize as a competitive equilibrium outcome the transition to the social planner's steady state.     

Ramsey fiscal policy and endogenous growth

This paper examines the effects of fiscal policies on capital accumulation and economic performance in a simple endogenous growth model with elastic labor supply by focusing on the implementability of a competitive equilibrium with productive public spending and distortionary taxation. Given a feasible exogenous fiscal policy, productive public spending can, at first, lead to positive short-run and long-run growth in the unique competitive equilibrium. However, although strictly positive growth is possible in the short run, a Ramsey policy with productive public spending does not implement positive capital accumulation in the long run. Also, the local indeterminacy of Ramsey allocations, in conjunction with the global multiplicity, arises as an implementable competitive equilibrium with Ramsey policies: namely, a continuum of transitional dynamics and multiple balanced growth paths. I am grateful to Kazuo Nishimura, Theodore Palivos, Sang Hee Won, John Conlon, Apostolis Philippopoulos, Arved Ashby, In Ho Lee, Katsuaki Terasawa, and an anonymous referee of this journal for valuable comments and suggestions. I also thank seminar participants at Ioannina University, Kyoto University, University of Mississippi, and Seoul National University. This paper is supported by 2006 Sabbatical Project, Kyung Hee University.     

Costly structural change and optimal growth

Summary This paper studies the optimal growth of a developing economy that has a choice to expend a fixed amount of resource for a structural change that advances its production technology. It is shown that structural change is undertaken if capital stock is above a critical level. Economies undertaking structural change converge to a larger steady state and economies not undertaking structural change converge to a smaller steady state. The optimal policy correspondences and growth paths are characterized. The social optimum is shown implementable by a competitive equilibrium with lump-sum taxation.We are grateful to Francis Cheung, Carmen Menezes, Peter Mueser, Don Schilling, two anonymous referees and an associate editor for their valuable suggestions.     

Optimal fiscal policy in the Uzawa-Lucas model with CES production

This paper devises an endogenous growth model with human capital in the Uzawa-Lucas framework in which the average human capital has a positive external effect on the goods sector. Unlike previous works, this paper assumes that output is produced with a CES technology and analyzes the existence, uniqueness, and stability of equilibrium. Also, a fiscal policy is devised that is capable of providing the required incentives to optimize the competitive equilibrium. In order to correct the market failure caused by the externality, the authors introduce a subsidy to human capital and analyze how it can be financed in an optimal way. Some simulation results are presented.     

Preparing for catastrophic climate change

We study optimal adaptation to climate change when the harmful consequences of global warming are associated with uncertain occurrence of abrupt changes. The adaptation policy entails the accumulation of a particular sort of capital that will eliminate or reduce the catastrophic damage of an abrupt climate change when (and if) it occurs. The occurrence date is uncertain. The policy problem involves balancing the tradeoffs between the (certain) investment cost prior to occurrence and the benefit (in reduced damage) that will be realized after the (uncertain) occurrence date. For stationary economies the optimal adaptation capital converges monotonically to a steady state. In most cases, investment begins immediately. However, if the initial adaptation capital exceeds a pre-specified threshold level, which lies above the optimal steady state, investment is delayed while the capital stock decreases (due to depreciation) and commences only when it reaches this threshold level. For growing economies the optimal adaptation capital stock approaches the maximal economic level above which further accumulation is ineffective.     

The taxation of capital returns in overlapping generations models

This paper shows that in the Diamond (1965) overlapping generations economy with production and capital savings, there is a period-by-period balanced fiscal policy supporting a steady state allocation that Pareto-improves upon the laissez-faire competitive equilibrium steady state (whether dynamically inefficient or efficient) without resorting to intergenerational transfers. The policy consists of taxing linearly (or subsidizing, in the dynamically efficient case) the returns to capital, while balancing the budget period by period through a lump-sum transfer (or tax, respectively) in second period. This intervention grants every generation the highest steady state utility attainable through markets (i.e. remunerating factors by their marginal productivities and without transfers) which under laissez-faire is not a competitive equilibrium outcome. A transition from the competitive equilibrium steady state to this other steady state is also Pareto-improving when the former is dynamically inefficient. The result disentangles from redistributive considerations the impact of the taxation of capital returns on steady state welfare, and thus provides a rationale for the taxation of capital returns that is based on efficiency considerations and not on redistributive goals.     

Collateral secured loans in a monetary economy

This paper presents a microfounded model of money where durable assets serve as a guarantee to repay consumption loans. We study a steady state equilibrium where money and credit coexist. In such an equilibrium, a larger investment in durable capital relaxes the borrowing constraint faced by consumers. We show that the occurrence of over-investment and the behavior of capital accumulation depend on the rate of inflation, the relative risk aversion of agents and the marginal productivity of the capital goods.     

Capital depreciation allowances,redistributive taxation,and economic growth

Are capital depreciation allowances when coupled with capital income taxes good instruments for redistribution in the long run? In a simple two-agent-economy I find that accelerated depreciation is good for growth, but bad for redistribution. The opposite holds for capital income taxes. However, in a feedback Stackelberg equilibrium, where the government is the leader and the private sector the follower, the depreciation allowance is maximal in the long run, time-consistent optimum. This removes the accumulation distortion of capital income taxes. Furthermore, the latter, and so redistribution, is found to be generically nonzero in the time-consistent optimum, and depends on the social weight of transfers receivers, the pretax factor income distribution, the intertemporal elasticity of substitution and the time preference rate. Thus, accelerated depreciation allowances are an important indirect tool for redistribution. The tax scheme allows for a separation of “efficiency” and “equity” concerns for redistributive policies.     

OPTIMAL CAPITAL TAXES FOR PUBLIC GOOD PROVISION*

This paper constructs a general equilibrium trade model of a small open economy that produces many traded private goods and one non-traded public consumption good. Trade in goods is free, but the country taxes the internationally mobile capital to finance the provision of the public good. Within this framework, the paper identifies the conditions under which the optimal policy on the internationally mobile capital calls for a tax. Under the assumptions that (i) the welfare function is concave with respect to the tax rate, and (ii) the net revenue-maximizing capital tax rate is positive, it is shown that the marginal cost of the public good always understates its social marginal cost.