Endogenous fertility and growth in a model with old age support

Summary. This paper examines the interrelationship between capital accumulation, fertility, and growth by introducing an endogenous fertility decision into Diamond's (1965) neoclassical growth model. Under the assumptions that children provide old age support and that individuals incur a variable time cost of raising children, it investigates the potential for cyclical fluctuations in the capital-labor ratio and fertility, as well as for development trap phenomena to be observed. It is shown that when capital and labor are highly substitutable in production, there is a unique steady state equilibrium, and either damped or undamped oscillations in fertility and the capital-labor ratio may occur. However, when the elasticity of substitution between capital and labor is less than one, two steady state equilibria may exist; one with a high capital-labor ratio and a high rate of population growth, and the other with a lower capital-labor ratio as well as a lower population growth rate. The former is a saddle, while the latter may be either a source or a sink. In the latter case development traps are possible. Received: June 16, 1997; revised version: December 18, 1997     

Hopf bifurcation and quasi-periodic dynamics in discrete multisector optimal growth models

This paper discusses the asymptotic stability of the steady state and the existence of a Hopf bifurcation in discrete time multisector optimal growth models. We obtain on the one hand a local turnpike theorem which guarantees the saddle point property for all discount rates. On the other hand, we provide a new proposition which gives some conditions ensuring local stability of the steady state if the impatience rate is not too high. A characterization of the boundδ*, above which the steady state is saddle-point stable, is also proposed in terms of indirect utility function's concavity properties. On this basis, some sufficient conditions for the existence of a Hopf bifurcation are stated. We thus prove the existence of quasi-periodic optimal paths in asymmetric models.     

Factors substitutability,heterogeneity and endogenous fluctuations in a finance constrained economy

Summary.   This paper examines the local properties of perfect foresight equilibrium of a finance constrained economy featuring two classes of infinitely-lived agents with heterogeneous general preferences. It is primarily concerned with the conceivability of endogenous fluctuations for large plausible capital-labor elasticities of substitution. It is notably shown that heterogeneity in preferences allows Hopf cycles to be entirely consistent with a wide range of elasticities of substitution including the unitary one (Cobb-Douglas specifications). Received: April 23, 1999; revised version: January 24, 2000     

Capital market imperfections in a monetary growth model

Summary. We consider a monetary growth model essentially identical to that of Diamond (1965) and Tirole (1985), except that we explicitly model credit markets, a credit market friction, and an allocative function for financial intermediaries. These changes yield substantially different results than those obtained in more standard models. In particular, if any monetary steady state equilibria exist, there are generally two of them; one of these has a low capital stock and output level, and it is necessarily a saddle. The other steady state has a high capital stock and output level; either it is necessarily a sink, or its stability properties depend on the rate of money creation. It follows that monetary equilibria can be indeterminate, and nonconvergence phenomena can be observed. Increases in the rate of money creation reduce the capital stock in the high-capital-stock steady state. If the high-capital-stock steady state is not a sink for all rates of money growth, then increases in the rate of money growth can induce a Hopf bifurcation. Hence dynamical equilibria can display damped oscillation as a steady state equilibrium is approached, and limit cycles can be observed as well. In addition, in the latter case, high enough rates of inflation induce the kinds of “crises” noted by Bruno and Easterly (1995): when inflation is too high there are no equilibrium paths approaching the high-activity steady state. Received: November 18, 1995; revised version: March 26, 1996     

Indeterminacy in dynamic models: When Diamond meets Ramsey

We consider an aggregate two-periods overlapping generations model with endogenous labor, consumption in both periods of life, homothetic preferences and productive external effects coming from the average capital and labor. We show that under realistic calibrations of the parameters, in particular a large enough share of first period consumption over the wage income, local indeterminacy of equilibria cannot occur with capital externalities alone. It can nevertheless occur when there are only, even very small, vanishing labor externalities provided that the elasticity of capital-labor substitution and the wage elasticity of the labor supply are large enough. We also show that if labor externalities are slightly stronger, but still small enough to be plausible, and the elasticity of labor supply is larger, local indeterminacy occurs in a Cobb-Douglas economy. Finally, we show that a locally indeterminate steady state is generically characterized by an under-accumulation of capital. It follows therefore that while agents live over a finite number of periods, the conditions for the existence of locally indeterminate equilibria are very similar to those obtained within infinite horizon models and that from this point of view, Diamond meets Ramsey.     

中国区域要素替代弹性变迁及其增长效应——基于异质劳动视角的随机前沿生产函数分析

文章采用1996-2014年省际面板数据构建区域随机前沿生产函数模型,从劳动异质性视角拓展要素替代弹性分析;并首次联合运用协整方程和误差修正模型,从长期均衡和短期波动过程分析来揭示要素替代约束对经济增长的影响.结果发现:尽管三大区域各自的要素替代弹性变化显著不同,但要素替代弹性的增长效应却彼此具有一致性.其中,东部地区的资本-劳动替代弹性明显地存在着0.805的增长门槛,只有西部地区的资本-劳动替代弹性越过了门槛值,与区域增长具有尚不显著的正相关性而支持德拉格兰德维尔假说;三大区域的资本-技能互补性提高对经济增长的推动作用都不明显;劳动-技能替代弹性则表现为显著的正向增长效应,显示出各区域存在着人力资本红利.值得注意的是,与均衡增长路径上"资本-劳动替代弹性提高能够推动经济增长"的德拉格兰德维尔假说不同,在考虑劳动异质性和技术非效率的前提下,中国地区增长更支持"劳动-技能替代弹性提高能够推动经济增长"的结论.文章为甄别新常态下的区域增长潜力转变、剖析要素匹配合理性及产业结构调整可行性奠定基础.     

Capital-labor substitution in a developing country: The case of Greece

The present paper reports an attempt to estimate the elasticity of capital-labor substitution, and the rate of technical change in the manufacturing sector of the Greek economy. It is found that the elasticity of substitution exceeds unity, and the annual rate of neutral technical change is e^0.05 = 1.05. It is concluded that because of the case of capital-labor substitution the existing labor shortages should not impair the further development of the economy.     

Two‐level CES Production Technology in the Solow and Diamond Growth Models*

The two‐level CES aggregate production function—that nests a CES into another CES function—has recently been used extensively in theoretical and empirical applications of macroeconomics. We examine the theoretical properties of this production technology and establish existence and stability conditions of steady states under the Solow and Diamond growth models. It is shown that in the Solow model the sufficient condition for a steady state is fulfilled for a wide range of substitution parameter values. This is in sharp contrast with the two‐factor Solow model, where only an elasticity of substitution equal to one is sufficient to guarantee the existence of a steady state. In the Diamond model, multiple equilibria can occur when the aggregate elasticity of substitution is lower than the capital share. Moreover, it is shown that for high initial levels of capital and factor substitutability, the effect of a further increase in a substitution parameter on the steady state depends on capital–skill complementarity.     

Complex dynamics of monopolies with gradient adjustment

This paper aims to show that delay matters in continuous- and discrete-time framework. It constructs a simple dynamic model of a boundedly rational monopoly. First the existence of the unique equilibrium state is proved under general price and cost function forms. Conditions are derived for its local asymptotical stability with both continuous and discrete time scales. The global dynamic behavior of the systems is then numerically examined, demonstrating that the continuous system is globally asymptotically stable without delay and in the presence of delay if the delay is sufficiently small. Then stability of the continuous system is lost via Hopf bifurcation. In the discrete case without delay, the steady state is locally asymptotically stable if the speed of adjustment is small enough, then stability is lost via period-doubling bifurcation. If the delay is one or two steps, then stability loss occurs via Neimark–Sacker bifurcation.     

Dynamic effects of government expenditure in a finance constrained economy

This paper introduces constant government expenditure in Woodford's finance constrained model (J. Econ. Theory, 1986) with capital-labor substitution as presented in Grandmont, Pintus and de Vilder (J. Econ. Theory, 1998) and investigates how government expenditure influences local dynamics near multiple steady states, depending upon the elasticity of substitution between capital and labor in production.     

Multiple equilibria and limit cycles in evolutionary games with Logit Dynamics

This note shows, by means of two simple, three-strategy games, the existence of stable periodic orbits and of multiple, interior steady states in a smooth version of the Best-Response Dynamics, the Logit Dynamics. The main finding is that, unlike Replicator Dynamics, generic Hopf bifurcation and thus, stable limit cycles, occur under the Logit Dynamics, even for three-strategy games. We also show that the Logit Dynamics displays another bifurcation which cannot occur under the Replicator Dynamics: the fold bifurcation, with non-monotonic creation and disappearance of steady states.     

Pollution effects on preferences: A unified approach

In this paper, we introduce a unified Ramsey model where pollution has an impact on preferences and affects both consumption demand and labor supply. Pollution comes from production activities and is viewed as a stock variable with a strong inertia. A government is introduced and levies a proportional tax on production to finance depollution expenditure. We find two interesting results when pollution raises the consumption demand (compensation effect). First, in the long run, a higher green‐tax rate increases the pollution level at the steady state (green paradox) when pollution raises the labor supply (disenchantment effect). Second, in the short run, local indeterminacy can arise through a Hopf bifurcation when pollution lowers the labor supply (leisure effect) even if pollution has a strong inertia.     

Intersectoral Externalities and Indeterminacy

We consider a two-sector economy with positive intersectoral external effects and nonincreasing social returns. We show that if the discount factor ρ is close to 1 then local indeterminacy may be obtained with mild market imperfections. Moreover, with additional conditions, when ρ is made smaller the steady state becomes totally unstable and quasi-periodic cycles, along which equilibrium paths are indeterminate, may appear through a Hopf bifurcation. This will be proved even if the investment good is capital intensive at the private level while this condition guarantees local determinacy in the sector specific case. Journal of Economic Literature Classification Numbers: C62, E32, O41.     

Will the consumption externalities' effects in the Ramsey model please stand up?

According to the prior literature, in a Ramsey model, consumption externalities have no impact on steady state behavior, once labor supply is exogenous. In contrast, this paper argues that — in the presence of technical change — consumption externalities always affect steady state behavior, via their impact on the elasticity of marginal utility of consumption.     

An optimal monetary policy in an aggregate neoclassical model of economic growth

This paper shows that the usual Ramsey-Cass-Koopmans optimal-growth theory is applicable to decentralized monetary economies and illustrates, with a simple model, how optimal growth can be achieved via a simple monetary policy. Securities and the endogeneity aspect of the money supply are explicitly introduced. This paper shows that the steady state under optimal growth is a saddle point, that the dynamic behavior of the capital-labor ratio and real per capita consumption is identical to that found in the usual literature in which money is not introduced, and that the optimal monetary policy is “counter-cyclical.”     

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.     

Multiple equilibria and global indeterminacy in an endogenous growth model with congestible public goods

This paper extends the findings in Chen and Lee (2007) to show that the use of congestible public goods can produce both local and global indeterminacy in a two‐sector endogenous growth model with productive public services financed by income taxation. Basically, we observe the effects on growth rates by changing parameters, and compare the case of a single steady‐state with the emergence of dual steady‐states, identifying the feasible ways to avoid a possible low‐growth poverty trap. The novelty of our analysis is to detect the presence of global indeterminacy by making use of the Bogdanov‐Takens bifurcation theorem. Some examples are also provided to achieve concrete policy implications.     

Environmental resilience and economic growth: Command economy's optimization and environmental Kuznets curve

This paper constructs a two-sector environmental growth model with explicit mathematical derivation and economic intuition in a social planning economy. Through the optimal allocation of man-made capital between the production sector and the environmental sector, this paper shows that the trade-off between economic growth and environmental protection exists only when an economy deviates from its steady state. We also provide short-run transitions for both the whole economic system and individual control and state variables. In addition, technological progress in the production sector benefits economic growth rate while the improvement of technology in the environmental sector has only level effects on economic variables. This paper ends with a link between the theory and a hot empirical issue — the environmental Kuznets curve (EKC) hypothesis.     

Applying input-output analysis to scenario analysis of ecological footprints

Application of input-output analysis to ecological footprints (EFs) is shifting from an ex-post static calculation toward an ex-ante scenario analysis for enhancing the policy relevance of EF analysis. This change in application prompts two issues requiring careful examination: (1) what is measured by Leontief inverses or extended environmental Leontief inverses, and (2) whether a sector's land multiplier (or compositions of land multiplier) can appropriately reflect the effect of delivering one unit of the sector's output to final demand on the required area(s) of production lands used by the sector itself and by other producing sectors whose products are contributed directly and indirectly to its production. The underlying message of these two questions is whether the assumed linear marginal relationship between a sector's output and its intermediate inputs (input-output coefficients)—a critical assumption made by W. Leontief to transform a transactions table from an accounting framework into the input-output model—can be extended to assume that the marginal relationship between a sector's output and the area of production land it uses for generating output is fixed (land-output marginal coefficient equal to average coefficient). By reviewing the literature on input-output analysis and its application to environmental issues and by theoretically and empirically examining the relation between sector output and land appropriation, this study advises against the use of land multipliers or their compositions in the EF scenario analysis.To apply the input-output model to EF scenario analysis for enhancing policy relevance with due attention to the relationship between sector output and land appropriation, this study suggests a two-stage EF calculation procedure. In the first stage, the input-output application estimates only the required raw materials (or generated pollutants) for meeting a given consumption pattern, which is the objective of environmental input-output analysis; in the second stage, the estimated amount of raw materials or pollutants is converted into land/water area, and a choice of conversion methods is suggested according to the research questions and the availability of conversion methods and required data.     

Capital accumulation and welfare: a note

Diamond's neoclassical growth model with National Debt is reconsidered with respect to dynamic welfare considerations. Conditions under which capital deepening implies increasing welfare are dependent upon the stability of the steady state, the interest elasticity of savings, and the relationship between the marginal propensity to save and the elasticity of substitution in production.