Age structure and capital dilution effects in neo-classical growth models

This paper reexamines the problem of the relationship between demographic growth and per capita income in neo-classical growth models with age-structured populations. It is suggested that, when they assume a constant rate of capital depreciation, such models overestimate the negative impact of population growth through capital dilution effects. With more realistic depreciation schedules, the ageing of the capital stock which results from lower growth implies a higher overall depreciation rate, which reduces benefits from lower capital dilution. The implications of this observation are examined for the existence of an optimum population growth rate, for models with heterogeneous capital, and for models where capital obsolescence is not fixed but is allowed to vary.This article is a modified version of a paper presented at the First Annual Meeting of the European Society for Population Economics, Rotterdam, September 1987. I am indebted to the anonymous referees for helpful comments and suggestions and to Linda Sergent for revising the English text.     

Mathematical investigations of the escape from the Malthusian trap

"We present a simulation model that synthesizes Malthusian and Boserupian notions of the way population growth and economic development were intertwined. The non-linear stochastic model consists of a system of equations whose dynamics culminate in an industrial revolution after hundreds of iterations. The Industrial Revolution [in Europe] can thus be conceptualized as a permanent 'escape' from the Malthusian trap that occurs once the economy is capable of permanently sustaining an ever growing population. We investigate the conditions for such an escape and their sensitivity to the parameters of the model....Our results show that the likelihood of an escape is sensitive to the savings rate and to the output elasticities of the two sectors of the economy. When not in a subsistence crisis, the chances that an escape will occur increase for larger values of the ratio of the savings rate to the growth rate of the population. The chances of an escape also increase substantially for larger values of the output elasticities of labor." (SUMMARY IN FRE)     

Mathematical investigations of the escape from the Malthusian trap

We present a simulation model that synthesizes Malthusian and Boserupian notions of the way population growth and economic development were intertwined. The non‐linear stochastic model consists of a system of equations whose dynamics culminate in an industrial revolution after hundreds of iterations. The Industrial Revolution can thus be conceptualized as a permanent “escape”; from the Malthusian trap that occurs once the economy is capable of permanently sustaining an ever growing population. We investigate the conditions for such an escape and their sensitivity to the parameters of the model. This is done in an attempt to understand why some economies might have had difficulties escaping from the Malthusian trap (in contrast to the European experience in the eighteenth and nineteenth centuries). Our results show that the likelihood of an escape is sensitive to the savings rate and to the output elasticities of the two sectors of the economy. When not in a subsistence crisis, the chances that an escape will occur increase for larger values of the ratio of the savings rate to the growth rate of the population. The chances of an escape also increase substantially for larger values of the output elasticities of labor.     

中国人口老龄化的宏观经济后果——应用一般均衡分析

本文运用“中国可计算一般均衡模型”(PRCGEM)对中国人口老龄化的宏观经济后果进行量化分析。模型结果显示,中国人口老龄化将通过劳动力的负增长以及由此导致的物质资本的低增长减缓了中国经济增长的速度。人均物质生活水平仍然会继续增长,但是增长的速度会不断下降。在人口老龄化背景下,技术进步和生产率的不断提高是维持中国经济可持续增长的主要源泉。     

人口老龄化的区域经济效应分析——基于新古典经济增长模型

人口老龄化与区域经济发展之间有着必然的内在关联性。因为生产和消费是区域经济发展中的重要环节,而人口老龄化对生产和消费均有影响,也就必然会影响区域经济的发展。因此,本文首先在梳理国内外相关研究的基础上提出人口老龄化对区域经济发展的双重效应——正效应和负效应;然后以新古典经济增长模型为基础,尝试引入人口老龄化因素从而对该模型进行扩展,分析得到的结论是:①进一步验证了人口老龄化对区域经济发展的双重效应的存在;②不同的区域,人口老龄化程度不同,人口再生产所处于的发展阶段不同,人口老龄化对区域经济发展的经济影响程度,即其正效应和负效应之和也就不尽相同,但存在的一个基本规律是,人口老龄化程度越高,其负效应就越大,其对区域经济发展的减速效应也就越明显。     

养老保险现收现付制的挤出效应——一个内生生育率模型

文章在一个内生经济增长的OLG模型框架下研究现收现付制养老保险计划的挤出效应。具体考察公共养老金税率变动对家庭的消费与储蓄、生育选择以及经济增长的长期影响。结果表明,存在向上利他动机的情况下,挤出效应的大小取决于养老基金的规模,适度规模的公共养老金计划不会挤出私人储蓄。而有利于消费增加与经济增长;较大规模的公共养老金计划会对私人自愿储蓄与消费产生负面影响,并且对储蓄的挤出作用要大于对消费的挤出。人口老龄化进程在一定程度上缓解挤出效应,促进资本积累与经济增长。     

Population aging, health care, and growth: a comment on the effects of capital accumulation

In a recent paper, Hashimoto and Tabata (J Popul Econ 23:571–593, 2010) present a theoretical model in which the increase in the rate of dependence due to aging of the population leads to a reallocation of labor from non-health to health production and, as a consequence, to a decline in economic growth. We argue that these results rely heavily on assumptions of a “small economy” and perfect capital mobility, which tie down the amount of capital. In this paper, we proceed by analyzing the case of an economy in which the availability of capital is endogenously determined by domestic savings. We find that the new “capital accumulation effect” is opposite to the previous “dependency rate effect,” leaving the effect on economic growth ambiguous. In particular, if the former prevailed, population aging would foster economic growth, a result that finds support in recent empirical work.     

人口老龄化、人口增长与经济增长——来自中国省际面板数据的实证证据

利用一个包含人力资本的柯布-道格拉斯生产函数,从索洛增长理论入手,分析人口老龄化和人口增长率对经济增长的影响,理论模型的推理结果表明人口老龄化和人口增长对经济增长均产生不利影响。再根据理论模型的结果构造了人口老龄化和人口增长影响经济增长的实证模型,收集和使用中国1990～2008年的省级面板数据对理论模型的推理结果进行实证检验,证实了理论模型的推理结果。实证研究还表明:(1)初始的人均GDP对经济增长的影响为负,说明中国的区域经济发展出现了条件收敛的情形;(2)人力资本投资、储蓄率和劳动参与率对经济增长有着显著的正向促进作用。     

Age structure,education, and the transmission of technical change

The significance of deviations from exponential population growth to economic development requires the construction of growth models that explicitly recognize demographic forces as a potential source of nonstationarities. This paper uses an overlapping generations approach to analyze the impact of population aging on technological innovations in the production process. Specifically, it is assumed that a newly invented technology can be used only if the production unit engages human labor that has been trained for this task (labor-embodied technical change). In a model of overlapping generations 1-sector optimal growth, there are 3 basic components: population, education and labor, and production and investment. An individual who has been in school continuously from the time of birth embodies, according to this model, the most up-to-date form of human capital. When the population growth rate is high, technological innovations are achieved largely through the constant influx of recently educated young people into the labor force. However, when population declines lead to a slowing down of this influx, increased adult education is necessary to stimulate the continued introduction of innovations into the productive process. The form of the optimality conditions, the comparative statistics properties, and the form of the nonstationary optimal economic growth path in this model are similar to those in the Van Imhoff model of homogeneous human capital.     

中国人口转变、人口红利与经济增长的实证

我国人口年龄结构的变动使得劳动负担逐渐下降,这对于储蓄水平的上升和劳动力投入效率的提高具有显著的促进作用;我国劳动负担比与经济增长呈现出明显的负相关,劳动负担比每下降1个百分点,经济增长将提高1.06个百分点,在过去的30年里劳动负担降低累计带来的经济增长占总增长的27.23%。通过计量检验证明人口年龄结构变动所产生的促进经济增长的人口红利是存在的。由此我们推断,由于未来的人口年龄结构变动趋向人口老龄化,劳动负担逐步上升,这将会对未来的经济增长造成制约。利用未来10～20年时间较轻的劳动负担的机遇期,我们应当建立良好的教育、人力资本投资、社会保障等方面的制度以及制定积极的人口政策,调整当前生育政策、适时执行宏观经济政策(劳动就业政策)来应对已发生的、正在进行的人口变动,使我国的经济继续保持强有力的增长态势。     

Beggar thy thrifty neighbour

This paper explores the international spillover effects of ageing through capital markets when countries have different pension systems. We use a two-country two-period overlapping-generations model, where the two countries only differ in their pension schemes. Two forms of population ageing are considered, namely, an increase in longevity and a fall in fertility. It is shown that, in the long run, a country using a funded pension system experiences negative spillovers from the fact that the other country uses a pay-as-you-go system. The short-run spillovers, however, are opposite to the spillovers in the long run.      

快速人口转变后的中国长期经济增长—从预期寿命、人力资本投资角度考察

在过去三十年里,中国历经了发达国家要用一百多年才能完成的人口转变过程。生育率、死亡率快速下降,接踵而至的是日益严重的少子、老龄化过程。基于以上背景,本文扩展了Diamond（1965）的基本叠代模型,以不确定性寿命为切入点,在个人的微观行为基础上,致力于分析以下问题：中国是否需要调整当前的计划生育政策;随着人口红利的逐渐消失,中国长期的经济增长如何持续。本文的分析结果显示,预期寿命与生育率、人力资本投资、储蓄率以及经济增长的关系是非单调性的。     

老龄化对储蓄和社会养老保障的影响研究

本文从一个两期的世代交叠模型入手,分析了人口老龄化对储蓄和社会养老保障支出的影响。在此基础上运用动态GMM模型对我国2000～2008年地区面板数据进行实证分析。研究结果表明:第一,人均居民储蓄滞后项对基期储蓄的影响作用较大且高度显著;当期老年人口抚养比对人均居民储蓄的影响为负,上期老年人口抚养比对居民储蓄并没有显著影响。第二,人均养老保障支出滞后项对当期人均养老保障支出影响作用较大且高度显著;当期老年人口抚养比对人均养老保障支出有促进作用,而上期老年人口抚养比抑制了人均养老保障支出的增加。     

The old age security hypothesis and optimal population growth

The old age security approach is used to study the relationship between the rate of growth of the population and capital accumulation, within a Samuelson-Diamond overlapping generations framework. It is shown that a decentralized economy will fail, in general, to achieve the Pareto optimal path. However, a pay-as-you-go social security scheme in which the old get transfers which are proportional to the number of their children may restore optimality. On the other hand, child support systems or subsidies to capital can guarantee the optimal capital: labor ratio, but not the optimal population growth rate, while a lump sum social security system can guarantee the optimal population growth rate, but not the optimal capital: labor ratio. Finally, in a monetary economy any policy aimed at correcting the interest rate will restore full optimality.An earlier version of this paper was written during a visit to the University of California, San Diego. The paper benefited from the comments of two referees.     

The impact of taxation on the distribution of wealth in an economy with changing population

The paper investigates into the determinants of the personal distribution of income and wealth. In an overlapping generations model all individuals are assumed to be identical except for their inherited wealth. Since life time is random the bequest of an individual and thus the inherited stock of capital of its children are stochastic variables. Taxation and social security contributions affect life cycle savings, bequests, and, eventually, the distribution of income and wealth in the society. It is shown that, in general, higher tax rates reduce distributive inequality as long as the rate of interest is exogenously given. In steady state, however, where the rate of interest is determined endogenously, increasing taxation and higher social security payments both diminish the capital labor ratio so that the rate of interest rises. If this interest effect is strong enough then it may outbalance the tendency toward more equality because higher interest rates enhance initial differences in the distribution of both income and wealth and, eventually, the inequality in the distribution of income and wealth in the society.     

预期寿命增长、年龄结构改变与我国国民储蓄率

人口年龄结构趋于老龄化和人均预期寿命逐步增长是目前我国人口发展的两个典型特征,而年龄阶段不同,个人的收入、消费与储蓄行为也不同。基于生命周期理论,在选定相关分析指标的基础上,文章使用我国省际平衡面板数据,实证分析了我国人口预期寿命增长和年龄结构改变对国民储蓄率的影响。分析结论表明,人口预期寿命增长提高了我国国民储蓄率;不考虑时间效应时,幼年人口负担比提高会减少国民储蓄率,而老年人口负担比提高会增加国民储蓄率;在考虑时间效应时,幼年人口负担比提高会增加国民储蓄率,而老年人口负担比提高会减少国民储蓄率。对此,文章给出了合理的解释。通过使用多种估计方法,我们发现所得到的结论是基本稳健的。     

A model on the escape from the Malthusian trap

We consider a demoeconomic model where output is produced using physical capital, human capital and technology as inputs. Human capital depends on the number of people and the level of education in the economy. The dynamics of labour, physical capital, education and technology are endogenously determined such as to reflect the interdependence between economic and demographic factors. The longrun path of the economy and in particular the possibility to escape the Malthusian trap crucially depend on technological progress, which provides for economy wide increasing returns to scale. The build up of technology is positively related to the stock of human capital. Our model predicts that positive population growth is sufficient to escape the Malthusian trap. Received: 22 August 1996 / Accepted: 11 December 1997     

Education funding and regional convergence

The aim of this paper is to discuss the process of regional convergence within the framework of an overlapping generations model in which the engine of growth is the accumulation of human capital. In particular, we consider different education funding systems and compare their performance in terms of growth rates and pace of convergence between two heterogeneous regions. The analysis suggests that the choice of a particular education system incorporates a possible trade-off between long run growth rate and short run convergence. In such choice, the initial capital stock and the extent of regional human capital discrepancy appear as central variables. Received: 27 January 1999/Accepted: 16 April 1999     

Endogenous population growth may imply chaos

We consider a discrete-time neoclassical growth model with an endogenous rate of population growth. The resulting one-dimensional map for the capital intensity has a tilted z-shape. Using the theory of nonlinear dynamical systems, we obtain numerical results on the qualitative behaviour of time paths for changing parameter values. Besides stable and periodic solutions, erratic time paths may result. In particular, myopic and far-sighted economies — assumed to be characterised by low and high savings rate respectively — are characterised by stable per capita capital stocks, while solutions with chaotic windows exist between these two extremes.This work was supported by a grant from the Austrian Academy of Sciences. G. Feichtinger acknowledges financial support from the Austrian Science Foundation under contract No. P 9608-SOZ. The helpful comments of C. H. Hommes, G. Lee and of an anonymous referee are gratefully acknowledged.     

The stable equivalent population,age composition,and Fisher’s reproductive value function

This paper deals with a further analysis of the stable equivalent population for human populations. It first shows that the arithmetic difference between the size of the stable equivalent population and the actual population captures the total prospective contribution of age composition to the growth of the present population, if fertility and mortality rates are held constant at their current levels. The second part of the paper examines Fisher’s reproductive value function and investigates the location of maxima in relation to alternative values of the intrinsic growth rate. One conclusion which follows from this analysis is that, contrary to what has been discovered by others in specific examples, the reproductive value function can possess a global maximum in the first one or two years of life, provided the intrinsic rate of population growth is sufficiently negative. This principle is illustrated by reference to reproductive value functions calculated from the recent experience of U.S. females.