A two-sector Kaleckian model of growth and distribution with endogenous productivity dynamics

This study extends a two-sector Kaleckian model of output growth and income distribution by incorporating endogenous labour productivity growth. The model is composed of investment goods and consumption goods production sectors. The impact of a change in wage and profit shares on capacity utilisation and output growth rates at the sectoral and aggregate levels are identified. The study reveals short-run cyclical capacity utilisation rates and productivity growth dynamics. Even if the short-run steady state is stable, the capital accumulation rate in the consumption goods sector must decrease more than that in the investment sector for long-run stability. When simultaneous rises in profit shares in both the sectors affect long-run aggregate economic growth differently at a steady state, the distributional interests between the same class in different sectors may hamper the long-run economic growth. A policy message is that the effect of income distribution on industrial output growth is not always beneficial. These phenomena are specific to two-sector models and cannot be observed when using conventional aggregate growth models.     

A Dynamic Model of the Choice of Technology in Economic Development

In this overlapping-generations model, there is unemployment in the manufacturing sector. Manufacturing firms engage in oligopolistic competition and choose technologies to maximize profits. With capital as a fixed cost of production, increasing returns in the manufacturing sector exist. In the unique steady state, first, when individuals become more patient, the savings rate increases while the level of an individual’s income decreases. Second, an increase in population or percentage of income spent on manufactured goods does not change steady-state technology while the level of an individual’s income decreases. Third, an increase in the wage rate leads manufacturing firms to choose more advanced technologies and the steady-state capital stock increases. Finally, an increase in the level of subsidies to technology adoption does not change steady-state technology.     

我国三大经济圈制造业结构变动趋向分析——对环渤海、长三角和珠三角的一项实证研究

基于1988—1997年和2000—2011年这两个时段环渤海、长三角和珠三角三大经济圈各省市分行业面板数据,从结构变化的资本集约度角度考察制造业结构变动的趋向。实证结果表明,1988—1997年时段,经济圈中除广东省外,绝大多数省市制造业劳动力要素是从劳动密集型产业向资本密集型产业转移的,而2000—2011年时段,不少省市的制造业结构呈劳动密集型化变动特征。而且,三大经济圈制造业结构向资本密集型调整在区域上由北向南递减,而向劳动密集型调整则由南向北递减。进一步的研究显示,三大经济圈制造业结构趋向于劳动密集型化的现象背后,存在制造业向技术密集型产业调整的明显趋势。另外,对制造业人均累积资本进行分解后发现,制造业结构变化本身并不是制造业人均累积资本变化的决定性因素;2000年以后三大经济圈制造业人均累积资本的提升差异较大,且劳动力要素在部门间的流动已开始抑制整体制造业人均累积资本的增加。     

OPTIMAL TRANSITION DYNAMICS IN THE LEONTIEF TWO‐SECTOR GROWTH MODEL WITH DURABLE CAPITAL: THE CASE OF CAPITAL INTENSIVE CONSUMPTION GOODS*

We present results on undiscounted optimal policies in the Leontief two‐sector growth model with durable capital. Unlike the results with a labour intensive consumption goods sector, we show that a monotonic optimal programme is only one special case out of many richer possibilities of transition dynamics. Depending on the initial capital stock, and a key parameter ζ that could be interpreted as a marginal rate of transformation of capital between today and tomorrow, an optimal programme may converge to a period‐two cycle; and even when it converges to the golden rule stock, it can do so (damped) cyclically or with a “jump”.     

Self-Enforcing Intergenerational Social Contracts for Pareto Improving Pollution Mitigation

We consider, in an overlapping generations model with an environmental externality, a scheme of contracts between any two successive generations. Under each contract, agents of the young generation invest a share of their labor income in pollution mitigation in exchange for a transfer in the second period of their lives. The transfer is financed in a pay-as-you-go manner by the next young generation. Different from previous work we assume that the transfer is granted as a subsidy to capital income rather than lump sum. We show that the existence of a contract which is Pareto improving over the situation without contract for any two generations requires a sufficiently high level of income. In a steady state with social contracts in each period, the pollution stock is lower compared to a steady state without contracts. Analytical and numerical analysis of the dynamics under Nash bargaining suggests that under reasonable conditions, also steady state income and welfare are higher. Delaying the implementation of a social contract for too long or imposing a contract with too low mitigation can be costly: Net income may inevitably fall below the threshold in finite time so that Pareto improving mitigation is no longer possible and the economy converges to a steady state with high pollution stock and low income and welfare. In the second part of the paper, we study a game theoretic setup, taking into account that credibly committing to a contract might not be possible. We show that with transfers granted as a subsidy to capital income, there exist mitigation transfer schemes which are both Pareto improving and give no generation an incentive to deviate from any of its contracts even in a dynamically efficient economy. Social contracts coexist with private savings.     

International trade and capital accumulation in an overlapping generations model with a public intermediate good

We investigate the effects of a public intermediate good on trade patterns, capital accumulation, and the gains from trade in a two‐country, three‐sector overlapping generations model. A public intermediate good affects not only the productivity of private production but capital accumulation; thus, the results differ from those obtained in previous studies. First, opening to trade may accelerate capital accumulation in the higher‐savings country. Additionally, the country producing a public intermediate good more (which is labor‐intensive) may be the importer of the investment good (which is the most capital‐intensive). Finally, the lower‐savings country may have lower steady‐state welfare under trade.     

Monopoly,intermediate goods and the pure theory of international trade

Conclusion In a model with two traded good sectors between which intersectoral flows of intermediate goods are allowed and with a monopolized non-traded good sector, the wage rate in terms of two traded goods increases and the rental of capital in terms of two traded goods decreases when the price of relatively more labor intensive traded good sector increases, though nothing definite can be said about the direction of change in the wage rate and rental in terms of the non-traded good. When prices of traded goods are kept constant and labor and/or capital increase(s), output of the non-traded good sector increases provided that the non-traded good is not inferior, having income elasticity of demand less than unity. The factor intensity condition for the traded goods is in general not sufficient for the validity of the Rybczynski theorem to hold with respect to net outputs of the traded goods. We have derived sufficient conditions for the magnification effect to be observed with respect to net outputs of the traded good sectors. Specifically, we have shown that the factor intensity condition (23) is sufficient for the magnification effect to prevail when only labor increases.     

Environmental Quality,Public Debt and Economic Development

This article analyzes the consequences on capital accumulation and environmental quality of environmental policies financed by public debt. A public sector of pollution abatement is financed by a tax or by public debt. We show that if the initial capital stock is high enough, the economy monotonically converges to a long-run steady state. On the contrary, when the initial capital stock is low, the economy is relegated to an environmental poverty trap. We also explore the implications of public policies on the trap and on the long-run stable steady state. In particular, we find that government should decrease debt and increase pollution abatement to promote capital accumulation and environmental quality at the stable long-run steady state. Finally, a welfare analysis shows that there exists a level of public debt that allows a long run steady state to be optimal.     

Multiplicity and stagnation under the Romer model with increasing returns of R&D

This study develops a simple growth model to explain stagnation and non-simple growth patterns by using increasing returns of R&D efficiency. The study adopts a type of the lab-equipment model, namely, the Romer model, where goods are used as R&D input. Here, we assume capital, or durable goods, as the R&D input factor, and R&D efficiency is assumed to be variable. This arrangement yields three steady states, namely: no-growth, low-growth, and high-growth steady states. These trajectories are jumpable. Accordingly, global indeterminacy is obtained. By uniting the numerical analysis, we obtain that all steady states are saddle stable. However, when the increasing R&D efficiency is small, the path converging to a high-growth-rate steady state shows local indeterminacy.     

ESTIMATES OF THE AGGREGATE QUARTERLY CAPITAL STOCK FOR THE POST-WAR U.S. ECONOMY

We construct quarterly aggregate gross and net capital stock series for the post-war U.S. economy using annual capital stock, capital depreciation, and capital discard figures along with quarterly investment series. We construct nominal and real measures of all three categories in the aggregate capital stock: consumer durable goods, producer durable goods, and business structures. In constructing the nominal series we take into account the changes in capital goods' prices. The series are constructed using four different methods. Using time- and frequency-domain techniques, we compare the constructed series and characterize their short-run, business cycle, and long-run cyclical properties. We find that the constructed series exhibit very different cyclical and shock persistence dynamics. Practial implications are discussed.     

Uninsured idiosyncratic investment risk and aggregate saving

This paper augments the neoclassical growth model to study the macroeconomic effects of uninsured idiosyncratic investment, or capital-income, risk. Under standard assumptions for preferences and technologies, individual policy rules are linear in individual wealth, ensuring that the equilibrium dynamics for aggregate quantities and prices are independent of the wealth distribution. The analysis thus remains highly tractable despite the incompleteness of markets. As compared to complete markets, the steady state is characterized by both a lower interest rate and a lower capital stock when the elasticity of intertemporal substitution is higher than the fraction of private equity in total wealth. For empirically plausible parameterizations, this condition is easily satisfied, and the reduction in aggregate saving and income is quantitatively significant. These findings contrast with Bewley models, where idiosyncratic labor-income risk leads to higher aggregate saving and income.     

Technology and obsolescence: A reinterpretation of the specific-factor model of production

We develop a two sector general equilibrium model with a continuum of sector-specific capital goods in each sector, where each capital good represents a particular type of technology. Even without the standard assumptions usually made in the context of specific-factor models, similar results are derived. This framework is used to analyze the impacts of growth and technological change on the degree of obsolescence in each sector. Innovation and an increasing capital stock increase the degree of obsolescence. On the other hand, growth of labor and modernization of existing technologies reduce the stock of obsolete capital.The paper has benefitted from the comments of the seminar participants at Rutgers University, Cornell University, Columbia University, and at the Indian Statistical Institute, Calcutta. Special thanks are due to Subhasis Gangopadhyay for helpful suggestions. Comments from two anonymous referees of this journal were extremely rewarding. The usual disclaimer applies.     

CONFORMISM AND STRUCTURAL CHANGE

Using a simple, multisector model of endogenous growth, we show that commodity‐specific consumption externalities can be a source of structural change. When the degrees of consumption externalities are different between goods, each sector grows at a different rate. However, the aggregate economy exhibits balanced growth in that capital stock and expenditure grow at the same constant rate. A three‐sector version of our model may reconcile Kaldor's stylized facts with empirically plausible profiles of industrial structure transformation.     

Growth with many agents and wages paid ex ante

In this paper, we consider a one-sector model of economic growth with several infinitely-lived heterogeneous agents, who are endowed with diverse discount factors as well as preferences over consumption. In line with the classical Ramsey model, agents are not allowed to borrow against future income. Unlike the traditional assumption of ex post wage payment, wages are paid ex ante in our model. We first explain the difference between the assumptions of wages being paid ex ante and wages being paid ex post in the framework of a simple illustrative two-class model. Our main result shows that in contrast to the many-agent Ramsey model with ex post wage payment, the capital stock sequence converges to the steady state stock irrespective of production technology employed by the firms. Further, all impatient agents own zero capital stock, whereas the most patient agent owns the entire capital stock from some time onward. Thus, we have shown that a slight modification in the timing of wage payment in growth models can lead to significant changes in the stability properties of equilibrium dynamics.     

The local bifurcation of Ramsey equilibrium

Summary The elasticity of substitution has been proposed as one factor in the generation of aggregate fluctuations in dynamic models with incomplete markets. We study the existence of periodic solutions in a one-sector neoclassical capital accumulation model under borrowing constraints with infinitely-lived heterogeneous agents. A dynamical system representing an equilibrium profile with only the most patient agent holding capital is analyzed when capital income is not an increasing function of total capital. Conditions for the linear approximation system at a steady state to have an eigenvalue of — 1 are found. A one-parameter family of maps based on a perturbation of the production function is introduced and the dynamical system is reduced to 1 dimension via an application of a center manifold theorem. Conditions for a stable flip bifurcation are shown to hold at the steady state.This paper is dedicated to Professor Nicolas Spulber, one of the great pioneers in the study of growth theory. He brought us together and encouraged our joint work on Ramsey equilibrium theory.We thank Nicolas Spulber for his usual insightful comments and we thank Michele Boldrin for a useful discussion. We also thank a referee for suggesting improvements in the paper as well as the seminar participants at the University of Rochester and Cornell University for their comments on the paper.     

Capital substitution in an industrial revolution

A unified growth model is presented in which productivity growth is driven by learning‐by‐doing. We show that the growth rate of productivity is an increasing function of the share of capital. It is assumed that the industrial sector has a higher capital share than the agricultural sector and that the ability to substitute one output for the other in the construction of capital goods slowly rises over time. Two distinct regimes of constant growth emerge, connected by a rapid transition in which the growth rate of income increases by an order of magnitude, indicative of an industrial revolution.     

农产品价格与农民收入增长关系的动态分析

实证分析表明,在1978～2010年的样本区间内,农产品生产价格上涨对我国农民收入水平的提高没有显著作用。因此,在出台提高农产品价格的政策选择上,应持谨慎的态度。农业生产资料价格上涨对农民收入增长具有较微弱的负向影响。切实控制农业生产资料价格的非理性上涨,应是政府的长期政策取向。而加大政府对农业的支持力度,建立和完善符合国际惯例和中国国情的农业综合补贴支持体系,推进农业产业化以加快农村劳动力的转移,不失为解决农民增收困难问题的重要途径。     

The transition to a globalized economy: Poverty,human capital and the informal sector in a structuralist CGE model

Recent econometric evidence suggests that trade liberalization has an elusive relationship to growth and income distribution. This paper provides an explanation for these results via numerical simulations of a dynamic structuralist CGE. The conclusion is that if families become too poor to finance human capital accumulation, or the state too stingy to supply it at a reasonable cost, exports of skill-intensive goods can become uncompetitive and the transition to openness may involve increasing poverty, unemployment and stagnation. The model design incorporates an informal sector as well as accumulation of human capital. The paper simulates two trajectories, a “green” path in which per capita income grows steadily with a rapid rate of human capital accumulation and a reduction in the level of economic informality. A second, or “red” path is also possible, however, with a growth rate that is much lower, an expanding informal sector and an inadequate rate of human capital formation.     

The choice of technology in economic development

The impact of capital accumulation on job creation is an important and interesting issue in economic development. This model provides a general-equilibrium framework for studying technology choice with unemployment in a developing economy based on micro-foundations. Unemployment in the urban sector results from the existence of efficiency wages. Manufacturing firms engage in oligopolistic competition and choose technologies to maximise profits. A more advanced technology uses more capital and less labour. In the steady state, an increase in the amount of capital induces firms to choose more advanced technologies and the wage rate increases. While a higher capital stock always induces firms to choose more advanced technologies, urban unemployment rate may decrease and agricultural sector employment may increase.     

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.