Micro-foundation for a constant elasticity of substitution production function through mechanization

We consider an increase in the range of capital use as a form of mechanization. A constant elasticity of substitution (CES) production function is dynamically derived from Leontief production functions through the endogenous complementary relationship between capital accumulation and mechanization. This implies that a CES production function can be resolved into technological change that does not involve changes in total factor productivity. Furthermore, using the normalizing procedure of the CES production function developed by de La Grandville [de La Grandville, O., 1989. In quest of the Slutsky diamond. American Economic Review 79, 468–481], we investigate how mechanization is related to the elasticity of substitution in our endogenous growth model.     

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.     

Factor Substitution, Income Distribution and Growth in a Generalized Neoclassical Model

Abstract. We analyze a generalized neoclassical growth model that combines a normalized CES production function and possible asymmetries of savings out of factor incomes. This generalized model helps to shed new light on a recent debate concerning the impact of factor substitution and income distribution on economic growth. We show that this impact relies on both an efficiency and a distribution effect, where the latter is caused by the distributional consequences of an increase in the elasticity of substitution. While the efficiency effect is always positive, the sign of the distribution effect depends on the particular savings hypothesis. If the savings rate out of capital income is substantial so that a certain threshold value is surpassed, the efficiency effect dominates and higher factor substitution accelerates the accumulation of capital and works as a major engine of growth.     

Product Differentiation,Competitive Toughness,and Intertemporal Substitution

Standard measures of competitive toughness fail to capture the fact that, as consumers optimize intertemporally, firms operating today compete with (as yet non‐existent) businesses, which will be started tomorrow. We develop a two‐tier constant elasticity of substitution (CES) model of dynamic monopolistic competition in which the impact of product differentiation on the market outcome depends crucially on the elasticity of intertemporal substitution (EIS). The degree of product differentiation per se fails to serve as a meaningful indicator of competitive toughness: what matters is its cross‐effect with EIS. We also extend the model to the case of non‐CES preferences in order to capture variable mark‐ups.     

Market Work, Home Work, and Taxes: A Cross-Country Analysis

This paper uses a simple model of labor supply extended to allow for home production to understand the extent to which differences in taxes can account for differences in time allocations between the US and Europe. Once home production is included, the elasticity of substitution between consumption and leisure is almost irrelevant in determining the response of market hours to higher taxes. But to account for observed differences in leisure and time spent in home production, one still requires a relatively large elasticity of substitution between consumption and leisure, combined with a relatively small elasticity of substitution between time and goods in home production.     

Balanced‐Budget Rules,Elasticity of Substitution,and Macroeconomic (In)Stability

This paper examines the relation between factor substitution and (local) stability of equilibria in a one‐sector real business cycle model under balanced‐budget rules. We show that under non‐unitary elasticity of factor substitution, the Schmitt‐Grohé‐Uribe indeterminacy result can be altered. Using the two‐step normalization procedure, we highlight two opposing effects of factor substitution, namely, the efficiency effect and the distribution effect, on aggregate stability. With endogenous distortionary taxes and gross substitutability between capital and labor, the existing literature overlooks the distribution effect and finds that balanced‐budget rules are likely to deliver indeterminacy. However, if capital stock is relatively more abundant, a higher elasticity of substitution generates a source of stability due to the distribution effect. Our calibration shows that the distribution effect is always the dominating force.     

Financing Public Investment through Foreign Aid: Consequences for Economic Growth and Welfare*

The paper develops a theoretical framework for understanding the mechanism through which foreign aid affects macroeconomic performance. The authors find that the long‐run impact of an aid program and the nature of the transitional dynamics it generates depend crucially on (i) the elasticity of substitution in production, (ii) whether the aid flow is tied to investment activity or not, (iii) how the recipient government chooses to react to the flow of external assistance, and (iv) whether the aid program is permanent or temporary. Structural characteristics of the recipient are important in determining the extent to which external assistance can aid growth and welfare.     

Government expenditure,external and domestic public debt,and economic growth

This paper analyzes the relationship between government expenditure, tax on returns to assets, public debt, and growth in an endogenous growth model. Public debt is composed of two components, domestic debt and external debt. We show conditions for existence, uniqueness, and multiplicity of the steady states. More precisely, existence of steady state requires a sufficiently high productivity and a sufficiently low tax on returns to assets. We also provide the effects of an increase in the tax rate on returns to assets on the steady state. In particular, the relation between public spending and the tax rate has a bell shape. Domestic debt unambiguously increases with tax whereas external debt displays an inverted U‐shaped curve. A high tax rate leads to a reallocation of public debt in favor of domestic debt (to the detriment of external debt). The effect of taxation on consumption (and production) also displays a nonlinear pattern when the output elasticity of capital is lower than unity (the effect is monotonously increasing if this elasticity is unity). We also derive the conditions under which a tax increase can boost or reduce the balanced growth rate.     

Public external debt,informality and production efficiency in developing countries

This paper proposes an alternative approach to investigate the non-linear effect of external debt on growth. In the theoretical part, we develop an endogenous growth model with formal and informal sectors to analyse the effect of the public external debt on the production efficiency. We show that an increase of the public external debt share increases the production efficiency through a positive externality effect. However, it generates an opposite effect via the reduction of the formal sector’s size in favour of a less efficient informal sector. The resultant effect becomes negative beyond an optimal level. Besides, we show that a large stock of public external debt reduces the production efficiency when it leads to a tight fiscal policy which reduces the formal sector size. Empirically, using a stochastic frontier technique with unobserved heterogeneity, for a panel of 27 developing countries for the period of 1970–2005, we confirm that the turning point associated to the effect of the share external public debt is apparent at 84%.     

Public Debt,Productive Public Spending and Endogenous Growth

We analyse the effects of public debt in a basic endogenous growth model with productive public spending. We demonstrate that a discretionary policy in general violates the intertemporal government budget constraint along a balanced growth path. A balanced government budget gives a unique saddle point stable growth path. With a rule‐based policy, two saddle point stable balanced growth paths can occur, depending on the intertemporal elasticity of substitution of consumption and on the primary surplus policy. Higher debt goes along with smaller long‐run growth and we derive a condition such that a deficit‐financed increase in public spending raises the growth rate.     

Structural Changes in Australian Manufacturing Industry*

The paper uses a neoclassical production function and historical data to test for structural stability in Australian manufacturing industry. The production function is an extended constant elasticity of substitution form in which factor substitution elasticity, returns to scale and market structure in output, capital and labour are testable hypotheses. Tests for structural changes in homogeneity and factor substitution elasticity relations are based on overall and individual tests of covariance analysis and also on a special version of the Swerling-Kalman filtering systems as proposed by Cooley and Prescott. The empirical findings possess desirable statistical properties and indicate the existence of structural instability in the industry. The evidence also repudiates the assumptions of unitary factor substitution elasticity, constant returns to scale and market competitiveness in output and factors of production.     

Currency Unions,Export Margins,and Product Differentiation: An Empirical Assessment for European Monetary Union

This paper reconsiders the trade effects of the euro, providing a decomposition into its effects on the extensive margin and intensive margin. Furthermore, it relates the more disaggregated estimates for 93 two‐digit HS product groups to the elasticity of substitution, thereby testing a key hypothesis of heterogenous firm trade theory. The estimates for the period 1996–2011 suggest a trade effect of the euro of some 28%, which has mainly materialized through the intensive margin. A negative net effect of the euro on the extensive margin is found for several product groups, supporting anecdotal evidence that firms have consolidated their product varieties in response to the elimination of exchange rate variability. Finally, the disaggregated estimates are in line with heterogenous firm trade theory models, suggesting that a large elasticity of substitution dampens the effect of a trade cost reduction on the extensive margin and amplifies its effect on the intensive margin.     

Productivity versus elasticity: a normalized constant elasticity of substitution production function applied to historical Soviet data

This study tests the extensive growth hypothesis, which would attribute the Soviet economic slowdown to low elasticity of substitution and over-investment rather than deteriorating productivity growth. To circumvent the low availability of data, widely applicable new methods for estimating productivity and elasticity of substitution were developed based on the normalized constant elasticity of substitution (CES) production function. One is an extended version of the Solow residual calculation, and the other is a direct estimation of the time-varying parameter normalized CES production function. The application of the methods to the Soviet data showed a decreasing trend in productivity growth and a low elasticity of substitution of approximately 0.25. The results neither reject nor support the extensive growth hypothesis because of uncertainty in the interpretation of the low elasticity of substitution. The results suggest that it is reasonable to assert that both deteriorating productivity growth and low elasticity of substitution caused the Soviet economic slowdown. Further empirical studies on productivity and elasticity of substitution in the Soviet and other economies are necessary to fully understand relations between productivity growth, elasticity of substitution and economic development.     

Unemployment, wage bargaining and capital-labour substitution

Many economists believe that capital accumulation, technicalprogress and labour force expansion have no lasting effect onunemployment. This view rests on the empirically doubtful assumptionthat the elasticity of substitution between labour and capitalis equal to unity (i.e., production is Cobb-Douglas). Usinga simple model based on the work of Layard, Nickell and Jackman,this paper demonstrates that, with a lower elasticity of substitution,the equilibrium unemployment rate is affected by all of theabove factors. It considers briefly how capital accumulationmay be endogenised and what long-run implications this has forunemployment.     

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.     

PETROLEUM REFINING INDUSTRY: AN ASSESSMENT OF ITS PRODUCTION STRUCTURE*

Cost structure of petroleum refining industry in Kuwait has been examined, with specific focus on factor substitution, and economies of scale and utilisation. This has been done by estimating translog cost functions, both long‐run and short‐run, using annual time‐series data covering the period from 1976 to 1998. The results indicate that the implied production structure is non‐homothetic, and the pattern of scale effect is labour and capital saving but material using. The evidence also supports presence of induced exogenous technical change, which is non‐neutral (labour and capital using, and material saving). The elasticity of substitution between capital and labour is negative, implying that the two inputs are complements. The results also indicate absence of economies and diseconomies of scale in the petroleum refining industry.     

Revenue-Neutral Environmental Tariff Reform, Growth, and Welfare

This paper analyzes the growth and welfare effects of revenue‐neutral tariff reform in a small open endogenous growth model with environmental externalities. As is the case in countries that depend primarily on imported energy, the employment of a foreign intermediate good causes negative environmental externalities in production. This paper shows that substituting a tariff on the foreign intermediate good for a tariff on the foreign consumption good in a revenue‐neutral way raises the growth rate and the welfare, if the environmental externality is sufficiently strong and if the elasticity of substitution between inputs lies within a certain range.     

Intertemporal Labor Supply and Human Capital Accumulation*

We solve and estimate a dynamic model that allows agents to optimally choose their labor hours and consumption and that allows for both human capital accumulation and savings. Estimation results and simulation exercises indicate that the intertemporal elasticity of substitution is much higher than the conventional estimates and the downward bias comes from the omission of the human capital accumulation effect. The human capital accumulation effect renders the life‐cycle path of the shadow wage relatively flat, even though wages increase with age. Hence, a rather flat life‐cycle labor supply path can be reconciled with a high intertemporal elasticity of substitution.     

Robots and humans – complements or substitutes?

The effect of the spread of Artificial Intelligence (AI) on wages depends on both the form of aggregate production relationships and the elasticity of substitution between human and robotic labor. With a conventional production function involving labor, robots, and ordinary capital, an increase in robotic labor can have either a positive or a negative effect on wages. Alternatively, it is possible to estimate the aggregate production relationship without measuring capital or other fixed factors explicitly, using the procedure developed by Houthakker in the 1950s. Houthakker's method is based on the probability distribution of the productivity of the variable factor. Fitting different distributions to cross-sectional data on U.S. productivity, it is shown that if the elasticity of substitution between human and robotic labor is greater than about 1.9, the burgeoning of AI technologies will cause a decline in aggregate wages, other things equal. For the manufacturing sector, an even smaller human-robot elasticity of substitution is likely to result in declining wages of industrial workers as robots proliferate.     

CES Production Functions and Economic Growth

We examine inconsistencies and controversies related to the use of CES production functions in growth models. First, we show that not all variants of CES functions commonly used are consistently specified. Second, using a simple growth model, we find that a higher elasticity of substitution leads to a higher steady state and makes the emergence of permanent growth more probable. It is also pointed out that the effect of a higher elasticity of substitution on the speed of convergence depends on the relative scarcity of the factors of production. Finally, we discuss possible explanations of variations in the elasticity of substitution.
JEL classification: O 41; O 11