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.     

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.     

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.     

Wealth Effects and the Valuation of Common Access Facilities: Some Calculations*

Using a CES utility function modified to allow for zero usage of one commodity, this paper calculates the relative difference between compensating and equivalent variation measures of the welfare loss due to withdrawal of a commodity, for various plausible values of the relevant demand function parameters (income elasticity, expenditure share and substitution elasticity). Contrary to what is frequently asserted these differences can be quite significant     

The theory of capital utilization and the putty-rubber production function

This paper extends the theory of optimal shift-work to the presumably realistic case in which the ex post elasticity of substitution between labor and capital services is neither zero nor equal to the ex ante elasticity. The paper considers both the CES and the VES as candidates for the ex post function, and gives reasons for preferring the latter. The introduction of ex post substitutability where none existed before is found to increase the profitability of shift-work.     

A Fiscal Stimulus and Jobless Recovery

We analyze the effects of a government‐spending expansion in a dynamic stochastic general equilibrium model with Mortensen–Pissarides labor‐market frictions, deep habits in private and public consumption, investment adjustment costs, a constant elasticity of substitution (CES) production function, and adjustments in employment at both intensive and extensive margins. The combination of deep habits and CES technology is crucial. The presence of deep habits magnifies the responses of macroeconomic variables to a fiscal stimulus, while an elasticity of substitution between capital and labor in the range of available estimates allows the model to produce a scenario compatible with the observed jobless recovery.     

Looking back, looking ahead: Biased technological change, substitution and the wage gap

The implications of ICT on wage inequality are studied by applying a CES production function with skilled and unskilled labour. Skill-biased technological change increases wage inequality. The result is reinforced in a two-sector general equilibrium model if the income elasticity of the demand for high-tech goods and the elasticity of substitution between final goods are larger than one.     

中国总量生产函数模型选择*——基于要素替代弹性与产出弹性视角的研究

总量生产函数是经济增长和宏观政策的研究基础,不同生产函数模型设定可能导致不同的研究结论。本文从生产函数模型中要素替代弹性和产出弹性的隐含假设出发,系统研究了中国总量生产函数模型选择。本文研究发现：中国要素替代弹性的上下限为［08,15］,且呈现向1收敛的趋势;时变弹性生产函数模型拓展Cobb Douglas生产函数为变参数形式,可以较好地刻画中国劳动收入份额变化;Cobb Douglas生产函数、标准化CES生产函数和时变弹性生产函数模型的生产率核算结果趋于一致。本文研究为中国总量生产函数模型选择提供了理论参考和实证支持。     

Avoiding Mis-estimation of the CES Function: Unit Matters

ABSTRACT

We demonstrate that unit errors of measurement will lead to significant biases in estimating the constant elasticity of substitution (CES) function. Monte-Carlo simulations show that estimation results tend to reach Cobb–Douglas (CD) functions or extreme values if units of input variables are incorrectly used. To avoid this problem, we suggest adding an overall efficiency parameter and a unit correction parameter which is similar to biased technological change parameter when estimating CES functions. Any unit error of measurement can be captured by these two parameters while allowing researchers to get unbiased estimation results of other parameters.     

DIVERSE ORGANIZATIONS AND THE COMPETITION FOR TALENT

We propose a theory of firm production that requires diverse inputs. We show that in a competitive labor market, firms differ in their skill composition. Organizations with higher total factor productivity (TFP) are larger and hire from a broader range of skills. Technological progress leads to an increase of all wages and results in downsizing. Quantifying productivity using our model shows that a constant elasticity of substitution (CES) production function generates unbiased estimates of TFP but biased estimates of marginal product and elasticity of substitution across skills. Our model also generates estimates of the TFP distribution based on CEO compensation alone.     

The macroeconomic effects of fiscal policy in a stochastically growing economy

This paper develops a stochastic model of endogenous growth with productive government expenditure. Herein, we specify the CES production function according to recent empirical evidence. The elasticity of substitution plays a key role in determining macroeconomic performance and the effectiveness of fiscal policy under uncertainty. Results demonstrate that a large elasticity of substitution provides a large expected growth rate and also large volatility of the growth rate. Regarding these effects, the growth-maximizing tax rate and welfare-maximizing tax rate under uncertainty are larger or smaller than those of deterministic economy according to the elasticity of substitution.     

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     

A note on aggregation of CES-type production functions

In this note we shall be concerned with the aggregation of the constant elasticity of substitution (CES) type of production function. In particular we will derive the error made by using the arithmetic averages as they are usually published, rather than the theoretically required averages.     

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.     

General equilibrium models with Morishima elasticities of substitution in production

Analytical general equilibrium (AGE) models are important tools that economists use to answer questions about theory and policy. When a production function has three or more inputs, the traditional modeling technique employs Allen elasticities of substitution to represent general functional forms. This paper builds an analytical general equilibrium model using the Morishima elasticity of substitution (MES). Specifically, an existing model using Allen elasticities is reformulated to employ the MES and the new, closed-form solutions are interpreted with additional insights from the reformulation. Importantly, the special case of constant elasticity of substitution (CES) production follows directly when using Morishima elasticities, but not Allen elasticities. This paper also provides a general technique for switching from Allen to Morishima elasticities in any existing AGE model and demonstrates a one-to-one numerical equivalence regardless of the elasticity measure employed. Replicating prior results, plausible parameter values are applied to the reformulated model to analyze the source-side, distributional effects of a pollution tax and highlight how the Allen and Morishima elasticities differ.     

Who provides the capital for Chinese growth: the public or the private sector?

We focus on the role of the government in the provision of investment in China, through the medium of a Dynamic Stochastic General Equilibrium model of the economy in which the form of the production function reflects this governmental role. Using indirect inference, we estimate and test for the elasticity of substitution between government and nongovernment capital in both Constant Elasticity of Substitution (CES) and Cobb–Douglas technologies. The results underscore the strong substitution relationship between government and nongovernment capital from 1949, supporting CES rather than the Cobb–Douglas technology. They also show that the orientation of public investment changed after the start of the ‘Socialist Market Economy’ in 1992: government capital became more complementary to nongovernment capital as it focused more on infrastructure and withdrew from industrial production, intervening only in times of crisis, for stabilization purposes, indirectly via the state banks.     

A class of changing elasticity of substitution production functions

This paper presents a new class of production functions with a changing elasticity of substitution between two input factors. Over a freely chosen number of intervals for the input factor intensity freely chosen elasticities of substitution can be imposed. The resulting production function can thus account for changing elasticities of substitution during the development of the factor intensity. The production function is applied in a calibration exercise and a novel normalization procedure is proposed. The theory behind this production technology builds on the functional normalization of CES production functions.     

Elasticity of substitution and the stagnation of Italian productivity

The aim of this paper is to investigate the roots of the stagnation in the Italian total factor productivity (TFP). The analysis focuses on the specific pattern of technical progress in determining the dynamics of the TFP. This analysis cannot be done with Cobb-Douglas technology, but requires the employment of a constant elasticity of substitution (CES) production function that allows distinguishing between the direction and the bias of technical progress. We employ a CES specification embodying both labor- and capital-augmenting technical change, with a σ less than 1. We obtain three main results. (1) There seems to have been a structural break around the mid-1990s in the direction and bias of technological change; (2) The first half of the sample features a labor-augmenting technical change and a capital bias; and (3) In the second part of the sample, both these characteristics seem to disappear, and the evolution of factor endowments assumes a key role. This fact may be seen as one of the potential causes of the stagnation in Italian productivity.     

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.     

A quantitative analysis of Chinese industrial structure and technological change: production functions for aggregate industry,sectoral industries and small scale industry

In this study we estimate the Chinese aggregate, sectoral and small-scale industrial production functions based of three models, the CES(1), CES(2) and Cobb–Douglas production functions. Testing the estimated results we find that the Cobb–Douglas production function is the appropriate functional form for underlying Chinese industrial struture. The study indicates some serious structural and technological problems, such as decreasing returns to scale, unitary substitution between labour and capital, slow technical progress and low economic efficienty. The findings suggest that an intensive industrial development policy should be pursued in China.