Comment on “Unwrapping some euro area growth puzzles: Factor substitution, productivity and unemployment”

This paper estimates the factor elasticity of substitution of the aggregate production function and then uses these estimates to resolve two puzzles relating to the Euro Area. The paper is novel in three ways: First it uses the CES production technology in the empirical strategy to understand real world economic phenomena; second it uses a frontier empirical methodology; and third it uses a new dataset.     

Elasticity of substitution and productivity, capital and skill intensity differences across firms

This paper, instrumented with six theorems, shows that differences between firms in labor productivity, capital intensity and relative demand for skilled labor can be explained by differences in the substitution parameters between capital, skilled and unskilled labor in the presence of skill biased technical change.     

Unwrapping some euro area growth puzzles: Factor substitution, productivity and unemployment

In this paper, we estimate a long run supply-side system incorporating a CES production function with time-varying factor-augmenting technical progress for the euro area over the period 1970–2005. We find that the elasticity of substitution lies below unity at 0.7, that labor-augmenting technical progress is dominant in the long run while capital-augmenting technical progress plays an important role in the interim period. Importantly, we also find evidence of a structural break in the pattern of biased technical progress towards the end of the 1990s. Our results help to solve two puzzles in Europe’s recent growth experience which differ markedly from the US experience. The first is related to the effects of the IT boom in the 1990s on productivity growth in Europe. The second puzzle concerns the changes in the “Okun’s law” relationship, linking growth to the reduction of unemployment, which are observable in Europe since the late 1990s.     

中国技术进步偏向性的测算与分析

借助不变替代弹性生产函数,利用1985—2013年中国的相关数据,测算了中国技术进步的总体偏向性以及资本增强型技术进步和劳动增强型技术进步的变化速率。结果表明:资本与劳动的替代弹性约为0.402,资本与劳动呈现互补特征,且中国的技术进步呈资本偏向性。指出:从技术进步偏向看,独立自主的发展方针、实现国家工业化的目标以及资本和技术的缺乏共同导致了目前中国的技术进步偏向;中国工业化向高技术发展仍会加强技术进步的资本偏向性,并将引发一系列问题。认为短期内中国仍需维持一定规模的传统劳动密集型产业,长期应大力发展人力资本密集的现代服务业等第三产业。     

中国钢铁行业能源内部的替代弹性分析

本文运用中国钢铁行业滞后一期的产出代替劳动和资本变量,把钢铁行业能源投入要素分解为煤炭、石油、天然气和电力的投入,建立了一个超越对数生产函数模型,用岭回归估算了中国钢铁行业各能源品种投入要素的产出弹性、替代弹性。结果表明:煤炭与石油、煤炭与天然气、煤炭与电力的替代弹性在1左右,中国钢铁行业可通过用石油、天然气、电力替代煤炭来实现其行业全要素能源效率的提高。     

技术进步偏向对要素收入份额的影响——基于中国工业行业数据的研究

本文利用CES生产函数考察了技术进步偏向与资本一劳动收入份额比值之间的关系,并利用中国工业1979—2011年的数据进行了实证分析。估计结果表明：中国工业的要素替代弹性大于0小于1;资本增强型技术进步变化率小于劳动增强型技术进步变化率,1987年后工业技术进步为劳动节约型的,资本一劳动收入份额比值提高;资本深化、技术进步偏向、外商直接投资以及国际贸易是我国工业资本收入份额持续上升、劳动收入份额持续下降的主要原因,其中劳动节约型技术进步对要素收入份额失衡的影响最大。工业要素分配份额的演变直接体现了国民收入分配格局的失衡,也间接拉大了我国居民之间的收入差距。     

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.     

Elasticity of substitution and technical efficiency: evidence from the US electricity generation

ABSTRACT

The implications of national or regional energy policies for technical efficiency and environmental outcomes in electricity generation depend on fossil fuel input substitution. This study uses state level data to examine fossil fuel (coal and natural gas) substitution in electricity generation under increased availability of natural gas in the United States. We observe that changes in elasticities of substitution from pre-2009 to post-2009 differ across states suggesting that the effects of increased availability of inexpensive natural gas on electricity generation have been spatially heterogeneous. We rely on the observed heterogeneity to assess the effects of fossil fuel input substitution on technical efficiency and CO₂ emissions. The results reveal that state level elasticity of substitution between natural gas and coal has a positive effect on technical efficiency and a negative effect on CO₂ emissions. Therefore, future policy design and analyses should reflect the implications for regional elasticities of fossil fuel substitution and associated environmental outcomes.     

Elasticity of substitution and growth: normalized CES in the Diamond model

Summary. It is often asserted that the more substitutable capital and labor are in the aggregate production the more rapidly an economy grows. Recently this has been formally confirmed within the Solow model by Klump and de La Grandville (2000). This paper demonstrates that there exists no such monotonic relationship between factor substitutability and growth in the Diamond overlapping-generations model. In particular, we prove that, if capital and labor are relatively substitutable, a country with a greater elasticity of substitution exhibits lower per capita output growth in transit and in steady state. Received: October 27, 2001; revised version: February 25, 2002     

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.     

Curvature and the elasticity of substitution: Straightening it out

This paper demonstrates that, contrary to deeply rooted beliefs, there is no link between curvature and the elasticity of substitution. We show that there is no direct, nor inverse, relationship between the two concepts, if curvature of the isoquant is defined either in its strict mathematical sense or as the isoquant's second derivative. We finally suggest to view the elasticity of substitution as an efficiency parameter.     

Long-run relationships between labor and capital: Indirect evidence on the elasticity of substitution

This paper proposes an indirect method for making empirical inference on the elasticity of substitution between capital and labor. The idea is that estimates of the elasticity may be retrievable from theory derived behavioral equations, by conducting comparative statics with respect to this parameter. This approach is readily applicable to more realistic models than those which are commonly used to derive estimates of the substitution elasticity. It is demonstrated that the conventional approach does not yield sensible estimates on quarterly Finnish manufacturing data. By applying the indirect method, a long-run empirical relationship is found that is consistent with an elasticity of substitution below one.     

Estimating productivity and returns to scale in the US textile industry

In light of the textile industry's growing foreign competition, trade deficit and job loss, we estimate its productivity and efficiency for the period 1975–93 utilizing a variable elasticity of substitution production function. The results indicate that, despite job losses, the industry adjusted by increasing labor productivity and maintaining fairly stable profits. This performance does not warrant protectionist policies. However, with an elasticity of factor substitution less than one and decreasing, the impact of factor price increases could result in higher apparel prices and preference for cheaper imports. Furthermore, with an elasticity of capital output rapidly decreasing, significant technological improvements will be required to improve competitiveness since textile production is capital intensive. Recently revised rules on trade liberalization could increase competition in the industry. First version received: October 1999/Final version received: August 2000     

中国制造业能源替代的区域差异

通过建立超越对数成本函数,首先测算了28个省份制造业资本、劳动和能源的替代关系,随后结合VAR模型,研究了28个省份的石油、电力和天然气对煤炭的替代关系。结果表明:就总体来看,制造业对资本依赖程度明显提高,且资本对劳动力和资本对能源都存在明显替代关系;虽然制造业的劳动力自价格弹性绝对值不断增大,但能源自价格弹性较低,甚至最近几年为正值;制造业生产过程中投入的石油和天然气都可以替代煤炭,但替代能力都较弱。从区域角度看,各地区制造业能源替代差异明显。     

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.     

Piketty’s Elasticity of Substitution: A Critique

This article examines Thomas Piketty’s explanation of a falling wage share. Piketty explains rising income inequality between labor and capital as a result of one parameter of a production function: an elasticity of substitution, σ, between labor and capital greater than one. This article reviews Piketty’s elasticity argument, which relies on a non-standard definition of capital. In light of the theory of land rent, it discusses why the non-standard capital definition is a measure of wealth, not capital and is problematic for estimating elasticities. It then presents simple long-run estimates of σ in constant elasticity of substitution functions for Piketty’s data as well as for a subset of his capital measure that comes closer to the standard definition of productive capital. The estimation results cast doubt on Piketty’s hypothesis that σ is greater than one.     

Factor substitution and labor market friction in the United States: 1948–2010

We re-estimate the capital-labor elasticity of substitution and the biased factor-augmenting technological progress using a system approach for the aggregate U.S. economy from 1948 to 2010. Due to (i) the significant impacts of labor market dynamics on economic growth and (ii) the fundamental tension between the short-run data that are available and the long-run parameter that is required in the estimation process, we incorporate labor market friction into a supply-side system to re-estimate these important growth parameters and to explore their sensitivity to the incorporation of labor market friction. Our estimation obtains a significantly smaller-than-unity elasticity of substitution. This result is consistent with labor input measured along the extensive and intensive margin, and in both competitive and imperfect labor markets. Technological progress tends to be purely labor-augmenting, with the average growth rate around 2% per year. These findings are robust to alternatively constructed data sets and different estimation strategies.     

Increasing marginal impatience and intertemporal substitution

For infinite-horizon models with recursive preferences the condition known as increasing marginal impatience is often adopted, but the condition is not fully understood in the literature. This paper shows that increasing marginal impatience is equivalent to the intuitive property that the substitutability between the consumption levels in two different periods is a decreasing function of the distance between the periods.     

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.     

Heterogeneous productivity shocks,elasticity of substitution and aggregate fluctuations

We use a Dixit-Stiglitz setting to show that aggregate productivity fluctuations can be generated through changes in the dispersion of firms’ productivity. When the elasticity of substitution among goods is larger than one, an increase in the dispersion raises aggregate productivity because firms at the top of the distribution produce most of output. When the elasticity is smaller than one, an increase in the dispersion reduces aggregate productivity because firms at the bottom of the distribution use most of inputs. We use individual firm level data from Spanish manufacturing firms to test the relationship between the dispersion of firms’ productivity and aggregate productivity. The estimated coefficients are consistent with the predictions of the model: we find that an increase in the coefficient of variation of firms productivity of 1% increases aggregate productivity by 0.16% in sectors with an elasticity of substitution larger than one while the same increase in the standard deviation reduces aggregate productivity by 0.36% in sectors with an elasticity of substitution smaller than one.