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.     

Child labor and household wealth: Theory and empirical evidence of an inverted-U

Some studies on child labor have shown that, at the level of the household, greater land wealth leads to higher child labor, thereby casting doubt on the hypothesis that child labor is caused by poverty. This paper argues that the missing ingredient may be an explicit modeling of the labor market. We develop a simple model which suggests the possibility of an inverted-U relationship between land holdings and child labor. Using a unique data set that has child labor hours it is found that, controlling for child, household and village characteristics, the turning point beyond which more land leads to a decline in child labor occurs around 4 ac of land per household.     

Intertemporal elasticity of substitution and risk aversion: are they related empirically?

This article examines the relationship between two types of preference: preference of intertemporal choices and preference towards risk. In the simplest form of the constant relative risk aversion utility function, the intertemporal elasticity of substitution (IES) and risk aversion have an inverse relationship. However, there is no empirical evidence that suggests this inverse relationship holds. We examine the relationship between risk aversion and IES using household consumption data from the Consumer Expenditure Survey during 1996–2010. Multiple risk domains are selected to represent risk preference, and for each domain, we consider some households to be more risk averse than others. We separately estimate IES for the more risk-averse and less risk-averse households. We find that the IES estimates are generally smaller for the more risk-averse households than for the less risk-averse households and that the difference is statistically significant in the majority of the financial domains. This finding supports the inverse relationship between the two parameters, although considerable heterogeneity is found across domains.     

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.     

Openness to trade as a determinant of the macroeconomic elasticity of substitution

Several theoretical and empirical studies on economic growth consider the macroeconomic elasticity of substitution between capital and labor as a measure of economic flexibility that depends on technological as well as institutional aspects. One institutional aspect of economic flexibility is openness to trade. I examine in a Heckscher–Ohlin model with two large countries trading intermediate goods how openness affects the elasticity of substitution. If the technology has a constant elasticity of substitution in a closed economy, opening up to trade raises the elasticity of substitution only in the country that accumulates capital at a faster rate.     

Comment on “The endogenous aggregate elasticity of substitution for a small open economy”

This note applies the approach of Miyagiwa and Papageorgiou [Miyagiwa, K. and Papageorgiou, C., 2007. Endogenous aggregate elasticity of substitution. Journal of Economic Dynamics and Control 31, 2899–2919] to provide simple frameworks for endogenizing the aggregate elasticity of substitution between capital and labor for a growing small open economy.     

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.     

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.     

Human capital accumulation and the intertemporal elasticity of substitution of labor: How large is the bias?

I consider two different skill accumulation technologies, learning by doing and Ben-Porath type training. The effect of human capital accumulation in the form of learning by doing is to increase the labor supply elasticity estimate by a factor of 2.1 relative to the estimate that ignores human capital accumulation. The results are similar for the Ben-Porath type training technology, although the estimate of the bias is somewhat higher.     

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.     

von Thünen: Capital,Production Functions,Marginal Productivity Wages,and the Natural Wage

This paper puts seminal contributions to theory of production functions and maximization of explicit quantitative objective functions by Johann Heinrich von Thünen into a systematic historical perspective. We show that his comprehensive ‘Tableau Economiques’ do imply two exact parametric production functions. Moreover, the renowned ‘geometric mean wage’ formula is restated as an exact CES marginal labor productivity wage for σ = 2. We review four alternative modes of normative (natural) wage calculations without an explicit production function, and conclude that von Thünen's natural wage differentiation formulas are bona fide alternatives for deriving the natural wage formula.     

On a generalization of a class of production functions

In Appl. Econ. Lett. 18 (2011), 1777–1784, as a natural generalization of some famous production models with two inputs, C.A. Ioan and G. Ioan introduced a new class of production functions with constant return to scale, called sum production function, and proved three theorems of characterization for such production models. In this article, we give new and more simple proofs of these theorems, extending also the results to the case of increased/decreased return to scale. The generalization to the case of an arbitrary number of inputs is also discussed.     

Capital theory and the origins of the elasticity of substitution (1932-35)

Elasticity of substitution was introduced into economics duringthe early 1930s. It was discovered independently by Hicks inThe Theory of Wages and by Joan Robinson in The Economics ofImperfect Competition, and then was the centre of a polemicinvolving Kahn and Sraffa, among others. The debate focusedon imperfect competition and capital-theoretical issues. Someelements of the 1950s and 1960s capital theory controversy,such as the idea of capital as a Giffen good or the difficultiesof measuring capital, were already discussed at this early stage.     

Comment on “σ: The long and short of it”

I comment on some of the issues discussed by Robert Chirinko (Chirinko, R.S., 2008. σ: The long and short of it. Journal of Macroeconomics 30 (2), 671-686). I also offer some additional evidence and discuss the theoretical implications of the empirical findings regarding σ.     

Present bias and the inefficiency of the centralized economy: The role of the elasticity of intertemporal substitution

We analyze an endogenous growth model considering agents with an isoelastic utility. Preferences are characterized by a utility affected by a negative externality, and a level of impatience which decays with the time distance from the present. Agents who cannot commit the actions of their future selves, play a game against them. The stationary equilibrium of this game defines a balanced growth path with a slower growth when played by subsequent central planners than when played by decision makers in the market economy. First, we prove that the fast growing market economy implies higher welfare if the negative externality is small, while the centralized economy is welfare improving above a given threshold for the externality (obtained for a specific family of non-constant discount functions). Secondly, we observe that this threshold increases with the elasticity of intertemporal substitution in consumption. Therefore, the greater this elasticity the more likely it is that the externality lies below this threshold, where policy interventions would not be adequate. Finally, as one would expect, the range of values of the externality for which the market equilibrium provides higher welfare widens the more different from constant discounting time preferences are, due either to a wider range of variation for the instantaneous discount rates or because these decay more slowly.     

Estimating the elasticity of intertemporal substitution taking into account the precautionary savings motive

This paper estimates the elasticity of intertemporal substitution for U.S. aggregate time series data, taking into account the precautionary savings motive. By making use of a recursive utility function, we estimate an Euler equation, via GMM. This procedure leads consumption growth rate to depend on asset returns, and on a time-varying variance, which captures the precautionary motive. When significant, the elasticity of intertemporal substitution estimates ranges from 0.4 to 1.8, which are higher than most of the results found in the literature. Furthermore, the evidence suggests that consumers react to risk; however, the contribution of precautionary motive to consumption growth seems to be limited.     

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.     

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.     

Austrian economics and the analysis of labor markets

Theory and policy relating to labor markets is dominated by the mainstream labor market model, although a less well-known, socioeconomic version can also be identified. The mainstream model is methodologically flawed and forced, thereby, to relegate any (serious) investigation of labor market institutions and/or social structures to the margins of its analysis. The socioeconomic account is not so much methodologically flawed, as methodologically ambivalent. While this ambivalence does not actually prevent the investigation of institutions and/or social structures, it does promote ambiguity whenever we inquire into the precise nature of the interaction between them and labor markets. Insights from Austrian economics, when used in collaboration with critical realist methodology, can play a part in augmenting the socioeconomic account, generating a totally new approach to the analysis of labor markets.