Constant Elasticity Of Substitution Research Articles

Subsistence, Substitutability and Sustainability in Consumption

We propose a representation of individual preferences with a subsistence requirement in consumption, and examine its implications for substitutability and sustainability. Specifically, we generalize the standard constant-elasticity-of-substitution (CES) utility specification for manufactured goods and environmental services, by adding a subsistence requirement for environmental services. We find that the Hicksian elasticity of substitution strictly monotonically increases with the consumption of environmental services above the subsistence requirement, and approaches the standard CES value as consumption becomes very large. Whether the two goods are market substitutes depends on the level of income. We further show that the subsistence requirement may jeopardize the existence of an intertemporally optimal and sustainable consumption path. Our results have important implications for growth, development and environmental policy.

An optimal portfolio, consumption-leisure and retirement choice problem with CES utility: a dynamic programming approach

In this paper, we study an optimal portfolio, consumption-leisure and retirement choice problem for an infinitely lived economic agent with a CES utility function. Using the dynamic programming method, we obtain the value function and optimal investment, consumption, leisure, and retirement strategies in analytic form. Numerically we observe that the threshold retirement wealth level is an increasing function with respect to the elasticity of substitution.

Sectoral Technology and Structural Transformation

We assess how the properties of technology affect structural transformation, i.e., the reallocation of production factors across the broad sectors of agriculture, manufacturing, and services. To this end, we estimate sectoral constant elasticity of substitution (CES) and Cobb-Douglas production functions on postwar US data. We find that differences in technical progress across the three sectors are the dominant force behind structural transformation whereas other differences across sectoral technology are of second-order importance. Our findings imply that Cobb-Douglas sectoral production functions that differ only in technical progress capture the main technological forces behind the postwar US structural transformation. (JEL E16, E25, O33, O47)

CES technology and business cycle fluctuations

We contribute to an emerging literature that brings the constant elasticity of substitution (CES) specification of the production function into the analysis of business cycle fluctuations. Using US data, we estimate by Bayesian-Maximum-Likelihood methods a standard medium-sized DSGE model with a CES rather than Cobb–Douglas (CD) technology. We estimate a elasticity of substitution between capital and labour well below unity at 0.15–0.18. In a marginal likelihood race CES decisively beats the CD production and this is matched by its ability to fit the data better in terms of second moments. We show that this result is mainly driven by the implied fluctuations of factor shares under the CES specification. The CES model performance is further improved when the estimation is carried out under an imperfect information assumption. Hence the main message for DSGE models is that we should dismiss once and for all the use of CD for business cycle analysis.

Critical Comparison of Soil Pollution Indices for Assessing Contamination with Toxic Metals

Aggregation of environmental monitoring data into indices is a common procedure when the objective of the assessment is the evaluation of some environmental criterion for large areas, usually with planning purposes. Two types of aggregation functions are commonly used in the construction of indices: the weighted sum and the constant elasticity of substitution. Several criteria have been proposed for the selection of aggregation functions, namely, (i) ambiguity, which happens when all indicators indicate non-contamination, but the index fails to reflect this observation; (ii) eclipsing, i.e., the index fails to reflect contamination indicated by one of the variables; (iii) rigidity occurs when the introduction of more variables result in increased failure in the classification given by the index, as indicated by a decrease of the index. The first two criteria are easily checked, but the latter is more difficult to evaluate. A method to assess rigidity is here proposed and applied. Two other criteria are also proposed: sensitivity and accuracy. The present study compares and discusses the use of pollution indices for the classification of soils as to heavy metal pollution, with both empirical and real-world data. In the end, some criteria for index selection are indicated, along with their ranking for different practical circumstances. The Nemerow pollution index and the ecological risk index complied with all the fundamental criteria making them good general-use indices.

Isoelastic Elasticity of Substitution Production Functions

We generalize the normalized Constant Elasticity of Substitution (CES) production function by allowing the elasticity of substitution to vary isoelastically with (i) relative factor shares, (ii) marginal rates of substitution, (iii) capital-labor ratios, or (iv) capital-output ratios. Ensuing four variants of Isoelastic Elasticity of Substitution (IEES) production functions have a range of intuitively desirable properties and yield empirically testable predictions for the functional relationship between relative factor shares and (raw or technology-adjusted) capital-labor ratios. As an empirical application, the parameters of IEES functions are estimated in a three-equation supply-side system with factor-augmenting technical change, based on data on aggregate production in the post-war US economy. Our estimates consistently imply that the elasticity of substitution between capital and labor has remained relatively stable, at about 0.8-0.9, from 1948 to the 1980s, followed by a period of secular decline.

Assessing the values of EC and IT separately and simultaneously and inputs substitution and complement: The CES-based stochastic frontier approaches

The objective of this research is to critically explore four interrelated issues at the country level by evaluating the values of e-commerce (EC) and information technology (IT) both separately and simultaneously; examining the possibilities of complementarity and substitutability phenomena; analyzing the impacts of substitution and complement relations among ordinary capital, ordinary labor, and IT capital on the business values of EC and IT; and revisiting the productivity paradox by using the stochastic frontier approaches, which incorporate the CES production functions. The empirical results imply that it is important to assess the values of EC and IT simultaneously rather than separately.

The increasing returns to scale CES production function and the law of diminishing marginal returns

This article analyzes the constant elasticity of substitution (CES) production function when there are increasing returns to scale and the elasticity of substitution exceeds 1, which I refer to as the explosive case of the CES. For this explosive case of the CES, the article demonstrates a new and surprising result: marginal and average products of labor and capital approach infinity as either labor or capital approach infinity. Obviously, in this explosive case of the CES, the law of diminishing marginal returns is eventually violated in a dramatic way. Some implications of this result for growth theory are discussed. The article concludes by deriving, for this explosive case of the CES, lower and upper bounds for the capital labor ratio which are consistent with the law of diminishing marginal returns.

Econometric Estimation of Capital-Labor Substitution Elasticities for Ukrainian CGE Model

The paper presents econometric estimates of the capital-labor substitution elasticities in terms of 10 economic activities based on the 2003-2009 data. Elasticities are estimated in the context of computable general equilibrium (CGE) methodology, particularly, based on the constant elasticity of substitution in production functions and cost minimization assumptions. Selection of methods and approaches to elasticities estimation is based on the literature review. Thus the paper considers several issues: minimum amount of statistical data, required to obtain reliable estimates; choice of functional forms; and specification of economic indicators for production functions variables representation. According to the received estimates, values of Ukrainian capital-labor substitution elasticities are rather low – 0,13-0,82. Service industries are characterized by lower elasticity values, compared to the real sector of Ukrainian economy, which can be explained by the fact that services have higher labor intensity.Despite the availability of relatively small amount of historical data and some methodological aspects, obtained estimates call into question the appropriateness of application of certain production functions for modeling the investigated processes. In particular, this includes the case of Cobb-Douglas production functions that have unitary elasticity of substitution.

Elasticity of substitution and the stagnation of Italian productivity

ABSTACTThe 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.

Wage Rigidity: A Quantitative Solution to Several Asset Pricing Puzzles

In standard production models, wage volatility is far too high, and equity volatility is far too low. A simple modification–sticky wages because of infrequent resetting together with a constant elasticity of substitution (CES) production function leads to both smoother wages and higher equity volatility. Further, the model produces several other hard-to-explain features of financial data: high Sharpe ratios, low and smooth interest rates, time-varying equity volatility and premium, a value premium, and a downward-sloping equity term structure. Procyclical, volatile wages are a hedge for firms in standard models; smoother wages act like operating leverage, making profits and dividends riskier. Received July 30, 2013; accepted July 6, 2015 by Editor Geert Bekaert.

A Tractable Monetary Model under General Preferences

This article studies an economy with both centralized and decentralized monetary exchanges under search frictions. A degenerate asset distribution is featured under a broad class of preferences including, for example, constant return to scale, constant elasticity of substitution, CARA and others from a range of macroeconomic literatures. Some novel applications impossible under quasi-linear preferences, for example endogenous growth, are illustrated under this class of preferences. This article finds that the welfare cost and growth loss of inflation can be much higher in these applications than previous estimates.

Економетрична оцінка еластичностей заміщення між працею та капіталом для обчислюваної моделі загальної рівноваги України

The paper presents econometric estimates of the capital-labor substitution elasticities in terms of 10 economic activities based on the 2003-2009 data. Elasticities are estimated in the context of computable general equilibrium (CGE) methodology, particularly, based on the constant elasticity of substitution in production functions and cost minimization assumptions. Selection of methods and approaches to elasticities estimation is based on the literature review. Thus the paper considers several issues: minimum amount of statistical data, required to obtain reliable estimates; choice of functional forms; and specification of economic indicators for production functions variables representation. According to the received estimates, values of Ukrainian capital-labor substitution elasticities are rather low – 0,13-0,82. Service industries are characterized by lower elasticity values, compared to the real sector of Ukrainian economy, which can be explained by the fact that services have higher labor intensity.

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.

On the Modeling of Size Distributions When Technologies are Complex

The study considers a stochastic R&D process where the invented production technologies consist of a large number n of complementary components. The degree of complementary is captured by the elasticity of substitution of the CES aggregator function. Drawing from the Central Limit Theorem and the Extreme Value Theory we find, under very general assumptions, that the cross-sectional distributions of technological productivity are well-approximated either by the lognormal, Weibull, or a novel “CES/Normal” distribution, depending on the underlying elasticity of substitution between technology components. We find the tail of the “CES/Normal” distribution to be fatter than the Weibull tail but thinner than the Pareto (power law) one. We numerically assess the rate of convergence of the true technological productivity distribution to the theoretical limit with n.

On the modeling of size distributions when technologies are complex

The study considers a stochastic R&D process where the invented production technologies consist of a large number n of complementary components. The degree of complementarity is captured by the elasticity of substitution of the CES aggregator function. Drawing from the Central Limit Theorem and the Extreme Value Theory we find, under very general assumptions, that the cross-sectional distributions of technological productivity are well-approximated either by the lognormal, Weibull, or a novel “CES/Normal” distribution, depending on the underlying elasticity of substitution between technology components. We find the tail of the “CES/Normal” distribution to be fatter than the Weibull tail but qualitatively thinner than the Pareto (power law) one. We also numerically assess the rate of convergence of the true technological productivity distribution to the theoretical limit with n as fast in the body but slow in the tail.

The Intergenerational Transfer Effects on Sport Activity

The intergenerational transfer effects from parents to their children are strong. If father or mother have been or are active sport exercisers, the probability that children are also active sport exercisers is rather large. We are testing the intergenerational transfer hypothesis using a Finnish data set collected in 2007. The survey allows not only studying intergenerational transfer effect in sport but also in movies at a cinema and classical music concerts participation. Consumers’ preferences are modelled using a CES utility function. If sport (movies, classical music) are normal goods, higher incomes result in higher demand but lost income due to time spent in these leisure activities should decrease the demand. It turns out that lost income (Linder’s disease) is important. Older persons who are already pensioners do not suffer from Linder’s disease are more active sport, movies and classical music consumers than younger (e.g. 55 – 64 years old). In Finland women are more active in any leisure activity.

Economic Impacts of Water Scarcity under Diverse Water Salinities

Exploitation of alternative water sources is expected to grow in the decades to come in water-stressed countries with fast population growth, especially in regions where a further decline of natural freshwater availability is expected due to climate change. Increasing utilization of non-freshwater usually leads to salinity build-up in fields and water sources as well as accumulation of various pollutants - both having a considerable impact on the suitability of non-freshwater for irrigation due to constraints associated with crop salinity tolerance and food safety regulations. We developed a linked CGE - farm-level model of a water economy with representation for multiple water types characterized by different qualities. We employ the model to assess the impact of water shortage on the Israeli economy, where a steadily growing water scarcity is leading to an increasing utilization of alternative water sources. We simulate water shortage scenarios based on the Long Term National Master Plan for The Water Economy developed by the Israeli Water Authority (IWA). The linked CGE - farm-level model provides a mechanism for estimating the Constant Elasticity of Substitution (CES) rates between different irrigation water types used in agriculture. This mechanism accounts for the effects of salinity on yields and takes into consideration food safety regulations for irrigating crops with treated wastewater. We demonstrate that, in contrast to previous studies, CES rates between different water types are not identical and generally lower than previously assumed – differences that can be attributed to the constraints associated with crop salinity tolerance and food safety regulations. Our results reveal that water shortage can lead to a significant decline of Israel’s GDP, where a considerable part of the decline is attributed to the decrease in agricultural outputs. The magnitude of the impact depends on the underlying assumptions regarding future desalination capacity. To further study the effect of desalination, we run simulations under various desalination levels and examine its impact on the GDP. We also examine the extent to which the impact of water shortage is sensitive to CES rates between different irrigation water types.

Consumer surplus and CES demand

This article presents the consumer surplus formula for constant elasticity of substitution (CES) demands. The formula is used to compare the monopoly and optimum provisions of product variety. It is shown that a monopolist under-provides variety. This result is contrasted with Lambertini’s analysis of the monopolist’s optimal R&D portfolio. I also contrast my approach with the indirect utility technique of Anderson, de Palma, and Thisse’s discrete choice theory of product differentiation.

Finite-sample refinement of GMM approach to nonlinear models under heteroskedasticity of unknown form

ABSTRACTIt is quite common to observe heteroskedasticity in real data, in particular, cross-sectional or micro data. Previous studies concentrate on improving the finite-sample properties of tests under heteroskedasticity of unknown forms in linear models. The advantage of a heteroskedasticity consistent covariance matrix estimator (HCCME)-type small-sample improvement for linear models does not carry over to the nonlinear model specifications since there is no obvious counterpart for the diagonal element of the projection matrix in linear models, which is crucial for implementing the finite-sample refinement. Within the framework of nonlinear models, we develop a straightforward approach by extending the applicability of HCCME-type corrections to the two-step GMM method. The Monte Carlo experiments show that the proposed method not only refines the testing procedure in terms of the error of rejection probability, but also improves the coefficient estimation based on the mean squared error (MSE) and the mean absolute error (MAE). The estimation of a constant elasticity of substitution (CES)-type production function is also provided to illustrate how to implement the proposed method empirically.