A Non‐parametric Examination of Capital–Skill Complementarity*

This paper uses non‐parametric kernel methods to construct observation‐specific elasticities of substitution for a balanced panel of 73 developed and developing countries to examine the capital–skill complementarity hypothesis. The exercise shows some support for capital–skill complementarity, but the strength of the evidence depends upon the definition of skilled labour and the elasticity of substitution measure being used. The added flexibility of the non‐parametric procedure is also capable of uncover ing that the elasticities of substitution vary across countries, groups of countries and time periods.     

Acknowledgement

On the basis of estimates of four input translog production and cost functions using data for Irish manufacturing, different inferences are obtained about price elasticities and the elasticities of substitution between inputs, indicating sensitivity to the primal or dual representation of the technology. the results strongly reinforce the findings of Burgees (1975) and Appelbaum (1978) from U.S. data.     

SUBSTITUTION ELASTICITIES IN A CONSTANT ELASTICITY OF SUBSTITUTION FRAMEWORK – EMPIRICAL ESTIMATES USING NONLINEAR LEAST SQUARES

Elasticities are key parameters for any economic analysis. Using the World-Input–Output Database, we estimate substitution elasticities for a three-level nested constant elasticity of substitution KLEM production structure using up to date nonlinear least squares estimation procedures. This allows us for the first time to use one coherent data set for the estimation process. Furthermore, it gives us the opportunity to derive elasticities from the same data which researchers can use to calibrate their models. On the basis of our estimations, we demonstrate that the practice of using Cobb–Douglas or Leontief production functions in economic models must be rejected for the majority of sectors. We provide a comprehensive set of estimated substitution elasticities covering a wide range of sectors. Our results suggest that no substantial change in input substitutability takes place during the time period we consider. Moreover, there is no substantial variation in substitution elasticities across regions.     

Elasticities of Substitution and Complementarity: A Synthesis

We derive the relationships between the net and gross elasticities of substitution and complementarity (i.e., the elasticities that refer either to the conditional or unconditional, direct or inverse demand system) in the general case of non-homothetic, variable-returns-to-scale technologies. We also show that the so-called Hicks Elasticity of Complementarity (Hicks, Oxford economic Papers 22, 289–296 (1970)) is dual to a full-fledged elasticity of gross input substitution that we call the Hotelling/Lau Elasticity of Substitution (Lau, Production Economics: A Dual Approach to Theory and Applications. Amsterdam: North-Holand (1978)). The former is, in fact, the proper elasticity of substitution in the case of the inverse, unconditional input demand. Our results should clarify some issues about the input substitutability classification.     

INTERFUEL SUBSTITUTION: A META‐ANALYSIS

Abstract This paper provides the first meta‐analysis of the interfuel substitutability literature. The sample includes 47 studies of interfuel substitution in the industrial sector, in manufacturing industry or manufacturing sub‐industries, or in the macro‐economy of a variety of developed and developing countries. Meta‐regressions are estimated for the six shadow elasticities of substitution between coal, oil, gas and electricity. I find that at the level of the industrial sector as a whole the oil–coal, oil–gas, oil–electricity and gas–electricity shadow elasticities of substitution are significantly greater than unity. The remaining elasticities – between coal and gas and coal and electricity – are insignificantly different from unity or zero due to their large standard errors. Substitution possibilities seem more constrained at the macro level and less constrained at lower levels of aggregation. Estimates of the elasticities of substitution from cross‐section regressions are generally largest whereas fixed effects panel estimates are intermediate in magnitude, and time‐series estimates are mostly much smaller. In order to obtain more precise and less biased estimates of long‐run elasticities of substitution, there is a need for additional primary studies using large samples and/or the between estimator which econometric research suggests is likely to provide the best estimates of long‐run elasticities.     

Cyclical equilibria in multi-sector productive economies: The role of substitution and factor intensity

The paper examines the existence of cyclical perfect foresight equilibria in a two-sector overlapping generations economy with production in which both goods enter consumption. Conditions for the existence of two types of cyclical equilibra are obtained in terms of elasticities of substitution in production and consumption, factor shares in production, and expenditure shares in consumption. The role of substitution possibilities and factor intensities is highlighted. It is shown that factor intensity assumptions are not enough to rule out cyclical equilibria and that limit cycles may exist for substantial amounts of substitution possibilities in production; what matters is the relative sizes of the consumption and production elasticities. The results are illustrated using CES functions. A dynamical simulation of an economy which exhibits a Hopf cycle is presented.     

Deunionization and job polarization – a macroeconomic model analysis for a small open economy

Declining unionization rates and job polarization are two important labor market developments of recent decades. A large body of literature has analyzed these phenomena separately, but little has been done to see whether there is a link between them. We employ a macroeconomic model for a small open economy with a large input–output core to analyze how deunionization may cause job polarization. Our analysis shows that medium-skilled workers are negatively affected by deunionization, mainly as a result of the heterogeneity of the elasticities of substitution between different types of labor. While the elasticities of substitution between high- and medium-skilled labor are relatively low, the elasticities of substitution between medium- and low-skilled are relatively high. As a result, when deunionization leads to increased wage dispersion, we find that demand for low-skilled increases at the expense of medium-skilled labor, thus yielding a more polarized labor market.     

Indeterminacy in discrete-time infinite-horizon models with non-linear utility and endogenous labor

We consider a discrete-time two-sector model with sector specific externalities in which the technologies are given by CES functions with asymmetric elasticities of capital–labor substitution, and the preferences of the representative agent are given by a CES additively separable utility function defined over consumption and leisure. We first show that when the labor supply is infinitely elastic, the steady state is always saddle-point stable, no matter what the elasticity of intertemporal substitution in consumption and the size of externalities are. We then prove that when the elasticity of intertemporal substitution in consumption is sufficiently large, local indeterminacy requires a low enough elasticity of the labor supply.     

CES and Translog parameter estimates in a SAM-based regional general equilibrium framework

The computation of General Equilibrium models crucially depends on Social Accounting Matrix (SAM)-based calibration and on how estimation/imputation are performed to reproduce the benchmark dataset as an equilibrium solution. In this paper, theoretical contributions are provided by suggesting a new procedure in which the production function parameters and the elasticity of substitution are estimated by resorting to the data contained in the SAM. To this aim, the Generalized Cross-Entropy estimator is used. Application of this self-contained procedure to the regional SAM for the Italian region Tuscany leads to empirical results consisting of the estimates of the elasticities of substitution of Constant Elasticity of Substitution and Translog production functions consistent with the theoretical background. This yields a more efficient and effective solution of Computable General Equilibrium models.     

An empirical analysis of the effect of volunteer labor on public library employment

This study is an empirical investigation of the effect of library volunteers on public library demand for paid workers. Unlike previous studies, it estimates the impacts on different types of paid labor. The main purpose is to test whether volunteer labor replaced or complemented paid employees. A translog cost function is used to derive cost shares and elasticities of substitution for Pennsylvania public libraries. Cross‐elasticity estimates of substitution and input demand suggest a strong complementary relation between volunteers and professional workers. Most of the other Allen cross elasticities were not statistically significant. None of the estimates indicate that paid labor was being replaced by volunteers. Copyright © 2007 John Wiley & Sons, Ltd.     

Empirical tests of impacts of rationing: the case of Poland in transition

This study tests hypothesis derived from the theory of rationing using data for Polish households during the transition. The demand system consists of six commodity groups, and virtual prices are derived for the rationed goods. The empirical results are consistent with the theory: larger own-price elasticities for non-rationed goods after the reform, increased complementarity and decreased substitutability. The results also show that ignoring rationing overstates the welfare decrease during transition.     

Evaluating food retailers using dual elasticities of substitution

Dual elasticities of substitution from a distance function model of the food retailing establishment are developed based on multiple performance measures integrated with store characteristics, staffing decisions, and employee benefits and incentives. The impacts of organizational and competitive conditions such as store format, membership in a self-distributing chain, and the presence of a supercenter on store management decisions are evaluated. Technical substitution relationships implied by the dual Morishima elasticities confirm that moderate changes in relative shadow factor prices are associated with input adjustments in retail operations, implying that the costs of adjusting input allocations are small. Both value added and service offerings decline in the presence of a supercenter, with food retailers relying on price adjustments as a primary strategy.     

中国工业部门的能源价格扭曲与要素替代研究

针对以往关于中国能源替代问题的研究未考虑价格扭曲因素的不足,本文以超对数成本函数为基础,对中国工业部门要素价格扭曲进行测度,并计算要素自价格弹性及要素间替代弹性。研究发现,能源的相对价格存在严重扭曲;能源自价格弹性在2004年前为正,其原因是价格管制与市场不完善阻碍了其调节功能的发挥;资本与能源间并不存在确定的替代关系,劳动与能源间在近期表现为替代关系,而其他投入与能源间表现为互补关系。本文最后根据实证研究结果提出三点政策建议。     

Geographic differences in production technology

This paper demonstrates that manufacturing plants within the same industry, but located in different places, often have different production characteristics. This conclusion is based on the time series estimation of a general production model for each of four industries in Los Angeles and Philadelphia. The paper discusses why differences in economies of scale, total factor productivity, factor distribution, elasticities of substitution, and other parameters, are important for regional production theory and public policy.     

THE NORMALIZED CES PRODUCTION FUNCTION: THEORY AND EMPIRICS

Abstract The elasticity of substitution between capital and labor and, in turn, the direction of technical change are critical parameters in many fields of economics. Until recently, though, the application of production functions with specifically non‐unitary substitution elasticities (i.e., non‐Cobb–Douglas) was hampered by empirical and theoretical uncertainties. As recently revealed, ‘normalization’ of production‐technology systems holds out the promise of resolving many of those uncertainties. We survey and assess the intrinsic links between production (as conceptualized in a production function), factor substitution (as made most explicit in Constant Elasticity of Substitution functions) and normalization (defined by the fixing of baseline values for relevant variables). First, we recall how the normalized Constant Elasticity of Substitution function came into existence and what normalization implies for its formal properties. Then we deal with the key role of normalization in recent advances in the theory of business cycles and of economic growth. Next, we discuss the benefits normalization brings for empirical estimation and empirical growth research. Finally, we identify promising areas of future research.     

Alternative functional forms for production,cost and returns to scale functions

We consider generalized production functions, introduced in Zellner and Revankar (1969), for output y=g(f) where g is a monotonic function and f is a homogeneous production function. For various choices of the scale elasticity or returns to scale as a function of output, differential equations are solved to determine the associated forms of the monotonic transformation, g(f). Then by choice of the form of f, the elasticity of substitution, constant or variable, is determined. In this way, we have produced and generalized a number of homothetic production functions, some already in the literature. Also, we have derived and studied their associated cost functions to determine how their shapes are affected by various choices of the scale elasticity and substitution elasticity functions. In general, we require that the returns to scale function be a monotonically decreasing function of output and that associated average cost functions be U- or L-shaped with a unique minimum. We also represent production functions in polar coordinates and show how this representation simplifies study of production functions' properties. Using data for the US transportation equipment industry, maximum likelihood and Bayesian methods are employed to estimate many different generalized production functions and their associated average cost functions. In accord with results in the literature, it is found that the scale elasticities decline with output and that average cost curves are U- or L-shaped with unique minima. © 1998 John Wiley & Sons, Ltd.     

COEFFICIENT CHANGE,PRICE EFFECTS,AND IMPLICIT ELASTICITIES: ESTIMATING MICROECONOMIC DETERMINANTS OVER TWO TIME PERIODS

This paper presents and estimates an input–output model in which input coefficient changes are functions of changing prices. The model produces results that mirror the characteristics of input demand functions based on the model of cost minimization subject to producing a desired level of output. It does not rely on the specification of a functional form for input coefficients, and it does not require the use of assumptions regarding the elasticity of substitution. Instead, it allows the actual price and coefficient changes that occur between periods to identify the implicit elasticities and own- and cross-price derivatives. Using this model, it is shown how accurate measures of price effects, including the full array of own and cross-elasticities of demand, can be estimated for models comprising up to 15 sectors given data for only two time periods.     

Estimating Input–Output Factor Demand Equations: Some Results on Hanoch's HCDES Production Function

In this paper, we estimate a factor demand system based on Hanoch's homogeneous constant differences of elasticities of substitution production function under a newly proposed specification of the contemporaneous covariance matrix. This admits that the variances of the factor demands may be different but, nevertheless, does not ask for many observations.     

ECONOMETRIC ESTIMATION OF ARMINGTON IMPORT ELASTICITIES FOR A REGIONAL CGE MODEL OF THE ILLINOIS ECONOMY

One of the main concerns associated with the development and use of regional CGE models is the determination of key parameter values, particularly substitution and other price elasticities. A common problem is the lack of appropriate regional data for econometric estimation. Consequently, it is important to identify key parameters that are likely to be important in determining quantitative results and then to prioritize these for estimation where appropriate data are available. In this paper, the focus is on the estimation of the regional trade (import) substitution parameters, which tend to be important in analysis for regional economies (given their openness to trade). Here, commodity import elasticities for the Illinois economy are estimated and tested in a single region CGE model of the Illinois economy. In our econometric estimation, we apply a model that takes account of market size and distance in estimating the substitutability between commodities produced in Illinois and other US states.     

On the Relationship between Input–Output Coefficients and Hanoch's Linear Homogeneous Constant Differences of Elasticities of Substitution Production Function

Tilanus's ‘mixed’ input–output coefficients are generalized and it is shown that the generalized coefficients stand in a fixed proportion to each other if and only if the technology is described by Hanoch ‘s linear homogeneous constant differences of elasticities of substitution production function.