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.     

Product diversification and attitudes toward risk in agricultural production

In this article we analyze the relationship between risk-avoidance behavior and economic jointness in a multi-output agricultural technology. We focus on farmer specific heterogeneity in attitudes towards risk-taking, while treating production uncertainty as unobserved stochastic error that is common to all region specific farms. We furthermore utilize a new flexible functional form, the Constant Elasticity of Transformation, Constant Elasticity of Substitution, Generalized Leontief (Behrman, Lovell, Pollak, and Sickles, [1992]) which has the appealing property of relative flexibility while ensuring proper curvature properties of the estimated multi-output technology over a larger sample region of the price/quantity space than a flexible form such as the Generalized Leontief [Diewert, 1971].Our empirical study deals with small-scale agriculture in the Indian Semi-Arid Tropics (SAT), partly because of the importance of yield-related risk in this region, but also because we have measures of farmer specific risk attitudes in the SAT data. Our modeling approach allows for the calculation of the shadow cost of farmer specific risk attitudes in terms of foregone profits, while at the same time controlliing for the technical factors that give rise to multi-output production in the absence of risk. We are thus able to estimate these opportunity costs while modeling a multiple output technology in which cost complementarities can lead to diversified production and in which joint production is not always undertaken.     

On the flexibility of flexible functional forms: An empirical approach

This paper analyzes empirically the ability of the Translog and Generalized Leontief functional forms to approximate Constant Elasticity of Substitution utility functions. Although these flexible forms provide a good local approximation they do not always provide a good approximation over a range of observations. Hence the finding in practice of observations for which the regularity conditions required by economic theory are not satisfied need not imply the absence of an underlying utility-maximizing process, but may simply reflect the inability of the flexible form to approximate the true utility function over the range of the data.     

公共投资就业效应的一个解释——基于CES生产函数的分析及其检验

本文在分析CES生产函数过程中引入劳动力市场,探讨了公共投资与就业的联系.本文认为,公共投资是通过劳动工资弹性来影响就业的.公共投资增加会引起劳动需求的工资弹性提高,而公共投资的溢出效应则会导致企业实际工资支出水平降低,两方面原因的共同作用引起就业的增长.在此分析基础上,本文用ARDL方法构建了一个多方程模型,并用中国的数据进行了检验.为提高分析的有效性,我们用SUR方法对模型做了系统估计,并进一步通过方程转化对变量的短期波动和长期均衡关系进行了探讨.实证研究发现,中国的公共投资增长在短期减少就业,但长期内对就业有显著的正效应.     

Production Technology Estimates and Balanced Growth

Capital‐labour substitution and total factor productivity (TFP) estimates are essential features of many economic models. Such models typically embody a balanced growth path. This often leads researchers to estimate models imposing stringent prior choices on technical change. We demonstrate that estimation of the substitution elasticity and TFP growth can be substantially biased if technical progress is thereby mis‐specified. We obtain analytical and simulation results in the context of a model consistent with balanced and near‐balanced growth (i.e. departures from balanced growth but broadly stable factor shares). Given this evidence, a constant elasticity of substitution production function system is then estimated for the US economy. Results show that the estimated substitution elasticity tends to be significantly lower using a factor‐augmenting specification (well below one). We are also able to reject conventional neutrality forms in favour of general factor augmentation with a non‐negligible capital‐augmenting component. Our work thus provides insights into production and supply‐side estimation in balanced‐growth frameworks.     

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.     

WHAT DETERMINES THE ELASTICITY OF SUBSTITUTION BETWEEN CAPITAL AND LABOR? A LITERATURE REVIEW

This paper provides the first comprehensive review of the empirical and theoretical literature on the determinants of the elasticity of substitution between capital and labor. Our focus is on the two-input constant elasticity of substitution (CES) production function. We start by presenting four concise observations that summarize the empirical literature on the estimation of . Motivated by these observations, the main part of this survey then focuses on potential determinants of capital–labor substitution. We first review several approaches to the microfoundation of production functions where the elasticity of substitution (EOS) is treated as a purely technological parameter. Second, we outline the construction of an aggregate elasticity of substitution (AES) in a multi-sectoral framework and investigate its dependence on underlying intra- and inter-sectoral substitution. Third, we discuss the influence of the institutional framework on the extent of factor substitution. Overall, this survey highlights that the effective elasticity of substitution (EES), which is typically estimated in empirical studies, is generally not an immutable deep parameter but depends on a multitude of technological, non-technological, and institutional determinants. Based on these insights, the final section identifies a number of potential empirical and theoretical avenues for future research.     

Identification and estimation of a class of household production models

We consider a class of household production models characterized by a dichotomy property. In these models the amount of time spent on household production does not depend on the household utility function, conditional on household members having a paid job. We analyse the (non‐parametric) identifiability of the production function and the so‐called jointness function (a function describing which part of household production time is counted as pure leisure). It is shown that the models are identified in the two‐adult case, but not in the single‐adult case. We present an empirical application to Swedish time‐allocation data. The estimates satisfy regularity conditions that were violated in previous studies and pass various specification tests. For this data set we find that male and female home production time are q‐substitutes. Copyright © 2003 John Wiley & Sons, Ltd.     

A new criterion for technical efficiency measures: non‐monotonicity across dimensions axioms

Based on non‐parametric deterministic production technologies radial and non‐radial measures of technical efficiency are evaluated using properties guaranteeing insensitivity to the dimensionality of technology. These new axioms are important in empirical research and may especially prevent manipulation of results when implementing these benchmark methodologies in private or public organizations. An empirical example illustrates to which extent a series of radial and non‐radial technical efficiency measures satisfies the proposed axioms. Copyright © 1999 John Wiley & Sons, Ltd.     

Does Education Matter for Economic Growth?

Empirical growth regressions typically include mean years of schooling as a proxy for human capital. However, empirical research often finds that the sign and significance of schooling depends on the sample of observations or the specification of the model. We use a non‐parametric local‐linear regression estimator and a non‐parametric variable relevance test to conduct a rigorous and systematic search for significance of mean years of schooling by examining five of the most comprehensive schooling databases. Contrary to a few recent articles that have identified significant nonlinearities between education and growth, our results suggest that mean years of schooling is not a statistically relevant variable in growth regressions. However, we do find evidence (within a cross‐sectional framework), that educational achievement, measured by mean test scores, may provide a more reliable measure of human capital than mean years of schooling.     

Duality theory and pitfalls in the specification of technologies

Principles of duality enable the investigator to model the technology of a multiple-input-single- output firm either by means of a production function or a cost function. For empirical implementation, both alternatives employ the assumption of competitive market behaviour. Recently, functional forms have been developed which are sufficiently flexible to describe the substitution possibilities among factors when the technology consists of more than two factors. However, contrary to the strongly separable multi-factor Cobb-Douglas and CES forms, these functional forms are not self-dual. This poses the problem of choosing between two different maintained hypotheses. In this paper, we compare the inferences with respect to substitution possibilities obtained by imposing the two alternative specifications of a production function and a cost function on the same set of data. We find that they give very different inferences with respect to substitution possibilities between factors. Furthermore, these inferences continue to differ even when we explicitly adopt the position that both the production and cost functions are each approximations of the true technology.     

Scarce or Abundant? The Economics of Natural Resource Availability

Most natural resources that are used in production are non‐renewable. When they become depleted they are lost for future use. Does it follow that the limited availability of natural resources will at some time in the future constrain economic growth as many environmentalists believe? While classical economists have shared the belief in limits to growth, the distinctive feature of modern neoclassical economics is its optimism about the availability of natural resources. This survey suggests that resource optimism can be summarised in four propositions. First, a rise in the price of a resource leads to a substitution of this resource with another more abundant resource and to a substitution of products that are intensive in this resource. Second, a rise in the price of a resource leads to increased recycling of the resource and to the exploration and extraction of lower quality ores. Third, man‐made capital can substitute for natural resources. Fourth, technical progress increases the efficiency of resource use and makes extraction of lower quality ores economical. In a critical analysis of these four propositions it is shown that while the conjecture that natural resources will never constrain future economic growth is logically conceivable, we do not and indeed cannot know whether it will be possible in practice to overcome any resource constraint. JEL Classification: Q20, Q30, Q40     

Variable elasticity of substitution in urban housing production

The notion that the elasticity of substitution in urban housing production should vary with changing intensities of land use seems to be realistic and theoretically viable. Hence the variable elasticity of substitution production function has been proposed by some authors. However, it suffers from a serious shortcoming that the elasticity of substitution should not exceed unity. To allow for flexibility in the range of the elasticity of substitution, we explore a general functional form for the housing production function, the weak disposability of inputs production function in particular. Our empirical findings, based on the Santa Clara County single-family housing data, provide evidence that this general function is a more accurate specification of urban housing production than the variable elasticity of substitution function.     

Hyperbolic Efficiency and Parametric Distance Functions: With Application to Spanish Savings Banks

Distance functions are gaining relevance as alternative representations of production technologies, with growing numbers of empirical applications being made in the productivity and efficiency field. Distance functions were initially defined on the input or output production possibility sets by Shephard (1953, 1970) and extended to a graph representation of the technology by Färe, Grosskopf and Lovell (1985) through their graph hyperbolic distance function. Since then, different techniques such as non parametric-DEA and parametric-SFA have been used to calculate these distance functions. However, in the latter case we know of no study in which the restriction to input or output orientation has been relaxed. What we propose is to overcome such restrictiveness on dimensionality by defining and estimating a parametric hyperbolic distance function which simultaneously allows for the maximum equiproportionate expansion of outputs and reduction of inputs. In particular, we introduce a translog hyperbolic specification that complies with the conventional properties that the hyperbolic distance function satisfies. Finally, to illustrate its applicability in efficiency analysis we implement it using a data set of Spanish savings banks.     

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.     

The Input Relationship Between Co-Authors in Economics: A Production Function Approach

A bstract .   This study addresses the question of what the relative input relationship is between co-authors in economics. Using the direct addilog production function, the partial elasticities of substitution between co-authors are estimated. The empirical results suggest that co-authors in economics are equivalent substitutes in production. The empirical results are robust whether the direct addilog production is estimated using each co-author's research capital stock, depreciated research capital stock, impact-adjusted research capital stock, or depreciated impact-adjusted research capital stock.     

A Review of Modern Computational Algorithms for Bayesian Optimal Design

Bayesian experimental design is a fast growing area of research with many real‐world applications. As computational power has increased over the years, so has the development of simulation‐based design methods, which involve a number of algorithms, such as Markov chain Monte Carlo, sequential Monte Carlo and approximate Bayes methods, facilitating more complex design problems to be solved. The Bayesian framework provides a unified approach for incorporating prior information and/or uncertainties regarding the statistical model with a utility function which describes the experimental aims. In this paper, we provide a general overview on the concepts involved in Bayesian experimental design, and focus on describing some of the more commonly used Bayesian utility functions and methods for their estimation, as well as a number of algorithms that are used to search over the design space to find the Bayesian optimal design. We also discuss other computational strategies for further research in Bayesian optimal design.     

The elasticity of substitution in urban housing production: A VES approach

Many of the models which have been developed to explain urban spatial structure and land-use patterns rest on the properties of production functions. Differing factor price ratios within urban areas, particularly land prices, result in capital-land ratios exemplified by high-rise apartments and single-family dwellings. The purpose of this paper is to explore a new functional form for the housing production function. Specifically, a variable elasticity of substitution production function is proposed and some preliminary empirical evidence is provided using data for single-family housing.     

Explaining economic growth in the Soviet Union, 1950–86

Production function estimates are provided for Soviet industrial production and gross national product for the period 1950–86. A variety of alternative specifications is tested, including Cobb-Douglas, constant elasticity of substitution and variable elasticity of substitution production functions, and an error correction mechanism is used to investigate the long-run properties of the estimated equation. The structural stability of the estimates is also examined. Constant-returns-to-scale Cobb-Douglas production functions suggest that the rate of total factor productivity growth in the Soviet economy has declined steadily over time, becoming negative sometime in the period between 1970 and 1980. However the extensive statistical tests can doubt on the validity of any production function estimated on Soviet data.     

Robust Inference on Average Economic Growth*

We discuss a method to estimate the confidence bounds for average economic growth, which is robust to misspecification of the unit root property of a given time series. We derive asymptotic theory for the consequences of such misspecification. Our empirical method amounts to an implementation of the subsampling procedure advocated in Romano and Wolf (Econometrica, 2001, Vol. 69, p. 1283). Simulation evidence supports the theory and it also indicates the practical relevance of the subsampling method. We use quarterly postwar US industrial production for illustration and we show that non‐robust approaches rather lead to different conclusions on average economic growth than our robust approach.