On the Equivalence of Two Concepts of Returns to Scale

We examine the relationship between two widely used concepts of returns to scale at different levels of analysis. We show that while their weak global versions are equivalent, the strict global versions are not so. Versions at a given input vector are never equivalent, which invalidates a result by Ide and Takayama (1987).     

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 estimating firm-level production functions using proxy variables to control for unobservables

In the common case where polynomial approximations are used for unknown functions, I show how proxy variable approaches to controlling for unobserved productivity, proposed by Olley and Pakes [Olley, S. and Pakes, A., 1996. The dynamics of productivity in the telecommunications equipment industry. Econometrica 64, 1263–1298.] and Levinsohn and Petrin (Levinsohn, J. and Petrin, A., 2003. Estimating production functions using inputs to control for unobservables. Review of Economic Studies 70, 317–341.], can be implemented by specifying different instruments for different equations and applying generalized method of moments. Studying the parameters within a two-equation system clarifies some key identification issues, and joint estimation of the parameters leads to simple inference and more efficient estimators.     

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.     

Productivity Growth and Input Demand: The Effect of Learning by Doing in a Gold Mining Firm in a Developing Economy

This paper analyzes the effect of learning by doing (LBD) on the firm’s productivity growth and its input demand decisions. The results indicate that LBD is an important determinant of the firm’s productivity growth. The contribution of LBD to the firm’s productivity growth is about 5.6%. Another observation is that LBD has a decreasing effect on the firm’s cost of production – a finding which is consistent with the results of many studies. Also, an increase in LBD measured by cumulative production increases the firm’s demand for capital, and decreases the firm’s demand for labor. Lastly, LBD has a significant effect on the firm’s elasticity of scale. A fundamental message derived from the study is the confirmation that the firms should invest in more large capital equipment, embark on new processing techniques, and create an environment that is conducive to on-the-job learning.     

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.     

Rates of Return to Four‐Year University Education: An Application of Regression Discontinuity Design

It is invariably difficult to estimate the rate of return to university education, because of the problem of omitted variable bias. Using a regression discontinuity design, we estimate the effect of a four‐year university education on earnings, and we explore the pathways through which the effect operates. Our estimation exploits the centralized, score‐based college/university admission system in China, where the minimum scores required for university admission are externally determined by the provincial governments. Our findings suggest that being eligible for four‐year university admission implies a sizable increase in earnings. The payoff can be attributed to the prolonged length of education and improvements in education quality, although the quality effects cannot be precisely estimated.     

Correcting for biases when estimating production functions: an illusion of the laws of algebra?

This paper shows that the endogeneity bias that allegedly appearswhen estimating production functions using value data, and whichthe literature has tried to deal with since the 1940s, is simplythe result of omitted-variable bias due to a poor approximationto an accounting identity. This problem has no econometric solution.As a result, recent attempts to solve the problem by developingnew estimators are questioned. The only possible way to estimatethe technological parameters of the production function is touse physical quantities.     

企业异质性、规模报酬与劳动力空间流动——基于新新经济地理学的理论研究

文章在对新新经济地理学假设进行拓展的基础上,从理论分析和数值模拟两个层面对企业异质性、规模报酬与劳动力空间流动进行了系统的研究,结论是:地区间企业生产技术水平的不同决定了企业与劳动力的转移方向,企业的生产技术水平与固定成本呈正向变动关系;落后地区和发达地区的发展与彼此对外市场开放相互依赖;由于落后地区总有一定的市场需求,棒—棒均衡在现实中存在的可能性很小。     

知识生产函数、规模报酬和经济增长模式——R＆D模型对中国的实证检验

R&D模型是经济增长理论的一个重要、前沿的部分,它认为技术进步和创新是一个国家经济增长的动力。R&D模型将经济长期增长的源泉归结于知识生产函数中两种投入要素——知识和资本的规模报酬,并且把经济的长期增长模式区分成三种类型:稳定性均衡、非稳定性均衡和半稳定性均衡。文章首次对知识生产函数进行实证检验,以此来判断我国经济增长模式。通过对2004-2006年中国243个城市面板数据的研究,发现中国的经济增长模式属于稳定性均衡的类型,新知识的生产对知识和资本的规模报酬是递减的,经济会在某个增长率稳定下来,劳动力和资本存量中用于研究和开发的比例和储蓄率的上升,在长期内都不会改变这个稳定的增长率。     

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.     

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.     

Comment on “On the openness to trade as a determinant of the macroeconomic elasticity of substitution”

This paper provides a comment on the analysis of the link between an economy’s openness to trade and its macroeconomic elasticity of substitution (ES) presented in Saam [Saam, M., 2008. Openness to trade as a determinant of the macroeconomic elasticity of substitution. Journal of Macroeconomics 30, 691–702.].     

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.     

On the long-run wealth distribution in a simple Ramsey model with heterogeneous households

This paper analyzes the long-run wealth distribution in a Ramsey model where individuals have a common rate of time preference but different intertemporal elasticities of substitution. As a result, it is shown that heterogeneity among households in intertemporal substitution is sufficient for the existence of a non-degenerate long-run wealth distribution. We also investigate the properties of the long-run wealth distribution and the transition of capital and consumption using the phase diagram.     

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 existence of a regulated production function

This paper examines the generalization of the regulated production function. It characterizes the set of admissible regulatory constraints that are compatible with the existence of a regulated production function in a sufficiently weak framework to encompass the usual rate-of-return constraints à la Averch and Johnson and value constraints.     

Economies of scale and mechanization in Chinese corn and wheat production

ABSTRACT

As the growth in Chinese farm productivity slowed down between 2000 and 2010, modernizing agriculture has become a priority of the Chinese government. Given the important role of mechanization and land reform policies in that context, this study investigates farm production in China with a specific emphasis on the potential role of mechanization as well as land and farm consolidation. A production function is estimated using farm household data on corn and wheat production in the Shandong and Hebei provinces. The results allowed us to explore the potential economies of scale across a range of farm size, the impact of land fragmentation, and assess the impact of machinery usage. Our findings suggest that, taken in isolation, the prospect for efficiency gains from mechanization and land reforms appears limited.     

Estimation of the value of the marginal product of emission in a country where emissions output is regulated — an empirical study

Emissions resulting from the production process can be characterized as use of the elimination and disposal services of the ecological system. Hence, they are use of natural resources and thus an input to production. The present paper discusses an approach to evaluate the returns of these kind of services as a production factor.First, four main types of industrial emission are chosen —SO ₂,CO ₂,NO _xandparticulate matter — and integrated in a Cobb-Douglas production function. With this approach, the production elasticities and the marginal product of these types of emission can be estimated.Based on these results and assuming that marginal product equals price, the demand curve for emission is estimated. With this demand curve the consequences of different kinds of environmental policy are considered. Under further assumptions of optimal behaviour it can be shown that the demand curve for emission is equal to the curve of marginal costs of avoidance (MCA). Thus, the estimates of the demand curves can be considered as estimates of the MCA-curves. Furthermore the price elasticities of these four types of emission are estimated with this approach. The method used in the paper is suggested for calibration of CGE models.     

Modeling the short-run costs of changes in water availability in a desert city: a modified input-output approach

This paper investigates the impact of change in sectoral water supply on employment, value-added output, and indirect business tax, in Maricopa County, Arizona using input–output model. We developed extended modified input–output approach that incorporates each source of water as a separate sector, and that allows for substitution between water sources, and estimated the economic impact of a change in surface water supplies under two scenarios. Scenario I assumes that total water supply/use decreases by 1%, but the reduction comes only from surface water use, holding groundwater use constant. Scenario II assumes that surface water supply/use in all industries decreases by 1%, and the reduction in surface water use is replaced by the exact amount of more expensive groundwater. We found that the magnitude of economic impact depends on consumer’s responsiveness to water price change. When price elasticity of water demand is relatively low (≤0.2), the economic impact of a 1% reduction in surface water supplies was smaller than under the first scenario. However, the more water users in all industries are responsive to a change in water price, the bigger are economic impacts in terms of reductions in jobs, value added, and indirect business taxes.