Estimating global returns to scale with a cone-homogeneous production function: some cross-section results

This paper employs a cone-homogeneous production function to approximate, as closely as desired, a ray-homogeneous production function. Points in input space are projected by an output scaling function on to a fixed ray and a Cobb-Douglas cone function is used to obtain an estimate of global returns to scale. The empirical results indicate that we get a good approximation to a ray-homogeneous production function from the estimated cone-homogeneous function.     

Constrained output maximization and US agriculture

This paper presents a framework for estimating an indirect production function and then applies it to aggregate US agriculture. Issues addressed include tests of standard hypotheses about the underlying technology (homotheticity, neutral technical change, etc.) as well as examination of consistency in aggregation and the effects of changes in the level of aggregate expenditure on farm output. Since there already exist several studies empirically describing agricultural production technologies with indirect objective functions, one might fairly ask whether this paper really breaks any new ground? We feel that it does. One reason is that existing studies (e.g. Binswanger, 1974; Lopez, 1980; Ball and Chambers, 1982; Ray, 1982; and Weaver, 1983) all rely on either profit or cost functions. To date there appears to be only one study using an indirect production (Appelbaum, 1979), and it is not in agriculture. This seems unfortunate because there are many instances in agriculture for which an indirect production function (or revenue function approach) seems more appropriate. The reason why relates directly to one's belief about the objective function and constraints farmers face. Ultimately, it seems plausible in a certainty framework that producers maximize profits. And since cost minimization and output maximization are just constrained versions of profit maximization, both cost and indirect production functions are more appropriately viewed as restricted profit functions. What differs is the constraint. Assuming cost minimization implies that farmers are constrained by a fixed output which they must produce; in most instances, this is implausible. More likely, the level of output is itself a choice variable. Output maximization, on the other hand, suggests that the main constraint is the amount of money that producers can muster to hire resources. In other words, farmers may face binding constraints in obtaining the profit maximizing level on expenditure on input utilization. One might think that expenditure may not be a binding constraint because there exists a relatively active US credit market. However, the US credit market is far from being perfectly competitive in a stylized sense, and thus, the possibility of a farmer being able to finance a given level of expenditure may be limited.

Readers familiar with the dual approach to production problems may already be asking why these ideas rule out cost functions since it is well known that the cost function is the distance function of the indirect production function (Blackorby et al., 1978)? In principle, therefore, one could always estimate a cost function and then invert it to obtain the indirect production function. There are two problems with this approach: the first is that if output maximization is truly the objective, output is not predetermined and cannot be treated as exogenous in cost function estimation. Second, estimation of direct and indirect functions using the same data set does not always yield comparable results. Estimation of a transcendental logarithmic (translog) indirect production function and a translog cost function, separately, does not generally yield identical estimates of the Allen elasticities of substitutions. Solving the first problem in simple, but the second suggests that estimation should proceed on the basis of the objective function the researcher deems most appropriate. Therefore, if output maximization is more plausible than cost minimization an indirect production function should be used.

The plan of the paper is as follows. We first outline the theoretical developments necessary to our approach (included are conditions necessary for consistent aggregation over firms). We then present estimates of an indirect production function and use these estimates to investigate the plausibility of various restrictions on the technology, consistency in aggregation, substitution possibilities in agricultural production, and the effect of expenditure on agricultural input utilization. The paper closes with a discussion of the results and suggestions for future research.     

Why do Aggregate Production Functions Work? Fisher’s simulations,Shaikh’s identity and some new results

The literature on aggregation has shown that the conditions for successful aggregation of micro production functions into an aggregate production function are far too stringent to be believable (Fisher 1969, 1971). Despite this, aggregate production functions continue being used. The reason is that they seem to 'work'. This happens, however, because underlying every aggregate production function is the income accounting identity that links input and output, i.e. output equals wages plus profits. A simple algebraic transformation of this identity yields a form that resembles a production function (Shaikh, 1974, 1980). This paper uses Monte Carlo simulations to study two questions. First, how much spuriousness can help explain the relatively good fits of the Cobb-Douglas production function? The simulations show that the contribution of spuriousness to a high R 2 is minor once we properly account for the fact that input and output data used in production function estimations are linked through the income accounting identity. It is mostly the link through this identity that explains the results. Secondly, we study how much factor shares have to vary in an economy so as to render the Cobb-Douglas production function with a time trend a bad choice for modelling and estimation purposes. We conclude that the Cobb-Douglas form is robust to relatively large variations in the factor shares. What makes this form often fail are the variations in the growth rates of the wage and profit rates.     

Shadow prices of environmental outputs and production efficiency of household-level paper recycling units in Vietnam

The production efficiency and shadow prices of three environmental outputs (BOD, COD, and SS) of 63 household-level paper-recycling units, from a recycling craft village in Vietnam, are assessed A two-stage procedure, linear programming and stochastic estimation, is used to estimate output distance function. Social capital as a production factor and environmental outputs are included in the output distance function. Results indicate that production efficiencies could potentially be improved by 28%. There is a substantial variation in the shadow prices of environmental outputs among the production units of different types of paper products. Furthermore, the average shadow prices of the three environmental outputs are all positive. This indicates a potential for improving environmental quality though introducing pollution-prevention methods to paper-recycling production processes in Vietnam (e.g., recirculation of wastewater), and suggests that it may be inappropriate to restrict the shadow prices of environmental outputs to be non-positive for the analysis of some production processes.     

The distribution approach to the aggregation of putty-clay production functions

The point of departure of the distribution approach is the efficiency distribution of the production units in an industry. From this distribution the full-capacity production function and the short-run aggregate production function of the industry are derived. The long-run production function of the industry then is derived from the full-capacity function and the short-run production function. Hence, in the context of the distribution approach the relation is analysed between the short-run, full-capacity and long-run aggregate production functions of the industry and the efficiency distribution (and related capacity distribution) of the production units in that industry. Finally, the distribution approach is applied for the case of the Japanese cotton spinning industry.     

Economic versus physical input measures in the analysis of technical efficiency in fisheries

The measurement of technical efficiency requires the estimation of an appropriate production frontier. This is based on a set of inputs that are assumed to influence the level of output. Deviations from this frontier production function are separated into random variation and inefficiency. However, mis-specification of the production function through the use of inappropriate input measures may result in a bias in the measures of inefficiency. In fisheries, production is generally assumed to be a function of stock size, fishing time and the level of physical inputs employed. Defining the appropriate levels of physical inputs, however, is not straightforward, and several alternative measures are available. While economic measures of capital are more intuitively appealing, physical measures are generally readily available and hence less costly to collect. In this study, technical efficiency is measured for three fleet segments operating in the North Sea using three different gear types. The effects of using different measures of capital in the production frontier on the efficiency estimates are examined.     

External Scale Economies in Turkish Manufacturing Industries

In this study, the relationship between external scale economies (agglomeration economies) and productivity is measured by using Turkish data. The productivity increase can be due to economies from locating closer to other firms in either the same industry (localisation economies) or different industries (urbanisation economies). Localisation economies are proxied by own industry size and urbanisation economies by city population. Productivity (output per worker) is regressed on industry size, city population, and other related variables. A measure of concentration of state enterprises is included in the regressions to control for the possible inefficiencies in public sector firms. The functional form of the estimating equations is derived from the translog production function. As a check, a constant elasticity of substitution (CES) form is also experimented with. Data are cross-section data and come from industrial and production surveys conducted by the State Institute of Statistics of Turkey in 1985. The study finds that agglomeration economies that are robust across different specifications of the agglomeration economy function and production function exist in food products, textiles, and wood products. Urbanisation economies are detected in food products and textiles. In wood products there are localisation economies.     

An investigation of issues relating to where energy should enter the production function

This paper examines the impact of imposing different separability assumptions in the specifications of the standard hierarchical KLEM production function in a computable general equilibrium (CGE) model. The appropriate means of introducing energy to production functions has been a source of debate for a number of years. However, while modellers often subject results to parametric sensitivy analysis regarding the values associated with elasticities of substitution between inputs, it is rarely the case that the structure of the production function is subjected to testing. However, the chosen structure reflects the modeller's view about elasticity between different inputs and will have implications for model results wherever there are changes in relative prices. We illustrate our argument by introducing a simple demand shock to a CGE model of the Scottish economy (targeted at the energy supply sector) under different assumptions regarding the structure of the KLEM production function and separability assumptions therein.     

A translogarithmic cost function approach: Greece, 1953–1977

In this paper we use a two-output three-input specification to model the aggregate Greek economy. We use a translog joint cost function in lieu of its primal dual production function. Output consists of consumption and investment goods produced by the primary inputs and imports classified as a third agent of production. It is found that the cost minimizing input-mix is independent of the composition of output, that traditional functions are inappropriate in modeling Greek technology, and that the three factor inputs are substitutes for each other. Policies concerning the intensity of domestic inputs' use and the BOP are discussed.     

Increasing Returns,Learning-By-Doing And Neural Networks ∗

In this paper we draw an analogy between the process of learning-bydoing and the learning process which develops in a neural network context. The bridging tool we refer to is a dynamic production function whose only variable input is labour. By concentrating on the ‘neural network production function’ we show that the learning process can lead to increasing returns. The simulations show that when learning is characterized by an upper limit. returns are increasing for some time, while in the long run they go back to the level where they are constant.     

资本服务加总度量与Divisia指数

有关总量生产函数的批评很多,最直接的批评来自于从微观生产函数到总量生产函数的可加总条件不满足。本文采用几何直观的方法显示了资本加总条件的含义,明确了不满足严格的可加总条件并不必然使得总量生产函数失去意义,不满足条件只不过使得"硬性"加总后的总量生产函数出现一定程度的模糊性,而这种模糊性无论如何都会存在,其来源远远不止加总条件的不满足。在此基础上,本文阐述了Hicks加总、函数可分性加总等各种加总方法的内在逻辑联系,并通过几何方法显示了在满足可准确加总条件时,Divisia指数是一种比定基指数更为优越的方法。     

Nachfragefunktionen für die Produktionsfaktoren Arbeit und Kapital

Summary In this paper we present dynamic factor demand functions for labour and capital, and the underlying production function for the Austrian economy. Our approach is neoclassical. By definition, the production function is of the Cobb-Douglas type; experiments with a CES production function were not successful. Our empirical results look very plausible. The adjustement speeds, the output and price elasticities of both factor demand functions, as well as the parameters of the underlying production function are of a order of magnitude highly compatible with neoclassical theory.     

循环经济条件下企业行为最优化的经济学分析

循环经济模式下企业的生产函数和成本函数都增加了新的内容,资源环境变量不再是外生的,而是被内生化到生产函数中。运用定性和定量分析方法,对企业生产函数进行改进研究的结果表明,当企业行为最优化条件中增加了资源环境的约束时,生产者均衡将受单位产品的资源消耗量、污染物排放量、废弃物资源化等条件的影响。     

A robust approach to the measurement of Farrell efficiency

Measurement of efficiency of the frontier production function by Farrell's convex hull method is generalized here in two aspects. One develops a minimax method of estimation by following the Chebyshev principle and the other develops a dummy-variable method of stratifying the entire data set before ordinary regressions are performed to estimate the production frontier. An empirical application to educational production functions illustrates these methods.     

C.E.S. production functions in the light of the Cambridge critique

The Cambridge debate of the 1960s showed conclusively that the aggregation of capital, so as to obtain a surrogate production function according to Samuelson, is not possible in general, with critical implications also for other variants of neoclassical theory. The framework for the demonstration is that of linear activity analysis.There is an individual wage curve in function of the rate of profit for each technique. If these individual wage curves were straight lines, their envelope would define a wage curve resulting from all techniques, from which a surrogate production function could be derived, but all wage curves are straight only, if there is only one industry. And if wage curves are not straight, phenomena such as reswitching show that essential neoclassical hypotheses need not hold. A recent empirical investigation by Han and Schefold has found one empirical example for reswitching and several for reverse capital deepening.A rigorous derivation of surrogate production functions thus is ruled out also on empirical grounds, but the paradoxes seem not to be as frequent as the critics once thought, so that the question arises whether approximate surrogate production functions could be derived, with individual wage curves which would be sufficiently linear to construct approximate surrogate production functions, indicating a relationship between the intensity of capital and output per head which would be sufficiently precise to work with.The paper is part of a wider investigation, in which conditions for the existence of quasi-linear wage curves and the possibility of the construction of approximate surrogate production functions are given. The emphasis here is on the special hypotheses needed to obtain C.E.S. production functions.     

江西省总量生产函数与全要素生产率估算:1952-2007

根据索洛余值法和C-D生产函数,建立了江西省总量生产函数模型,并利用江西省1952-2007年相关指标数据进行了测算。研究发现,江西省总量生产函数是一个规模报酬递减的生产函数,江西省经济增长模式为投资驱动型的粗放型经济增长模式,代表技术进步的全要素生产率对江西省经济增长的贡献率长期在20%左右。因此,要提高江西省的全要素生产率贡献率,必须把技术进步放在江西经济社会发展的优先战略地位。     

A Cross-Country Empirical Investigation of the Aggregate Production Function Specification

Many growth models assume that aggregate output is generated by a Cobb-Douglas production function. In this article we question the empirical relevance of this specification. We use a panel of 82 countries over a 28-year period to estimate a general constant-elasticity-of-substitution (CES) production function specification. We find that for the entire sample of countries we can reject the Cobb-Douglas specification. When we divide our sample of countries up into several subsamples, we find that physical capital and human capital adjusted labor are more substitutable in the richest group of countries and are less substitutable in the poorest group of countries than would be implied by a Cobb-Douglas specification.     

Tanzanian formal sector workers' participation in informal production

A theoretical model is developed explaining formal sector workers participation in the informal sector. A reduced-form informal sector participation function is derived from a specific utility function, a specific informal sector production function, and a specific informal sector earnings function. The participation function can be estimated consistently, and provides a solution to the problem that informal sector ‘wages’ in developing countries are hard to observe. A sample of Tanzanian formal sector workers is used to estimate the participation function. A majority of Tanzanian formal sector workers participate in informal production. Participation in informal production is inversely related to household income, to living in Dar es Salaam, and to being a mother with small children. Participation is positively related to age, and multiple-job-holding seems to play a very different role in the transition from work to retirement in Tanzania compared to industrialized countries.     

A collaborating inventory model in a supply chain

The present article investigates an economic order quantity/ economic production quantity model in three-layer (manufacturer, vendor and retailer) supply chain management. In each stage, the products may undergo non-conforming quality items which have less value in the market. This model maximizes a collaborating expected profit function while production rate, order quantity, number of shipments with equal sizes are decision variables and unit production cost is a function of production rate. Numerical example is illustrated to test the model.