两种等效益面生产函数与全要素生产率变化率的分解

本文根据规模报酬可变还是规模报酬不变，分别定义了一般等效益面生产函数和典型等效益面生产函数。由一般等效益面生产函数的离散型分解式可以测算一个生产单元的纯技术进步，以及纯技术效率变化对经济增长的贡献；而由典型等效益面生产函数可以将全要素生产率的变化率分解为典型技术进步率、纯技术效率和规模效率的变化率之和。进而由具有明确几何意义的离散型分解式分别测算典型技术进步和规模效率对经济增长的贡献。等效益面生产函数与分解式的几何意义还说明，全要素生产率的改变最终是由技术创新、制度创新和管理创新共同推动的。     

The Effect of Technological Change and Technical Inefficiencies on the Performance of Functional Forms

Technological change is one of the most important determinants of the technological structure of the firm. Unfortunately, this crucial factor is often unobserved and must therefore be approximated. It is also well recognized that firms are not necessarily located on their efficient production frontier, a phenomenon known as technical inefficiency. This paper compares the performance of three flexible functional forms (the Translog, Symmetric McFadden and Symmetric Generalized Barnett) to properly infer theoretical properties and technology measurements when: (i) unobserved technological change is approximated by a time trend in the variable-cost-function specification and, (ii) firms may be technically inefficient. Our results indicate that no functional form dominates and that measuring the shifts of the production (cost) function has a clear and negative effect on the performance of the functional forms. Furthermore, we find that technical inefficiencies have a significant and negative effect on the measurement of, notably, returns to scale and the implicit rental price of capital. However, all forms over-reject theoretical properties and provide adequate technology measurements only on a sample-average basis. In addition, the performance of the functional forms is closely related to the true underlying rate of technological change.     

Australia’s mining productivity decline: implications for MFP measurement

This paper investigates the mining sector’s poor productivity performance as measured by the growth accounting formula for multifactor productivity (MFP) index during the recent mining boom in Australia. We provide an alternative measure of productivity growth by estimating a translog variable cost function, with parameters that separate productivity growth due to technical change from that due to the effects of returns to scale, capacity utilisation and natural resource inputs. The results show that the average MFP growth in Australian mining based on the dual cost-function measure of technical change is 2 % over the sample period 1974–1975 to 2007–2008, rather than ?0.2 % from the published index. The difference arises because declining natural resource inputs, the effects of capacity utilisation and returns to scale have all reduced the ‘true’ MFP growth.     

Productivity differences in multiple output industries: An empirical application to electricity distribution

Given that electricity distribution is undertaken via a network, it is expected that costs of production are affected both by the nature of the network and the volume of physical output distributed via the network. This two-dimensional concept of firm size, that is involving network size (number of customers) and the level of physical output (kWh), also corresponds to the distinction between productivity measures of returns to density and returns to scale.This approach has been used to specify a restricted multioutput cost function and to estimate this function for the Norwegian electricity distribution industry through the use of a flexible functional form (translog). The results indicate that no economies of scale are present in the industry even for small plants when measured correctly, but that economics of density are present.     

Comment: further sufficient conditions for an inverse relationship between productivity and employment

Extant empirical studies document that productivity gains due to technological progress often lead to reductions in employment. This paper rationalizes the stated empirical finding within the context of the theory of the competitive firm under price uncertainty. We show that technological progress affects employment adversely if the firm’s coefficient of relative risk aversion is no less than unity and its production technology exhibits non-decreasing returns to scale. On the other hand, technological progress unambiguously increases output if the firm’s preference has non-increasing absolute risk aversion.     

Accumulation, Technical Progress, and Increasing Returns in the Economic Growth of East Asia

Adopting homothetic variable returns to scale functional specifications, this study identifies the returns to scale in the aggregate production functions of four East Asian newly industrialized economies–Hong Kong, Korea, Singapore, and Taiwan–and the Group of Five economies based on a maximum likelihood estimation. The study finds evidence of increasing returns in the early developmental stage of the East Asian economies. Separating out the scale contribution from the non-scale factor contributions, the decomposition of the sources of East Asian economic growth differs significantly from the conventional constant returns to scale results, indicating that the role of technical progress is overestimated when constant returns to scale is assumed.     

Malmquist Indexes Using a Geometric Distance Function (GDF). Application to a Sample of Portuguese Bank Branches

Traditional approaches to calculate total factor productivity (TFP) change through Malmquist indexes rely on distance functions. In this paper we show that the use of distance functions as a means to calculate TFP change may introduce some bias in the analysis, and therefore we propose a procedure that calculates TFP change through observed values only. Our total TFP change is then decomposed into efficiency change, technological change, and a residual effect. This decomposition makes use of a non-oriented measure in order to avoid problems associated with the traditional use of radial oriented measures, especially when variable returns to scale technologies are to be compared. The proposed approach is applied in this paper to a sample of Portuguese bank branches.     

Adapting Productivity Theory to the Quadratic Cost Function. An Application to the Spanish Electric Sector

In this article we have adapted productivity analysis to the case of a cost model using a quadratic cost function and discrete data. The main theoretical result is a productivity index that can be decomposed into modified versions of the contribution of technical change and the effect of the variations in the scale of production. This framework has been applied to the study of the Spanish electric sector from 1985 to 1996, during which relevant regulatory changes were introduced in order to increase productivity. For this, a normalized quadratic cost function was estimated. The results show important productivity gains with both technical change and scale effect playing important roles.     

Productive Efficiency of the Swine Industry in Hawaii: Stochastic Frontier vs. Data Envelopment Analysis

Improving productive efficiency is an increasingly important determinant of the future of the swine industry in Hawaii. This paper examines the productive efficiency of a sample of swine producers in Hawaii by estimating a stochastic frontier production function and the constant returns to scale (CRS) and variable returns to scale (VRS) output-oriented DEA models. The technical efficiency estimates obtained from the two frontier techniques are compared. The scale properties are also examined under the two approaches. The industry's potential for increasing production through improved efficiency is also discussed.     

Decompositions of profitability change using cost functions

The paper presents a decomposition of a production unit’s cost ratio over two periods into explanatory factors. The explanatory factors are growth in the unit’s cost efficiency, output growth, changes in input prices and technical progress. In order to implement the decomposition, an estimate of the industry’s best practice cost function for the two periods under consideration is required. Profitability at a period of time is defined as the value of outputs produced by a production unit divided by the corresponding cost. Using the earlier work by Balk and O’Donnell, the paper provides a decomposition of profitability growth over two periods into various explanatory factors that are similar to the cost ratio decomposition except that change in outputs explanatory factor is replaced by two separate factors: an index of output price growth and a measure of returns to scale.     

Unbiased determination of production technologies

To determine whether an industry exhibits constant returns to scale, whether the production function is homothetic, or whether inputs are separable, a common approach is to specify a cost function, estimate its parameters using data such as prices and quantities of inputs, and then test the parametric restrictions corresponding to constant returns, a homothetic technology, or separability. Statistically, such inferences are valid if the true cost function is a member of the parametric class considered, otherwise the inference is biased. That is, the true rejection probability is not necessarily adequately approximated by the nominal size of the statistical test. The use of fixed parameter flexible functional forms such as the Translog, the generalized Leontief, or the Box-Cox will not alleviate this problem.The Fourier flexible form differs fundamentally from other flexible forms in that it has a variable number of parameters and a known bound, depending on the number of parameters, on the error, as measured by the Sobolev norm, of approximation to an arbitrary cost function. Thus it is possible to construct statistical tests for constant returns, a homothetic technology, or separability which are asymptotically size α by letting the number of parameters of the Fourier flexible form depend on sample size. That is, the true rejection probability converges to the nominal size of the test as sample size tends to infinity. The rate of convergence depends on the smoothness of the true cost function; the more times is differentiable the true cost function, the faster the convergence.The method is illustrated using the data on aggregate U.S. manufacturing of Berndt and Wood (1975, 1979) and Berndt and Khaled (1979).     

A Cost Indirect Evaluation of Productivity Change in UK Universities

The study provides an empirical analysis of productivity change in publicly-funded UK universities, against a background of government policy specifically designed to enhance the productive efficiency of universities in the provision of teaching and research. The nonparametric analysis employs a cost indirect approach to measuring productivity change, taking explicit account of the quality of research output and decomposing productivity change into technical change and efficiency change. The latter is also decomposed into changes in pure technical efficiency, scale efficiency and output congestion. Changes in size efficiency are also computed. On average, productivity declined by 4% over 1989–92, mainly as a result of regressive technical change. Evidence of biased technological change was found, with the frontier shifting out in favour of the teaching outputs and in relative to the research output.     

Estimation of stochastic frontier production functions with input-oriented technical efficiency

This paper deals with estimation of input-oriented (IO) technical inefficiency using a stochastic production frontier model. Econometrically the model is similar to a class of models that arise in specifying technical inefficiency in cost-minimizing and profit-maximizing frameworks. The standard maximum likelihood (ML) method that is used to estimate output-oriented (OO) technical efficiency cannot be applied to estimate these models. We use a simulated ML approach to estimate the IO production function and compare results from the IO and OO models, mainly to emphasize the point that estimated efficiency, returns to scale, technical change, etc., differ depending on whether one uses the model with IO or OO technical inefficiency.     

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 evolution of scale economies in US banking

Continued consolidation of the US banking industry and a general increase in the size of banks have prompted some policymakers to consider policies that discourage banks from getting larger, including explicit caps on bank size. However, limits on the size of banks could entail economic costs if they prevent banks from achieving economies of scale. This paper presents new estimates of returns to scale for US banks based on nonparametric, local‐linear estimation of bank cost, revenue, and profit functions. We report estimates for both 2006 and 2015 to compare returns to scale some 7 years after the financial crisis and 5 years after enactment of the Dodd–Frank Act with returns to scale before the crisis. We find that a high percentage of banks faced increasing returns to scale in cost in both years, including most of the 10 largest bank holding companies. Also, while returns to scale in revenue and profit vary more across banks, we find evidence that the largest four banks operate under increasing returns to scale.     

Dynamic Factor Demands and Technology Measurement under Arbitrary Expectations

We present a dynamic model of factor demands based on expected discounted costs minimization. While making only very mild assumptions on expectations and technology, we are able to establish a duality relationship between contemporary factor demands and the technology, and we provide formula for easily recovering marginal products, returns to scale, and technological change from estimated factor demands. Parametrization and implementation are illustrated in a detailed example.     

A Switching Regime Approach to Measuring the Effects of Technological Change in Ocean Shipping

this study examines the dramatic change in production technology of the U.S. ocean liner shipping industry over the period 1971 through 1982 using panel data on 15 subsidized U.S.-flag liner firms. To estimate the changes in the production function due to the new technology, the switching regime method of Goldfeld and Quandt is applied to a translog variable profit function. Three regimes based on the proportion of the new technology reflected in a firm's fleet are identified. The constant returns to scale fleet size more than doubles across the three regimes.     

A General Procedure to Recover the Marginal Products of a Cost Minimizing Firm

Inthis paper we develop a new method, based on generalized inverse,to recover the first derivatives of the production function.This allows us to retrieve returns to scale, technological progressand, in a dynamic setting, a measure of the adjustment cost.The method is general and systematic and it applies in caseswhere the traditional method does not. It is especially relevantwhen examining dynamic models or regulated firms.     

FLEXIBLE COST FUNCTION ESTIMATES FOR A GAS AND FUEL CORPORATION IN AUSTRALIA

This paper reviews and empirically tests the available evidence concerning economies of scale and technological change at Australian Gas Limited of New South Wales (AGL). a gas and fuel corporation. Since energy corporations are considered to need scale economies, they are regulated 'n both developed and developing countries. In keeping with the trend of deregulation stemming from the beginning of the 1980s in Western countries, many kinds of public corporations have been privatized and deregulated. Energy corporations are not an exceptional case, but very little evidence on this industry has been reported so far. From empirical tests, it is shown in a trans-log-type cost function that AGL has scale economies. the degree of which increased after the corporation changed its energy source from coal oil to liquid natural gas. Moreover, from the results of the trans-log cost function including technological change, a Hicksian neutral type technical progress exists. In a Hicksian non-neutral type, stock-intensive technical progress exists. while labor productivity deterioates. Energy productivity is not significant.     

Productivity accounting for separable technologies

This paper develops a method for decomposing total factor productivity growth in separable production technologies and uses it to examine the role of pest-damage prevention on agricultural productivity. The rate of technical change is decomposed into output-enhancing and damage-preventing components. Growth accounting cannot provide separate estimates of these two components of technical change, and instead a parametric model is developed based on the dual cost function. The proposed model captures both components of technical change, properly accounts for environmental effects, and also accommodates the presence of capacity utilization and scale biases. The empirical application of the model is to a sample of Cretan olive-oil producers, and the results show that output-enhancing technical change is more important than damage-preventing technical change in explaining observed total factor productivity (TFP) changes. The second largest source of TFP growth is due to the scale effect.