Efficiency measurement with multiple outputs and multiple inputs

This paper discusses modeling technical and allocative inefficiencies in both cost minimizing and profit maximizing frameworks with special emphasis on multiple inputs and multiple outputs. Both primal and dual models are considered for this purpose. In the primal approach we use a separable output and input function (the constant elasticity of transformation output function and Cobb-Douglas input function). The dual models assume translog cost or profit functions. Technical inefficiency is assumed to be random in the cross-sectional models, and fixed firm-specific parameter in the panel data models. Allocative inefficiencies are always treated as input-specific parameters. We derive exact relations linking technical inefficiency and allocative inefficiencies to cost and profit when the underlying technology is represented by a flexible functional form such as the translog. It is shown that appending a one-sided homoscedastic error term to model technical inefficiency, or neglecting technical inefficiency altogether in a translog profit tunciton results in model misspecification and inconsistent parameter estimates.     

Estimating substitution elasticities with the Fourier cost function: Some Monte Carlo results

The Fourier flexible form possesses desirable asymptotic properties that are not shared by other flexible forms such as the translog, generalized Leontief, and generalized Box-Cox. One of them is that an elasticity of substitution can be estimated with negligible bias in sufficiently large samples regardless of what the true form actually is, save that it be smooth enough. This article reports the results of an experiment designed to determine whether or not this property obtains in samples of the sizes customarily encountered in practice. A three-input, homothetic version of the generalized Box-Cox cost function was used to generate technologies that were oriented in a two-dimensional design space according to a central composite rotatable design; the two factors of the design were the Box-Cox parameter and a measure of the dispersion of the substitution matrix. The Fourier cost function was used to estimate the substitution elasticities at each design point, and the bias at each point was estimated using the Monte Carlo method. A response surface over the entire design space was fitted to these estimates. An examination of the surface reveals that the bias is small over the entire design space. Roughly speaking, the estimates of elasticities of substitution are unbiased to three significant digits using the Fourier flexible form no matter what the true technology. Our conclusion is that the small bias property of the Fourier form does obtain in samples of reasonable size; this claim must be tampered by the usual caveats associated with inductive inference.     

Comparisons of Economic Inefficiency Between Output and Input Measures of Technical Inefficiency Using the Fourier Flexible Cost Function

The current paper constructs a Fourier flexible cost function, which is commonly known to be a more general function form than the typical translog form, and can globally approximate a true (but unknown) cost function. Both allocative and technical inefficiencies are considered using the Fourier function in the context of the parametric approach. The former is modeled using shadow input prices and the latter is formulated either by adding an extra term of scale parameter (when the Farrell's (1957) input technical inefficiency is assumed), or by correcting all the terms involving output quantities by a scale parameter (when the Farrell's output technical inefficiency is assumed). It is found that sample banks could save up to 23% of total costs, within the range of 3 and 69% uncovered by the previous works, in which allocative inefficiency plays a more important role than technical inefficiency. Furthermore, the cost of misallocated labor input alone constitutes more than 80% of total allocative inefficiency. Financial deregulation starting from 1991 in Taiwan appears to have improved economic efficiency of the banking industry.     

Union algebra: Unionization,productivity and labor intensity restrictions

Two models are developed to investigate unionism effects. The first assumes Cobb-Douglas technology, derives an explicit cost function allowing for noncost minimization and separates productivity and labor intensity effects. The second assumes a more flexible translog shadow cost function and isolates a neutral productivity effect and factor-specific composite effects. The models are estimated using Allen's construction data. Both models indicate a positive union productivity effect in office construction and a negative union productivity effect in school construction. The Cobb-Douglas model indicates a binding labor-to-materials restriction in both office and school construction, but this evidence disappears with the nonminimum cost function.     

A nonlinear multivariate error components analysis of technology and specific factor productivity growth with an application to the U.S. Airlines

This study outlines a nonlinear model of technology and specific factor productivity growth and uses the model to analyze a new panel of sixteen domestic carriers in the U.S. airline industry over 35 quarters from 1970.I to 1978.III. We outline mapping procedures which allow construction of the production surfaces implied by the translog cost function used in our analysis. To our knowledge this study is the first to estimate such a general nonlinear multivariate error components model using full-information maximum likelihood.     

Ownership structure and cost efficiency: A study of publicly owned passenger-bus transportation companies in India

This paper estimates the determinants of cost inefficiency of several publicly operated passenger-bus transportation companies in India in terms of their ownership structure as well as other firm-specific characteristics. A panel data on publicly operated passenger-bus transportation companies is used to estimate a translog cost system with inefficiency. Inefficiency is specified in such a way that both its mean and variance are firm- and time-specific. For the estimation of production technology and cost inefficiency we have used a multi-step estimation procedure instead of the single-step maximum likelihood (ML) method. In the first step we estimate the translog cost system with heteroskedastic cost function without using any distributional assumptions on the error terms. The second stage uses the ML method to estimate the parameters associated with inefficiency, conditional on the parameter estimates obtained from the first stage. Finally, the residual of the cost function is decomposed to obtain firm-and time-specific measures of cost inefficiency, with ownership type and other firm-specific characteristics as explanatory variables.Financial support of the Nevada Agricultural Experiment Station is gratefully acknowledged.     

A Note on the Importance of Testing for Regularities for Estimated Flexible Functional Forms

In empirical productivity analysis it has become customary to use flexible functional forms to represent a firm's production technology by estimating cost functions. In this note we suggest a procedure to calculate the region where an estimated translog cost function meet the required regularities (positive cost, positive marginal cost, homogeneous, monotonicity and concavity in input prices). We calculate this region for the US Bell cost function as reported by Evans and Heckman (1984, 1986), and show that the estimated cost function had negative marginal cost in most of the test region.     

Evaluating the Adequacy of Parametric Functional Forms in Estimating Monotone and Concave Production Functions

We consider situations where the a priori guidance provided by theoretical considerations indicates only that the function linking the endogenous and exogenous variables is monotone and concave (or convex). We present methods to evaluate the adequacy of a parametric functional form to represent the relationship given the minimal maintained assumption of monotonicity and concavity (or convexity). We evaluate the adequacy of an assumed parametric form by comparing the deviations of the fitted parametric form from the observed data with the corresponding deviations estimated under DEA. We illustrate the application of our proposed methods using data collected from school districts in Texas. Specifically, we examine whether the Cobb–Douglas and translog specifications commonly employed in studies of education production are appropriate characterizations. Our tests reject the hypotheses that either the Cobb–Douglas or the translog specification is an adequate approximation to the general monotone and concave production function for the Texas school districts.     

Estimation of technical and allocative inefficiency: A primal system approach

The estimation of technical and allocative inefficiencies using a flexible (translog) cost system is found to be quite difficult, especially when both the inefficiencies are random. In this paper we use the alternative primal system consisting of the production function (translog) and the first-order conditions of cost minimization. The estimation of the primal system is more straightforward and it enables us to estimate observation-specific technical and allocative inefficiencies, and their impact on input demand and cost. We use data on steam-electric generating plants from the U.S. to estimate the model using both Cobb–Douglas and translog production functions.     

Empirical Evaluation of Regulatory Regimes in Local Telecommunications Markets

This paper relies on an engineering optimization model of the local telecommunication exchange network to calibrate the functions entering various regulatory mechanisms, from both traditional and modern (incentive) regulation, and evaluate their relative performance. The engineering process model is used to generate data, which are econometrically synthesized in a translog economic cost function. Using this estimated cost function and some empirical and institutional information on market and regulatory conditions, we then calibrate demand, social-surplus, and disutility-of-(cost-reducing)-effort functions. These functions, together with probability distributions reflecting the regulator's beliefs about technology characteristics, allow us to quantitatively assess the social value of regulatory transfers and of good cost auditing procedures, the redistributive consequences of the various forms of regulation, and the sensitivity of their relative performance to the cost of public funds.     

Modeling technical progress and total factor productivity: A plant level example

Shifts in the production frontier occur because of changes in technology. A model of how a firm learns to use the new technology, or how it adapts from the first production frontier to the second, is suggested. Two different adaptation paths are embodied in a translog cost function and its attendant cost share equations. The paths are the traditional linear time trend and a learning curve. The model is estimated using establishment level data from a non-regulated industry that underwent a technological shift in the time period covered by the data. The learning curve resulted in more plausible estimates of technical progress and total factor productivity growth patterns. A significant finding is that, at the establishment level, all inputs appear to be substitutes.This paper was processed by N.R. Adam.     

The temporal behavior of scale economies within A banking firm

Examining the time path of the scale economies has not received much attention until recently. Moreover, the time path of scale economies for a given firm has not been studied in the banking literature at all. Examining scale economies, either from cross-sectional or panel data, based only on a single estimate ignores the dynamic behavior (both cost- and production-wise) of a banking firm as well as of the banking industry. We study the time-varying scale economies of commercial banking firms. We employ the Kalman-filter approach in estimating the translog cost function. The Kalman filter allows the parameters of the translog cost function and therefore the scale economies to be time dependent and varying. The estimation results indicate significant variation in inter- and within-firm scale economies over time for sample banks.     

Scope and scale economies in merging hospitals prior to merger

During the 1980s, the impact of the Prospective Payment System and increased pressure from payers for discounts placed pressure on hospitals to become more efficient. An increase in the number of hospital mergers during this period suggests that merger was a strategy used by hospitals to improve efficiency. This hypothesis is tested by estimating multiproduct scope and scale economies in merging hospitals one year prior to the merger and comparing these with a group of controls using estimates from a hybrid translog cost function. Diseconomies of scale were present when the estimated hybrid translog cost function is evaluated at variable means. The results suggest that merging hospitals could obtain operational efficiencies through merger.     

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).     

The Structure of Production in the Norwegian Fish-Processing Industry: An Empirical Multi-Output Cost Analysis Using a Hybrid Translog Functional Form

An empirical analysis of production structure in the Norwegian fish-processing industry is undertaken, based on data for the period 1985–90. This industry processes raw materials into fresh, frozen, salted and dried fish products. Two technologies coexist in the industry. Producer behaviour is represented by a multi-output variable, or restricted cost function for each technology. The hybrid translog functional form is adopted for estimation, as this form can be evaluated even if some of the output values are zero. Results from the empirical analysis provide important information for the restructuring currently taking place in the industry.     

Production cost structure of us hospital pharmacies: Time-series,cross-sectional bed size evidence

There are current concerns about potential factor substitutions and their implications for factor employments and cost containment in US hospital pharmacies. A translog production cost model is estimated for these pharmacies, using 1981–9 times-series data consisting of seven cross-sectional bed size classes per year. Zellner's joint GLS estimation of three-factor cost share equations and the parent translog cost function reveals that pairwise factor substitutions are severely limited; production is non-homothetic, occurring in the range of scale diseconomies; biased and pure technical change effects dominate the scale-augmenting component. Implications of findings are rationalized in the context of the emerging biopharmaceutical technologies.     

Estimating demand with distance functions: Parameterization in the primal and dual

Our purpose is to investigate the ability of different parametric forms to ‘correctly’ estimate consumer demands based on distance functions using Monte Carlo methods. Our approach combines economic theory, econometrics and quadratic approximation. We begin by deriving parameterizations for transformed quadratic functions which are linear in parameters and characterized by either homogeneity or which satisfy the translation property. Homogeneity is typical of Shephard distance functions and expenditure functions, whereas translation is characteristic of benefit/shortage or directional distance functions. The functional forms which satisfy these conditions and include both first- and second-order terms are the translog and quadratic forms, respectively. We then derive a primal characterization which is homogeneous and parameterized as translog and a dual model which satisfies the translation property and is specified as quadratic. We assess functional form performance by focusing on empirical violations of the regularity conditions. Our analysis corroborates results from earlier Monte Carlo studies on the production side suggesting that the quadratic form more closely approximates the ‘true’ technology or in our context consumer preferences than the translog.     

Imposing regional monotonicity on translog stochastic production frontiers with a simple three-step procedure

We show that the monotonicity condition is conceptually important in Stochastic Frontier Analysis (SFA). Despite its importance, most empirical studies do not impose monotonicity—probably because existing approaches are rather complex and laborious. Therefore, we propose a three-step procedure that is much simpler than existing approaches. We demonstrate how monotonicity of a translog function can be imposed regionally at a connected set (region) of input quantities. Our method can be applied not only to impose monotonicity on translog production frontiers but also to impose other restrictions on cost, distance, or profit frontiers.     

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.     

Production of public safety: Are socioeconomic characteristics of local communities important factors?

This paper uses the translog cost function and cross section data from Florida to investigate the importance of socioeconomic characteristics (SEC) of local communities in the production of public safety. The approach used is noteworthy in four respects: (1) the underlying production function is specified as an AGEM production function; (2) SEC are treated as non-purchased fixed inputs; (3) two variables are used to proxy SEC in estimation; and (4) the paper test for the existence of endogenous quality differences in safety. It is shown that exclusion of SEC from the production (cost) function of safety leads to misspecification; and hence they provide a misleading guide to policy.