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.     

Measuring technical and allocative inefficiency in the translog cost system: a Bayesian approach

In this paper, we propose simulation-based Bayesian inference procedures in a cost system that includes the cost function and the cost share equations augmented to accommodate technical and allocative inefficiency. Markov chain Monte Carlo techniques are proposed and implemented for Bayesian inferences on costs of technical and allocative inefficiency, input price distortions and over- (under-) use of inputs. We show how to estimate a well-specified translog system (in which the error terms in the cost and cost share equations are internally consistent) in a random effects framework. The new methods are illustrated using panel data on U.S. commercial banks.     

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.     

Estimation and decomposition of inefficiency when producers maximize return to the outlay: an application to Norwegian fishing trawlers

This paper deals with estimation of a production technology where endogeneous choice of input and output variables is explicitly recognized. In particular, we assume that producers maximize return to the outlay (RO). For simplicity and tractability we start with a Cobb–Douglas transformation function with multiple inputs and outputs and show how the first-order conditions of RO maximization can be used to derive an estimating equation which is nothing but a partial input productivity equation. This equation does not suffer from the econometric endogeneity problem although the output and input variables are endogenous. First, we consider the case where producers are fully efficient allocatively but technically inefficient. The model is estimated using a single equation stochastic frontier approach. The model is then extended to allow allocative inefficiency and it is estimated as a system using generalized method of moment. Algebraic expressions are derived to decompose the effect of technical and allocative inefficiencies on RO. We also consider translog specifications that are estimated as (1) a single equation frontier model as well as (2) a system. We use a panel of Norwegian fishing trawlers data to estimate the model. Outputs are different species caught while inputs are labor and vessel size. We also control for number of days of operation, age of the vessel and year effects. Empirical results show that the average rate of RO is reduced by about 20 to 30 % due to technical inefficiency. On the other hand, average allocative efficiency is found to be about 78 %. The average overall efficiency is found to be around 60 %.     

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 Consistent Approach to Cost Efficiency Measurement*

Consistent specifications of the allocative inefficiency function in ‘cost plus input share equations’ systems may be difficult, if not impossible, to find because most plausible ones violate certain reasonable a priori conditions. Moreover, the models to which they lead give rise to highly non‐linear likelihood functions that are very hard to estimate. In an effort to confront these difficulties, this paper adapts an idea first suggested by Greene (1993) that allocative inefficiency ought to be related to input prices and allocative distortions in the input share equations. The system of ‘cost plus input demand equations’ that emerges is estimated by standard seemingly unrelated regression (SUR) techniques using data from private and state firms that operated in Greek manufacturing during the 1979–88 period. Among other findings, the estimates show that overall inefficiency for private and state firms was 63.5% and 102.2%, respectively in comparison with the least inefficient firms in their class. In relative terms these figures imply that state firms were almost 61% less efficient than private firms were. Technical and allocative reasons amounting to 64% and 36%, respectively, accounted for this excess inefficiency of state firms, in addition to differences in the utilization of labour, capital and debt. Lastly, it is found that the magnitudes of technical and allocative inefficiencies depend critically upon a self‐consistent specification of the allocative inefficiency function.     

Stochastic error specification in primal and dual production systems

In this paper we derive both primal and dual‐cost systems in which the stochastic specifications arise from the model (random environment or measurement errors and optimization errors)—not tacked on at the end after the deterministic system is worked out. Derivation of the error structures is based on cost‐minimizing behavior on the firms. The primal systems constitute the production function and the first‐order conditions of cost minimization. We consider two dual‐cost systems. The first dual system is based on the cost function and cost share equations. The second dual system is based on a multiplicative general error production model that is an alternative to McElroy's additive general error production model. Our multiplicative general error model gives a clear and intuitive economic meaning to the error components. The resulting cost system is easy to estimate compared to the alternative cost systems. The error components in the multiplicative general error model can capture heterogeneity in the technology parameters even in a cross‐sectional model. Panel data are not necessary to estimate either the primal or dual systems. The models are estimated using data on 72 fossil fuel‐fired steam electric power generation plants (observed for the period 1986–1999) in the USA. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

Economic Efficiency and Productivity Growth in the Post-Privatization Chilean Hydroelectric Industry

Chiles hydroelectric industry was privatized in 1985, but required to operate within a regulatory framework designed to achieve a competitive outcome. A centralized dispatch center was established to ensure production at minimum cost, subject to constraints on minimum release and minimum reservoir stock. A reluctance to rapidly reduce the industry work force may also have existed. We develop a constrained cost-minimization model for thermal and hydro generation to obtain the shadow price of water and to determine the qualitative effect of these constraints on allocative efficiency. Using panel data from 1986–1997, we assess the economic efficiency of the hydro industry by estimating a stochastic distance frontier and price equations from the dual cost-minimization problem. We find dramatic increases in technical change and productivity change, with positive efficiency change for all years but the last. We also observe a dramatic decline in allocative inefficiencies over our sample period. The share of hydro generation from run-of-river and thermal plants relative to reservoir plants has increased, presumably in reaction to the water release and reservoir stock constraints, reducing the relative over-utilization of capital to water from the pre-1985 regime. Further, the over-utilization of labor to capital and water has fallen over time. However, considerable allocative inefficiencies remain, consistent with our finding of industry-wide scale economies. Substantial cost savings would result if technical and allocative efficiency were eliminated.JEL Classification: L94, D24     

Measuring Hospital Performance in the Presence of Quasi-Fixed Inputs: An Analysis of Québec Hospitals

This research proposes an approach to measure hospital performance based on a generalization of Banker and Morey (1986) and Førsund (1996). This approach considers quasi-fixed inputs explicitly, calculates their implicit cost, and quantifies returns to scale. The performance measure is decomposed into allocative and technical inefficiencies. Based on a very complete data set of Québec hospitals, we find that significant inefficiencies of up to 17% ($700 CAN million) could have been saved through improved performance. Postestimation analyses that include qualitative measures of care suggest that differences in performance are attributable to differences in management or unobservable quality of care rather than patient case mix.     

Pitfalls in the estimation of a cost function that ignores allocative inefficiency: A Monte Carlo analysis

In the stochastic frontier literature, it is a widely held view that allocative inefficiency can be lumped together with technical inefficiency in the estimation of cost frontiers. Therefore, a one-sided error term in the cost function is believed to capture the cost of overall (technical plus allocative) inefficiency. In this paper we challenge that view through a detailed Monte Carlo investigation. The results show that failure to include the cost of allocative inefficiency explicitly in the cost function biases the estimates of: (i) the cost function parameters, (ii) returns to scale, (iii) input price elasticities, and (iv) cost-inefficiency.     

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.     

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.     

Feasible estimation of firm‐specific allocative inefficiency through Bayesian numerical methods

Both the theoretical and empirical literature on the estimation of allocative and technical inefficiency has grown enormously. To minimize aggregation bias, ideally one should estimate firm and input‐specific parameters describing allocative inefficiency. However, identifying these parameters has often proven difficult. For a panel of Chilean hydroelectric power plants, we obtain a full set of such parameters using Gibbs sampling, which draws sequentially from conditional generalized method of moments (GMM) estimates obtained via instrumental variables estimation. We find an economically significant range of firm‐specific efficiency estimates with differing degrees of precision. The standard GMM approach estimates virtually no allocative inefficiency for industry‐wide parameters. Copyright © 2009 John Wiley & Sons, Ltd.     

An Integrated Assessment of Productivity and Efficiency Impacts of Information Technology Investments: Old Data,New Analysis and Evidence

We reexamine the Information Technology (IT) productivity paradox from the standpoints of theoretical basis, measurement issues and potential inefficiency in IT management. Two key objectives are: (i) to develop an integrated microeconomic framework for IT productivity and efficiency assessment using developments in production economics, and (ii) to apply the framework to a dataset used in prior research with mixed results to obtain new evidence regarding IT contribution. Using a stochastic frontier with a production economics framework involving the behavioral assumptions of profit maximization and cost minimization, we obtain a unified basis to assess both productivity and efficiency impacts of IT investments. The integrated framework is applied to a manufacturing database spanning 1978–1984. While previous productivity research with this dataset found mixed results regarding the contribution from IT capital, we show the negative marginal contribution of IT found in an important prior study is attributable primarily to the choices of the IT deflator and modeling technique. Further, by ignoring the potential inefficiency in IT investment and management, studies that have reported positive results may have significantly underestimated the true contribution of IT. This positive impact of IT is consistent across multiple model specifications, estimation techniques and capitalization methods. The stochastic production frontier analysis shows that while there were significant technical, allocative and scale inefficiencies, the inefficiencies reduced with an increase in the IT intensity. Given that the organizational units in our sample increased their IT intensity during the time period covered by the study, management was taking a step in the right direction by increasing the IT share of capital inputs. Our results add to a small body of MIS literature which reports significant positive returns from IT investments.     

Estimation of market power in the presence of firm level inefficiencies

“The quiet life hypothesis” (QLH) by Hicks (1935) argues that, due to management’s subjective cost of reaching optimal profits, firms use their market power to allow inefficient allocation of resources. Increasing competitive pressure is therefore likely to force management to work harder to reach optimal profits. Another hypothesis, which also relates market power to efficiency is “the efficient structure hypothesis” (ESH) by Demsetz (1973). ESH argues that firms with superior efficiencies or technologies have lower costs and therefore higher profits. These firms are assumed to gain larger market shares which lead to higher concentration. Ignoring the efficiency levels of the firms in a market power model might cause both estimation and interpretation problems. Unfortunately, the literature on market power measurement largely ignores this relationship. In the context of a dynamic setting, we estimate the market power of US airlines in two city-pairs by both allowing inefficiencies of the firms and not allowing inefficiencies of the firms. Using industry level cost data, we estimate the cost function parameters and time-varying efficiencies. An instrumental variables version of the square root Kalman filter is used to estimate time-varying conduct parameters.     

Estimating technical and allocative inefficiency relative to stochastic production and cost frontiers

Earlier papers by Aiger, Lovell and Schmidt and by Meeusen and van den Broeck have considered stochastic frontier production functions. this paper extends that work by considering the duality between stochastic frontier production and cost funstions, under the assumtions of exact cost minimization (tecchnical inefficiency only) and of inexact cost minimization (technical and allocative inefficiency). We show how to measure both types of inefficiency, and the associated cost of inefficiency. The techniques are illustrated using data on steam-electric generating plants.     

On the Determinants of School District Efficiency: Competition and Monitoring

A number of researchers have asserted that inefficiency in the U.S. school system arises from a lack of incentives for public schools to behave efficiently. This paper uses a Shephard input distance function to model educational production, and a switching-regressions estimation to explore the relationship between school district efficiency and two existing incentive mechanisms—competition and voter monitoring. We find evidence that ease of monitoring enhances both technical and allocative efficiency of urban school districts, and that increased competition reduces allocative inefficiency in communities above a competitive threshold. We find no evidence that competition is related to technical inefficiency.     

Impact of conversion to Critical Access Hospital status on hospital efficiency

This study examines the impact of Critical Access Hospital (CAH) Program on hospital efficiency using a two-stage approach, where data envelopment analysis is used in the first stage to estimate cost, technical, and allocative efficiency scores of a sample of rural hospitals. Densities of efficiency scores of CAHs and prospectively paid rural hospitals are estimated and compared using a nonparametric kernel density estimator and a bootstrap-based test. In the second stage, efficiency scores are regressed on environmental variables using bootstrapped truncated regressions. Density analysis and results from bootstrapped truncated regressions show that CAHs are less cost and allocatively efficient compared to prospectively paid rural hospitals, without being less technically efficient. Relative to their pre-conversion selves, CAHs appear to be slightly less allocatively efficient, while they are slightly more technically efficient and no less cost efficient. Overall, our results suggest that the CAH Program may have decreased the allocative and cost efficiencies of those rural hospitals that converted to CAH status relative to prospectively paid rural hospitals, without significantly increasing their technical efficiency.