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.     

Expansion and Efficiency in Banking: Evidence from Ghana

We use a translog functional form to estimate a stochastic frontier function of cost and profit efficiency (PE) of Ghanaian banks under the Battese–Coelli time‐varying decaying inefficiency parameterization for (unbalanced) panel data. We regressed efficiency estimates on a distance variable controlling for bank size, total cost, and profits. We find that Ghanaian bank PE is worsening, whereas cost efficiency is improving for the period analyzed. Our results show that PE is not related to distance, size, or cost and profitability ratios. Distance is however positively and significantly related to cost efficiency. Cost efficiency is however not influenced by size or cost and profit ratios. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

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.     

Profitability and Efficiency in the U.S. Life Insurance Industry

This study explores the relationship between cost inefficiency and profitability in the U.S. life insurance industry. Earnings have particular importance to life insurance companies because earnings and capital determine the viability of the insurer. Since the life insurance industry is mature and highly competitive, cost efficiency may be the main driver of profitability. We derive cost efficiency using the stochastic frontier (SF) method allowing the mean inefficiency to vary with organizational form and the outputs. In addition, the estimation of the cost efficiency measure takes into account the underlying accounting concepts that generate the data and, consequently, the product mix (long-duration policies vs. short-duration policies) to avoid distorted estimates. Our results suggest that cost inefficiency in the life insurance industry is substantial relative to earnings, and that inefficiency is negatively associated with profitability measures such as the return on equity. The analysis of inefficiency and organizational form suggest that stock (shareholder-owned) companies are as efficient and profitable as mutual (policyholder-owned) companies.     

Separating Technical Change from Time-Varying Technical Inefficiency in the Absence of Distributional Assumptions

This paper proposes an alternative model for separating technical change from time-varying technical inefficiency. The proposed formulation uses the general index, developed by Baltagi and Griffin (1988), to model technical change in the production frontier function and a quadratic function of time, as in Cornwell, Schmidt and Sickles (1990), to capture the temporal pattern of technical inefficiency. In such a setting, all parameters associated with the rate of technical change and the temporal pattern of technical inefficiency are identified separately. Moreover, the proposed formulation is independent of any distributional assumption concerning the one-sided error term associated with technical inefficiency, and it can be estimated in a single stage with non-linear FGLS. Empirical results based on a translog production frontier, and estimates of technical inefficiency and technical change are presented for the UK dairy sector over the period 1982–1992.     

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.     

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.     

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.     

Estimation of a dynamic stochastic frontier model using likelihood-based approaches

This paper considers a panel stochastic production frontier model that allows the dynamic adjustment of technical inefficiency. In particular, we assume that inefficiency follows an AR(1) process. That is, the current year's inefficiency for a firm depends on its past inefficiency plus a transient inefficiency incurred in the current year. Interfirm variations in the transient inefficiency are explained by some firm-specific covariates. We consider four likelihood-based approaches to estimate the model: the full maximum likelihood, pairwise composite likelihood, marginal composite likelihood, and quasi-maximum likelihood approaches. Moreover, we provide Monte Carlo simulation results to examine and compare the finite-sample performances of the four above-mentioned likelihood-based estimators of the parameters. Finally, we provide an empirical application of a panel of 73 Finnish electricity distribution companies observed during 2008–2014 to illustrate the working of our proposed models.     

How Fast Do Banks Adjust? A Dynamic Model of Labor-Use with an Application to Swedish Banks

This paper deals with a dynamic adjustment process in which adjustment of a key variable input (labor) towards its desired level is modeled in a panel data context. The partial adjustment type model is extended to make the adjustment parameter both firm- and time-specific by specifying it as a function of firm- and time-specific variables. Desired level of labor use is represented by a labor requirement function, which is a function of outputs and other firm-specific variables. The catch-up factor is defined as the ratio of actual to desired level of employment. Productivity growth is then defined in terms of a shift in the desired level of labor use and the change in the catch-up factor. Swedish banking data is used as an application of the above model.     

Labour-use efficiency in Swedish social insurance offices

This paper considers the estimation of frontier production functions in panel data models. It proposes a multi-stage method to obtain estimates of (1) the parameters of a flexible input requirement function and (2) technical inefficiency decomposed into time-invariant (firm-specific), time-varying, and the residual components. The proposed method is used to analyse labour-use efficiency of Swedish local social insurance offices on the basis of a large panel of observations during the time period 1974–84. Empirical results show: (1) substantial variations in labour-use efficiency among these offices, with the mean efficiencies declining over time; (2) presence of economies of scale, thereby meaning that most of the offices were of suboptimal size.     

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.     

Investigating the impact of endogeneity on inefficiency estimates in the application of stochastic frontier analysis to nursing homes

This paper examines the impact of an endogenous cost function variable on the inefficiency estimates generated by stochastic frontier analysis (SFA). The specific variable of interest in this application is endogenous quality in nursing homes. We simulate a dataset based on the characteristics of for-profit nursing homes in California, which we use to assess the impact on SFA-generated inefficiency estimates of an endogenous regressor under a variety of scenarios, including variations in the strength and direction of the endogeneity and whether the correlation is with the random noise or the inefficiency residual component of the error term. We compare each of these cases when quality is included and excluded from the cost equation. We provide evidence of the impact of endogeneity on inefficiency estimates yielded by SFA under these various scenarios and when the endogenous regressor is included and excluded from the model.     

Estimating X-Efficiency in Taiwanese Banking Using a Translog Shadow Profit Function

A multiproducttranslog normalized shadow profit function is used to examineX-efficiency and related issues with respect to Taiwan's bankingsector. The model developed here is theoretically more appropriatecompared to that proposed by Berger, Hancock, and Humphrey (1993);as the former is obtained within the framework of profit maximization.Parameter estimates from our parametric translog profit functionare shown to be robust against different model specifications.More than half of all potential profits are estimated to be lostdue to economic inefficiency. The relatively more important roleof technical inefficiency, compared with that of allocative inefficiency,implies that deficient output revenues outweigh excessive inputcosts. Translog evidence indicates that larger banks tend tobe more technically efficient than smaller ones. The data showstrong technical progress during the sample period, while themodel failing to include X-inefficiency yields no technical advance.     

Reform and Efficiency Gains in the New Zealand Electrical Supply Industry

As part of a general program of market-based reform, New Zealand transformed the electrical supply industry from state-owned to commercially-oriented power companies. This paper tests the hypothesis that such privatization is efficiency-improving. A translog cost function is specified and estimated with controls for system (engineering) characteristics and environmental variables, and it is found that the reforms had substantial cost-reducing effects. The reforms are found to have benefitted customers, with the real price of electricity falling 16.4 percent, over the period.     

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.     

Technology and Cost Efficiency in Universal Banking A “Thick Frontier”-Analysis of the German Banking Industry

Using 1992 data of 1490 banks covering about 40% of German banking, we specify a multi-product translog cost function and follow the thick frontier-approach to control for cost inefficiency when evaluating the technology of banking. Scale economies are found to exist up to a size of about 5 billion DM of total assets, with diseconomies being caused by non-operating costs. There is hardly any evidence of economies of scope. Compared to cost inefficiency external factors play a surprisingly strong role in explaining cost differences between high-cost and low-cost banks. Smaller banks turn out to be more responsive to input prices.