Decomposing profit change: Konüs,Bennet and Luenberger indicators

We introduce complementary decompositions of profit change that, relying on the duality between the profit function and the directional distance function, shed light on the different sources of profit growth including measures of technical efficiency, allocative efficiency and technological change. Our decompositions extend the literature on Konüs and Bennet quantity and price indicators to profit change. The first decomposition is ‘exact’ in the sense of Diewert, by completely exhausting the sources of profit change into profit inefficiency change (including technical and allocative inefficiency change), technological change, and output and input price change. The second decomposition equates the Bennet quantity indicator to a productivity measure represented by the Luenberger indicator plus allocative inefficiency change. We deem it ‘complete’ because in contrast to the existing literature, it retains the information on allocative inefficiency change while preventing the existence of residual terms capturing price variations, whose meaningful interpretation has not been addressed until now. Our proposed solution takes advantage of the flexibility of the directional distance function when choosing a suitable directional vector. All decompositions have the same structural form and therefore their components can be compared to each other vis-à-vis, providing alternative measures of equivalent sources of profit growth.     

A zero inefficiency stochastic frontier model

Traditional stochastic frontier models impose inefficient behavior on all firms in the sample of interest. If the data under investigation represent a mixture of both fully efficient and inefficient firms then off-the-shelf frontier models are statistically inadequate. We introduce the zero inefficiency stochastic frontier model which can accommodate the presence of both efficient and inefficient firms in the sample. We derive the corresponding log-likelihood function, conditional mean of inefficiency, to estimate observation-specific inefficiency and discuss testing for the presence of fully efficient firms. We provide both simulated evidence as well as an empirical example which demonstrates the applicability of the proposed method.     

Safety margins versus profit maximization

Under uncertainty, firms risk bankruptcy. We ask, in symmetric duopoly with stochastic demand, what happens when one firm minimizes the probability of negative profits while the other maximizes expected profits. When fixed costs are small, a firm can reduce the likelihood of negative profits. However, under a large fixed cost, the chance of negative profits increases upon deviation from a profit‐maximizing strategy. In any event, if one firm adopts a safety‐first strategy, the other firm has higher profits and a better survival chance by maximizing expected profit. Finally, we compare a profit maximizing to a safety‐first strategy in relation to ownership and control in firms.     

Managerial and program inefficiency for European meat manufacturing firms: A dynamic multidirectional inefficiency analysis approach

This paper proposes a dynamic multidirectional inefficiency analysis approach within the context of Data Envelopment Analysis to measuring input- and investment-specific managerial and program inefficiency for groups of firms characterized by different technologies. Dynamic managerial inefficiency refers to the distance to the firms’ group-specific dynamic frontier of best practices, and dynamic program inefficiency measures the difference between the group-specific dynamic frontier and the pooled dynamic frontier. The empirical application focuses on panel data of large meat processing firms in Eastern, Western and Southern Europe over the period 2005–2012. The results show that Eastern European firms have the highest dynamic managerial inefficiency for all inputs, but have the smallest values for dynamic program inefficiency. Western European firms perform worst in terms of program inefficiency for all inputs, while Southern European firms are the best with regard to dynamic managerial inefficiency. The results also reveal that regardless the dynamic inefficiency dimension considered, investments is the most inefficient input, followed by labor, and materials.     

DEA target setting using lexicographic and endogenous directional distance function approaches

Directional Distance Function (DDF) is an approach often used in data envelopment analysis (DEA) due to its clear interpretation and to the flexibility provided by the possibility of choosing the projection direction towards the efficient frontier. In this paper two new DDF approaches are considered. The first one uses an exogenous directional vector and a multi-stage methodology that at each step uses the projection along the input and output dimensions of the directional vector that can be improved. This lexicographic DDF approach also computes a directional efficiency score and a directional inefficiency indicator for each input and output variable. The second approach is a non-linear optimization model that endogenously determines the directional vector so that the smallest improvement required to reach the efficient frontier is computed.     

Profit efficiency in the European Union banking industry: a directional technology distance function approach

We employ the directional technology distance function approach and present estimates of profit efficiency in the 25 European Union (EU) member states over the period 1998–2008. This method decomposes profit efficiency into its technical and allocative components. We investigate potential efficiency differences across the old EU region and the new EU member states, across countries and across banks of different size. Our results indicate a significant level of profit inefficiency for the EU region, which is predominantly attributed to allocative inefficiency. Our findings also suggest that banks operating in the old EU region are, on average, more profit efficient than credit institutions in the new EU member states. Overall, we observe considerable variation of efficiency scores across countries and different patterns in efficiency change over time, as well as a negative relationship between bank size and efficiency.     

Cost and profit efficiency of conventional and Islamic banks in GCC countries

Using stochastic frontier approach, this paper investigates the cost and profit efficiency levels of 71 commercial banks in Gulf cooperation council countries over the period 1999–2007. This study also conducts a comparative analysis of the efficiency across countries and between conventional and Islamic banks. Moreover, we examine the bank-specific variables that may explain the sources of inefficiency. The empirical results indicate that banks in the Gulf region are relatively more efficient at generating profits than at controlling costs. We also find that in terms of both cost and profit efficiency levels, the conventional banks on average are more efficient than Islamic banks. Furthermore, we observe a positive correlation of cost and profit efficiency with bank capitalization and profitability, and a negative one with operation cost. Higher loan activity increases the profit efficiency of banks, but it has a negative impact on cost efficiency.     

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.     

Theory and Application of Directional Distance Functions

In 1957 Farrell demonstrated how cost inefficiency could be decomposed into two mutually exclusive and exhaustive components: technical and allocative inefficiency. This result is consequence of the fact that—as shown by Shephard—the cost function and the input distance function (the reciprocal of Farrell's technical efficiency measure) are dual to each other. Similarly, the revenue function and the output distance function are dual providing the basis for the decomposition of revenue inefficiency into technical and allocative components (see for example, Färe, Grosskopf and Lovell (1994)). Here we extend those results to include the directional distance function and its dual, the profit function. This provides the basis for defining and decomposing profit efficiency. As we show, the output and input distance functions (reciprocals of Farrell efficiency measures) are special cases of the directional distance function. We also show how to use the directional distance function as a tool for measuring capacity utilization using DEA type techniques.     

A General Method of Deriving the Inefficiencies of Banks from a Profit Function

This article develops a new method of estimating inefficiencies in joint production and shows that unlike the approaches utilized in the previous studies of inefficiency, this method maintains a consistent relationship between the error term of a profit function and the error terms of its price derivatives. A useful by-product of the method is a proof of a Hotelling-like lemma that relates stochastic input demand and output supply functions to stochastic profit functions. While the previous studies fit a single frontier to data on all firms, this paper estimates a frontier unique to every observed firm to allow each one to have a different potential of achieving maximal levels of profit. The new method is applied in the analysis of annual data, 1984–1989, for U.S. commercial banks. Both the analytical and numerical results of the paper show that the residual that the previous studies attribute to inefficiency includes the effects of excluded variables and of inaccuracies in the specified functional forms. Once accurate estimates of these effects are subtracted from the residual, the distortions in the measured inefficiencies should be considerably reduced. Consequently, this article considers how such estimates might be obtained.     

A directional slacks-based measure of technical inefficiency

Radial measures of efficiency estimated using linear programming (LP) methods can be biased since slack in the constraints defining the technology suggests that at least one input can be reduced, or one output can be expanded, even though a firm is deemed to be “technically efficient.” In this paper, we propose a directional slacks-based measure of technical inefficiency to account for the potential of slack in technological constraints. When no such slacks exist, directional slacks-based inefficiency collapses to the directional technology distance function. Our proposed measure helps to generalize some of the existing slacks-based measures of inefficiency. We examine the financial services provided by Japanese cooperative Shinkin banks, and estimate their inefficiency during the period 2002–2005. This inefficiency declined slightly during the period. We thus propose that slack is an important source of inefficiency which is often not captured by the directional technology distance function.     

A Metafrontier Production Function for Estimation of Technical Efficiencies and Technology Gaps for Firms Operating Under Different Technologies

This paper presents a metafrontier production function model for firms in different groups having different technologies. The metafrontier model enables the calculation of comparable technical efficiencies for firms operating under different technologies. The model also enables the technology gaps to be estimated for firms under different technologies relative to the potential technology available to the industry as a whole. The metafrontier model is applied in the analysis of panel data on garment firms in five different regions of Indonesia, assuming that the regional stochastic frontier production function models have technical inefficiency effects with the time-varying structure proposed by Battese and Coelli (1992).     

Efficiency and productivity in the Thai non-life insurance industry

This paper estimates a stochastic cost frontier for a sample of the non-life insurance industry in Thailand from 2000 to 2007. Our model explicitly considers the heteroscedasticity in the variances of the noise and inefficiency components that could affect the position of the cost frontier as well as the measurement of efficiency. Tests for double heteroscedasticity and appropriate specification for the cost frontier are performed. The chosen model is used to examine whether economies of scale and a change in technology exist. In addition, this paper calculates total factor productivity (TFP) change and decomposes it into scale effect, cost efficiency effect, technology effect, output effect, price effect, and environmental effect. Our results reveal that, on average, Thai non-life insurance firms are between 74 and 79 % efficient, that economies of scale exist, and that regress in technology shifts the cost frontier upward by 2.2 %. The regress in technology is the dominant contributor to a negative TFP growth of 1.15 %. The restructuring of the industry following the 1997 Asian financial crisis finally paid off when the industry experienced technology progress in 2005 and beyond. Between 2005 and 2007, technology progress and productivity growth occurred at a little over 2 % a year. In-depth analysis of the most and the least efficient firms reveals that most efficient firms tend to strategically select types of insurance services and underwrite average and small size sum insured per policy to diversify their risks. In addition, they tend to be savvy investors. The opposite holds for the least efficient firms which concentrate in providing labor-intensive, small sum automobile insurance policies or underwrite large coverage policies for fewer policyholders. Balancing the mix of insurance types, spreading risk across insurance types or across number of policyholders, investing in high yield assets, or developing a market niche may prove beneficial for improving cost efficiency.     

A Monte Carlo study of ranked efficiency estimates from frontier models

Parametric stochastic frontier models yield firm-level conditional distributions of inefficiency that are truncated normal. Given these distributions, how should one assess and rank firm-level efficiency? This study compares the techniques of estimating (a) the conditional mean of inefficiency and (b) probabilities that firms are most or least efficient. Monte Carlo experiments suggest that the efficiency probabilities are easier to estimate (less noisy) in terms of mean absolute percent error when inefficiency has large variation across firms. Along the way we tackle some interesting problems associated with simulating and assessing estimator performance in the stochastic frontier model.     

A new method to decompose profit efficiency: an application to US commercial banks

We propose a new method to estimate profit efficiency which makes explicit how revenue and cost efficiencies contribute to overall profit efficiency. Using data from US commercial banks from 2001 to 2010, we find that losses due to profit inefficiency represent about 3.5% of banks’ equity of which 1% is due to revenue inefficiency and 2.4% to cost inefficiency. Revenue efficiency changes affect more overall profit efficiency than equivalent cost efficiency changes. In contrast to previous studies, but in line with economic intuition, we find that while revenue and cost efficiencies tend to be negatively correlated, both correlate positively with profit efficiency.     

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.     

Compensation Schemes and Labor Market Competition: Piece Rate versus Wage Rate

We investigate the choice of compensation scheme by firms. Our basic model shows that the unique equilibrium choice for profit maximizing duopsonists in a labor market is for one firm to offer a wage rate and for the other to offer a piece rate. This result arises because the firms recognize that, by offering different compensation schemes, they induce self-selection among workers, which thereby decreases the intensity of competition in the labor market. We find this asymmetry to be robust to allowing for firing, free entry, and a class of more general compensation schemes. When we broaden our model to permit firms to be differentiated in the eyes of workers (either geographically or by "other working conditions," e.g.), we find that our results are preserved when differentiation is low, but that both firms choose to offer a piece rate when differentiation is high.     

Nonparametric least squares methods for stochastic frontier models

When analyzing productivity and efficiency of firms, stochastic frontier models are very attractive because they allow, as in typical regression models, to introduce some noise in the Data Generating Process . Most of the approaches so far have been using very restrictive fully parametric specified models, both for the frontier function and for the components of the stochastic terms. Recently, local MLE approaches were introduced to relax these parametric hypotheses. In this work we show that most of the benefits of the local MLE approach can be obtained with less assumptions and involving much easier, faster and numerically more robust computations, by using nonparametric least-squares methods. Our approach can also be viewed as a semi-parametric generalization of the so-called “modified OLS” that was introduced in the parametric setup. If the final evaluation of individual efficiencies requires, as in the local MLE approach, the local specification of the distributions of noise and inefficiencies, it is shown that a lot can be learned on the production process without such specifications. Even elasticities of the mean inefficiency can be analyzed with unspecified noise distribution and a general class of local one-parameter scale family for inefficiencies. This allows to discuss the variation in inefficiency levels with respect to explanatory variables with minimal assumptions on the Data Generating Process.     

A semiparametric stochastic input distance frontier model with application to the Indonesian banking industry

This paper proposes a semiparametric smooth-varying coefficient input distance frontier model with multiple outputs and multiple inputs, panel data, and determinants of technical inefficiency for the Indonesian banking industry during the period 2000 to 2015. The technology parameters are unknown functions of a set of environmental factors that shift the input distance frontier non-neutrally. The computationally simple constraint weighted bootstrapping method is employed to impose the regularity constraints on the distance function. As a by-product, total factor productivity (TFP) growth is estimated and decomposed into technical change, scale component, and efficiency change. The distance elasticities, marginal effects of the environmental factors on the distance elasticities, temporal behavior of technical efficiency, and also TFP growth and its components are investigated.

     

Reconciling the Porter hypothesis with the traditional paradigm about environmental regulation: a nonparametric approach

This paper estimates the impact of pollution abatement investments on the production technology of firms by pursuing two new directions. First, we take advantage of recent econometric developments in productivity, efficiency analysis and nonparametric kernel regression by adopting a conditional nonparametric frontier analysis. Second, we focus not only on the average effect but also search for potential nonlinearities. We provide new results suggesting that pollution abatement capital affects with a bell-shaped fashion technological catch-up (inefficiency distribution) and does not affect technological change (shifts in the frontier). These results have relevant implications both for modeling and for the purposes of advice on environmentally friendly policy.