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Keywords:

  • performance measurement;
  • data envelopment analysis;
  • stochastic frontier analysis;
  • research methodology;
  • efficiency

Abstract

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. FRONTIER METHODOLOGIES
  5. ILLUSTRATION: JAPAN AND U.S. AUTOMOTIVE SECTORS
  6. CONCLUSION
  7. REFERENCES
  8. APPENDIX: 1: MATHEMATICAL FORMULATIONS OF DATA ENVELOPMENT ANALYSIS
  9. APPENDIX: 2: SOFTWARE PACKAGES FOR DEA AND SFA
  10. APPENDIX: 3: STUDIES UTILIZING DEA AND SFA IN THE STRATEGIC MANAGEMENT RESEARCH (SMJ, AMJ, AND MGMT SCI ARTICLES)

The measurement of corporate performance is central to strategic management research. A common objective of this research is to identify top performers in an industry and their sources of competitive advantage. Despite this focus on best firms and practices, most researchers utilize statistical methods that identify average effects in a sample, and they assess a single performance dimension while ignoring other relevant dimensions. Emphasis on purely financial measures can overlook the fact that a firm's efficiency in transforming resources has been shown as a major source of competitive advantage. In this article we demonstrate how frontier methodologies, such as Data Envelopment Analysis and the Stochastic Frontier approach, can address these challenges. We provide an illustration based on longitudinal data from U.S. and Japanese automobile producers. Copyright © 2013 John Wiley & Sons, Ltd.


INTRODUCTION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. FRONTIER METHODOLOGIES
  5. ILLUSTRATION: JAPAN AND U.S. AUTOMOTIVE SECTORS
  6. CONCLUSION
  7. REFERENCES
  8. APPENDIX: 1: MATHEMATICAL FORMULATIONS OF DATA ENVELOPMENT ANALYSIS
  9. APPENDIX: 2: SOFTWARE PACKAGES FOR DEA AND SFA
  10. APPENDIX: 3: STUDIES UTILIZING DEA AND SFA IN THE STRATEGIC MANAGEMENT RESEARCH (SMJ, AMJ, AND MGMT SCI ARTICLES)

Research in strategic management is focused on finding strategies and attributes that enable an organization to outperform its competitors. One or more firms in an industry are often argued to have attained “competitive advantage” relative to the majority of rivals (Porter, 1985). A common challenge facing strategic management scholars is to identify objectively the leading competitors and assess the reasons for their superiority.

The purpose of this article is to present an introduction to a useful methodology, the frontier methodology, which measures the relative efficiency of firms in transforming resources to achieve business goals. Although the idea of relative efficiency is closely tied to the concept of competitive advantage (which occurs when an organization acquires or develops some combination of attributes that allows it to outperform its competitors), surprisingly few studies have used frontier methods in strategic management research. A search for studies using these approaches in three prestigious management journals (Strategic Management Journal, Academy of Management Journal, and Management Science) yields only 16 articles as compared to hundreds of articles using profit measures such as Return on Assets or Sales.1 This note demonstrates the potential of these methods for studies in strategic management and provides practical guidance on the relative benefits of the different approaches.

Identifying firms that possess advantage over competitors is a straightforward exercise if performance can be succinctly captured by a single measure. However, the strategic management literature points to a diverse array of objectives and actions regarding the creation of competitive advantage (e.g., Douglas and Judge, 2001; Dyer, 1996; Hillman and Keim, 2001). As a consequence, researchers are faced with a range of performance measures that relate to various aspects of corporate activities, including accounting, finance, operations, marketing and corporate social responsibility, and often there is no clear guideline to select valid measures for corporate performance (Dess and Robinson, 1984; Godfrey, Merrill, and Hansen, 2009; Hull and Rothenberg, 2008; Ray, Barney, and Muhanna, 2004; Waddock and Graves, 1997). For example, in a survey of 374 studies published in the Strategic Management Journal from 1980 to 2004, Combs, Crook, and Shook (2005) found that 56 different measures were used to operationalize the corporate performance construct. It is seldom the case that a single firm will top the list all the available performance measures. Identifying the firms that define the best performance frontier across the relevant measures is an important task that is seldom performed. Some of the methods described in this article can be applied to perform this task.

Although performance includes multiple dimensions, studies in strategic management focus most commonly on firms' financial returns. Superior profitability is achieved through some combination of cost efficiency and the ability of the firm to charge a price premium (Porter, 1985). Strategies designed to enhance a firm's efficiency are often quite different from those oriented toward charging a higher price. Yet few empirical studies consider these two sources of advantage separately. By providing a technique to assess efficiency, the frontier methods described in this article enable an understanding of firm performance that is deeper than a mere comparison of profitability or financial returns. Indeed, as we demonstrate below, the major American automotive companies demonstrated relatively strong financial performance in the 1980s and 1990s, even though their Japanese rivals maintained higher efficiency. But when the market segments that sustained the U.S. producers—trucks and SUVs—contracted in the wake of increasing oil prices, the financial performance of the U.S. companies collapsed, leading to the bankruptcies of General Motors (GM) and Chrysler in 2009.

Frontier methods have been designed to assess an individual firm's performance relative to the best performers in an industry and are therefore well suited to address the challenges of measuring competitive advantage (Delmas and Tokat, 2005; Durand and Vargas, 2003; Knott and Posen, 2005; Lieberman and Dhawan, 2005; Majumdar, 1998). Frontier methods represent performance by an efficiency score, calculated as the firm's distance to the best practice industry frontier. The efficient frontier is estimated directly through the observed input(s) and output(s) of each firm.

Frontier methods can be used by strategy researchers to test theories of various factors that lead to competitive advantage. They are also particularly suited to conceptualize and measure firm-specific capabilities. As Dutta, Narasimhan, and Rajiv (2005: 278) point out, “one can think of capabilities as the efficiency with which a firm uses the inputs available to it (i.e., its resources, such as R&D expenditure) and converts them into whatever output(s) it desires…”

This research note covers the two main frontier approaches: Data Envelopment Analysis (DEA) (Banker, Charnes, and Cooper, 1984; Charnes, Cooper, and Rhodes, 1978), and the Stochastic Frontier Approach (SFA) (Aigner, Lovell, and Schmidt, 1977; Kumbhakar and Lovell, 2003; Meeusen and van den Broeck, 1977).2 A fundamental distinction between them is that DEA is nonparametric whereas SFA is a parametric approach. This distinction makes these two approaches have their own specific areas of strength, as we elaborate.

We begin by introducing the fundamentals of the DEA and SFA methods. We then illustrate the methodologies with data on U.S. and Japanese automobile producers. This illustration demonstrates the advantages of the frontier methods as well as caveats that researchers should consider when applying these methods or interpreting works that make use of them.

FRONTIER METHODOLOGIES

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. FRONTIER METHODOLOGIES
  5. ILLUSTRATION: JAPAN AND U.S. AUTOMOTIVE SECTORS
  6. CONCLUSION
  7. REFERENCES
  8. APPENDIX: 1: MATHEMATICAL FORMULATIONS OF DATA ENVELOPMENT ANALYSIS
  9. APPENDIX: 2: SOFTWARE PACKAGES FOR DEA AND SFA
  10. APPENDIX: 3: STUDIES UTILIZING DEA AND SFA IN THE STRATEGIC MANAGEMENT RESEARCH (SMJ, AMJ, AND MGMT SCI ARTICLES)

In frontier methodologies, a firm's performance is measured in terms of distance from the industry's efficient frontier. The efficient frontier is a function that indicates the maximum attainable level of output corresponding to a given quantity of input. The frontier is estimated based on the observed inputs and outputs of all firms in the industry (or a representative sample). For example, consider firms that employ two inputs, labor and capital, to produce one or more outputs, such as cars, trucks, and consumer loans. The efficient frontier represents the maximum amount of output(s) that can be produced from a specific amount of labor and capital. Each firm's relative efficiency can be defined, based on the distance between the firm's actual output and the estimated “best practice” frontier (e.g., expressed as the ratio of the firm's observed output relative to the fully efficient output). DEA and SFA are two alternative approaches through which the industry-efficient frontier and the firm-specific efficiencies can be estimated.

Basic DEA model

DEA generates the efficient frontier through a mathematical optimization model (Banker et al., 1984; Charnes et al., 1978). The DEA frontier is a linear surface or “piecewise hyperplane” extrapolated from all efficient firms in the sample such that the inefficient firms are “enveloped” by the frontier. We illustrate the DEA frontier in Figure 1(a), where we consider a simple case with one input and one output variable for seven firms (firm a to firm g). The figure depicts this frontier, along with the input and output of the seven firms. The DEA frontier is the line emanating from the origin O through firm a, which corresponds to the highest ratio of output to input. The area below the frontier consists of feasible yet inefficient input–output combinations.3 Firm a is therefore efficient, while firms b to g that are below the frontier are inefficient. Figure 1(a) also contains an OLS regression line with the intercept set to 0. It illustrates that the OLS model would underestimate the frontier because it does not permit inefficiency and assumes that deviation from the average input-output correspondence is purely random.4

image

Figure 1. (a) Illustration of the DEA frontier. (b) Illustration of the SFA frontier

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Inefficiency is measured by a firm's distance to the frontier. For example, the DEA efficiency score of firm f is calculated as inline image (observed output level) divided by inline image (efficient output level given firm f's input). Therefore firm f is inefficient with an efficiency score less than one.5 Firm a is on the DEA frontier and therefore it is efficient with an efficiency score of one. The DEA model works similarly when there are multiple outputs; in that case the efficiency score is calculated as the possible percentage increase of “all outputs,” given the current input. We provide detailed mathematical formulations of DEA in Appendix 1.

As shown in the above example, the DEA efficiency score is calculated based on input and output quantities. In the presence of multiple inputs and outputs, prior studies show that inadvertent aggregation of different performance measures can sometimes result in overlooked competitive strength in some performance dimensions (Chen and Delmas, 2011; Ray et al., 2004). DEA does not require explicit weight specifications or assumptions about the production function and probability distributions for technical inefficiency. The DEA model calculates weights for each firm through an optimization procedure, which is detailed in Appendix 1. The weights are calculated based on which input(s) a specific firm excels at utilizing, or which output(s) a firm excels at generating in comparison to the other firms in the sample. By assigning higher weights to the input and output variables a specific firm excels in utilizing or generating and low weights to the others, the algorithm maximizes the performance of each firm in light of its particular competence.6 In addition, DEA does not specify a specific production function, and the efficiency scores are obtained from solving linear programming problems. This feature enhances the computational convenience of DEA and reduces the risk of model misspecifications, but the trade-off is that DEA is a deterministic approach and can be sensitive to outliers.

Basic SFA model

In contrast to the DEA frontier, the SFA specification involves a production or cost function with an error term that includes two components: a random noise effect and an inefficiency effect (Aigner and Chu, 1968; Aigner et al., 1977; Meeusen and van den Broeck, 1977). The stochastic efficient frontier assumes that production outputs are subject to random shocks that are not under the direct control of firms. Specifically, let yit  denote the output of firm i produced at time t, and let Xit = (xit1,xit2, …,xitm) be the collection of m inputs or resources consumed for the purpose of producing yit. For example, a firm's inputs may include its capital assets and employees, and the output can be revenue, value-added (revenue minus materials costs), or physical quantity of output. The stochastic production function with panel data is given by

  • display math(1)

On the right-hand side of (1), there are three components. The first involves a production function f that transforms input factors Xit into output without any loss due to inefficiency. The second and the third components represent the random and stochastic inefficiency factors that capture the difference between the observed output, yit, and f(Xit), the output that a fully efficient firm i would secure in the absence of uncertainty. Specifically, νit is the random error assumed to be i.i.d. standard normal inline image, and μit represents the inefficiency effect, which is nonnegative and often assumed to follow a half-normal distribution (i.e., inline image) (Coelli et al., 2005; Kumbhakar and Lovell, 2003).7 The production function f(Xit) is commonly assumed to be a Cobb-Douglas production function,8 which enables us to rewrite (1) as

  • display math(2)

We can express (2) in a linear form after taking logarithms on both sides:

  • display math(3)

We illustrate the SFA frontier model (3) in Figure 1(b), which considers the same firms a to g that appeared in Figure 1(a). The frontier displayed in Figure 1(b) is determined based on maximum likelihood estimation (MLE) of the parameters β, and observations therefore deviate from the frontier as a result of joint effect of the random noise and inefficiency. The constant term β0 is negative, indicating there is a minimal input requirement before any output can be produced. For firm a, the net effect from inefficiency and noise is positive, and therefore firm a is above the frontier  f(Xit). For other firms, the net effect is negative and they are below the frontier and inefficient. The inefficiency of firm i at time period t can then be calculated as

  • display math(4)

In implementation, the separation of the inefficiency effect from the random noise effect is made possible by the distributional assumptions, which allow the efficiency index in (4) to be estimated.

The SFA frontier can be contrasted with the DEA frontier in Figure 1(a), where all firms are on or below the frontier and are driven below the frontier only by the inefficiency effect. The positions of firms in the SFA model are determined by both the inefficiency effect and the random error. Firms can temporarily lie above the frontier given the random error νit. Another important observation is that, since the inefficiency term μit is a continuous random variable, we will observe μit = 0 (so TEit = 1) with a zero probability, which means we will not observe any firms on the SFA efficient frontier. In contrast, we can identify at least one firm on the DEA efficient frontier.

The SFA approach requires an assumption on the functional forms of the production function and the inefficiency term, whereas DEA only requires much weaker assumptions on the production possibility set, such as convexity and minimal extrapolation (Banker et al., 1984). SFA recognizes that there may be errors in data or measurement of the underlying efficiency. DEA assumes that there is no random error in the model, and therefore any error and statistical noise will be reflected in the efficiency score. Another weakness of DEA is that it defines the frontier of the most efficient firms within the sample; if the sample is too small, the frontier may not be representative of the potentially most efficient frontier of the industry because of missing observations.

DEA and SFA in the strategy literature

We compare various features of DEA and SFA in Table 1 and describe how these methods have been used in the strategy literature based on an analysis of studies published in three prestigious journals: Strategic Management Journal, Academy of Management Journal, and Management Science listed in Appendix 3. In these studies, the most represented industries are the financial and electric utility sectors. This mix of industries is similar to that of the more general DEA literature, which also includes many studies of airlines and healthcare (see, e.g., Chilingerian and Sherman, 2004). Because these industries are highly regulated, publicly available data on outputs and resource inputs are more readily available to researchers than in other industries.

Table 1. Comparing DEA and SFA
Implementation aspectsDEASFA
Frontier shapeThe DEA frontier is a piece-wise linear surface.The SFA frontier follows a specific functional form (e.g., Cobb-Douglas, translog).
Applicable to multiple outputsDEA allows for multiple outputs in the production function. However, including additional outputs may decrease the discrimination power.Production frontier model requires that output be specified as a single measure; cost frontier model can accommodate multiple outputs.
Statistical assumptionsDEA is a deterministic approach and therefore does not require assumptions about the probability distributions of parameters.SFA requires a priori specification of the model, including the distribution form of the inefficiency term.
Sampling errorsThe DEA efficiency score is confounded with both statistical noise and inefficiency; it is also more susceptible to the influence of sampling errors and outliers.SFA incorporates a statistical error term in the formulation.
Panel data structurePanel data can be incorporated with assumptions on total productivity changes.SFA can make use of the panel data structure.
Hypothesis tests for the impacts of inputs and exogenous factors on outputsDEA generates the efficiency score only. To estimate the impacts (coefficients) of inputs and exogenous factors on outputs, it is necessary to fit an auxiliary regression model that uses the DEA efficiency score as the dependent variable.SFA can estimate the marginal influence of each input and exogenous factors on the output.
ComputationThe DEA efficiency score can be easily obtained by solving a number of linear programming problems.SFA relies on maximum likelihood estimation; ill-structured data or misspecification of the SFA model can lead to numerical problems when estimating the coefficients.

In the strategic management field, it is often of crucial interest to seek an explanation for a firm's performance deviation below the leading firms in the industry. One technique applicable to both the DEA and SFA models is to proceed with the analysis in two stages. In the first stage, the DEA or SFA models calculate the efficiency scores of the firms in the sample. In the second stage, the efficiency scores obtained in the first stage are regressed on a collection of explanatory variables.9 Eight of the studies presented in Appendix 3 use efficiency scores as a dependent variable (Cummins, Weiss, and Zi, 1999; Delmas and Tokat, 2005; Knott and Posen, 2005; Knott, Posen, and Wu, 2009; Majumdar and Marcus, 2001; Majumdar and Venkataraman, 1998; Schefczyk, 1993; Wu and Knott, 2006).

Although commonly used, this two-stage approach is often criticized because assumptions are required for the inferences made in the second stage to be statistically valid. For example, Wang and Schmidt (2002) show that the SFA two-stage approach can generate substantially biased estimates in both stages. To avoid these problems, a recommended option within SFA is to express the inefficiency term μit as a function of explanatory variables (Battese and Coelli, 1995; Lieberman and Dhawan, 2005). Here the inefficiency term μit is assume to be independently distributed as a normal distribution inline image truncated below at zero, where Zit is a vector of explanatory variables and δ is a vector of parameters to be estimated.10 Thus, the econometric structure of SFA allows for simultaneously estimating the impacts of inputs and exogenous factors on outputs. The two-stage approach for DEA has also been criticized for lacking a sound statistical foundation (Simar and Wilson, 2007), although Banker and Natarajan (2008) show that the two-stage approach for DEA can yield statistically consistent coefficient estimators under certain general distributional assumptions. Johnson and Kuosmanen (2012) further show that the estimators remain statistically consistent even when the first-stage input and output variables in DEA are correlated with the second-stage variables in the regression model. However, the precision of the second-stage estimates will decrease when this correlation is high and when the data have high statistical noise. Johnson and Kuosmanen (2012) develop a robust one-stage estimation approach to address some of the limitations of the traditional two-stage approach for DEA.

One advantage of DEA is that it readily allows for multiple outputs, while SFA in the production frontier form described above is most applicable to a single output or aggregate measure, such as sales or value added.11 In Appendix 3, we see that almost all studies that use DEA have multiple outputs. For example, Delmas, Russo, and Montes-Sancho (2008) in their study of the electricity sector, use three outputs that correspond to three different cost and market structures: low voltage sales, high voltage sales and sales for resale. Having multiple outputs, however, also implies that researchers need to be careful in selecting a meaningful set of output variables for their DEA model. Different outputs may represent different conceptualizations and orientations of business performance. Majumdar and Venkataraman (1998) present an excellent example of comparing DEA efficiency scores that are calculated based on different selections of outputs.

Another advantage of DEA is that it is capable of handling inputs and outputs expressed in different measurement units. For example, Dutta et al. (2005) measured firm capabilities by using patent counts weighted by citations as an output and R&D and marketing expenses as inputs. This allows researchers to measure capabilities and intangible resources, which are often difficult to approximate in monetary terms. It also allows researchers to conceptualize capabilities as the ability to combine efficiently a number of resources to engage in productive activity (Dutta et al., 2005).

Both SFA and DEA can incorporate panel data to estimate efficiency scores and other parameters. SFA incorporates the panel information via the traditional econometric framework (Aigner et al., 1977; Battese and Coelli, 1995).12 In Appendix 3, all the SFA studies use panel data, where cost efficiency is estimated based on a pooled sample across the observation years (Dutta et al., 2005; Knott and Posen, 2005; Knott, Posen, and Wu, 2009; Lieberman and Dhawan, 2005; Miller and Parkhe, 2001; Wu and Knott, 2006).

In DEA there are two different approaches to deal with panel data. The first approach is to calculate the DEA scores year by year. This means that the DEA score of year t is determined based on the data of year t.13 This approach is recommended over calculating DEA scores based on multiyear data, because incorporating multiyear data to estimate the frontier would raise the concern that firms may be compared with the best performers operating under different technological conditions (Delmas and Montes-Sancho, 2010; Delmas and Tokat, 2005; Delmas et al., 2008; Majumdar and Marcus, 2001; Majumdar and Venkataraman, 1998). The other approach is to calculate productivity change between two consecutive periods in DEA by using the Malmquist productivity index (Banker, Chang, and Natarajan, 2005; Cummins et al., 1999; Färe et al., 1994). The Malmquist index indicates how much of each firm's total factor productivity change from one period to the next is due to frontier shift and how much is due to its efficiency change.

Finally, for both DEA and SFA, there are a number of software options available. We provide a list of commonly used of software packages in Appendix 2.

ILLUSTRATION: JAPAN AND U.S. AUTOMOTIVE SECTORS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. FRONTIER METHODOLOGIES
  5. ILLUSTRATION: JAPAN AND U.S. AUTOMOTIVE SECTORS
  6. CONCLUSION
  7. REFERENCES
  8. APPENDIX: 1: MATHEMATICAL FORMULATIONS OF DATA ENVELOPMENT ANALYSIS
  9. APPENDIX: 2: SOFTWARE PACKAGES FOR DEA AND SFA
  10. APPENDIX: 3: STUDIES UTILIZING DEA AND SFA IN THE STRATEGIC MANAGEMENT RESEARCH (SMJ, AMJ, AND MGMT SCI ARTICLES)

Data

To illustrate the DEA and SFA methodologies, we use data from the U.S. and Japanese automotive sectors from 1977 to 1997 (Lieberman and Dhawan, 2005).14 Performance of the automotive sector has been of significant interest to strategy researchers (Dyer, 1996; Jiang, Tao, and Santoro, 2010), and the U.S. and Japan represented the top motor vehicle producing countries in the world during the sample period (OICA, 2005–2006). The data contain a balanced panel of 11 automobile producers and their input and output variables. We specify one SFA and two DEA models. In the SFA and the first DEA model, we consider two inputs, capital and number of employees, and one output, value-added.15 Descriptive statistics of the inputs and outputs are provided in Table 2. We also compare the results of our efficiency frontier models with a more traditional profit measure.

Table 2. Descriptive statistics
 Obs.MeanStd. dev.MinMax[1][2][3][4][5][6][7][8]
[1] Value added (V, in 1982 yen)2311,259,7761,909,81442,4337,336,3331       
[2] Capital stock (K, in 1982 yen)2312,530,5954,018,20180,327.31.68E + 070.961      
[3] Number of employees (L)231135,375.3223,921.17,890846,0000.970.941     
[4] Work-in-progress/sales (WIP/sales)2310.020.020.000.120.180.180.221    
[5] Value-added/sales (V/sales)2310.220.100.120.490.150.110.160.411   
[6] Production volume per plant (Q/N)231313,766.3172,986.889,926.52842,474.6−0.12−0.09−0.10−0.27−0.491  
[7] Number of trucks produced231579,512.5491,572.688,3002,200,8860.860.840.760.130.13−0.121 
[8] Number of cars produced2311,183,9301,114,57625,5325,285,7000.750.650.730.150.19−0.060.631

DEA model

In the DEA model, we consider two inputs, capital and number of employees, and one output, value-added. We apply the DEA model to cross-sectional yearly samples in the period of analysis. For illustrative purposes, we assume that the production technology exhibits constant returns-to-scale (CRS) in the DEA model. The CRS assumption implies that, regardless of firm size, expansion or reduction of a firm's inputs by a factor will lead to the same proportion of change in the firm's outputs. We assume CRS because the CRS technology is more intuitive when represented in graphics and also because our cross-sectional sample size is relatively small. Methods to impose a variable returns-to-scale assumption in DEA are described in Appendix 1. Summary statistics of the efficiency scores are provided in Table 3.

Table 3. Summary of efficiency scores and financial rate of return (full sample)
ModelInput variablesOutput variablesObs.MeanStd. dev.MinMax[1][2][3]
  1. a

    Correlation coefficients significant at the one percent significance level.

[1] DEACapital stock, and no. of employeesValue-added2200.7970.1610.34811  
[2] SFACapital stock, and no. of employeesValue-added2200.8860.12590.41210.562a1 
[3] Financial rate 2200.16840.1838−0.530.860.439a0.294a1
of returns (operating profit/net property, plant and equipment)         

Figure 2 contains a three-dimensional scatter plot of the inputs and output of the 1997 sample, as well as the corresponding efficient frontier (i.e., the shaded plane). The arrows in the figure represent each firm's trajectory to its efficient benchmark on the frontier. As in Figure 1, firms' efficiency scores are calculated as the “observed value-added” divided by “efficient value-added.” In this case efficiency scores range from 0.43 to 1, which represents firms on the efficiency frontier. The results show that Honda and Toyota have scores of 1 and are on the 1997 efficient frontier. The frontier under the CRS assumption is a plane containing these two firms and the origin. The efficint output levels for inefficient firms are points on the frontier that have the same input levels but a higher output level. For example, GM's input and output quantities (capital, labor, value-added) in 1997 are $16.8 billion of capital stock; 627,500 employees; and $6.6 billion of value-added. GM's efficiency score in that year is 0.43. Based on the efficiency score, we can calculate GM's efficient level of output (value-added) as: $6.6 billion/0.43 = $15.3 billion.

image

Figure 2. Three-dimensional efficient frontier (year 1997)

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DEA allows the inclusion of multiple output variables. Similar to the single-output DEA, the multioutput DEA calculates efficiency scores by measuring the distance between a firm and the efficient frontier in the multidimensional space. In addition to value-added, we could, for example, introduce the number of trucks and the number of cars produced. Thus, outputs can be measured in terms of physical quantities or monetary values. When longitudinal panel data are available, we can also graphically depict how the industry efficient frontier changes over different time periods. To measure the productive changes of individual firms, however, we need to account for both the efficiency change (i.e., relative position to the efficient frontiers in two periods) and the frontier movements. Under the DEA framework, a commonly used approach to calculating productivity change is the Malmquist productivity index that measures productivity change over time; see also our earlier discussion about incorporating panel data in DEA.

SFA model

In the SFA model we use capital stock and number of employees as the inputs and value-added as the output. In the inefficiency component of this SFA model, we follow Lieberman and Dhawan (2005) in using volume per plant (Q/N), Work-in-process/sales (WIP/sales) and value-added/sales (V/sales) as the explanatory variables for productive inefficiency. Our choice of variables in the production function model of SFA also follows Lieberman and Dhawan (2005). The first variable (Q/N) provides a measure of plant scale, through which we can test whether scale economies at the level of individual manufacturing plants affect firms' efficiency. The second variable (WIP/sales) serves as a proxy measure of factory management skills, as a large WIP/sales ratio implies that firms need to maintain a high inventory level to counter disruptions in production (Lieberman and Demeester, 1999; Lieberman and Dhawan, 2005). The third variable (V/sales) indicates the level of vertical integration. Specifically, the SFA model is formulated as

  • display math(5)

where the inefficiency effect is a function of the three explanatory variables and a random inefficiency term:

  • display math(6)

where ωit is a truncation of N(0, σ2μ) such that μit ≥0.

Table 4 tabulates the estimation results of the SFA model. The coefficient of the time variable (β1) is positive and highly significant, which suggests that firm efficiency tends to improve over time. The coefficients of the capital and labor variables are both significant; the sum of these two coefficients is larger than 1 (i.e., 1.036), which signifies a small degree of increasing returns to scale, based on the size of the firm as a whole. The coefficient for plant scale (δ1) is negative and also highly significant, suggesting that the automakers with larger plants in general have gained higher efficiency (i.e., economies of scale exist at the level of individual plants, as well as for the firm as a whole). These findings are consistent with prior studies and reaffirm that exploiting economies of scale is an important factor in attaining efficiency in the automotive sector (Lieberman and Dhawan, 2005; Lieberman, Lau, and Williams, 1990).

Table 4. Parameters estimates of the SFA model
Dependent variable: value-added
Independent variablesCoefficientStd. error.
  1. a

    Significant at the one percent level

  2. b

    significant at the five percent level.

Production function model
Time parameter (β1)0.025a0.004
No. of employees (β2)0.910a0.053
Capital stock (β3)0.126b0.058
Inefficiency model
Constant (δ0)1.4140.440
No. cars produced per plant (δ1)−0.819a0.116
Value-added/sales (lag one year) (δ2)−0.0180.302
WIP/sales (lag one year) (δ3)−0.0450.094
Variance estimates
inline image 0.2630.109
inline image 1.690.193
Log likelihood76.9 
No. of observations220 

In our results, the coefficients for the WIP/sales and Value-added/sales ratios are both insignificant. These results differ slightly from those in Lieberman and Dhawan (2005), which apply SFA to data from the automotive sector from 1965 to 1997. This might be due to a difference in the time frame observed since our panel starts in 1977, after Japanese producers had made their major inventory reductions.

DEA, SFA and profit

The DEA and SFA efficiency scores are summarized in Table 3. The significant correlation between these scores implies that they capture similar notions of firm performance in the case of our automotive sample. But to what degree are these measures of efficiency related to company profitability? To answer this question we used the available data to compute an annual financial rate of return (operating profit/net property plant and equipment) for each of the 11 automotive companies. Table 3 shows that this measure of profit is also significantly correlated with DEA and SFA but to a lesser level.

In order to further compare these measures, we ranked the 11 firms based on the three alternative performance measures: DEA score, SFA score, and financial return. The results of this ranking are illustrated in Figure 3, where we have aggregated the data by country of origin. The contrast between U.S. and Japanese producers is striking. For the Japanese producers, the efficiency score rankings are uniformly higher than the profit rankings. The reverse is true of the U.S. producers (except during the U.S. recession of the early 1980s).

image

Figure 3. Efficiency andprofit scores rankings

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How did the Americans sustain these high financial returns despite comparatively low levels of efficiency? Although our analysis cannot answer this question directly, a better understanding of the U.S. political economy of the time can help us understand what happened. One major reason relates to tariff protection of a key segment: trucks and SUVs. The United States protects its domestic market of trucks and vans with a 25 percent import tariff while regular cars only face a tariff of 2.5 percent (Ikenson, 2003). This protection allowed the Big Three U.S. manufacturers to dominate the U.S. market with more than 85 percent of pickup truck sales and benefit from high profit margins (Ikenson, 2003). These margins were particularly high from the mid-1980s to the early 2000s, when oil prices remained low favoring the development of the market for nonfuel efficient vehicles.

While the U.S. car manufacturers were protected by high trade tariffs, Japanese automakers invested in efficiency improvements. In their comparison of a U.S. and a Japanese car plant, Abegglen and Stalk (1985: 105) show that U.S. plants needed 250 percent as many employees as the Japanese one to make a vehicle. The crucial difference was that the Japanese car manufacturers developed lean production systems whereas the U.S. car manufacturers were slow to do so (Womack, Jones, and Roos, 1990). In the 2000s, when high gas prices shifted the market toward more fuel efficient cars, the big three automobile manufacturers, which had specialized in building trucks, were unable to respond adequately.16

In general, our application of DEA and SFA to a panel dataset on 11 U.S. and Japanese automobile producers illustrates several features of frontier methodologies, as well as issues to be considered in their application. Most fundamentally, we show how the methods characterize the distance of firms from the frontier defined by the most efficient competitors (typically, Toyota and Honda in most years of our sample). The automotive example demonstrates the ability of DEA to accommodate simultaneously multiple performance measures and the ability of SFA to incorporate tests of hypotheses about sources of advantage without resorting to a separate stage of statistical analysis. The example shows how corporate performance based on efficiency differs from profitability based on pricing power derived from barriers to entry.

CONCLUSION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. FRONTIER METHODOLOGIES
  5. ILLUSTRATION: JAPAN AND U.S. AUTOMOTIVE SECTORS
  6. CONCLUSION
  7. REFERENCES
  8. APPENDIX: 1: MATHEMATICAL FORMULATIONS OF DATA ENVELOPMENT ANALYSIS
  9. APPENDIX: 2: SOFTWARE PACKAGES FOR DEA AND SFA
  10. APPENDIX: 3: STUDIES UTILIZING DEA AND SFA IN THE STRATEGIC MANAGEMENT RESEARCH (SMJ, AMJ, AND MGMT SCI ARTICLES)

Performance measurement is at the heart of strategic management research. This paper has provided an overview on the frontier methodology as a tool for performance measurement by strategic management scholars. Specifically, we have introduced the two most prevalent frontier methodologies, Stochastic Frontier Analysis and Data Envelopment Analysis, and offered a comparative discussion regarding the strengths and limitations of these two approaches.

The DEA and SFA methodologies provide a way of characterizing competitive advantage in an industry. Both methods focus on firms' efficiencies in converting inputs to outputs, and both allow researchers to identify top performing firms, which lie on or near the industry best-practice frontier. DEA and SFA estimate the best-practice frontier and quantify the gap between the observed firm and the frontier (i.e., inefficiency). The efficiency score of a firm is defined as the ratio between the firm's present performance and the performance that the firm would have achieved if it were fully efficient, based on the estimated frontier.

By providing a technique to assess efficiency, the frontier methods described in this paper enable an understanding of firm performance that is deeper than a mere comparison of company profits. Indeed, as we demonstrate, the major American automotive companies exhibited relatively strong financial performance in the 1980s and 1990s, even though their Japanese rivals maintained higher efficiency. But when the market segments that sustained the U.S. producers— trucks and SUVs—contracted in the wake of increasing oil prices, the financial performance of the U.S. companies collapsed, leading ultimately to the bankruptcy of General Motors (GM) and Chrysler.

We see a great potential for the use of frontier methodologies in strategy research. Two different views on the sources of corporate profits have dominated strategy research: the industry view and the firm-efficiency view (McGahan and Porter, 1999). In the industry view, industry structure drives profit while in the efficiency view companies achieve profits in a line of business when they operate more efficiently than their competitors. Production frontier methodologies allow researchers to assess the efficient use of resources within the existing industry structure. Our auto example illustrates both types of effects: U.S. producers earning high returns by dominating attractive (albeit protected) market segments, and Japanese producers, such as Toyota and Honda, earning their returns through greater efficiency.

The frontier methodologies have proved particularly useful when firm performance is characterized by multiple dimensions with different units of analysis. A key strength of DEA lies in its capability to simultaneously incorporate multiple inputs and outputs, a requirement for analysis of many industries and for studies that seek to incorporate nonfinancial measures of performance. It also allows the incorporation and comparison of variables with different units (such as, for example, number of employees, tons of input, and dollars of profit). By comparison, SFA is most applicable when multiple outputs can reasonably be aggregated into a single measure or when price and quantity data are available for inputs and outputs so that a cost frontier model can be estimated. For problems with limited dimensions, the methods can provide an intuitive graphical interpretation of the efficient frontier in the industry and the sampled firms' relative distances.

DEA and SFA have wide potential applications in strategic management research. They provide vehicles for characterizing performance in ways that go beyond conventional analysis of common financial measures. For example, the ability of DEA to deal with multiple outputs and different units may be particularly useful for resource-based view (RBV) analyses of heterogeneous collections of resources, including physical capacities such as capital and machinery, as well as intangible properties such as technological know-how and managerial skills. In RBV, sustained competitive advantage is resulted from leveraging the organizational resources and capabilities that are valuable, rare, inimitable, and nonsubstitutable (Barney, 1991; Newbert, 2008). What constitutes “valuable and inimitable resources” depends on both the distribution of the critical resources in the industry and the standing of a firm among its competitive peers. The ability of DEA to include such resources in a comparative way is well suited for RBV analyses when suitable measures are available. DEA and SFA can also facilitate the development of newer areas of strategic management research. For example, the field of frontier methodologies has seen emerging extension to topics such as the measurement of eco-efficiency and corporate social performance, where some of the outputs may be undesirable (such as pollution, labor issues, etc.; see Chen and Delmas, 2011, 2012; Reinhard, Lovell, and Thijssen, 2000). We encourage strategic management researchers to exploit frontier methodologies to explore agendas in these and other topic areas.

REFERENCES

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. FRONTIER METHODOLOGIES
  5. ILLUSTRATION: JAPAN AND U.S. AUTOMOTIVE SECTORS
  6. CONCLUSION
  7. REFERENCES
  8. APPENDIX: 1: MATHEMATICAL FORMULATIONS OF DATA ENVELOPMENT ANALYSIS
  9. APPENDIX: 2: SOFTWARE PACKAGES FOR DEA AND SFA
  10. APPENDIX: 3: STUDIES UTILIZING DEA AND SFA IN THE STRATEGIC MANAGEMENT RESEARCH (SMJ, AMJ, AND MGMT SCI ARTICLES)

APPENDIX: 1: MATHEMATICAL FORMULATIONS OF DATA ENVELOPMENT ANALYSIS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. FRONTIER METHODOLOGIES
  5. ILLUSTRATION: JAPAN AND U.S. AUTOMOTIVE SECTORS
  6. CONCLUSION
  7. REFERENCES
  8. APPENDIX: 1: MATHEMATICAL FORMULATIONS OF DATA ENVELOPMENT ANALYSIS
  9. APPENDIX: 2: SOFTWARE PACKAGES FOR DEA AND SFA
  10. APPENDIX: 3: STUDIES UTILIZING DEA AND SFA IN THE STRATEGIC MANAGEMENT RESEARCH (SMJ, AMJ, AND MGMT SCI ARTICLES)

(7) Max inline image

Subject to inline image inline image

λj ≥ 0 for j = 1, …, n

(8) Min inline image

Subject to inline image inline image

λj ≥ 0 for j = 1, …, n

The DEA formulations are shown in (7) and (8). In the Models xji and yjr denote the i-th input and r-th output of firm j, respectively. Depending on whether the efficiency pertains to inputs or outputs, we have a choice between the output- or input-oriented DEA models. Model (7) is called the output-oriented DEA model, because the efficiency score θ1 is attached to the outputs of firm #1. For firm #1, for example, l (7) attempts to increase firm #1's outputs by maximizing inline image, given the inputs x1i, i = 1, …, m. An output-oriented inefficient firm can increase its output levels with its current input consumption level (i.e., the optimal value of inline image will be larger than 1). The efficiency scores of efficient firms are equal to 1.

Model (8) is the input-oriented DEA model. In (8), the efficiency score θ1 is attached to the input variables, and the objective function seeks to reduce inputs by minimizing inline image, given a firm's current output level. An input-oriented inefficient firm can reduce its input usage while maintaining its current output level (i.e., the optimal value of inline image is less than 1). The efficiency scores of efficient firms in the input-oriented model are also equal to 1. We assume that the production technology in (7) and (8) has constant returns-to-scale (CRS), which implies that the marginal rate of transformation between inputs and outputs is constant. Therefore the optimal value of inline image and inline image in the CRS model are reciprocals of each other (i.e., inline image). The variable returns-to-scale (VRS) DEA model can be implemented by adding an additional constraint inline image to the CRS DEA model (Banker et al., 1984). This additional constraint makes the VRS efficiency score closer to 1 than the CRS score, and thus firms are closer to the efficient frontier in the VRS model.

Solving (7) or (8) will yield the efficiency score of one firm. Thus, to obtain the efficiency scores for all n firms, we need to solve the model for n iterations, and in each iteration the constants on the right-hand-side of the constraints are updated.

APPENDIX: 2: SOFTWARE PACKAGES FOR DEA AND SFA

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. FRONTIER METHODOLOGIES
  5. ILLUSTRATION: JAPAN AND U.S. AUTOMOTIVE SECTORS
  6. CONCLUSION
  7. REFERENCES
  8. APPENDIX: 1: MATHEMATICAL FORMULATIONS OF DATA ENVELOPMENT ANALYSIS
  9. APPENDIX: 2: SOFTWARE PACKAGES FOR DEA AND SFA
  10. APPENDIX: 3: STUDIES UTILIZING DEA AND SFA IN THE STRATEGIC MANAGEMENT RESEARCH (SMJ, AMJ, AND MGMT SCI ARTICLES)

Below is a partial list of the software programs for implementing DEA and SFA models. Since DEA models are linear programming problems, the DEA algorithm can be implemented in most optimization programs with the basic programming functionality.

SoftwareDeveloperWebsite
  1. a

    See Bogetoft and Otto (2011) for detail about implementing SFA and DEA in R.

FEAR: frontier efficiency analysis with RaPaul Wilsonhttp://www.clemson.edu/economics/faculty/wilson/Software/FEAR/fear.html
DEA FrontierJoe Zhuhttp://www.deafrontier.net/
(add-in for Microsoft Excel)
DEAP, FrontieraTim Coellihttp://www.uq.edu.au/economics/cepa/software.htm
Frontier analystBanxia softwarehttp://www.banxia.com/frontier/
LimdepEconometric Software, Inc.http://www.limdep.com/
 
RaFreewarehttp://www.r-project.org/
StataStata Corp.http://www.stata.com/
LimdepEconometric Software, Inc.http://www.limdep.com/
SASSAS Institute Inc.http://www.sas.com/

APPENDIX: 3: STUDIES UTILIZING DEA AND SFA IN THE STRATEGIC MANAGEMENT RESEARCH (SMJ, AMJ, AND MGMT SCI ARTICLES)

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. FRONTIER METHODOLOGIES
  5. ILLUSTRATION: JAPAN AND U.S. AUTOMOTIVE SECTORS
  6. CONCLUSION
  7. REFERENCES
  8. APPENDIX: 1: MATHEMATICAL FORMULATIONS OF DATA ENVELOPMENT ANALYSIS
  9. APPENDIX: 2: SOFTWARE PACKAGES FOR DEA AND SFA
  10. APPENDIX: 3: STUDIES UTILIZING DEA AND SFA IN THE STRATEGIC MANAGEMENT RESEARCH (SMJ, AMJ, AND MGMT SCI ARTICLES)
Authors/journalsUsageaRegression modelSample size and typeTypes of inputsType of outputsSampleAvg. efficiencyStd dev.
  1. a

    A: efficiency scores used as the dependent variable in the regression model. B: efficiency scores used as the independent variable in the regression model. C: efficiency scores are not used in regression.

DEA studies
Schefczyk (SMJ 1993).A, BOLS regressionN = 15; cross section(1) Aircraft capacity, (2) operating costs, (3) nonflight assets(1) Passenger-related revenue, (2) nonpassenger revenueAirlines0.8780.097
Howard and Miller (AMJ 1993).CN/AN = 443; cross section14 baseball performance indicatorsPlayers' salaryMajor league baseball playersN/AN/A
Cummins, Weiss, and Zi (Mgmt Sci 1999)A, COLS regressionN = 417 (pooled); 10 years panel(1) Labor, (2) business services, (3) debt capital, (4) equity capital(1) Present value of losses, (2) total invested assetsInsurers0.901 (pooled)
Majumdar (SMJ 1998)CN/AN = 39. Cross section(1) Total number of switches, (2) total number of access lines, and (3) total number of employees(1) Local revenues, (2) toll revenues, and (3) other revenuesTelecom firms0.9030.104
Majumdar and Venkataraman (SMJ 1998)BTobit regressionN = 40. 5-year panel(1) Number of switches, (2) number of lines, and (3) number of employees(1) Local revenues, (2) toll revenues, and (3) access and misc. revenuesTelecom firms5.121.34
Majumdar and Marcus (AMJ 2001)ATobit regressionN = 150, cross section(1) Production expenses, (2) transmission expenses, (3) distribution expenses, (4) the total number of employees, (5) amount of purchased power(1) Total sales, (2) dispositions of energy in megawatt hoursElectric utility firms0.78.158
Thursby and Thursby (Mgmt Sci 2002)CN/AN = 64, from 1993 to1997 (balanced)(1) Faculty size, (2) research funds, (3) number of full-time equivalent personnelNumber of patentsUniversitiesN/AN/A
Durand and Vargas (SMJ 2003)Aancova and mancovaN = 162. Cross section(1) Total fixed assets; expenditures in (2) R&D, (3) marketing, (4) education(1) Gross profits, (2) salesPrinting, auto parts, chemical firms0.5520.253
SFA studies
Delmas and Tokat (SMJ 2005)ATobit regressionN = 707 (pooled); 4-year panel(1) Labor cost, (2) plant value, (3) production expenses, (4) transmission expenses, (5) distribution expenses, (6) sales, (7) admin. and general expenses, (8) electricity purchases(1) Low-voltage sales (2) high-voltage sales (3) sales for resaleElectric utility firms0.860.18
Delmas, Russo, and Montes-Sancho (SMJ 2008)BOLS regressionN = 177; 3-year panelSame as above(1) Low-voltage sales, (2) high-voltage sales, (3) sales for resaleElectric utility firms0.9260.09
Delmas and Montes-Sancho (SMJ 2010)BTwo-stage logit modelN = 132; 6-year panelSame as above(1) Low-voltage sales, (2) high-voltage sales, (3) sales for resaleElectric utility firms0.880.15
SFA studies
Miller and Parkhe (SMJ 2001)CSFAN = 1300; 7-year panel(1) Total loans, (2) earning assets, (3) labor, (4) physical capital, (5) funds and depositsProfitsBanksN/AN/A
Dutta, Narasimhan, and Rajiv (SMJ 2005)CSFAN = 64; 9-year panel(1) Cumulative R&D expenditure, (2) cumulative marketing expenditureR&D patent counts weighted with citationsSemi-conductor firmsN/AN/A
Lieberman and Dhawan (Mgmt Sci 2005)CSFAN = 11; 32-year panel(1) Employee, (2) capitalEconomic value-addedAuto producersN/AN/A
Knott and Posen (SMJ 2005)BSFA (cost efficiency model)170,859 firm–year observations over 14 years(1) Labor, (2) physical capital, (3) mortgage loans, (4) nonmortgage loans, (5) investment securitiesTotal costsBanks0.81N/A
Wu and Knott (Mgmt Sci 2006)BSFA (cost efficiency model)Same as above.Same as aboveTotal costsBanks0.81N/A
Knott, Posen, and Wu (Mgmt Sci 2009)ASFA (cost efficiency model)Same as above.Same as aboveTotal costsBanks0.81N/A
  1. 1

    A search for profit, return on sales, return on assets, and Tobin's q on the publisher's website of these three journals yields 4,174 articles (access date: July 22 2013).

  2. 2

    Several papers introduce both SFA and DEA (e.g., Coelli et al., 2005; Hjalmarsson, Kumbhakar, and Heshmati, 1996; Murillo-Zamorano, 2004). These sources provide information from a technical or economic standpoint without specific focus on strategic management.

  3. 3

    Here we assume the production technology has constant returns-to-scale (CRS), which, in the presence of multiple inputs and outputs, means that a proportional change in a firm's inputs (e.g., all inputs are increased by 50%) should lead to the same proportional change in a firm's outputs (all outputs should increase 50%).

  4. 4

    See Coelli et al. (2005: 258–259) for statistical tests for the existence of inefficiency effects.

  5. 5

    The DEA model used to measure output inefficiency is presented in (7) in Appendix 1. We should note that the efficiency score obtained from formulation (7) (i.e., the θoutput) is the reciprocal of our definition provided here, and the score is greater than or equal to . For example, firm b's DEA score from formulation (7) is equal to inline image, which is greater than 1. We provide a more in-depth discussion in Appendix 1.

  6. 6

    This flexibility in the assignment of weights can lead to a situation where a large proportion of firms are found to be efficient or a specific firm appears efficient because it specializes in a few rather than most outputs or inputs, and thus DEA loses its discriminatory power. Lack of discriminatory power can also occur when the number of input and output variables is high relative to the sample size: having more variables increases the likelihood that firms are found efficient because DEA optimizes the weights of their “niche” inputs or outputs. If we have prior knowledge about the relative importance of inputs and outputs, it is possible to constrain the weight of one input or output relative to that of another in the DEA models. For example, we can impose that the weight of input A must be three times to five times higher than that of input B. Note that when weight restriction constraints are imposed, the efficient frontier and therefore the efficiency scores would both change. See Cooper, Ruiz, and Sirvent (2011) for a detailed discussion about weight restriction methods in DEA.

  7. 7

    Other distributional assumptions for the inefficiency terms have also been used in the literature, including gamma and exponential distributions. The choice of distributions may influence the predicted firm efficiency score, but not efficiency ranking (Coelli et al., 2005: 252). The z-test or the likelihood ratio statistics can be used to test whether the half-normal SFA model is adequate; see Coelli et al. (2005: 259).

  8. 8

    The Cobb-Douglas function is a widely used functional form to specify the relationship between multiple inputs to an output. However, there are other functional forms in common use. For example, Knott and Posen (2005) adopt the Translog function in their SFA model. See Coelli et al. (2005) p. 211 for a list of commonly used functional forms.

  9. 9

    The regression models commonly used in the second stage include the ordinary least square (OLS), censored regression (e.g., probit and Tobit models), truncated regression, and panel data models. See the discussion in Simar and Wilson (2007) and Knott, Posen, and Wu (2009).

  10. 10

    This option can now be implemented within standard statistical packages, such as Limdep and R.

  11. 11

    The SFA cost efficiency model can accommodate multiple outputs; see Knott and Posen (2005) for an illustration. Other SFA models for multiple inputs and outputs do exist (e.g., Banker, Conrad, and Strauss, 1986; Coelli and Perelman, 1999). However, studies have identified several statistical issues regarding these models; see Chap. 10 in Coelli et al. (2005) for a further discussion.

  12. 12

    We should note that SFA can work with a cross-sectional sample, but maximum likelihood estimation of the model requires strong statistical assumptions on error components, and efficiency scores cannot be estimated consistently with a cross-sectional sample (Schmidt and Sickles, 1984).

  13. 13

    Recently Chen and van Dalen (2009) used a panel vector autoregressive (PVAR) regression model to estimate the correlation between frontiers in different years. They incorporated the PVAR estimations in the first approach of calculating the efficiency scores for panel data.

  14. 14

    Data for Japanese companies are from annual issues of the Daiwa Analyst's Guide. The Japanese data are limited to motor vehicle production within Japan; all transplant operations outside of Japan are excluded. The U.S. data are from the companies' annual financial reports and Standard & Poor's COMPUSTAT. Details of the calculation of the variables can be found in Lieberman and Dhawan (2005).

  15. 15

    Value-added represents the monetary value created and retained by the firm and is calculated as the firm's sales during the fiscal year minus the costs of purchased materials and services.

  16. 16

    To further explain the patterns in Figure 3, we regressed the company profit rates and efficiency scores on a series of variables, including the firm's degree of focus on trucks (measured as annual production of trucks and SUVs as a proportion of total vehicle output). These regressions showed that firms' profit rates were strongly and positively linked to truck production, whereas the DEA and SFA efficiency scores were not. Thus, truck and SUV production was unrelated to efficiency but highly related to profitability, particularly for the American companies.