production frontier methodologies and ... - …...3 anderson school of management, university of...

Strategic Management JournalStrat. Mgmt. J., 36: 19–36 (2015)

Published online EarlyView 18 December 2013 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/smj.2199

Received 9 December 2011 ; Final revision received 5 August 2013

PRODUCTION FRONTIER METHODOLOGIESAND EFFICIENCY AS A PERFORMANCE MEASUREIN STRATEGIC MANAGEMENT RESEARCH

CHIEN-MING CHEN,1 MAGALI A. DELMAS,2,3 and MARVIN B. LIEBERMAN3*1 Nanyang Business School, Nanyang Technological University, Singapore,Singapore2 Institute of the Environment & Sustainability, University of California, Los Angeles,California, U.S.A.3 Anderson School of Management, University of California, Los Angeles, California,U.S.A.

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

INTRODUCTION

Research in strategic management is focusedon finding strategies and attributes that enablean organization to outperform its competitors.One or more firms in an industry are oftenargued to have attained “competitive advantage”relative to the majority of rivals (Porter, 1985).A common challenge facing strategic managementscholars is to identify objectively the leadingcompetitors and assess the reasons for theirsuperiority.

Keywords: performance measurement; data envelopmentanalysis; stochastic frontier analysis; research methodo-logy; efficiency*Correspondence to: Marvin B. Lieberman, UCLA AndersonSchool of Management, Los Angeles, California, 90095-1481,USA. E-mail: [email protected]

Copyright © 2013 John Wiley & Sons, Ltd.

The purpose of this article is to present anintroduction to a useful methodology, the fron-tier methodology, which measures the relativeefficiency of firms in transforming resources toachieve business goals. Although the idea ofrelative efficiency is closely tied to the conceptof competitive advantage (which occurs when anorganization acquires or develops some combina-tion of attributes that allows it to outperform itscompetitors), surprisingly few studies have usedfrontier methods in strategic management research.A search for studies using these approaches inthree prestigious management journals (StrategicManagement Journal , Academy of ManagementJournal , and Management Science) yields only16 articles as compared to hundreds of articlesusing profit measures such as Return on Assets or

20 C.-M. Chen, M. A. Delmas, and M. B. Lieberman

Sales.1 This note demonstrates the potential ofthese methods for studies in strategic managementand provides practical guidance on the relativebenefits of the different approaches.

Identifying firms that possess advantage overcompetitors is a straightforward exercise if per-formance can be succinctly captured by a sin-gle measure. However, the strategic managementliterature points to a diverse array of objectivesand actions regarding the creation of competi-tive advantage (e.g., Douglas and Judge, 2001;Dyer, 1996; Hillman and Keim, 2001). As aconsequence, researchers are faced with a rangeof performance measures that relate to variousaspects of corporate activities, including account-ing, finance, operations, marketing and corporatesocial responsibility, and often there is no clearguideline to select valid measures for corporateperformance (Dess and Robinson, 1984; Godfrey,Merrill, and Hansen, 2009; Hull and Rothenberg,2008; Ray, Barney, and Muhanna, 2004; Waddockand Graves, 1997). For example, in a survey of374 studies published in the Strategic Manage-ment Journal from 1980 to 2004, Combs, Crook,and Shook (2005) found that 56 different measureswere used to operationalize the corporate perfor-mance construct. It is seldom the case that a singlefirm will top the list all the available performancemeasures. Identifying the firms that define the bestperformance frontier across the relevant measuresis an important task that is seldom performed.Some of the methods described in this article canbe applied to perform this task.

Although performance includes multiple dimen-sions, studies in strategic management focus mostcommonly on firms’ financial returns. Superiorprofitability is achieved through some combina-tion of cost efficiency and the ability of the firmto charge a price premium (Porter, 1985). Strate-gies designed to enhance a firm’s efficiency areoften quite different from those oriented towardcharging a higher price. Yet few empirical stud-ies consider these two sources of advantageseparately. By providing a technique to assess effi-ciency, the frontier methods described in this arti-cle enable an understanding of firm performancethat is deeper than a mere comparison of profitabil-ity or financial returns. Indeed, as we demonstrate

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

below, the major American automotive compa-nies demonstrated relatively strong financial per-formance in the 1980s and 1990s, even thoughtheir Japanese rivals maintained higher efficiency.But when the market segments that sustained theU.S. producers—trucks and SUVs—contracted inthe wake of increasing oil prices, the financial per-formance of the U.S. companies collapsed, leadingto the bankruptcies of General Motors (GM) andChrysler in 2009.

Frontier methods have been designed to assessan individual firm’s performance relative to thebest performers in an industry and are thereforewell suited to address the challenges of measur-ing competitive advantage (Delmas and Tokat,2005; Durand and Vargas, 2003; Knott and Posen,2005; Lieberman and Dhawan, 2005; Majum-dar, 1998). Frontier methods represent perfor-mance by an efficiency score, calculated as thefirm’s distance to the best practice industry fron-tier. The efficient frontier is estimated directlythrough the observed input(s) and output(s) ofeach firm.

Frontier methods can be used by strategyresearchers to test theories of various factors thatlead to competitive advantage. They are alsoparticularly suited to conceptualize and measurefirm-specific capabilities. As Dutta, Narasimhan,and Rajiv (2005: 278) point out, “one can thinkof capabilities as the efficiency with which a firmuses the inputs available to it (i.e., its resources,such as R&D expenditure) and converts them intowhatever output(s) it desires . . . .”

This research note covers the two main frontierapproaches: Data Envelopment Analysis (DEA)(Banker, Charnes, and Cooper, 1984; Charnes,Cooper, and Rhodes, 1978), and the StochasticFrontier Approach (SFA) (Aigner, Lovell, andSchmidt, 1977; Kumbhakar and Lovell, 2003;Meeusen and van den Broeck, 1977).2 A fun-damental distinction between them is that DEAis nonparametric whereas SFA is a parametricapproach. This distinction makes these twoapproaches have their own specific areas ofstrength, as we elaborate.

We begin by introducing the fundamentals ofthe DEA and SFA methods. We then illustrate the

2 Several papers introduce both SFA and DEA (e.g., Coelliet al., 2005; Hjalmarsson, Kumbhakar, and Heshmati, 1996;Murillo-Zamorano, 2004). These sources provide informationfrom a technical or economic standpoint without specific focuson strategic management.

Copyright © 2013 John Wiley & Sons, Ltd. Strat. Mgmt. J., 36: 19–36 (2015)DOI: 10.1002/smj

Production Frontier Methodologies in Strategic Management Research 21

methodologies with data on U.S. and Japaneseautomobile producers. This illustration demon-strates the advantages of the frontier methods aswell as caveats that researchers should considerwhen applying these methods or interpretingworks that make use of them.

FRONTIER METHODOLOGIES

In frontier methodologies, a firm’s performance ismeasured in terms of distance from the industry’sefficient frontier. The efficient frontier is a functionthat indicates the maximum attainable level ofoutput corresponding to a given quantity of input.The frontier is estimated based on the observedinputs and outputs of all firms in the industry (ora representative sample). For example, considerfirms that employ two inputs, labor and capital,to produce one or more outputs, such as cars,trucks, and consumer loans. The efficient frontierrepresents the maximum amount of output(s) thatcan be produced from a specific amount oflabor and capital. Each firm’s relative efficiencycan be defined, based on the distance betweenthe firm’s actual output and the estimated “bestpractice” frontier (e.g., expressed as the ratio ofthe firm’s observed output relative to the fullyefficient output). DEA and SFA are two alternativeapproaches through which the industry-efficientfrontier and the firm-specific efficiencies can beestimated.

Basic DEA model

DEA generates the efficient frontier through amathematical optimization model (Banker et al.,1984; Charnes et al., 1978). The DEA frontieris a linear surface or “piecewise hyperplane”extrapolated from all efficient firms in the samplesuch that the inefficient firms are “enveloped”by the frontier. We illustrate the DEA frontierin Figure 1(a), where we consider a simple casewith one input and one output variable for sevenfirms (firm a to firm g). The figure depictsthis frontier, along with the input and output ofthe seven firms. The DEA frontier is the lineemanating from the origin O through firm a , whichcorresponds to the highest ratio of output to input.The area below the frontier consists of feasible

(a)

(b)

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

yet inefficient input–output combinations.3 Firma is therefore efficient, while firms b to g thatare below the frontier are inefficient. Figure 1(a)also contains an OLS regression line with theintercept set to 0. It illustrates that the OLS modelwould underestimate the frontier because it doesnot permit inefficiency and assumes that deviationfrom the average input-output correspondence ispurely random.4

3 Here we assume the production technology has constantreturns-to-scale (CRS), which, in the presence of multiple inputsand outputs, means that a proportional change in a firm’s inputs(e.g., all inputs are increased by 50%) should lead to the sameproportional change in a firm’s outputs (all outputs shouldincrease 50%).4 See Coelli et al. (2005: 258–259) for statistical tests for theexistence of inefficiency effects.



Inefficiency is measured by a firm’s distanceto the frontier. For example, the DEA efficiencyscore of firm f is calculated as Oi (observedoutput level) divided by Oi ∗ (efficient outputlevel given firm f ’s input). Therefore firm f isinefficient with an efficiency score less than one.5

Firm a is on the DEA frontier and thereforeit is efficient with an efficiency score of one.The DEA model works similarly when there aremultiple outputs; in that case the efficiency scoreis calculated as the possible percentage increase of“all outputs,” given the current input. We providedetailed mathematical formulations of DEA inAppendix 1.

As shown in the above example, the DEA effi-ciency score is calculated based on input andoutput quantities. In the presence of multipleinputs and outputs, prior studies show that inad-vertent aggregation of different performance mea-sures can sometimes result in overlooked com-petitive strength in some performance dimensions(Chen and Delmas, 2011; Ray et al., 2004). DEAdoes not require explicit weight specifications orassumptions about the production function andprobability distributions for technical inefficiency.The DEA model calculates weights for eachfirm through an optimization procedure, which isdetailed in Appendix 1. The weights are calculatedbased on which input(s) a specific firm excels atutilizing, or which output(s) a firm excels at gen-erating in comparison to the other firms in thesample. By assigning higher weights to the inputand output variables a specific firm excels in utiliz-ing or generating and low weights to the others, thealgorithm maximizes the performance of each firmin light of its particular competence.6 In addition,

5 The DEA model used to measure output inefficiency ispresented in (7) in Appendix 1. We should note that theefficiency score obtained from formulation (7) (i.e., the θoutput )is the reciprocal of our definition provided here, and the scoreis greater than or equal to 1. For example, firm b’s DEA scorefrom formulation (7) is equal to Oi ∗/Oi , which is greater than1. We provide a more in-depth discussion in Appendix 1.6 This flexibility in the assignment of weights can lead to asituation where a large proportion of firms are found to beefficient or a specific firm appears efficient because it specializesin a few rather than most outputs or inputs, and thus DEA losesits discriminatory power. Lack of discriminatory power can alsooccur when the number of input and output variables is highrelative to the sample size: having more variables increases thelikelihood that firms are found efficient because DEA optimizesthe weights of their “niche” inputs or outputs. If we have priorknowledge about the relative importance of inputs and outputs,it is possible to constrain the weight of one input or output

DEA does not specify a specific production func-tion, and the efficiency scores are obtained fromsolving linear programming problems. This featureenhances the computational convenience of DEAand reduces the risk of model misspecifications,but the trade-off is that DEA is a deterministicapproach and can be sensitive to outliers.

Basic SFA model

In contrast to the DEA frontier, the SFA spec-ification involves a production or cost functionwith an error term that includes two compo-nents: a random noise effect and an inefficiencyeffect (Aigner and Chu, 1968; Aigner et al., 1977;Meeusen and van den Broeck, 1977). The stochas-tic efficient frontier assumes that production out-puts are subject to random shocks that are notunder the direct control of firms. Specifically, letyit denote the output of firm i produced at timet , and let X it = (x it1,x it2, . . . ,x itm ) be the collec-tion of m inputs or resources consumed for thepurpose of producing yit . For example, a firm’sinputs may include its capital assets and employ-ees, and the output can be revenue, value-added(revenue minus materials costs), or physical quan-tity of output. The stochastic production functionwith panel data is given by

yit = f (Xit ) eνit e−μit (1)

On the right-hand side of (1), there are threecomponents. The first involves a production func-tion f that transforms input factors X it into outputwithout any loss due to inefficiency. The secondand the third components represent the randomand stochastic inefficiency factors that capture thedifference between the observed output, yit , andf (X it ), the output that a fully efficient firm i wouldsecure in the absence of uncertainty. Specifically,ν it is the random error assumed to be i.i.d. stan-dard normal N

(0, σ 2

ν

), and μit represents the inef-

ficiency effect, which is nonnegative and oftenassumed to follow a half-normal distribution (i.e.,∣∣N (

0, σ 2μ

)∣∣) (Coelli et al., 2005; Kumbhakar and

relative to that of another in the DEA models. For example, wecan impose that the weight of input A must be three times tofive times higher than that of input B. Note that when weightrestriction constraints are imposed, the efficient frontier andtherefore the efficiency scores would both change. See Cooper,Ruiz, and Sirvent (2011) for a detailed discussion about weightrestriction methods in DEA.



Lovell, 2003).7 The production function f (X it ) iscommonly assumed to be a Cobb-Douglas produc-tion function,8 which enables us to rewrite (1) as

yit = eβ0

⎛⎝ m∏

p=1

xβpitp

⎞⎠ eνit e−μit (2)

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

log yit = β0 +m∑

p=1

βp log xitp + νit − μit (3)

We illustrate the SFA frontier model (3) inFigure 1(b), which considers the same firms ato g that appeared in Figure 1(a). The frontierdisplayed in Figure 1(b) is determined based onmaximum likelihood estimation (MLE) of theparameters β, and observations therefore deviatefrom the frontier as a result of joint effect of therandom noise and inefficiency. The constant termβ0 is negative, indicating there is a minimal inputrequirement before any output can be produced.For firm a , the net effect from inefficiency andnoise is positive, and therefore firm a is abovethe frontier f (X it ). For other firms, the net effectis negative and they are below the frontier andinefficient. The inefficiency of firm i at time periodt can then be calculated as

TEit = e−μit (4)

In implementation, the separation of the inef-ficiency effect from the random noise effect ismade possible by the distributional assumptions,which allow the efficiency index in (4) to beestimated.

7 Other distributional assumptions for the inefficiency termshave also been used in the literature, including gamma andexponential distributions. The choice of distributions mayinfluence the predicted firm efficiency score, but not efficiencyranking (Coelli et al., 2005: 252). The z-test or the likelihoodratio statistics can be used to test whether the half-normal SFAmodel is adequate; see Coelli et al. (2005: 259).8 The Cobb-Douglas function is a widely used functional formto specify the relationship between multiple inputs to an output.However, there are other functional forms in common use. Forexample, Knott and Posen (2005) adopt the Translog functionin their SFA model. See Coelli et al. (2005) p. 211 for a list ofcommonly used functional forms.

The SFA frontier can be contrasted with theDEA frontier in Figure 1(a), where all firms areon or below the frontier and are driven belowthe frontier only by the inefficiency effect. Thepositions of firms in the SFA model are determinedby both the inefficiency effect and the randomerror. Firms can temporarily lie above the frontiergiven the random error ν it . Another importantobservation is that, since the inefficiency term μit

is a continuous random variable, we will observeμit = 0 (so TE it = 1) with a zero probability,which means we will not observe any firms onthe SFA efficient frontier. In contrast, we canidentify at least one firm on the DEA efficientfrontier.

The SFA approach requires an assumption onthe functional forms of the production functionand the inefficiency term, whereas DEA onlyrequires much weaker assumptions on the pro-duction possibility set, such as convexity andminimal extrapolation (Banker et al., 1984). SFArecognizes that there may be errors in data ormeasurement of the underlying efficiency. DEAassumes that there is no random error in themodel, and therefore any error and statistical noisewill be reflected in the efficiency score. Anotherweakness of DEA is that it defines the fron-tier of the most efficient firms within the sam-ple; if the sample is too small, the frontier maynot be representative of the potentially most effi-cient frontier of the industry because of missingobservations.

DEA and SFA in the strategy literature

We compare various features of DEA and SFAin Table 1 and describe how these methods havebeen used in the strategy literature based on ananalysis of studies published in three prestigiousjournals: Strategic Management Journal , Academyof Management Journal , and Management Sciencelisted in Appendix 3. In these studies, the mostrepresented industries are the financial and elec-tric utility sectors. This mix of industries is similarto that of the more general DEA literature, whichalso includes many studies of airlines and health-care (see, e.g., Chilingerian and Sherman, 2004).Because these industries are highly regulated, pub-licly available data on outputs and resource inputsare more readily available to researchers than inother industries.



Table 1. Comparing DEA and SFA

Implementation aspects DEA SFA

Frontier shape The DEA frontier is a piece-wise linearsurface.

The SFA frontier follows a specificfunctional form (e.g.,Cobb-Douglas, translog).

Applicable to multipleoutputs

DEA allows for multiple outputs in theproduction function. However, includingadditional outputs may decrease thediscrimination power.

Production frontier model requiresthat output be specified as a singlemeasure; cost frontier model canaccommodate multiple outputs.

Statistical assumptions DEA is a deterministic approach andtherefore does not require assumptionsabout the probability distributions ofparameters.

SFA requires a priori specification ofthe model, including thedistribution form of theinefficiency term.

Sampling errors The DEA efficiency score is confoundedwith both statistical noise andinefficiency; it is also more susceptible tothe influence of sampling errors andoutliers.

SFA incorporates a statistical errorterm in the formulation.

Panel data structure Panel data can be incorporated withassumptions on total productivitychanges.

SFA can make use of the panel datastructure.

Hypothesis tests for theimpacts of inputs andexogenous factors onoutputs

DEA generates the efficiency score only. Toestimate the impacts (coefficients) ofinputs and exogenous factors on outputs,it is necessary to fit an auxiliaryregression model that uses the DEAefficiency score as the dependent variable.

SFA can estimate the marginalinfluence of each input andexogenous factors on the output.

Computation The DEA efficiency score can be easilyobtained by solving a number of linearprogramming problems.

SFA relies on maximum likelihoodestimation; ill-structured data ormisspecification of the SFA modelcan lead to numerical problemswhen estimating the coefficients.

In the strategic management field, it is oftenof crucial interest to seek an explanation for afirm’s performance deviation below the leadingfirms in the industry. One technique applicableto both the DEA and SFA models is to proceedwith the analysis in two stages. In the firststage, the DEA or SFA models calculate theefficiency scores of the firms in the sample. Inthe second stage, the efficiency scores obtainedin the first stage are regressed on a collectionof explanatory variables.9 Eight of the studiespresented in Appendix 3 use efficiency scores asa dependent variable (Cummins, Weiss, and Zi,1999; Delmas and Tokat, 2005; Knott and Posen,2005; Knott, Posen, and Wu, 2009; Majumdar

9 The regression models commonly used in the second stageinclude the ordinary least square (OLS), censored regression(e.g., probit and Tobit models), truncated regression, and paneldata models. See the discussion in Simar and Wilson (2007) andKnott, Posen, and Wu (2009).

and Marcus, 2001; Majumdar and Venkataraman,1998; Schefczyk, 1993; Wu and Knott, 2006).

Although commonly used, this two-stageapproach is often criticized because assumptionsare required for the inferences made in the secondstage to be statistically valid. For example, Wangand Schmidt (2002) show that the SFA two-stageapproach can generate substantially biased esti-mates in both stages. To avoid these problems, arecommended option within SFA is to express theinefficiency term μit as a function of explanatoryvariables (Battese and Coelli, 1995; Liebermanand Dhawan, 2005). Here the inefficiency termμit is assume to be independently distributed as anormal distribution N

(Zitδ, σ 2

μ

)truncated below

at zero, where Z it is a vector of explanatoryvariables and δ is a vector of parameters tobe estimated.10 Thus, the econometric structure

10 This option can now be implemented within standard statisti-cal packages, such as Limdep and R.



of SFA allows for simultaneously estimatingthe impacts of inputs and exogenous factors onoutputs. The two-stage approach for DEA hasalso been criticized for lacking a sound statisticalfoundation (Simar and Wilson, 2007), althoughBanker and Natarajan (2008) show that thetwo-stage approach for DEA can yield statisticallyconsistent coefficient estimators under certaingeneral distributional assumptions. Johnson andKuosmanen (2012) further show that the estima-tors remain statistically consistent even when thefirst-stage input and output variables in DEA arecorrelated with the second-stage variables in theregression model. However, the precision of thesecond-stage estimates will decrease when thiscorrelation is high and when the data have highstatistical noise. Johnson and Kuosmanen (2012)develop a robust one-stage estimation approach toaddress some of the limitations of the traditionaltwo-stage approach for DEA.

One advantage of DEA is that it readily allowsfor multiple outputs, while SFA in the productionfrontier form described above is most applicableto a single output or aggregate measure, such assales or value added.11 In Appendix 3, we seethat almost all studies that use DEA have multipleoutputs. For example, Delmas, Russo, and Montes-Sancho (2008) in their study of the electricitysector, use three outputs that correspond to threedifferent cost and market structures: low voltagesales, high voltage sales and sales for resale.Having multiple outputs, however, also impliesthat researchers need to be careful in selecting ameaningful set of output variables for their DEAmodel. Different outputs may represent differentconceptualizations and orientations of businessperformance. Majumdar and Venkataraman (1998)present an excellent example of comparing DEAefficiency scores that are calculated based ondifferent selections of outputs.

Another advantage of DEA is that it is capableof handling inputs and outputs expressed in differ-ent measurement units. For example, Dutta et al.(2005) measured firm capabilities by using patentcounts weighted by citations as an output and R&D

11 The SFA cost efficiency model can accommodate multipleoutputs; see Knott and Posen (2005) for an illustration. OtherSFA 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 issuesregarding these models; see Chap. 10 in Coelli et al. (2005) fora further discussion.

and marketing expenses as inputs. This allowsresearchers to measure capabilities and intangibleresources, which are often difficult to approximatein monetary terms. It also allows researchers toconceptualize capabilities as the ability to com-bine efficiently a number of resources to engagein productive activity (Dutta et al., 2005).

Both SFA and DEA can incorporate panel datato estimate efficiency scores and other parameters.SFA incorporates the panel information via thetraditional econometric framework (Aigner et al.,1977; Battese and Coelli, 1995).12 In Appendix3, all the SFA studies use panel data, where costefficiency is estimated based on a pooled sampleacross the observation years (Dutta et al., 2005;Knott and Posen, 2005; Knott, Posen, and Wu,2009; Lieberman and Dhawan, 2005; Miller andParkhe, 2001; Wu and Knott, 2006).

In DEA there are two different approaches todeal with panel data. The first approach is to calcu-late the DEA scores year by year. This means thatthe DEA score of year t is determined based on thedata of year t .13 This approach is recommendedover calculating DEA scores based on multiyeardata, because incorporating multiyear data to esti-mate the frontier would raise the concern thatfirms may be compared with the best perform-ers operating under different technological condi-tions (Delmas and Montes-Sancho, 2010; Delmasand Tokat, 2005; Delmas et al., 2008; Majumdarand Marcus, 2001; Majumdar and Venkataraman,1998). The other approach is to calculate produc-tivity change between two consecutive periods inDEA by using the Malmquist productivity index(Banker, Chang, and Natarajan, 2005; Cumminset al., 1999; Fare et al., 1994). The Malmquistindex indicates how much of each firm’s total fac-tor productivity change from one period to the nextis due to frontier shift and how much is due to itsefficiency change.

Finally, for both DEA and SFA, there are anumber of software options available. We provide

12 We should note that SFA can work with a cross-sectionalsample, but maximum likelihood estimation of the modelrequires strong statistical assumptions on error components, andefficiency scores cannot be estimated consistently with a cross-sectional sample (Schmidt and Sickles, 1984).13 Recently Chen and van Dalen (2009) used a panel vectorautoregressive (PVAR) regression model to estimate the cor-relation between frontiers in different years. They incorporatedthe PVAR estimations in the first approach of calculating theefficiency scores for panel data.



Table 2. Descriptive statistics

Obs. Mean Std. dev. Min Max [1] [2] [3] [4] [5] [6] [7] [8]

[1] Value added(V, in 1982 yen)

231 1,259,776 1,909,814 42,433 7,336,333 1

[2] Capital stock(K , in 1982 yen)

231 2,530,595 4,018,201 80,327.3 1.68E + 07 0.96 1

[3] Number of employees(L)

231 135,375.3 223,921.1 7,890 846,000 0.97 0.94 1

[4] Work-in-progress/sales (WIP/sales)

231 0.02 0.02 0.00 0.12 0.18 0.18 0.22 1

[5] Value-added/sales(V/sales)

231 0.22 0.10 0.12 0.49 0.15 0.11 0.16 0.41 1

[6] Production volumeper plant (Q/N)

231 313,766.3 172,986.8 89,926.52 842,474.6 −0.12 −0.09 −0.10 −0.27 −0.49 1

[7] Number of trucksproduced

231 579,512.5 491,572.6 88,300 2,200,886 0.86 0.84 0.76 0.13 0.13 −0.12 1

[8] Number of carsproduced

231 1,183,930 1,114,576 25,532 5,285,700 0.75 0.65 0.73 0.15 0.19 −0.06 0.63 1

a list of commonly used of software packages inAppendix 2.

ILLUSTRATION: JAPAN AND U.S.AUTOMOTIVE SECTORS

Data

To illustrate the DEA and SFA methodologies,we use data from the U.S. and Japanese automo-tive sectors from 1977 to 1997 (Lieberman andDhawan, 2005).14 Performance of the automotivesector has been of significant interest to strategyresearchers (Dyer, 1996; Jiang, Tao, and Santoro,2010), and the U.S. and Japan represented the topmotor vehicle producing countries in the worldduring the sample period (OICA, 2005–2006). Thedata contain a balanced panel of 11 automobileproducers and their input and output variables. Wespecify one SFA and two DEA models. In theSFA and the first DEA model, we consider twoinputs, capital and number of employees , and oneoutput, value-added .15 Descriptive statistics of the

14 Data for Japanese companies are from annual issues of theDaiwa Analyst’s Guide. The Japanese data are limited to motorvehicle production within Japan; all transplant operations outsideof 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 inLieberman and Dhawan (2005).15 Value-added represents the monetary value created andretained by the firm and is calculated as the firm’s sales duringthe fiscal year minus the costs of purchased materials andservices.

inputs and outputs are provided in Table 2. We alsocompare the results of our efficiency frontiermodels with a more traditional profit measure.

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 theproduction technology exhibits constant returns-to-scale (CRS) in the DEA model. The CRSassumption implies that, regardless of firm size,expansion or reduction of a firm’s inputs bya factor will lead to the same proportion ofchange in the firm’s outputs. We assume CRSbecause the CRS technology is more intuitivewhen represented in graphics and also becauseour cross-sectional sample size is relatively small.Methods to impose a variable returns-to-scaleassumption in DEA are described in Appendix 1.Summary statistics of the efficiency scores areprovided in Table 3.

Figure 2 contains a three-dimensional scatterplot 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 figurerepresent each firm’s trajectory to its efficientbenchmark on the frontier. As in Figure 1, firms’efficiency scores are calculated as the “observedvalue-added” divided by “efficient value-added.”In this case efficiency scores range from 0.43



Table 3. Summary of efficiency scores and financial rate of return (full sample)

Model Input variables Output variables Obs. Mean Std. dev. Min Max [1] [2] [3]

[1] DEA Capital stock, andno. of employees

Value-added 220 0.797 0.161 0.348 1 1

[2] SFA Capital stock, andno. of employees

Value-added 220 0.886 0.1259 0.412 1 0.562** 1

[3] Financial rate 220 0.1684 0.1838 −0.53 0.86 0.439** 0.294** 1of returns(operatingprofit/netproperty, plantand equipment)

**Correlation coefficients significant at the one percent significance level.

to 1, which represents firms on the efficiencyfrontier. The results show that Honda and Toyotahave scores of 1 and are on the 1997 efficientfrontier. The frontier under the CRS assumptionis a plane containing these two firms and theorigin. The efficient output levels for inefficientfirms are points on the frontier that have the sameinput 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 capitalstock; 627,500 employees; and $6.6 billion ofvalue-added. GM’s efficiency score in that yearis 0.43. Based on the efficiency score, we cancalculate GM’s efficient level of output (value-added) as: $6.6 billion/0.43 = $15.3 billion.

DEA allows the inclusion of multiple outputvariables. Similar to the single-output DEA, themultioutput DEA calculates efficiency scores bymeasuring the distance between a firm and theefficient frontier in the multidimensional space. Inaddition to value-added, we could, for example,introduce the number of trucks and the numberof cars produced. Thus, outputs can be measuredin terms of physical quantities or monetary val-ues. When longitudinal panel data are available,we can also graphically depict how the industryefficient frontier changes over different time peri-ods. To measure the productive changes of individ-ual firms, however, we need to account for boththe efficiency change (i.e., relative position to theefficient frontiers in two periods) and the frontiermovements. Under the DEA framework, a com-monly used approach to calculating productivitychange is the Malmquist productivity index thatmeasures productivity change over time; see alsoour earlier discussion about incorporating paneldata in DEA.

SFA model

In the SFA model we use capital stock andnumber of employees as the inputs and value-added as the output. In the inefficiency com-ponent of this SFA model, we follow Lieber-man and Dhawan (2005) in using volume perplant (Q /N ), Work-in-process/sales (WIP /sales)and value-added/sales (V /sales) as the explana-tory variables for productive inefficiency. Ourchoice of variables in the production functionmodel of SFA also follows Lieberman and Dhawan(2005). The first variable (Q /N ) provides a mea-sure of plant scale, through which we can testwhether scale economies at the level of individ-ual manufacturing plants affect firms’ efficiency.The second variable (WIP /sales) serves as a proxymeasure of factory management skills, as a largeWIP/sales ratio implies that firms need to main-tain a high inventory level to counter disruptionsin 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

log Vit = β1t + β2 log Kit + β3 log Lit + νit − μit

(5)where the inefficiency effect is a function ofthe three explanatory variables and a randominefficiency term:

μit = δ0 + δ1 log

(Q

N

)it

+ δ2 log

(WIP

sales

)it

+ δ3 log

(V

sales

)it

+ ωit , (6)



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



where ωit is a truncation of N (0, σ 2μ) 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, whichsuggests that firm efficiency tends to improve overtime. The coefficients of the capital and laborvariables are both significant; the sum of these twocoefficients is larger than 1 (i.e., 1.036), whichsignifies a small degree of increasing returns toscale, based on the size of the firm as a whole. Thecoefficient for plant scale (δ1) is negative and alsohighly significant, suggesting that the automakerswith larger plants in general have gained higherefficiency (i.e., economies of scale exist at the levelof individual plants, as well as for the firm as awhole). These findings are consistent with priorstudies and reaffirm that exploiting economies ofscale is an important factor in attaining efficiencyin the automotive sector (Lieberman and Dhawan,2005; Lieberman, Lau, and Williams, 1990).

In our results, the coefficients for the WIP/salesand Value-added/sales ratios are both insignificant.These results differ slightly from those in Lieber-man and Dhawan (2005), which apply SFA to datafrom the automotive sector from 1965 to 1997.This might be due to a difference in the timeframe observed since our panel starts in 1977,

Table 4. Parameters estimates of the SFA model

Dependent variable: value-added

Independent variables Coefficient Std. error.

Production function modelTime parameter (β1) 0.025** 0.004No. of employees (β2) 0.910** 0.053Capital stock (β3) 0.126* 0.058

Inefficiency modelConstant (δ0) 1.414 0.440No. cars produced per

plant (δ1)−0.819** 0.116

Value-added/sales(lag one year) (δ2)

−0.018 0.302

WIP/sales (lag one year)(δ3)

−0.045 0.094

Variance estimatesσ 2 = σ 2

u + σ 2ν 0.263 0.109

λ = σ 2u /σ 2

ν 1.69 0.193Log likelihood 76.9No. of observations 220

**Significant at the one percent level; *significant at thefive percent level.

after Japanese producers had made their majorinventory reductions.

DEA, SFA and profit

The DEA and SFA efficiency scores are sum-marized in Table 3. The significant correlationbetween these scores implies that they capture sim-ilar notions of firm performance in the case ofour automotive sample. But to what degree arethese measures of efficiency related to companyprofitability? To answer this question we used theavailable data to compute an annual financial rateof return (operating profit/net property plant andequipment) for each of the 11 automotive com-panies. Table 3 shows that this measure of profitis also significantly correlated with DEA and SFAbut to a lesser level.

In order to further compare these measures, weranked the 11 firms based on the three alternativeperformance measures: DEA score, SFA score, andfinancial return. The results of this ranking areillustrated in Figure 3, where we have aggregatedthe data by country of origin. The contrast betweenU.S. and Japanese producers is striking. For theJapanese producers, the efficiency score rankingsare uniformly higher than the profit rankings. Thereverse is true of the U.S. producers (except duringthe U.S. recession of the early 1980s).

How did the Americans sustain these highfinancial returns despite comparatively low levelsof efficiency? Although our analysis cannot answerthis question directly, a better understanding ofthe U.S. political economy of the time can helpus understand what happened. One major reasonrelates to tariff protection of a key segment:trucks and SUVs. The United States protectsits domestic market of trucks and vans witha 25 percent import tariff while regular carsonly face a tariff of 2.5 percent (Ikenson, 2003).This protection allowed the Big Three U.S.manufacturers to dominate the U.S. market withmore than 85 percent of pickup truck sales andbenefit from high profit margins (Ikenson, 2003).These margins were particularly high from themid-1980s to the early 2000s, when oil pricesremained low favoring the development of themarket for nonfuel efficient vehicles.

While the U.S. car manufacturers were protectedby high trade tariffs, Japanese automakers investedin efficiency improvements. In their comparisonof a U.S. and a Japanese car plant, Abegglen and



12

34

56

78

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23

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67

89

1011

78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97

U.S. firms

Japanese firms

Profit ranking SFA ranking DEA ranking

Ave

rage

ran

king

Year

Figure 3. Efficiency and profit scores rankings

Stalk (1985: 105) show that U.S. plants needed250 percent as many employees as the Japaneseone to make a vehicle. The crucial differencewas that the Japanese car manufacturers developedlean production systems whereas the U.S. carmanufacturers were slow to do so (Womack, Jones,and Roos, 1990). In the 2000s, when high gasprices shifted the market toward more fuel efficientcars, the big three automobile manufacturers,which had specialized in building trucks, wereunable to respond adequately.16

In general, our application of DEA and SFA to apanel dataset on 11 U.S. and Japanese automobileproducers illustrates several features of frontiermethodologies, as well as issues to be consideredin their application. Most fundamentally, we show

16 To further explain the patterns in Figure 3, we regressedthe company profit rates and efficiency scores on a seriesof variables, including the firm’s degree of focus on trucks(measured as annual production of trucks and SUVs as aproportion of total vehicle output). These regressions showedthat firms’ profit rates were strongly and positively linked totruck production, whereas the DEA and SFA efficiency scoreswere not. Thus, truck and SUV production was unrelated toefficiency but highly related to profitability, particularly for theAmerican companies.

how the methods characterize the distance of firmsfrom the frontier defined by the most efficientcompetitors (typically, Toyota and Honda in mostyears of our sample). The automotive exampledemonstrates the ability of DEA to accommodatesimultaneously multiple performance measuresand the ability of SFA to incorporate tests ofhypotheses about sources of advantage withoutresorting to a separate stage of statistical analysis.The example shows how corporate performancebased on efficiency differs from profitability basedon pricing power derived from barriers to entry.

CONCLUSION

Performance measurement is at the heart of strate-gic management research. This paper has providedan overview on the frontier methodology as a toolfor performance measurement by strategic man-agement scholars. Specifically, we have introducedthe two most prevalent frontier methodologies,Stochastic Frontier Analysis and Data Envelop-ment Analysis , and offered a comparative discus-sion regarding the strengths and limitations ofthese two approaches.



The DEA and SFA methodologies provide away of characterizing competitive advantage in anindustry. Both methods focus on firms’ efficienciesin converting inputs to outputs, and both allowresearchers to identify top performing firms, whichlie on or near the industry best-practice frontier.DEA and SFA estimate the best-practice frontierand quantify the gap between the observed firmand the frontier (i.e., inefficiency). The efficiencyscore of a firm is defined as the ratio between thefirm’s present performance and the performancethat the firm would have achieved if it were fullyefficient, based on the estimated frontier.

By providing a technique to assess efficiency,the frontier methods described in this paper enablean understanding of firm performance that isdeeper than a mere comparison of company profits.Indeed, as we demonstrate, the major Americanautomotive companies exhibited relatively strongfinancial performance in the 1980s and 1990s,even though their Japanese rivals maintainedhigher efficiency. But when the market segmentsthat sustained the U.S. producers— trucks andSUVs—contracted in the wake of increasing oilprices, the financial performance of the U.S.companies collapsed, leading ultimately to thebankruptcy of General Motors (GM) and Chrysler.

We see a great potential for the use of fron-tier methodologies in strategy research. Two dif-ferent views on the sources of corporate prof-its have dominated strategy research: the indus-try view and the firm-efficiency view (McGahanand Porter, 1999). In the industry view, indus-try structure drives profit while in the efficiencyview companies achieve profits in a line of busi-ness when they operate more efficiently thantheir competitors. Production frontier methodolo-gies allow researchers to assess the efficient useof resources within the existing industry structure.Our auto example illustrates both types of effects:U.S. producers earning high returns by dominatingattractive (albeit protected) market segments, andJapanese producers, such as Toyota and Honda,earning their returns through greater efficiency.

The frontier methodologies have proved partic-ularly useful when firm performance is character-ized by multiple dimensions with different units ofanalysis. A key strength of DEA lies in its capabil-ity to simultaneously incorporate multiple inputsand outputs, a requirement for analysis of manyindustries and for studies that seek to incorpo-rate nonfinancial measures of performance. It also

allows the incorporation and comparison of vari-ables with different units (such as, for example,number of employees, tons of input, and dollarsof profit). By comparison, SFA is most applicablewhen multiple outputs can reasonably be aggre-gated into a single measure or when price andquantity data are available for inputs and outputsso that a cost frontier model can be estimated. Forproblems with limited dimensions, the methodscan provide an intuitive graphical interpretation ofthe efficient frontier in the industry and the sam-pled firms’ relative distances.

DEA and SFA have wide potential applicationsin strategic management research. They providevehicles for characterizing performance in waysthat go beyond conventional analysis of commonfinancial measures. For example, the ability ofDEA to deal with multiple outputs and differ-ent units may be particularly useful for resource-based view (RBV) analyses of heterogeneouscollections of resources, including physical capac-ities such as capital and machinery, as well asintangible properties such as technological know-how and managerial skills. In RBV, sustainedcompetitive advantage is resulted from leveragingthe organizational resources and capabilities thatare valuable, rare, inimitable, and nonsubstitutable(Barney, 1991; Newbert, 2008). What constitutes“valuable and inimitable resources” depends onboth the distribution of the critical resources in theindustry and the standing of a firm among its com-petitive peers. The ability of DEA to include suchresources in a comparative way is well suited forRBV analyses when suitable measures are avail-able. DEA and SFA can also facilitate the devel-opment of newer areas of strategic managementresearch. For example, the field of frontier method-ologies has seen emerging extension to topics suchas the measurement of eco-efficiency and corpo-rate social performance, where some of the outputsmay be undesirable (such as pollution, labor issues,etc.; see Chen and Delmas, 2011, 2012; Rein-hard, Lovell, and Thijssen, 2000). We encouragestrategic management researchers to exploit fron-tier methodologies to explore agendas in these andother topic areas.

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APPENDIX 1: MATHEMATICALFORMULATIONS OF DATAENVELOPMENT ANALYSIS

(7) Max θoutput1

Subject ton∑

j=1

λj xji ≤

x1i for i = 1, . . . , mn∑

j=1

λj yjr ≥ θoutput1 y1r

for r = 1, . . . , sλj ≥ 0 for j = 1, . . . , n

(8) Min θinput1

Subject ton∑

j=1

λj xji ≤

θinput1 x1i for i = 1, . . . , mn∑

j=1

λj yjr ≥ y1r for

r = 1, . . . , sλj ≥ 0 for j = 1, . . . , n



The DEA formulations are shown in (7) and(8). In the Models x ji and yjr denote the i-th input and r-th output of firm j , respectively.Depending on whether the efficiency pertains toinputs or outputs, we have a choice between theoutput- or input-oriented DEA models. Model (7)is called the output-oriented DEA model, becausethe efficiency score θ1 is attached to the outputs offirm #1. For firm #1, for example, l (7) attempts toincrease firm #1’s outputs by maximizing θ

output1 ,

given the inputs x1i , i = 1, . . . , m . An output-oriented inefficient firm can increase its outputlevels with its current input consumption level (i.e.,the optimal value of θ

output1 will be larger than 1).

The efficiency scores of efficient firms are equalto 1.

Model (8) is the input-oriented DEA model.In (8), the efficiency score θ1 is attached tothe input variables, and the objective functionseeks to reduce inputs by minimizing θ

input1 ,

given a firm’s current output level. An input-oriented inefficient firm can reduce its input usagewhile maintaining its current output level (i.e.,the optimal value of θ

input1 is less than 1). The

efficiency scores of efficient firms in the input-oriented model are also equal to 1. We assumethat the production technology in (7) and (8) hasconstant returns-to-scale (CRS), which implies that

the marginal rate of transformation between inputsand outputs is constant. Therefore the optimalvalue of θ

output1 and θ

input1 in the CRS model are

reciprocals of each other (i.e., θoutput1 = 1/θ

input1 ).

The variable returns-to-scale (VRS) DEA modelcan be implemented by adding an additional

constraintn∑

j=1λj = 1 to the CRS DEA model

(Banker et al., 1984). This additional constraintmakes the VRS efficiency score closer to 1 thanthe CRS score, and thus firms are closer to theefficient frontier in the VRS model.

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

APPENDIX 2: SOFTWARE PACKAGESFOR DEA AND SFA

Below is a partial list of the software programsfor implementing DEA and SFA models. SinceDEA models are linear programming problems, theDEA algorithm can be implemented in most opti-mization programs with the basic programmingfunctionality.

Software Developer Website

FEAR: frontier efficiencyanalysis with Ra

Paul Wilson http://www.clemson.edu/economics/faculty/wilson/Software/FEAR/fear.html

DEA Frontier Joe Zhu http://www.deafrontier.net/(add-in for Microsoft Excel)DEAP, Frontiera Tim Coelli http://www.uq.edu.au/economics/cepa/software.htmFrontier analyst Banxia software http://www.banxia.com/frontier/Limdep Econometric Software, Inc. http://www.limdep.com/Ra Freeware http://www.r-project.org/Stata Stata Corp. http://www.stata.com/Limdep Econometric Software, Inc. http://www.limdep.com/SAS SAS Institute Inc. http://www.sas.com/

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



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