Empir Econ(2010)38:119–137DOI10.1007/s00181-009-0258-xORIGINAL PAPERAnalysis of product efficiency in the Korean automobile market from a consumer’s perspectiveInha Oh·Jeong-Dong Lee·Seogwon Hwang·Almas HeshmatiReceived:15June2007/Accepted:16November2008/Published online:31January2009©Springer-Verlag2009Abstract In this study we develop and describe a conceptual and methodological framework to measure technical and allocative efficiency at the product level consider-ing consumer choice,which encompasses overall efficiency.Empirically,we combined data envelopment analysis and a discrete choice model in order to measure efficiency levels.The suggested framework is applied to the Korean automobile market.The relationship between the level of efficiency and market performance is discussed in terms of market share.Keywords DEA·Product efficiency·Consumers utility·Automobile market·South KoreaJEL Classification C14·C25·D13·D61·L921IntroductionPorter(1990)previously cited four key factors of the competitiveness of an economic agent:(1)firm strategy,structure and rivalry;(2)factor conditions;(3)related andI.Oh(B)Korea Energy Economics Institute,665-1,Naeson2-dong,Uiwang-si,Gyeonggi-do437-713,Koreae-mail:ioh@keei.re.kr;whistle3@snu.ac.krJ.-D.Lee·A.HeshmatiTechnology Management,Economics and Policy Program(TEMEP),Seoul National University,San56-1,Shillim-Dong,Gwanak-Gu,Seoul151-742,South KoreaS.HwangScience and Technology Policy Institute,Specialty Construction Center26F/27F,Shindaebang-dong,Dongjak-gu,Seoul156-714,South Korea120I.Oh et al. supporting industries;and(4)demand condition.Among them,the demand condition plays a significant role,driving the producer to innovate.The demand condition con-sists of a mix of consumer needs and the consumer’s ability to distinguish products with lower prices and superior quality.Afirm producing products that match consumer needs will make a profit,and will thus enjoy an increased likelihood of survival.Thus, if we know how accurately a given product conforms to the needs of the consumer, we can better understand the competitiveness of thefirm that produces that product. This workfirst requires a systematic framework by which consumer needs may be analyzed at the product level.Unfortunately,there has been little progress in research designed to analyze the products from the perspective of consumers.We canfind some research which investigates the competitiveness of products by comparing prices with quality.In this research,the product is described as a point in the price-quality space,a conceptfirst described by Lancaster(1966),after which a frontier is constructed which consists of products with the lowest price and highest quality.The competitiveness of a product has been measured by the distance between the product and the frontier.Papahristodoulou(1997),Fernandez-Castro and Smith (2002),and Lee et al.(2005)among others,have pursued this avenue of research. They referred to the measured index as the degree of efficiency or,in short,technical efficiency.If a product has a higher price and lower quality,the product will not be selected by consumers able to discern the difference between products.In this regard,prod-uct efficiency is one of the determining factors of market performance with regard to market share.However,we frequentlyfind that an efficient product is not selected by consumers,even when it has the highest quality and lowest price.This is not due to the absolute level of quality,but because the mix of qualities does not match the con-sumer’s preference structure.In this regard,there remains the possibility of allocative efficiency,in addition to that of technical efficiency.The technical efficiency refers to the distance between the position of a product and the frontier in the price-quality space.The allocative efficiency refers to the degree of match of quality mix with the preference structure.If we know the allocative efficiency of products,we will know which products provide the highest utility.However,there has been little discussion regarding allocative efficiency at the product level from the consumer’s perspective.This research is,to the best of our knowledge,thefirst to introduce the concept of allocative efficiency at the product level.Fortunately,we can utilize the recent devel-opment of the discrete choice theory to recover the utility function on the basis of market data.This provides a basis for the measurement of allocative efficiency(i.e., the match between quality mixes and consumer preference structure).The principal contribution of this research is that it introduces the concept of allocative efficiency at the product level,and presents a framework for the analy-sis of technical and allocative efficiency with information regarding the consumer’s preference structure.Methodologically,we employ a combination of the framework of data envelopment analysis(DEA)and discrete choice theory.The proposed frame-work is then applied to the Korean automobile market.The characteristic features of the study are as follows:(1)the development of an empirical framework by which allocative efficiency can be analyzed at the product level;(2)accommodation of the discreteness of the product quality attribute,by employing the discrete version ofAnalysis of product efficiency in the Korean automobile market121 the additive DEA model;and(3)combination of the information from the estimated results of the discrete choice model with DEA to generate an integrated model that enables efficient product analysis from the perspective of the consumer.This paper is organized as follows.Section2presents the theoretical framework for technical,allocative,and overall efficiency.Section3describes the empirical mod-els of DEA and discrete choice theory.Section4explains the characteristics of the Korean automobile market and the data used in empirical analysis.Section5contains the principal empirical results,and Sect.6presents the conclusions drawn from this study.2Theoretical framework2.1Efficiencies in productionThe term defined as“technical efficiency”is utilized commonly in the literature to describe the level of performance of a production unit with regard to its utilization of input resources in generating a given set of outputs.Koopmans(1951)defined“tech-nical efficiency”as a state in which it is technically impossible to increase outputs without simultaneously reducing another output or increasing inputs.Farrel(1957) showed that the“overall efficiency(OE)”of a production unit is comprised of two separate efficiency measures,referred to as“technical efficiency(TE)”and“alloca-tive efficiency(AE)”.He also proposed a method by which the technical inefficiency could be measured as the maximum equi-proportional reduction in all inputs consistent with the equivalent production of observed output.Allocative efficiency measures the degree of match of the current mix of input with the cost minimizing input mix.Even in cases in which production unit is technically efficient,it may not be allocatively efficient.Figure1shows a production technology with two inputs(x1,x2)and a single output (y).The production technology is denoted by an input requirement set L(y).For a production unit,P,with the output level y,technical efficiency can be defined as TE=d(OQ)/d(OP),where d(OQ)is the distance from the origin,O,to point Q.If input prices w1and w2are given,the iso-cost line is denoted by w1x1+w2x2=C, which is represented by the dotted line in Fig.1.In this case,we know that production at Q cannot achieve minimum cost,even though it is technically efficient by virtue of its location on the production frontier.The inefficiency due to an inappropriate mix of inputs(allocative efficiency),can be defined as AE=d(OR)/d(OQ).The overall efficiency is the combination of both technical efficiency and allocative efficiency, such that OE=d(OR)/d(OP).The above discussion can be applied to the definitions of efficiencies at the product level from the consumer’s perspective in the following discussion.2.2Efficiency in consumptionThe framework of cost minimization compels us to define technical,allocative,and overall efficiency on the production side.If we employ the framework of utility122I.Oh et al. Fig.1Technical(OQ/OP),(OR/OP)efficiency inproduction sideFig.2Technical(OI/OJ),allocative(OJ/OK)and overall efficiency(OI/OK)in consumption sidemaximization,then we can define the same efficiency terms on the consumption side.1 This is illustrated in Fig.2.In Fig.2,we assume that there are only two quality attributes,q1and q2.All prod-ucts in the market are assumed to have the same price.Each of the points I,J,K and U1Cost minimization on the production side corresponds to the expenditure minimization on the consumption side.Instead of expenditure function,we directly employ the utility function in this study.Analysis of product efficiency in the Korean automobile market123 denotes a product,and the solid line shows a frontier or boundary of the consumption possibility set faced by the consumers.As the prices are the same,any point on the consumption possibility set requires an equal expenditure to consume a product.Thus, we can alternatively refer to this consumption frontier as the budget line.In this case, the technical efficiency of product I can be defined as TE=d(OI)/d(OJ).If we understand the indifference curve or iso-utility curve,then we know the prod-uct or combination of products that yields the highest utility with a given budget.For example,in Fig.2,where the indifference curve is shown by a dotted line,product U provides the highest utility to the consumer among all the products observed in the market.Then,the allocative efficiency of the product I can be defined as the utility difference between product J,which is a projection to the frontier of product I,and product U.More formally,the allocative efficiency of product I can be expressed as AE=d(OJ)/d(OK).In a fashion similar to that of production analysis,the overall efficiency of product I can be defined as OE=d(OI)/d(OK).The above discussion tells us that inefficiency causes consumers to obtain lower utility for equal expenditure.We also know that the utility difference can be trans-formed into monetary terms on the basis of the concepts of money-metric utility functions and marginal willingness-to-pay(WTP)(Train2003;Ley and Steel1996). This transformation will be explained in detail in the following section describing the empirical framework.3Empirical frameworkThe empirical implementation of the above discussion requires measuring the distance in the price-quality space and understanding the structure of the utility function.For the measurement of distance,although a DEA model can be employed,the discreteness of consumer choices poses certain special challenges.As consumer choices are intrinsi-cally discrete and global convexity or concavity should not be imposed a priori on the shape of the frontier,we applied the free disposal hull(FDH)models(Deprins et al. 1984).The FDH model can accommodate the discreteness of the consumer choice in the real market,and makes no assumptions regarding the shape of the frontier (De Borger and Kerstens1996),when applied with the existing DEA model.In this section,we propose a modified version of an additive model,termed the “discrete additive model”.This proposed model allows us to accommodate the dis-creteness of qualities.Further,it does not specify input or output orientation.For the utility function,we show how the framework allows us to recover the random utility function on the basis of discrete choice theory.3.1Discrete additive model for efficiency measurementThe DEA model generally builds its production frontier with a linear combination of production possibility points.When we apply that framework to a price-quality space, we should be able to account for the discreteness of the quality of the product.Consum-ers are unable to combine different qualities of products,and can select a product only among the products already existing in the markets.In order to measure the distance124I.Oh et al. in this price-quality space,Lee et al.(2005)defined the consumption efficiency con-sidering this discreteness,and suggested using the discrete range adjusted measure (D-RAM)in order to measure product efficiency.Although the model is useful for measuring technical efficiency,it cannot accommodate the concept of utility,and thus cannot be utilized to measure allocative efficiency,one of the principal missions of the current study.Cooper et al.(1999)suggested a method by which allocative efficiency and over-all efficiency could measured using an additive DEA model on the production side, thereby demonstrating that the overall efficiency of a decision making unit(DMU) can be defined as the sum of the allocative efficiency and technical efficiency.The principal advantage of the additive DEA model of Cooper et al.can be found in the combination of the input-output orientation within a single model.We modified the additive DEA model by considering the discreteness of quality in order to construct a new DEA model,referred to as the“discrete additive DEA model”.The discrete additive DEA model is quite similar to the additive model,but the weights given to the reference points can have values only of one or zero.Before discussing thefinal efficiency model,an indifference curve must be defined to describe the utility struc-ture of the representative consumer.For the ease of empirical calculation of welfare loss,we assume the following linear indifference curve,which has become a common practice of the discrete choice theory(McFadden1974;Anderson et al.1992;Train 2003).Indifference curve:β z j−αp j(1) in which z j is a matrix of the quality attributes of product j,and p j is the price of prod-uct j.The method by which the parametersαandβare estimated will be explained in the next section.Once we have determined the values of the parameters,the overall efficiency of a product indicated by subscript0from the viewpoint of the representative consumer and measured by the additive model can be expressed as follows:Maxβ s++αs−s.t.p0=p+s−z0=z−s+(2)p=P λ,z=Z λe λ=1λj∈{0,1}s−,s+:freewhere,e:unit vector,λ:vector of weights whose elements take the value of0or1,s−,s+:slack vectors between the0th product and the frontier,P,Z:matrix which contains price and quality attribute variables of all products. The solutions for(2)are designated asλ,s−,s+.Analysis of product efficiency in the Korean automobile market125 Likewise,the technical efficiency can be expressed as follows:Max e s++es−s.t.p0=p+s−z0=z−s+(3)p=P λ,z=Z λe λ=1λj∈{0,1}s−,s+:non-negativeThe solutions for(3)are designated asλ∗,s−∗,and s+∗.Now,the allocative efficiency of product0can be expressed as follows:Maxβ s++αs−s.t.ˆp0=p+s−ˆz0=z−s+(4)p=P λ,z=Z λe λ=1λj∈{0,1}s−,s+:freewhereˆp0=p0−s−∗,ˆz0=z0+s+∗and the solutions are denoted byˆλ,ˆs−,andˆs+.In order to calculate the overall efficiency of products,program(2)seeks a product which gives the highest level of utility to the representative consumer,then compares its utility level with the product under investigation(product0).In order to calculate the technical efficiency,the program(3)looks for the most technically efficient prod-uct in relation to product0on the piecewise consumption frontier,and then compares its utility level with that of the technically efficient product.For a certain product, when it is impossible tofind any product which is not more expensive and,at the same time,is not inferior in every quality attribute,the product is considered a technically efficient product.The technically efficient product is then used as a reference for all products which are not cheaper and are not superior in every quality attribute to the technically efficient product.Program(4)calculates the gap in utility levels between the technically efficient product in relation to product0,and the product which gives highest utility to the consumers,and this gap is referred to as the allocative efficiency.Figure3is introduced to more intuitively illustrate the concept.In thefigure,when we think of a single quality attribute and price space for simplicity,and assume that there are four products(A,B,C,D),then the piecewise consumption frontier can be depicted by the solid line,considering the discreteness of the product.If the linear indifference curve is drawn along the dotted line,then product C yields the highest utility level to the consumer among thefive products.If we measure the inefficiency of product D,then the arrow from D to B indicates technical inefficiency,the arrow126I.Oh et al.Fig.3Technical,allocative and overall inefficiency in price-quality spacefrom B to C indicates allocative inefficiency,and the arrow from D to C shows the overall inefficiency.Here,the inefficiency terms are expressed as the sum of slacks compared to each reference point,and as the sum of slacks increases,the inefficiency of a product also increases.3.2Recovering the utility functionAs was explained in the previous section,we should know the utility function in order to measure the product efficiency from the viewpoint of the consumer.For this purpose, we utilized the instrumental variable(IV)Logit model of the discrete choice theory, which wasfirst suggested by Berry(1994)and adopted by Wojcik(2000,2001)and Kaiser(2002).However,the IV-Logit model suffers from its restrictive assumptions regarding elasticity(Berry1994;Berry et al.1995).Recent research has suggested a moreflexible random coefficient model for product differentiation models(Berry et al. 1995;Berry et al.1999;Nevo2000).However,in cases in which the measurement of elasticity is not the primary interest,a Logit model serves well for these purposes and is less burdensome in terms of econometric estimation.In the current study,we were interested only in estimating the parameters of the utility function.Thus,we will maintain the Logit method,which is easy to estimate and requires fewer observations to generate statistically significant estimates.The IV-Logit model assumes that a con-sumer’s purchasing behavior is predicated on the following linear utility functional form,where a consumer is confronted with a differentiated product market.u i j=β x j−αp j+ξj+εi j(5)Analysis of product efficiency in the Korean automobile market127 where u i j denotes the utility of consumer i when buying product j,the vector x j defines the quality attributes other than the price of product p j,andβandαare the parameters to be estimated.The termξj denotes a quality attribute,which is known to consumers and producers,but is unknown to the researchers.The termεi j denotes an identically and independently distributed(i.i.d.)extreme value,which has a double exponential distribution.The mean utility level provided to the consumer by obtaining product j,is then:δj=β x j−αp j+ξj(6)when we assume that the consumption of the outside product is normalized to be equal to zero and the market share of product j is assumed to be the same as the purchase probability of product j,then:s j(δj)=eδj1+Jj=1eδjand s0(δ0)=11+Jj=1eδj(7)for j=0,1,...,J,in which s j refers to the market share of product j and the subscript0denotes the outside product(McFadden1973).Rearranging the terms and taking the natural logarithm of(7)leads to the Logit-type market share equation for estimation,as follows:ln(s j)−ln(s0)=β x j−αp j+ξj(8) Now,we can estimate the parameters of the utility function by regressing(8),usingξj as an error term,ln(s j)−ln(s0)as a dependent variable,and x j and p j as independent variables.We have to pay attention to the fact that the unobserved quality attribute,ξj, is surely correlated with market share and price,as the unobserved quality attributes that influence demand are also likely to affect the marginal cost.Thus,we must use IV.The instruments used in this paper are exactly the identical to those suggested by Berry et al.(1995),such as:x j,r=j,r∈Firm f x r,r=j,r∈Firm fx r(9)in which Firm f is the set of products produced byfirm f.These instruments include the quality attributes of product j,the sum of each of these quality attributes over other products made by the samefirm,and the sum of each of these quality attributes over the products produced by otherfirms.2Intuitively,these IV attempt to proxy for the degree of competition with which thefirm is confronted.By using two-stage least 2For example,if one of our quality attributes is the volume of a car,then the instrument vector for product j includes the volume of car j,the sum of volume across own-firm products,and the sum of volume across rivalfirm products.Note also that one of our quality attributes is a constant term,so that the number of own-firm products and rival-firm products become instruments.128I.Oh et al. squares(2SLS)on(8)using instruments,we can estimate the parameters of the utility function.3.3Interpretation of technical,allocative and overall efficiencyHalme et al.(1999),Korhonen et al.(2002),and Korhonen and Syrjänen(2005)devel-oped the concept of value efficiency in the framework of the DEA model.The unique contributions of their work can be seen in proposing a value function that reflects the decision maker’s preferences.They prove that,if the underlying value function satis-fies some restrictions of homogeneity and continuity,etc.,then the measured distance in the input-output space will represent the difference in overall value attainment.As we are assuming a linear utility function,which is continuous,strictly increasing and homogenous with degree one in price and qualities,we can measure the difference in value in terms of the money-metric measure of willingness to pay of consumers. In the practical DEA framework employed in this study,the proportional terms are utilized as efficiency indices for WTP differences.Under the assumption of linear random utility functional form,marginal WTP for an increment of one unit of a quality attribute equals the ratio between the parameter of each quality attribute and the price parameter(Álvarez-Farizo and Hanley2002; Lee et al.2004b).The ratio of utility between the0th product and its counterpart on the frontier can be described as follows:WTP∗/WTP0=V(z∗)−p∗V(z0)−p0(10)in which V(z0)refers to the utility level with the aggregated quality attributes of the 0th product and p0is the price of the0th product,whereas the star denotes the quality attributes and the price of a product on the frontier.The above ratio tells us the ratio between the current level of utility and its optimal level.As calculated slacks denote the difference from the models on the frontier for each quality attribute and price,each efficiency term as measured by the proportion of WTP with an efficient model can be described as follows:OE=β (z∗−s+)α−(p∗+s−)/β z∗α−p∗TE=β (z∗−s+)α−(p∗+s−)/β (z∗−ˆs+)α−(p∗+ˆs−)AE=β (z∗−ˆs+)α−(p∗+ˆs−)/β z∗α−p∗(11)where(s+,s−),(s+∗,s−∗)and(ˆs+,ˆs−)are optimal solutions of slacks for the DEA model measuring the overall efficiency,technical efficiency,and allocative efficiency, respectively,and(z∗,p∗)denotes the quality attributes and the price of the product, which is overall efficient.When we apply this normalization process,OE is equal to the product of AE and TE,and all the indices are confined in the range between zero and one.Analysis of product efficiency in the Korean automobile market129Table1Production,export, import and stock of cars in Korea(in1,000) Source:Korean Automobile Manufacturers Association Year Production Export Import Number of car stock19932,050639136,27419942,312738147,40419952,526979198,46919962,8131,210259,55319972,8181,3172010,41319981,9541,362310,47019992,8431,510611,16420003,1151,6761112,06020012,9461,5011712,91520023,1481,5103013,94920033,1781,8153114,5874Data and variables4.1The South Korean automobile marketThe automobile industry comprises a large portion of the Korean economy.Accord-ing to the statistics from the Korean Automobile Manufacturers Association(KAMA), the total number of cars produced in Korea exceeded3million per year in20033,thus making South Korea the sixth largest automobile-producing country in the world.The number of cars exported was approximately1.8million per year in2003.The percent-age of workers engaged in automobile and automobile-related industries is over10% of the total workforce.Table1summarizes the overall picture for the development of the Korean automobile industry.According to Table1,the number of domestically produced cars per year increased steadily,except in1998due to the Asianfinancial crisis.Car exports have increased, whereas imports have not increased greatly.As the economy grows,the number of cars per thousand people has also increased,from6.5in1980to214.5in2003.The Korean automobile industry can be distinguished from the automobile indus-tries of other developed economies.In the specific case of Korea,five domestic auto-mobile manufacturers4are intensively competing within a limited domestic market.5 The market share among themfluctuated fairly wildly during the Asianfinancial cri-sis.Table2shows the distribution and development of production shares of different producers.Since1994,Hyundai was responsible for nearly50%of total production shares.The production share of Daewoo exceeded30%in1998,but it endured a 3These statistics do not include licensed production outside Korea.4Thefive car manufacturers include:Hyundai,Daewoo,Kia,Samsung and Ssangyong.5The ownership of these enterprises changed significantly as they pass through the Asianfinancial crisis in1997/1998.Some of the enterprises merged one another and others made coalition with foreign auto-mobile producers like General Motors(GM)and Renault.However,their own brand names did not change throughout the analysis period and we assigned each enterprise according to their brand name for further analysis.123130I.Oh et al.Table2Development of domesticfirm’s share in total production(%)Source:Korean Automobile Manufacturers Association Year Hyundai Daewoo Kia Samsung Ssangyong199450.7917.9029.22– 2.01 199549.6720.6027.36– 2.15 199647.7122.4926.91– 2.74 199746.5027.1223.27– 2.84 199843.2632.3519.93 2.13 2.26 199944.6626.6824.630.22 3.45 200048.9620.0525.790.92 3.75 200151.3713.1428.91 2.33 4.24 200254.089.3427.70 3.72 5.12 200351.8112.6125.97 3.70 4.77bankruptcy during the Asianfinancial crisis,and subsequently its share decreased steeply.Daewoo remained in operation by entering into a coalition/merger with Gen-eral Motors in2002.The production share of Kia was nearly30%,but decreased to levels below20%in1998.Kia forged a coalition with Hyundai in1999and has now nearly completely recovered the market share it enjoyed prior to the Asianfinan-cial crisis.Samsung automobile was established in1998and merged with Renault in2000.Ssangyong focuses principally on sport utility vehicles(SUV)and premium class cars.Its market share is increasing as the result of an increased preference for SUVs,reaching approximately5%in2003.Other characteristic features of the automobile market include that the cumulative market share of foreign cars was still less than one percent in2003,and that the period of owning a car before replacement is very short as compared to other developed countries.The time for replacement is approximately3.8years on average,while the average years for replacement in the US,Japan,and France are at least8years.As the overall life expectancy of Korean cars is comparable to those of other non-Korean cars, the time difference for replacement across countries does not reflect the quality of the cars.Rather,this trend is reflective of South Korean consumers’preference for newly manufactured models.Therefore,in the Korean domestic car market,frequent model changes to keep up with the evolving tastes of consumers is an important strategy for the success of automotive manufacturers.In addition,it enhances the competitiveness of industries in the international market.4.2Data for empirical analysisIn an effort to preserve the homogeneity of consumer preferences,we confined our analysis to passenger cars only.We obtained the sales data from periodicals published by rmation regarding the price and detailed quality attributes of each car model was obtained from the magazine“car vision”.The collected data covers each quarterly period from the third quarter of1998to the second quarter of2003.This gives us a total of1,373car-model-quarter observations with140distinct car models for20quarters.Each model is distinguished by its name and version.123。
