Evolution of efficiency and its determinants in the retail sector in Spain: new evidence

Technical efficiency and itsdeterminants factors in Spanishtextiles industry (2002-2009)

Justo De Jorge-MorenoDepartment of Economics and Business, University of Alcala,

Alcala de Henares, Spain, andOscar Rojas Carrasco

Escuela de Auditoria e Ingeniería en control de gestión,Universidad de Talca, Talca, Chile

AbstractPurpose – The purpose of this paper is to provide new evidence about the technical efficiency and itsdeterminants in Spanish textile sector during the period 2002-2009. The empirical results suggest thatthe effects of trade liberalization have led to higher levels of inefficiency in the Spanish sector, due tothe lack of flexibility of firms to adjust to the environment, and perhaps to aggressive competition withfuzzy rules of the game. Controlling for specific factor like age, intensity of capital, salary by worker,regions and market share, the authors have obtained that the interaction between market share andsize indicates that as firms have more size are also more inefficient.Design/methodology/approach – In this paper, the stochastic frontier production function isconsidered, specifically, a panel data version of Battese and Coelli (1995), in which the technicalinefficiency is estimated from the stochastic frontier and simultaneously explained by a set ofvariables. This approach avoids the inconsistency problems of the two-stage approach used in otherempirical works when analyzing the inefficiency determinants.Findings – This work provides new evidence about the technical efficiency and its determinants canbe due to environmental or firm-specific factors in Spanish textile sector during the period 2002-2009.The authors have estimated the Cobb-Douglass stochastic production frontier following Battese andCoelli (1995) model to analyze an unbalanced panel.Originality/value – The empirical results suggest that the trend of the inefficiency shows a curvilinearbehavior in the form of U (turning point third-quarter of 2004). This result is related to the efficiencyanalysis through Kernel distributions (in static and dynamic form) confirmed a clear process ofdivergence. In the period 2002-2005 the efficiency of the firms analyzed maintained higher levels than the2005-2009 period where there is deterioration. This may be related to the increased competition due tothe end of the Multi-Fiber Arrangement in January 2005 and the entry of Chinese products in 2004.Keywords Efficiency, Stochastic frontier, Size, Market share, Multi-fibre AgreementPaper type Research paper

1. IntroductionOn the Uruguay Round in 1995 agreements to eliminate trade restrictions on textileswere reached and garment factories were defined by the Multi-fiber Agreement (AMF),which was replaced by the Agreement on Textiles and Clothing of World TradeOrganization. This agreement was expected to gradually both importers as exportersof textiles and clothing, because of the new situation in 2005 the sector was fullyintegrated into normal General Agreement on Tariffs and Trade (GATT) rules. This isa great change in the international trade scenario for textile manufacturers across theworld offering opportunities for penetration into markets, that have been off limitsunder the previous regime while posing threats of market loss in the face of competition

Journal of Economic StudiesVol. 42 No. 3, 2015pp. 346-357©EmeraldGroup Publishing Limited0144-3585DOI 10.1108/JES-06-2013-0085

Received 18 June 2013Revised 3 December 20139 May 2014Accepted 12 May 2014

The current issue and full text archive of this journal is available on Emerald Insight at:www.emeraldinsight.com/0144-3585.htm

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from other countries Bhandari and Ray (2012). The growing and increasingly aggressivecompetition experienced by the European textile industry from countries likeChina, India, Pakistan, Vietnam, etc., mainly based on low cost, has led to a deep crisis(Coll and Blasco, 2009).

We are interested in analyze determinants of technical efficiency in Spanish textilefirms on the microeconomic level during the period 2002-2009. The objective of thispaper is to analyze the effect on efficiency, of some organizational factors relatedto the managerial ability, to use properly and adjust capital and labor according toenvironmental conditions, as the change of the regulatory environment conditions. Sizeand Market share are included in the analysis as two of the most important factors thatcondition the organization of firms and then the degree of their efficiency. Our papercontributes to the empirical evidence of efficiency in Spain, adding to the previous papersthe relevance of changes affecting the factors of production and the way these factors areused and combined. Second, our paper differs from previous literature in Spain by the waythat we use an improved frontier model that not only allows us to estimate the firm’stechnical inefficiency but, simultaneously, it identifies the variables that are statisticallyrelated to inefficiency, i.e. the determinants of the reached inefficiency.

For this purpose, we want to explain firm differences in efficiency, following themethodology proposed by Lieberman and Dhawan (2005), which tries to connectthe resource-based view of the firm and the frontier analysis, specifically; we applyBattese and Coelli’s (1995) model. This frontier model not only allows us to estimate thefirm’s technical inefficiency but, simultaneously, to identify the variables that arestatistically related to inefficiency, to avoid the econometric problem of the two-stepprocedure. By using frontier techniques, several studies have analyzed both externaland internal factors to explain the sources of technical inefficiency and with differentmodels but normally with Battese and Coelli (1992, 1993) models.

Some authors who have used the stochastic production frontier approach (SFA),in textile sector at international level are as follows: Pitt and Lee (1981) using data fromestablishments in Indonesia found a relationship between efficiency and ownership, ageand firm size. Jaforullah (1999) investigates the production technology, the possibilities ofsubstitution between, factors of production and technical efficiency of the textileindustry (handlooms) in Bangladesh. Mini and Rodríguez (2000) study the relationshipbetween size, measured by total employees and technical efficiency in the Philippinetextile industry. Goaïed and Ayed-Mouelhi (2000) investigate technical efficiencyadjusted for the age of capital and types of labor in Tunisian textile, clothing andleather. Battese and Prasada Rao (2001) conducted an empirical study to evaluate theefficiency technique in midsize and large companies, in the Indonesian garmentindustry. Kim (2003) investigates in Korean textile sector, whether technical efficiencyis related with firm size, dependency on external funds, research and developmentinvestments and exports. Kouliavtsev et al. (2007) estimate a variable elasticity ofsubstitution (VES) production function using the NBER database. Bhandari andMaiti (2007) examine the relation between both size and age with technical efficiency tofirm-level cross-sectional data on India’s textile firms. El-Atroush and Montes-Rojas(2011) examine factors that affect textile and apparel supply chain operations for firmsoperating under different technologies and ownership structures. Bhandari and Ray(2012) investigate how location, proprietary and organizational characteristics of a firmaffect its efficiency. Bhandari and Maiti (2012) observe a significant positive associationbetween a firm’s size and its technical efficiency, but no such clear relation betweena firm’s age and technical efficiency of the Indian leather firms.

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On a national level in textile sector in Spain, we only record of the works of Gumbau(1988) and Coll and Blasco (2009) who analyze the evolution of efficiency in the period1980-1986 and 1995-2005, respectively.

The structure of this paper is as follows. Section 2 presents a descriptive analysisof the data. Section 3 describes the frontier methods used to measure for firms inSpanish textile. Section 4 discusses the frontier results. Section 5 provides someconcluding remarks.

2. DataThe statistical information comes from the SABI database, produced jointly byBureau van Dijk and Informa, from the financial information that firms must presentto the firms Registration Office (BORME). This database covers all sectors ofSpanish business activity. It is highly representative of firms from 17 Spanishautonomous “communities” (i.e. regions). The study samples taken from SABI includeall the firms belonging to the Retail sale of clothing in specialized stores (CNAE 4771)(download February 2012). Our sample includes 789 firms from the SABI databaseand refers to an unbalanced panel where we have eliminated those firms, whichwe do not have two consecutive years of data for. Summary statistics of the data arepresented in Table I.

3. Methodology and model specificationOn this paper, the stochastic frontier production function is considered, specifically,a panel data version of Battese and Coelli (1995), in which the technicalinefficiency is estimated from the stochastic frontier and simultaneously explainedby a set of variables. This approach avoids the inconsistency problems of thetwo-stage approach used in other empirical works when analyzing the inefficiencydeterminants[1].

The Battese and Coelli (1995) model can be expressed as:

Yit ¼ f U Xit; bð ÞexpU Vit�Uitð Þ (1)

where Yit denotes the production of the observation in t (t¼ 1, 2,…,T) for firm i(i¼ 1, 2,…,N), Xit is a (1× k) vector of known values, function of the production inputsand other explanatory variables associated with firm i in observation t, β is a (k× 1)vector of unknown parameters to be estimated, Vit is distributed as independent andidentically distributed N(0, σv

2), and distributed independently of the Uit which arenon-negative random variables which are assumed to account for technical inefficiency

Variable Mean SD Minimum Maximum

Lnsales 6.561 1.414 2.302 14.312LnFixes Assets 4.453 1.945 0.691 13.022Lmaterials 6.063 1.436 0.682 13.745Lemployment 2.002 1.299 0.000 9.547Capital by worked 31.02 99.39 0.004 3,232.38Salary by worked 20.14 11.64 0.489 273.73Age 22.36 9.723 9 98Market share 0.0012 0.010 0.00 0.2362Source: SABI and own elaboration

Table I.Summary statistic

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in production and which are assumed to be independently distributed as truncationsat zero of the N(mit, σu

2) distribution. The mean of this distribution is:mit ¼ zitd (2)

where zit it is a p× 1 vector of variables, which may influence the efficiency, of a firm;and δ it is a (1× p) vector of parameters, to be estimated.

The production function coefficients (β) and the inefficiency model parameters (δ)are estimated by maximum likelihood together with the parameterization from Batteseand Corra (1977), replacing σV

2 and σu2 with σ2¼ σv

2+ σu2 and γ¼ σu

2/(σv2+ σu

2).Given that technical efficiency is the ratio of observed production over the

maximum technical output obtainable for a firm (when there is no inefficiency),the efficiency (TE) of firm i in year t could be written as:

TE ¼ f X it; bð Þ exp Vit�Uitð Þf X it; bð Þ exp Vitð Þ ¼ exp �Uitð Þ (3)

The efficiency scores obtained from expression (3) have a value of one when the firm isefficient and less than one otherwise.

This work assumes the Cobb-Douglas production function, with non-neutraltechnological progress[2]. In this way it is possible to observe the frontier shifting aftercontrolling for the other factors considered. In particular, the function to estimate hasthe following form:

Ln salesð Þ ¼ boþb1Ln Kitþb2Ln Citþb3Ln Eitþb4tþb5Ln Kit � tþb6Ln Cit

� tþb7Ln Eit � tþVit–Uit (4)

where the technical inefficiency effects are assumed to be defined by:

Uit ¼ d0þd1tþd2t2þd3Aþd4A2þd5K_Witþd6S_Witþd7MSþd8MS

� Size_1þd9MS � Size_2þX17

i¼1

di10RegþWit (5)

where, considering the variables in logarithms. In particular, to measure the output, theproduction of goods and services, we consider the sum of the sales and the variation insales inventory for each of the firms analyzed. K is the fixed asset as proxy capitalvariable (Coll and Blasco, 2009; Bhandari and Ray, 2012), C is materials (El-Atroushand Montes-Rojas, 2011), E is employment (Kouliavtsev et al., 2007; Bhandari and Ray,2012). These variables are converted into constant Euros using deflators from theSpanish National Statistics Institute (INE). Finally, this stochastic frontier modelincludes years of observation (t) in such a way that non-neutral technical changeis specified (see e.g. Battese and Broca, 1997). However, neutral technical change ispresent if the coefficients of the interactions between year of observation and the inputvariables are zero. Regarding the inefficiency term, t, t2 and A, A2 represents thetemporal evolution of inefficiency and age of the firm, respectively in a quadratic form.K_W and S_W represents capital per worker (the ratio of the fixes assets overemployment) and salary per worker (the ratio of personnel cost over employment). MSrepresents market share (the ratio of the sales of an individual firm over sector sales byyear). MS× Size represents the iterations between MS and size (size_1¼ 1-10 workers;size_2¼ 11-50 workers; size_3¼ firms with a number of workers higher than 50).

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Finally Reg denotes a vector of dummies capturing the 17 Spanish autonomous“communities” (i.e. regions).

The coefficients t and t2 in Equation (5) measure how inefficiency changes overtime[3]. Consequently, if δ1 and δ2 is negative and positive and statistically significant(inefficiency in the U-shaped), technical change (improving efficiency, depending on thearea where the observations were found) is observed, and δ1, δ2 can be indicated asthe coefficient of technological change in Uit. If δ1 and δ2 it is positive and negative andstatistically significant (inefficiency in the inverted U-shaped).

4. Estimation of model and resultsTable II shows the results of the model estimated simultaneously according to themaximum likelihood (Equations (4) and (5)). The data used, as mentioned above, are anunbalanced panel in the period 2002-2009 from the SABI database.

As it was mentioned in the previous section, the results shown in Table II assumea Cobb-Douglas stochastic production function, which has found ample acceptance inthe literature[4]. The χ2 is statistically significant at the 1 percent level (w234 ¼ 3.8E+05).

The positive and statistically significant coefficient of the time variable t shows theexistence of technological progress, indicating that there has been the incorporation ofproduction technologies that can contribute to improvements in the productive system,the coefficient of the variable indicates that the rate of output growth of firms in thesample is 8.9 percent annually. The elasticity of mean output with respect to the kthinput variable, for example, employment, in Equation (4) has two components:β3+ β6× t. The first component is the traditional elasticity of the output with respect tothe input, this is referred to the elasticity of frontier output, and the second componentof the elasticity is the non-neutral factor which is referred to the elasticity of thetechnical efficient (this component is zero for neutral stochastic frontier models). Theelasticities are estimated in Table III. The elasticity of mean output are all positive andstatistically significant at the 1 percent level and the elasticity of technical efficiency areonly substantial components of the elasticity of the mean output for employment,materials and fixes assets these last inputs with a negative sign. The non-neutraltechnical change across all inputs is an adequate hypothesis for this model because thehypothesis of neutral technical change: H0: β7¼ β8¼ β9¼ 0 is χ2(3)¼ 345.11 is rejectedand, also, H0: β5¼ β7¼ β8¼ β9¼ 0 is χ2(4)¼ 289.75 is rejected. Model 1 is preferred tomodel 2. Also, we accept the hypothesis of constant returns to scale (w2(1)¼ 0.31).

One of the most important stylized facts refers to the results obtained in the part ofthe error term where the explanatory variable of inefficiency, shows interesting relationand curvilinear behavior.

We now look more closely at the distribution of the firms and its relation with thetechnical inefficiency, by examining the curvilinear model from the coefficientsestimated in the model. The function is as follows:

Uit ¼ �1:45�0:21 � tþ0:04 � t2þ0:03 � A�0:00003 � A2þ0:00009 � K_W�0:08

� S_W�3035 �MS�22897 �MS � Size_1�5763 �MS � Size_2þX17

i¼1

b7Regi

The trend of the inefficiency t and t2, shows a curvilinear behavior (in U shape), since itscoefficients δ1 (−0.21) and δ2(0.04) are negative and positive, respectively, andstatistically significant at the 1 percent level. The turning point is in the middle of 2004,

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when the inefficiency began to grow. The trajectory of age also shows a curvilinearbehavior (in inverted U shape), since its coefficients δ3 and δ4 are positive andnegative, respectively, and statistically significant at the 1 percent level. The positiverelationship between age and efficiency is expected. Older firms have greater marketknowledge “Know how,” reputation and economies of scale. However, older companiesmay have a harder and less flexible adaptation to environmental conditions, as in thecase of textiles sector.

Model 1* Model 2Est. Coef. SD Est. Coef. SD

β0 1.379** 0.033 1.731** 0.017β1 (Fixes Assets) 0.023** 0.003 0.022** 0.002β2 (Materials) 0.775** 0.007 0.695** 0.003β3 (Employment) 0.204** 0.007 0.282** 0.004β5 (trend) 0.089** 0.006 0.013** 0.001β7 (trend×Fixes Assets) −2.0E-04 0.006 – –β8 (trend×Materials) −0.017** 0.006 – –β9 (trend×Employment) 0.017** 0.006 – –Equation uitδuo −1.459** 0.27 −1.032** 0.257δ1 (t) −0.210** 0.082 −0.317** 0.078δ2 (t2) 0.044** 0.008 0.049** 0.008δ3 (Age) 0.039** 0.012 0.039** 0.012δ4 (Age2) −3.0E-04** −1.0E-04 −1.5E-04** −3.3E-04δ5 (Capital per worker) 9.0E-04** 2.0E-04 0.001** 3.7E-04δ6 (Salary per worker) −0.086** 0.005 −0.083** 0.005δ7 (Market Share) −3,035** 525.3 3,031** 523.6δ8 (Market Share×size1) −22,897** 2,271.4 −21,960** 2,120.3δ9 (Market Share×size2) −5,763** 846.4 −5,511.2** 815.6δ10.2 Aragon −0.978** 0.201 −0.987** 0.199δ10.3 C.Valenciana −0.509 0.300 −0.571** 0.283δ10.4 Murcia −0.800** 0.244 −0.670** 0.283δ10.5 Andalusie −0.847** 0.265 −0.831** 0.261δ10.6 Castilla La Mancha −0.250 1.626 −0.631 2.147δ10.7 Extremadura −0.539** 0.179 −0.505** 0.176δ10.8 Castilla La Mancha −0.339 0.182 −0.255 0.176δ10.9 Castilla Leon −0.574** 0.130 −0.553** 0.126δ10.10 Galicia −0.555** 0.145 −0.599** 0.144δ10.11 Asturias −0.434 0.311 −0.404 0.301δ10.12 Cantabria 0.543** 0.147 0.559** 0.145δ10.13 País Vasco 0.135 0.481 −0.119 0.488δ10.14 Navarra −0.469** 0.142 −0.486** 0.140δ10.15 La Rioja −0.275 0.212 −0.236 0.202δ10.16 Baleares 0.268 0.242 −0.164** 0.241δ10.17 Canarias −0.405 0.213 −0.398 0.210

Equation vitδvo −3.389** 0.023 −3.792** 0.023σv 0.146** 0.001 0.148** 0.001

Log-Likelihood 2,271.8 2,268No. of observations 6,310 6,310Notes: Omitted variables: Andalusie and market share×size_3. *,**Significant at 5 and 1 percentlevels, respectively

Table II.Results of estimation

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Unexpectedly, the effect of the intensity of capital (capital by worker, K_W) ispositive and significantly different from zero, which means the higher the intensity ofcapital is, the lower the level of firm’s efficiency is. This variable picks the effect onefficiency of the combination of inputs. One possible explanation is that changes inefficiency generated by a technical innovation depend on their nature and diffusion.If it is easy for firms to adopt it, then this change affects efficiency positively, while if itrequires an important investment as well as organizational modification, then it couldcause a shift in the frontier, thus the relative distance augment. This means that even ifan increase in the stock of capital improves efficiency to do it in a different timing thanthe rest of the firms, this could cause losses of productivity derived from the capitaladjustment in the short-term (Diaz and Sanchez, 2008, p. 321).

The negative and statistically significant ratio of personnel costs over employment(S_W), indicates that considering the theory of efficiency wages, better qualified staffincreases efficiency.

The market share variable (MS), is significant and shows a negative sign, whichmeans that the higher the market share is, the lower the inefficiency of the firm is.This variable captures the relevance of the market power of the firm inside its sector.The evidence related to the effect of this determinant on efficiency is not conclusive.Authors such as Hay and Liu (1997), Nickell et al. (1997), Díaz and Sénchez (2008) finda positive relationship between a firm’s efficiency and its market share. The marketshare is related to firm size. empirical studies that have investigated the relationbetween firm size and technical efficiency seem to provide more evidence for positiverelation between these two variables. Some empirical studies have reported eitheran ambiguous or negative correlation or curvilinear behavior (inverted U shape)(see Kim, 2003).

The variable that captures the interaction of market share and firm size shows that,as the market share on the size increases, so does inefficiency. That is, firms adjust theircapacity in the market in which they operate. Larger sizes and greater market sharecould be related with both diseconomies of scale and scope. Finally, the firm’s locationshows statistically significant differences in the efficiency differences.

As we mentioned before, one of the most important environmental factors refers tothe process of market deregulation in the textile industry since early 2005. We discussthe distribution of the efficiency of the companies analyzed in different periods of time.A variety of techniques to estimate density functions non-parametrically exists. Kernelsmoothing is used here, (Silverman, 1986; Wand and Jones, 1995). It is a technique thatprovides a way of uncovering the data structure without imposing any parametricstructure. Figure 1 shows the Kernel density distributions for initial year (2002),intermediate year (2005) and final year (2009).

In our case, to confirm the divergence analysis of Kernel functions, we have testedthe hypothesis of equal density functions. In order to do this, we applied the test chart

Elasticity withrespect to*

Elasticity of frontieroutput

Elasticity of the technicalefficiency

Elasticity of meanoutput

β1 (fixes assets) 0.023 (0.003)** −2.0E−04 (0.006) 0.022 (0.003)**β2 (materials) 0.775 (0.007)** −0.017 (0.006)** 0.758 (0.001)**β3 (employment) 0.204 (0.007)** 0.017 (0.001)** 0.221 (0.001)**

Note: *,**significance at 5 and 1 percent levels, respectively

Table III.Elasticities of meanoutput with respectto inputs

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and through bootstrap techniques to obtain the p-value (see Bowman and Azzalini,1997). The tests shows rejects the null hypothesis of equal distributions Kernels (2002vs 2005, p-value¼ 0.000, 2005 vs 2009, p-value¼ 0.000, 2002 vs 2009, p-value¼ 0.000)

The results in Figures 1 and 2 shows the changes in the external form of thedistribution of efficiency on the initial year 2002, intermediate (2005) and final (2009) ofthe companies in the Spanish textile sector. As can be seen, these changes confirmedthe process of divergence occurred.

5. ConclusionsThis work provides new evidence about the technical efficiency and its determinantscan be due to environmental or firm-specific factors in Spanish textile sector during theperiod 2002-2009. We have estimated the Cobb-Douglass stochastic production frontierfollowing Battese and Coelli (1995) model to analyze an unbalanced panel.

The theory suggests that cases involving technical inefficiency may be due to timelags in firms’ acquisition of new technology and commensurate skills upgrades amongstaff; differential incentive systems; organizational factors associated with X-efficiency(Leibenstein, 1966) or associated with human capital, such as lack of incentives to theimprovement of efficiency (Mirrelees and Miller, 1996) or dimensional factors associateswith scale and scope economies (Johnston et al., 2000) among others factors.The empirical results achieved in this work suggest that the trend of the inefficiencyshows a curvilinear behavior in the form of U (turning point third-quarter of 2004).This result is related to the efficiency analysis through Kernel distributions whichconfirmed a clear process of divergence. In the period 2002-2005 the efficiency of thefirms analyzed maintained higher levels than the 2005-2009 periods where there isdeterioration. This may be related to the increased competition due to the end of theMulti-fibre Arrangement in January 2005 and the entry of Chinese products in 2004.

In relation to specific factors, a positive relationship between efficiency and marketshare exist. The firm size has significant effects on technical efficiency. However, theinteraction between market share and size indicates that as firms are bigger are alsomore inefficient.

This result could be explained by the complexity of larger firms in organization andmanagerial control. The smaller companies can adjust their resources and capabilities

Efficiency

Den

sity

Efficiency_2002Efficiency_2005Efficiency_2009

10

8

6

4

2

0

0.2 0.4 0.6 0.8 1.0

Figure 1.Distribution Kernel

by years

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to the needs of the market segment they serve. Also the small firms which are lessefficient will exit the market under economic difficulties, more easily than large firms.

The relationship between age and inefficiency shows a curvilinear behavior in theform of inverted U shape. Older firms have greater market knowledge “Know how,”reputation and economies of scale. Finally, better trained employees and the ratiocapital over employed has a positive and negative effect over efficiency, respectively.In this sense, the theory suggests that cases involving technical inefficiency may be dueto time lags in firms’ acquisition of new technology and commensurate skills upgradesamong staff; differential incentive systems; organizational factors associated withX-efficiency (Leibenstein, 1966) or associated with human capital, such as lack of incentivesfor the improvement of efficiency (Mirrelees and Miller, 1996) or dimensional factorsassociates with scale and scope economies (Johnston et al., 2000) among others factors.

To sum up, after controlling for specific factor like age, intensity of capital, salary byworker, regions and market share, we have obtained that the interaction between marketshare and size indicates that as firms are bigger are also more inefficient. Environmentalfactors in deregulation terms affect at the levels of efficiency. The effects of tradeliberalization, with the exemption of tariffs on imports from Asian countries with lowlabor costs such as China, India, etc., implies the loss of protection and the creation ofa highly competitive market. This could lead to higher levels of inefficiency in the Spanishtextile sector due to the lack of flexibility of firms to adapt to the environment, andperhaps with fuzzy rules of the game.

The lack of studies analyzing the textile sector in Spain in the time period chosen inthis work and the methodology chosen for the time prevented any comparison at nationallevel. The generalizability of these results, perhaps it is only possible by working ata micro-level data and a four-digit disaggregation. This could lead to future research.

Notes1. In a two-stage procedure, first, a stochastic frontier production function is estimated and the

inefficiency is obtained under the assumption of independently and identically distributedinefficiency effects. But in the second step inefficiency effects are assumed to be a function ofsome variables, which contradicts the assumption of identically distributed inefficiencyeffects.

2. The Cobb-Douglas production function was chosen because of its simplicity and validity indifferent works (Zellner et al., 1966). Nevertheless, we also tried to use the trans-log function,but the likelihood function had problems of convergence.

3. We try to introduce a non-neutral measure of change in inefficiency over time but it has notsignificant impact on the inefficiency model.

4. Authors such as Gumbau (1998), Martín and Suárez (2000), De Jorge and Suarez (2011),El-Atroush and Montes-Rojas (2011) used this type of specification among others.

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Corresponding authorDr Justo De Jorge-Moreno can be contacted at: [email protected]

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