Tecnicas Para Una Eficiente Asignacion Para La Manipulacion de Cargas

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Int. J. Production Economics 109 (2007) 149–161

Firm and time varying technical and allocative efficiency:

An application to port cargo handling firms

Ana Rodrı´guez-A´lvarez


, Beatriz Tovar


, Lourdes Trujillo


aUniversity of Oviedo, Spain

bResearch Group Economics of Infrastructure and Transport, EIT, University of Las Palmas de Gran Canaria, Spain

Received 30 December 2005; accepted 27 November 2006 Available online 9 January 2007


In this paper we present an econometric model to calculate both, the technical and the allocative efficiency in cargo handling firms in the port of Las Palmas (Spain). To achieve these aims, we estimate a system of equations consisting of a translog input distance function and cost shares equations. Using this procedure we can check the hypothesis in which, given technology and prices, terminal port inputs are not optimally allocated in the sense that costs are not minimized. The main contribution of this paper is to apply an empirical model that allows the unbiased estimation of allocative inefficiency of input use in two ways: an error components approach and a parametric approach. We also avoid the Greene Problem and allow allocative inefficiency to be systematic. Both size and traffic mix are first shown to be sufficiently diverse as to allow for a reliable estimation of a representative flexible (translog) function.

r2007 Elsevier B.V. All rights reserved.

Keywords: Distance function system; Morishima elasticities; Technical and allocative efficiency; Spanish ports terminals

1. Introduction

In the last decade, several models have been proposed to estimate time-varying technical effi-ciency. These models could be grouped depending

on the approach chosen to model the inefficiency. On the one hand, there are those who model technical inefficiency through an error component (see, for example, Kumbhakar, 1990; Battese and Coelli, 1992, 1995; Heshmati and Kumbhakar, 1994;Heshmati et al., 1995orCuesta, 2000). These models involve the disadvantage of making parti-cular distributional assumptions for the one-sided error term associated with technical efficiency. On the other hand, there are those who model technical inefficiency through the intercept of the function (see, for example, Cornwell et al., 1990; Lee and Schmidt, 1993or Atkinson and Primont, 2002). In this way, these models avoid making particular distributional assumptions. In this paper we can obtain technical efficiency indices, which may vary www.elsevier.com/locate/ijpe

0925-5273/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2006.12.048

Corresponding author. Departamento de Economı´a, Uni-versidad de Oviedo, Campus del Cristo, 33071 Oviedo, Spain. Tel.: +34 985 10 48 84; fax: +34 985 10 48 71.

E-mail address:ana@uniovi.es (A. Rodrı´guez-A´lvarez). 1

A Previous version of this paper has been published like working paper in FUNCAS (Fundacio´n Espan˜ola de las Cajas de Ahorro) n


o 201/2005 and were presented at the Permanent Seminar on Efficiency and Productivity, Oviedo, April 2004 and at the North American Productivity Workshop, Toronto, Canada June 2004. This research was funded with grants from Gobierno Auto´nomo de Canarias, Project PI2003/188.


through time as well as across firms following this second approach.

With regard to allocative efficiency,Atkinson and Cornwell (1994) present two methods that permit the calculation of allocative inefficiency: the para-metric approach and the error component ap-proach. Fa¨re and Grosskopf (1990) and Atkinson and Primont (2002)demonstrate that replacing the usual cost frontier with an input distance function, the main drawbacks of the parametric approach can be overcome by obtaining firm and time allocative efficiency indices. With regard to the error compo-nent approach, the advantages of the distance function are developed inRodrı´guez-A´lvarez et al. (2004) which dealt with a hypothesis in which allocative efficiency is time-invariant and only varies across firms.

In this paper we extend the analysis to the case when the efficiency is firm and time-varying in both approaches. In adition, we can calculate firm and time-varying technical efficiency and, separately, a measure of technical change. To do this, we present a distance system that comprises an input distance function and the associated share cost equations. Finally, we also extend the analysis by calculating Morishima elasticities.

To illustrate our methodology we apply it to panel data using a sample of cargo handling firms in Spanish ports. The first empirical studies that have attempted to measure port efficiency based on frontier models appear in the 1990s. There are two different techniques to carry out this type of study. The first one, a non-parametric programming method, is called data envelopment analysis (DEA), (i.e. Roll and Hayuth, 1993; Martı´nez Budrı´a et al., 1999; Tongzon, 2001; Valentine and Gray, 2001; Bonilla et al., 2002; Martı´n, 2002; Pestana, 2003;Estache et al., 2004), and the second is through stochastic frontier analysis (SFA), (i.e. Liu, 1995;Ban˜os Pino et al., 1999; Coto Milla´n et al., 2000; Notteboom et al., 2000; Cullinane et al., 2002; Estache et al., 2002; Cullinane and Song, 2003;Dı´az, 2003; Tongzon and Heng, 2005). Both methods allow the derivation of estimates of relative efficiency levels for all the operators compared.2

Out of these, only four of them have investigated the efficiency of Port Terminals: Notteboom et al. (2000);Cullinane et al. (2002);Cullinane and Song (2003); Tongzon and Heng (2005) and they have several characteristics in common. Firstly, they

estimate a stochastic frontier production function; secondly, they model technical inefficiency through an error component thirdly; they only measure technical efficiency and finally, they consider that technical efficiency is time-invariant. However, Song et al. (2001) estimate the efficiency of the terminal operating companies based on both pooled data set variant) and panel data (time-invariant). Our paper is the first one dealing simultaneously with firm and time varying technical and allocative port terminals efficiency, and it is also the first one applying a distance function to port terminals.

The paper is organized as follows: Section 2 provides an overview of port terminals and their regulation in Spain. In Section 3 the model is presented. Section 4 concerns itself with the econo-metric model. The data are described and the results are presented in Section 5. The final section contains brief concluding comments.

2. Port terminals and their regulation in Spain Although there are cases where several firms share a port terminal, in our case each cargo handling firm exclusively operates its own terminal in a consessional basis. The terminals analyzed are typical medium size port ones. Terminal prices are subject to price caps, which are seldom binding, but employment is highly regulated. This is not an unusual situation around the world.

Economic activities within a port are multiple and heterogeneous. On the one hand, among them cargo handling has been one of the most affected by technological changes and by competition among ports on the other. The importance of this activity is evident when realizing that it means from 70% to 90% a vessel’s disbursement account (De Rus et al., 1994). Cargo handling services are usually per-formed in port terminals.

Technological changes have increased the relative importance of specific terminals within port areas (e.g. multi-purpose,3 containers, liquid and solid bulk). Terminal facilities have now become heavily capital intensive and, depending on port size, more specialized as well, playing a key role in the choice of port by shippers. The role of the port terminals

2For more details, seeCoelli et al. (1999).

3A multiple-purpose (MP) terminal is designed to serve

heterogeneous traffic, including containerized and non-contain-erized cargo. It can be transformed into a specialized one (e.g. containers only) by changing equipment.


within the logistic system makes them key actors of the port industry, playing a central role in the increasing competition within the sector.

In addition, the private sector has become increasingly interested in this type of activity. This has shifted the focus of port authorities competitive strategy design from the port as a whole to the terminals, making them the most important ele-ments within the port industry. As pointed out by Heaver (1995), this change of focus is the main factor explaining the increased competition within the sector.

The cargo handling service is usually viewed as one that has to be directly provided by the public sector or by private firms through concession contracts. The regulation of the Spanish ports system is based upon a scheme that allows the combination of public ownership of the port infrastructure (docks, land, and so on) with private ownership of the superstructure (warehouses, cranes, etc). The public authority determine the conditions under which the private initiative has to operate by fixing maximum prices, characteristics and length of concessions, and other conditions (for more details seeTovar et al., 2004).

In the production of cargo handling services, the following groups of factors are required: basic infrastructure, superstructure, machines and mobile equipment, as well as labor. Traditionally, labor in a port has been strongly regulated, although changes have taken place worldwide during the last decade or so.

The stevedores or port workers working in Spanish port terminals are divided into two categories: those who are on the payroll (ordinary employment—LC) and those who are not (special employment—LE). These latter can be recruited on a provisional basis by any company to work 6 h shifts. Regulation drives the level and composition of port labor (including the choice between LE and LC) for each terminal.

The possibility of contracting port workers for specific operations (LE) provides the stevedoring companies4with some flexibility, allowing them to adjust employment to terminal traffic levels. How-ever, this flexibility has its limits, since under the current legislation the operators do not have total

freedom to decide how and to what extent each type of worker has to be used.5 The stevedoring companies have:

The obligation to perform at least 25% of their activities (in tons) with port workers on their payroll (LC).

The obligation to use at least one LE port worker in each shift.

A global limit on the number of operations they can perform with LC workers of 22 per month; once they have reached this level, they are required to rely on LE workers. Moreover, as we can check in the empirical application, the regulation imposes certain degrees of comple-mentarity between both types of port workers so as to use them jointly.

3. Modelling firm and time-varying technical and allocative efficiency

To calculate firm and time-varying technical and allocative efficiency we propose an empirical model, which consists of an input distance function and the associated input cost share equations:

ln 1 ¼ ln Dðypt; xpt; Kpt; DTÞ þ vptþupt, (1) xiptwipt Cpt ¼q ln Dðypt; xpt; Kpt; DTÞ q ln xipt þviptþAipt, (2) where D(ypt,xpt,Kpt, DT) is the short-run input

distance function; y is an output vector, x is a variable input vector, K is a quasi-fixed input, DT is a time year dummy to control for neutral technical change, p denotes port terminal and t time. The vpt

and vipterror components represent statistical noise,

and are assumed to be distributed as multivariate normal with zero mean.

3.1. Measuring technical efficiency

The error component uptX0 in (1) represents the

magnitude of technical efficiency (TE). We follow Cornwell et al. (1990) who specifies a model that allows us to estimate time-varying technical effi-ciency levels for individual firms, without making strong distributional assumptions for technical inefficiency or random noise. Thus, if the constant 4These are firms that are allowed to handle cargo. In our case,

the three terminals are also stevedoring companies; conversely they could not do handling cargo by their own, but by contracting a stevedoring company.

5A collective agreement is a three-way agreement among the

State Stevedoring Association, the port workers, and the stevedoring companies.


in (1) is B0, then, it is possible to write:

bpt¼B0þupt¼bpaDpþbpbDpt þ bpcDpt2, (3) where Dpis a dummy variable for the port terminal

p, bpa; bpb; bpc are parameters to be estimated for

this port terminal, and t is a time trend. However, there is an interpretation problem because there is no easy way to empirically distinguish in (3) between technical inefficiency or technical change (for example, there are contradictory interpretations inCornwell et al., 1990orGood et al., 1995).

To solve this problem, and following Heshmati and Kumbhakar (1995)andHeshmati et al. (1995) we have included in (1), the dummy time (DT). In this way, by including a time variable among the regressors, it would be possible to resolve the interpretation problem in the Cornwell et al. (1990) specification, since the time variable is associated with technical change and the error component (3) is associated with technical effi-ciency, which is allowed to vary across producers and through time (for details see, for example, Lovell, 1996).

In this sense, the bpa captures time-invariant TE

whereas bpband bpccapture time-varying TE. Thus,

each producer has its own intercept (bpt), which is

allowed to vary quadratically through time at producer-specific rates. The TE of a port terminal in a time period is obtained from the estimated intercepts as TEpt¼exp(upt) where upt¼bpt

min(bpt). The efficiency index constructed in this

way, ranges from 0 to 1. Thus, in each period at least one port terminal is estimated to be 100% technically efficient (with value 1), although the identity of the most technically efficient port terminal may vary through time.

3.2. Measuring allocative efficiency

To calculate allocative efficiency two econometric approaches are available (Atkinson and Cornwell, 1994): (a) an error components approach, and (b) a parametric approach

(a) The error components approach In this approach we model allocative inefficiency through an error component. Thus in (2) the error compo-nents Aipt4 ¼o0, i ¼ 1,y,n, represent allocative

inefficiency, here represented by the difference between actual and stochastic shadow input cost shares form (for more details seeRodrı´guez-A´lvarez and Lovell, 2004). Moreover, if Aipt is positive, the

input i is being over-utilized with regard to other inputs and vice versa.

In our case it is possible to specify allocative inefficiency for the input i as

Aipt¼aipaDpþaipbDpt þ aipcDpt2, (4) where Dpis a dummy variable for the port terminal

p and aipa;aipb; aipcare parameters to be estimated

for this port terminal and for the input i and t is a time trend. The aipa captures time-invariant

alloca-tive inefficiency, whereas aipb and aipccapture

time-varying allocative inefficiency.

(b) The parametric approach: After estimation of systems (1)–(2), shadow price ratios are determined from the dual of Shephard’s Lemma as

qDðy; x; K; DT Þ=qxi qDðy; x; K; DT Þ=qxj ¼w s i ws j , (5)

where ws is the shadow prices vector. If the allocative efficiency assumption is satisfied, these shadow price ratios coincide with market price ratios. However, if there is allocative inefficiency, the two price ratios differ. To study such deviations, a relationship between the shadow prices (obtained through the distance function) and the market input prices is introduced by means of a parametric price correction:

wsi ¼kiwi. (6)

Dividing (6) by the corresponding expression for input j we obtain ws i ws j ¼kij wi wj , (7)

where kij¼ki/kj. From (7) the degree to which

shadow price ratios differ from market price ratios is calculated. If kij¼1, there is allocative efficiency;

while if kij4(o)1, input i is under-utilized

(over-utilized) relative to input j.

If we have panel data, it is possible to obtain, for each pair of inputs, producer and time-specific allocative efficiency indices kij. Thus, with both

proposed approaches (the error component and the parametric approach) we can get time and firm varying indices of allocative efficiency. Moreover, it is important to distinguish between these two measures of allocative inefficiency (the parametric approach and the error components approach). In the error components approach, the aipts represent

the systematic allocative inefficiency for each input. In the parametric approach, kij indicates the


Moreover, in the error components approach, behind the aipt lies the assumption of an additive

relationship between wi and wis. In the parametric

approach a multiplicative relationship between wi

and wis is specified, yielding the coefficients kij as

indices of allocative inefficiency.

However, it is also important to emphasize the existing relationship between the two approaches. When persistent inefficiency exists (that is, if the aipt

have mean values significantly different from zero), their inclusion is necessary if the estimated para-meters, and consequently the estimated kij, are

unbiased. This implies that the inclusion of the parameter aiin the empirical model is indispensable,

in order to obtain unbiased estimates of the kij.

4. Econometric specification

We now consider how to estimate systems (1)–(2). To do this, we have chosen a flexible functional form, a translog short run multiproduct input distance function which is specified as

ln 1 ¼ B0þ Xm r¼1 arln yrptþ 1 2 Xm r¼1 Xm s¼1 ars ln yrptln yspt þX n i¼1 biln xiptþ 1 2 Xn i¼1 Xn j¼1 bij ln xiptln xjpt þxf ln Kptþxff 1 2ln K 2 ptþ Xn i¼1 xfiln Kpt ln xipt þX m r¼1 xfrln Kpt ln yrptþ Xn i¼1 Xm r¼1 rri ln yrptln xipt þX T T ¼1 gTDT þ uptþvpt, ð8Þ xiptwipt Cpt ¼biþ Xn j¼1 bij ln xjptþ Xm r¼1 rri ln yrpt þxfi ln KptþAiptþvipt, ð9Þ where y ¼ ðy1; . . . ; ymÞ is an output vector, x ¼ ðx1; . . . ; xnÞis a variable input vector, K is a quasi-fixed input, DT is a time dummy for year T, p denotes port terminal; t denotes months and vpt, vipt,

uptand Aipt are disturbance terms which have been

already defined. a, b, x, r, g are parameters related to outputs, inputs, quasi-fixed input, cross term between outputs and inputs and time, respectively.

Homogeneity of degree +1 of the input distance function in variable inputs is enforced by imposing

the restrictions P n i¼1 bi¼1; Pn j¼1 bij¼0; Pn i¼1 rri¼ 0 ð8 r ¼ 1;. . . ; mÞ; P n i¼1

xfi ¼0: We also impose the symmetry conditions ars¼asr; bij¼bji; xfi ¼xif; xfr¼xrf; rri¼rir.

The estimation of this equation system provides the suitable empirical context to calculate the technical and allocative efficiency by means of the above proposed methodology.

5. Data and results 5.1. Data description

The sample consists of three multipurpose port terminals operating within the area of Las Palmas Port, located in the Canary Islands (Spain). The fact that all the port terminals considered are in the same port is a key advantage in the coherence and uniformity of the accounting data used. Thus, the regulation is the same, and environmental factors are equal or very similar for all of them.

We have monthly data from 1992 until 1997 for Terminal 1 (T.1), from 1991 until 1999 for Terminal 2 (T.2), and from 1992 till 1998 for Terminal 3 (T.3). The final panel data set consists of 264 observations. Although these terminals mainly deal with con-tainers, they also operate roll-on/roll-off cargo (ro-ro) as well as general break-bulk cargo, so we distinguish three outputs measured in total tons: containers (CONT), ro-ro cargo (ROD) and general break-bulk cargo (MG).

The input variables are: port workers: ordinary (LC) and special6 (LE), capital (GK), intermediate consumption (GI). We also consider a quasi-fixed input: total area (K).

The information available regarding the amount of workers7used is expressed in number of shifts per month. A shift is a 6 h work schedule. The total monthly labor expense for the terminals is calcu-lated as the sum of the cost of each type of worker. Capital covers all the components of tangible assets of the company —i.e. buildings, machines, etc. The monthly cost results from the addition of

6This can be recruited on a provisional basis by any company

to work 6 h shifts.

7Information about port labor is very difficult to obtain. Out of

the previous papers dealing with port terminal efficiency only


the accounting depreciation for the period plus the return on the active capital of the period.8

With regard to area, the terminals under analysis can make use of a specific area that has been granted under concession, which may be increased by provisionally renting—upon prior request— additional area from the Port Authority. The addition of both types of areas is called total area, which is monthly measured in square meters.

Lastly, the rest of the productive factors used by the company that have not been included in any of the three preceding categories, such as office supplies, water, electricity, and the like, have been denominated as intermediate consumption. The monthly expense results from the aggregation of the rest of the current expenses other than depreciation, personnel expenses and payment for area, after the pertinent corrections, in such a manner that, the resulting monthly expense truly reflects consumption and not accountancy.

The total monthly production expenses for the terminals result from the aggregation of expenses of all the productive factors defined above. Table 1

shows the monthly values obtained for the entire sample and for each of the three terminals, both in terms of the defined inputs and outputs, as well as the total expense incurred during service provision.9 It is worth stressing that data was gathered directly from the firms files and that all the details were discussed with executives when necessary, particu-larly for the monthly assignment of expenses. Data is described in detail inTovar (2002).

On the one hand, out of the three products, general break-bulk cargo (‘‘general cargo’’) repre-sents an average of 9.9% of the monthly total tons moved, containers represent a 87.4% and ro-ro 2.7%. On the other hand, labor costs account for an average of 53%10 of the monthly expenses for the entire sample. Total area represents 13%, capital amounts to 8% and intermediate consumption reaches 26%. Within port workers, ordinary ones account for 46% while special workers represent 54%. The figures reveal similar patterns per company.

Moreover, the analysis of the information con-tained in Table 1 leads to a first approximation of the size of companies. Thus, taking into considera-tion the aggregated product volume, the largest company is T.3., followed by T.1. and by T.2. in last

Table 1

Monthly average input, output and expense values get for the entire sample and for each terminal

Variable Unit Terminals

Sample T.1 T.2 T.3

Mean S.E. Mean S.E. Mean S.E. Mean S.E.


CONT 1000 Ton 59.2 41.57 53.1 9.72 33.5 7.45 97.4 54.36

MG 1000 Ton 5.6 6.35 0.6 0.78 9.9 7.39 4.4 3.12

ROD 1000 Ton 2.1 2.36 1.0 0.71 0.8 0.86 4.7 2.49


LC Number of shifts per month 336.4 206.13 344.0 140.28 251.0 49.90 439.8 306.94 LE Number of shifts per month 339.4 161.40 207.5 93.11 400.4 193.44 374.0 75.70 GI 1000 PTAS deflated 24,534.2 8445.04 21,961.4 5,485.22 20,573.2 3,556.72 31,832.1 10192.23 GK 1000 PTAS deflated 12,985.4 7728.52 6,063.2 429.87 11,043.0 3,939.85 21,416.1 7119.51 K M2 61,484.4 11758.16 63,971.8 7,892.55 57,530.6 2,597.86 64,435.8 18481.79 Expenditure

GLC 1000 PTAS deflated 17,964.1 8563.95 13,113.6 6,826.70 14,463.6 3,592.70 26,622.4 7979.02 GLE 1000 PTAS deflated 21,447.9 12515.12 18,759.9 6,911.54 20,738.9 9,453.66 24,663.6 17967.74

8This rate of return evidences the compensation earned by

risk-free capital, which is made up of bank interest plus a risk premium. It has been considered that, for the period under analysis, the return for both concepts amounts to 8% per annum. The price of capital is the quotient of the cost of capital divided by the active capital of the period (net fixed assets under exploitation for a given period t.)

9All monetary variables have been deflacted.

10Note this is the same percentage thatCullinane and Song (2003)report as a typical expenditure of a port.


position. It is to be noted that, where the variable used as the size indicator is the total monthly production expense (mean value), even though T.3. is still found to be in the first place, the other two companies, T.1 and T.2. swap positions. This result is due to monthly expenses and do not vary monotonically with total production. This makes the different composition of outputs a likely explanation for cost differentials when factor prices are similar for the three companies. For example, the only explanation for the expenses of T2, being larger than those of T1 would be the difference in the traffic mix, particularly, the larger volume of general cargo. This already suggests higher marginal costs for general cargo, which

reinforces the need for a multioutput analysis Jara-Dı´az et al. (2005).

5.2. Results

We have estimated systems (8)–(9) by means of iterative seemingly unrelated regressions (ITSUR), which is invariant to the omitted share equation.

In Tables 2–4 we present the estimated values from the input distance system. The variables have been divided by the geometric mean. Therefore, the first-order coefficients can be interpreted as elasti-cities. At the sample mean, the regularity conditions are satisfied: it is non-decreasing and quasi-concave in inputs and decreasing in outputs.

Table 2

Distance system estimated

Variable Coefficient Standard error t-Statistic Variable Coefficient Standard error t-Statistic L(CONT) 0.32822 0.3947 8.3160 L(ROD).L(GI) 0.00130 0.0009 1.4431 L(MG) 0.35813 0.0057 6.3068 L(ROD).L(K) 0.08451 0.0929 0.9100 L(ROD) 0.01642 0.0095 1.7225 L(ROD).L(GK) 0.00099 0.0005 2.1150 L(LC) 0.14139 0.0369 3.8291 L(LC).L(LC) 0.02116 0.0122 1.7274 L(LE) 0.25114 0.0279 8.9895 L(LC).L(LE) 0.05233 0.0114 4.6108 L(GI) 0.27117 0.0458 5.9193 L(LC).L(GI) 0.04950 0.0055 8.9437 L(K) 0.18176 0.1415 1.2847 L(LC).L(K) 0.01692 0.0340 0.4972 L(GK) 0.33629 0.0435 7.7245 L(LC).L(GK) 0.02399 0.0035 6.8374 L(CONT).L(CONT) 0.13236 0.0747 1.7714 L(LE).L(LE) 0.05444 0.0138 3.9455 L(CONT).L(MG) 0.02318 0.0086 2.6832 L(LE).L(GK) 0.03723 0.0030 12.4542 L(CONT).L(ROD) 0.01045 0.0111 0.9447 L(LE).L(GI) 0.06949 0.0054 12.7574 L(CONT).L(LC) 0.02655 0.0132 2.0089 L(LE).L(K) 0.10786 0.0311 3.4794 L(CONT).L(LE) 0.03048 0.0155 1.9698 L(GI).L(GI) 0.17636 0.0053 33.0481 L(CONT).L(GI) 0.00436 0.0074 0.5858 L(GI).L(GK) 0.05736 0.0031 18.4742 L(CONT).L(K) 0.33217 0.1905 1.7438 L(GI).L(K) 0.0433 0.0158 2.7515 L(CONT).L(GK) 0.00830 0.0046 1.8100 L(K).L(K) 0.31434 0.6175 0.5091 L(MG).L(MG) 0.00856 0.0016 5.6796 L(K).L(GK) 0.04762 0.0102 4.6748 L(MG).L(ROD) 0.00155 0.0014 1.1364 L(GK).L(GK) 0.11858 0.0029 41.0775 L(MG).L(LC) 0.00184 0.0017 1.1019 DT92 0.12548 0.0396 3.1696 L(MG).L(LE) 0.00071 0.0017 0.41710 DT93 0.09536 0.0790 1.2067 L(MG).L(GI) 0.00092 0.0008 1.0878 DT94 0.13487 0.0945 1.4279 L(MG).L(K) 0.03581 0.0317 1.1298 DT95 0.15500 0.1052 1.4727 L(MG).L(GK) 0.00021 0.0005 0.4520 DT96 0.02817 0.1173 0.2402 L(ROD).L(ROD) 0.00322 0.0027 1.2079 DT97 0.13772 0.1303 1.0566 L(ROD).L(LC) 0.00789 0.0022 3.6192 DT98 0.18434 0.1393 1.3232 L(ROD).L(LE) 0.00561 0.0022 2.5637 DT99 0.13160 0.1511 0.8710

Equation Mean R2 Std. error of regression

Input distance function — — 0.079379

Ordinary worker share equation 0.236319 0.7541 0.044199

Special worker share equation 0.278165 0.8406 0.042865

Intermediate consumption share equation 0.323562 0.8505 0.020191

Capital share equation 0.161953 0.9602 0.012590

Statistically significant at 10%. Statistically significant at 5%.


InTable 2, the estimated parameters are shown. It can be seen that all first-order parameters are statistically significant and have the correct sign, except the quasi-fixed input total area (K). As the quasi-fixed input total area (K) is not statistically significant this means that the marginal productivity of total area could be zero. This could be due to the fact that port terminal infrastructure and super-structure must be built with determined minimum

dimensions, so it is not possible to enlarge a terminal port in a continuous way. So, given that terminals keep growing, they are having more total area than previously needed.

5.2.1. Technical efficiency

InTable 3, and following Section 3.1 we present the estimated coefficients from which it is possible to obtain the technical efficiency index (upt). These

indices have been represented in Fig. 1 (following Cornwell et al. (1990) approach). The temporal pattern of technical efficiency for the three terminals shows that T.3 is the most efficient for almost the whole period, when its technical efficiency score begins getting worse. This occurs, more or less, when T.3 moves from a smaller to another bigger place inside the port area. This change of size requires a huge investment which probably drives this result. Remember that T3 is the largest company, so it seems to exhibit a relationship between size and efficiency (this relationship has also been reported in Cullinane et al. (2005). Terminal T.2 presents a declining technical effi-ciency score in the first years and an increasing one in the latter ones, being finally substituted by T.3 at the end of the period. Lastly, T.1 shows a general decline in technical efficiency.

Other technical efficiency scores are shown in Fig. 2. These are calculated considering the best observation as the reference technology.Fig. 2tells us a similar story. In terms of the trend in technical efficiency, T.3 shows a general decline (with the exception of the few first periods), T.2 and T.1 present a similar, but softer, pattern than inFig. 1.

Table 3

bptComponents (from Eq. 3)

Parameters Coefficients Standard error t-Statistic b1A 0.0425450 0.1105030 0.3850170 b1B 0.0000061 0.0057844 0.0010705 b1C 0.0000782 0.0000493 1.5836800 b2A 0.1322430 0.0458950 2.8814200** b2B 0.0049411 0.0035596 1.3880800 b2C 0.0000437 0.0000294 1.4861700 b3A 0.2295630 0.1167930 1.9655600** b3B 0.0251980 0.0061530 4.0951200** b3C 0.0002957 0.0000526 5.6142100** Table 4

AiptComponents (from Eq. 4)

Parameters Coefficients Standard error t-Statistic aLC1A 0.3719030 0.0456560 8.145760** aLC1B 0.0091169 0.0020863 4.369740** aLC1C 0.0000545 0.0000187 2.911360** aLC2A 0.2436080 0.0470980 5.172390** aLC2B 0.0061470 0.0007202 8.534300** aLC2C 0.0000365 0.0000053 6.786440** aLC3A 0.1496150 0.0527010 2.838960 aLC3B 0.0006403 0.0014934 0.428774 aLC3C 0.0000066 0.0000141 0.470838 aLE1A 0.3003560 0.0479150 6.268500** aLE1B 0.0131560 0.0020900 6.294670** aLE1C 0.0001023 0.1849460 5.534250** aLE2A 0.0951980 0.0342090 2.782840 ** aLE2B 0.0056841 0.0008852 6.420770 aLE2C 0.0000380 0.0000068 5.569630 aLE3A 0.0117950 0.0440560 0.267731 aLE3B 0.0011804 0.0011371 1.038090 aLE3C 0.0000091 0.0000103 0.887793 aGK1A 0.1602610 0.0437710 3.661320** aGK1B 0.014876 0.0004296 3.462580** aGK1C 0.0000181 0.0000042 4.257970** aGK2A 0.1904440 0.0437210 4.355870** aGK2B 0.0000873 0.0002108 0.414233 aGK2C 0.0000018 0.0000017 1.057590 aKI3A 0.1849410 0.0456000 4.055760** aGK3B 0.0006198 0.0005529 1.120990 aGK3C 0.0000031 0.0000051 0.622118 0 0.2 0.4 0.6 0.8 1 1.2 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 Time (CSS-1990) Technical Efficiency T.1 T.2 T.3

Fig. 1. Temporal pattern of technical efficiency for the three terminals.


5.2.2. Allocative efficiency: error components approach

In Table 4, following the error component approach, estimated coefficients and asymptotic standard errors for AE parameters (Aipt

compo-nents) are shown. Remember that Aiptrepresent the

systematic allocative inefficiency for each input. The results of the estimation of the firm-specific temporal pattern of allocative inefficiencies follow-ing the error components approach are reported in Figs. 3 and 4for the three terminals with respect to ordinary and special port workers (LC and LE), respectively.

It is interesting to note that the two graphs represent the inverse image of each other. At the very beginning T.1 and T.2 over-utilized LC and underutilized LE, but as time passes these two terminals achieve allocative efficiency in LC but not in LE, which goes on being over-utilized. However, T.3 over-utilized LC and underutilized LE during the whole period. The joint analysis ofFigs. 3 and 4 shows that each terminal has a preferred adjustment factor. It is LC for T.1 and T.2, while it is LE for T.3. This would suggest that firms are operating with allocative efficiency with respect to one factor

and with inefficiency with respect to the other factor.

This behavior is best understood by considering the relevance of regulation. Indeed, it is useful to remember that regulation drives the level and composition of port labor (including the choice between LE and LC) for each terminal. Regulation impedes the labor adjustments for both types of workers jointly. This is why they end up trying to maintain one degree of freedom and may tend to focus on adjustments in one of the workers’ categories at a time. Figs. 3 and 4, indeed, clearly show that the employment policies of T.1 and T.2 differ from those followed by T.3.

Finally, as we can see fromFigs. 5 and 6the three terminals are allocatively inefficient in the use of the two other factors considered: intermediate con-sumption (GI) is over-utilized and capital (GK) is under-utilized. The orders of magnitude are quite small in GI. In the case of capital this probably simply reflects the difficulty of adjusting capital perfectly in a situation of growth as was the case for these terminals during the period of analysis. The area comes first and then, the rest of capital (buildings, cranes, and so on).

5.2.3. Allocative efficiency: parametric approach In the parametric approach we get firm and time-specific measures of AE for each pair of inputs. However, in order to conserve space we have only reported their values evaluated at the sample mean inTable 511which have been estimated from Eqs. (5) and (7).

Remember that kijo1 means that the ratio of the

shadow prices of input i to that input j is lower than -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 1 9 17 25 33 41 49 57 65 73 81 89 97 105 Time Allocative Inefficiency LCT.1 LCT.2 LCT.3

Fig. 3. Firm-specific temporal pattern of allocative inefficiencies for LC (error components approach).

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 1 10 19 28 37 46 55 64 73 82 91 100 Time Allocative Inefficiency


Fig. 4. Firm-specific temporal pattern of allocative inefficiencies for LE (error components approach).

0 0.2 0.4 0.6 0.8 1 1.2 1 9 17 25 33 41 49 57 65 73 81 89 97 105 Time Technical Efficiency T.1 T.2 T.3

Fig. 2. Technical efficiency score considering the best observa-tion as the reference technology.

11Firm and time-specific results are available from the authors


the corresponding ratio of actual prices. The analysis of the average estimated values for the kij

reinforced the conclusions of the previous para-graphs and shows that LC is over-utilized relative to LE and GK. Moreover, GK is under-utilized relative to all the other production factors. Finally, the coefficient kij which links GI with the other

productivity factor is always not statistically sig-nificant, except in the case of GK.

With respect to labor, the result may reflect the labor-specific regulatory environment which im-pedes the adjustments needed by the operators. As for capital, it may be useful to point out that the levels of inefficiency are probably due to the impossibility of full adjustment as a result of indivisibility as previously mentioned; terminal or port infrastructure and superstructure must be built with determined minimum dimensions.12

The figures per company reveal similar patterns as we can see fromFig. 7.

In addition, it is possible to analyze the degree of substitutability between inputs (or the isoquant curve) by means of Morishima elasticities of substitution. Formally, Morishima elasticities in-form us about the variations of shadow prices given a variation in the input quantity. Positive values of the elasticities indicate complementarity between inputs and negative values imply substitutability. The Morishima elasticities have been divided into two components: Mij¼EijEii. The term Eijis the

cross-elasticity shadow price, and tells us whether the input pairs are net substitutes or net comple-mentaries, while Eii represents the elasticity price

characteristic of each input. Formally:

Mijðy; xÞ ¼  d ln ½ðDiðy; x=xiÞ=Djðy; x=xjÞ=d ln ½xi=xj

¼xiDijðy; xÞ=Djðy; xÞ  xiDiiðy; xÞ=Diðy; xÞ

¼Eijðy; xÞ  Eiiðy; xÞ. ð10Þ

The calculations made of the Morishima substitu-tion elasticities (Mij) and their two components (Eij

and Eii) are shown inTables 6–8. From the results,

we can deduce little scope for substitution possibi-lities among the different pairs of inputs. The estimation of the Eiishows the proper sign.

More-over, our estimation of the cross-elasticities shadow price Eij, behaves quite well. As expected, due to

regulation, LC and LE are net soft complemen-taries, and the degree of complementarity between

Table 5

Average values for coefficients kij

Coefficients Meana t-Statistic kOrdinary Worker, Special Worker 0.327803 1.726430


KOrdinary Worker, Intermediate Consumption

0.287873 1.547900 KLC,GI

KOrdinary Worker, Capital 0.696075 6.500820


kSpecial Worker, Intermediate Consumption

0.059402 0.504053 KLE,GI

KSpecial Worker, Capital 0.547863 6.949870


KIntermediate Consumption, Capital 0.573215 10.37480


Note: We have tested the significance of the indices using the Wald test.

aEvaluated at the means of the data using parameter estimates

of (8)–(9).

Statistically significant different from one at 10% level. Statistically significant different from one at 5% level.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 1 9 17 25 33 41 49 57 65 73 8 1 89 97 105 Time Allocative Inefficiency


Fig. 5. Firm-specific temporal pattern of allocative inefficiencies for GI (error components approach).

-0.25 -0.2 -0.15 -0.1 -0.05 0 1 9 17 25 33 41 49 57 65 73 81 89 97 105 Time Allocative Inefficiency GKT.1 GKT.2 GKT.3

Fig. 6. Firm-specific temporal pattern of allocative inefficiencies for GK. (error components approach).

12It is not possible to enlarge a terminal port in a continuous


LE and LC is higher than the one between LC and LE. This could be due to the fact that operators always have to include at least one LE port worker per shift. On the other hand, as we also expected, the cross-elasticities shadow price between port

labor (LC or LE) and capital show that these factors are net complementaries. It happens exactly the same way between capital and GI. Finally, our estimation of cross-elasticities shadow prices be-tween labor (LC or LE) and GI are not statistically significant.

5.2.4. Technical change

The time year dummy coefficients show the effect on the distance function of unobserved variables which, when evolving over time, affect all firms equally. We can check how these time effects influence the distance function from one year to another through the following expression:

TCTþ1;T¼gTþ1gT. (11) 0 0.2 0.4 0.6 0.8 1 1.2 1.4


Sample T1 T2 T3

Fig. 7. Average firm allocative inefficiencies for each pair of inputs (parametric approach).

Table 6

Morishima substitution elasticities: Mij

Meana t-Statistic Meana t-Statistic Mlc,le 1,0587 10.2714** Mle, lc 1.1535 6.0648** Mlc, gi 0.6678 4.2113** Mgi, lc 0.004 0.0035 Mlc, gk 0.7790 10.4009** Mgk, lc 0.4777 10.019** Mle, gi 0.5271 6.7505** Mgi, le 0.0729 0.7081 Mgi, gk 0.1790 1.7666* Mgk, gi 0.4358 10.1179** Mle, gk 0.6726 9.9710 ** Mgk, le 0.4991 9.9215 ** Table 7

Cross and own elasticities: Eijand Eii

Meana t-Statistic Meana t-Statistic Elc, le 0.3497 7.5443** Ele, lc 0.6212 4.0677** Elc, gi 0.0411 0.9777 Egi, lc 0.0789 0.9052 Elc,gk 0.7000 2.3167** Egk, lc 0.1666 3.9478** Ele, gi 0.0051 0.1292 Egi, le 0.0055 0.1312 Egi, gk 0.1006 2.6778** Egk, gi 0.1247 3.1301** Ele, gk 0.1404 4.7940** Egk, le 0.1880 4.1426** Elc, lc 0.7098 8.3117** Ele, le 0.5312 9.7235** Egi, gi 0.0784 1.1577 Egk, gk 0.3110 33.7855**

Note: We have tested the significance of the indices using the Wald test. * Statistically significant at 10%. ** Statistically significant at 5%. a

Evaluated at the means of the data using parameter estimates of (8)–(9). Table 8 Time effects Period TCa t-Statistic 1991–92 0.125484 3.169570** 1992–93 0.030120 0.605594 1993–94 0.039505 1.465350 1994–95 0.020130 0.880385 1995–96 0.183165 6.922290** 1996–97 0.109557 3.172850** 1997–98 0.046616 1.231000 1998–99 0.052731 1.272980

Note: We have tested the significance of the indices using the Wald test.

*Statistically significant at 10%. **Statistically significant at 5%.

aEvaluated at the means of the data using parameter estimates


A positive (negative) value for TC indicates an upward (downward) shift in the distance function (see Fa¨re and Grosskopf, 1995). This measure is usually associated with technological change. The indices obtained from expression (10) are presented inTable 6.

There were only two periods where these indices were statistically significant, and therefore, where time had an influence on firm activity. The first one, from 1991 to 1992 where the indices evolved favorably, and the second one, from 1995 until 1997, where the indices had a negative sign, which indicates that time had a negative influence on firm activity. However, it can be observed that in the last period (1998–1999) the coefficient returns to being positive, but not statistically significant.

6. Conclusions

In this paper, we present an approach which allows us to estimate time-varying efficiency levels for individual firms without invoking strong dis-tributional assumptions for inefficiency or random noise. Using a Spanish ports panel, we have applied this methodology to a frontier input distance system. In this way, the operations of cargo handling firms in ports are analyzed by means of a multioutput input distance function estimation using monthly data on firms located at Las Palmas Port, Spain.

Both size and traffic mix are firstly shown to be sufficiently diverse as to allow for a reliable estimation of a multioutput translog function which permitted us the calculation of firm and time-variant indices of technical and allocative ineffi-ciency (by using both the parametric and the error component approaches) which further add to the contribution of the paper to the literature.

Implementing our approach with typical medium size port terminals data we highlight two main conclusions. The first one is that, it seems there is a relationship between firm size and technical effi-ciency. The second one is that, our result with respect to allocative efficiency suggests that the port labor-specific regulatory environment impedes ad-justments that are needed by the operators. Finally, we have calculated Morishima elasticities.


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