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doi:10.1016/j.ijp

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

www.elsevier.com/locate/ijpe

Firm and time varying technical and allocative efficiency:

An application to port cargo handling firms

Ana Rodrı́guez-Álvarez

a,�

, Beatriz Tovar

b

, Lourdes Trujillo

b,1

a

University of Oviedo, Spain

b

Research 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

Abstract

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.

r 2007 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

front matter r 2007 Elsevier B.V. All rights reserved

e.2006.12.048

ng author. Departamento de Economı́a, Uni-

iedo, Campus del Cristo, 33071 Oviedo, Spain.

48 84; fax: +34985 10 48 71.

ss: [email protected] (A. Rodrı́guez-Álvarez).

version of this paper has been published like

FUNCAS (Fundación Española de las Cajas de

1/2005 and were presented at the Permanent

ciency and Productivity, Oviedo, April 2004 and

American Productivity Workshop, Toronto,

04. This research was funded with grants from

omo de Canarias, Project PI2003/188.

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., 1995 or Cuesta, 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, 1993 or 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

dx.doi.org/10.1016/j.ijpe.2006.12.048

mailto:[email protected]

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3

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

heterogeneous traffic, including containerized and non-contain-

A. Rodrı́guez-Álvarez et al. / Int. J. Production Economics 109 (2007) 149–161150

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. Färe 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 in Rodrı́guez-Álvarez 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; Martı́nez

Budrı́a et al., 1999; Tongzon, 2001; Valentine and

Gray, 2001; Bonilla et al., 2002; Martı́n, 2002;

Pestana, 2003; Estache et al., 2004), and the second

is through stochastic frontier analysis (SFA), (i.e.

Liu, 1995; Baños Pino et al., 1999; Coto Millán et

al., 2000; Notteboom et al., 2000; Cullinane et al.,

2002; Estache et al., 2002; Cullinane and Song,

2003; Dı́az, 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

2

For more details, see Coelli et al. (1999).

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 (time-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

erized cargo. It can be transformed into a specialized one (e.g.

containers only) by changing equipment.

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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.

Outputs

CONT 1000Ton 59.2 41.57 53.1 9.72 33.5 7.45 97.4 54.36

MG 1000Ton 5.6 6.35 0.6 0.78 9.9 7.39 4.4 3.12

ROD 1000Ton 2.1 2.36 1.0 0.71 0.8 0.86 4.7 2.49

INPUTS

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 1000PTAS deflated 24,534.2 8445.04 21,961.4 5,485.22 20,573.2 3,556.72 31,832.1 10192.23

GK 1000PTAS deflated 12,985.4 7728.52 6,063.2 429.87 11,043.0 3,939.85 21,416.1 7119.51

K M

2

61,484.4 11758.16 63,971.8 7,892.55 57,530.6 2,597.86 64,435.8 18481.79

Expenditure

GLC 1000PTAS deflated 17,964.1 8563.95 13,113.6 6,826.70 14,463.6 3,592.70 26,622.4 7979.02

GLE 1000PTAS deflated 21,447.9 12515.12 18,759.9 6,911.54 20,738.9 9,453.66 24,663.6 17967.74

A. Rodrı́guez-Álvarez et al. / Int. J. Production Economics 109 (2007) 149–161154

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

8

This 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.)

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 in Tovar (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

9

All monetary variables have been deflacted.

10

Note this is the same percentage that Cullinane and Song

(2003) report as a typical expenditure of a port.

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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

Table 2

Distance system estimated

Variable Coefficient Standard error t-Statistic

L(CONT) �0.32822 0.3947 �8.3160

��

L(MG) �0.35813 0.0057 �6.3068

��

L(ROD) �0.01642 0.0095 �1.7225

�

L(LC) 0.14139 0.0369 3.8291

��

L(LE) 0.25114 0.0279 8.9895

��

L(GI) 0.27117 0.0458 5.9193

��

L(K) �0.18176 0.1415 �1.2847

L(GK) 0.33629 0.0435 7.7245

��

L(CONT).L(CONT) �0.13236 0.0747 �1.7714

�

L(CONT).L(MG) 0.02318 0.0086 2.6832

��

L(CONT).L(ROD) �0.01045 0.0111 �0.9447

L(CONT).L(LC) �0.02655 0.0132 �2.0089

��

L(CONT).L(LE) 0.03048 0.0155 1.9698

��

L(CONT).L(GI) 0.00436 0.0074 0.5858

L(CONT).L(K) �0.33217 0.1905 �1.7438

�

L(CONT).L(GK) 0.00830 0.0046 �1.8100

�

L(MG).L(MG) �0.00856 0.0016 �5.6796

��

L(MG).L(ROD) �0.00155 0.0014 �1.1364

L(MG).L(LC) �0.00184 0.0017 �1.1019

L(MG).L(LE) 0.00071 0.0017 0.41710

L(MG).L(GI) 0.00092 0.0008 1.0878

L(MG).L(K) �0.03581 0.0317 �1.1298

L(MG).L(GK) 0.00021 0.0005 0.4520

L(ROD).L(ROD) �0.00322 0.0027 �1.2079

L(ROD).L(LC) �0.00789 0.0022 �3.6192

��

L(ROD).L(LE) 0.00561 0.0022 2.5637

��

Equation Mean

Input distance function —

Ordinary worker share equation 0.236319

Special worker share equation 0.278165

Intermediate consumption share equation 0.323562

Capital share equation 0.161953

�

Statistically significant at 10%.

��

Statistically significant at 5%.

reinforces the need for a multioutput analysis

Jara-Dı́az 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.

Variable Coefficient Standard error t-Statistic

L(ROD).L(GI) 0.00130 0.0009 1.4431

L(ROD).L(K) 0.08451 0.0929 0.9100

L(ROD).L(GK) 0.00099 0.0005 2.1150

��

L(LC).L(LC) 0.02116 0.0122 1.7274

�

L(LC).L(LE) 0.05233 0.0114 4.6108

��

L(LC).L(GI) �0.04950 0.0055 �8.9437

��

L(LC).L(K) �0.01692 0.0340 �0.4972

L(LC).L(GK) �0.02399 0.0035 �6.8374

��

L(LE).L(LE) 0.05444 0.0138 3.9455

��

L(LE).L(GK) �0.03723 0.0030 �12.4542

��

L(LE).L(GI) �0.06949 0.0054 �12.7574

��

L(LE).L(K) 0.10786 0.0311 3.4794

��

L(GI).L(GI) 0.17636 0.0053 33.0481

��

L(GI).L(GK) �0.05736 0.0031 �18.4742

��

L(GI).L(K) �0.0433 0.0158 �2.7515

��

L(K).L(K) �0.31434 0.6175 0.5091

L(K).L(GK) �0.04762 0.0102 �4.6748

��

L(GK).L(GK) 0.11858 0.0029 41.0775

��

DT92 0.12548 0.0396 3.1696

��

DT93 0.09536 0.0790 1.2067

DT94 0.13487 0.0945 1.4279

DT95 0.15500 0.1052 1.4727

DT96 �0.02817 0.1173 �0.2402

DT97 �0.13772 0.1303 �1.0566

DT98 �0.18434 0.1393 �1.3232

DT99 �0.13160 0.1511 �0.8710

R

2

Std. error of regression

— 0.079379

0.7541 0.044199

0.8406 0.042865

0.8505 0.020191

0.9602 0.012590

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A positive (negative) value for TC indicates an

upward (downward) shift in the distance function

(see Färe and Grosskopf, 1995). This measure is

usually associated with technological change. The

indices obtained from expression (10) are presented

in Table 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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manipulación de mercancı́as en terminales portuarias. El

Puerto de La Luz y de Las Palmas. (A multioutput cost

analysis for cargo handling services in port terminals. La Luz

y de Las Palmas’ Port) Ph.D. Departamento de Análisis

Económico Aplicado. Universidad de Las Palmas de Gran

Canaria. España (available on: /http://www.eumed.net/tesis/

btf/index.htmS).

Tovar, B., Trujillo, L., Jara-Dı́az, S., 2004. Organization and

regulation of the port industry: Europe and Spain. In: Coto-

Millan, P. (Ed.), Essays on Microeconomics and Industrial

Organisation, second Ed. Physica-Verlag. A springer-Verlag

Company, Germany.

Valentine, V.F., Gray, R., 2001. The measurement of port

efficiency using data envelopment analysis. Ninth World

Conference on Transport Research, Seoul, Korea.

http://www.eumed.net/tesis/btf/index.htm

http://www.eumed.net/tesis/btf/index.htm

gr3.eps

ARTICLE IN PRESS

0925-5273/$ - see

doi:10.1016/j.ijp

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

www.elsevier.com/locate/ijpe

Firm and time varying technical and allocative efficiency:

An application to port cargo handling firms

Ana Rodrı́guez-Álvarez

a,�

, Beatriz Tovar

b

, Lourdes Trujillo

b,1

a

University of Oviedo, Spain

b

Research 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

Abstract

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.

r 2007 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

front matter r 2007 Elsevier B.V. All rights reserved

e.2006.12.048

ng author. Departamento de Economı́a, Uni-

iedo, Campus del Cristo, 33071 Oviedo, Spain.

48 84; fax: +34985 10 48 71.

ss: [email protected] (A. Rodrı́guez-Álvarez).

version of this paper has been published like

FUNCAS (Fundación Española de las Cajas de

1/2005 and were presented at the Permanent

ciency and Productivity, Oviedo, April 2004 and

American Productivity Workshop, Toronto,

04. This research was funded with grants from

omo de Canarias, Project PI2003/188.

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., 1995 or Cuesta, 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, 1993 or 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

dx.doi.org/10.1016/j.ijpe.2006.12.048

mailto:[email protected]

Page 2

ARTICLE IN PRESS

3

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

heterogeneous traffic, including containerized and non-contain-

A. Rodrı́guez-Álvarez et al. / Int. J. Production Economics 109 (2007) 149–161150

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. Färe 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 in Rodrı́guez-Álvarez 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; Martı́nez

Budrı́a et al., 1999; Tongzon, 2001; Valentine and

Gray, 2001; Bonilla et al., 2002; Martı́n, 2002;

Pestana, 2003; Estache et al., 2004), and the second

is through stochastic frontier analysis (SFA), (i.e.

Liu, 1995; Baños Pino et al., 1999; Coto Millán et

al., 2000; Notteboom et al., 2000; Cullinane et al.,

2002; Estache et al., 2002; Cullinane and Song,

2003; Dı́az, 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

2

For more details, see Coelli et al. (1999).

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 (time-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

erized cargo. It can be transformed into a specialized one (e.g.

containers only) by changing equipment.

Page 6

ARTICLE IN PRESS

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.

Outputs

CONT 1000Ton 59.2 41.57 53.1 9.72 33.5 7.45 97.4 54.36

MG 1000Ton 5.6 6.35 0.6 0.78 9.9 7.39 4.4 3.12

ROD 1000Ton 2.1 2.36 1.0 0.71 0.8 0.86 4.7 2.49

INPUTS

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 1000PTAS deflated 24,534.2 8445.04 21,961.4 5,485.22 20,573.2 3,556.72 31,832.1 10192.23

GK 1000PTAS deflated 12,985.4 7728.52 6,063.2 429.87 11,043.0 3,939.85 21,416.1 7119.51

K M

2

61,484.4 11758.16 63,971.8 7,892.55 57,530.6 2,597.86 64,435.8 18481.79

Expenditure

GLC 1000PTAS deflated 17,964.1 8563.95 13,113.6 6,826.70 14,463.6 3,592.70 26,622.4 7979.02

GLE 1000PTAS deflated 21,447.9 12515.12 18,759.9 6,911.54 20,738.9 9,453.66 24,663.6 17967.74

A. Rodrı́guez-Álvarez et al. / Int. J. Production Economics 109 (2007) 149–161154

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

8

This 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.)

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 in Tovar (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

9

All monetary variables have been deflacted.

10

Note this is the same percentage that Cullinane and Song

(2003) report as a typical expenditure of a port.

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A. Rodrı́guez-Álvarez et al. / Int. J. Production Economics 109 (2007) 149–161 155

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

Table 2

Distance system estimated

Variable Coefficient Standard error t-Statistic

L(CONT) �0.32822 0.3947 �8.3160

��

L(MG) �0.35813 0.0057 �6.3068

��

L(ROD) �0.01642 0.0095 �1.7225

�

L(LC) 0.14139 0.0369 3.8291

��

L(LE) 0.25114 0.0279 8.9895

��

L(GI) 0.27117 0.0458 5.9193

��

L(K) �0.18176 0.1415 �1.2847

L(GK) 0.33629 0.0435 7.7245

��

L(CONT).L(CONT) �0.13236 0.0747 �1.7714

�

L(CONT).L(MG) 0.02318 0.0086 2.6832

��

L(CONT).L(ROD) �0.01045 0.0111 �0.9447

L(CONT).L(LC) �0.02655 0.0132 �2.0089

��

L(CONT).L(LE) 0.03048 0.0155 1.9698

��

L(CONT).L(GI) 0.00436 0.0074 0.5858

L(CONT).L(K) �0.33217 0.1905 �1.7438

�

L(CONT).L(GK) 0.00830 0.0046 �1.8100

�

L(MG).L(MG) �0.00856 0.0016 �5.6796

��

L(MG).L(ROD) �0.00155 0.0014 �1.1364

L(MG).L(LC) �0.00184 0.0017 �1.1019

L(MG).L(LE) 0.00071 0.0017 0.41710

L(MG).L(GI) 0.00092 0.0008 1.0878

L(MG).L(K) �0.03581 0.0317 �1.1298

L(MG).L(GK) 0.00021 0.0005 0.4520

L(ROD).L(ROD) �0.00322 0.0027 �1.2079

L(ROD).L(LC) �0.00789 0.0022 �3.6192

��

L(ROD).L(LE) 0.00561 0.0022 2.5637

��

Equation Mean

Input distance function —

Ordinary worker share equation 0.236319

Special worker share equation 0.278165

Intermediate consumption share equation 0.323562

Capital share equation 0.161953

�

Statistically significant at 10%.

��

Statistically significant at 5%.

reinforces the need for a multioutput analysis

Jara-Dı́az 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.

Variable Coefficient Standard error t-Statistic

L(ROD).L(GI) 0.00130 0.0009 1.4431

L(ROD).L(K) 0.08451 0.0929 0.9100

L(ROD).L(GK) 0.00099 0.0005 2.1150

��

L(LC).L(LC) 0.02116 0.0122 1.7274

�

L(LC).L(LE) 0.05233 0.0114 4.6108

��

L(LC).L(GI) �0.04950 0.0055 �8.9437

��

L(LC).L(K) �0.01692 0.0340 �0.4972

L(LC).L(GK) �0.02399 0.0035 �6.8374

��

L(LE).L(LE) 0.05444 0.0138 3.9455

��

L(LE).L(GK) �0.03723 0.0030 �12.4542

��

L(LE).L(GI) �0.06949 0.0054 �12.7574

��

L(LE).L(K) 0.10786 0.0311 3.4794

��

L(GI).L(GI) 0.17636 0.0053 33.0481

��

L(GI).L(GK) �0.05736 0.0031 �18.4742

��

L(GI).L(K) �0.0433 0.0158 �2.7515

��

L(K).L(K) �0.31434 0.6175 0.5091

L(K).L(GK) �0.04762 0.0102 �4.6748

��

L(GK).L(GK) 0.11858 0.0029 41.0775

��

DT92 0.12548 0.0396 3.1696

��

DT93 0.09536 0.0790 1.2067

DT94 0.13487 0.0945 1.4279

DT95 0.15500 0.1052 1.4727

DT96 �0.02817 0.1173 �0.2402

DT97 �0.13772 0.1303 �1.0566

DT98 �0.18434 0.1393 �1.3232

DT99 �0.13160 0.1511 �0.8710

R

2

Std. error of regression

— 0.079379

0.7541 0.044199

0.8406 0.042865

0.8505 0.020191

0.9602 0.012590

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A positive (negative) value for TC indicates an

upward (downward) shift in the distance function

(see Färe and Grosskopf, 1995). This measure is

usually associated with technological change. The

indices obtained from expression (10) are presented

in Table 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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