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Table of Contents
                            Firm and time varying technical and allocative efficiency: An application to port cargo handling firms
	Port terminals and their regulation in Spain
	Modelling firm and time-varying technical and allocative efficiency
		Measuring technical efficiency
		Measuring allocative efficiency
	Econometric specification
	Data and results
		Data description
			Technical efficiency
			Allocative efficiency: error components approach
			Allocative efficiency: parametric approach
			Technical change
Document Text Contents
Page 1


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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 Rodrı́guez-Álvarez

, Beatriz Tovar
, Lourdes Trujillo


University of Oviedo, Spain

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

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


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
mailto:[email protected]

Page 2


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.


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
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

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,

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


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 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


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


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


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.


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
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.


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%

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

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
All monetary variables have been deflacted.

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


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. Rodrı́guez-Álvarez et al. / Int. J. Production Economics 109 (2007) 149–161160
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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