Directory UMM :Data Elmu:jurnal:I:International Journal of Production Economics:Vol69.Issue3.Feb2001:
Int. J. Production Economics 69 (2001) 277}285
The calculation of shadow prices for industrial
wastes using distance functions: An analysis for
Spanish ceramic pavements "rms
Ernest Reig-MartmH nez!,", AndreH s Picazo-Tadeo!,*, Francesc HernaH ndez-Sancho!
!Department of Applied Economics II, University of Valencia, Avda dels Tarongers s/n, 46022 Valencia, Spain
"Valencian Institute of Economic Research (IVIE), Guardia Civil 22, 46020 Valencia, Spain
Received 10 August 1999; accepted 27 January 2000
Abstract
This paper deals with the calculation of shadow prices for two industrial wastes generated on their production
processes by 18 "rms belonging to the Spanish ceramic pavements industry. These prices are then used to calculate an
extended productivity index which takes into consideration wastes going with the production of marketable goods. We
follow the methodological approach "rst proposed by FaK re et al. (The Review of Economics and Statistics 75 (1993)).
A negative correlation is found between absolute shadow prices and wastes production intensity, re#ecting a greater
marginal cost of eliminating wastes for those "rms using less contaminant production processes. Di!erences between
a conventional labour productivity index and an extended productivity index are also statistically related to "rms
characteristics such as size, previous investments in cleaner technologies and a$liation to a Technological Institute. ( 2001 Elsevier Science B.V. All rights reserved.
Keywords: Shadow prices; Distance functions; Ceramic pavements industry; Environment; Productivity
1. Introduction
The growing recognition of the environment as a public good has unleashed a debate
with regard to the convenience of breaking the
tradition of assessing the value of industrial
production by implicitly assuming that all goods
produced are socially desirable. If it is accepted that
a part of industrial production is undesirable,
* Corresponding author.
E-mail address: [email protected](A. Picazo-Tadeo).
and public authorities establish regulations to
limit the emissions of polluting wastes, the cost
that "rms face to ful"l legal environmental restrictions, should be evaluated. Therefore, shadow prices for undesirable outputs have to be computed in
order to measure in terms of opportunity costs the
impact on "rms performance of environmental restrictions preventing free disposal of industrial
wastes.
Shadow prices of undesirable outputs are understood in this context as the marginal cost due to
a marginal reduction in the possibility of freely
disposing of wastes generated in the production
0925-5273/01/$ - see front matter ( 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 5 - 5 2 7 3 ( 0 0 ) 0 0 0 1 8 - 9
278
E. Reig-Martn& nez et al. / Int. J. Production Economics 69 (2001) 277}285
process.1 From the point of view of public policies
for environmental protection, the availability of
these shadow prices reports several important bene"ts; among them, the possibility of comparing
the marginal bene"ts of environment policies, with
the cost they generate for private "rms; the chance
of checking if all "rms face the same shadow prices;
and, "nally, the feasibility to adapt traditional productivity indexes to allow for the consideration of
di!erent intensity of waste production among
"rms, sectors or even countries.
This paper deals with the calculation of shadow
prices for undesirable outputs that are by-products
of the industrial production of ceramic pavements,
with data coming from a sample of Spanish "rms
located at Castellon, on the Valencian region. We
follow the distance function approach suggested by
FaK re et al. [1] (FGLY henceforth), recently applied
by Coggins and Swinton [2]. This method uses
output distance functions to derive shadow prices
for all outputs (desirable and undesirable) generated by "rms in their productive processes. In particular, it makes it feasible to obtain shadow prices
for undesirable outputs without having to use exogenous information on wastes elimination costs
coming from other studies (as Pittman [3] does in
a paper aimed to adapt the multilateral productivity indexes pioneered by Caves et al. [4] for taking
stock of polluting emissions). Secondly, this paper
aims to propose an extended measure of productivity that takes into account residuals emerging as
a by-product of current industrial production processes. Availability of residuals output data for each
of the "rms in our sample allows us to undertake
this correction.
This introduction is followed by a description of
the methodology. Section 3 describes the sample
1 This can be veri"ed by de"ning a cost function and setting
up a maximising pro"t problem. Given a vector of (desirable and
undesirable) outputs u, with prices r, and being x and p the
quantity and price input vectors, respectively, the cost function
is c(u, p)"min Mpx : x can produce uN, while the pro"t function
can be set up as n(r, p)"max Mru!c(u, p)N. From "rst-order
condition for undesirable output j we get
Lc(u, p)
r"
,
j
Lu
j
where r is the shadow price of waste j.
j
and establishes the main results, while Section 4
concludes.
2. The output distance function and the derivation of
shadow prices
In order to illustrate the basic aspects of the
methodological approach proposed by FGLY to
derive output shadow prices from distance functions, let us assume that we have a set of "rms using
a vector of inputs x3RN to produce a vector of
`
outputs u3RM , some of which can be considered
`
undesirable or bad outputs. The technology of reference is represented by an output correspondence
which is a mapping P : RN PP(x)-RM , where
`
`
the output set P(x) represents the set of all feasible
vectors of outputs given a vector of inputs x. It is
also assumed that the technology satis"es the usual
axioms initially proposed by Shephard [5], which
allows to de"ne the distance function in outputs as
the inverse of the maximum radial expansion of
a given output vector, in such a way that the resulting output vector remains within P(x). The distance
function can be de"ned on the output set as2
D (x, u)"infMh : (u/h)3P(x)N.
(1)
0
The assumptions made on the disposability
properties of the technology are a key issue in order
to derive output shadow prices. In particular, it is
assumed that "rms cannot freely eliminate (without
any cost) the industrial wastes (undesirable outputs) that they generate in their production processes, either because it would require a greater use
of inputs or because resources would have to be
diverted from marketable production in order to
eliminate undesirable outputs. This condition can
be incorporated to the characterisation of the technology by means of the axiom of weak disposal of
outputs, in the sense that if u3P(x), it will also hold
that hu3P(x), being in this case 0)h)1. This
assumption is consistent with the opportunity cost,
measurable in terms of the loss of desirable produc-
2 This expression is equivalent to the reciprocal of the output
oriented e$ciency measure of Farrell [6,7]. Also note that
u3P(x) if and only if D (x, u))1.
0
E. Reig-Martn& nez et al. / Int. J. Production Economics 69 (2001) 277}285
tion, that "rms would have to incur to ful"l environmental regulations imposing a reduction of industrial wastes, and allows for these undesirable
outputs to have nonpositive shadow prices.
Following FGLY's approach, under certain
assumptions, the shadow prices we seek can be
obtained from the gradient vector of partial derivatives of an output distance function. The formal
reasoning starts recognising the existence of a duality between the revenue function R(x, r) and the
output distance function D (x, u). Denoting by r the
0
output price vector, some of which components
can be negative, the revenue function can be
expressed as
R(x, r)"sup Mru : D (x, u))1N,
0
u
(2)
and the dual distance function in outputs is given
by
D (x, u)"sup Mru : R(x, r))1N,
0
r
(4)
where + is the gradient operator.
Expression (3) can be developed as a relationship
between the distance function and the shadow
prices, so that
D (x, u)"rH(x, u)u,
0
(5)
where rH(x, u) represents the output price vector
that maximises revenue. Applying Shephard's dual
lemma to expression (5), yields
+ D (x, u)"rH(x, u),
u 0
(6)
which combined with (4), leads to
r"R(x, r)rH(x, u).
In expression (7), rH(x, u) are obtained from the
gradient of the distance function, and denote revenue-de#ated output prices. The main di$culty to
obtain absolute shadow prices from expression (7)
is the dependence of the revenue function R(x, r) on
r, that is precisely the vector of shadow prices we
seek. If we assume that the observed price of an
output m, r0 , equals its absolute shadow price,
m
represented by r , then the maximum revenue is
m
R(x, r0 )"r0 /rH (x, u),
m m
m
(8)
which can be used to compute the absolute shadow
prices of the remaining outputs from its de#ated
shadow prices. Denoting by r
the absolute
m{
shadow prices for outputs other than m, we get
LD (x, u)
r "RrH (x, u)"R 0
m{
m{
Lu
m{
(3)
being ru the inner product of the output prices and
quantity vectors.
Then, assuming that the revenue and distance
functions are both di!erentiable, a Lagrange problem can be set up to maximise revenue, and "rstorder conditions yield the relationship [8]:
r"R(x, r)+ D (x, u),
u 0
279
(7)
LD (x, u)/Lu
m{ .
"r0 0
m LD (x, u)/Lu
0
m
(9)
An alternative way to handle the problem above
is to suppose that a zero-pro"t and revenue-maximising "rm would incur in an observed cost equivalent to its observed revenue R(x, r) [8], and simply
use expression (7) to obtain absolute shadow prices.
Finally, the distance function has to be parameterised and estimated to proceed with the calculation of the absolute shadow prices along the lines
we have showed.
After absolute shadow prices have been computed, we make use of them to formulate an
extended productivity index allowing for the consideration of di!erent waste production intensity
among "rms. Let us make a partition of the quantity and output price vectors, so that u"(u , u )
a b
and r"(r , r ), where u "(u , 2, u ) and
a b
a
1
J
u "(u
,
, u ) are the quantity vectors of deb
J`1 2 M
sirable and undesirable outputs, respectively, while
r "(r , 2, r ) and r "(r
,
, r ) are the
a
1
J
b
J`1 2 M
price vectors also for good and bad outputs.
Considering only the production of desirable
outputs, the partial productivity index for input x
j
280
E. Reig-Martn& nez et al. / Int. J. Production Economics 69 (2001) 277}285
can be denoted as
r u
(10)
PI" a a .
x
j
However, the estimation of shadow prices for
undesirable outputs allows to de"ne an extended
index of partial productivity for input x :
j
(r u )#(r u ) ru
b b " .
EPI" a a
(11)
x
x
j
j
Given that shadow prices for bad outputs are
nonpositive, the extended productivity index proposed by expression (11) will always take values
equal or smaller than the traditional productivity
index of expression (10); this allows for calculating
the productivity deviation index as
r u
PI
" a a.
PDI"
ru
EPI
(12)
Expression (12) will be equal or greater than one
and measures the degree of overvaluation in quantifying input x productivity levels when only marj
ketable output (good output) is being considered
with disregard of those wastes that arise as a byproduct and have potential harmful e!ects on the
environment.
ish Mediterranean coast. The source of the data is
the Valencian Region Inventory of Industrial Residuals elaborated in 1995 by the Department of Environment of the Valencian Regional Government. All
"rms face the same productive process, which is
characterised by the production of one desirable
output, ceramic pavements (u ), and two wastes or
1
undesirable outputs, watery muds (u ) and used oil
2
(u ). Intermediate input is clay, kaolin, felspar and
3
limestones (x ), while labour (x ) and capital (x ) are
1
2
3
primary inputs. Labour input is measured as the
number of workers, and capital is proxied by energy consumption in kilowatts/hour. Table 1 presents some descriptive statistics of the data.
As in FGLY, the distance function in output is
parameterised as a translog function, which is given
by the expression
3
3
ln D (x, u)"/# + b ln x # + a ln u
0
n
n
m
m
n/1
m/1
1 3 3
# + + b (ln x )(ln x )
nn{
n
n{
2
n/1 n{/1
3
1 3
# + + a (ln u )(ln u )
mm{
m
m{
2
m/1 m{/1
3 3
# + + c (ln x )(ln u ),
nm
n
m
n/1 m/1
3. Data and empirical 5ndings
The sample used in this paper comes from
a cross-section data set of 18 Spanish ceramic pavements producers located at Castellon, on the Span-
(13)
where m and n denote outputs and inputs, respectively.
Table 1
Sample description
Variable
Description
Units
Mean
Standard deviation Maximum
Minimum
u
1
u
2
u
3
x
1
Ceramic pavements
m2
2,031,077
1,168,311
4,500,000
200,000
Watery muds
t
2,908
4,108
15,648
14
Used oil
kg
1,822
3,135
12,000
100
Clay, kaolin, felspar and
limestones
Labour
t
50,192
40,762
144,000
3,300
Number of workers
128
121
428
25
Capital
kw/h
4,573
4,705
20,000
500
Observed price
Euros/m2
6.76
3.74
15.91
2.80
x
2
x
3
r01
u
E. Reig-Martn& nez et al. / Int. J. Production Economics 69 (2001) 277}285
The translog function is a #exible functional form
that does not impose strong disposability of outputs; however, given the large number of parameters in relation to the size of our sample it is not
possible to estimate using econometric methods.
Alternatively, the parameters in expression (13) are
obtained using mathematical programming techniques [9], by solving the following optimisation
program (see again FGLY):
18
Max + [ln D (xk, uk)!ln 1]
0
k/1
(14)
s.t.
ln D (xk, uk))0, k"1, 2, 18,
0
(14a)
L ln D (xk, uk)
0
*0,
L ln uk
m
(14b)
m"1, k"1, 2, 18,
L ln D (xk, uk)
0
)0, m"2, 3, k"1, 2, 18, (14c)
L ln uk
m
3
+ a "1,
m
m/1
3
m"1, 2, 3, m@"1, 2, 3,
(14d)
+ a "0,
mm{
n"1, 2, 3,
m{/1
3
+ c "0,
nm
m/1
a "a , m"1, 2, 3, m@"1, 2, 3,
(14e)
mm{
m{m
H
b "b , n"1, 2, 3, n@"1, 2, 3,
nn{
n{n
(14f)
where k denotes "rms.
The set of restrictions in (14a) imply that each
observation is located either on or below the technological frontier; the restrictions contained in
(14b) guarantee that the desirable output will have
a nonnegative shadow price for all "rms, while (14c)
assures that undesirable outputs will have nonpositive shadow prices, also for all "rms. The assumption of weak disposal of outputs is introduced by
restriction (14d) that imposes homogeneity of
degree#1 in outputs; "nally (14e) and (14f) impose
symmetry.
The objective function in (14) minimises the sum
of the deviations of individual observations from
281
Table 2
Estimated parameters of the translog distance function. Expression (13)
Parameter
/
b
1
b
2
b
3
a
1
a
2
a
3
b
11
b
12
b
13
b
22
b
23
b
33
a
11
Parameter
47.253
!13.459
!0.403
1.459
3.112
!2.322
0.210
1.519
0.250
!0.898
0.080
!0.401
2.327
0.039
a
12
a
13
a
22
a
23
a
33
c
11
c
12
c
13
c
21
c
22
c
23
c
31
c
32
c
33
!0.014
!0.025
0.001
0.013
0.012
!0.131
0.098
0.033
!0.079
0.134
!0.055
!0.018
0.013
0.005
the frontier. However, we are in fact maximising
because the distance function takes positive values
lower or equal than one, and therefore its log can
take negative or zero values; in consequence, to
maximise the deviations of the distances expressed
in logs from zero (represented by the log of one) is
equivalent to minimise the sum of the absolute
deviations of the individual observations.
Table 2 shows the parameter estimates of the
translog function given by expression (13). Using
those "gures and the available information, the
output distance function for each individual "rm is
computed, with an average value of 0.927. It is well
known that the output distance function is the
reciprocal of Farrell's measure of output e$ciency
whose average value is then 1.079. This means that
making an e$cient use of their available resources,
the "rms of the sample would be able to increase
their production of ceramic pavements almost by
8% on average.
The estimation of the distance function allows us
to obtain output shadow prices for each "rm in our
sample, as we explained above. In order to get the
shadow income of each productive unit, we use
expression (13) under the hypothesis that the
shadow price of good output (ceramic pavements) is
equal to its observed market price; this is equivalent
to assume that r0 "r01 , r01 being the square meter
u u
m
282
E. Reig-Martn& nez et al. / Int. J. Production Economics 69 (2001) 277}285
Table 3
Output shadow prices!
r0
u1
Mean
6.76
Standard deviation 3.74
Weighted mean
6.84
Maximum
15.91
Minimum
2.81
r2
u
r3
u
!9,830.6
23,345.9
!336.6
!79,893.5
0.0
!1,043.7
2,512.8
!125.5
!9,998.6
0.0
!Euros.
of pavement market price, a "gure which is di!erent
for each company. Table 3 shows the computations
for output shadow prices; simple means and standard deviations, as well as weighted means3 are
reported.
The shadow prices of the industrial wastes could
be interpreted as the marginal loss of revenue corresponding to the volume of resources that a "rm
would need to reduce its emission by a marginal
unit. Therefore, in average terms, a reduction of one
ton of watery mud production, residual u , would
2
require the use of resources valued in 336.6 euros,
which in terms of marketable output would imply
an implicit loss of 49.2 square meters of pavements,
considering that the market price for square meter
is 6.84 euros on average. Similarly, and in order to
reduce the production of used oil in a kilogram,
residual u , the opportunity cost would be valued
3
in 125.5 euros, equivalent to a reduction in good
output production of 18.3 square meters.
Shadow price estimates di!er signi"cantly
among "rms, as the high standard deviation of
those prices reveals; this result is consistent with
FGLY, and it is also related to important di!erences among "rms in terms of quantities of residuals discharged per unit of desirable output
produced. After shadow prices at "rm level have
been obtained, the correlation between absolute
values of these prices and waste emission for square
meter of ceramic pavements has been computed,
3 Weights are the quantity of wastes produced by each "rm;
they are chosen to obtain a weighted mean of shadow prices for
bad outputs that represents the cost of reducing in one unit its
production in the sample.
getting a negative value close to 30% in the case of
watery mud and around 25% for used oil. The
correlation coe$cient has the expected sign since
companies that produce a greater volume of residuals per unit of marketable production are very
likely to be those that rely on technical equipment
less adapted to recycling those residuals or minimising their delivery; for these "rms, investments
intended to cut the volume of e%uents would have
a relatively small cost in comparison with their
prospective yields in terms of reduction of emissions. On the other hand, those "rms that have
already reached a high performance according to
their ability to control the environmental impact of
their production processes would face a higher
marginal cost in case of stepping-up their e!orts
to reduce waste discharges. This would be re#ected
in a higher shadow price for bads in these
companies.
These results could be of interest in devising an
e$cient regulation of some aspects related to the
industrial contamination issue. The shadow prices
that have been estimated re#ect a wide variety of
"rms positions as for the marginal cost of reducing
the emission of residuals in the Spanish ceramic
industry. On the other hand, the close knitted geographical location of these "rms makes it reasonable to assume that marginal social bene"ts of
cutting current levels of industrial contamination
are probably similar among companies, because
they share a common natural landscape, and the
same natural resources and human habitat. If an
e$cient regulation means that the marginal cost of
decreasing current contamination levels has to be
made equal to the marginal social bene"ts, it makes
sense to deduce that the current situation is
not e$cient in terms of the allocation of resources.
It is di$cult to go further from these basic statements without being able to make use of more
detailed data on "rms technology and output
mix, but it seems "ne to infer that some conditions exist so that a market of emission permits
could be developed where some "rms would wish
to enter as buyers and others as suppliers. In
order to ful"l environmental regulations, each
"rm would have to make a choice between carrying
out fresh investments or acquiring emission
permits.
E. Reig-Martn& nez et al. / Int. J. Production Economics 69 (2001) 277}285
Finally, it seems right to remark that knowledge
on shadow prices allows the researcher to approach
a valuation of industrial production not con"ned to
marketable production and market prices, but able
to include an estimate of the (negative) value of
a likely increase in industrial refuses, linked to the
expansion of good output levels. The type of
shadow prices computed in this paper are derived
strictly from technical relations between inputs and
outputs and should be considered as estimates
arising from a producer approach. Externalities
on consumers or other producers are not taken into
account, but could be incorporated in a straightforward way, provided adequate data are made available, within the same framework of analysis, as
shown in FaK re and Grosskopf [10]. Despite their
shortcomings, the shadow prices we have used
illustrate well enough the e!ects on production
valuation of including in the price vector several
components with a negative sign, each corresponding to a di!erent undesirable output.
We now proceed to compute two di!erent
measures of labour productivity, one along the
conventional lines, as a quotient between the monetary value of each "rm marketable output (ceramics pavements) and labour sta!, and an extended
one, de"ned by expression (11). The outcome of
using both types of productivity indexes appear in
Table 4. Both productivity measures di!er by
values that go from 3% to 30% in the sample, with
an average gap close to 12%. It means that di!erences are important enough to make an impact on
"rms comparisons. As an example, "rm 8 is more
productive in conventional terms than "rm 5, but it
changes when an environmental-friendly approach
is taken and waste production from both "rms are
included in the numerator of the productivity quotient, using shadow prices to translate residuals
quantities to monetary "gures. Now "rm 5 is more
productive than "rm 8. Ranking between "rms
4 and 10 is also inverted when moving from a productivity measure to the other, and two "rms
(11 and 13), that have quite similar labour productivity levels when only good output is compared,
show marked di!erences when bads are also contemplated.
From society's comprehensive view it is clearly
a serious matter of concern. It is not possible to
283
Table 4
Labour productivity measures!
Firm
Productivity
Labour
Extended
deviation
productivity labour
productivity index
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
57.81
202.81
120.65
79.30
96.66
91.07
64.96
97.02
127.83
77.38
127.91
194.59
127.83
121.29
115.48
105.18
126.67
166.61
44.33
179.74
109.12
65.71
91.72
80.38
62.49
84.59
124.01
73.64
114.24
167.23
118.42
105.28
94.10
92.58
108.74
159.20
1.304
1.128
1.106
1.207
1.054
1.133
1.040
1.147
1.031
1.051
1.120
1.164
1.079
1.152
1.227
1.136
1.165
1.047
Mean
116.73
104.20
1.127
39.97
36.41
0.072
Standard deviation
!Euros per worker.
remain aloof to the fact that a given productivity
level can be achieved with very di!erent volumes of
real or potential noxious wastes, and a virtue of the
very simple indicator we propose is to ease the
transition to a new way of analysing entrepreneurial performance, apt enough to accueil a growing
public interest in environmental values. Firms that
have undertook costly investments in new equipments that allow cleaner production processes
should have their e!orts (that consume productive
resources), recognised and not merely dismissed as
less productive in conventional terms.
The next step we have followed is to disclose if
there exists a relationship between our deviation
productivity index and some "rm's characteristics,
making use of variance analysis. We have broken
our sample in two groups; group A includes those
"rms with a deviation smaller than the average
deviation for the whole sample (8 "rms), while
group B comprises all those "rms with deviation
equal or higher than average deviation (10 remain-
284
E. Reig-Martn& nez et al. / Int. J. Production Economics 69 (2001) 277}285
ing "rms). Then we have tried to ascertain if there is
a statistically signi"cant di!erence between both
subsamples concerning to "ve variables: size, azliation to a Technological Institute,4 spatial location,5
a record of past investments in cleaner technologies,
and use of external services for waste management.
Results are shown in Table 5 and are clearly
conclusive for all the variables under consideration.
Firms of greater size show a smaller deviation and
the same happens for "rms that have recorded
investments conducive to clean production processes. External management of wastes is mainly
associated to the "rms with higher bias; this was an
expected outcome, given that those "rms are more
intensive in terms of production of industrial
wastes, what forces them into a greater dependence
of external suppliers of services (transport, storage)
for waste disposal. A$liation to a Technological
Institute specialised in the ceramics industry (AICE)
helps to reduce the deviation, as variance analysis
shows. This "nding is probably linked to the services provided by the Institute in terms of technological consultancy, easing the access to R&D in
di!erent "elds, including the development and application of waste reducing techniques, and favouring di!usion of industry's best practice. The
variable spatial location is employed to distinguish
the "rms that are located in one area of very dense
concentration of this type of industry (the Plana
Baixa zone) and the others. We presume that the
4 The Region of Valencia has a network of Technological
Institutes specialised by branches of industrial production,
AICE being the one concerned with the ceramics industry. They
are non-pro"t entities under the form of business associations
sponsored and mostly funded by the public authorities and
oriented to promote technological innovation, best practice diffusion and quality tests. They provide external services (R&D,
among others) at low cost to their a$liates, that are mostly small
and medium sized "rms. A$liation is normally considered as an
index of innovative behaviour on the part of "rm's management.
5 The ceramics pavements industry is highly concentrated in
a small number of contiguous municipalities in the CastelloH n
Province, where "rms are supposed to enjoy important external
economies that could be broadly de"ning a Marshallian type
industrial district in the sense coined by the economic geography
literature. We hypothesize that close proximity improves the
chances of "rms being more sensible to good practice in terms of
waste management, trough imitation and easier technical information di!usion.
"rst enjoy an advantage in terms of sharing the
external economies generated by a dynamic industrial district, that gives them rapid access to information released by suppliers of new industrial
equipments and competitors and facilitates the
acquisition of better practices in dealing with
industrial residuals. Evidence, after performing
variance analysis, conforms to it.
4. Concluding remarks
This paper has been devoted to estimate shadow
prices for two di!erent types of undesirable outputs
or industrial wastes generated in their production
processes by eighteen Spanish "rms in the ceramic
pavements industry. The methodology follows the
approach suggested by FaK re et al. [1]. Accordingly,
central importance has been given to the duality
between output distance and revenue functions, using the former to derive output shadow
prices.
The shadow prices obtained for watery muds and
used oil (industrial wastes that are by-products in
the production of marketable ceramic pavements)
have made it feasible to measure in terms of loss of
marketable output production (square meters of
ceramic pavements) or its equivalent in cash revenue, the opportunity costs "rms would have to
incur in order to achieve a marginal decrease in the
production of those refuses. A negative correlation
has been observed between waste production intensity by "rms (as a proportion of their own output of
ceramic pavements) and absolute shadow prices
computed for these bads outputs. This feature probably re#ects a greater marginal cost of polluting
residues elimination for those "rms that had previously invested in cleaner technologies directed to
get rid of undesirable outputs, and are currently
generating less units of wastes for square meter of
ceramic pavements produced.
Another empirical result of some importance is
the observation of a high dispersion of shadow
prices "gures among "rms. This should be a matter
of concern for policy makers aiming to develop an
e$cient environmental regulation for the Spanish
ceramics pavement "rms located at the industrial
district of Castellon (a densely populated area),
E. Reig-Martn& nez et al. / Int. J. Production Economics 69 (2001) 277}285
285
Table 5
Variance analysis
Mean group A!
Mean group B"
Statistic F
p-value
Firm's size#
A$liation to
Technological
Institute$
Spatial
location%
Investments on
cleaner
technologies&
External
management
of waste u '
2
2,966.2
1,283.0
18.983
0.000
0.63
0.10
7.063
0.017
0.75
0.30
4.000
0.063
1.00
0.60
4.740
0.045
0.13
0.90
24.063
0.000
!Deviation smaller than average deviation for the whole sample; 8 "rms.
"Deviation greater or equal average deviation for the whole sample; 10 "rms.
#Thousand of square meters of ceramic pavements.
$Dummy variable that equals to 1 if the "rm is a$liated to Technological Institute AICE and 0 otherwise.
%Dummy equal to 1 if the "rm is located at the industrial district of Plana Baixa and 0 otherwise.
&Dummy equal to 1 if the "rm has invested on clean technologies and 0 otherwise.
'Dummy that equals to 1 if external management of waste u is carried out and 0 otherwise.
2
since for a similar marginal social bene"t obtained
from a cut in current pollution levels across sample
"rms, the marginal costs that those "rms would
have to face would be quite di!erent.
Finally we wish to use shadow prices to
emphasise on the need to improve current
productivity indexes in order to take industrial
waste into consideration. Our results show that
clear di!erences arise within the sample when computing conventional and extended measures of labour productivity at "rm level. These di!erences
are statistically associated to "rms characteristics,
such as size, record of former investments in cleaner
technologies, and azliation to a Technological Institute for the Ceramics Industry.
Acknowledgements
We thank the Bureau of Environmental Quality
of the Valencian Regional Government for statistical help, as well as two anonymous referees for
useful comments. We are also grateful tothe Ministry of Science and Technology of the Spanish Government for the Financial aid received (Project
SEC 2000-0803).
References
[1] R. FaK re, S. Grosskopf, C. Lovell, S. Yaisawarng, Derivation of shadow prices for undesirable outputs: a distance
function approach, The Review of Economics and Statistics 75 (1993) 374}380.
[2] J.S. Coggins, J.R. Swinton, The price of pollution: A dual
approach to valuing SO allowances, Journal of Environ2
mental Economics and Management 30 (1996) 58}72.
[3] R.W. Pittman, Multilateral productivity comparisons
with undesirable outputs, Economic Journal 93 (1983)
883}891.
[4] D.W. Caves, L.R. Christensen, W.E. Diewert, Multilateral
comparisons of output, input, and productivity using
superlative index numbers, Economic Journal 92 (1982)
73}86.
[5] R.W. Shephard, The Theory of Cost and Production
Functions, Princeton University, Princeton, NJ, 1970.
[6] M. Farrell, The measurement of productive e$ciency,
Journal of the Royal Statistics Society, Serie A 120 (3)
(1957) 253}282.
[7] R. FaK re, C. Lovell, Measuring the technical e$ciency of
production, Journal of Economic Theory 19 (1978) 150}172.
[8] R. FaK re, D. Primont, Multi-output Production and
Duality: Theory and Applications, Kluwer Academic
Publishers, Dordrecht, 1995.
[9] D. Aigner, S. Chu, On estimating the industry production
function, American Economic Review 58 (1968) 826}839.
[10] R. FaK re, S. Grosskopf, Shadow pricing of good and bad
commodities, American Journal of Agricultural Economics 80 (3) (1998) 584}590.
The calculation of shadow prices for industrial
wastes using distance functions: An analysis for
Spanish ceramic pavements "rms
Ernest Reig-MartmH nez!,", AndreH s Picazo-Tadeo!,*, Francesc HernaH ndez-Sancho!
!Department of Applied Economics II, University of Valencia, Avda dels Tarongers s/n, 46022 Valencia, Spain
"Valencian Institute of Economic Research (IVIE), Guardia Civil 22, 46020 Valencia, Spain
Received 10 August 1999; accepted 27 January 2000
Abstract
This paper deals with the calculation of shadow prices for two industrial wastes generated on their production
processes by 18 "rms belonging to the Spanish ceramic pavements industry. These prices are then used to calculate an
extended productivity index which takes into consideration wastes going with the production of marketable goods. We
follow the methodological approach "rst proposed by FaK re et al. (The Review of Economics and Statistics 75 (1993)).
A negative correlation is found between absolute shadow prices and wastes production intensity, re#ecting a greater
marginal cost of eliminating wastes for those "rms using less contaminant production processes. Di!erences between
a conventional labour productivity index and an extended productivity index are also statistically related to "rms
characteristics such as size, previous investments in cleaner technologies and a$liation to a Technological Institute. ( 2001 Elsevier Science B.V. All rights reserved.
Keywords: Shadow prices; Distance functions; Ceramic pavements industry; Environment; Productivity
1. Introduction
The growing recognition of the environment as a public good has unleashed a debate
with regard to the convenience of breaking the
tradition of assessing the value of industrial
production by implicitly assuming that all goods
produced are socially desirable. If it is accepted that
a part of industrial production is undesirable,
* Corresponding author.
E-mail address: [email protected](A. Picazo-Tadeo).
and public authorities establish regulations to
limit the emissions of polluting wastes, the cost
that "rms face to ful"l legal environmental restrictions, should be evaluated. Therefore, shadow prices for undesirable outputs have to be computed in
order to measure in terms of opportunity costs the
impact on "rms performance of environmental restrictions preventing free disposal of industrial
wastes.
Shadow prices of undesirable outputs are understood in this context as the marginal cost due to
a marginal reduction in the possibility of freely
disposing of wastes generated in the production
0925-5273/01/$ - see front matter ( 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 5 - 5 2 7 3 ( 0 0 ) 0 0 0 1 8 - 9
278
E. Reig-Martn& nez et al. / Int. J. Production Economics 69 (2001) 277}285
process.1 From the point of view of public policies
for environmental protection, the availability of
these shadow prices reports several important bene"ts; among them, the possibility of comparing
the marginal bene"ts of environment policies, with
the cost they generate for private "rms; the chance
of checking if all "rms face the same shadow prices;
and, "nally, the feasibility to adapt traditional productivity indexes to allow for the consideration of
di!erent intensity of waste production among
"rms, sectors or even countries.
This paper deals with the calculation of shadow
prices for undesirable outputs that are by-products
of the industrial production of ceramic pavements,
with data coming from a sample of Spanish "rms
located at Castellon, on the Valencian region. We
follow the distance function approach suggested by
FaK re et al. [1] (FGLY henceforth), recently applied
by Coggins and Swinton [2]. This method uses
output distance functions to derive shadow prices
for all outputs (desirable and undesirable) generated by "rms in their productive processes. In particular, it makes it feasible to obtain shadow prices
for undesirable outputs without having to use exogenous information on wastes elimination costs
coming from other studies (as Pittman [3] does in
a paper aimed to adapt the multilateral productivity indexes pioneered by Caves et al. [4] for taking
stock of polluting emissions). Secondly, this paper
aims to propose an extended measure of productivity that takes into account residuals emerging as
a by-product of current industrial production processes. Availability of residuals output data for each
of the "rms in our sample allows us to undertake
this correction.
This introduction is followed by a description of
the methodology. Section 3 describes the sample
1 This can be veri"ed by de"ning a cost function and setting
up a maximising pro"t problem. Given a vector of (desirable and
undesirable) outputs u, with prices r, and being x and p the
quantity and price input vectors, respectively, the cost function
is c(u, p)"min Mpx : x can produce uN, while the pro"t function
can be set up as n(r, p)"max Mru!c(u, p)N. From "rst-order
condition for undesirable output j we get
Lc(u, p)
r"
,
j
Lu
j
where r is the shadow price of waste j.
j
and establishes the main results, while Section 4
concludes.
2. The output distance function and the derivation of
shadow prices
In order to illustrate the basic aspects of the
methodological approach proposed by FGLY to
derive output shadow prices from distance functions, let us assume that we have a set of "rms using
a vector of inputs x3RN to produce a vector of
`
outputs u3RM , some of which can be considered
`
undesirable or bad outputs. The technology of reference is represented by an output correspondence
which is a mapping P : RN PP(x)-RM , where
`
`
the output set P(x) represents the set of all feasible
vectors of outputs given a vector of inputs x. It is
also assumed that the technology satis"es the usual
axioms initially proposed by Shephard [5], which
allows to de"ne the distance function in outputs as
the inverse of the maximum radial expansion of
a given output vector, in such a way that the resulting output vector remains within P(x). The distance
function can be de"ned on the output set as2
D (x, u)"infMh : (u/h)3P(x)N.
(1)
0
The assumptions made on the disposability
properties of the technology are a key issue in order
to derive output shadow prices. In particular, it is
assumed that "rms cannot freely eliminate (without
any cost) the industrial wastes (undesirable outputs) that they generate in their production processes, either because it would require a greater use
of inputs or because resources would have to be
diverted from marketable production in order to
eliminate undesirable outputs. This condition can
be incorporated to the characterisation of the technology by means of the axiom of weak disposal of
outputs, in the sense that if u3P(x), it will also hold
that hu3P(x), being in this case 0)h)1. This
assumption is consistent with the opportunity cost,
measurable in terms of the loss of desirable produc-
2 This expression is equivalent to the reciprocal of the output
oriented e$ciency measure of Farrell [6,7]. Also note that
u3P(x) if and only if D (x, u))1.
0
E. Reig-Martn& nez et al. / Int. J. Production Economics 69 (2001) 277}285
tion, that "rms would have to incur to ful"l environmental regulations imposing a reduction of industrial wastes, and allows for these undesirable
outputs to have nonpositive shadow prices.
Following FGLY's approach, under certain
assumptions, the shadow prices we seek can be
obtained from the gradient vector of partial derivatives of an output distance function. The formal
reasoning starts recognising the existence of a duality between the revenue function R(x, r) and the
output distance function D (x, u). Denoting by r the
0
output price vector, some of which components
can be negative, the revenue function can be
expressed as
R(x, r)"sup Mru : D (x, u))1N,
0
u
(2)
and the dual distance function in outputs is given
by
D (x, u)"sup Mru : R(x, r))1N,
0
r
(4)
where + is the gradient operator.
Expression (3) can be developed as a relationship
between the distance function and the shadow
prices, so that
D (x, u)"rH(x, u)u,
0
(5)
where rH(x, u) represents the output price vector
that maximises revenue. Applying Shephard's dual
lemma to expression (5), yields
+ D (x, u)"rH(x, u),
u 0
(6)
which combined with (4), leads to
r"R(x, r)rH(x, u).
In expression (7), rH(x, u) are obtained from the
gradient of the distance function, and denote revenue-de#ated output prices. The main di$culty to
obtain absolute shadow prices from expression (7)
is the dependence of the revenue function R(x, r) on
r, that is precisely the vector of shadow prices we
seek. If we assume that the observed price of an
output m, r0 , equals its absolute shadow price,
m
represented by r , then the maximum revenue is
m
R(x, r0 )"r0 /rH (x, u),
m m
m
(8)
which can be used to compute the absolute shadow
prices of the remaining outputs from its de#ated
shadow prices. Denoting by r
the absolute
m{
shadow prices for outputs other than m, we get
LD (x, u)
r "RrH (x, u)"R 0
m{
m{
Lu
m{
(3)
being ru the inner product of the output prices and
quantity vectors.
Then, assuming that the revenue and distance
functions are both di!erentiable, a Lagrange problem can be set up to maximise revenue, and "rstorder conditions yield the relationship [8]:
r"R(x, r)+ D (x, u),
u 0
279
(7)
LD (x, u)/Lu
m{ .
"r0 0
m LD (x, u)/Lu
0
m
(9)
An alternative way to handle the problem above
is to suppose that a zero-pro"t and revenue-maximising "rm would incur in an observed cost equivalent to its observed revenue R(x, r) [8], and simply
use expression (7) to obtain absolute shadow prices.
Finally, the distance function has to be parameterised and estimated to proceed with the calculation of the absolute shadow prices along the lines
we have showed.
After absolute shadow prices have been computed, we make use of them to formulate an
extended productivity index allowing for the consideration of di!erent waste production intensity
among "rms. Let us make a partition of the quantity and output price vectors, so that u"(u , u )
a b
and r"(r , r ), where u "(u , 2, u ) and
a b
a
1
J
u "(u
,
, u ) are the quantity vectors of deb
J`1 2 M
sirable and undesirable outputs, respectively, while
r "(r , 2, r ) and r "(r
,
, r ) are the
a
1
J
b
J`1 2 M
price vectors also for good and bad outputs.
Considering only the production of desirable
outputs, the partial productivity index for input x
j
280
E. Reig-Martn& nez et al. / Int. J. Production Economics 69 (2001) 277}285
can be denoted as
r u
(10)
PI" a a .
x
j
However, the estimation of shadow prices for
undesirable outputs allows to de"ne an extended
index of partial productivity for input x :
j
(r u )#(r u ) ru
b b " .
EPI" a a
(11)
x
x
j
j
Given that shadow prices for bad outputs are
nonpositive, the extended productivity index proposed by expression (11) will always take values
equal or smaller than the traditional productivity
index of expression (10); this allows for calculating
the productivity deviation index as
r u
PI
" a a.
PDI"
ru
EPI
(12)
Expression (12) will be equal or greater than one
and measures the degree of overvaluation in quantifying input x productivity levels when only marj
ketable output (good output) is being considered
with disregard of those wastes that arise as a byproduct and have potential harmful e!ects on the
environment.
ish Mediterranean coast. The source of the data is
the Valencian Region Inventory of Industrial Residuals elaborated in 1995 by the Department of Environment of the Valencian Regional Government. All
"rms face the same productive process, which is
characterised by the production of one desirable
output, ceramic pavements (u ), and two wastes or
1
undesirable outputs, watery muds (u ) and used oil
2
(u ). Intermediate input is clay, kaolin, felspar and
3
limestones (x ), while labour (x ) and capital (x ) are
1
2
3
primary inputs. Labour input is measured as the
number of workers, and capital is proxied by energy consumption in kilowatts/hour. Table 1 presents some descriptive statistics of the data.
As in FGLY, the distance function in output is
parameterised as a translog function, which is given
by the expression
3
3
ln D (x, u)"/# + b ln x # + a ln u
0
n
n
m
m
n/1
m/1
1 3 3
# + + b (ln x )(ln x )
nn{
n
n{
2
n/1 n{/1
3
1 3
# + + a (ln u )(ln u )
mm{
m
m{
2
m/1 m{/1
3 3
# + + c (ln x )(ln u ),
nm
n
m
n/1 m/1
3. Data and empirical 5ndings
The sample used in this paper comes from
a cross-section data set of 18 Spanish ceramic pavements producers located at Castellon, on the Span-
(13)
where m and n denote outputs and inputs, respectively.
Table 1
Sample description
Variable
Description
Units
Mean
Standard deviation Maximum
Minimum
u
1
u
2
u
3
x
1
Ceramic pavements
m2
2,031,077
1,168,311
4,500,000
200,000
Watery muds
t
2,908
4,108
15,648
14
Used oil
kg
1,822
3,135
12,000
100
Clay, kaolin, felspar and
limestones
Labour
t
50,192
40,762
144,000
3,300
Number of workers
128
121
428
25
Capital
kw/h
4,573
4,705
20,000
500
Observed price
Euros/m2
6.76
3.74
15.91
2.80
x
2
x
3
r01
u
E. Reig-Martn& nez et al. / Int. J. Production Economics 69 (2001) 277}285
The translog function is a #exible functional form
that does not impose strong disposability of outputs; however, given the large number of parameters in relation to the size of our sample it is not
possible to estimate using econometric methods.
Alternatively, the parameters in expression (13) are
obtained using mathematical programming techniques [9], by solving the following optimisation
program (see again FGLY):
18
Max + [ln D (xk, uk)!ln 1]
0
k/1
(14)
s.t.
ln D (xk, uk))0, k"1, 2, 18,
0
(14a)
L ln D (xk, uk)
0
*0,
L ln uk
m
(14b)
m"1, k"1, 2, 18,
L ln D (xk, uk)
0
)0, m"2, 3, k"1, 2, 18, (14c)
L ln uk
m
3
+ a "1,
m
m/1
3
m"1, 2, 3, m@"1, 2, 3,
(14d)
+ a "0,
mm{
n"1, 2, 3,
m{/1
3
+ c "0,
nm
m/1
a "a , m"1, 2, 3, m@"1, 2, 3,
(14e)
mm{
m{m
H
b "b , n"1, 2, 3, n@"1, 2, 3,
nn{
n{n
(14f)
where k denotes "rms.
The set of restrictions in (14a) imply that each
observation is located either on or below the technological frontier; the restrictions contained in
(14b) guarantee that the desirable output will have
a nonnegative shadow price for all "rms, while (14c)
assures that undesirable outputs will have nonpositive shadow prices, also for all "rms. The assumption of weak disposal of outputs is introduced by
restriction (14d) that imposes homogeneity of
degree#1 in outputs; "nally (14e) and (14f) impose
symmetry.
The objective function in (14) minimises the sum
of the deviations of individual observations from
281
Table 2
Estimated parameters of the translog distance function. Expression (13)
Parameter
/
b
1
b
2
b
3
a
1
a
2
a
3
b
11
b
12
b
13
b
22
b
23
b
33
a
11
Parameter
47.253
!13.459
!0.403
1.459
3.112
!2.322
0.210
1.519
0.250
!0.898
0.080
!0.401
2.327
0.039
a
12
a
13
a
22
a
23
a
33
c
11
c
12
c
13
c
21
c
22
c
23
c
31
c
32
c
33
!0.014
!0.025
0.001
0.013
0.012
!0.131
0.098
0.033
!0.079
0.134
!0.055
!0.018
0.013
0.005
the frontier. However, we are in fact maximising
because the distance function takes positive values
lower or equal than one, and therefore its log can
take negative or zero values; in consequence, to
maximise the deviations of the distances expressed
in logs from zero (represented by the log of one) is
equivalent to minimise the sum of the absolute
deviations of the individual observations.
Table 2 shows the parameter estimates of the
translog function given by expression (13). Using
those "gures and the available information, the
output distance function for each individual "rm is
computed, with an average value of 0.927. It is well
known that the output distance function is the
reciprocal of Farrell's measure of output e$ciency
whose average value is then 1.079. This means that
making an e$cient use of their available resources,
the "rms of the sample would be able to increase
their production of ceramic pavements almost by
8% on average.
The estimation of the distance function allows us
to obtain output shadow prices for each "rm in our
sample, as we explained above. In order to get the
shadow income of each productive unit, we use
expression (13) under the hypothesis that the
shadow price of good output (ceramic pavements) is
equal to its observed market price; this is equivalent
to assume that r0 "r01 , r01 being the square meter
u u
m
282
E. Reig-Martn& nez et al. / Int. J. Production Economics 69 (2001) 277}285
Table 3
Output shadow prices!
r0
u1
Mean
6.76
Standard deviation 3.74
Weighted mean
6.84
Maximum
15.91
Minimum
2.81
r2
u
r3
u
!9,830.6
23,345.9
!336.6
!79,893.5
0.0
!1,043.7
2,512.8
!125.5
!9,998.6
0.0
!Euros.
of pavement market price, a "gure which is di!erent
for each company. Table 3 shows the computations
for output shadow prices; simple means and standard deviations, as well as weighted means3 are
reported.
The shadow prices of the industrial wastes could
be interpreted as the marginal loss of revenue corresponding to the volume of resources that a "rm
would need to reduce its emission by a marginal
unit. Therefore, in average terms, a reduction of one
ton of watery mud production, residual u , would
2
require the use of resources valued in 336.6 euros,
which in terms of marketable output would imply
an implicit loss of 49.2 square meters of pavements,
considering that the market price for square meter
is 6.84 euros on average. Similarly, and in order to
reduce the production of used oil in a kilogram,
residual u , the opportunity cost would be valued
3
in 125.5 euros, equivalent to a reduction in good
output production of 18.3 square meters.
Shadow price estimates di!er signi"cantly
among "rms, as the high standard deviation of
those prices reveals; this result is consistent with
FGLY, and it is also related to important di!erences among "rms in terms of quantities of residuals discharged per unit of desirable output
produced. After shadow prices at "rm level have
been obtained, the correlation between absolute
values of these prices and waste emission for square
meter of ceramic pavements has been computed,
3 Weights are the quantity of wastes produced by each "rm;
they are chosen to obtain a weighted mean of shadow prices for
bad outputs that represents the cost of reducing in one unit its
production in the sample.
getting a negative value close to 30% in the case of
watery mud and around 25% for used oil. The
correlation coe$cient has the expected sign since
companies that produce a greater volume of residuals per unit of marketable production are very
likely to be those that rely on technical equipment
less adapted to recycling those residuals or minimising their delivery; for these "rms, investments
intended to cut the volume of e%uents would have
a relatively small cost in comparison with their
prospective yields in terms of reduction of emissions. On the other hand, those "rms that have
already reached a high performance according to
their ability to control the environmental impact of
their production processes would face a higher
marginal cost in case of stepping-up their e!orts
to reduce waste discharges. This would be re#ected
in a higher shadow price for bads in these
companies.
These results could be of interest in devising an
e$cient regulation of some aspects related to the
industrial contamination issue. The shadow prices
that have been estimated re#ect a wide variety of
"rms positions as for the marginal cost of reducing
the emission of residuals in the Spanish ceramic
industry. On the other hand, the close knitted geographical location of these "rms makes it reasonable to assume that marginal social bene"ts of
cutting current levels of industrial contamination
are probably similar among companies, because
they share a common natural landscape, and the
same natural resources and human habitat. If an
e$cient regulation means that the marginal cost of
decreasing current contamination levels has to be
made equal to the marginal social bene"ts, it makes
sense to deduce that the current situation is
not e$cient in terms of the allocation of resources.
It is di$cult to go further from these basic statements without being able to make use of more
detailed data on "rms technology and output
mix, but it seems "ne to infer that some conditions exist so that a market of emission permits
could be developed where some "rms would wish
to enter as buyers and others as suppliers. In
order to ful"l environmental regulations, each
"rm would have to make a choice between carrying
out fresh investments or acquiring emission
permits.
E. Reig-Martn& nez et al. / Int. J. Production Economics 69 (2001) 277}285
Finally, it seems right to remark that knowledge
on shadow prices allows the researcher to approach
a valuation of industrial production not con"ned to
marketable production and market prices, but able
to include an estimate of the (negative) value of
a likely increase in industrial refuses, linked to the
expansion of good output levels. The type of
shadow prices computed in this paper are derived
strictly from technical relations between inputs and
outputs and should be considered as estimates
arising from a producer approach. Externalities
on consumers or other producers are not taken into
account, but could be incorporated in a straightforward way, provided adequate data are made available, within the same framework of analysis, as
shown in FaK re and Grosskopf [10]. Despite their
shortcomings, the shadow prices we have used
illustrate well enough the e!ects on production
valuation of including in the price vector several
components with a negative sign, each corresponding to a di!erent undesirable output.
We now proceed to compute two di!erent
measures of labour productivity, one along the
conventional lines, as a quotient between the monetary value of each "rm marketable output (ceramics pavements) and labour sta!, and an extended
one, de"ned by expression (11). The outcome of
using both types of productivity indexes appear in
Table 4. Both productivity measures di!er by
values that go from 3% to 30% in the sample, with
an average gap close to 12%. It means that di!erences are important enough to make an impact on
"rms comparisons. As an example, "rm 8 is more
productive in conventional terms than "rm 5, but it
changes when an environmental-friendly approach
is taken and waste production from both "rms are
included in the numerator of the productivity quotient, using shadow prices to translate residuals
quantities to monetary "gures. Now "rm 5 is more
productive than "rm 8. Ranking between "rms
4 and 10 is also inverted when moving from a productivity measure to the other, and two "rms
(11 and 13), that have quite similar labour productivity levels when only good output is compared,
show marked di!erences when bads are also contemplated.
From society's comprehensive view it is clearly
a serious matter of concern. It is not possible to
283
Table 4
Labour productivity measures!
Firm
Productivity
Labour
Extended
deviation
productivity labour
productivity index
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
57.81
202.81
120.65
79.30
96.66
91.07
64.96
97.02
127.83
77.38
127.91
194.59
127.83
121.29
115.48
105.18
126.67
166.61
44.33
179.74
109.12
65.71
91.72
80.38
62.49
84.59
124.01
73.64
114.24
167.23
118.42
105.28
94.10
92.58
108.74
159.20
1.304
1.128
1.106
1.207
1.054
1.133
1.040
1.147
1.031
1.051
1.120
1.164
1.079
1.152
1.227
1.136
1.165
1.047
Mean
116.73
104.20
1.127
39.97
36.41
0.072
Standard deviation
!Euros per worker.
remain aloof to the fact that a given productivity
level can be achieved with very di!erent volumes of
real or potential noxious wastes, and a virtue of the
very simple indicator we propose is to ease the
transition to a new way of analysing entrepreneurial performance, apt enough to accueil a growing
public interest in environmental values. Firms that
have undertook costly investments in new equipments that allow cleaner production processes
should have their e!orts (that consume productive
resources), recognised and not merely dismissed as
less productive in conventional terms.
The next step we have followed is to disclose if
there exists a relationship between our deviation
productivity index and some "rm's characteristics,
making use of variance analysis. We have broken
our sample in two groups; group A includes those
"rms with a deviation smaller than the average
deviation for the whole sample (8 "rms), while
group B comprises all those "rms with deviation
equal or higher than average deviation (10 remain-
284
E. Reig-Martn& nez et al. / Int. J. Production Economics 69 (2001) 277}285
ing "rms). Then we have tried to ascertain if there is
a statistically signi"cant di!erence between both
subsamples concerning to "ve variables: size, azliation to a Technological Institute,4 spatial location,5
a record of past investments in cleaner technologies,
and use of external services for waste management.
Results are shown in Table 5 and are clearly
conclusive for all the variables under consideration.
Firms of greater size show a smaller deviation and
the same happens for "rms that have recorded
investments conducive to clean production processes. External management of wastes is mainly
associated to the "rms with higher bias; this was an
expected outcome, given that those "rms are more
intensive in terms of production of industrial
wastes, what forces them into a greater dependence
of external suppliers of services (transport, storage)
for waste disposal. A$liation to a Technological
Institute specialised in the ceramics industry (AICE)
helps to reduce the deviation, as variance analysis
shows. This "nding is probably linked to the services provided by the Institute in terms of technological consultancy, easing the access to R&D in
di!erent "elds, including the development and application of waste reducing techniques, and favouring di!usion of industry's best practice. The
variable spatial location is employed to distinguish
the "rms that are located in one area of very dense
concentration of this type of industry (the Plana
Baixa zone) and the others. We presume that the
4 The Region of Valencia has a network of Technological
Institutes specialised by branches of industrial production,
AICE being the one concerned with the ceramics industry. They
are non-pro"t entities under the form of business associations
sponsored and mostly funded by the public authorities and
oriented to promote technological innovation, best practice diffusion and quality tests. They provide external services (R&D,
among others) at low cost to their a$liates, that are mostly small
and medium sized "rms. A$liation is normally considered as an
index of innovative behaviour on the part of "rm's management.
5 The ceramics pavements industry is highly concentrated in
a small number of contiguous municipalities in the CastelloH n
Province, where "rms are supposed to enjoy important external
economies that could be broadly de"ning a Marshallian type
industrial district in the sense coined by the economic geography
literature. We hypothesize that close proximity improves the
chances of "rms being more sensible to good practice in terms of
waste management, trough imitation and easier technical information di!usion.
"rst enjoy an advantage in terms of sharing the
external economies generated by a dynamic industrial district, that gives them rapid access to information released by suppliers of new industrial
equipments and competitors and facilitates the
acquisition of better practices in dealing with
industrial residuals. Evidence, after performing
variance analysis, conforms to it.
4. Concluding remarks
This paper has been devoted to estimate shadow
prices for two di!erent types of undesirable outputs
or industrial wastes generated in their production
processes by eighteen Spanish "rms in the ceramic
pavements industry. The methodology follows the
approach suggested by FaK re et al. [1]. Accordingly,
central importance has been given to the duality
between output distance and revenue functions, using the former to derive output shadow
prices.
The shadow prices obtained for watery muds and
used oil (industrial wastes that are by-products in
the production of marketable ceramic pavements)
have made it feasible to measure in terms of loss of
marketable output production (square meters of
ceramic pavements) or its equivalent in cash revenue, the opportunity costs "rms would have to
incur in order to achieve a marginal decrease in the
production of those refuses. A negative correlation
has been observed between waste production intensity by "rms (as a proportion of their own output of
ceramic pavements) and absolute shadow prices
computed for these bads outputs. This feature probably re#ects a greater marginal cost of polluting
residues elimination for those "rms that had previously invested in cleaner technologies directed to
get rid of undesirable outputs, and are currently
generating less units of wastes for square meter of
ceramic pavements produced.
Another empirical result of some importance is
the observation of a high dispersion of shadow
prices "gures among "rms. This should be a matter
of concern for policy makers aiming to develop an
e$cient environmental regulation for the Spanish
ceramics pavement "rms located at the industrial
district of Castellon (a densely populated area),
E. Reig-Martn& nez et al. / Int. J. Production Economics 69 (2001) 277}285
285
Table 5
Variance analysis
Mean group A!
Mean group B"
Statistic F
p-value
Firm's size#
A$liation to
Technological
Institute$
Spatial
location%
Investments on
cleaner
technologies&
External
management
of waste u '
2
2,966.2
1,283.0
18.983
0.000
0.63
0.10
7.063
0.017
0.75
0.30
4.000
0.063
1.00
0.60
4.740
0.045
0.13
0.90
24.063
0.000
!Deviation smaller than average deviation for the whole sample; 8 "rms.
"Deviation greater or equal average deviation for the whole sample; 10 "rms.
#Thousand of square meters of ceramic pavements.
$Dummy variable that equals to 1 if the "rm is a$liated to Technological Institute AICE and 0 otherwise.
%Dummy equal to 1 if the "rm is located at the industrial district of Plana Baixa and 0 otherwise.
&Dummy equal to 1 if the "rm has invested on clean technologies and 0 otherwise.
'Dummy that equals to 1 if external management of waste u is carried out and 0 otherwise.
2
since for a similar marginal social bene"t obtained
from a cut in current pollution levels across sample
"rms, the marginal costs that those "rms would
have to face would be quite di!erent.
Finally we wish to use shadow prices to
emphasise on the need to improve current
productivity indexes in order to take industrial
waste into consideration. Our results show that
clear di!erences arise within the sample when computing conventional and extended measures of labour productivity at "rm level. These di!erences
are statistically associated to "rms characteristics,
such as size, record of former investments in cleaner
technologies, and azliation to a Technological Institute for the Ceramics Industry.
Acknowledgements
We thank the Bureau of Environmental Quality
of the Valencian Regional Government for statistical help, as well as two anonymous referees for
useful comments. We are also grateful tothe Ministry of Science and Technology of the Spanish Government for the Financial aid received (Project
SEC 2000-0803).
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