Sus ainabili y 2013, 5, 1568-1576; doi:10.3390/su5041568
sus ainabili y
ISSN 2071-1050
www.mdpi.com/jou nal/sus ainabili y
A icle
Consis en Agg ega ion o Gene alized Sus ainable Values om
he Fi m Le el o Sec o al, Regional o Indus y Le els
Na alia Kuosmanen 1,*, Timo Kuosmanen 2 and Timo Sipiläinen 3
1 MTT Ag i ood Resea ch Finland, Economic Resea ch, La oka anonkaa i 9,
00790 Helsinki, Finland
2 Aal o Uni e si y School o Business, P.O. Box 21220, 00076 Aal o, Helsinki, Finland;
E-Mail: [email p o ec ed]
3 Uni e si y o Helsinki, P.O. Box 27, La oka anonkaa i 9, 00014 Helsinki, Finland;
E-Mail: [email p o ec ed]
* Au ho o whom co espondence should be add essed; E-Mail: [email p o ec ed];
Tel.: +358-295-317-403.
Recei ed: 11 Feb ua y 2013; in e ised o m: 28 Ma ch 2013 / Accep ed: 28 Ma ch 2013 /
Published: 11 Ap il 2013
Abs ac : This s udy p esen s a sys ema ic me hod o agg ega ing i m le el sus ainable
alue indica o s o sec o , egion o indus y le els. The p oposed me hod applies he
gene alized sus ainable alue ha is based on on ie p oduc ion unc ions. The me hod is
illus a ed by an empi ical applica ion o he Finnish c op and dai y sec o s, whe e he
benchma k echnology is es ima ed by da a en elopmen analysis. Ou e iciency
assessmen shows ha he ep esen a i e c op a m achie es only abou a hal o i s
po en ial ou pu . E iciency o he ep esen a i e dai y a m is somewha highe .
Keywo ds: sus ainabili y assessmen ; sus ainable alue; p oduc i e e iciency analysis
1. In oduc ion
Sus ainabili y is a mul idimensional concep co e ing en i onmen al, social and economic
dimensions. Ope a ionalizing he quali a i e concep o sus ainabili y o p ac ical quan i a i e
measu es has p o ed challenging due o he a ie y o meanings a ached o sus ainabili y [1–3]. The
sus ainable alue (SV) me hod [4,5] is one o he app oaches measu ing he con ibu ion o an
economic en i y owa ds he sus ainabili y (o sus ainable de elopmen ) and has been applied in a
OPEN ACCESS
Sus ainabili y 2013, 5 1569
numbe o s udies [6–9]. A i m c ea es a posi i e SV whene e i uses i s bundle o esou ces mo e
e icien ly han ano he i m would ha e used i . In o he wo ds, i compa es pe o mance o a i m o a
benchma k. The benchma k can be seen as a e e ence g oup ha se s he pe o mance a ge o he
e alua ed i m. The p oduc ion echnology a ailable o he benchma k i m is he benchma k
echnology. I can be cha ac e ized by he p oduc ion unc ion, which indica es he maximum amoun
o ou pu ha he benchma k echnology can p oduce using he gi en amoun s o inpu esou ces.
The ecen s udy by Kuosmanen and Kuosmanen [10] shows ha he con en ional SV me hod es s
on a numbe o s ong and un ealis ic assump ions. Building an explici link be ween he SV me hod
and on ie app oach o en i onmen al pe o mance assessmen , Kuosmanen and Kuosmanen de elop
he gene alized sus ainable alue me hod (GSV). In his app oach, a benchma k echnology is
es ima ed om empi ical da a using es ablished econome ic me hods. Fu he mo e, hey demons a ed
ma hema ically ha he SV and sus ainable e iciency a e he special cases o he s anda d e iciency
indices known in he ield o p oduc i e e iciency analysis o mo e han i e decades. In he ollow
up s udy [11], he GSV me hod was applied o i m le el da a o assess co po a e con ibu ions owa ds
sus ainabili y in ag icul u e. The s udy included a de ailed examina ion and classi ica ion o al e na i e
me hods a ailable o es ima ing he benchma k echnology in he con ex o GSV, and demons a ed
he use o GSV in es ima ing he benchma k echnology by an empi ical applica ion o Finnish
dai y a ms.
P e ious empi ical applica ions o he con en ional SV and GSV me hods assess da a o indi idual
i ms o agg ega e en i ies such as indus ies, sec o s, o coun ies (see [6–9,11]). Howe e , he
connec ion be ween he i m le el analysis and he agg ega e le el analysis has no been o mally
in es iga ed. The esul s om he pa allel li e a u e on e iciency indices (see [12–14]) sugges ha
consis en agg ega ion o SV and GSV indices is a om sel -e iden . In gene al, he coo dina ion and
e icien alloca ion o esou ces ac oss indi idual i ms is o c i ical impo ance o e iciency o an
agg ega e en i y, such as a coun y o an indus y, bu he coo dina ion does no play any ole a he
i m le el e iciency assessmen . Al hough indus y da a a e ob ained by summing he da a o all i ms
ope a ing in he indus y, he e is no gua an ee ha he SV o GSV indices o i ms sum up o he
indus y le el SV and GSV measu es.
The objec i e o his pape is o de elop a sys ema ic amewo k o a consis en agg ega ion o he
i m le el GSV indices o a sec o al, a egional, o an indus y le els. By consis en agg ega ion, we
mean ha he gene alized sus ainable alue measu es o indi idual i ms can be added up o ob ain he
gene alized sus ainable alue measu e o he agg ega e en i y, and ha he same esul is ob ained i we
assess he gene alized sus ainable alue o he agg ega e en i y di ec ly. The main con ibu ion o his
s udy is o show ha he GSV me hod p oposed in [10] is no es ic ed o he i m le el, and ha
consis en agg ega ion is indeed possible.
We i s de elop a consolida ed heo e ical amewo k o es ima ing an agg ega e sus ainabili y
measu e o i m’s pe o mance o any g oup o i ms in a speci ic sec o , specializa ion, egion, o any
o he g oup, such ha esul ing measu es a e consis en wi h he i m le el es ima es. We hen apply
da a o he Fa m Accoun ancy Da a Ne wo k (FADN) o Finland and illus a e he p oposed me hod
by an empi ical applica ion o c op and dai y sec o s. We es ima e he benchma k echnologies by da a
en elopmen analysis (DEA) [15,16]. Finally, he esul s o he empi ical applica ion show ha he
agg ega e GSV me hod can be use ully applied in a compa a i e analysis o di e en sec o s.
Sus ainabili y 2013, 5 1570
The emainde o he pape is o ganized as ollows. Sec ion 2 b ie ly e iews he gene alized
app oach o es ima ing co po a e con ibu ions owa ds sus ainabili y a he i m le el. Sec ion 3
es ablishes a heo e ical amewo k o es ima ing con ibu ions owa ds sus ainabili y a he agg ega e
le el, such as a sec o , egion o an indus y. In Sec ion 4 he p oposed me hodology is illus a ed by
an empi ical applica ion and Sec ion 5 concludes.
2. Measu ing Con ibu ions Towa ds Sus ainabili y a Fi m Le el
Following he de ini ion o he gene alized sus ainable alue (GSV) p esen ed in [10], assume i m
i ans o ms a ec o o R esou ces, including na u al, physical, human, and in ellec ual capi al,
 
1i i iR
xx

x
, in o he economic ou pu deno ed by
i
y
, o e e y
1, ,in
, whe e n is he numbe
o i ms in he sample. We assume ha ou pu y is measu ed in mone a y uni s (e.g., eu os, dolla s,
pounds). GSV is de ined as he di e ence be ween i m i’s economic ou pu ,
i
y
, p oduced by using a
bundle o esou ces
 
1i i iR
xx

x
and hei oppo uni y cos , deno ed by
 
i
OC x
:
 
i i i
SV y OC x
.
(1)
The a ionale behind Equa ion (1) is analogous o he concep ual de ini ion o he con en ional SV
me hod p oposed in [4], bu di e s om i s ope a ional measu e. Impo an ly, in (1), he oppo uni y
cos can be a nonlinea unc ion o esou ces, and he unc ional o m does no need o be assumed
a p io i.
Since oppo uni y cos o esou ces is no di ec ly obse able, i mus be es ima ed in one way o
ano he . In economics, he oppo uni y cos o using a esou ce o a speci ic ac i i y e e s o he
income o egone by no using he esou ce in he bes al e na i e ac i i y. Howe e , he bes al e na i e
use is no always sel -e iden : i gene ally depends on he echnology and he o he esou ces a ailable
o he al e na i e ac i i y. In ma hema ical e ms, he echnology a ailable o a i m is desc ibed by a
neoclassical p oduc ion unc ion (x), which is he maximum amoun o ou pu ha can be ob ained
om he gi en amoun s o inpu esou ces. We assume ha unc ion is an inc easing and conca e
unc ion. Hence, wi hou loss o gene ali y, we may in e p e he nume ical alue o he p oduc ion
unc ion (x) as he o al oppo uni y cos o esou ce bundle x.
Applying he p e ious insigh s, he GSV measu e (1) can be ew i en as:
 
i i i
SV y x
.
(2)
No e ha Equa ion (2) is no es ic ed o any pa icula unc ional o m o he p oduc ion unc ion
. I allows esou ces o be in e dependen and allows non-subs i u abili y be ween esou ces.
Fu he mo e, i allows p ese ing some c i ical le el o esou ces, which is in line wi h he s ong
sus ainabili y concep . In (2), he p oduc ion echnology can be es ima ed om empi ical da a using
well es ablished econome ic me hods, such as s ochas ic on ie analysis (SFA) o da a en elopmen
analysis (DEA), see e.g., [17] o a e iew o hese me hods. In he con ex o he GSV, o a e iew o
econome ic app oaches o es ima ing p oduc ion unc ions and en i onmen al pe o mance can be
ound in [11].
Sus ainabili y 2013, 5 1571
3. Measu ing Con ibu ions Towa ds Sus ainabili y a he Agg ega e Le el
We nex conside an agg ega ion o i m le el GSV measu es o a sec o , egion and an indus y
le el. This exe cise is no as s aigh o wa d as i migh seem. Fi s ly, conside he ollowing example.
Suppose he e a e wo i ms: A:
   
, 1,1
AA
xy
and B:
   
, 9,3
BB
xy
, whe e x and y a e inpu
esou ce uni and ou pu uni , espec i ely. The p oduc ion unc ion is gi en by he equa ion:
 
0.5
x x
. Thus, o al esou ce use is simply sum o he i ms’ esou ce uni s:
1 9 10
AB
xx   
,
and o al ou pu is
1 3 4
AB
yy   
. No e ha bo h i ms a e echnically e icien , which means ha i
is impossible o inc ease ou pu a he gi en alloca ion o esou ces. Howe e , i is possible o inc ease
ou pu by ealloca ing esou ces. Fo ins ance, i i m B is spli in o nine sepa a e i ms, each endowed
wi h one uni o esou ce o p oduce 1 uni o ou pu , he o al ou pu would inc ease om 4 o 10.
In heo y, he op imal alloca ion in his example would in ol e c ea ing an in ini e numbe o
in ini esimally small i ms ha use a posi i e bu in ini esimally small quan i y o esou ce, i.e., x
app oaches o 0 o all i ms. This example demons a es ha e en i i ms a e echnically e icien a
he i m le el, he e may be a lack o coo dina ion, which shows as ine iciency a he agg ega e le el.
Al hough he a e age ine iciency o he wo i ms is ze o, he a e age ec o :
     
, , 2 5,2
A A B B
x y x y


is ine icien , because
 
5 2.236 
, and hus
 
 
 
2 2 2 2.236 0.236
A B A b
y y x x      
.
Hence, he a e age o he i m le el GSV is di e en om he GSV o he a e age ec o . Whe he
we use he i m le el o he agg ega e le el da a, i is impo an o ensu e ha he i m le el GSV
measu es ma ch wi h hei coun e pa s a he agg ega e le el.
The pu pose o he p e ious nume ical example is o illus a e he impo ance o coo dina ion and
e icien alloca ion o esou ces ac oss i ms a he agg ega e le el e iciency assessmen . In he
p e ious example, he p oduc ion unc ion exhibi s dec easing e u ns o scale, which a o s small
scale p oduc ion. Howe e , he example could be easily adap ed o cons an o inc easing e u ns o
scale. The main poin o he example is o demons a e ha he SV o GSV s a is ics o he i m do no
always add up o hei coun e pa s a he indus y le el.
To de elop a simple bu sys ema ic agg ega ion scheme, we p opose he ollowing agg ega e GSV
measu e. Conside a g oup o i ms
 
1, ,In
, ep esen ing i ms in a speci ic sec o , specializa ion,
egion, coun y, o any o he g oup. Assume ha i ms in g oup I ha e access o he same p oduc ion
echnology desc ibed by he p oduc ion unc ion (x). The p oduc ion unc ion is inc easing and
conca e unc ion and indica es he maximum amoun o ou pu ha can be ob ained om he gi en
amoun s o inpu esou ces.
To pa e he way o he agg ega e GSV o mula ion, we in oduce a ep esen a i e i m o g oup I
ha is cha ac e ized by he a e age ou pu and a e age esou ce ec o . The a e age esou ce ec o is
calcula ed as:
i
iI
n


xx
,
(3)
whe e ec o
 
1i i iR
xx

x
cha ac e izes he esou ce use by i m i.
The a e age ou pu o g oup I is calcula ed as:
Sus ainabili y 2013, 5 1572
i
iI
y y n


,
(4)
whe e
i
y
is ou pu o i m i.
These a e age alues
x
and
y
cha ac e ize he ep esen a i e i m o g oup I. The ep esen a i e
i m’s da a a e nex included in he da a se as an addi ional en i y; and he p oduc ion echnology is
es ima ed by some econome ic me hod a ailable (see e.g., [11]).
Gi en he p oduc ion unc ion , he agg ega e GSV measu e is calcula ed as he GSV o he
ep esen a i e i m o g oup I, deno ed as
ep
GSV
, mul iplied by he numbe o i ms in g oup I:
I ep
agg GSV n GSV
,
(5)
whe e he sus ainable alue measu e o he ep esen a i e i m
ep
GSV
is he di e ence be ween he
a e age ou pu o g oup I,
y
(o ou pu o he ep esen a i e i m), and he nume ical alue o he
p oduc ion unc ion
 
x
in poin
x
:
 
ep
GSV y  x
.
(6)
Al e na i ely, he agg ega e GSV can be p esen ed as:
 
 
I
agg GSV n y    x
.
(7)
No e ha he p oposed agg ega e GSV measu e has a compelling p o i in e p e a ion. De ine he
p o i unc ion as:
   
 
 
 
max maxy y


    
xx
w w x x x w x
.
(8)
Wi hou loss o gene ali y, he ou pu p ice can be no malized as one, so ha y ep esen s bo h he
ou pu quan i y and he e enue. The p o i unc ion indica es he maximum p o i ob ainable a gi en
inpu p ices w [18]. The no ion o p o i e iciency was i s in oduced in [19], whe e wo al e na i e
measu es o p o i e iciency we e sugges ed: he a io measu e as a a io o obse ed p o i o
maximum p o i and he di e ence measu e as a di e ence be ween obse ed and maximum p o i .
The a io measu e is gene ally ill-de ined i he maximum p o i equals ze o. Mo eo e , i is di icul o
in e p e when maximum and/o ac ual p o i le els a e nega i e. In con as , he di e ence measu e
has a na u al in e p e a ion in e ms o chosen cu ency uni s, and i is allows managing nega i e o
ze o p o i s.
The agg ega e GSV can be in e p e ed as he p o i e iciency o he g oup I a he mos a o able
p ices om he pe spec i e o g oup I.
Theo em: The agg ega e GSV measu e
 
 
I
agg GSV n y    x
indica es he sum o p o i
e iciencies o he i ms in g oup I a he mos a o able non-nega i e inpu p ices. Speci ically:
 
1
max ( ) ( )
n
I i i
i
agg GSV y



  

w0 w x w
.
The p oo o he heo em is p o ided in he appendix.
Fo mula ion o he agg ega e GSV can be ex ended o any g oup o i ms, o example, i ms
loca ed in a speci ic egion. Fo es ima ing p oduc ion on ie and agg ega e GSV measu es, he
e alua ed g oups o i ms should be su icien ly compa able, in he sense ha all i ms ha e access o

Sus ainabili y 2013, 5 1573
he same p oduc ion echnology . Fo example, le he a e age ou pu and he a e age esou ce ec o
o g oup g be
g
y
and
g
x
. Then, he agg ega e GSV o g oup g is
 
 
g g g
agg GSV n y    x
,
(9)
whe e n is he numbe o i ms in g oup g.
We nex ou line wo ex ensions o he agg ega ion me hod de eloped abo e.
Fi s ly, suppose we obse e a sample o n i ms, which o m a subse o he popula ion o N i ms.
We can calcula e he agg ega e GSV measu e o he obse ed sample by applying Equa ion (9).
Howe e , i we a e in e es ed in he GSV o he ull popula ion o N i ms, we need o assume ha
obse ed sample is ep esen a i e enough o es ima ing he popula ion a e ages
g
y
and
g
x
by using
he sample means (e.g., he obse ed i ms a e andomly d awn om he popula ion o he sample). I
he sample is indeed ep esen a i e o he popula ion, hen he agg ega e GSV o mula (9) can be
adap ed o calcula ing he GSV o he popula ion by simply eplacing he sample size n by he size o
he popula ion N.
Secondly, suppose he i ms loca ed in a speci ic egion do no engage in a simila se o ope a ions
and ha e di e en p oduc ion echnology, e.g., dai y and c op a ms. In his case, one can es ima e he
agg ega e GSV o each g oup i s . Since he GSV measu e is exp essed in mone a y uni s (e.g., eu os,
dolla s, o pounds), one can subsequen ly add oge he he esul ing GSV measu es. Fo example, he
agg ega e GSV o dai y and c op a ms as wo sepa a e g oups loca ed in he same egion can be
calcula ed as he sum o he agg ega e GSV measu es o each g oup:
c op dai y
o al g g
GSV k agg GSV m agg GSV   
(10)
o :
 
 
 
 
c op c op c op dai y dai y dai y
o al g g g g
GSV k y m y      xx
,
whe e k and m a e he numbe o a ms in he g oups o dai y and c op a ms, espec i ely. In o mula (10),
he exp essions wi hin he b acke s a e he GSVs o he ep esen a i e c op and dai y a ms, espec i ely.
4. Empi ical Applica ion
This sec ion p esen s wo illus a i e applica ions o es ima ing he agg ega e GSV measu e a
sec o le el based on he da a o 332 Finnish dai y a ms and 142 c op a ms. The da a we e ex ac ed
om he Fa m Accoun ancy Da a Ne wo k (FADN) da abase. Acco ding o [20], he e we e 17,480
dai y a ms and 28,979 c op a ms in Finland in 2004.
The economic ou pu o c op a ms is he o al e enue om c ops and c op p oduc s and he
economic ou pu o dai y a ms is he o al e enue om milk and o he p oduc s in eu o. Economic
esou ces include labo in hou s, o al u ilized ag icul u al a ea (UAA) measu ed in hec a es and a m
capi al, which is comp ised o li es ock, pe manen c ops, land imp o emen s, buildings, machine y
and equipmen , ci cula ing capi al, and measu ed in eu o. En i onmen al esou ces include he o al
ene gy cos and cos o e ilize s. An o e iew o he key cha ac e is ics o he da a is p esen ed in
Tables 1 and 2 in he o m o mean, s anda d de ia ion, minimum and maximum alues.
Sus ainabili y 2013, 5 1574
Table 1. Desc ip i e s a is ics o he sample o dai y a ms; yea 2004, sample size n=332.
Va iable
Mean
S . De .
Min
Max
To al ou pu , €
91,676
52,336
16,671
393,392
Labo , h
5,123
1,719
399
13,458
Fa m capi al, €
261,150
191,099
18,779
1,481,375
Ene gy, €
5,843
3,561
713
25,541
UAA, ha
49.1
25.4
13.1
146.8
Fe ilise , €
4,746
3,558
0
22,922
Table 2. Desc ip i e s a is ics o he sample o c op a ms; yea 2004, sample size n = 141.
Va iable
Mean
S . De .
Min
Max
To al ou pu , €
54,838
54,349
2,493
342,863
Labo , h
2,139
1,286
160
6,807
Fa m capi al, €
228,020
162,428
32,599
997,866
Ene gy, €
7,074
4,770
692
34,973
UAA, ha
80.5
44.5
22.1
324.3
Fe ilise , €
7,018
5,209
0
28,535
Fi s ly, he a e age alues o he ep esen a i e dai y
 
,
dai y dai y
yx
and c op a ms
 
,
c op c op
yx
we e calcula ed. Nex , he ep esen a i e a ms’ da a we e included in he da a samples and he
benchma k echnologies o bo h sec o s we e es ima ed using ou pu o ien ed DEA model wi h
a iable e u ns o scale:
01 1 1
( ) max ; 1
n n n
DEA i i i i i
i i i
y
  
  

  


  
x x x
.
(11)
The esul ed e iciency sco e o he ep esen a i e c op a m was 0.513, which means ha he
ep esen a i e c op a m achie ed only abou hal o i s po en ial ou pu . The e iciency sco e o he
ep esen a i e dai y a m was 0.649, ha is, somewha highe han o he ep esen a i e c op a m.
Nex , he GSV alues o bo h ep esen a i e a ms we e calcula ed and esul ed in abou −52,102 eu o
o he ep esen a i e c op a m and −49,615 eu o o he ep esen a i e dai y a m. The esul s a e
nega i e by cons uc ion, since in he DEA model, he on ie en elopes he obse ed da a om abo e
and only a ms wi h GSV = 0 a e diagnosed as e icien . This means ha he loss due o ine iciency
was abou 50 housand eu o o bo h he ep esen a i e c op and he ep esen a i e dai y a m.
To ob ain he agg ega e GSV measu es o dai y and c op sec o s, he es ima ed GSV alues o he
ep esen a i e a ms we e mul iplied by he numbe o a ms in he sec o s (17,480 dai y a ms and
28,979 c op a ms). Thus, he agg ega e GSV o he Finnish c op sec o esul ed in abou −1,510
million eu os in yea 2004 and he agg ega e GSV o he Finnish dai y sec o esul ed in abou −876
million eu os o he same yea .
Finally, i is wo h o ecognize he limi a ions o he p e ious analysis, which is in ended as an
illus a ion o he me hodological de elopmen . Fi s ly, he FADN sample is no a andom sample, and
hence no necessa ily ep esen a i e o he Finnish ag icul u e as a whole. We would expec he FADN
a ms o be on a e age mo e e icien han he non-FADN a ms. Secondly, he en i onmen al
indica o s conside ed in his applica ion a e e y ough p oxies. Thi dly, he DEA me hod used o
Sus ainabili y 2013, 5 1575
es ima ing he on ie assumes away noise, which is a e y es ic i e assump ion in he p esen
applica ion. Add essing hese p oblems would p o ide a ui ul a enue o u u e esea ch.
5. Conclusions
This pape ex ends he scope o p e ious s udies o he i m le el gene alized sus ainable alue
measu es, by p oposing a sys ema ic app oach o measu ing sus ainabili y pe o mance o i ms a he
agg ega e le el. An agg ega e sus ainabili y measu e can be es ima ed om empi ical da a by applying
on ie app oaches and is consis en wi h he i m le el es ima es. The p oposed agg ega ion me hod
was illus a ed by an empi ical applica ion o he Finnish c op and dai y sec o s. The es ima ed
e iciencies o he ep esen a i e a ms allow, i s ly, o assess he pe o mance o an a e age a m in
each sec o in e ms o esou ces used and, secondly, o compa e he pe o mance o a e age a ms
be ween he sec o s. Finally, he es ima ed GSVs o each sec o p o ide a simple, bu p ac ical,
measu e o sus ainabili y pe o mance. This measu e can be use ully applied no only in he
compa a i e analysis o di e en ag icul u al sec o s, bu also o any o he g oup o i ms in a speci ic
specializa ion, egion, o o he ca ego y.
Supplemen a y Ma e ials
Supplemen a y ma e ials can be accessed a : h p://www.mdpi.com/2071-1050/5/4/1568/s1.
Con lic o In e es
The au ho s decla e no con lic o in e es .
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© 2013 by he au ho s; licensee MDPI, Basel, Swi ze land. This a icle is an open access a icle
dis ibu ed unde he e ms and condi ions o he C ea i e Commons A ibu ion license
(h p://c ea i ecommons.o g/licenses/by/3.0/).