Eas on, S ephen T.; Rocke bie, Duane Wesley
A icle
Economies o scale and scope o Canadian uni e si ies
Economies
P o ided in Coope a ion wi h:
MDPI – Mul idisciplina y Digi al Publishing Ins i u e, Basel
Sugges ed Ci a ion: Eas on, S ephen T.; Rocke bie, Duane Wesley (2025) : Economies o scale and
scope o Canadian uni e si ies, Economies, ISSN 2227-7099, MDPI, Basel, Vol. 13, Iss. 8, pp. 1-15,
h ps://doi.o g/10.3390/economies13080238
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Ci a ion: Eas on, S., & Rocke bie, D. W.
(2025). Economies o Scale and Scope
o Canadian Uni e si ies. Economies,
13(8), 238. h ps://doi.o g/10.3390/
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A icle
Economies o Scale and Scope o Canadian Uni e si ies
S ephen Eas on 1and Duane Wesley Rocke bie 2,*
1
Depa men o Economics, Simon F ase Uni e si y, 8888 Uni e si y D i e, Vancou e , BC V5A 1S6, Canada
2
Depa men o Economics, Uni e si y o Le hb idge, 4401 Uni e si y D i e, Le hb idge, AB T1K 3M4, Canada
*Co espondence: [email p o ec ed]
Abs ac
We es ima e measu es o economies o scale and scope o a sample o 48 Canadian uni-
e si ies ha p oduce mul iple ou pu s. Es ima es ha e no been p e iously a emp ed
o Canadian uni e si ies o ou knowledge. Declining inancial suppo om p o incial
go e nmen s makes inding cos e iciencies a p io i y o policy make s. Ou app oach
ea u es wo use ul inno a ions: by using panel da a o 2011–2019, ins ead o a c oss-
sec ion o a single yea , he e is mo e a ia ion in he a iables o es ima e a mul i-p oduc
ans-log cos unc ion; and we conside he app op ia eness o using esea ch unding as
a measu e o esea ch ou pu by al e na i ely using publica ion coun s. We did no ind
economies o scale a any uni e si y size bu did ind ay economies o scale up o 60% o
he median uni e si y size. Economies o scope we e e iden up o oughly 1.2 imes he
median uni e si y size. No signi ican di e ences in esul s we e ound be ween using
publica ion coun s o esea ch unding. Small ins i u ions ha ca e o di e en ou pu s
could be me ged in o comp ehensi e ins i u ions. The lack o economies o scope o
Canada’s la ge uni e si ies sugges s ha hey could be b oken up in o smalle specialized
ins i u ions i cos e iciencies a e a p io i y.
Keywo ds: economies o scale; economies o scope; Canadian uni e si ies
1. In oduc ion
To economis s, discussion o he e icien size o an o ganiza ion gene ally boils down
o i s economies o scale, he le el o ou pu ha achie es cons an e u ns o scale— he le el o
ou pu whe e a small inc ease o dec ease in ou pu does no change he a e age cos (cos
pe uni o ou pu ). In a ma ke economy, compe i i e p essu es o ce p o i -maximizing
i ms cons an ly o s i e o p oduce mo e e icien ly and achie e cons an e u ns o
scale. Fi ms ha p oduce wi h inc easing e u ns o scale (dec easing a e age cos ) should
inc ease hei ou pu , i demand allows, o achie e hei e icien scale o ou pu (size).
Likewise, i ms ha p oduce wi h dec easing e u ns o scale (inc easing a e age cos )
should conside dec easing hei ou pu o di es ing hemsel es o pa s o hei business.
In o ma ion abou he e icien o ganiza ion o p oduc ion can be deduced by obse ing
o ganiza ions in he same indus y ha su i e and p ospe in a compe i i e en i onmen .
Howe e , in he con ex o publicly unded highe educa ion in Canada, he answe is
no so simple o a leas h ee easons: (i) ui ion ees paid by s uden s do no co e
he ull cos o hei educa ional expe ience and a e egula ed by Canada’s p o incial
go e nmen s; (ii) ope a ing g an s ha und la ge po ions o uni e si y ope a ions a e
de e mined by p o incial go e nmen s using a mix o o mula-based and disc e iona y
me hods; and (iii) all uni e si ies in Canada and elsewhe e p oduce mul iple ou pu s, no
Economies 2025,13, 238 h ps://doi.o g/10.3390/economies13080238
Economies 2025,13, 238 2 o 15
jus unde g adua e educa ion. The inancial cons ain s placed on Canada’s uni e si ies
imply ha he only ma gin ha hey ha e is o choose an en ollmen size ha achie es an
e icien scale o ope a ion in e ms o o al cos s. Rocke bie and Eas on (2024) p o ide a
e iew o he Canadian uni e si y sys em and i s challenges.
Ou s udy will es ima e economies o scale and scope o Canadian uni e si ies by
inco po a ing se e al inno a ions. Fi s , due o he much la ge a ailabili y o inancial
da a om he CAUBO da abase (Canadian Associa ion o Uni e si y Business O ice s),
economies o scale and scope can be es ima ed using panel da a co e ing se e al yea s.
P e ious s udies o Canadian uni e si ies ha e su e ed by only ha ing access o a single
yea o inancial da a; hus, hey a e only able o es ima e scale and scope economies o e y
la ge g oups o ins i u ions wi h limi ed a ia ions in he da a. Second, he a ailabili y o
publica ion coun s o Canadian uni e si ies o e s an imp o emen in measu ing esea ch
ou pu in compa ison o he use o esea ch unding o en used by o he s udies. Publica ion
coun s we e used as a measu e o esea ch ou pu by de G oo e al. (1991) o a sample o
U.S. uni e si ies. The associa ion be ween publica ion coun s and esea ch unding was
in es iga ed by G alka e al. (2019) in he con ex o pe o ming a da a en elope analysis o
measu e cos e iciencies o uni e si ies in Ge many. They ound li le di e ence using
ei he measu e. Ou esul s will add e idence o his ques ion. In addi ion, ou esul s
will p o ide use ul policy ecommenda ions o Canada’s uni e si y adminis a o s and
p o incial go e nmen s conce ning u u e pa hs o specializa ion in p og ams and he
possible di e si ica ion o exis ing p og ams o achie e cos e iciencies.
Es ima ing he cos o p oducing academic ou pu s is complica ed by he ac ha
many, i no all, uni e si ies p oduce mul iple p oduc s. Typically, he p oduc s include
unde g adua e and/o g adua e ins uc ion and esea ch ou pu . In addi ion o hese basic
ou pu s, many ins i u ions also p oduce public se ices such as medical se ices, business
assis ance p og ams, museums o a ious so s, hea e p oduc ions, and he like. And, o
cou se, uni e si ies p oduce bo h in amu al and ex amu al a hle ics. Thus, o pu poses o
es ima ing uni cos s, i is essen ial o ea uni e si ies as mul ip oduc “ i ms.” Fu he , i
seems highly likely ha he p oduc ion o ce ain ou pu s a ec s he uni cos o p oducing
o he ou pu s. Fo example, he p oduc ion o g adua e ins uc ion equi es hi ing acul y
wi h mo e ex ensi e aining and abili y han is equi ed o each only a he unde g adua e
le el. Doc o ally quali ied acul y a e mo e expensi e o hi e han non-doc o ally quali ied
acul y. To he ex en ha he se o acul y p o iding g adua e ins uc ion and he se
o acul y p o iding unde g adua e ins uc ion a e mu ually exclusi e, he p o ision o
he o me has no cos spillo e o he la e . Howe e , i he g adua e acul y also each
unde g adua e cou ses, hen he uni cos o p o iding unde g adua e educa ion will be
highe a uni e si ies ha p oduce bo h g adua e and unde g adua e educa ion han a
hose ha p oduce only unde g adua e educa ion. On he o he hand, o he ex en ha
ela i ely low-paid g adua e s uden s a e used o each unde g adua e cou ses, uni cos s
o he la e may be lowe han one would ind a adi ional unde g adua e-educa ion-
only ins i u ions.
The abili y o achie e lowe a e age cos s by o e ing a g ea e a ie y o ou pu s
is e med economies o scope. The e is e idence ha highe educa ion is cha ac e ized by
(dis)economies o scope. Using da a om 1981 o 1982, Cohn e al. (1989) es ima ed
mul ip oduc cos unc ions o 1195 U.S. public colleges and uni e si ies and 692 p i a e
U.S. colleges and uni e si ies and ound ha a he mean le els o ou pu s in hei samples
he e we e economies o scope in p i a e sec o ins i u ions and diseconomies o scope in
public sec o ins i u ions.
The empi ical me hod o es ima e economies o scale and scope in ol es he es ima-
ion o a non-linea cos unc ion using mul iple eg ession me hods. Da a a e acqui ed
Economies 2025,13, 238 3 o 15
ega ding he a ious cos s ha uni e si ies incu , as well as measu es o hei a ious
“ou pu s”. S a is ical es s o es ic ions o he eg ession coe icien s sugges e idence o
he e u ns o scale o a e age cos s and he p esence o economies o scope.
The empi ical li e a u e es ima ing scale and scope economies o uni e si ies is
mode a ely ex ensi e, al hough a single s udy exis s o Canadian uni e si ies. Dickson
(1994) ound e idence o inc easing e u ns o scale o Canadian uni e si ies using da a
o 1986. The empi ical me hod employed is simplis ic and ela i ely mo e powe ul
econome ic me hods ha e become a ailable ecen ly, he sample is limi ed only o one yea ,
and he ypes o deg ees o e ed a e no con olled o . We hope o imp o e on his s udy
by using mo e de ailed da a o a la ge sample o yea s and mo e powe ul econome ic
echniques o educe he likelihood o bias in he esul s.
A much la ge sample o li e a u e exis s o es ima ing scale and scope economies
o U.S. uni e si ies, only a sample o which is gi en he e. de G oo e al. (1991) ound
economies o scale and scope o a sample o 147 uni e si ies using 1982–1983 da a. Koshal
and Koshal (1995) g ouped uni e si ies in o ou ca ego ies based on hei size (measu ed
by s uden en ollmen s and e enues) and ype o deg ee o e ed (unde g adua e only o
comp ehensi e). The esul s o 204 U.S. uni e si ies o he yea 1990 sugges inc easing
e u ns o scale and la ge posi i e epu a ional e ec s on o e all cos s. Koshal and Koshal
(1999) ollow up hei ea lie s udy wi h a la ge sample ha con ols o deg ee ype, public
and p i a e ins i u ions, and mul iple ou pu s, using 171 public and 158 p i a e in ui ions,
espec i ely, o he yea 1991. They es ima e signi ican inc easing e u ns o scale and
economies o scope; howe e , hey also es ima e lowe economies o scope o smalle
ins i u ions. Libe al a s colleges also exhibi ed economies o scale and scope, bu no
su p isingly, cos ine iciencies in p oducing esea ch (Koshal & Koshal,2000). Hashimo o
and Cohn (1997) ound economies o scale and scope in a sample o 94 p i a e uni e si ies
in Japan using da a o he yea 1991. Unde g adua e and g adua e s uden s we e ound o
demons a e s onge e u ns o scale and scope o smalle uni e si ies, while esea ch
ou pu s onge o la ge uni e si ies. Laband and Len z (2003) use a much la ge sample
o 1492 p i a e ins i u ions and 1450 public ins i u ions in he U.S. using da a o 1995.
Thei esul s sugges uni e si ies ope a e wi h inc easing e u ns o scale, bu do no bene i
om economies o scope when ou pu s a e classi ied as unde g adua e educa ion, g adua e
educa ion, and esea ch ou pu . Sa (2007) ound economies o scale o U.S. p i a e sec o
ins i u ions, bu only o small public sec o ins i u ions. Sa (2011) ound diseconomies
o scale a e con olling o he ype o ins i u ion (Ph.D, Mas e s, unde g adua e), wi h
economies o scope o all ypes using a sample o U.S. ins i u ions o e 2000–2007.
Longlong e al. (2009) es o economies o scale and scope in a sample o 74 uni e -
si ies in China, in he yea 2000. They ound economies o scale in esea ch ou pu bu
diseconomies o scale in unde g adua e and g adua e en ollmen s. Economies o scope
we e ound o smalle ins i u ions bu no la ge ins i u ions. Tes ing o economies o
scale and scope has p o en popula using U.K. uni e si ies. An ea ly example is Johnes
(1996), who ound economies o scale and scope, ollowed by Johnes (1997) wi h la gely he
same esul s. Johnes and Johnes (2016) es o economies o scale and scope using a sample
o 103 uni e si ies in he U.K. o he yea 2013. The me hod di e s om ha p oposed
he e in ha i uses a on ie es ima ion me hod ha es ima es he “dis ance” a which an
ins i u ion achie es i s o al cos s ela i e o an es ima e o he “e icien ” cos ( ha which
lies on he cos -minimizing p oduc ion on ie ). This has become a popula es ima ion
me hod (see also Izadi e al. (2002) and Hashimo o and Cohn (2014)), howe e , i asks a
di e en se o ques ions. Rega dless, he esul s sugges inc easing e u ns o scale and ha
U.K. uni e si ies ope a e e y close o hei e icien on ie s, lea ing li le oom o achie e
g ea e e iciencies. Mo e ecen con ibu ions include Vamosiu e al. (2018) and Vamosiu
Economies 2025,13, 238 4 o 15
e al. (2024) ha bo h u ilize da a o U.S. colleges. A use ul e iew o p e ious esea ch
is p o ided by Tou koushian and Lee (2018). Zhang and Wo hing on (2018) p o ide a
use ul e iew using me a-analysis. Whe he uni e si ies can achie e cos sa ings and
scope economies by me ging was es ed by Mizu ani e al. (2024) o a sample o Japanese
uni e si ies using 2014 and 2018 da a. They could no ind e idence o ei he e ec .
The plan o ou pape is as ollows. Sec ion 2desc ibes he esea ch me hodology used,
speci ically he speci ica ion o a mul i-ou pu cos unc ion ha possesses he s anda d
heo e ical p ope ies o a cos unc ion, and he measu es o economies o scale and scope.
Sec ion 3desc ibes he measu es o ou pu , a ac o p ice used in he cos unc ion, as well
as he sou ces o da a. The es ima ed cos unc ion is p esen ed in Sec ion 3. And p o ides
he es ima es o e u ns o scale and scope. Conclusions a e p o ided in Sec ion 4.
2. Me hodology
2.1. Me hod
Es ima ing economies o scale o a mul i-p oduc i m equi es he es ima ion o a
cos unc ion ha includes he i m ou pu s and ac o p ices. The cos unc ion should
con o m o he economic p ope ies o a p ope cos unc ion (G ee ,2012). These p ope ies
include p oducing non-nega i e quan i ies o ou pu , non-nega i e ma ginal cos s, and
linea homogenei y in ac o p ices ( ac o p ices and cos inc ease by he same p opo ion).
The quad a ic cos unc ion is simple o ope a ionalize and con o ms o hese p ope ies. In
ou case, he cos unc ion con ains kou pu s o each o he Nuni e si ies in ou panel
es ima e, wi h ou pu s deno ed by jand mand uni e si y deno ed by i= 1 o N. Each o he
kou pu s o uni e si y iis deno ed as
Qj
, he ac o p ice is deno ed as
Si
, and o al cos is
deno ed as Ci.
Ci=e(αo+γo+∑k
j=1αjQij+1
2∑k
j=1∑k
mαjmQjQim)Sβ
i(1)
Taking he na u al log o (1) gi es he o m o he es ima ing equa ion o uni e si y i
in pe iod .
lnCi =αo+γo+∑k
j=1αjQj +1
2∑k
j=1∑k
m=1αjmQj Qm +βlnSi +zi (2)
Ou panel da a con ains obse a ions o e a sample o yea s o each uni e si y;
howe e , we exclude ime subsc ip s in u he equa ions o con enience. Each ou pu is
cap u ed in a linea e m, a quad a ic e m, and a c oss-p oduc e m o each o he o he k
−
1 ou pu s. The e m
γo
is a ixed e ec ha accoun s o di e en ixed cos s among ou
sample uni e si ies. The andom e o e m is deno ed by z. Ou quad a ic cos unc ion
does no include in e ac ion e ms be ween he ac o p ice Sand he ou pu s o p ese e
he linea homogenei y in he ac o p ice S. Linea homogenei y is con i med in ou model
i he es ima e o
β
is no signi ican ly di e en om one, bu ha may no be he case
i he e exis excluded ac o p ices ha we canno obse e (such as adminis a i e and
suppo s a sala ies, a iable equipmen and supply p ices, and so on).
Ou ou pu s include annual unde g adua e FTE’s (
QU
), annual g adua e FTE’s (
QG
),
and annual esea ch ou pu (
QR
) measu ed by he o al numbe o acul y publica ions.
Agasis i (2016) could no ind scale economies o a sample o I alian uni e si ies when
using FTE’s bu did ind scale economies when using he numbe o g adua ing s uden s.
Ou da ase did no include he numbe o g adua ing s uden s. In ou opinion, including
only g adua ing s uden s could o e es ima e bo h he a e age and ma ginal cos o se ice
s uden s. While many o he pape s jus i y he use o esea ch unding as a measu e o
esea ch ou pu , he ac emains ha esea ch unding is an inpu in o a esea ch p oduc ion
p ocess ha has an unknown ou pu elas ici y. I is likely he case ha some esea ch
Economies 2025,13, 238 5 o 15
unding esul s in ew o no publica ions while a lo o esea ch is published wi hou any
explici esea ch unding. Publica ion coun s a e now a ailable o Canadian uni e si ies,
and we iew hem as a supe io and ul ima e measu e o esea ch ou pu . Un o una ely, a
measu e o he quali y o he publica ions is no a ailable. This would be use ul in weighing
he publica ion coun s; howe e , i is no clea ha uni e si y cos s would be a unc ion o
publica ion quali y, al hough i could be he case ha e y high-quali y esea che s ea n
highe sala ies ha inc ease cos s. This would be a aluable addi ion o u u e esea ch i
a measu e o uni e si y-speci ic esea ch quali y could be ob ained. We use he median
acul y uni e si y sala y as he ac o p ice since acul y sala ies con ibu e a la ge sha e o
uni e si y cos s. This is a s anda d p ac ice in p e ious s udies.
Se e al s anda d measu es o mul i-p oduc e u ns o scale a e used in he li e a u e
ha we e ini ially sugges ed by Baumol e al. (1982). The i s s ep is o calcula e he
ma ginal cos o each ou pu ,
MCU
,
MCG
, and
MCR
. In he case o unde g adua e FTE’s,
he calcula ion o ma ginal cos is gi en below. The log-linea o m o he cos unc ion
equi es an adjus men o each es ima ed coe icien o es ima e he ma ginal cos in le els.
MCU=∂C
∂QU
=¯
Cα1+α11 ¯
QU+α12 ¯
QG
2+α13 ¯
QR
2(3)
In (3) we choose o use he median alue o each ou pu , which is indica ed by a ba
o e he a iable, due o he hea y skewness in he obse ed ou pu s in ou sample. The
ma ginal cos s
MCG
and
MCR
a e symme ic o he calcula ion in (3). Ma ginal cos s ha
lie below a e age cos s con i m inc easing e u ns o scale o he ele an ou pu , bu
hese mus be aken in con ex wi h he o he measu es in a mul i-p oduc uni e si y. The
a e age inc emen cos
AICU
o
QU
measu es he inc ease in a e age cos by ha ing he
obse ed numbe o unde g adua e FTE’s e sus ha ing none. As such, i is he e ical
shi in he a e age cos when p oducing QU>0 e sus QU=0.
AICU=C(QU,QG,QR)−C(0, QG,QR)
QU
(4)
Ma ginal cos s can be inc easing bu s ill be below a e age cos s. Re u ns o scale a e
e alua ed by aking he a io o a e age inc emen al cos s o ma ginal cos ,
Ei=AICi/MCi
,
o each o he ou pu s. Inc easing e u ns o scale a e said o exis o each ou pu i
Ei> 1
,
meaning ha a e age inc emen al cos lies abo e ma ginal cos a he median le el o
ou pu . This measu e is calcula ed a a ying le els o ou pu in he esul s o ollow o
de ec changes in scale economies.
Ray economies o scale measu e how o al a e age cos beha es as all ou pu s inc ease
by he same p opo ion. Panza and Willig (1978) p o ed ha ay economies o scale can
be measu ed by aking he a io o o al cos o he e enue ob ained om ma ginal cos
p icing e alua ed a he median ou pu s.
RE =C(QU,QG,QR)
QUMCU+QGMCG+QRMCR
(5)
Ray economies o scale a e said o exis i RE >1.
Economies o scope only exis when mul iple ou pu s a e p oduced. In ou case, i he
o al cos o p oducing all he ou pu s is less han he sum o he cos o p oducing each
ou pu indi idually, global economies o scope (GES) a e p esen . Again, he ou pu s ake
on hei median alues ini ially.
GES =C(QU, 0, 0)+C(0, QG, 0)+C(0, 0, QR)−C(QU,QG,QR)
C(QU,QG,QR)(6)
Economies 2025,13, 238 6 o 15
Global economies o scope exis i
GES >
0, sugges ing ha he e a e e iciencies o be
gained in join p oduc ion. This can be he case in uni e si ies, o example, i mo e esea ch
ou pu imp o es unde g adua e and g adua e eaching, esul ing in highe en ollmen s
and lowe a e age cos s. Howe e , his complemen a i y o p oducing ou pu s need no
hold o each ou pu indi idually. P oduc -speci ic economies o scope (PES) measu e
scope economies when only one o he ou pu s is p oduced sepa a ely om he o he
ou pu s ha a e p oduced oge he . I unde g adua e en ollmen s a e p oduced sepa a ely
om g adua e en ollmen s and esea ch, PES is as measu ed below:
PESU=C(QU, 0, 0)+C(0, QG,QR)−C(QU,QG,QR)
C(QU,QG,QR)(7)
The PES o g adua es and esea ch a e calcula ed symme ically o (7). P oduc -
speci ic economies o scope o p oducing unde g adua e s uden s exis i
PESU>
0. This
may be he case i he e exis a numbe o uni e si ies ha p oduce only unde g adua e
s uden s wi h li le o no esea ch expec a ions o acul y and uni e si ies ha p oduce
mo e g adua e s uden s han unde g adua es wi h acul y esea ch (such as he Uni e si y
o Chicago). The o me could be he case o smalle uni e si ies in Canada, bu he la e
would no seem o exis in Canada.
Calcula ing he measu es in (3)–(7) equi ed he es ima ion o (2) using a sample o 48
Canadian uni e si ies ou o a o al o 103 uni e si ies ope a ed in Canada’s en p o inces
in 2019. Excluded ins i u ions had e y small en ollmen s wi h many omissions in hei
inancial da a. The 48 included ins i u ions comp ised jus o e 85% (C$35.5 billion) o
he o al expendi u es o all Canadian uni e si ies in 2019 (C$41.19 billion), wi h o al
en ollmen s a abou he same pe cen age. These include all he op- ie uni e si ies in he
coun y. A ull lis is p o ided in Appendix A(Table A1). The nex sec ion desc ibes he
sample da a used in ou panel eg ession o (2).
2.2. Ma e ials
Es ima ion o he cos unc ion in (2) equi ed da a o uni e si y cos s, unde g adua e
and g adua e s uden en ollmen s, esea ch publica ions, and acul y sala ies. Ou panel
da ase included obse a ions o 48 Canadian uni e si ies o e he pe iod 2011–2019.
Mo e ecen yea s we e excluded om conside a ion due o he COVID-19 pandemic ha
dis o ed he cos and en ollmen da a. Obse a ions we e missing o acul y sala ies
o some o he yea s, esul ing in an unbalanced panel o 365 obse a ions. Uni e si y
cos
(C)
includes all ele an ope a ing cos s excluding expenses o land and buildings
as hese we e deemed as capi al asse s ha a e dep ecia ed and yield a p oduc i e e u n
o e hei li e ime. Cos s included in ele an ope a ing cos s include sala ies and wages,
bene i s, a el, lib a y acquisi ions, p in ing and duplica ing, ma e ials and supplies,
communica ions, o he ope a ional expendi u es, u ili ies, schola ships, bu sa ies, p izes,
ex e nally con ac ed se ices, p o essional ees, cos s o goods sold, and in e es .
Cos da a was ob ained om he CAUBO (Canadian Associa ion o Uni e si y
Business O ice s) uni e si y inancial da abase ha is a ailable upon eques (h ps://
www.caubo.ca, accessed on 5 Oc obe 2023). Unde g adua e
(QU)
and g adua e en oll-
men s
(QG)
we e con e ed o FTE’s by weighing pa - ime s uden s wi h a weigh o 0.5,
and hey included s uden s om all p og ams including p o essional schools (medical, legal,
enginee ing, e c.). The en ollmen da a we e ob ained om Table 37-10-0234-03 main ained
by S a is ics Canada (h ps://www.s a can.gc.ca/en/s a , accessed on 5 Oc obe 2023).
Ac ual c edi hou s aken by pa - ime s uden s a e no a ailable so he weigh o 0.5 is an
es ima e bu one we deem easonable. To al annual esea ch publica ions
(QR)
we e ob-
ained by sea ching he Scopus da abase ha co e ed some 34,377 schola ly i les. Scopus is
Economies 2025,13, 238 7 o 15
main ained by Else ie , Inc. (h ps://www.else ie .com/p oduc s/scopus, accessed on 28
Feb ua y 2024). The numbe o i les is as o 28 Feb ua y 2024 when he da a was aken. Mul-
iple au ho s o a publica ion who a e housed in he same ins i u ion we e coun ed as one
publica ion o ha pa icula ins i u ion. Median acul y sala ies
(S)
we e ob ained om
Table 37-10-0108-01 main ained by S a is ics Canada (h ps://www.s a can.gc.ca/en/s a ,
accessed on 5 Oc obe 2023). Median sala ies we e used ins ead o a e age sala ies o
accoun o any skewness in he sala y da a ha could in la e he a e age sala y, al hough
he coe icien o skewness o sala ies in Table 1sugges s his migh no be an issue. Bo h
uni e si y cos and median acul y sala y we e de la ed o ob ain eal cos s using a p o in-
cial consume p ice index (CPI, 2002 = 100) o all i ems ob ained om Table 18-10-0005-01
main ained by S a is ics Canada.
Table 1. Desc ip i e s a is ics o a iables in cos unc ion (2), 2011–2019. No e ha C,S, and
QR
( esea ch unds) a e measu ed in Canadian Dolla s (C$) and de la ed by he p o incial CPI
(2002 = 100).
C(C$) QU
(En ollmen )
QG
(En ollmen )
QR
(Publica ions) S(C$) QR
(Resea ch Funds)
Mean 514,000,000 20,977 3477 2431 100,267 39,962,000
Median 401,000,000 17,005 2832 1456 99,928 17,094,000
Minimum 45,707,000 2059 9 70 73,800 235,000
Maximum 2,760,000,000 87,640 19,366 17,567 127,900 329,688,000
S d. De . 520,000,000 16,452 3450 3035 11,242 58,307
Skewness 2.051 1.393 1.806 2.361 0.139 2.543
N 365 365 365 365 365 365
To assess he e ec s o using esea ch g an unding as a measu e o esea ch ou pu ,
Equa ion (2) was also es ima ed using de la ed g an unding in place o o al publica ions.
G an unding is composed o se e al sou ces, including Social Sciences and Humani ies
Resea ch Council (SSHRC), Na u al Sciences and Enginee ing Resea ch Council (NSERC),
Canadian Ins i u es o Heal h Resea ch (CIHR), and Canada Founda ion o Inno a ion
(CFI), and we e ob ained om he CAUBO da abase. Canada Resea ch Chai (CRC) unding
was omi ed as i is used o pay acul y sala ies and bene i s o hose chosen h ough a
na ional compe i ion ha alloca es he numbe o CRCs o each uni e si y. This unding
is no used o und esea ch ac i i ies di ec ly. The desc ip i e s a is ics o he comple e
da ase a e p o ided in Table 1.
3. Resul s
3.1. Cos Func ion Es ima es
We add ess he issue o he p e e ed measu e o esea ch ou pu be o e es ima ing he
cos unc ion in (2). A panel eg ession using ixed e ec s and a co ec ion o he e oskedas-
ici y was used o in es iga e he associa ion be ween publica ions pe acul y membe and
eal esea ch unding. The numbe o acul y membe s (excluding session con ac s) was
ob ained om Table 37-10-0108-01 main ained by S a is ics Canada, deno ed as acul y. A
quad a ic e m was included o accommoda e he possibili y o diminishing e u ns o eal
esea ch unding. The -s a is ic o each coe icien appea s in pa en heses.
QR
acul y =1.941 +1.44 ×10−5RF
acul y −7.37 ×10−11 RF
acul y
2
(30.09) (4.64) (−3.65)(8)
Economies 2025,13, 238 8 o 15
Equa ion (8) i s e y well wi h an adjus ed R
2
equal o 0.971 wi h s a is ically signi i-
can ixed e ec s (p= 0.000 o an F es excluding ixed e ec s). The in e cep sugges s ha
each acul y membe publishes abou wo publica ions each yea wi h no esea ch unding
(p= 0.000) o he a e age Canadian uni e si y. Publica ions pe acul y membe inc ease
wi h esea ch unding a a diminishing a e (p= 0.000 o bo h coe icien s). A he median
le el o esea ch unding pe acul y membe ($19,760), he ma ginal e ec o esea ch
unding is 1.15
×
10
−5
. To inc ease he publica ion/ acul y a io by one publica ion will
equi e an addi ional $87,050 pe acul y membe in esea ch unding. Pu ano he way, he
alue o he wo publica ions pe acul y membe wi h no esea ch unding is $174,100 in
esea ch unding pe acul y membe —a signi ican sa ing in esea ch unding. The i ed
eg ession model in (8) is plo ed in Figu e 1. A linea model is app op ia e up o he me-
dian le el o esea ch unding pe acul y membe , bu a highe alues diminishing e u ns
en e . We p e e o use publica ions as he measu e o esea ch ou pu o his eason.
0
1
2
3
4
5
6
7
8
0 20,000 40,000 60,000 80,000 100,000 120,000 140,000 160,000 180,000
Publicai ons/Facul y
Resea chFunds/Facul y($)
Figu e 1. Publica ions pe acul y membe agains esea ch unding pe acul y membe ob ained
om he es ima e o Equa ion (8).
The quad a ic cos unc ion in (2) was es ima ed using a weigh ed leas squa es
p ocedu e. An LM es o c oss-sec ion he e oskedas ici y ejec ed he null hypo hesis
o no he e oskedas ici y a a high le el o con idence. As a esul , (2) was e-es ima ed
calcula ing he panel-co ec ed s anda d e o s de eloped by Beck and Ka z (1995) ha
co ec s he slope s anda d e o s o he e oskedas ici y and se ial co ela ion. Time-wise
ixed e ec s o each ins i u ion we e included in he es ima ion o (2) bu we e ound o be
e y small and s a is ically signi ican . C oss-sec ion ixed e ec s we e no included due
o he inclusion o he dummy a iables o he ins i u ional ca ego ies desc ibed below.
The es ima ed coe icien s appea in column (2) o Table 2, and all ha e he expec ed sign
excep he nega i e sign o he c oss-p oduc o unde g adua e and g adua e en ollmen s,
sugges ing a complemen a i y in cos . All coe icien s a e s a is ically signi ican a 95%
con idence, excep o he quad a ic e m o g adua e en ollmen s. The es ic ion ha
sala y elas ici y was equal o one could no be ejec ed (p= 0.351), con i ming he desi able
p ope y ha he cos unc ion is homogeneous o deg ee one in he ac o p ice.
Economies 2025,13, 238 15 o 15
Mizu ani, F., Tanaka, T., & Nakayama, N. (2024). Economies o scale and scope, me ge e ec s, and owne ship di e ence: An empi ical
analysis o uni e si ies in Japan. Educa ion Economics,32(6), 882–905. [C ossRe ]
Panza , J., & Willig, R. (1978). Economies o scale in mul i-ou pu p oduc ion. Qua e ly Jou nal o Economics,91(3), 481–493. [C ossRe ]
Rocke bie, D., & Eas on, S. (2024). Go e nmen unding alloca ions o uni e si ies and he business cycle: An analysis o Canada’s
p o incial go e nmen s. Economies,12(4), 94. [C ossRe ]
Russell, L. (2021). P ice e ec s o nonp o i college and uni e si y me ge s. Re iew o Economics and S a is ics,103(1), 88–101. [C ossRe ]
Sa , G. T. (2007). Highe educa ion cos s and scale and scope economies. Applied Economics,36(6), 607–614. [C ossRe ]
Sa , G. T. (2011). Panel da a es ima es o public highe educa ion scale and scope economies. A lan ic Economic Jou nal,39, 143–153.
[C ossRe ]
Tou koushian, R., & Lee, J. (2018). Re isi ing economies o scale and scope in highe educa ion. In M. Paulsen (Ed.), Highe educa ion:
Handbook o heo y and esea ch (pp. 371–416). Sp inge Na u e.
Vamosiu, A., McClu e, K., & Ti us, M. (2018). Economies o scale and scope a public mas e ’s ins i u ions: E idence accoun ing o
spa ial independency. Educa ion Economics,26(5), 516–533. [C ossRe ]
Vamosiu, A., Ti us, M., & Sandy, J. (2024). Neighbo -E ec s and Economies o Scale and Scope a Public Communi y Colleges. Highe
Educa ion Policy,37, 138–166. [C ossRe ]
Zhang, L.-C., & Wo hing on, A. (2018). Explaining es ima ed economies o scale and scope in highe educa ion: A me a- eg ession
analysis. Resea ch in Highe Educa ion,59(2), 156–173. [C ossRe ]
Disclaime /Publishe ’s No e: The s a emen s, opinions and da a con ained in all publica ions a e solely hose o he indi idual
au ho (s) and con ibu o (s) and no o MDPI and/o he edi o (s). MDPI and/o he edi o (s) disclaim esponsibili y o any inju y o
people o p ope y esul ing om any ideas, me hods, ins uc ions o p oduc s e e ed o in he con en .
