O'Neill, Robe
A icle
Teaching Index Numbe s o economis s
Cogen Economics & Finance
P o ided in Coope a ion wi h:
Taylo & F ancis G oup
Sugges ed Ci a ion: O'Neill, Robe (2015) : Teaching Index Numbe s o economis s, Cogen
Economics & Finance, ISSN 2332-2039, Taylo & F ancis, Abingdon, Vol. 3, Iss. 1, pp. 1-10,
h ps://doi.o g/10.1080/23322039.2015.1115625
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GENERAL & APPLIED ECONOMICS | REVIEW ARTICLE
Teaching Index Numbe s o economis s
Robe O’Neill
1
*
Abs ac :Economic s a is ics a e equen ly epo ed in he o m o index numbe s.
This a icle conside s how he ield o Index Numbe s should be app oached in he
eaching o a gene al economic deg ee. While he opic inds a na u al home in s a-
is ics modules, i is emphasised ha he a ea can also be e e ed o in he each-
ing o o he a eas o economics. I is also emphasised ha he di e ences be ween
Index Numbe s heo y and he p ac ice o compiling economic s a is ics such as
in la ion can help s uden s gain a be e unde s anding o applied economic s a is-
ics. Me hods o assessing lea ning in he a ea a e also conside ed and a ailable
ma e ial o suppo eaching is also summa ised.
Subjec s: Teaching & Lea ning; Economics; Educa ion; S a is ics o Business; Finance &
Economics
Keywo ds: Index Numbe s; economic s a is ics; o icial s a is ics; in la ion; economic ools
o eaching
1. In oduc ion
Index Numbe s1 me hods a e among he mos commonly used s a is ical echniques in he a ea o
economic s a is ics. Index Numbe s a e commonly used o combine la ge amoun s o da a abou a
gi en a iable in o a single numbe ; he a iable is hen (usually) allowed o a y o e ei he a spa ial
o empo al dimension. S a is ics measu ed using some ype o index numbe include, in la ion,
s ock ma ke pe o mance, olumes o p oduc ion and human de elopmen . Despi e he widesp ead
applied use o ools which all unde he heading o index numbe s, he a ea is ypically augh o
economics unde g adua es wi hin a i s -yea s a is ics cou se in which a ew o mulae a e in o-
duced and hen li le emphasis is gi en o he subjec a ea in o he modules o in la e yea s.
In his a icle, I will a emp o desc ibe an al e na i e app oach o he eaching o index numbe s.
I is a gued ha i is bene icial o mo e beyond he applica ion o a small se o o mulae o a i icial
*Co esponding au ho : Robe O’Neill,
The Business School, The Uni e si y o
Hudde s ield, Queensga e, Hudde s ield
HD1 3DH, UK
E-mail: .o’[email p o ec ed]
Re iewing edi o :
Ca oline Ellio , Uni e si y o
Hudde s ield, UK
Addi ional in o ma ion is a ailable a
he end o he a icle
ABOUT THE AUTHOR
Robe O’Neill is a senio lec u e in Economics
a he Uni e si y o Hudde s ield. P io o aking
up his posi ion, he wo ked o he O ice o
Na ional S a is ics as pa o he Index Numbe s
me hodology eam. He has ecen ly published
a book, alongside wo o his o me colleagues
on he opic o Index Numbe s. In addi ion o
esea ch in his a ea, he main ains an ac i e
in e es in ola ili y o ecas ing o inancial asse
po olios.
PUBLIC INTEREST STATEMENT
Index Numbe s me hodology is used o c ea e
many o he economic s a is ics we see quo ed
in he news on a egula basis, o en hey a e
used o measu e changes in p ices o economic
ac i i y compa ed wi h some p io pe iod. This
pape discusses how economis s migh go abou
eaching he subjec o inexpe ienced colleagues
and a emp s o highligh linkages wi h o he
a eas o economics as well as highligh ing he
di e ences s uden s migh encoun e when
applying heo y in he eal wo ld. Al hough his
a icle does no in oduce he un amilia eade o
he subjec o Index Numbe s, i does ecommend
a numbe o sou ces which may be o in e es o
an indi idual who wan s o know mo e abou his
a ea.
Recei ed: 07 Sep embe 2015
Accep ed: 28 Oc obe 2015
Published: 20 No embe 2015
© 2015 The Au ho (s). This open access a icle is dis ibu ed unde a C ea i e Commons A ibu ion
(CC-BY) 4.0 license.
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Robe O’Neill
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da a and conside ha a deepe app ecia ion o Index Numbe s can p o ide economics s uden s
wi h a be e unde s anding o he link be ween heo y and applica ion in he a ea o economic
s a is ics. The p oposed app oach will enhance s uden s’ unde s anding o bo h he s eng hs and
weaknesses inhe en in he s a is ics p oduced by Na ional S a is ical Ins i u ions such as he O ice
o Na ional S a is ics (ONS) in he UK. A be e unde s anding o his en i onmen will hen po en-
ially uel hei unde s anding o applied wo k in o he a eas o economics and make hem be e
placed o analyse and make use o o he economic s a is ics.
Sec ions 2 and 3 o his a icle highligh wha migh be augh o economics s uden s in he a ea
o Index Numbe s wi h a dis inc ion d awn be ween he heo e ical ma e o app oaching he a ea
and issues which migh be aised ela ing o he applica ion o he heo y in he wo ld o applied
economic s a is ics. Assessmen o hese key a eas is hen b ie ly discussed be o e linkages be ween
a s a is ical in oduc ion o Index Numbe s and o he co e a eas o an economics syllabus a e b ie ly
e iewed. Sec ion highligh s ma e ials and esou ces which may be use ul o s uden s and lec u e s
a a ious le els o an economics educa ion.
2. Index Numbe s heo y
This sec ion will deal wi h he subjec ma e which migh be in oduced o economics s uden s
s udying Index Numbe s unde he heading o “ heo y”, gene ally his will be used o cap u e all
ma e ial which is no explici ly linked o he compila ion o a se o index numbe s om sampled
da a and includes he cons uc ion o indices om idealised da a. We migh hink o he ma e ial
discussed in his sec ion as o ming an in oduc ion o he wo ld o Index Numbe s in which he e
a e no es ic ions on da a and in which e e y hing equi ed o an index will be knowable.
The na u al home o an in oduc ion o he use o index numbe s in economics cou ses is in a
i s -yea s a is ics module. This is acili a ed by he ac ha Index Numbe s equi es li le echnical
sophis ica ion beyond ha which would be ound in mos seconda y educa ion ma hema ics cou se.
Fo example, wo o he simples indices, he Du o and Ca li indices, equi e no hing mo e han he
use o a i hme ic means, he Laspey es and Paasche o mulae make use o basic a i hme ic skills,
while he Fishe and Je ons indices equi e only he abili y o aise o als o he second and n h oo s,
espec i ely. The co e Index Numbe o mulae a e ep oduced below o e e ence in Table 1, whe e
he p ice o he i h good a ime is ep esen ed as
Pi
and quan i y as
Qi
.
I is wo h no ing ha in oduc ions o he opic o Index Numbe s o en ely on applied examples
as o e ing s uden s a de ini ion o an index numbe is di icul and no sa is ac o y o mal de ini ion
has been iden i ied which adequa ely in oduces he me hod in ui i ely.2 When using Index Numbe s,
economis s gene ally a emp o combine mul iple pieces o da a in o a single numbe which
in o ms us abou he change in he le el o some a iable o e some well-unde s ood dimension. I
Table 1. Index Numbe o mulae
Fo mula name Fo mula
Ca li
1
N∑N
i=1
P
i1
P
i0
Je ons
(
Pi1
P
i0)1∕N
Du o
1
N∑
N
i=1Pi
1
1
N∑
N
i=1
P
i0
Laspey es
∑N
i=1Pi1Qi0
∑
N
i=1
P
i0
Q
i0
Paasche
∑N
i=1Pi1Qi1
∑
N
i=1
P
i0
Q
i1
Fishe
√Laspey es ×Paasche
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is he e o e unsu p ising ha examples such as measu ing changes in he p ice le el o e ime, how
income changes ac oss coun ies o how p oduc ion quan i y a ies ac oss egions a e equi ed o
in oduce he subjec .
The e a e se e al po en ial s a ing poin s o he s udy o Index Numbe s and a na u al one o
economics s uden s will be o conside he Index Numbe s p oblem. The Index Numbe s p oblem
poses he ques ion o how o decompose changes in alues in o con ibu ing changes in quan i y
and p ice. This can be in oduced ia a small-scale p oblem simila o ha in oduced in Table 1, In
his example, expendi u e inc eases and his is mainly d i en by an inc eases in he quan i ies pu -
chased. The numbe s in such an example can be cha ac e ised as expendi u es o e enues and an
ini ial index can be cons uc ed which shows he ela i e change in he o al be ween he wo ime
pe iods. As a nex s ep, s uden s can hen be in oduced o he idea ha his change is d i en by wo
e ec s, a p ice e ec and a quan i y e ec . Gi en his s a ing poin , s uden s’ in oduc ion o he
a ious a ailable o mulae can be d i en by del ing in o he change in his simple alue index.
Ha ing been in oduced o he concep o a alue index and shown some examples, s uden s can
hen p og ess on o conside a ions o p ice and quan i y ela i es and om he e mo e on o he
a ious ways in which he in o ma ion can be combined o p oduce a se ies o index numbe s. Once
he o mulae ha e been in oduced, i may be he case ha s uden s hink li le mo e abou he use
o o mulae in he cons uc ion o economic s a is ics, ea ing hei use as an ex empo aneous
choice. Howe e , Index Numbe heo y may well go u he o desc ibe and compa e he di e en
concep ual bases ac oss which o make a choice be ween o mulae. Such a compa ison may be
beyond s uden s on an in oduc o y s a is ics cou se who iew such subjec s as an exe cise in lea n-
ing how o apply a ious ools o da a.
The o mulae hemsel es can be p ac ised wi h he aid o a ela i ely small da a-se , and his can
be ela ed o s uden s’ own pe sonal expe ience, o example, es ima ing he changing cos o an
e ening ou o e a ime pe iod.3 An example o such a da a-se is p o ided in Table 2 o s a ione y
i ems hough s uden s may be encou aged o popula e such an example om hei own
expe ience.4
While eaching index numbe s o a ious g oups, including unde g adua es and hose s udying o
he Royal S a is ical Socie y (RSS) Highe Ce i ica e, mysel and colleagues ha e ound ha he e is
no be e me hod o ge ing o g ips wi h wha he indices a e ying o do han o ha e s uden s
calcula e index numbe s o hemsel es. As he o mulae a e gene ally e y simila and e o s in
mixing up ime pe iods a e common, his will almos ine i ably lead o some miscalcula ions. Despi e
encoun e ing e o s and ha ing cons uc ed a se o index numbe s by hand, s uden s should hen
be be e placed o discuss wha he indices a e doing and app ecia e he di e ence be ween hem.
I is also wo h no ing ha his would ha e been close o he echnique used when he Re ail P ices
Index was i s in oduced as a measu e o he p ice le el in 1947, and help s uden s o app ecia e
he need o so wa e which will speed up he p ocess o much la ge da a-se s.5 S uden s migh
well be asked o es ima e Ca li, Du o , Je ons, Paasche, Laspey es and Fishe indices.6 As an addi-
ional bonus s uden s can also es ima e quan i y indices om he da a in Table 1, which means a
ela i ely small da a-se can gene a e a la ge se o applied examples o s uden s o wo k on.
Table 2. Example da a o an Index Numbe s exe cise
2010 2014
I em Quan i y P ice Quan i y P ice
Book 10 10 6 11
No epad 4 5 12 6
Ebook 6 9 16 8.5
Bookma k 5 1 1 0.5
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Once s uden s ha e been in oduced o he p ac icali ies o calcula ing index numbe s, hey a e
likely o ind i easie o pe o m algeb aic manipula ions o Index Numbe s o mulae. Fo example,
i is ela i ely easy o show ha a alue index can be decomposed in o a Laspey es P ice index mul-
iplied by a Paasche Quan i y index as is showing ha a Laspey es index is a base pe iod expendi u e
weigh ed a e age o p ice ela i es. The abili y o go beyond c anking h ough he calcula ions in o
his so o algeb aic manipula ion o he o mulae is likely o p epa e s uden s o discuss choices
be ween index numbe s in mo e dep h. The algeb aic manipula ions equi ed o his so o wo k
may also p o ide a ela i ely sa e en i onmen in which s uden s can p ac ice he algeb aic manipu-
la ion o summa ion symbols, hus p epa ing hem o mo e complex wo k a a la e da e.
An impo an ac o in he s udy o index numbe s has been he ways in which economis s and
ins i u ions ha e a gued o he use o di e en o mulae. This equi es s uden s o hink analy ically
abou choices in s a is ical me hodology and is a logical nex s ep in he discussion o he ange o
o mulae which may be u ilised in he p epa a ion o an index. The in oduc ion o he economic, axi-
oma ic and s a is ical app oaches7 allows o a wide discussion o how economic s a is ics a e
applied in he eal wo ld, which would be especially use ul o s uden s who in end o pu sue a
ca ee in his a ea as he a gumen su ounding his a ea is indica i e o simila issues in o he simi-
la a eas.
Ha ing conside ed how index numbe s a e cons uc ed, s uden s can be in oduced o hei uses,
o example, de la ing se ies o alues so ha eal g ow h is iden i ied. I is also s aigh o wa d o
demons a e how index numbe s can be e- e e enced in o de o make se e al se ies mo e compa-
able. In addi ion he p ac ice o up a ing paymen s by indices can be demons a ed, which will be
use ul in highligh ing he compounding e ec s o ela i ely modes a es changes in an index. The
p ocess o using an index numbe in his manne , ha ing discussed he choices in ol ed should p o-
ide s uden s wi h a mo e ho ough unde s anding o he op ions a ailable when cons uc ing a
heo e ical index. Ha ing knowledge o how o app oach he choice be ween he a ious op ions as
well as demons a ing some knowledge ega ding how he esul ing es ima es will be used in p ac i-
cal ci cums ances will add o s uden s unde s anding o he opic beyond a simple eci a ion and
applica ion o o mulae.
3. Index Numbe s and applied economic s a is ics
S uden s s udying Index Numbe s can be in oduced ia his opic o he di icul y o p oducing
accu a e and use ul economic s a is ics in a imely manne and he p ac ical ade-o s equi ed in
he eal wo ld o economic s a is ics and he po en ial echniques which may be needed o balance
hese compe ing aims. I migh be possible o s uden s o un hei own p ice collec ion expe imen
a ound campus o see some o hese issues in p ac ice. Howe e , his may be a ime-consuming
p ocess o such a ela i ely mino opic. The di icul ies o p oducing s a is ics in a imely manne
a e one which may help s uden s o ques ion o icial s a is ics mo e igo ously. The e a e se e al
issues ela ed o he compila ion o index numbe s by ONS which a e well documen ed and can be
used o explain and highligh he ange o po en ial issues in compiling O icial S a is ics. Mo e
de ails can be ound in ONS (2015a). Howe e , a b ie summa y o some such issues can be de ailed
he e:
• Goods o be included in an o icial baske o goods should be ep esen a i e o consume habi s.
How migh his be done, especially o new goods o which he e is no cu en da a, he annual
baske e esh is use ul o demons a e his (see ONS, 2015b).
• Collec ion o p ices on a egula basis on “index day” can be used o demons a e se e al sam-
pling issues. Fu he issues such as he non-a ailabili y o goods, o how special o e s should be
eco ded aise addi ional p oblems o compile s o index numbe s.
• Wha popula ions should an index co e , o example, should he Consume P ice Index (CPI)
include spending by non- esiden s in he UK, should i include spending by esiden s when
ab oad? Should he RPI exclude people a he ex emes o he income dis ibu ion as i does?

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• How should i ems be ca ego ised ( his could be used as an in oduc ion o s anda d indus ial
classi ica ions)
• How o compile an index o p ices when he i ems unde conside a ion a e no sold egula ly,
such as in he case o he House P ice Index?
• How o s anda dise he cos o p o iding a se ice in he case o an indus y such as ci il engi-
nee ing o accoun ing o de e mine changing p ice and quan i y le els?
• The ade-o s be ween ime and accu acy in p oduc ion, o example, many house p ice indices
a e published p io o he elease o he ONS igu es. Howe e , hey a e ine i ably based on a
smalle da a-se and less anspa en me hodology.
• The p ac ice o e eshing he index on a egula basis, hus equi ing a chain linking oge he o
indi idual da a se ies, as is done o mos o icial index se ies.
All o he abo e p o ide examples o issues which may a ec he compila ion o an index and may
make i clea ha he closed, well-de ined wo ld discussed when in oducing Index Numbe heo y
is a ely a good app oxima ion o he applied en i onmen economis s a e likely o ind in he eal
wo ld. Al hough his poin can be made wi h a numbe o s a is ical measu es and hei empi ical
applica ions, i is wo h s essing when eaching Index Numbe s as s uden s a e likely o see egula
news epo s which ely on hese so s o s a is ics and his co e age can be used o ame some
discussion o hese issues.
I may be possible o highligh all o he abo e issues in he applica ion o Index Numbe heo y by
asking s uden s o compile hei own index which will measu e he change in p ice le el o s uden s
be ween wo a eas o ac oss wo ime pe iods. This would allow hem o documen any di icul ies
hey had and o ce hem o documen any assump ions hey had o make du ing he p ocess. Gi en
e en a limi ed da a-se , s uden s would be able o compile some index numbe s while commen ing
on he di icul ies o p oducing s a is ics in line wi h heo y.
As well as discussing he issues ela ed o cons uc ing indices, i migh also be use ul o s uden s
o conside he ange o di e en uses o which hese indices migh be pu beyond academic analy-
sis o he economy. S uden s may be able o discuss he a ious ways in which businesses, policy-
make s, esea che s, jou nalis s and indi iduals migh be able o use indices in hei a ious sphe es.
A good example o illus a e how his migh no always be s aigh o wa d is o conside he go e n-
men ’s use o wo di e en measu es o in la ion o indexing paymen s nega i ely a ec ing go e n-
men inancing (bene i s, ax allowances) using a gene ally highe a e han paymen s posi i ely
a ec ing public inances (s uden loan paymen s, ain a es, GILT in e es ).
S uden s who a e no exposed o he p ac ical p oblems and conside a ions o compiling Index
Numbe s in he eal wo ld may eel ha he opic is o li le in e es o hose o he han s a is icians.
This is unlikely o be he case as mos economis s a e likely o make use o numbe s p oduced using
an Index Numbe s app oach and economis s should be able o assess he app op ia eness, accu acy
and ep esen a i eness o hese s a is ics based on he s a is ical me hodology used o p oduce
hem, which will almos always di e om a simple applica ion o one o he o mulae in oduced
abo e.
S uden s app oaching heses applied p oblems o he i s ime may be daun ed o some ex en
by he issues and a good g asp o he ideas behind hem, such as sampling app oaches o p ice col-
lec ion and mul iple eg essions o p icing o complex i ems ia hedonics, is equi ed. Fo his ea-
son, i is sugges ed ha he ype o discussion ou lined abo e migh only be unde aken in de ail
wi h s uden s who ha e al eady comple ed a cou se in s a is ical ounda ions, al hough s uden s
can be in oduced o a leas some o he ma e ial on a i s encoun e wi h Index Numbe s.
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I is wo h no ing ha as “Big Da a” becomes mo e o an issue in he a ea o economic s a is ics
Index Numbe s p o ides an a ea o discuss p ac ical applica ions o la ge da a-se s. This is aided by
he wo k o he ONS Big Da a p ojec using web-sc aped da a (see ONS, 2015c o mo e in o ma ion)
and he wo k o he Billion P ices p ojec (see h p://bpp.mi .edu/ o de ails). Mos s uden s should
be com o able discussing his ma e ial once hey ha e mas e ed he basics o p ice indices and so
i migh be hough ha his a ea p o ides a sa e en i onmen in which o discuss issues ela ed o
inc eased da a-se sizes, a opical issue o hose handling da a and p oducing analysis.
4. Assessing lea ning in index numbe s
S uden s will na u ally engage wi h eaching di ec ly ocused on a echnical opic such as Index
Numbe s a a ange o le els. The e a e a numbe o ways o assessing how s uden s ha e a ained
hese di e en le els and in Table 3 a desc ip ion o le els o lea ning o he subjec a ea is
p oposed.
In o de o assess he di e en le els o lea ning a s a egy is needed which allows weake s u-
den s o show ha hey ha e a ained he basic le el skills while allowing ad anced s uden s a
chance o de elop u he . The ob ious i s s ep is o allow s uden s o calcula e one o wo index
numbe s. This migh hen be ollowed by a ques ion asking s uden s o pe o m an algeb aic ma-
nipula ion o o mulae and s a e wha he esul means in wo ds. Highe and ad anced le el skills
can be demons a ed ia ques ions which migh ask s uden s o commen on he choice be ween
wo compe ing Index Numbe s o mulae and commen on why an index numbe d awn om a da-
a-se simila o ha in Table 2 is unlikely o be app op ia e o use in a high-le el economic analysis.
A ange o po en ially use ul example exam ques ions which ollow a simila o ma o his can be
ound in pas RSS highe pape s which include an Index Numbe s componen .8
The sugges ed amewo k is mos ob iously sui ed o an examina ion ques ion spli in o pa s.
Howe e , lea ning in Index Numbe s migh also be assessed ia assignmen . This migh ake he
o m o a epo which asks s uden s o desc ibe he calcula ion me hods used in an index o hei
choice and commen on he choices made in cons uc ion o hese s a is ics. A mo e in ol ed p o-
jec migh equi e s uden s o collec o sou ce da a wi h which o cons uc an index o hei own
be o e commen ing on he me hodology hey ha e chosen o employ and he po en ial uses o
which hei index migh be pu . This exe cise would b ing s uden s close o he p ac ice o compiling
economic s a is ics o end use s, while also allowing assessmen o lea ning in o he a eas such as
sampling a he same ime as assessing lea ning in index numbe s.
Table 3. Le els o achie emen o Index Numbe s lea ning
Le el o unde s anding Desc ip ion o abili y ou comes
Basic Able o use da a o es ima e index numbe s om a
o mula and able o s a e he main inding esul ing om
he index
In e media e In addi ion o he Basic le el skills, s uden s a e able o
manipula e and in e p e di e en o ms o index num-
be s, also able o desc ibe di e en me hods o choosing
be ween o mulae.
Highe In addi ion o In e media e, able o discuss and analyse
he ela i e p ope ies o a ious index numbe s as well
as iden i y app op ia e eal-wo ld applica ions o he
echnique.
Ad anced In addi ion o Highe , able o discuss he p ac ical
ade-o s which migh a ec he use o index numbe s
in p ac ice and able o assess uses o index numbe s as
app op ia e o no .
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5. Index Numbe s o he han in la ion: spa ial indices, human de elopmen and
mo e
Index Numbe s a e mos commonly encoun e ed in ea ly discussions o in la ion measu emen
ac oss ime. Howe e , i is also possible o emphasise o s uden s he a ied ways in which index
numbe s can be used in Economic S a is ics. The In e na ional P ice Compa ison P og amme (ICP)
(h p://si e esou ces.wo ldbank.o g/ICPEXT/Resou ces/ICP_2011.h ml) collec s p ice s a is ics o e a
spa ial, a he han empo al dimension and can be used as a s a is ical app oach o a conside a ion
o pu chasing powe pa i y. Again he applied di icul ies o such an exe cise can be used o mo i a e
mo e discu si e sessions on he compila ion o such s a is ics. Fo example, in he ICP, he e a e
egional link coun ies o ci cum en he p oblem o no all coun ies ha ing common goods o sale,
due o di e ences in ansla ing in o di e en languages and dialec s pic u es a e issued o p ice
collec o s, e c. Expanding he discussion o index numbe s in one dimension he e o e aises a num-
be o o he issues which need o be conside ed.
As well as p oducing a wide ange o p ice indices, he ONS also compile a numbe o quan i y
indices migh be used o illus a e how Index Numbe s is pu o use in economic s a is ics. The Re ail
Sales Index (RSI) measu es he olume o pu chases by consume s and is o en in he news ela ing
o high s ee expendi u es a ound Ch is mas, he Index o P oduc ion measu es manu ac u ing
ou pu ac oss he UK while se e al G oss Domes ic P oduc (GDP) se ies a e epo ed as olume indi-
ces (indeed he aw ma e ial is de la ed by ano he ONS p oduced p ice index - he GDP de la o .)
Some imes, he ange o quan i y indices p oduced by Na ional S a is ical Ins i u ions is gi en less
a en ion han p ice indices in he Index Numbe s li e a u e. Howe e , i is impo an o include such
indices in an economis s’ in oduc ion o he subjec as hese indices will be mo e ocused on iden-
i ying a ia ions in eal economic ac i i y and so should be o mo e undamen al in e es .
The Human De elopmen Index, h p://hd .undp.o g/en/con en /human-de elopmen -index-hdi,
uses an Index Numbe s me hodology o combine se e al s a is ics, se e al o hem which a e hem-
sel es indices. This p o ides a good example o he ways in which Index Numbe s may also be pu o
use in he s udy o de elopmen economics. The Human De elopmen Index ep esen s jus one
way in which Index Numbe s me hodologies can be pu o a wide use and migh be used o s imu-
la e discussion o he po en ial wide uses o he me hodology.
6. Index Numbe s in mac o, mic o and economic his o y cou ses
Va ious a eas o economics eaching make use o index numbe s (o a iables which a e o en cap-
u ed using he echnique in hei applied se ing) and his can be ein o ced in a ange o ways on
modules ou side o s a is ics modules. I should be clea ha i is no p oposed ha Index Numbe s
me hodology become a key conce n in such modules. Howe e , he opics i s me in he s a is ics
en i onmen migh be be e unde s ood as hey a e e-in o ced in o he economics modules. Again
his will help de elop s uden s’ wide hinking abou he issues a ec ing economic s a is ics hey
may use o ead abou in he u u e.
6.1. Mic o
A gumen s which make use o mic oeconomic heo y ha e been impo an in he de elopmen o
index numbe s, pa icula ly in he measu emen o in la ion. A dis inc ion is d awn in he s a is ical
li e a u e on he use o Index Numbe s in measu ing in la ion be ween a “Cos o Goods Index”,
which measu es he change in p ice o a ixed lis o goods an se ices, and a “Cos o Li ing Index”
which measu es he change in p ice o a aining a cons an le el o u ili y. The “Economic App oach”
o index numbe s has gene a ed much deba e be ween Index Numbe s p ac i ione s, and ideas me
in mic oeconomics a e impo an o unde s anding hese a gumen s. The concep o a Cos -o -
Li ing p ice index, i s o mally conside ed in Konus (1924), which measu es he equi ed change in
income o main ain a ixed u ili y le el, is di ec ly mo i a ed by conside a ion o expendi u e unc-
ions and subs i u ion beha iou . The e o e, i would be di icul o in oduce cons an u ili y indices
o s uden s un amilia wi h hese concep s.
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Be o e discussing a o mal de ini ion o a Cos o Li ing Index, based on expendi u e unc ions, i
is possible o show s uden s ha he Laspey es and Paasche o mulae ep esen uppe and lowe
bounds o a cos -o -li ing index o a a ional consume .9 I is qui e s aigh o wa d o show s u-
den s, who a e amilia wi h he unde lying ma e ial, ha he Je ons index ep esen s a cos -o -
li ing index o an indi idual wi h a Cobb-Douglas u ili y unc ion whe e as e pa ame e s a e all se
o be 1/n in an n good se ing. This esul has i sel been he basis o se e al use s o index numbe s
o conclude ha his index will be e ep esen a cos -o -li ing index han o he unweigh ed indi-
ces.10 These a gumen s can be aken u he as s uden s a e exposed o mo e complex u ili y unc-
ions, o example, Balk (1999) de i es a cos -o -li ing index o a cons an elas ici y o subs i u ion
u ili y unc ion. Simila issues migh be discussed o p oduce s. Howe e , i emains clea ha he e
a e ways in which he po en ial use o index numbe s migh be emphasised e en wi hin mic oeco-
nomic discussions. Concep s such as elas ici y o subs i u ion, he impac o new goods on demand
o exis ing goods, he po en ial di icul ies o iden i ying ep esen a i e goods a e all also po en ial
a eas o mic oeconomics which can be ela ed back o he cons uc ion o an in la ion measu e.
The abo e discussion conside s how Index Numbe s migh be discussed in a mic oeconomic
cou se. While i would clea ly no be a cen al pa o such a cou se he sugges ed mo e o mal
in oduc ion o economic heo y in o he Index Numbe s en i onmen will se e s uden s well in wo
senses. Fi s ly, s uden s will unde s and he o mal heo y behind he mo i a ion o unde s and
in la ion and inco po a e his in o hei b oade unde s anding o Index Numbe heo y. Secondly,
such a discussion will g ea ly assis in he discussion o p ac ical issues a ec ing Index Numbe s, o
example, how o measu e u ili y, how o measu e subs i u ion beha iou , wha can be done o
app oach es ima ion o a Cos -o -li ing index as migh be equi ed by economis s. Such ein o ce-
men and discussion o ma e ial ac oss modules should u he ein o ce how economic heo y
should in o m economic s a is ics and how he eal wo ld o en p e en s a s aigh o wa d applica-
ion o he heo y.
6.2. Mac o
By necessi y, he s udy o mac oeconomic heo y o en p oceeds wi hou a deep conside a ion o
he economic s a is ics which migh be used and i would be a e o such a cou se o spend much
ime in he conside a ion o Index Numbe s. I would no p opose ha his change howe e applied
mac o-economis s a e likely o use index numbe se ies mo e han mos economis s and i would be
good o emphasise ha he choice o Index Numbe migh in luence how hings a e seen.
A good example o his om he ecen his o y o in la ion measu emen ela es o he impac o
he inancial c isis on mo gage in e es paymen s (MIPs). As he RPI inco po a es MIPs, he e was a
concu en downwa d shi in RPI in la ion which was no ma ched by a all in he CPI. Simila ly, as
GDP g ow h in he UK has been close o ze o in ecen yea s, his has p omp ed a discussion ega d-
ing he amoun o e o in he measu emen in GDP g ow h. Simila a gumen s migh be discussed
ega ding in la ion s a is ics and p oduc ion measu es which migh p omp mac o-economis s o
ea o icial s a is ics wi h mo e suspicion han in he case in which NSIs’ measu emen o GDP, e c.
is assumed o be consis en wi h he heo e ical de ini ions o hese a iables.
As one o he p ima y end use s o economic s a is ics mac oeconomis s should be awa e o he
s eng hs and de iciencies in o icial s a is ics. I would be hoped ha by s udying Index Numbe s
and he a gumen s su ounding he implemen a ion o such me hods ha s uden s migh be mo e
ques ioning o he ools which hey use in an applied mac oeconomics en i onmen . This migh
esul in some di icul ques ions when in oducing applied subjec ma e bu would suppo in e-
g a ion o s a is ical lea ning wi hin mac oeconomic modules and, as in he mic oeconomics case,
help s uden s in embedding he s a is ical knowledge wi hin hei wide knowledge o economics.
7. Resou ces o suppo eaching index numbe s
The e a e se e al use ul esou ces which a e a ailable o suppo he eaching o index numbe s and
o allow s uden s o mo e beyond he in oduc o y ma e ial. Un il ecen ly Allen (1974) was he