Teaching Index Numbers to economists

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 This Ve sion is a ailable a : h ps://hdl.handle.ne /10419/147778 S anda d-Nu zungsbedingungen: Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen Zwecken und zum P i a geb auch gespeiche und kopie we den. Sie dü en die Dokumen e nich ü ö en liche ode komme zielle Zwecke e iel äl igen, ö en lich auss ellen, ö en lich zugänglich machen, e eiben ode ande wei ig nu zen. So e n die Ve asse die Dokumen e un e Open-Con en -Lizenzen (insbesonde e CC-Lizenzen) zu Ve ügung ges ell haben soll en, gel en abweichend on diesen Nu zungsbedingungen die in de do genann en Lizenz gewäh en Nu zungs ech e. Te ms o use: Documen s in EconS o may be sa ed and copied o you pe sonal and schola ly pu poses. You a e no o copy documen s o public o comme cial pu poses, o exhibi he documen s publicly, o make hem publicly a ailable on he in e ne , o o dis ibu e o o he wise use he documen s in public. I he documen s ha e been made a ailable unde an Open Con en Licence (especially C ea i e Commons Licences), you may exe cise u he usage igh s as speci ied in he indica ed licence. h p://c ea i ecommons.o g/licenses/by/4.0/ O’Neill, Cogen Economics & Finance (2015), 3: 1115625 h p://dx.doi.o g/10.1080/23322039.2015.1115625 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. Page 1 o 10 Robe O’Neill Page 2 o 10 O’Neill, Cogen Economics & Finance (2015), 3: 1115625 h p://dx.doi.o g/10.1080/23322039.2015.1115625 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 Page 3 o 10 O’Neill, Cogen Economics & Finance (2015), 3: 1115625 h p://dx.doi.o g/10.1080/23322039.2015.1115625 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 Page 4 o 10 O’Neill, Cogen Economics & Finance (2015), 3: 1115625 h p://dx.doi.o g/10.1080/23322039.2015.1115625 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? Page 5 o 10 O’Neill, Cogen Economics & Finance (2015), 3: 1115625 h p://dx.doi.o g/10.1080/23322039.2015.1115625 • 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. Page 6 o 10 O’Neill, Cogen Economics & Finance (2015), 3: 1115625 h p://dx.doi.o g/10.1080/23322039.2015.1115625 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 . Page 7 o 10 O’Neill, Cogen Economics & Finance (2015), 3: 1115625 h p://dx.doi.o g/10.1080/23322039.2015.1115625 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. Page 8 o 10 O’Neill, Cogen Economics & Finance (2015), 3: 1115625 h p://dx.doi.o g/10.1080/23322039.2015.1115625 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