Online Data, Fixed Effects and the Construction of High-Frequency Price Indexes

Transcription

1 Onlne Daa, Fxed Effecs and he Consrucon of Hgh-Frequency Prce Indexes Jan de Haan* and Rens Hendrks** * ascs eherlands / Delf Unversy of Technology ** ascs eherlands EMG Worksho 23

2 Ams of he aer Exlan why he mullaeral Tme-Produc Dummy ndex (TPD ndex dffers from s chaned mached-model counerar. how ha he mullaeral TPD or fxed effecs mehod does no roduce qualy-adjused rce ndexes. Invesgae wheher he TPD mehod s useful for esmang hgh-frequency rce ndexes from onlne daa (for goods where qualy change s no a major concern. 2

3 Oulne Background Tme dummy hedonc rce ndexes Tme-roduc dummy ndexes Unmached ems and he me-roduc dummy ndex A comarson wh he GEK-Jevons ndex Issues wh daly onlne daa and daly ndexes Emrcal resuls Conclusons 3

4 Background Possble use by as eherlands of onlne rces obaned hrough web scrang Effcency reasons Daly observaons: hgh-frequency rce ndexes ossble However, no quany nformaon Choce of ndex number mehod Dewer (24: TPD mehod roduces a mached-model ndex n he blaeral (wo-erod case. Azcorbe, Corrado and Doms (23: TPD roduces qualyadjused rce ndex n he mullaeral (many-erod case. Ths seems o good o be rue. 4

5 5 Tme dummy hedonc ndexes We only consder he log-lnear hedonc model. Esmang equaon on he ooled daa for erods =,,,T s Esmang hs me dummy model by OL regresson yelds k K k k T z D ε β δ δ = = = ln = = = K k k k k TD z z P ( ˆ ex ( ( ˆ ex( β δ

6 6 Tme dummy hedonc ndexes In words: he me dummy ndex can be wren as he roduc of he rao of geomerc mean rces and a qualyadjusmen facor. Ths exonenal facor deends on he changes over me of he average characerscs. The me dummy ndex s ransve and can be wren as a chan ndex: = = = K k k k k TD z z P ( ˆ ex ( ( β

7 Tme-roduc dummy (TPD ndexes Characerscs and her arameers are assumed consan over me n he me dummy model. o characerscs avalable: relace unobservable hedonc K β z k = k k effecs by em-secfc fxed values. γ Fxed effecs or me-roduc dummy model ln T = + δ D + = = α γ D + ε Counerar of Counry-Produc Dummy (CPD model for cross-counry comarsons 7

8 8 TPD ndexes TPD ndex can be wren as or, because s ransve, n chaned form as [ ] TPD P γ γ δ ˆ ˆ ex ( ( ˆ ex( = = [ ] γ γ ˆ ˆ ex ( ( = = TPD P

9 9 Unmached ems and he TPD ndex How are unmached ems reaed n he TPD ndex? Chan lnk of TPD ndex can be wren as he roduc of he adjacen-erod mached-model Jevons ndex and he effecs of new ems and dsaearng ems: D M M D D M M M M f f TPD TPD P P,,,,,,,,,,,,, ˆ ex( ˆ ex( ˆ ex( ˆ ex( = γ γ γ γ

10 Unmached ems and he TPD ndex Take clohng, for examle. Prces ycally declne over me, so a chaned-mached model ndex wll have a downward rend. If TPD mehod would work,.e. f fxed effecs aroxmae hedonc effecs well, hen he unmached ems are lkely o couner hs downward rend average qualy-adjused rces of new (dsaearng ems lkely above (below average qualy-adjused rces of mached ems. Bu does he TPD mehod really accoun for new and dsaearng ems?

11 Unmached ems and he TPD ndex o, doesn. Iems whch are observed only once durng he whole samle erod are zeroed ou: hey are effecvely droed from he esmaon. Thus, sll s a mached-model aroach and does no adjus for qualy change, even hough.. hetpd ndex dffers from he chaned mached model Jevons as ems whch are new or dsaearng n erodon-erod comarsons are ofen observed mulle mes durng he samle erod.

12 A comarson wh he GEK-Jevons ndex Ivancc, Dewer and Fox (2 and ohers adaed he GEK mehod for makng ransve rce comarsons across counres o rce comarsons across me. P GEK l P = T l l ( P P l= P l T + and are blaeral rce ndexes beween and l, and l and ; l (l=,,t s he lnk erod. Onlne daa: no quany nformaon. Use of blaeral Jevons ndexes (raher han Fsher ndexes. 2

13 A comarson wh he GEK-Jevons ndex ome fndngs: If some (unknown me dummy hedonc model descrbes he daa well, hen TPD s a (smoohed aroxmaon of he mached-model GEK-Jevons he wo mehods essenally am a he same ndex number formula. o surrsng: boh mehods use he exac same nformaon,.e. he rces all maches across he samle erod or wndow,,t. Trends may dffer f e.g. he rue characerscs arameers change over me. TPD mehod robably easer o esmae. 3

14 Issues wh daly onlne daa and daly ndexes Rollng wndow aroach can overcome revsons roblem. Wndow lengh: no longer han maxmum erod ems are offered for sale. Deends on ye of roduc; marke crcumsances; olcy of assgnng and changng em denfers. In racce: ems denfed by arcle numbers (EAs n scanner daa or web IDs (onlne daa. These denfers may be oo dealed smlar ems havng dfferen IDs. 4

15 Issues wh daly onlne daa and daly ndexes Poenal roblems: em churn overesmaed; mached-model ndexes based on fewer maches han desrable; mached-model mehods, ncludng TPD (and GEK, mss hdden rce changes. Issues wh web scrang daa onlne rces dfferen from ransacon rces; reresenavy of onlne daa; changes made o webse; 5

16 Issues wh daly onlne daa and daly ndexes reamen of sales versus regular rces - daly rajecory n offer rces does no necessarly reflec correc rend from he average consumer s on of vew due o romoonal sales; volaly of daly rce ndexes; monhly un values no ossble wh onlne daa. oe: scanner daa mgh no be an deal source for onlne urchases, arcularly on clohng. Poenal roblem: regsraon of goods whch are reurned by cusomers. 6

17 Emrcal resuls Man goal: o llusrae ha dfferen yes of ndexes - TPD, chaned mached-model Jevons and GEK-Jevons - can have dfferen rends and can be hghly volale when consruced a a daly frequency. Daa se daly rces exraced from webse of Duch onlne sore - no hyscal sore so only (oenal onlne urchases women s T-shrs; men s waches, kchen alances 6 Ocober 22 8 Arl 23 (2 Augus 23 7

18 Daly ndexes; women s T-shrs; small daa se,,9,8,7,6,5, TPD arhm. average chaned Jevons geom. average TPD above chaned Jevons, as execed ubsanal downward bas oo dealed denfers Exremely volale; rend n average rces more lausble 8

19 Daly ndexes; men s waches; small daa se Heerogeney errac behavor average rces TPD and chaned Jevons very smlar and reasonable 9

20 Daly ndexes; kchen alances; small daa se Comosonal change early ovember 22 2

21 Daly TPD ndexes; women s T-shrs; large daa se Confrms downward bas of TPD ndex (declne of almos 6% whn monhs! Comarson wh small daa se: revsons very small 2

22 Weekly ndexes; women s T-shrs; large daa se GEK Jevons does no fall as fas as TPD Only small dfferences beween he wo samles Drawng samles does no change he cure 22

23 Weekly ndexes; men s waches; large daa se TPD and GEK-Jevons very smlar, as execed 23

24 Weekly ndexes; kchen alances; large daa se TPD and GEK-Jevons very smlar, as execed 24

25 Conclusons Whle fxed effecs n TPD model can be vewed as emsecfc hedonc effecs,.. hs does no mean ha TPD roduces a qualy-adjused ndex. Where qualy change s unmoran: mullaeral ndexes (TPD, GEK referred over erod-on-erod chaned ndexes. Regresson-based TPD wll be easer o esmae han GEK. Poenal roblem: hdden rce changes - denfcaon ssue. Weghed TPD or GEK f quany daa s avalable, bu.. quany daa for onlne urchases mgh be unrelable. 25