1.Purposes of this research

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1 Isabiliy of he Hedoic Model ad Is Effec o he Qualiy Adjuse of Price Idex -- The case of deskop PCs Naohisa Hirakaa Bak of Japa 1.Purposes of his research How is isable over ie he hedoic odel for deskop PC? How do hese isabiliies effec o he qualiy adjuse? Are hese iflueces o qualiy adjuse differe bewee he fucioal fors?

2 2.Fraework for Measurig he Hedoic Fucio Depreciaio 2.1 Qualiy Adjuse Usig he Hedoic Mehod where p p ew old : price of pˆ = p ew p g ew produc : price of old produc old * g : qualiy raio bewee old ad ew produc qualiy of ew produc prediced price of ew produc g = = qualiy of old produc prediced price of old produc

3 2.2 Qualiy Adjuse Usig he Hedoic Mehod Dae of Esiaig hedoic fucio Dae of price replacee. Dae of price replacee. Dae of qualiy evaluaio. = Creaig hedoic fucio: f = = x f x f g Calculaig qualiy raio. x x 2.3 Defiiio of isabiliy easure i hedoic fucio g g x f x f g = = g g d = where. produc a dae a characerisic vecor of : hedoic qualiy idex. :. characerisic produc wih prediced price of :. hedoic price fucio esiaed a dae : isabiliy i hedoic fucio. he exe of : x g x x f f d

4 3. Daa ad Esiaio Mehods 3.1 Characerisic ad price daa The saples are he release-oh prices of producs placed o sale bewee 1999 ad The prices of each produc appears i our daa se oly oce eve if i coiues o be sold i he arke saples Mohly daa Daa source : Nikkei PC published by Nikkei BP ail-order price saples. Prices are a he reail level.

5 3.2 Explaaory variables of Characerisic ad price daa CPU clock frequecy RAM capaciy Hard Disk Drive HDD capaciy TFT oior duy oior size Tie duy dae of release 3.3 Fucioal for i hedoic regressio Liear Log-Liear Log-Log Box-Cox Liear Double Box-Cox

6 3.4 Saple period 12 ohs is adoped as he saple period i esiaig each hedoic regressio. To capure he ie-series chages i he paraeers we coduc rollig regressio wih welve ohs daa. 3.5 Produc se for virual price replacee Assue ha he prices ad characerisics of he represeaive produc is backward ovig averages over 6 ohs. Siulae he virual price replacees usig he represeaive producs a each poi.

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10 6. Esiaio Resuls of Hedoic fucios For he liear ad sei-log fucioal fors he CPU clock frequecy RAM capaciy ad HDD capaciy paraeers declie overall. The Double Box-Cox fucioal for shows chages i he paraeer i cerai periods. he Double Box-Cox fucioal for idicaes ha he exed of o-lieariy chages grealy depedig o he esiaio period.

11 7.Ifluece of he Oudaed Paraeers d differeial approach Regressio approach where M N : upper lii of : upper lii of R i MN = Pr dd i dd = d d = 1... M = 1... N d = α + β MN + ε i i MN = 1... M = 1... N > 0 M N dbbox ierval of updaig hedoic fucio ierval of price replacee Exaple of seig M N I case of M = 12 N = 6 whe he hedoic fucio is updaed oce per year he price replacee fro he old producs o he ew producs every hree ohs o average.

12 d Differeial Approach i R i MN = Pr dd dd = 1... M = 1... N i = d i i > 0 M N d dbbox liear sei - log double - log sei Box - Cox dbbox : double Box - Cox 7-1 he disribuio of dd Liear for M=12 N=12 Liear Desiy R liear MN = Pr dd dd liear liear = = = d > = liear d dbbox

13 7-2. he disribuio of dd sei-log for Sei Log Desiy R dd sei-log MN sei-log = Pr dd = d sei-log sei-log = = = d > dbbox he disribuio of dd double log for Double Log Desiy R double-log MN dd double-log = Pr dd = = = = d double-log double-log d > dbbox

14 7-4. he disribuio of dd Sei Box-Cox for Desiy R dd Sei Box-Cox sei Box-Cox MN sei Box-Cox = Pr dd = = = = d sei Box-Cox sei Box-Cox d > dbbox

15 7.5 Resul of d differeial approach For he liear ad Sei Box-Cox fucioal fors R MN geerally exceeds 0.5 wih soe excepios. Moreover uder hese fucioal fors R MN approaches 0.5 as he value of M icreases. For he sei-log fucioal for all he calculaed values of R MN exceed 0.5. For his fucioal for he value of R MN rises alog wih he value of M. For he double-log fucioal for all he calculaed values of R MN do exceed 0.5. Ad he value of R MN declies as he value of M rises. d : i 8.1 Regressio approach d : he exe of i i i = α + β + ε MN = 1... M = 1... N MN hedoic fucio isabiliy. he ie - lag bewee he ie of hedoic odel esiaio ad ha of applicaio o acual price replacees. liear sei - log double - log sei Box - Coxdouble Box - Cox

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17 8.3 Exaple:CGPI case The persoal copuers'' ie i CGPI he average ohly rae of chage i he persoal copuers'' ie i he Bak of Japa's Corporae Goods Price Idex CGPI fro Jauary 2000 hrough Deceber 2003 was approxiaely - 3.1%. Price idex copilig Codiios M = 6 N = 6 : β 66 = double Box-Cox The hedoic fucio is updaed oce per 6 oh double Box-Cox for is adoped for hedoic fucio he price replacee fro he old producs o he ew producs every 3-4 ohs o average. he prices of oe-hird of he surveyed prices used are arked dow a approach used whe he qualiy of he ew producs exceeds he qualiy of he old producs i every oh. Esiaed error fro isabiliy The error fro he isabiliy of he fucio is approxiaely 0.2% per oh. 8.4 The resuls of regressio approach For all of he fucioal fors oher ha liear he value of β icreases as N grows larger. For he sei-log hedoic fucio he error i he evaluaio of he qualiy raio icreases cospicuously alog wih he lag i he esiaio period. For he double-log fucioal for he error caused by he lag i he esiaio period is sall. This is because he elasiciy of characerisics does o deped o he level of he characerisic values i his fucioal for.

18 9. Suary i Ifluece of he Oudaed Paraeers he exe of isabiliy uder he Double Box-Cox fucioal for is coparaively saller ha ha uder he liear sei-log ad Sei Box-Cox fucioal fors he exe of he isabiliy uder he Double Box-Cox fucioal for is bu greaer ha ha uder he double-log fucioal for. Cocludig rearks1 As he ie-lag bewee he ie of hedoic odel esiaio ad ha of applicaio o acual price replacees becoes loger he evaluaio of qualiy by he hedoic regressio ehod eds o diverge fro he ideal value. I paricular whe characerisics bewee he old ad ew producs chage grealy he esiaio error icreases.

19 Cocludig rearks2 The selecio of fucioal for should deped o oly o he crierio of he saple fi whe he hedoic fucio is esiaed bu also o he icrease i error caused by he ie lag fro he origial esiaio o he updae. Whe he iprovee i produc qualiy is rapid ad he ierval of fucio updaig is exreely log i is desirable o selec doublelog ad oher siple fucioal fors.