Quality Adjustment of Second-hand Motor Vehicle Application of Hedonic Approach in Hong Kong s Consumer Price Index

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1 Qualty Adustment of Second-hand Motor Vehcle Applcaton of Hedonc Approach n Hong Kong s Consumer Prce Index Prepared for the 14 th Meetng of the Ottawa Group on Prce Indces May 2015, Tokyo, Japan Presented by James L. Y. Cheng, Census and Statstcs Department, Hong Kong, Chna Abstract Adustment for qualty change s mportant n complng pure prce ndces. In complng a prce relatve of second-hand motor vehcle, comparng the prce for the same brand and model between two reference tme ponts may not be able to remove the porton of prce change due to tme deprecaton perfectly. Whle a matched model approach s currently adopted n complng the Consumer Prce Index (CPI) for second-hand motor vehcle, hedonc regresson models usng characterstcs prce and tme dummy varable methods have recently been examned. Ths paper presents the fndngs and shares some practcal consderatons. 1

2 Introducton In complng a pure prce ndex, t s crucal to compare the prce of a product of constant qualty over tme. However, the qualty of some products changes over tme. The value of a second-hand motor car, for example, deprecates naturally n the course of tme. In complng a prce relatve for such products, comparng the prce for the same brand and model between two reference tme ponts may not be able to remove the porton of prce changes due to such tme deprecaton perfectly. As an alternatve to the matched model approach currently adopted n complng Hong Kong s CPI for second-hand motor vehcle, the hedonc regresson technque for qualty adustment, whch s an explct method practced n some economes, has recently been examned. Hedonc regresson models usng characterstcs prce and tme dummy varable methods have been consdered for smulaton study. Ths paper presents the prelmnary results as compared wth that compled by the current approach; and shares some practcal consderatons n applyng hedonc approach for qualty adustment of second-hand motor vehcle. Hedonc regresson 2. A hedonc prce functon descrbes the relatonshp between characterstcs of a product and ts prce. The economc theory underlyng hedonc prce functons rests on the hedonc hypothess: goods are aggregaton of characterstcs. They are used to predct the prce of new goods to adust for qualty change (Trplett, 2004). A hedonc prce functon uses regresson analyss to predct the nfluence of product features on the sales prce. Therefore prce changes due to qualty change n certan features can be dstngushed and purged from the pure prce change whch the prce ndex s actually called upon to measure. 3. The characterstc prce ndex method and the tme dummy varable method are common methodologes of applyng hedonc regresson. For the latter, prce data n dfferent reference perods are pooled together to form one sngle regresson model, usng addtonal tme dummy varables to dstngush the reference tme ponts of a partcular record. As for the former, prce data n dfferent reference perods are treated by dfferent models. 2

3 Characterstc Prce Index Method 4. For second-hand motor vehcles, characterstcs beng transacted ncluded () dsplacement of the car engne; () age of the motor vehcle at the tme of transacton; and () brand of the motor vehcle. These characterstcs can be expressed as ndependent varables of a regresson model on the prce of motor vehcle n the form of ln( P ) ln( cc age D (1) where 1 ) 2 P : prce of motor vehcle for the -th observaton cc : dsplacement of the car engne (n c.c.) for the -th observaton age : age (n year) of motor vehcle for the -th observaton D : ndcator varable for whether the -th observaton s of a specfc brand 5. To comple the prce relatve for quarter t, a regresson model based on the n observatons for quarter t and another model based on m observatons for quarter t-1 are constructed. The motor vehcles data collected n quarter t-1 were then put n the model of quarter t n order to estmate the transacted prce f the motor vehcle had been transacted n quarter t. Average prce relatve s then compled by takng geometrc means of all cases. Tme Dummy Varable Method 6. The tme dummy varable method, whch s another wdely-used hedonc functon approach, was also consdered. A dummy varable t s added to ndcator the reference quarter of the observatons. In terms of the formulaton of the ndex, there are two popular methods: fxed-based formulaton and chaned formulaton. 7. The fxed-based formulaton approach uses data of two consecutve quarters where a dummy varable T ndcatng the current quarter s added. The model can be expressed n the form of D ln( P ) ln( cc age T (2) where T 1 ) 2 3 = 1 for observaton collected n quarter t = 0 for observaton collected n quarter t-1 3

4 8. The chaned formulaton approach deploys data of several successve quarters. Suppose data collected from four successve quarters are to be used, the regresson model wll contan three tme dummy varables and look lke ln( P ) ln( cc age T T T D (3) 1 ) 2 0 0, 1 1, 2 2, where T 0, = 1 for observaton collected n quarter t = 0 otherwse T 1, = 1 for observaton collected n quarter t-1 = 0 otherwse T 2, = 1 for observaton collected n quarter t-2 = 0 otherwse 9. By poolng data of four successve quarters, the average prce relatves can be derved through matchng dfferent combnatons of the prce data (e.g. comparng the actual transacton prces of each vehcle transacted n quarter t-3 wth the estmated prces at quarter t; and then takng arthmetc mean, whch can be denoted as PR t,t-3 ). As such, the average prce change for quarter t as compared to quarter t-1 can be derved n three ways, namely PR t,t-1 ; [PR t,t-2 / PR t-1,t-2 ] and [PR t,t-3 / (PR t-2,t-3 PR t-1,t-2 )]. An overall average prce relatve from t-1 to t can then be derved by takng geometrc mean of these three prce relatves. Smulaton results 10. Prce relatves for second-hand motor vehcle for the perod October 2009 September 2014 are recompled by usng formulae (1), (2) and (3). All three hedonc approaches yeld smlar goodness of ft as ndcated by the R-square of around The publshed CPI sub-ndex for Purchases of and repars to motor vehcles, of whch the purchase of second-hand motor vehcles s the maor component, usng the matched-model approach s compared to the smulated ndex usng the above three hedonc methods (see Chart 1). The general trend for those compled usng the characterstc prce and tme dummy varable (chaned formulaton) approaches are rather smlar, whereas relatvely large fluctuatons are observed for that smulated usng the tme dummy varable (fxed-based formulaton). The drecton of movement and the level of the ndces compled by the former two approaches are broadly n lne as compared to the publshed ndex. 4

5 Chart 1: Index for Purchases of and repars to motor vehcles n the Composte CPI compled by the current and hedonc approaches Advantages of applyng hedonc approach 12. Beng an explct method of qualty adustment, hedonc regresson s approprate where data on prce and characterstcs are avalable for a range of models and where the characterstcs are found to predct and explan prce varablty well n terms of pror reasonng and econometrc terms. Ths fts n well wth the data avalablty of second-hand cars and the general percepton on the relatonshp between prce and characterstcs of a second-hand motor vehcle. 13. Moreover, prce quotatons collected can be more thoroughly utlzed when applyng hedonc approach because all observatons under those selected brands are consdered as nputs to the regresson model. Ths contrast to the matched-model approach where only those observatons whch can be matched wth those transacted n the prevous perod would be ncluded n the ndex complaton. 5

6 Practcal consderatons 14. Large amount of data s requred to ensure good predctve power of the regresson model. Gatherng adequate data s costly n terms of human resources and tme. In partcular, the chaned formulaton of tme dummy varable approach requres more observatons for the regresson model snce more ndependent varables are nvolved. Addtonal prce quotaton would thus need to be collected. Whle data collecton s now performed n varous second-hand car dealers each month, t s worthwhle explorng ways of collectng more prce quotatons through alternatve channels such as the Internet. 15. The selecton of ndependent varables has to be revewed from tme to tme (say once per few years) so as to catch up wth the market development as some brands may become more popular or alternatve factors (e.g. odometer readng) whch would affect the prces of second-hand motor vehcles may emerge. 16. Perodc revew on the selecton of model and transformaton of varables s also necessary. In partcular, for the characterstc prce ndex approach, each hedonc functon can be dfferent n each reference perod. There can be numerous choces on the model and transformaton of varables. Dfferent transformaton may result n dfferent nterpretaton over the parameter estmates. For some functonal forms, those estmates may even be mpossble to nterpret n an economc way (Trplett, 2004). Concludng remarks 17. Ths paper presents the smulaton results of deployng hedonc methods for qualty adustments of second-hand motor vehcles for the CPI complaton. Hedonc method s preferred to the matched-model method snce t could utlze the data collected more thoroughly and take nto account the qualty characterstcs. The sample sze of second-hand motor vehcle and the effectveness of the hedonc models wll be kept under revew and optmzed as approprate. Wth the accumulaton of suffcent data collected under the hedonc approach, tmely assessments wll be made to compare the results of the parallel complaton concurrent wth that under the current matched model wth a vew to swtchng to the hedonc approach n relevant CPI complaton. 6

7 References Krsnch, F. (2011). Measurng the Prce Movements of Used Cars and Resdental Rents n the New Zealand Consumer Prce Index,, Paper presented at the Ottawa Group, Wellngton, New Zealand, Statstcs New Zealand. Moulten, B. (2001). The Expandng Role of Hedonc Methods n the Offcal Statstcs of the Unted States, Washngton: Bureau of Economc Analyss, US Department of Commerce. Nar, B. P. (2004). Use of hedonc regresson methods for qualty adustments n Statstcs NZ. New Zealand Assocaton of Economsts Conference 2004, Inflaton Measures Dvson, Statstcs New Zealand. Okamoto, M. and Sato T. (2001). Comparson of Hedonoc Method and Matched Models Methods usng Scanner Data: The Case of PCs, TVs and Dgtal Cameras, Paper presented at the Sxth Meetng of the Internatonal Workng Group on Prce Indexes, Canberra. Australa, Statstcs Bureau of Japan. Trplett, J. (2004). Handbook on Hedonc Indexes and Qualty Adustments n Prce Indexes: Specal Applcaton to Informaton Technology Products, OECD Scence, OECD. Wooldrdge, J. M. (1999). Introductory Econometrcs: A Modern Approach, South-Western College. 7

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