Measuring the Price Movements of Used Cars and Residential Rents in the New Zealand Consumers Price Index

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1 aper presened o he Oawa Group, 20 easuring he rice ovemens of Used Cars and Residenial Rens in he New Zealand Consumers rice Index aper presened a he Oawa Group, Wellingon, New Zealand, 4 ay 20 Frances Krsinich Senior Research Saisician, rices Uni, Saisics New Zealand O Box 2922 Wellingon, New Zealand frances.rsinich@sas.gov.nz

2 aper presened o he Oawa Group, 20 Acnowledgemens The auhor would lie o han Alisair Gray for discussion and inpu o his wor. Crown copyrigh This wor is licensed under he Creaive Commons Aribuion 3.0 New Zealand licence. You are free o copy, disribue, and adap he wor for non-commercial purposes, as long as you aribue he wor o Saisics NZ and abide by he oher licence erms. lease noe you may no use any deparmenal or governmenal emblem, logo, or coa of arms in any way ha infringes any provision of he Flags, Emblems, and Names roecion Ac 98. Use he wording 'Saisics New Zealand' in your aribuion, no he Saisics NZ logo. Liabiliy While all care and diligence has been used in processing, analysing, and exracing daa and informaion in his publicaion, Saisics New Zealand gives no warrany i is error free and will no be liable for any loss or damage suffered by he use direcly, or indirecly, of he informaion in his publicaion. Ciaion Krsinich, F (20, ay). easuring he price movemens of used cars and residenial rens in he New Zealand consumers price index. aper presened a he Oawa Group, Wellingon, New Zealand. 2

3 aper presened o he Oawa Group, 20 easuring Used Cars and Residenial Rens, by Frances Krsinich Absrac rice movemens of second hand cars and residenial housing renals in he New Zealand consumers price index (CI) are boh based on large samples of daa ha lend hemselves well o hedonic mehods. In 200 he exising sraificaion mehod for second hand cars was replaced by a hedonic mehod, and his is being updaed wih an improved hedonic model in 20. The renal index, which currenly uses a mached-sample approach, was recenly assessed using a hedonic index as a benchmar. The longiudinal naure of he renal survey les us conrol for unobserved characerisics in he hedonic model, bu quesions were raised abou how well his formulaion deals wih he newly rened dwellings. We build on a resul from Aizcorbe, Corrado and Doms (2003) o asser ha he implici impuaions for new renal dwellings are appropriae. Aging is an issue for boh of he measures. For used cars we are able o include age of car in he hedonic model. Age of renal dwelling, however, is unobserved. We are sill deermining how o formulae individual aging effecs ino he hedonic model. Inroducion Saisics New Zealand has used hedonics for wo major componens of he New Zealand consumers price index: used cars and residenial renals. Used cars conribued 2.4 percen o he New Zealand CI a he June 2008 quarer, and renals conribued 7 percen. The price movemen of used cars has been esimaed using hedonics since 200, and a hedonic index was recenly used o benchmar he exising mached-sample index for housing renals. The used cars index has been esimaed using a hedonic model for 0 years, and he model is currenly being improved by adoping a log-linear formulaion and including more characerisics. Wih his more efficien esimaion here is scope o reduce responden burden by decreasing he large sample originally designed for a sraified esimaion of average prices. Housing renals are currenly esimaed from a mached sample derived from a probabilisic area-based sample, which is regularly updaed wih newly lodged bonds. A hedonic index was consruced as a benchmar when concerns were raised abou poenial undersaemen from he maching procedure. The used cars survey Each quarer, daa on he sales of approximaely 3,500 cars are colleced from a sample of used car dealers. rice, year of manufacure, mae and model, engine size (cc raing), and odomeer reading are colleced for each car sold. This sample was designed iniially o suppor he calculaion of average prices wihin esimaion cells based on combinaions of mae and model, cc raing ranges, and age of car. To ensure robus esimaion of averages, cells wih oo few observaions were excluded, which resuled in use of only around 25 percen of he daa colleced. Inroducion of hedonic esimaion in 200 Saisics New Zealand inroduced a hedonic esimaion for used cars in 200 (Krsinich, 2000). rice is modelled agains quarer, region, mae and model, age of car, cc raing, and odomeer reading, shown in formula (). () C D c c c c 3

4 aper presened o he Oawa Group, 20 easuring Used Cars and Residenial Rens, by Frances Krsinich Where: c is he price of car c (noe ha here is no erm as we can assume each individual car is only sold once) D c = in he quarer ha car c is sold and 0 oherwise The following characerisics K are included in he model for each car c sold: own of purchase (5 caegories) mae and model (47 caegories) age (in years) size of engine (cc raing, eg 2300) odomeer reading (in ilomeres). The linear formulaion was used iniially as his made he hedonic index a more efficien version of he exising esimaion cell mehod. Hedonic indexes are calculaed for each of five broad regions of New Zealand (Aucland, Wellingon, Res of Norh Island, Chrischurch, and Res of Souh Island) and hese are weighed ogeher wih populaion-based expendiure shares ha are updaed a he hreeyearly CI reviews, o ge he naional used car index. To mae he mehod operaional, a rolling window of he laes eigh quarers is used o esimae he hedonic model each quarer, and he derived index for he mos recen quarer is lined o he previous quarer s index number. The new hedonic esimaion In 20 Saisics New Zealand will inroduce an improved hedonic formulaion for used cars. A he same ime, he producion process will be sreamlined o mae i simpler and more robus. The hedonic model has been updaed as follows: rice is now logged, which gives he model a beer fi o he daa. A more deailed classificaion of mae and model is incorporaed from 47 caegories o 96. Squared erms have been added for age of car and cc raing. An idenifier for he used car dealer is now included. The updaed model is: (2) ln C D c Wih c and c c c D c as for formula (), characerisics K are now: own of purchase (5 caegories) dealer (approximaely 300) mae and model (96 caegories) age (in years) and age squared size of engine (cc raing, eg 2300) and cc raing squared 4

5 aper presened o he Oawa Group, 20 easuring Used Cars and Residenial Rens, by Frances Krsinich odomeer reading (in ilomeres). R-squared saisics of models wih differen dependen variables (ha is, price and log of price) are no comparable, bu a lower bound of he improvemen in he used cars hedonic model is given by comparing he R-squareds for log-linear models wih he old and new ses of explanaory variables. This is shown in able. Table R-squared saisics for log-linear hedonic models using he old and new ses of explanaory variables Region Old se of explanaory variables New se of explanaory variables Aucland Wellingon Oher Norh Island Chrischurch Oher Souh Island Figure shows ha he indexes based on successive eigh-quarer windows are very sable across ime, which reinforces confidence in lining on jus he mos recen index movemen each quarer. Figure Successive eigh-quarer hedonic indexes for used cars a he New Zealand level Index arch 08 December 09 June 08 arch 0 Sepember 08 June J S D 09 J S D 0 J Source: Saisics New Zealand Noe: Base: Dec 2008 quarer (=00) Fuure improvemens o he used cars esimaion The inroducion of a hedonic approach for he esimaion of used cars, in paricular now ha he hedonic formulaion has been opimised, means ha here is poenial for significanly reducing he sample size, and hence he responden burden of he used cars survey. Wor is now underway o deermine he minimum sample size required for an accurae esimaion. Along wih redesigning he sample s size and allocaion, represenaion of he price movemens of used cars sold hrough aucion and online needs o be considered when designing he sample. These channels are no included in he curren sample. 5

6 aper presened o he Oawa Group, 20 easuring Used Cars and Residenial Rens, by Frances Krsinich The residenial rens survey The residenial rens survey uses an area-based probabiliy sample of approximaely 2,000 renal dwellings. Landlords of he seleced dwellings are ased each quarer for renal informaion. The sample is updaed every quarer wih dwellings ha ener he renal mare wihin he seleced areas. These are idenified from bond daa by reconciling dwellings wih newly lodged bonds agains he exising sample. Average rens are esimaed from he sample wihin sraa based on bedroom number and five broad regions. For example, average ren is esimaed for hree-bedroom renal dwellings in he Aucland region. ovemens in hese averages are weighed ogeher using regional populaion-based expendiure shares, which are updaed a hree-yearly CI reviews o creae a naional index. Table 2 shows, for 2007 and 2008, he sample each quarer, wih he percenages of he dwellings ha are new o he sample, and abou o leave he sample ie sample birhs and sample deahs. Sample birhs conribue an average of 6.6 percen each quarer, while sample deahs conribue on average 3.2 percen. This reflecs he increasing size of he renal populaion in New Zealand, as a resul of populaion growh and a shif away from home ownership. Table 2 Ren survey sample size and conribuion of sample birhs and deahs in 2007 and 2008 quarer number of dwellings in sample () percenage of sample birhs percenage of sample deahs 07q q q q q q q q Inroducion of a mached sample in 2000 The renal survey was iniially designed in 998, and in 2000 i was modified by resricing he conribuing sample o hose dwellings exising in boh he previous and curren quarers ha is, a mached sample. This was adoped o ensure ha differences in he composiion of he sample due o newly rened dwellings and dwellings leaving he renal soc would no conaminae he esimaion of price movemens. Concerns raised abou he mached sample in 2008 Smih (2008), from he Reserve Ban of New Zealand, speculaed ha he use of a mached sample migh be biasing he index downwards by removing pure price change associaed wih he dwellings new o he renal mare (and, o a lesser exen, hose leaving he renal mare). This concern was in par promped by higher price movemens observed for newly rened dwellings, a measure regularly produced by he Deparmen of Building and Housing. There is no reason ha price movemens for he enire soc of renal dwellings, which is wha he CI measures, mus mach he price movemens for newly rened dwellings. This concern was also promped by he fac ha he index produced from curren quarer averages based on he full sample moves more rapidly han ha from he mached sample. This is shown in figure 2. Saisics NZ decided o invesigae he issue furher. 6

7 aper presened o he Oawa Group, 20 easuring Used Cars and Residenial Rens, by Frances Krsinich Hedonic benchmaring exercise As a benchmar, a hedonic index was esimaed from he renal daa. This gave a very similar resul o he curren mached-sample index, suggesing ha any bias in he curren approach is no significan (Krsinich, 2009). Figure 2 shows he comparison in he conex of he index ha would be produced from averages based on he full sample if no maching were used ha is, if no adjusmen were made for he change in sample composiion due o birhs o, and deahs from, he sample. Figure 2 ached sample index compared wih hedonic benchmar index and full sample index 5 Index Full sample Hedonic ached sample J 06 Source: Saisics New Zealand S D 07 J S D 08 J Noe: Base: June 2006 quarer (=00) In he sandard hedonic formulaion, jus he limied se of characerisics available in he daa ha is, fine-level region and number of bedrooms can be incorporaed. The hedonic formulaion used o benchmar he renal index oo advanage of he longiudinal naure of he renal daa by fiing dwelling-specific inerceps. In oher words, a fixed-effecs model was used. This mean ha all characerisics of he renal dwellings fixed across ime were conrolled for. However, any ime-varying characerisics a he dwelling level such as renovaions or deerioraion of he dwelling are no conrolled for by he fixed-effecs model. I is imporan o noe ha his hedonic index would suffer a similar issue o he machedsample index if used in producion, because a leas wo ime poins are required for each dwelling in he fixed effecs esimaion. This means ha, as wih he mached sample, new dwellings will no be included in he esimaion unil hey have been in he sample for wo quarers. Because only he mos recen movemen is spliced ino he index each quarer, any price change associaed wih he inroducion of newly rened dwellings will be missed. However, unlie he mached-sample index, he movemen due o sample deahs would no be missed. For he benchmaring exercise, however, he hedonic index was applied rerospecively o he enire se of daa. This means ha only he mos recen quarer s movemen suffers from he issue above. For he res of he index he hedonic index can be used as a benchmar. Appropriaeness of he fixed effecs hedonic formulaion Doubs were raised abou he appropriaeness of he fixed effecs formulaion. os seriously, given he conex of he invesigaion, is a zero movemen being implicily impued for new renal dwellings? If so, he benchmaring hedonic index migh also suffer from any downwards bias in a similar way o he mached-sample index. 7

8 aper presened o he Oawa Group, 20 easuring Used Cars and Residenial Rens, by Frances Krsinich The oher quesion was wheher, and how o, incorporae he price effec of he aging of renal dwellings. Implici impuaion for new renals The probabiliy sample of he renal survey is perhaps unfamiliar in he price measuremen conex, where i is common for producs newly inroduced o a sample o be direcly replacing old producs ha can no longer be priced. If new renal dwellings in he sample were one-o-one replacemens for renals leaving he sample, hen i does seem reasonable o hypohesise ha a fixed-effecs model which models he difference from he mean ren across ime of each dwelling migh be lining ou any qualiy difference beween he old and new dwellings. Bu in he renal probabiliy sample, he birhs and deahs are represenaive of he underlying dynamics of he populaion, by consrucion of he area-based sample selecion and quarerly mainenance. As shown in able 2, he sample size is gradually increasing, in line wih he increasing populaion of renal dwellings. We build on a resul from Aizcorbe, Corrado & Doms (2003) o asser ha he implici impuaion in he fixed effecs hedonic model for a newly rened dwelling is no zero, bu raher he movemen from he average qualiy-adjused rens of coninuing dwellings in he previous quarer o he qualiy-adjused ren of he new dwellings in he curren quarer. This means ha he movemen being implicily conribued o he index by he new renal dwelling is due o price only, raher han qualiy. The appendix fills in some deail beween equaions () and (5) in Aizcorbe, Corrado & Doms (2003), and hen exends equaion (5) o he fixed effecs case. Bias due o aging of dwellings By consrucion, he mached-sample index will be biased o he exen ha here is a price effec associaed wih aging for individual renal dwellings. For example, if here were a percen decrease in price associaed wih each year of aging of a renal dwelling, hen he mached-sample index will be biased downwards by percen annually, even if he overall age disribuion of he populaion of renal dwellings, as refleced by he coninually updaed sample, remains consan over ime. If he hedonic benchmar index is no affeced by aging bias, i can be used o esablish wheher he aging bias is significan enough o cause concern. Unforunaely, here is no informaion available in he renal survey daa on he age of he renal dwellings, so age canno be incorporaed explicily ino he model. A he ime of wriing we have no ye formulaed aging effecs in he fixed effecs hedonic model. Our hypohesis, which we welcome discussion abou, is ha he index will be biased by changes in he age disribuion of he sample, bu no by individual aging as such. Tha is, if he age disribuion of he populaion, as refleced by he sample, is reasonably sable hen he hedonic esimaion will be unbiased even if here is a price effec of aging a he individual renal dwelling level. Fuure plans for he measuremen of renals If he fixed effecs hedonic formulaion is appropriae boh in erms of he implici impuaion for newly rened dwellings and he pricing effecs of aging, i is a valid benchmar for he curren mached-sample index. This would give reassurance ha, despie he nown limiaions of he mached-sample approach, he biases are no of pracical significance. A hedonic esimaion may be considered in he fuure, as his would enable a more efficien esimaion and herefore a reducion in sample size and responden burden. 8

9 aper presened o he Oawa Group, 20 easuring Used Cars and Residenial Rens, by Frances Krsinich Appendix The following is an exension of he Aizcorbe, Corrado and Doms (2003) formulaion, showing ha he implici impuaion for new renal dwellings in he fixed effecs hedonic index is appropriae. Given model m a ime wih characerisics : () log m C m s D s ms m Noe ha in he second erm D ms is a ime dummy so D ms if m is observed a ime s, and 0 oherwise, ie he 2nd erm is jus So he average (2) Noe ha (3) log m is log m m m m m m m C and aing he mean over he models of he residuals will be close o zero, as heir expeced value is zero, ie (4) m 0 m So (2), (3), and (4) (5) Hence (6) m log m Cm log m Cm log m m If he models are he same a boh ime poins hen So (7) log m m m C m and m m log m m Cm Cm m Inroduce a new model and call i N Noe ha in general (8) n n n n X i X i X n X i X n i n i n n i n and from (5), in he period ha N is inroduced n 9

10 aper presened o he Oawa Group, 20 easuring Used Cars and Residenial Rens, by Frances Krsinich (9) (9) and (8), N m log m C m (0) m log m C m log N C and from (5) and because N is inroduced a ime (and herefore no here in ime ) we have () log (0) and () (2) Bu m m m log C log m m m m N so C N C log m N C m (3) log N log m Cm log m C m m C N m log m C m m This means ha he change in price beween and is a weighed average of he price change of he coninuing iems and he new iem, wih he implici impuaion for he change in price of he new iem being he difference beween he average qualiy-adjused price for he coninuing iems in he previous ( ) period, and he qualiy adjused price of he new iem in he curren ( ) period. If models' characerisics are consan over ime in our daase, so ha C for all hen we can rewrie () as (4) log C m m m m Cm Then if we use fixed effecs o conrol for qualiy differences across models, ha is, if we assume C m m hen we can rewrie (4) as (5) log m m m C m 0

11 and subsiuing m and above, from (2) o (3) we ge (6) easuring Used Cars and Residenial Rens, by Frances Krsinich N for C and ms s, C Ns in he derivaions log log log log m m m m m aper presened o he Oawa Group, 20 m log log log log m m m N N N N m m m m m m which has he same inerpreaion as equaion 3. Tha is, he implicily impued price change for a newly rened dwelling is he change beween he average of he qualiyadjused prices of he coninuing renals in he previous period, and he qualiy-adjused price of he new iem in he curren period. Which is wha we wan, in he case of he renal esimaion. References Aizcorbe, A, Corrado, C, & Doms, (2003, June). When do mached-model and hedonic echniques yield similar price measures? (Federal Reserve Ban of San Francisco woring paper no ). Rerieved 24 arch 20 from Krsinich, F (2000). The hedonic regression parameer mehod for calculaing he used cars index. Unpublished documen, Saisics New Zealand. Krsinich, F (2009, July). Using hedonic regression o assess he housing renals componen of he New Zealand consumers price index. aper presened a he New Zealand Associaion of Economiss conference, Wellingon. Rerieved 24 arch 20 from sas.gov.nz. Smih, (2008). easuring rens in he CI. Unpublished documen, Reserve Ban of New Zealand. Saisics NZ (2007). How used-car price changes are measured in he CI. Rerieved 24 arch 20 from sas.gov.nz.