Real estate ownershp and the demand for cars n Denmark - A pseudo-panel analyss Abstract Jens Erk Nelsen, Dansh Transport Research Insttute Ths paper examnes how real estate ownershp, ncreasng real estate values and the fallng nterest rates affect car demand. It uses data from the Dansh Transport Dary Survey together wth data from Statstcs Denmark to estmate a smple partal adjustment model for car avalablty n Dansh households. We fnd that car avalablty dffers among households ownng real estate and households not ownng real estate. Furthermore we show that both households groups have ncreased ther demand for cars due to the fallng nterest rate. 1. Introducton The modelng and forecastng of car avalablty s often based on cross secton data n a dscrete model settng (e.g. logt or probt) where t s assumed that the parameters estmated reman constant over tme. There are two underlyng assumptons behnd ths. The frst s that that the economy s n equlbrum. The other s that observed dfferences n consumpton between, e.g., a hgh ncome person and a low ncome person s a vald descrpton of what would happen f a low ncome person suddenly receved the same ncome as the hgh ncome person, all other thngs beng equal. Both these assumptons are probably not vald. What s needed s a dynamc model whch explctly takes account of ths and recent models (e.g. Dargay and Vythoulkas (1999) and Fosgerau et al. (2004)) use ths knd of specfcaton. Ideally, tme seres data should be used but snce these are rarely avalable n the transport sector and snce many cross secton data exst the smpler approach of cross-secton modelng s often adopted. The use of pseudo-panel data s an attempt to crcumvent some of the shortcomngs of the cross-sectonal data and use the strength of the tme seres analyss. Deaton (1985) shows that t s possble to create panel data from repeated cross-secton data named pseudo-panel data. He show that by usng a characterstc that s nvarant over tme for gven household types (e.g. year of brth) t s possble to create a pseudo panel descrbng average behavor for the household type n queston. The pseudo panel approach also allows for the ncluson of macro varables whch mght affect both the transport behavor (e.g. number of klometers traveled) and the demand for transport vehcles (e.g. cars). The approach suggested by Deaton has snce been utlzed n a number of papers. The estmaton of dynamc car ownershp models s undertaken n Dargay and Vythoulkas (1999) where the UK Famly Expendture Survey was used. They demonstrate that the method can be appled gvng satsfactory results when t comes to descrbe the dynamcs of transport Per Revewed ISSN 1397-3169 1
behavor. They also show that there are large dfferences between short and long run elastctes wth the latter beng three tmes bgger than the former. Brkeland et al. (2000) use the Dansh Tranport Dary Survey data n a pseudo panel analyss of personal transport n Denmark. They dentfy cohort effects and lfe-cycle effects and they compare ncome elastctes estmated by smple cross-secton analyss wth those found by the use of pseudo panel data concludng that the two approaches yeld very dfferent results. They conclude that pseudo panel methods are preferable when predctng future demand for transport. In Dargay (2001) the approach s used to show that hysteress effects are present for car ownershp. She shows that the elastctes wth regard to rsng ncome were hgher than the elastctes for fallng ncome. Ths hysteress shows that a car after t s purchased becomes a necessty whch s not easly dsposed of. The approach was later used n Dargay (2002) to show that there are mportant dfferences n the elastctes between rural and urban households. In Denmark the real estate values have ncreased steadly and at very hgh rates snce 1993 and at the same tme the long term nterest rate has dropped from around 10% to around 5%. Ths s shown n fgure 1 and fgure 2. 1200 1000 Prces on apartments 12 10 800 600 400 Prces on one-famly houses 8 6 4 200 2 0 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 0 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 Fgure 1: Real estate prces (1.000 DKr.) Source: Statstcs Denmark Fgure 2: Interest on 30-years bonds Source: Statstcs Denmark Households already ownng real estate could (after a few years) captalze wealth wthout ncreasng monthly mortgage payments due to the fall n the long term nterest rate. Such an ncrease n wealth could ncrease the number of cars n households. For households enterng the real estate market the effect s less clear. The fact that the real estate value ncreases wll make t more expensve to purchase a house or an apartment and the mortgage payments wll go up. The decreasng nterest rate wll counter ths by reducng the mortgage payments. If the frst effect domnates the households wll have less ncome avalable for consumpton whch wll reduce the number of cars. If the latter effect domnates the mortgage payments wll go down and the household wll have more ncome avalable for consumpton whch could ncrease the number of cars n the households. Per Revewed ISSN 1397-3169 2
Snce the nterest rate s the same for all households n the country we examne real estate owners and non-real estate owners separately. Ths enables us to see f the changng real estate prces and the changng nterest rate has affected the two groups dfferently. Our expectaton s that the fallng nterest rate could affect both groups but the ncreasng real estate values only affect the real estate owners. One problem s that the nterest rate and the housng prces are correlated and that non-real estate owners may be more captal restrcted than real estate owners. If ths captal restrcton s strong we expect that the nterest rate has affected the real estate owners more and may even have had no effect on non real estate owners. Ths paper utlzes the Dansh Transport Dary Survey together wth data from Statstcs Denmark to create a pseudo-panel data set for the Dansh populaton based on the year of brth for the ntervewee. It examnes how real estate ownershp and a fallng nterest rate affect cars avalable n Dansh households and to what extends these households dffer wth regards to ncome elastctes. The paper extends the fndngs n prevous studes by lookng at the dfferences between real estate owners and non-real estate owners thus provdng more nsght nto the behavor of dfferent household groups. The paper proceeds as follows. Secton 2 dscusses the data and the constructon of the pseudo-panel. Secton 3 sets up the model and secton 4 contans estmates and dscussons as well as elastctes. Secton 5 concludes. 2. The pseudo-panel data The data utlzed n the present paper come from two sources, the Dansh Transport Dary Survey () and Statstcs Denmark (SD). The people partcpatng n the are selected by random draw from the Dansh Central Personal Regstry (CPR). Data concernng the ndvdual as well as the household s collected and the travel pattern for a sngle day for the ntervewee s recorded. In the years 1992 to 1997 a monthly sample of 1800 was drawn for people between the age of 16 and 74. In 1998 ths was extended to 2100 and the age group was extended to 10 to 84. The response rate n the survey s about 65-70%. The varables ncluded n the present analyss are after-tax ncome, number of adult household members, degree of urbanzaton (lvng n a major Dansh cty or not), car avalablty (how many cars the household has access to), and nformaton about whether the household owns real estate. Due to data lmtatons on certan varables the sample used here s restrcted to the years 1996 to 2002. Car avalablty ncludes both ownershp of cars and other cars whch the household can use for personal transport. Car avalablty s calculated as the total number of cars avalable to the households dvded by the number of households for every cohort year. These are shown n fgure 3 and fgure 4 where the car avalablty for dfferent cohorts over tme accordng to age s shown. Fgure 3 shows the cohorts for households lvng n owner-occuped houses and fgure 4 shows the cohorts for households rentng ther home. It s clear from these fgures Per Revewed ISSN 1397-3169 3
that there s a huge dfference not only between households lvng n ctes and on the countrysde but also between real estate ownng households and others. Fgure 3: Car avalablty by cohort for real estate owners Fgure 4: Car avalablty by cohort for non-real estate owners Per Revewed ISSN 1397-3169 4
The fgures show that the lfe-cycle effect s larger for households lvng n owner-occuped houses. It s also clear that households lvng n less urbanzed areas have hgher car avalablty than households lvng n large ctes or n Copenhagen. One explanaton for ths s the fact that the publc transport network s better and dstances are smaller n ctes thus reducng the need for a car. Fgure 5: Number of adults n the household by cohort Fgure 5 gves another pcture of a lfe cycle effect. It depcts the number of adults lvng n a household. As the age of the ntervewee ncreases, the number of adults also ncreases. Ths s due to the fact that people get marred and have chldren. We are not able to see f households move when these changes happen but t s lkely that more adults and more chldren wll ncrease the demand for cars. When the chldren reach a certan age they also count as adults 1. Ths goes on untl the ntervewee reaches the age of 50 where the chldren start to move away from ther parents thus reducng the sze of the households. The sze of the households also decreases as a result of dvorce and death. Unfortunately the does not hold nformaton concernng the value of real estate owned by the households. It s well known that the development n housng prces have dffered sgnfcantly between dfferent regons n Denmark. Data for the average housng prces n the Per Revewed ISSN 1397-3169 5
separate muncpaltes can be obtaned from SD and these data can be lnked to the nformaton n the for each household lvng n a gven muncpalty and we thus assume that these average values are the same for each household n a gven muncpalty. The nterest rate s also obtaned from SD on an annual bass. Snce ths s a general macro varable all households n the economy face the same nterest rate. Some households mght have lmted access to the fnancal market but we gnore ths and assume that all household have the same opportuntes for borrowng money and that they all face the same long term nterest rate. The pseudo panel was constructed by dvdng the data nto cohorts. Followng Deaton (1985) the cohorts have to be based on some characterstc that reman nvarant n the perod analyzed. In the present study we have used the year of brth of the ntervewee as the determnng factor. For each of the cohorts averages for all the varables ncluded are then calculated resultng n a representatve observaton for the gven cohort. Ths means that for a representatve person born n e.g. 1945 or n 1960 we have a seres of observatons from 1996 to 2002 descrbng the behavor of the person each year. Ths data can then be lnked to the macro data for development n housng prces and nterest rate obtaned from SD gvng us the panel used n the paper. 3. The car avalablty model Wth the examnaton of the real estate ownershp and the nterest rate as the objectve we specfy a smple partal adjustment model nspred by Dargay & Vythoulkas (1999). The data we use were descrbed n secton 2 and due to the aggregaton each varable has the form of an average for the cohort t comes from. The average at the cohort levels s thus gven by At c c c = At where n t s the number of households n cohort c and A s the varable. In Dargay nt (2001) dfferent specfcatons 2 are tested and compared. She conclude that the sem-log specfcaton domnate and also argues that ths specfcaton makes most sense economcally. Based on her result we use a sem-log specfcaton. For each cohort-representatve household we let C t represent the number of cars at tme t for cohort, I t the number of adults n the household, G the generaton parameter (or cohort number), (whch s dentcal for all cohorts), Y t the yearly after tax ncome and real estate values experenced durng the last year. Ths gves the functonal form t = α + βy log( t) + βw log( t ) + βr t + βi t + βg + βc t 1 C Y W R I G C R t the long term nterest rate W t s the ncrease n where Ct 1 s the number of cars n the prevous perod. We note that the ncrease n real estate value experenced by one cohort does not have to be dentcal to the ncrease experenced by other cohorts snce we have been able to dstngush between the housng 1 A problem wth the classfcaton of adults n the s that people over the age of 16 are counted as adults but a drvng lcense can not be acqured before the age of 18. 2 Lnear, Double-log and Sem-log. Per Revewed ISSN 1397-3169 6
prces n dfferent muncpaltes. Ths means that f the households beng part of a cohort prmarly lvng n muncpaltes wth hgh growth n real estate values the cohort wll have experenced a hgh growth. To capture saturaton effects n both ncome and ncreases n real estate values we take the logarthm of both Y t and W t. As argued by Dargay & Vythoulkas ths type of model can be estmated usng standard technques. 4. Estmates and dscusson A lst of the varables ncluded n the model can be seen n table 1 together wth ther sources. The hypothess put forward n the ntroducton s modeled by the varables value ncrease and nterest rate. Varable Source Descrpton Cars Income (log) Adults Generaton Value ncrease (log) Interest rate Urbanzaton Real estate ownershp SD SD Number of cars avalable to the household Household yearly after-tax ncome Number of adults n the household Generaton effect (cohort number) Increase n housng prces durng last year Average 30 years nterest rate Lvng n urban area (Copenhagen or large cty) Dummy for households ownng real estate Table 1: Varables used n the model The number of observatons used to construct each of the cohorts can be seen n table 2 dvded nto groups comng from urban areas (Copenhagen and suburbs together wth the 3 largest ctes) or rural areas (medum and small ctes or the countrysde) and ownng or not ownng real estate. It should be noted that especally for the rural non-owners the number of observatons for some cohort s qute low. The number could be ncreased by reducng the number of cohorts and ncreasng the number of observatons wthn each of these. Cohort number Cohort date of brth Urban owner Rural owner Urban non-owner Rural non-owner 1 2 3 4 5 6 7 8 9 10 11 1920-24 1925-29 1930-34 1935-39 1940-44 1945-49 1950-54 1955-59 1960-64 1965-69 1970-74 479 713 906 1079 1463 1772 1530 1592 1593 1543 1125 1323 2079 2565 3214 4254 5184 4818 4567 4458 3831 2104 688 767 720 715 714 800 702 834 1093 1608 2162 482 617 519 475 510 604 584 610 749 1030 1299 Average 1254 3491 982 680 Table 2: Number of observatons Per Revewed ISSN 1397-3169 7
Snce we have a lagged dependent varable n the specfcaton we use the Durbn-h statstcs to test for the presence of autocorrelaton. The test confrms that autocorrelaton s present n all the models. Furthermore we know that snce the number of households n each cohort s not the same we face the problem of heteroscedastcty. To avod ths problem we weght all observatons by the square root of the number of households n the gven cohort. The error structure we specfy as a smple AR(1). The estmaton results are shown n table 3 together wth test statstcs. The models for non-real estate owners nclude the varable for the ncreasng real estate values. Ths we do to see f t s sgnfcant. If so we should be skeptcal about our hypothess snce we do not expect non-real estate owners to beneft from ncreasng real estate values. The problem wth the varable for wealth s that households who have lved n ther house for a longer perod of tme have accumulated hgher wealth than ndcated by ths varable. The dynamc model specfcaton s capable of handlng ths snce past ncreases n real estate values are ncluded but movng patterns are stll left out. Varable All Real-estate owners Non-real estate owners Intercept Real estate owner Urbanzaton Interest rate Value ncrease (log) Income (log) Generaton (cohort) Adults Cars (t-1) AR1-0.1065 (-0.74) 0.0736 (6.69) -0.0534 (-5.09) -0.0572 (-5.38) 0.0187 (2.24) 0.0772 (4.06) 0.0043 (3.49) 0.0691 (4.55) 0.7158 (21.28) 0.2788 (4.73) -0.1013 (-0.29) -0.0835 (-3.97) -0.0780 (-4.64) 0.0479 (3.01) 0.1056 (4.09) 0.0040 (2.40) 0.0685 (3.62) 0.6757 (13.45) 0.1973 (2.23) -0.0870 (-0.28) -0.0541 (-3.18) -0.0600 (-3.73) -0.0109 (-1.05) 0.1207 (3.19) 0.0022 (0.81) 0.0489 (1.27) 0.6591 (11.53) 0.3913 (4.85) 2 R SSE MSE 0.9941 139.1771 0.4686 0.9933 77.9114 0.5373 Table 3: Estmates, t-values and summary statstcs 0.9112 53.7066 0.3730 2 All parameters have the expected sgn and from the R values we see that the models ft the data well. In the model for all households we have ncluded a varable for real estate ownershp. We see that ths varable s postve and hghly sgnfcant ndcatng that real estate owners have hgher car ownershp levels than non-real estate owners. In the model for all households the effect of the ncrease n real estate values s also postve. To determne f real estate owners and non-real estate owners are affected dfferently we splt the sample and estmate the model on these two. A hgh degree of urbanzaton reduces the number of cars whch we also saw n fgure 3 and 4. Ths s not surprsng snce urban households generally have access to better publc transport facltes, they have access to fewer parkng spaces and n general have to travel shorter dstances to reach ther destnaton. Hgher ncome affects car avalablty postvely. Agan ths s expected snce cars are assumed to be normal goods. Generaton effects are found to be present for real estate owners. Younger generatons have a hgher tendency to purchase cars. For non-real estate owners the generaton effect s also Per Revewed ISSN 1397-3169 8
postve but statstcally nsgnfcant. Ths s n lne wth fndngs of generaton effects n Dargay (2001) and Dargay (2002) where less sgnfcant generatonal effects were found whch could be seen as a confrmaton of the fndngs here that the generaton effects are not present n all household groups. We also have that the number of adults affect the demand for cars postvely but the effects are only statstcally sgnfcant for real estate owners. Turnng to the nterest rate we see that both real estate owners and non-real estate owners experence an ncrease n ther demand for cars when the nterest rate decreases. Lookng at the effect of the ncreasng real estate values we get the expected result that only real estate owners are affected and as expected the households have ncreased ther demand for cars as a consequence of the ncreasng wealth. Lettng θ = (1 β C ) we have θ = 0.28 for real estate owners and θ = 0.32 for non-real estate owners. We thus see that 28% and 32% of the adjustment n car avalablty for the two household groups happen wthn the frst year. The hgh degree of sgnfcance for the adjustment parameter tells us that the dynamc specfcaton s needed snce households n general do not adjust to changes nstantaneously. 4.1 Elastctes Short run elastctes can be calculated drectly from the estmated parameters, snce we know sr C x x that the short term elastcty, ε, wth regard to varable s gven by ε = = β. The sr x C C long term elastcty, lr lr ε ε, s gven by ε = θ. For the dfferent models estmated the elastctes are shown n table 5. Real estate owners Non-real estate owners Assumng car avalablty at group average 3 (0.096) (0.296) (0.228) (0.668) Assumng car avalablty equal to 1 (0.106) (0.326) (0.121) (0.354) Table 5: Income elastctes for car avalablty (short run long run). sq What can be seen from table 5 s that real estate ownng households n general have lower ncome elastcty than non-real estate ownng households both n the short run and n the long run. One explanaton for ths could be that real estate ownng households have hgher car ownershp and thus are closer to some knd of natural saturaton pont for car ownershp. The value for the elastctes are lower than those found n other studes for Denmark (Dargay and Gately (1999), Chrstens and Fosgerau (2004)) and perhaps more n lne wth the fndngs n Bjørner (1999) and Brkeland et. al. (2000) but stll below the values reported n these papers. The nfluence of the nterest rate on car avalablty can be seen drectly from ts parameter and the long run elastcty s calculated. The same goes for the elastcty of real estate values. The results are shown n table 6 below. 3 For real estate owners and non-real estate owners the average car avalablty s 1.10 and 0.53. Per Revewed ISSN 1397-3169 9
All Real estate owners Non-real estate owners Assumng car avalablty at group average Assumng car avalablty equal to 1 (-0.071) (-0.219) (-0.078) (-0.241) (-0.113) (-0.332) (-0.060) (-0.176) Table 6: Elastctes for nterest rates on car ownershp (short run - long run) From the models we know that the nterest rate affects both owners and non owners of real estate and we see from table 6 that both short run elastctes and long run elastctes are lower for real estate owners. 5. Concluson We have shown that dfferences between real estate owners and non-real estate owners exst when t comes to car avalablty. We found ndcatons of a wealth effect for real estate owners due to the ncreasng housng prces. The effect should be examned n more detal usng real panel data but the fndngs here suggest that real estate owners have ncreased ther car avalablty due to the ncreasng real estate values. Examnng the effect of the fallng nterest rate we found that both real estate owners and non-real estate owners have ncreased ther car avalablty due to the decreasng nterest rate. Bblography Brkeland, M. E., Brems, C. R. and Kabelmann, T. (2000) Analyse af personers transportarbejde, 1975-1998, Trafkdage på Aalborg Unverstet 2000, Conference paper (www.trafkdage.dk) Chrstens, P. F. and Fosgerau, M. (2004) Rådghed over bl - en beskrvelse af sammenhængen mellem husstandsndkomst, blrådghed og geograf, DTF Notat 3:2004, Note, Dansh Transport Research Insttute, www.dtf.dk. Dargay, J. M. and Gately, D. (1999) Income s effect on car and vehcle ownershp, worldwde: 1960-2015, Transportaton Research Part A, 33, 101-138. Dargay, J. M and Vythoulkas, P. C. (1999) Estmaton of a Dynamc Car Ownershp Model: A Pseudo-panel Approach, Journal of Transport Economcs and Polcy 33:3, 287-302. Dargay, J. M. (2001) The effect of ncome on car ownershp: evdence of asymmetry, Transportaton Research Part A 35, 807-821. Dargay, J. M. (2002) Determnants of car ownershp n rural and urban areas: a pseudo-panel analyss, Transportaton Research Part E, 38, 351-366. Deaton, A. (1985) Panel Data from Tme Seres of Cross Sectons, Journal of Econometrcs 30, 109-126. Fosgerau, M., Holmblad, M. and Plegaard, N. (2004) ART En aggregeret prognosemodel for dansk vejtrafk, Notat 5:2004, Dansh Transport Research Insttute. Per Revewed ISSN 1397-3169 10