Decomposing Changes in Aggregate Loan-to-Value Ratios

Transcription

1 Decompong hnge n Aggrege Lon-o-Vlue o Jn de Hn nd André vn den Berg b Ocober 26, 2 Abrc: The Lon-o-Vlue ro for group of houehold cn be defned he ol moun of oundng morgge lon dvded b he ol vlue of he houng ock. ompoonl chnge of he houehold group cn ffec he Lon-o-Vlue ro. In h pper we decompoe chnge n he overll ro no hree erm: he conrbuon of connung houehold, whch re preen n ech me perod, nd he conrbuon of enerng nd eng houehold. Smlr decompoon n h ce relng o frm e n he lerure on producv nl. However, fr we know, our decompoon h no been decrbed before. We provde n emprcl lluron for he eherlnd, bed on mcrod from he Duch offce. Ke word: decompoon, houehold dnmc, morgge lon, proper vlue. JEL lfcon: 43, G2, 2. Sc eherlnd nd OTB eerch Inue, Delf nver of Technolog. Pol ddre: Dvon of Mcroeconomc Sc, Sc eherlnd, P.O. Bo 245, 249 HA The Hgue, The eherlnd; eml: [email protected]. b Dvon of Mcroeconomc Sc, Sc eherlnd. Pper prepred for he Economc Meuremen Group Workhop, ovember 3 December 2, 2, Sdne, Aurl. The vew epreed n h pper re hoe of he uhor nd do no necerl reflec he vew of Sc eherlnd. The fgure re preened for lluron purpoe onl; he re no offcl nd hould no be rbued o Sc eherlnd.

2 . Inroducon The fnncl cr of 28 underlned he need for ccure nd mel nformon on he houng mrke. Scl gence round he world hve ndeed been mprovng nd eendng her houng mrke c. A mjor chevemen n Europe w he eng up nd hrmonzon of houe prce ndee, coordned b Euro. In he eherlnd, uer lo ked for ndcor of he fnncl rk fced b homeowner nd morgge lender. One emple of uch ndcor he Lon-o-Vlue ro for group of houehold. Th ro defned he ol moun of oundng morgge lon dvded b he ol vlue of he correpondng houng ock. ecenl, Sc eherlnd decded o publh Lon-o-Vlue ro, bed on d h em from he Duch offce. The Lon-o-Vlue LTV ro ke erm n rel ee fnncng, prculrl n he ce of morgge lon. 2 I refer o he moun of mone borrowed gn he mrke vlue of he proper. The proper vluon re ofen done b pprer. In everl counre, lon wh n LTV ro eceedng.8 requre morgge nurnce, he rk of he borrower defulng deemed oo gre for he lender. 3 The LTV ro lo ued b lender o e he rk nvolved when omeone who own proper for number of er wn o refnnce he proper n order o ke ch ou. Due o repmen, he oundng lon moun uull dmnhe over me. Bu wheher he owner equ poon n proper mnu he LTV ro ncree, depend lo on he vlue chnge of he proper. A reul of he fnncl nd economc cr, mn counre hve wneed ubnl drop n houe prce, o mo homeowner LTV ro hve probbl gone up. A wll be hown ler on, he ggrege LTV ro for group of houehold weghed verge of he LTV ro pernng o he conuen houehold. If ll of Euro lo funded he complon of Hndbook on edenl Proper Prce Indee. The le drf of he hndbook cn be downloded from 2 In Aurl nd ew Zelnd, he Lon-o-Vlue o uull bbreved LV. 3 Th he ce n e.g. he.s. nd Aurl. The purcher h o mke down pmen of 2% or more o vod png morgge nurnce premum. In he eherlnd, morgge nurnce unuul. Mn fr-me buer mke no down pmen ll. Ther LTV ro re omeme well bove he me of purche becue he borrow n moun h lo cover ddonl co whch llowed n he eherlnd. Duch bnk chrge hgher nere re when he LTV ro eceed.8, however, o here cull n ncenve for png down.

3 he ndvdul ro ncree, nd f he wegh do no chnge, he ggrege ro lo ncree. However, group of houehold for whch cl nformon colleced pcll dnmc; unlke conn pnel, ze nd compoon wll chnge over me. In prculr, pr from he connung houehold, whch re preen n ech me perod, here m lo be enerng nd eng houehold. Such compoonl chnge cn ffec he overll LTV ro. To gve n emple: houehold h recenl purched houe ofen hve relvel hgh LTV ro becue he hve no e been ble o rep lrge pr of he morgge lon; when hee houehold ener he group n queon, he wll pu n upwrd preure on he overll ro. Moreover, he wegh ched o he ndvdul houehold need no be conn, whch could lo ffec he overll ro. The purpoe of h pper o how how chnge n he ggrege LTV ro cn be decompoed no hree erm: he conrbuon due o chnge n he LTV ro of he connung houehold plu he conrbuon of enerng nd eng houehold. Smlr decompoon n h ce relng o frm ned of houehold cn be found n he lerure on producv nl. Aggrege producv defned he ro of ggrege oupu o ggrege npu. Our decompoon redl pplcble o producv bu, fr we know, h no been decrbed before. In conr o mo oher decompoon, we follow wo-ge pproch. We fr decompoe he chnge n he overll ro no conrbuon of he ub-e of connung, enerng nd eng elemen nd hen dggrege he reul no ndvdul conrbuon, where oher drecl focu on he mcro level. 4 The remnder of he pper orgnzed follow. In econ 2 we oulne he propoed decompoon n generl erm nd pek of he -o- ro. In econ 3 we dcu wo decompoon h hve been uggeed n he producv meuremen lerure nd rgue wh we prefer he propol n econ 2. Secon 4 focue on he LTV ro nd epln wh n unweghed meure, or he medn, unfcor. A number of problem reled o houehold dnmc, uch he denfcon of he connung houehold, re lo ddreed. Secon 5 decrbe he d ulzed, whch em from he Duch offce nd cover 26-27, nd preen he emprcl reul. Secon 6 conclude. 4 See Blk 23 for n overvew of ngle-ge decompoon of producv chnge propoed n he lerure. Blk nd Hoogenboom-Spjker 23 ppl hee decompoon o Duch mcrod. 2

4 3 2. A Two-Sge Decompoon In h econ we wll derve decompoon of he chnge dfference n he ro of wo ggrege vlue. Le denoe e of elemen peron, houehold, or frm n perod, 5 nd uppoe h d on wo vrble, nd, colleced; nd denoe he obervon for elemen n perod. The ggrege vlue re nd, repecvel. The -o- ro defned. oce h cn be wren weghed verge of ndvdul or mcro -o- ro / : /, 2 where / denoe he hre of elemen n he ggrege. In wh follow we wll dnguh wo me perod, he be perod nd he compron perod. ng epreon 2, he chnge dfference n beween perod nd perod cn be wren Le denoe he e of connung elemen, whch re preen n boh me perod. The e of eng elemen, whch re onl preen n perod, denoed b ; he e of enerng elemen, whch re onl preen n perod, denoed b. Thu, we hve nd, nd 3 cn be decompoed. 4 Anoher w of wrng 4, 5 5 We wll ue he erm me perod hroughou he pper even hough he vrble cn rele o pon n me rher hn dcree perod.

5 4 n whch /, /, / nd / re he hre of he ndvdul elemen wh repec o he e o whch he belong, nd wh /, /, / nd / denong he hre of he ub-e, nd. Smlr o nd 2, we wre he -o- vlue for, nd ; ; ;. 6 Subuon of 6 no 5 eld. 7 Equon 7 convenen rng pon for decompong he chnge n he ggrege -o- ro,, no he conrbuon of he ub-e, nd. We fr rewre 7. 8 Alernvel, 7 cn be rewren. 9 Decompoon 8 nd 9 re equll vld. To vod mkng n rbrr choce nd o re 8 nd 9 n mmerc mnner, we wll ke he men. Th led o 2] / [ 2] / [, where we defned 2 / nd 2 / n he econd epreon nd ued nd. The fr erm n he l epreon of meure he conrbuon of he e of connung elemen b mulplng he chnge n he -o- ro for e,, b verge hre n he wo perod. The econd erm meure he conrbuon of he e of enerng elemen. oe h f greer hn he verge ro for he

6 connung elemen,, hen he e of enerng elemen wll re he overll ro. The e of eng elemen wll lower he overll ro f he hrd erm. bove, hown b For ome purpoe could be ueful o epre he chnge n he ggrege -o ro n erm of he conrbuon of he ndvdul elemen rher hn he e, nd. ng 6, he chnge n he ggrege ro for he e of connung elemen cn be decompoed [ ], or lernvel [ ]. 2 Agn, for reon of mmer we prefer kng he men of nd 2: [ ], 3 where / 2 nd / 2 for. Equon 3 how h he chnge n he ggrege -o- ro for he connung elemen depend no onl on he weghed verge of he chnge n he mcro ro bu lo on he chnge n he mcro hre. Pu dfferenl, due o hf owrd elemen wh lower hre, he ggrege -o- ro cn decree even when ll mcro ro ncree. 6 nd ung Subung epreon 3, nd [ The conrbuon of eld ] nd no. 4, for emple, equl [ ]. oe h we follow wo-ge pproch: n he fr ge we dnguh beween he e ub-ggrege of connung, enerng nd eng elemen nd n he econd ge we ep down o he mcro level. 6 In producv cone, h prdo w noed b Fo 22. Pror o h, Fo 999 decrbed h fr prdo: ng ndrd defnon of co effcenc, mul-produc frm m be more effcen n producng ech produc hn n oher frm, e m no be he mo effcen frm overll. 5

7 6 A number of lernve decompoon hve been propoed n he lerure on producv growh. In econ 3 below, we wll dcu wo of hem nd rgue wh we prefer decompoon nd Alernve Decompoon One lernve pproch could be he followng. The rng pon gn equon 4 bu now we focu drecl on he mcro level,.e., on he conrbuon of he ndvdul connung, enerng nd eng houehold rher hn he ub-ggrege, nd. A noed b Blk 23, n rbrr clr clng fcor cn be ncorpored no 4:, 5 becue. Equon 5 cn be wren. 6 Two poble w of wrng he rgh-hnd de of 6 re ; 7. 8 Tkng he verge of 7 nd 8 nd ome rerrngng eld ] [, 9 where 2 /, before, nd 2 /. Wh vlue for hould be choen? Blk 23 cll 2 /, he verge ggrege level of n h ce producv, rher nurl choce. Bu h choce would mke he conrbuon of he connung elemen dependen on nd. In our opnon more uble choce for 2 /, he verge vlue for he e of connung elemen. Decompoon 9 hen become

8 7 ] [. 2 If for ll, he conrbuon due o hre chnge dpper. I el demonred h h lo hold for our decompoon 4. The econd nd hrd erm n 2, he ggrege conrbuon of he enre nd e, re equl o hoe n 4. Hence, he fr erm n 2, he ggrege conrbuon of he connung elemen, equl o he fr erm n 4. However, he conrbuon of n ndvdul elemen n 2,, dfferen from h n 4, whch w ] [. There re wo reon wh we prefer 4 over 2. If he me for ll, hen n decompoon 4 he ol conrbuon due o hre chnge vnhe. Th nce proper doe no hold for decompoon 2, ecep when for ll. More mpornl, meurng he conrbuon of he e of connung elemen requre clculng ggrege -o- ro n mlr w he overll ro. Thu, kng equon 7 he rng pon, nd followng wo-ge pproch, mke lo of ene. I worhwhle menonng h we mde n mplc umpon n dervng equon from 7. Smlr o wh w done bove, we could nclude n rbrr clr n 7, becue, eldng. 2 A before, here re number of w o proceed. Equon 2 cn be wren, 22 or, lernvel,. 23 Tkng he men of 22 nd 23 eld. 24

9 The econd erm n he l epreon of 24 meure he conrbuon of chnge n hre of he e of connung elemen o he chnge n he overll -o- ro. We prefer choong n order o ge rd of h nunce erm. Bu hen of coure 24 mplfe o our decompoon. Dewer nd Fo 2 propoe noher decompoon. Srng from equon 7, whch we repe for convenence, he proceed follow:. 25 Equon 25 dffer n wo mporn repec from our propol. Fr, n 25 he conrbuon of he e of connung elemen ndependen of relve ze, whch eem counernuve, where n he conrbuon depend on verge hre. Second, n equon 25 he conrbuon of he enerng nd eng elemen depend on he dfference beween her -o- ro nd hoe of he connung elemen n he repecve perod, whle n nd re evlued gn he fed verge. Our pproch h he dvnge h he conrbuon of he enerng nd eng elemen cncel ech oher ou when he wo e hve dencl -o- ro nd her relve mpornce n erm of he me. 7 Dewer nd Fo 2 lo ppl he Benne 92 pe decompoon 3 o decompoe he -o- chnge of he e of connung elemen. The follow mlr wo-ge pproch we do, bu her fr-ge decompoon 25 dffer from our decompoon. The mke fnl djumen o enure h he reul nvrn o chnge n he un of meuremen b dvdng boh de of 25 b he be perod vlue. In he ce of Lon-o-Vlue ro, h djumen le relevn nd wll pcll be epreed n he me currenc un, e.g., n euro or n hound of euro. In econ 4 we wll urn o Lon-o-Vlue ro. A wll become cler, one of he bgge problem o fnd defnon of he houehold h enble u o denf connung houehold. 7 Hlwnger 2 rgue h f he producv level of enerng nd eng frm re he me, hen he um of he conrbuon of enerng nd eng frm hould be zero. Th doe no hold for equon unle he hre re lo dencl. In Append we how how decompoon rele o n nde of producv chnge when he hre re equl. 8

10 4. Lon-o-Vlue o The meuremen of he Lon-o-Vlue LTV ro nd he prccl mplemenon of he decompoon no conrbuon of he connung, enerng nd eng houehold re number of queon, uch Wh he ppropre rge populon? Wh ecl do we men b lon nd vlue? Wh re he unweghed LTV ro nd he medn ro unuble? How hould he connung, enerng nd eng houehold be defned? I he necer d vlble? Before gong no hee queon, we ke bref look wo defnon of he houehold. The Sem of onl Accoun 28 nd he.s. enu Bureu defne he houehold dfferenl: A houehold group of peron who hre he me lvng ccommodon, who pool ome, or ll, of her ncome nd welh nd who conume cern pe of good nd ervce collecvel, mnl houng nd food. Euro e l., 29 A houehold nclude ll he people who occup houng un her uul plce of redence..s. enu Bureu, Glor for he 2 enu, hp://fcfnder2.cenu.gov Shrng houng un or lvng ccommodon, uch houe or n prmen, pl crucl role n boh defnon, bu he SA plce few ddonl rercon. For our purpoe, he enu Bureu defnon wll uffce. Accordng o hem, houng un owner-occuped f he owner or co-owner lve n he un even f morgged or no full pd for. LTV ro re obvoul onl relevn for homeowner, no for rener, o he nwer o he fr queon eem que rghforwrd: he rge populon con of houehold lvng n owner-occuped houng un. In ddon, could be ueful o eclude houehold whou morgge lon; he pd off her deb nd here no rk nvolved n more, n n ce no rk of deful. 8 er need hould lo be ken no ccoun, epecll when come o dnguhng ub-populon. er m requre LTV ro for dfferen ncome group, houehold n dfferen regon of he counr, ec. 8 Sc eherlnd ndeed nend o publh LTV ro boh for ll owner-occuper nd for owneroccuper wh morgge lon. 9

11 The owner h uull ken ou morgge lon o fnnce he purche of he proper. Some people lo own econd houe, for nnce vcon home, whch m be morgged well. In h pper, we eclude he ler nd look prmr fr home onl, ncludng propere h hve more hn one morgge len. oe h we eclude non-morgge lon. The vlue of he houe hould reflec he mrke vlue. Proper vluon re pcll deermned b pprer. In ome counre, proper emen re needed for purpoe nd re vlble for he enre houng ock. If he propere re re-eed regulrl, for emple on n nnul b, hen hee offcl vluon could be ued o compue LTV ro. A hown b equon 2, he ggrege LTV ro weghed verge of he LTV ro pernng o he ndvdul houehold, where he wegh re equl o he propere vlue hre. We could lernvel compue he unweghed verge of he ndvdul ro. However, h meure no repreenve of he group whole. Some houehold re more mporn hn oher, nd he proper vlue reflec he economc mpornce. The weghed verge h rghforwrd nerpreon: wh percenge of he vlue of he owner-occuped houng ock morgged. Th no o h he unweghed verge h no menng. Lke he medn, meure of cenrl endenc locon meure of he drbuon of he ndvdul ro. Th drbuon cn be of mpornce o uer, n prculr for deermnng how mn houehold hve n LTV ro h eceed ome hrehold vlue. The bgge concepul nd prccl problem wh decompong chnge n he LTV ro denfng he connung houehold. Once h done, he enerng nd eng houehold re mplcl denfed, gven he rge populon. 9 The dffcul n eblhng wheher houehold he me n old problem h h frured longudnl houehold nle for long me. Brodl pekng, here re wo ue nvolved whch re ofen nerreled: chngng houehold compoon nd redenl mobl. A long he compoon of he houehold remn unchnged nd none of he member move houe, we cn fel pek of he me houehold. omplcon cn re f hee requremen do no hold. 9 Houehold h cull defuled nd becme rener wll be clfed eng houehold becue he re no longer pr of he rge populon even f he ll hve lbl remnng deb fer he houe h been old. Mn houehold chrcerc do chnge, of coure. For emple, he ge of ll he member defnel chnge over me!

12 Suppoe h he houehold move houe whle compoon doe no chnge. If move o renl home, hen he houehold e he rge populon. Bu wh f bu noher plce? Accordng o he defnon bove, he houehold connuou o e. On he oher hnd, he home nd he locon re dfferen, nd new morgge lon mgh replce he former one. For our purpoe could be more ppropre o vew h houehold boh eng nd provded h he new locon f no he rge populon enerng rher hn connung. Anoher problem re he plng up of houehold, becue of dvorce. A le one of he houehold member lkel o move ou nd r new houehold or move n wh omeone ele. Aumng he oher member n he home, hould we conder hem he me houehold before bu wh dfferen compoon or new houehold? And, for our purpoe, hould he choce depend on wheher he condon of he morgge lon chnge? In econ 5 we preen emprcl evdence for he eherlnd nd decrbe how houehold re denfed nd followed over me. We re unble o offer rel oluon o he problem menoned bove. Our denfcon mehod prgmc one, drven b d vlbl. Admedl, h wll mke he nerpreon of he decompoon lle uncler. There re ome oher ue whch hould lo be ken no ccoun when nerpreng our reul. 5. D nd eul for he eherlnd Our d e bed on ncome fle nd conn mcrod on houehold welh fnncl cpl nd lble n December 26, 27 nd 28. I bcll cover ll prve houehold n he eherlnd, from whch we eleced he owner-occuper. Oundng morgge on he prmr fr dwellng re dnguhed epre cegor. The offcll ppred vlue of he propere re lo ncluded n he d e. Duch propere re re-eed nnull, nd we hve vluon our dpol for ech er. However, he pprl rele o Jnur nd hence lg behnd lmo In he eherlnd, he vluon re needed for boh ncome nd locl proper purpoe. The re deermned b prve compne peclzed n m pprl, bu he muncple re ulmel reponble for he reul. Sc eherlnd houe prce nde bed on he Sle Prce Apprl o SPA mehod whch combne ellng prce nd offcl vluon. For more nformon, ee de Vre e l. 29.

13 full er. We ued he overll houe prce nde o upde he pprl o December. Th equl re-clng of ndvdul LTV ro poenl ource of error becue n rel, dfferen mrke egmen ehb dfferen prce rend. The reul lo depend on he ccurc of he pprl d. A he mcro level, hee d re que no nd do no lw reflec he rue mrke vlue. On he oher hnd, we epec he qul of he d o be good enough o compue LTV ro he ggrege level. Bede d qul ue, cern pe of morgge hmper he nerpreon of he LTV ro meure of fnncl rk. T remen of deb-fnnced owneroccuped houng n he eherlnd ver fvorble. Morgge nere pmen re full deducble he mrgnl re, o Duch houehold hve rong ncenve o mnn hgh level of morgge deb. Due o deregulon nd ncreed compeon mong cred provder, new fnncl produc were nroduced n he 99. Morgge fnncng combned wh cpl nurnce polc n prculr becme populr. Wh h pe of morgge, prncpl repmen re pd no n nurnce polc rher hn deduced from he oundng morgge. The borrower cn mmze morgge nere deducon b no png off he deb whle he me me ccumulng cpl n he nurnce polc o p off he deb when he morgge erm epre. onequenl, he emed LTV ro wll overe he rk compred o uon whou h pe of morgge. Everone n he eherlnd h peronl czen ervce number, whch ncluded n he orgnl d fle. Th number ued b mn Duch orgnzon. To vod cl dcloure, Sc eherlnd replced b rndoml choen denfcon number. A reference peron h been gned o ech houehold n he d e, pcll he peron, or one of he people, n whoe nme he home owned or rened. 2 All oher houehold member ll of he people h occup he me houng un receve he reference peron denfcon number, nd o h number denfe he houehold. We wll ue o rck houehold over me. In oher word, we ume h houehold he me, nd wll be clfed connung, long he denfcon number e. In generl he number lef unchnged when he reference peron move houe or when he compoon of he houehold chnge. A menoned n econ 4, h m no be he preferred w o denf he connung houehold, bu h ge he be we cn do. 2 Th n greemen wh he.s. enu Bureu defnon of he houeholder. 2

14 Tble l ome decrpve c for our mcrod e. The ol number of houehold wh n owned dwellng ncreed from 3.8 mllon n 26 o 4. mllon n Th ncree w mnl due o hf from renl o owner-occuped home; he hre of owner-occuper ncreed from 53.7% o 55.2%. The verge vlue of he oundng morgge lon per houehold, ncludng houehold whou morgge lon mouned o 34, n 26 nd ncreed b 5.3% nd 3.6% n 27 nd 28, repecvel. In ech er he verge vlue of he houe w lghl more hn wce he verge moun of he lon; rounded o wo decml plce, he ggrege LTV ro w.47 n 26 nd 27 nd.48 n 28. Tble. Decrpve c owner-occuper* umber of houehold 3,76,4 3,854,5 4,34,4 Dpoble ncome men 38, 4,5 8.8% 42,.5% Morgge lon men 34, 4, 5.3% 46, 3.6% Appred vlue men 285,2 3,6 5.8% 37,2.9% LTV ro * hnge wh repec o he precedng er n prenhee. Purel bckground nformon, Tble lo provde he verge dpoble houehold ncome for ll owner-occuper on n nnul b. Dpoble ncome grew b 8.8% n 27 nd.5% n 28 wh repec o he precedng er. Dvdng verge dpoble ncome b he verge vlue of he morgge lon gve n ndcon of he ggrege Lon-o-Income LTI ro. 4 The LTI ro w 3.5, 3.4 nd 3.47 n 26, 27 nd 28. The decompoon dcued n econ 2 nd 3 cn lo be ppled o LTI ro. We hve choen no o do h dpoble ncome n our d e doe no ecl mee Sc eherlnd defnon nd, n h repec, h been meured onl crudel. 3 Thee fgure dffer omewh from he offcl fgure publhed on Sc eherlnd onlne dbe Slne. One of he reon h we denfed owner-occuper houehold h hve pove vlue for owned dwellng n our d e. The offcl fgure on he oher hnd rel on combned nd clened mcrod from number of ource nd on dfferen rule for denfng owner-occuper houehold. 4 The LTI ro noher fmou ndcor of fnncl rk n he cone of owner-occuped houng. Agn, we could lernvel rerc he populon o owner-occuper houehold wh morgge lon. 3

15 Fgure, b nd c depc he moohed relve frequenc drbuon of he ndvdul LTV ro n 26, 27 nd 28. Thee grph llure he dvnge of workng wh negrl mcrod, when we do no hve o worr bou mplng ue. Fgure. Frequenc drbuon of LTV ro, Houehold % 5 > < Lon / Vlue Fgure b. Frequenc drbuon of LTV ro, Houehold % 5 > < Lon / Vlue 4

16 Fgure c. Frequenc drbuon of LTV ro, Houehold % 5 > < Lon / Vlue A couple of pon re worh nong. Appromel 5% of he owner-occuper houehold do no hve morgge on her houe. Mo lkel, mn of hem belong o he elderl, who hve pd off her deb. 5 Some 2% hve n LTV ro of greer hn. Pr of h group probbl con of fr-me buer, mo of whom re relvel oung, who dd no mke down pmen. Anoher pr of h group m con of houehold wh he pe of morgge decrbed bove, where he ccumule cpl n n nurnce polc nd p off he deb when he morgge erm epre. The ler houehold, well fr-me buer who dd mke down pmen or pd off mll pr of her deb, mgh lo epln he remrkble bmodl of he frequenc drbuon,.e., he could be he cue of he econd mode pek n LTV ro of.8-. ncludng. The fr mode n LTV ro of.2-.4, nd become le mporn n he coure of me. 6 5 A neglgble frcon of hee houehold h negve lon, whch dffcul o undernd. I doe remnd u of he fc h, whle mplng errorr ben, non-mplng error cn be mporn. For he complon of offcl c, ome clenng of he mcrod wll clerl be needed. A menoned prevoul, we hve no horoughl checked nd clened he d. 6 The frequenc drbuon of morgge lon nd houe vlue re hown n Append 2. The hpe of he drbuon of houe vlue much more ble over me hn h of oundng morgge lon. 5

17 Tble 2 dpl he ggrege d o be ued npu o decompoon nd 25. oe h we do no preen n reul for econd-ge decompoon no he conrbuon of ndvdul houehold nce h doe no eem prculrl relevn n he cone of LTV, n conr o, for emple, producv meuremen. Three pr of er or rher, December monh wll be compred: 26 wh 27, 27 wh 28, nd 26 wh 28. The noon n Tble 2 correpond o he noon n econ 2 nd 3. For emple, nd denoe he overll LTV ro n he fr nd econd er of ech blerl compron. The vlue re of coure dencl o hoe n he l row of Tble. Tble 2. Aggrege d for decompoon nd Lookng Tble 2, wo nereng obervon cn be mde. Fr, he LTV ro of he enerng houehold, perod,, hgher hn h of he connung houehold n. Th n ccordnce wh pror epecon. However, he vlue of.67,.53 nd.6 re much lower hn we would hve epeced. A menoned erler, commonl known h mn fr-me buer n he eherlnd do no mke down pmen nd hve n LTV ro of roughl. Thu, our fndng ugge h he e of enerng houehold lo nclude houehold h re no fr-me buer. 7 Th h o do wh how we denfed connung, hence enerng nd eng houehold. 7 In 27 nd 28, we record 7% nd 8% enerng houehold wh repec o he precedng er. In 28, we record 3% enerng houehold wh repec o 26. Indeed, here cnno be h mn frme buer. A puzzlng fndng h he number of enerng houehold beween 26 nd hound lo mller hn he um of he enerng houehold beween 26 nd hound nd beween 27 nd hound. 6

18 Second, for ech of he hree compron, he perod hre of enerng houehold n he vlue of he houng ock eceed he perod hre of eng houehold. 8 We herefore cnno ume connc over me of he vlue hre for he connung houehold, done n he Append. Tble 3 conn he reul for our preferred decompoon of he chnge n he ggrege LTV ro pernng o he hree blerl compron. Gven he eremel mll chnge, he reul uch re no overl ecng. However, he do llure he mpornce of dnguhng beween he ub-group, n prculr beween connung nd enerng houehold. For emple, he chnge n he LTV ro for he ne reul of negve conrbuon of he connung houehold -.443, n lmo offeng pove effec of he enerng houehold.327, nd ver mll negve conrbuon of he eng houehold -.7. oce h he conrbuon of ech ub-group for he compron nd do no dd up o he correpondng conrbuon for he compron Th feure of he mehod ued. Tble 3. Decompoon LTV ro onnung Enerng Eng Fnll, Tble 4 preen he reul for he decompoon propoed b Dewer nd Fo 2, gven b equon 25. We were b crcl of her pproch, mong oher hng becue we feel overe he conrbuon of he connung houehold. The meured h conrbuon mpl b he chnge n he -o- ro n h ce he LTV ro, where n our decompoon he chnge mulpled b he verge hre ppred vlue hre of he connung houehold. For emple, for he compron we mulpled he vlue of -.8 n Tble 4 b he vlue for Tble 2,.978, o obn our eme of -.5 n Tble 3. n 8 The vlue hre for he enerng houehold re roughl he me he populon hre menoned n foonoe 7. The emed vlue of he Duch owner-occuped houng ock moun o 54 bllon euro, 543 bllon euro, nd 589 bllon euro n 26, 27, nd 28. 7

19 Tble 4. Decompoon 25 LTV ro onnung Enerng Eng oncluon Sc eherlnd decded o publh LTV ro for ll owner-occuper houehold, nd for number of ub-populon. The d ource wll be he Income Pnel Surve, whch mple of ppromel 7, houehold drwn from he negrl d. The urve d re clened nd ugmened o mee Sc eherlnd concep nd defnon, uch he defnon of dpoble ncome. There re pln o chnge over o he full d e o comple ncome nd welh c nd hence o compue LTV ro. In h pper we ncped hee developmen nd lred eploed he full d e bu we dd no do much d clenng. Th w necer o denf he connung, enerng nd eng houehold nd compue her effec on he chnge n he overll LTV ro. Snce he LTV ro hrdl chnged durng 26-27, he reul m eem omewh dpponng. Ye he do how he uefulne of dnguhng beween connung nd unmched enerng nd eng houehold. Moreover, n he long run, nd prculrl for mll group of houehold, chnge n he LTV ro could be much bgger, whch would renghen he ce for decompoon nl n order o beer undernd he ource of hee chnge. We propoed wo-ge pproch. In he fr ge he chnge n he -o- ro decompoed no he conrbuon of he ub-e of connung, enerng, nd eng houehold, nd n he econd ge he conrbuon of he ub-e of connung houehold cn be furher decompoed no he conrbuon of chnge n he -o- ro of he ndvdul houehold. In h pper we dd no ppl he econd ge h no ver ueful for LTV ro, gven he huge number of houehold nvolved. I relevn for producv growh hough, nd could be worhwhle o r nd ppl our fr nd econd ge decompoon o producv mcrod. 8

20 Lke n oher counre, houe prce n he eherlnd wen down fer 28. For connung houehold n prculr, h mpled n ncree n rk, nd eendng our decompoon nl o more recen er mgh gve ddonl ngh. Followup reerch hould nclude kng cloer look how he connung houehold hve been denfed. If he denfcon procedure cn be mproved, hen we m be ble o dnguh fr-me buer epre group, whch could be of mpornce o bnk nd oher morgge lender nd m lo hve polc mplcon. I would be helpful f we knew more bou he chrcerc of he houehold nd he owned propere. Th ndeed wh Sc eherlnd currenl mng. Vrou dmnrve d e, connng d h re relevn for houng mrke nle, re lnked he houehold level. 9 nforunel, nformon on he pe of morgge unvlble, o we cnno qunf he mpc of morgge where prncpl repmen re pd no n nurnce polc rher hn deduced from he oundng morgge. Append : Decompoon under onn Shre In h Append we dwell lle b upon our fr-ge decompoon n ce he hre of he e of connung elemen conn. Wh e nd of enerng nd eng elemen re hen reduce o, he hre of he. Decompoon. A. If we conolde he conrbuon of nd, gven b he econd nd hrd erm n A., we hve. A.2 Alhough unnecer for pplcon uch Lon-o-Vlue ro, n generl recommendble o mke A.2 nvrn o chnge n he un of meuremen. For nnce, we could dvde boh de of A.2 b, uggeed b Dewer nd Fo 2. Th eld 9 The lnked mcrod e wll be ued b Sc eherlnd o comple offcl c nd wll lo be vlble o reercher unvere nd oher nuon. 9

21 2. A.3 Provded h nd, A.3 cn be wren ~ ~, A.4 where / ~. Decompoon A.4 h when he hre of he e nd re equl, her combned conrbuon o he percenge chnge n he overll -o- ro zero f. I convenen o epre A.4 n erm of nde number: ~ ~. A.5 Equon A.5 he ro counerpr of A.2. The overll -o- nde ue he be perod hre, ~ nd ~, o ggrege he nde of he connung elemen nd he -nde of he enerng nd eng elemen. Equon A.5 hold for. An uncondonl equvlen of A.5 ~ ~, A.6 whch el checked b ubung he vrou ene. In A.6, he nde of he connung elemen nd he -nde of he enerng nd eng elemen re djued for chnge n he hre. I follow h ~ ~. A.7 A.7 decompoe he percenge chnge n he overll -o- ro no he conrbuon of he e of connung elemen nd he e of unmched elemen. Alhough he do provde ddonl ngh, decompoon A.6 nd A.7 re no rell helpful becue he chnge n he ndee re no epred from he chnge n he hre.

22 Append 2: Frequenc drbuon Fgure 2. Frequenc drbuon of oundng morgge lon, Houehold % 5 5 > < Lon euro Fgure 2b. Frequenc drbuon of oundng morgge lon, Houehold % 5 > < Lon 2

23 Fgure 2c. Frequenc drbuon of oundng morgge lon, Houehold % 5 > < Lon Fgure 3. Frequenc drbuon of ppred houe vlue, Houehold % 5 5 > > - 5 Vlue euro 22

24 Fgure 3b. Frequenc drbuon of ppred houe vlue, Houehold % 5 5 > > - 5 Vlue Fgure 3c. Frequenc drbuon of ppred houe vlue, Houehold % 5 5 > > - 5 Vlue 23

25 eference Blk, B.M. 23, The edul: On Monorng nd Benchmrkng Frm, Indure nd Econome wh epec o Producv, Journl of Producv Anl 2, Blk, B.M. nd E. Hoogenboom-Spjker 23, The Meuremen nd Decompoon of Producv hnge: Eerce on he eherlnd Mnufcurng Indur, Dcuon Pper o. 3, Sc eherlnd. Benne, T.L. 92, The Theor of Meuremen of hnge n o of Lvng, Journl of he ol Scl Soce 83, Dewer, W.E. 998, Inde umber Theor ng Dfference her Thn o, Dcuon Pper o. 98-, Deprmen of Economc, nver of Brh olumb. Dewer, W.E. nd K.J. Fo 2, On Meurng he onrbuon of Enerng nd Eng Frm o Aggrege Producv Growh, pp n W.E. Dewer, B.M. Blk, D. Fler, K.J. Fo nd A.O. kmur ed., Prce nd Producv Meuremen Volume 6: Inde umber Theor, Trfford Pre. Alo vlble Euro, Inernonl Moner Fund, OED, ned on nd World Bnk 29, Sem of onl Accoun 28, Luembourg: Euro. Fo, K.J. 22, Problem wh DAggregng Producv nd Anoher Producv Prdo, Dcuon Pper, School of Economc, nver of ew Souh Wle, Sdne. Fo, K.J. 999, Effcenc Dfferen Level of Aggregon: Publc v. Prve Secor Frm, Economc Leer 652, Grlche, Z. nd H. egev 995, Frm Producv n Irel Indur, , Journl of Economerc 65, Hlwnger, J. 997, Meurng nd Anlzng Aggrege Flucuon: The Impornce of Buldng from Mcroeconomc Evdence, Federl eerve Bnk of S. Lou Economc evew 793, Hlwnger, J. 2, Aggrege Growh: Wh hve we Lerned from Mcroeconomc Evdence?, OED Economc Deprmen Workng Pper o. 267, OED, Pr. Vre, P. de, J. de Hn, E. vn der Wl nd G. Mrën 29, A Houe Prce Inde Bed on he SPA Mehod, Journl of Houng Economc 83,