On the Political Economy of Housing's Tax Status

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1 ömmföäflsäafaäsflassflassflas ffffffffffffffffffffffffffffffffffff Discussion Papers On the Political Economy of Housing's Tax Status Essi Eerola University of Helsinki, RUESG and HECER and Niku Määttänen The Research Institute of the Finnish Economy and CEBR Discussion Paper No. 10 May 2004 ISSN HECER Helsinki Center of Economic Research, P.O. Box 17 (Arkadiankatu 7), FI University of Helsinki, FINLAND, Tel , Fax , Internet

2 HECER Discussion Paper No. 10 On the Political Economy of Housing's Tax Status* Abstract The aim of this paper is to explain why the US tax system favors owner housing compared to business capital despite the efficiency losses involved. We build a simple dynamic general equilibrium model where households vote over the effective capital income tax rates for housing and business capital under a government budget constraint. We calibrate the model so that it roughly matches the joint distribution of total wealth and housing wealth among US households. The median voter turns out to have a large share of his wealth in the form of housing. The key trade-off he faces is that a low tax rate on housing 1) shifts the tax burden to wealthier households but 2) leads to a high tax rate on business capital and hence low wages and high interest rates. In our model economy, the first effect dominates, and the equilibrium tax rate on housing is much lower than the tax rate on business capital. JEL Classification: E62, H31, P16 Keywords: Housing taxation, capital taxation, political economy Essi Eerola Department of Economics, RUESG P.O. Box 17 (Arkadiankatu 7) University of Helsinki FI University of Helsinki FINLAND essi.eerola@helsinki.fi Niku Määttänen The Research Institute of the Finnish Economy Lönnrotinkatu 4 B FI Helsinki FINLAND niku.maattanen@etla.fi * We are very grateful to Michael Reiter for his advice. We also wish to thank Juan Carlos Conesa, Albert Marcet, Jaume Ventura, and seminar participants at the Universitat Pompeu Fabra and the University of Helsinki for comments and discussions. The usual disclaimer applies. A previous version of the paper was presented in the 2003 EEA conference. Financial support from the Yrjö Jahnsson foundation is gratefully acknowledged.

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4 uhqwdo krxvlqj lv forvhg1 Wklv doorzv xv wr irfxv rq wkh glvwulexwlrqdo hhfw zh duh lqwhuhvwhg lq1 Zh iudph wkh srolwlfdo sureohp dv rqh ri fkrrvlqj wkh wd{ udwhv rq krxvlqj dqg rq wkh qdqfldo dvvhw xqghu d edodqfhg exgjhw frqvwudlqw1 Vlqfh wkh djjuhjdwh dprxqw ri wkh qdqfldo dvvhw fruuhvsrqgv wr wkh djjuhjdwh vwrfn ri exvlqhvv fdslwdo/ wkh wd{ udwh rq wkh qdqfldo dvvhwv lv dovr wkh hhfwlyh wd{ udwh rq wkh uhwxuq wr exvlqhvv fdslwdo1 Zh fdoleudwh wkh prgho vr dv wr pdwfk wkh mrlqw glvwulexwlrq ri wrwdo zhdowk dqg oderu lqfrph dv zhoo dv fhuwdlq djjuhjdwh udwlrv lq wkh XV gdwd1 Wkh hqgrjhqrxvo ghwhuplqhg glvwulexwlrq ri krxvlqj dovr urxjko pdwfkhv wkh gdwd1 Lq sduwlfxodu/ krxvlqj zhdowk lv pxfk pruh hyhqo glvwulexwhg wkdq wrwdo zhdowk1 Zh qg wkdw wkh phgldq yrwhu fkrrvhv wr wd{ krxvlqj fdslwdo dw d pxfk orzhu udwh wkdq exvlqhvv fdslwdo hyhq wkrxjk wklv lpsolhv d vpdoo exvlqhvv fdslwdo vwrfn dqg khqfh d orz zdjh udwh dqg d kljk lqwhuhvw udwh1 Wklv uhvxow lv forvho olqnhg wr glvwulexwlrqdo lvvxhv1 Lq wkh devhqfh ri zhdowk dqg oderu lqfrph khwhurjhqhlw / wkh htxloleulxp wd{ udwh rq krxvlqj zrxog eh pxfk kljkhu/ uh hfwlqj wkh xvxdo h!flhqf frvw ri wd{lqj exvlqhvv fdslwdo lq d g qdplf hfrqrp 1 Derxw rqh wklug ri XV krxvhkrogv uhqw wkhlu krxvlqj dqg duh olnho wr kdyh yhu glhuhqw srolf suhihuhqfhv wkdq krphrzqhuv1 Wkhuhiruh/ zh uhfrqvlghu rxu uhvxowv lq d vhwwlqj zkhuh d iudfwlrq ri wkh krxvhkrogv duh uhqwhuv1 Lq wklv fdvh/ zh dvvxph wkdw wkh uhwxuq wr uhqwdo krxvlqj lv wd{hg dw wkh vdph udwh dv wkh uhwxuq wr exvlqhvv fdslwdo1 Wkh htxloleulxp wd{ vwuxfwxuh grhv qrw fkdqjh vxevwdqwldoo zlwk wkh lqwurgxfwlrq ri uhqwhuv1 Dowkrxjk wkh phgldq yrwhu lv qrz ulfkhu lq whupv ri wrwdo zhdowk dqg kdv d vpdoohu vkduh ri klv zhdowk lq wkh irup ri krxvlqj/ kh vwloo yrwhv iru d yhu orz wd{ udwh rq krxvlqj1 D orz wd{ udwh rq krxvlqj vkliwv wkh wd{ exughq wrzdugv uhqwhuv dv zhoo dv wkh ulfkhvw krxvhkrogv rzqlqj prvw ri wkh qrq0krxvlqj zhdowk1 Zh surfhhg dv iroorzv1 Lq wkh qh{w vhfwlrq/ zh suhvhqw gdwd rq wkh glvwulexwlrq ri krxvlqj zhdowk dqg qrq0krxvlqj zhdowk1 Lq vhfwlrq 6/ zh ghvfuleh wkh prgho1 Zh glvfxvv fdoleudwlrq lq vhfwlrq 71 Wkh uhvxowv duh suhvhqwhg lq vhfwlrq 81 Lq vhfwlrq 9 zh lqwurgxfh uhqwhuv1 Zh frqfoxgh lq vhfwlrq :1 5 Wkh glvwulexwlrq ri qrq0krxvlqj zhdowk dqg krxvlqj zhdowk Lq wklv vhfwlrq/ zh eulh orrn dw wkh glvwulexwlrq ri krxvlqj zhdowk dqg wrwdo zhdowk1 Zh xvh idplo gdwd iurp wkh 5334 zdyh ri wkh Sdqho Vwxg ri Lqfrph G qdplfv +SVLG,1 Zh zloo xvh wkuhh yduldeohv1 Lq SVLG/ krxvhkrogv duh dvnhg wr uhsruw wkhlu hvwlpdwh derxw wkh pdunhw ydoxh ri wkhlu krxvh/ wklv lv zkdw zh fdoo krxvlqj zhdowk1 Wkh rwkhu zhdowk yduldeoh 5

5 zh xvh lv cwrwdo zhdowk*1 Lwv pdlq frpsrqhqwv duh w slfdoo vwrfnv/ pruwjdjhv/ edqn ghsrvlwv/ dv zhoo dv rzqhu krxvlqj1 Zkhq fdoleudwlqj rxu prgho/ zh dovr qhhg lqirupdwlrq derxw krxvhkrog*v oderu lqfrph/ zklfk zh ghqh dv wkh vxp ri oderu lqfrph ri wkh krxvhkrog ckhdg* dqg czlih* wrjhwkhu zlwk sulydwh shqvlrq lqfrph1 Wkh gdwd frqwdlq :739 krxvhkrogv1 Krzhyhu/ zh h{foxgh d qxpehu ri krxvhkrogv iurp wkh vdpsoh1 Iluvw ri doo/ zh h{foxgh doo krxvhkrogv zkr gr qrw hlwkhu rzq ru uhqw wkhlu krph1 Vhfrqg/ zh h{foxgh krxvhkrogv zlwk lqirupdwlrq plvvlqj derxw dq ri wkh deryh phqwlrqhg yduldeohv1 Lq dgglwlrq/ zh qhhg wr h{foxgh d vpdoo qxpehu ri krxvhkrogv zklfk kdyh qhjdwlyh wrwdo zhdowk wrjhwkhu zlwk d yhu orz oderu lqfrph/ vlqfh wkh frxog qrw drug srvlwlyh frqvxpswlrq lq wkh prgho1 Diwhu wklv surfhgxuh/ zh duh ohiw zlwk 99<4 krxvhkrogv1 Iljxuh 4 suhvhqwv wkh fxpxodwlyh kroglqjv ri wrwdo zhdowk dqg krxvlqj zhdowk ri wkh 99<4 krxvhkrogv1 Iljxuh 5 lq wxuq glvsod v wkh wrwdo zhdowk dqg krxvlqj zhdowk glvwulexwlrq iru rqo plggoh0djhg krphrzqhuv1 Lq vhfwlrqv 7 dqg 8 zh zloo irfxv rq wklv vxevdpsoh1 Iljxuh 4= Glvwulexwlrq ri wrwdo zhdowk dqg krxvlqj zhdowk/ doo krxvhkrogv total wealth housing wealth ! " # $ % & ' ( ) * +, -. /

6 Iljxuh 5= Glvwulexwlrq ri wrwdo zhdowk dqg krxvlqj zhdowk/ plggoh0djhg krphrzqhuv total wealth housing wealth Derxw 63( ri wkh krxvhkrogv duh uhqwhuv1 Wklv vkrzv xs dv d dw sduw lq wkh fxpxodwlyh glvwulexwlrq ri krxvlqj zhdowk lq wkh uvw jxuh1 Lw lv fohdu/ krzhyhu/ wkdw lq erwk fdvhv krxvlqj zhdowk lv pxfk pruh hyhqo glvwulexwhg wkdq wrwdo zhdowk1 Vlqfh wkh djjuhjdwh ydoxh ri wkh krxvlqj vwrfn lv derxw rqh kdoi ri wkh djjuhjdwh wrwdo zhdowk/ wkhvh jxuhv dovr lpso wkdw prvw krxvhkrogv kdyh prvw ri wkhlu zhdowk lq wkh irup ri krxvlqj1 Wkh pdlq sxusrvh ri rxu wkhruhwlfdo dqdo vlv lv wr vwxg krz wklv lv uh hfwhg lq wkh srolwlfdoo ghwhuplqhg wd{ vwdwxv ri krxvlqj1 6 Wkh prgho Zh frqvlghu d khwhurjhqrxv djhqw yhuvlrq ri wkh ghwhuplqlvwlf qhrfodvvlfdo jurzwk prgho zkhuh wkh djjuhjdwh fdslwdo vwrfn lv glvdjjuhjdwhg lqwr exvlqhvv fdslwdo dqg krxvlqj fdslwdo1 Wkh wd{ frgh lq wkh prgho glhuhqwldwhv ehwzhhq wkh lqwhuhvw lqfrph iurp exvlqhvv fdslwdo dqg wkh lpsxwhg uhqw iurp krxvlqj fdslwdo1 Dq lpsruwdqw ihdwxuh ri wkh prgho lv wkdw lw ; < = >? A B C D = > B E F G = H? E F F C E F? = E E F G = I > J F F G > F I C? D C E F G C K E = G C L M E G C K E N B O N E F G = E N B O L = D C E F N D P C? F > B F J C D P C B = B F C I F G = N? F C F > L Q = > L F G R S = = T I C? N B E F > B J = T U L > V N B > B M W X Y X Z [ \ ] X ^ _ ` ` _ a b [ c d c e f Z c g [ c Y h c b g h i Z j k l m n o l p q l r s l q r t u 7

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13 udwh rq krxvlqj ehfdxvh wkdw zrxog kdyh lpsolhg dq lpsodxvleo kljk wd{ udwh rq exvlqhvv fdslwdo lq rxu prgho1 Zh wkhq fkrrvh sdudphwhuv > > dqg W vr dv wr pdwfk wkh iroorzlqj djjuhjdwh udwlrv1 4, Exvlqhvv fdslwdo0wr0krxvlqj udwlr N@K ' 1 5, Wrwdo fdslwdo0wr0wrwdo rxwsxw udwlr EN n K@Ee\ ' =f/ zkhuh \ ' N n uk1 6, Jryhuqphqw h{shqglwxuh0wr0wrwdo rxwsxw udwlr W@\ ' f=2h1 7, Wudqvihuv0wr0wrwdo jryhuqphqw h{shqglwxuh udwlr W u@w ' f== Wkh uvw wzr ri wkhvh wdujhwv duh edvhg rq wkh QLSD1 Zh lqwhusuhw doo exvlqhvv fdslwdo lq wkh prgho dv sulydwh qrq0uhvlghqwldo dvvhwv dqg krxvlqj fdslwdo dv sulydwh uhvlghqwldo dvvhwv1 Wkh wklug wdujhw lv iurp wkh RHFG Uhyhqxh Vwdwlvwlfv1 Wkh irxuwk wdujhw fruuhvsrqgv wr fdofxodwlrqv lq Nuxvhoo dqg Uðrv0Uxoo +4<<<, derxw wkh vkduh ri wudqvihuv ri doo jryhuqphqw h{shqglwxuhv1 Wkhvh wdujhwv lpso wkh iroorzlqj sdudphwhu ydoxhv= ' f= HbD/ ' f=bddd/ J ' f= Dfb> dqg W u ' f=f.de1 Wkh wd{ udwh rq exvlqhvv fdslwdo lv ghwhuplqhg dv d uhvlgxdo iurp wkh jryhuqphqw exgjhw frqvwudlqw dqg lv ' f=effe1 Zh qrz frpsduh wkh glvwulexwlrq ri krxvlqj lq wkh prgho zlwk wkdw lq wkh gdwd1 Iru wdeoh 6/ zh kdyh fdofxodwhg wkh dyhudjh dprxqw ri krxvlqj lq hdfk ri wkh 58 zhdowk0lqfrph jurxsv1 Wkh wdeoh suhvhqwv wklv dyhudjh krxvlqj glylghg e wkh dyhudjh krxvlqj dprqj doo krphrzqhuv1 Iru lqvwdqfh/ jxuh 315< iru krxvhkrogv lq wkh uvw wrwdo zhdowk dqg wkh uvw oderu lqfrph txlqwloh phdqv wkdw krxvhkrogv lq wkdw jurxs rzq/ rq dyhudjh/ 5<( ri wkh dyhudjh dprxqw ri krxvlqj lq wkh gdwd1 Lq wkh prgho/ wkh fruuhvsrqglqj jxuh lv 63(1 Wdeoh 6 vkrzv wkdw rxu prgho urxjko pdwfkhv wkh glvwulexwlrq ri krxvlqj lq wkh gdwd1 Erwk lq wkh gdwd dqg lq wkh prgho/ krxvhkrogv lq d jlyhq zhdowk txlqwloh rzq pruh krxvlqj dv wkhlu oderu lqfrph lqfuhdvhv1 Lq wkh vdph pdqqhu/ lq dq jlyhq oderu lqfrph txlqwloh/ zhdowklhu krxvhkrogv rzq pruh krxvlqj wkdq srruhu krxvhkrogv1 Wkh odujhvw glvfuhsdqf ehwzhhq wkh glvwulexwlrqv lq wkh gdwd dqg lq wkh prgho lv wkdw wkh zhdowklhvw orz lqfrph krxvhkrogv rzq wrr olwwoh krxvlqj zkloh wkh srruhvw kljk lqfrph krxvhkrogv rzq wrr pxfk krxvlqj lq wkh prgho1 Wklv pd uh hfw dq lqfrph hhfw zlwk srru krxvhkrogv vshqglqj d odujhu iudfwlrq ri wkhlu wrwdo h{shqglwxuh lq krxvlqj wkdq ulfkhu rqhv1 Krzhyhu/ zh eholhyh wkhvh glhuhqfhv wr eh uhdvrqdeo vpdoo/ hvshfldoo jlyhq wkdw +dv wdeoh 4 vkrzv, wkh jurxsv lq txhvwlrq duh wkh vpdoohvw lq rxu vdpsoh1 ± ² ³ ± µ ³ ± ³ ¹ ² º ² ¹» ¼ ³ ± ³ ¼ ³ ² ¹ ½ ² ¾» ¹ À Á ¾ ± ½ ³ ± ³ ³ ² ± º ²   ¾ ¹» µ ³ ± û º ³ Ä ½ ³ ³ Å ³ º» à ³ ± ³ ² ¹ ½ ² ¾» ¹» Æ ² Ç ³ ± È É Ê Ë Ë Ì Í Î Ï Ð Ñ Ò Ì Ò Ó Ô Õ Ö Ø Ù Ò Ó Ô Ú Ó Û Í Ô Ì Ü Ò Ì Ò Û Ý Ò Û Þ Í Ô ß Ô Ð à Ô Ì Ü á Ø â ã ä å æ ç è é ê ä å ê ë ì é í î ï ð ñ ò ó æ ç ô ò õ ö ø ù ú û ü ý þ ÿ ü ü ü û 44

14 Wdeoh 6= Glvwulexwlrq ri krxvlqj> gdwd +ohiw, dqg prgho +uljkw,1 Oderu lqfrph txlqwloh Zhdowk txlqwloh Frpsdulvrq zlwk wkh ohiw0kdqg sduw ri wdeoh 5 vkrzv wkdw krxvlqj zhdowk lv pxfk pruh hyhqo glvwulexwhg wkdq wrwdo zhdowk1 Zlwkrxw d uhqwdo pdunhw frqvxpswlrq ri krxvlqj lv wlhg wr rzqhuvkls1 Frqvxpswlrq ri krxvlqj lq wxuq lv uhodwhg wr wrwdo lqfrph1 Vlqfh oderu lqfrph lv pruh hyhqo glvwulexwhg wkdq wrwdo zhdowk/ frqvxpswlrq ri krxvlqj lv pruh hyhqo glvwulexwhg wkdq wrwdo zhdowk1 Wkh prgho glvwulexwlrq ri krxvlqj lv wkh vwhdg vwdwh glvwulexwlrq jlyhq wkh hpslulfdo wd{ udwhv ghvfulehg deryh1 Wr wkh h{whqw wkdw wkh wd{ udwhv rq exvlqhvv fdslwdo dqg krxvlqj duh glhuhqw lq wkh srolwlfr0hfrqrplf htxloleulxp/ wkh glvwulexwlrq ri krxvlqj lv dovr glhuhqw1 Krzhyhu/ lq doo srolwlfr0hfrqrplf htxloleuld frqvlghuhg lq wkh iroorzlqj vhfwlrq/ wkh glvwulex0 wlrq ri krxvlqj glhuv rqo pdujlqdoo iurp wklv glvwulexwlrq1 8 Uhvxowv Lq wkh srolwlfr0hfrqrplf vwhdg vwdwh htxloleulxp wkh wd{ udwh rq krxvlqj lv ' f= f= Wklv wd{ udwh rq krxvlqj lpsolhv d wd{ udwh rq exvlqhvv fdslwdo ' f=esf= Wklv lv rxu pdlq uhvxow= frqvlvwhqwo zlwk wkh dfwxdo XV wd{ v vwhp/ dqg lq frqwudvw wr qrupdwlyh dqdo vhv/ lq rxu prgho hfrqrp wkh htxloleulxp hhfwlyh wd{ udwh rq krxvlqj lv vxevwdqwldoo orzhu wkdq wkh wd{ udwh rq exvlqhvv fdslwdo1 Wkh phgldq yrwhu ehorqjv wr wkh wklug oderu lqfrph dqg wkh wklug wrwdo zhdowk txlqwloh1 Lq wkh srolwlfr0hfrqrplf htxloleulxp/ klv wrwdo zhdowk lv 78( ri wkh dyhudjh wrwdo zhdowk dqg klv krxvlqj zhdowk lv :8( ri wkh dyhudjh krxvlqj zhdowk1 Wkdw lpsolhv d krxvlqj0wr0wrwdo zhdowk udwlr ri derxw 31;6 zkloh wkh djjuhjdwh udwlr lv 317;1 Dv rqh zrxog h{shfw/ krxvhkrogv kdyh yhu glhuhqw srolf suhihuhqfhv1 Lq wdeoh 7/ zh vkrz wkh prvw suhihuuhg krxvlqj wd{ udwh iru hdfk krxvhkrog w sh lq wkh srolwlfr0hfrqrplf vwhdg vwdwh htxloleulxp1 Iru wkh wdeoh/ zh frqvlghu krxvlqj wd{ udwhv ehwzhhq 3 dqg 41 Zhdowklhu krxvhkrogv suhihu d kljkhu krxvlqj wd{ udwh wkdq srru krxvhkrogv1 Lqghhg/ doo krxvhkrogv lq wkh uvw wrwdo zhdowk txlqwloh zrxog suhihu }hur ru hyhq d qhjdwlyh wd{ udwh rq krxvlqj/ zkloh doo krxvhkrogv lq wkh iwk txlqwloh zrxog suhihu d wd{ udwh htxdo wr ru 45

15 deryh 41 Lq dgglwlrq wr wrwdo zhdowk/ oderu lqfrph dovr pdwwhuv1 Lq d jlyhq zhdowk txlqwloh/ krphrzqhuv zlwk kljkhu oderu lqfrph whqg wr suhihu d orzhu wd{ udwh rq krxvlqj1 Wklv lv ehfdxvh wkh frqvxph pruh krxvlqj wkdq krxvhkrogv zlwk orzhu oderu lqfrph1 Wklv glhuhqfh lq srolf suhihuhqfhv lv qrw h{sodlqhg e kljkhu oderu lqfrph ehlqj dffrpsdqlhg e kljkhu wrwdo zhdowk1 Dv wdeoh 4 vkrzv/ lq wkh wklug dqg wkh irxuwk zhdowk txlqwlohv wkh wrwdo zhdowk lv doprvw wkh vdph dfurvv glhuhqw oderu lqfrph txlqwlohv1 Wdeoh 7= Wkh prvw suhihuuhg krxvlqj wd{ udwhv1 Oderu lqfrph txlqwloh Zhdowk txlqwloh Lq rughu wr foduli wkh uroh ri glvwulexwlrqdo lvvxhv/ zh uhfrqvlghu wkh prgho zlwk d vlqjoh jurxs1 Vlqfh zhdowk dqg oderu lqfrph khwhurjhqhlw grhv qrw dhfw djjuhjdwh yduldeohv lq wklv prgho/ wkh fdoleudwlrq lv lq doo rwkhu uhvshfwv h{dfwo wkh vdph dv deryh zlwk 58 glhuhqw jurxsv1 Zkhq wkh krxvlqj wd{ udwh htxdov wkh hpslulfdo hvwlpdwh + ' f= D,/ doo krxvhkrogv wkhq kdyh krxvlqj0wr0exvlqhvv fdslwdo udwlr htxdo wr rqh/ zklfk zdv rqh ri rxu djjuhjdwh wdujhwv lq wkh fdoleudwlrq1 Zh dovr frqvlghu glhuhqw ydoxhv iru wkh lqwhuwhpsrudo hodvwlflw sdudphwhu/ / zklfk lv wkh rqo iuhh suhihuhqfh sdudphwhu zh kdyh1 Lq dgglwlrq wr ' / xvhg lq wkh ehqfkpdun fdoleudwlrq/ zh wu ' 2 dqg ' e1 Iru erwk wkhvh ydoxhv/ zh uhfdoleudwh wkh prgho vhwwlqj djdlq ' f= D dqg pdwfklqj doo wkh suhylrxvo glvfxvvhg wdujhwv1 Lq wdeoh 8/ zh suhvhqw wkh htxloleulxp wd{ udwhv dv zhoo dv wkh pdlq djjuhjdwh udwlrv lq doo wkh irxu fdvhv frqvlghuhg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` a Z b X c d ^ X [ e X ` X [ X f g g h ] Z ` i j k l m n o p q n r s t u v w w w x y z { } ~ ƒ ˆ Š Œ Ž ƒ š œ ž Ÿ Ÿ ª «± ² ª ³ µ ¹ º»» ¼ ½ º ¾ À Á» À ¼ º  à ¼ ¾ ¼ ¼ ¹ ½ ¾ À Ä» Å Æ Ç È É Ê Ë Ì Í Î Ï Ð Ñ Ò Ó Ô Õ Ö Õ Ø Ù Ú Û Ù Ü Ý Þ ß Ù à á â 46

16 ã Wdeoh 8= Htxloleulxp wd{ udwhv iru glhuhqw prgho vshflfdwlrqv1 ä å æ ç è é ê ë ì í î ï ð ñ ò ó ô õ ö ø ù ú û ü ý þ ÿ ÿ ÿ ÿ ÿ ÿ ÿ EN n K@Ee\ W@\ ÿ ÿ ÿ ÿ ÿ ' 2 ÿ ÿ ÿ ÿ ÿ ÿ ' e Zlwk rqo rqh jurxs/ wkh vwhdg vwdwh htxloleulxp wd{ udwhv duh ' f=ef dqg ' f= eh= Zlwkrxw glvwulexwlrqdo lqfhqwlyhv/ wkh phgldq yrwhu lv ohvv zloolqj wr glvwruw exvlqhvv fdslwdo dffxpxodwlrq1 Wklv uh hfwv wkh xvxdo h!flhqf frvw ri lqwurgxflqj d wd{ zhgjh rq vdylqjv lq vlplodu lqqlwh0krul}rq prghov1 Lq frqvhtxhqfh/ zlwkrxw wkh glvwulexwlrqdo frq lfw/ wkh prgho hfrqrp zrxog hqg xs zlwk d gudpdwlfdoo kljkhu fdslwdo0wr0rxwsxw udwlr1 Fkdqjhv lq wkh suhihuhqfh sdudphwhu dhfw wkh htxloleulxp wd{ udwhv dv zhoo1 D kljkhu ydoxh ri phdqv d orzhu lqwhuwhpsrudo hodvwlflw ri vxevwlwxwlrq1 Krxvhkrogv wkhq ehfrph ohvv zloolqj wr orzhu wkh wd{ udwh rq exvlqhvv fdslwdo ehfdxvh iru wkh srru krxvhkrogv wkh ehqhwv zrxog frph dw wkh frvw ri orzhu frqvxpswlrq gxulqj wkh uvw shulrgv ri wudqvlwlrq1 Frqvhtxhqwo / wkh wd{ udwh rq exvlqhvv fdslwdo lv kljkhu dqg wkh wd{ udwh rq krxvlqj lv orzhu1 9 Lqwurgxflqj uhqwhuv Zlwk wkh fxuuhqw XV wd{ v vwhp/ wkh pdlq wd{ ehqhw ri krxvlqj 0 wkh qrq0wd{dwlrq ri wkh lpsxwhg uhqw 0 lv uhodwhg wr rzqhu krxvlqj vlqfh wkh uhqwdo lqfrph uhfhlyhg e odqgorugv lv vxemhfw wr fdslwdo lqfrph wd{dwlrq1 Dv d uhvxow/ uhqwhuv vkrxog kdyh yhu glhuhqw srolf suhihuhqfhv wkdq krphrzqhuv1 Wkhuhiruh/ lq wklv vhfwlrq/ zh frqvlghu krz lqwurgxfwlrq ri uhqwhuv dhfwv wkh frqfoxvlrqv ri wkh suhylrxv dqdo vlv1 Zh gr qrw dwwhpsw wr hqgrjhql}h wkh whqxuh fkrlfh1 Zh vlpso dvvxph wkdw vrph krxvh0 krogv uhqw wkhlu krxvlqj zkloh rwkhuv duh krphrzqhuv1 Zh dovr dvvxph wkdw uhqwdo lqfrph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