Marginal tax rates and tax-favoured pension savings of the self-employed Evidence from Sweden. Håkan Selin

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1 Margnal ax raes and ax-favoured penson savngs of he self-employed Evdence from Sweden Håkan Seln CESfo GmbH Phone: +49 ( Poschngersr. 5 ax: +49 ( Munch E-mal: offce@cesfo.de Germany Web:

2 Margnal ax raes and ax-favoured penson savngs of he self-employed Evdence from Sweden by Håkan Seln Uppsala Unversy Absrac. In recen years he role of alernaves o publc pensons has changed and he sudy of how ndvduals respond o polces ha am a promong penson savngs has emerged as a val area of economc research. The purpose of hs paper s o add o hs leraure by esmang he ax prce elascy of conrbuons o ax-favoured penson savngs accouns on a populaon of self-employed ndvduals. To hs end I explo a unque oal daa base over he Swedsh populaon ha covers he years 1999 o The emprcal analyss s complcaed by he fac ha penson conrbuons and ax prces are deermned smulaneously. When nsrumenal varables are used o address hs endogeney problem, I fnd ha he self-employed sgnfcanly ncrease her conrbuons o ax-favoured penson savngs accouns when ax prces decrease and vrual ncome ncreases. I oban a ax prce elascy of and a vrual ncome elascy of On he conrary, OLS produces esmaes wh sgns ha conflc wh sandard consumer heory. Key words: Income axaon, frnge benefs, ndvdual penson savngs, self-employmen. JEL classfcaon: G23; H24; J33; J26. Ths paper has benefed from valuable dscussons wh Thomas Aronsson, Lennar Berg, Sören Blomqus, Alex Gelber, Per Johansson, Henry Ohlsson and semnar parcpans a Uppsala Unversy and a he SUDSWEC conference. nancal suppor from he Jan Wallander and Tom Hedelus oundaon s graefully acknowledged.

3 1. Inroducon Snce he early 1990 s publc penson reforms have occuped a promnen place on he nernaonal polcal agenda and several OECD counres have subsanally reformed her polces. As documened n a recen overvew (OECD 2007, hese reforms ypcally share one crucal feaure: In order o preserve sysem susanably oday s workers are promsed less compensaon by he publc penson sysem compared wh pas generaons. As a consequence, he role of alernaves o publc pensons has changed and he sudy of how ndvduals respond o polces ha am a promong penson savngs has emerged as a val area of economc research. The purpose of hs paper s o supply new evdence on hs ssue by esmang he ax prce elascy and ncome elascy of conrbuons o ax-favoured penson savngs accouns on a populaon of Swedsh self-employed ndvduals. The emprcal analyss s complcaed by he fac ha penson conrbuons and ax prces are deermned smulaneously. When nsrumenal varables are used o address hs endogeney problem, I fnd ha he self-employed sgnfcanly ncrease her conrbuons o ax-favoured penson savngs accouns when ax prces decrease and vrual ncome ncreases. I oban a ax prce elascy of and a vrual ncome elascy of On he conrary, OLS produces esmaes wh sgns ha conflc wh sandard consumer heory. The sudy explos a unque daa base ha covers he oal of he Swedsh populaon beween he years 1999 o Ths was a perod of calm wh respec o ncome ax reforms. Also, he nsuonal framework governng ax-favoured savngs accouns was fxed. I ulse he fac ha before-ax profs, and accordngly he ax prce facng he selfemployed, vary on a year-o-year bass due o facors ha are exogenous o he sngle busness owner. The ncluson of a fxed effec, whch conrols for any me-nvaran unobserved facors ha mgh obscure denfcaon, s herefore a cenral feaure of he emprcal model. Comparsons wh e.g. random effecs IV esmaons confrm ha hs s mporan. The paper s srucured as follows. The nex secon provdes a background and dscusses he denfcaon sraegy n he lgh of prevous leraure. Secon 3 oulnes he model framework and he mehodologcal problems nvolved n he emprcal analyss. Secon 4 1

4 descrbes he daa source, whereas secon 5 presens he regresson resuls. Secon 6 concludes. 2. Background 2.1 General background Chef among he complemens o he publc sysem n Sweden, a counry ha experenced a profound penson reform n he 1990 s, s employer-provded occupaonal pensons. 1 In several respecs, employer conrbuons o occupaonal pensons are reaed ax preferenally n relaon o wage compensaon and convenonal savngs. Conrbuons are deducble boh from ncome and pay-roll axaon, bu are sll subjec o a specal wage ax. When penson asses accumulae, he yeld s normally axed a a lower rae han he capal ncome ax rae ha apples o mos oher knds of asse ncome. urhermore, afer whdrawal penson ncome s axed ogeher wh axable earned ncome. As he ncome ax schedule ypcally s progressve -- and mos people earn more ncome when hey are workng-age han when hey have rered hs sysem s poenally benefcal o he ndvdual ax-payer. However, penson asses are exremely llqud as hey canno be whdrawn before he age of 55. The desgn of he Swedsh occupaonal penson plans s deermned a a cenral level as a barganng oucome beween he employer assocaons and he unons. A vas majory, approxmaely 90 %, of he Swedsh workers s auomacally covered by a negoaed penson plan hrough collecve agreemens. In pracse, he ndvdual employee or employer lacks power o affec he relaon beween he ax-deferred amoun and he money wages. However, hs s no rue for he self-employed ndvdual, n parcular no f (she runs a busness ha s axed a he personal level. 2 As he erm suggess, he self-employed are boh n a sense employers and employees and are no covered by any collecve agreemen. In conras o he employee, he self-employed ndvdual s n poson o choose her own opmal mx of wage compensaon and penson conrbuons. Thus, f one s o emprcally examne how occupaonal pensons respond o 1 See Sundén (2006 for a descrpon of he new Swedsh penson sysem. 2 The populaon suded n hs paper does only nclude self-employed who are organsed as sole propreors or parnershps. Owners of closely held corporaons are no ncluded n he analyss as hey have he opporuny o deduc deferrals o penson accouns a he frm level. These deducons are no observed n he ndvdual ax regser daa. 2

5 changes n he ax sysem n an approprae manner one needs o urn o hs specfc group of ax payers Prevous leraure The presen paper prmarly relaes o a raher exensve leraure ha hghlghs he effec from margnal ax raes on ax-deducble conrbuons o ndvdual reremen accouns. 4 I am aware of wo prevous sudes n he leraure ha focus on he behavour of he selfemployed, namely Long (1993 and Power and Rder (2002. Boh sudes are carred ou on U.S. daa. 5 A ypcal procedure has been o regress he margnal ax rae, along wh oher explanaory varables of neres, on he conrbued amoun o ndvdual reremen accouns or alernavely he probably o conrbue. Vewed from a sylsed perspecve, papers belongng o he leraure fall no wo groups. The frs caegory, whch nvolves works by Collns and Wyckoff (1988, O Nell and Thompson (1987 and Long (1990, employ sngle cross secons and OLS or Tob echnques. Some auhors, e.g. Long (1990, dscuss he endogeney of margnal ax raes and uses he frs-dollar margnal ax rae,.e. he margnal ax rae ha apples o he frs dollar of conrbuon, n place of he endogenous regressor. However, no aemps are made o address a more suble endogeney problem: If here s a correlaon beween unobserved facors ha deermne he ncome level and he level of conrbuons an omed varable bas mgh plague he esmaes. A second caegory of papers, Mllgan (2002 for Canada, Veall (2001 also for Canada and Power and Rder (2002 for he U.S., explos ncome ax reforms, and he fac ha dfferen groups of ax payers are reaed dfferenly by such polcy changes, as he denfyng source of varaon. Panel daa s used n he wo laer sudes, whereas Mllgan (2002 uses 3 Ths s no he frs paper ha emprcally sudes he provson of frnge benefs and o hs end explos a sample of self-employed o overcome problems assocaed wh collecve decson mechansms. Wh a relaed argumen Gruber and Poerba (1994 examnes purchases of ax-deducble healh nsurance, whch consues he man bulk of frnge benefs n he U.S., on a sample self-employed persons before and afer he U.S. ax reform ac of Bascally, he rules for he savngs accouns of he Swedsh self-employed only dffer n one essenal respec from hose applyng o ndvdual reremen accouns for employees: In order o compensae he self-employed for her non-elgbly o collecvely agreed occupaonal pensons, he maxmum conrbuon lms are noceably hgher han for employees. 5 As far as I know, nohng has been wren abou he mpac of he Swedsh ncome ax sysem on frnge benefs or on penson savngs. rom a ax clenele model Agell and Edn (1990 have suded how Swedsh asse porfolos are affeced by margnal ax raes. The sock of penson wealh s, however, no ncluded n her sudy. Johannsson (2008 has esmaed he relaonshp beween lfe-cycle varables and savngs n ax-deferred ndvdual penson savngs accouns on Swedsh regser daa. She resrcs her sample o hose who have no prevously saved n prvae penson accouns. In addon, lood (2004, also on longudnal ax regser daa, has esmaed he sock of penson wealh ha relaes o hese ndvdual reremen accouns for employees. 3

6 repeaed cross secons. The resuls vary subsanally beween sudes. Whle hs approach has he mer of usng a separae exogenous source of varaon, one can recognse wo possble mehodologcal problems. rs, f ax payers ancpae major ax changes s lkely ha ncome ax reforms nduce hem o reme her conrbuons. 6 In a general dscusson of he consequences of ax reforms, Slemrod (1992 places remng of fnancal ransacons, lke he realsaon of capal gans, a he very op of he herarchy of behavoural responses o ax reforms. The sudy by Power and Rder (2002 may serve as an llusraon o he problem. They explo U.S. panel daa from 1985, 1989 and 1993, daa ha surround he 1986 reform (TRA86 ha sharply reduced margnal ax raes for hgh ncome payers and he more modes reforms of 1990 and 1993 ha somewha ncreased margnal ax raes for hgh-ncome ax payers. When Power and Rder perform dfference-n-dfference regressons separaely for and he coeffcen for he neracon erm beween he pos-reform dummy and he reamen group (hgh ncome payers akes on he expeced sgn and s sgnfcan for he frs perod bu no for he second one. I canno be excluded ha hs dfference s relaed o he naure of he ax reforms and ha larger reforms affec he mng of conrbuons. Second, large ncome ax reforms end no only o change presen ax raes, bu ypcally also expecaons of fuure raes. Snce penson asses n mos OECD counres are axed ogeher wh earned ncome when whdrawn, ncenves o save n ax-favoured accouns also depend on hese. 7 Thus, ax prce esmaes obaned from large ncome ax reforms can be dffcul o nerpre for hs reason as well. Ths paper crcumvens he above enumeraed dffcules by ulsng rch panel daa from a perod wh no major ax changes. 3. The model framework 3.1 The basc model 6 Bakja (2000 has dscussed hs problem n he conex of ax-deducble charable gvng n he U.S. 7 Generally, ncenves o save n ax-favoured accouns depend on he lengh of he holdng perod, he ax reamen of he yeld from he penson asses whle hey accumulae as well as he srucure of wealh axaon See Kar and Lyykänen (2004 for a proposal of a defnon of he effecve ax rae for prvae penson savngs. The dlemma ha fuure ax raes are unobservable s no specfc o he sudy of penson savngs. As dscussed by Poerba (2002, hs ndeed poses a general mehodologcal dffculy when conducng emprcal sudes on capal formaon and porfolo choce. 4

7 In wha follows, I wll formalse he self-employed s decson of how much o conrbue o ax-preferred penson savngs accouns as a choce beween fully axed n-cash compensaon and a ax-favoured frnge benef. Suppose ha before ax profs of he frm, Y, s gven exogenously, bu ha he ndvdual can choose wheher o exrac compensaon n he form wages or a more lenenly axed frnge benef. Toal compensaon can hen be expressed as Y ( 1 q W (1 q (1 W where W refers o wage compensaon, denoes he frnge benef, q W he pay-roll ax rae applyng o wage paymens and q s a specal ax leved on. A he personal level, W s axed accordng o a non-lnear ncome ax funcon T ( ;, where s a vecor of ax parameers. In he basc heorecal model we can hnk of T ( ; as a smooh funcon. If we le C refer o unresrced consumpon he bndng budge consran of he ndvdual has he srucure C W T ( W; m, where all marke prces are normalsed o one and m s oher exogenous ncome. Ths mples ha we are able o defne he non-lnear budge consran as a funcon of C and : (1 q Y (1 q g( C, C T ; B (2 (1 qw (1 qw (1 qw Y, where B m s oal exogenous ncome. Suppose ha he ndvdual maxmses (1 q W he well-behaved uly funcon U ( C, subjec o g( C, B and ha a unque opmum exss. An essenal feaure of he model s ha he prce of n general depends on he consumed amoun of,.e. s prce s endogenous. We now lnearse he budge consran around he opmum pon. Le q, q, Y W, be a vecor of exogenous parameers and X = {C, } he vecor of he endogenous choce varables. Suppose, *, B B* and le * C *, * X be he vecor of he opmal values for X for hese gven values of and B. As saed by Blomqus (1989, s hen rue ha Lm *, B * X P( *, B*, M m X* X (3 5

8 a he opmum, where he super scrps m and Lm denoe non-lnear and lnear Marshallan demand funcons respecvely. P refers o he vecor of lnear prces and M o exogenous ncome for he lnearsed budge consran (vrual ncome. Lnear prces are gven by P g 1 and c C P g T 1 q 1 q ( 1. In hs paper I wll esmae lnear W uncompensaed prce elasces, P, and lnear ncome elasces M. As usual uncompensaed and compensaed prce elasces are relaed by he Slusky equaon n elascy form,.e. P, c P M P M, where P M s he lnear expendure share of A pecewse lnear budge consran In realy he ax funcon s pece-wse lnear and how o descrbe he budge consran on hs premse s a key ssue f one s o arrve a a proper emprcal specfcaon. Le represen he margnal ax rae a he h segmen of he ncome ax funcon T. Moreover, le b and 1 b denoe he lower and upper lms correspondng o segmen. When axable busness ncome W Y (1 q falls n he k h bracke of he ax funcon ax ( 1 q (1 q W W paymens T can be wren as T ( W; k 1 1 ( b 1 b k ( W bk. The segmens of he 8 Suppose ha we are neresed n he effec when an arbrary elemen of, say, changes. In hs conex could be before-ax profs or a ax parameer. If we dfferenae (3 wh respec o we oban B m *, * P Lm P M Lm M, where P equaon. As dscussed by Blomqus (1989 urns ou ha Lm can be decomposed accordng o he Slusky P and M do no only depend on he srucure of he budge consran. The dervaves are also affeced by he fac ha he opmum pon changes when changes. Thus, one should keep n mnd ha here s no sraghforward relaonshp beween he sgns of he lnear and non-lnear demand elasces. 6

9 ncome ax funcon, ogeher wh Y 1 q W, generae a pece-wse lnear budge consran n he ( C, -plane. 9 Suppose ha he ndvdual s locaed a segmen l of he budge consran n he ( C, - plane and segmen k of he ncome ax funcon. The budge consran can hen locally be expressed as C P, M where l l P, l (1 q (1 k (4 (1 q W and M l k 1 1 ~ y ( b b ( ~ y b m (5 1 k k and ~ Y y. A dervaon of M s provded n Appendx C. Vrual ncome, 1 l q W M l, s he prolonged nercep of he slope of he budge lne a segmen l a he C -axs. Vrual ncome dffers from exogenous ncome a zero owng o he fac ha nframargnal conrbuons o penson schemes are deduced a a dfferen (usually hgher rae han he local rae a segmen l. In he emprcal applcaon y ~ s compued as assessed busness ncome plus (1 q (1 q W. A defnon of P, s provded n Appendx A. l 3.3 Emprcal model Lm Suppose ha ( P, M Lm 1 a2 can be represened by he reduced form ( P, M a P M 0 a such ha a1 P and a2 M. Of course, when esmang hese parameers one mus also ake ndvdual heerogeney and randomness no accoun. Le be an ndvdual ndex and a me ndex. The followng emprcal equaon for all wh 0 s posed: 9 In he conex of ax deducble charable conrbuons Reece and Zeschang (1985,p.274 provdes a formal descrpon of he budge consran n he ( C, -plane. In essenal respecs, her model s equvalen o he one presened here, even hough he emprcal approaches dffer. 7

10 ln Q (6 ln a0 a1 ln P, a M 2 ln a3 A log-log specfcaon was also used by Power and Rder (2002. Ths funconal form can also be jusfed on sascal grounds as he dsrbuon of penson conrbuons s skewed o he rgh. I assume ha, where E( 0 and s allowed o be correlaed wh he regressors. Noe ha any me-nvaran expecaons of fuure ax raes and permanen lfe me ncome wll be absorbed by he ndvdual level fxed effec. Q s a vecor of varables, ncludng a full se of me dummes, whch are assumed o be srcly exogenous. I also assume ha he selecon mechansm s srcly exogenous. Wheher or no oher exogenous ncome,.e. m n (5, should ener he vrual ncome measure, M, n he esmaons s a somewha rcky ssue. m conans ne-of-ax earnngs of he spouse, publc ransfers and asse ncome. Indeed, s a jusfed belef ha he amoun of penson conrbuons relaes dfferenly o ones own busness ncome han o e.g. he ncome of he spouse. As he ndvdual, and no he household, s he axable eny n Sweden ndvdual busness ncome s also a cenral deermnan of he ax prce. If no appropraely conrolled for, he ax prce coeffcen mgh pck up some of he varaon ha works hrough he busness ncome of he ndvdual. Therefore, oher exogenous ncome wll be excluded from he vrual ncome measure. Insead, wll ener he s coeffcen wll be separaely repored. Q vecor n logarhmc form and 3.4 Endogenous regressors Boh key regressors,.e. he lnear prce, P, and he vrual ncome, M, crucally depends on he locaon of he ndvdual a he ncome ax schedule. Ths locaon, n urn, s a funcon of he choosen amoun of volunary penson conrbuons,. Therefore, f we were o esmae (6 by OLS, a correlaon beween P and M on he one hand and he conemporaneous error erm,, on he oher s very lkely o occur owng o reversed causaly. As a consequence, he coeffcens would no be conssenly esmaed. I wll address hs problem by consrucng nsrumens ha are assumed o be correlaed wh he endogenous regressors bu uncorrelaed wh he error erm. The dea wll be o consruc a ax prce, P, and a measure of vrual ncome M ha s no a funcon of he deduced amoun of penson savngs. The new measure s creaed n he followng way. To he 8

11 assessed ncome I add back (1 q (1 q W, where ~ s he amoun of penson conrbuons ha ~ have been deduced. 10 I hen recompue margnal ax raes and vrual ncomes based on he new adjused measure of assessed ncome. In spr, hs approach o nsrumenng s close o he so-called frs-dollar ax rae nsrumen ha earler has been exploed n he leraure on ax-deducble charable gvng. 11 The excluson resrcon s ha here should be no effec on from. nsrumen P and nsrumen M gven P, M, Q and he ndvdual specfc effec I s worh nong ha he nsrumen essenally s a funcon of he ax sysem and beforeax profs. Undenably, even hough profs flucuae on a year-by-year bass due o facors ha are ousde he conrol of he ndvdual, busness ncome s sll o some exen a resul of work effor. Accordngly, as one mgh expec ases for work and savngs o be correlaed a concern mgh be ha a smulaney problem sll prevals. If so, he src exogeney assumpon s volaed. A key feaure of he model s herefore ha nsrumen P and are assumed o be srcly exogenous condoned on he ndvdual specfc effec,. M nsrumen 4. Descrpon of daa 4.1 Daa and selecon of populaon The daa maeral n hs sudy s a unque regser daa se, specally consruced by Sascs Sweden for he purpose of hs projec. or he years 1999 o 2005 conans he oal populaon of Swedsh axpayers. 12 The daa se enals very dealed ax regser nformaon. Accordngly, margnal ax raes can be compued wh a very hgh degree of precson. urhermore, a number of demographc varables are ncluded. The dependen varable, he naural log of he conrbued amoun o ax-favoured penson savngs accouns, s based on nformaon from he regser of ncome saemens. I mrrors he conrbued amoun o penson savngs repored o he ax auhores by fnancal nsuons durng he relevan ax year See Appendx E for he compuaon of ~. 11 See eldsen and Taylor (1976 for an early applcaon. One should recognse one poenal problem wh he nsrumen. If he nvesmen n penson savngs s fnanced from oher fnancal sources han frm profs a correlaon beween and he adjused measure of assessed ncome canno be compleely ruled ou. 12 I also have access o daa from 1998 ha are used o approxmae conrbuon lms for Informaon on penson conrbuons s avalable from wo sources. rs, he regser of ncome saemens enals daa on he conrbued amoun o penson savngs, whch are repored o he ax auhores by fnancal 9

12 When selecng he suded populaon he nsuonal framework governng deducons for penson savngs pose some mporan consrans. rs, he ax payer should repor posve ncome from self-employmen. Income from self-employmen can eher be n he form of ncome from sole-propreorshps ( nkoms av enskld närngsverksamhe or from parnershps ( handelsbolag. Second, he axpayer s no allowed o repor any wage ncome from employmen. Ths excluson s made snce self-employed who earn wage ncome may choose wheher o make he deducon agans wage ncome or self-employmen ncome. To nclude he laer group would herefore complcae he analyss. Thrd, he age of he ndvdual should fall beween 19 and 54. Ths resrcon s made snce penson ncome can be whdrawn from he age of 55. Afer hese exclusons a populaon of around 70,000 o 85,000 ndvduals for each year remans. Ths subpopulaon corresponds o approxmaely 2 % of he Swedsh labour force. Ths fgure s consderably lower hen he share of enrepreneurs repored n he labour force surveys of Sascs Sweden, where hs share ypcally s abou 10 percen. Ths s because my suded populaon does no nclude ndvduals who earn wage ncome n addon o busness ncome. In addon, he seleced populaon excludes corporae owners. These are poenally subjec o collecve agreemens and/or have he opporuny o deduc deferrals o penson accouns a he frm level. Ths laer knd of deducons s no observed n he ndvdual ax regser daa. 4.2 A look a he daa Summary sascs, boh for he enre seleced populaon and he populaon condoned on makng posve penson conrbuons, are repored n Appendx D for all varables appearng n he emprcal analyss. I s noceable ha he populaon s heavly domnaed by males and by relavely elderly persons. When all observaons for he years 1999 o 2005 are pooled 57 percen of he populaon makes penson conrbuons. gure 1 reveals ha hs share vares very lle durng he me perod. The mean conrbued amoun s also relavely sable around SEK 16,000, even hough a small rend wse ncrease n penson conrbuons can be dscerned. I canno be excluded, however, ha hs rend s due o composonal changes n he underlyng populaon. gure 2 shows ha here were no major changes n he average of nsuons (varable label: akupens. Second, n he ax regsers here s also nformaon on he amoun ha he busness owner has deduced and for whch (she has pad a specal wage ax (varable label: aslspe. In mos cases, hese wo varables are dencal. There s, however, a consderable fracon of busness owners wh zero aslspe bu posve akupens, probably because specal wage ax s no leved on all deducons. Therefore, I have chosen o ulse akupens as my dependen varable. I do, however, explo aslspe when I approxmae conrbuon lms (see Appendx E. 10

13 margnal ax prces durng he perod. The compuaon of ax prces s descrbed n Appendx A Share of conrbuors Conrbued amoun gure 1. The share of conrbuors and mean conrbued amoun by year, expressed n SEK n he prce level of gure 2. Mean margnal ax prce n he seleced populaon by year. Table 1 characerses mean ax prces, he mean proporon wh conrbuons and he mean conrbued amoun condonal on conrbung wh a posve amoun by ax bracke n

14 Snce hs was a perod of calm n he area of ncome axaon, he ax schedule was que smlar n oher years. The populaon means for each bracke refers o he group of ndvduals whose acual assessed ncome falls n ha specfc nerval. I s srkng ha only a small mnory of he suded populaon s o be found n brackes (7-(9 where he federal ax rae apples. Conversely, a large majory of axpayers resde n nervals where he margnal ax rae s affeced by he phase ou (segmen 5 and phase n raes (segmen 3 of he sandard deducon. The proporonal local ax rae s pad on all segmens excep for (1. The rghmos column of Table 1 repors he dsrbuon of axpayers when hese are sored by her adjused busness ncome. The laer ncome measure s dencal o ha used n he nsrumenaon procedure,.e. I have added back penson deducons o he acual busness ncome. Thus, dscrepances beween he wo rghmos columns reflec ransons along he ax schedule ha are due o penson deducons. I s noeworhy ha he hree uppermos ax brackes, where ax prces are he lowes, n oal conans 2,179 fewer axpayers when adjused busness ncome s used o sor ax payers. I s also vsble from Table 1 ha boh he proporon wh conrbuons and he conrbued amoun ncreases wh ncome. A regresson analyss s needed o separae he effecs from ncome and ax prces. Table 1. Summary sascs by ax bracke n Bracke Upper segmen lm n SEK Mean ax prce Share wh posve conrbuons Mean conrbued amoun (condonal on conrbung Number of observaons wh acual busness ncome n he nerval Number of observaons wh adjused busness ncome n he nerval ( (0.000 (0.467 (14411 ( (0.009 (0.484 (9379 ( (0.007 (0.500 (10933 ( (0.009 (0.499 (11565 ( (0.010 (0.486 (

15 ( (0.009 (0.446 (25668 ( (0.009 (0.435 (34448 ( (0.009 (0.437 (41283 ( (0.009 (0.433 (58005 Sandard devaons are n parenhess. The box-plo of gure 3, whch vsualses he dsrbuon of log conrbuons by ncome decle, confrms ha conrbuons end o ncrease wh ncome. I have creaed decles by orderng all 180,380 unque ndvduals n he populaon by her medan adjused busness ncome for he years ha hey parcpae n he underlyng populaon. gure 4 nsead dsplays he dsrbuons of he log ax prce nsrumen and he log ax prce by decles ha are defned n he same way. The dsperson of ax prces s he hghes a he boom and a he op of he ncome dsrbuon. A he boom, hs s explaned by he combned effec from hgh ransory busness ncomes and a szable dscree jump n ax prces beween he frs and he second ax bracke (see Table 1. The large dspersons n ax prces n he wo hghes decles are relaed o he sharp ax prce dscrepancy beween brackes where federal ax raes are leved (brackes (7-(9 n Table 1 and oher nervals of he ax funcon. In he wo uppermos decles, here are marked dfferences n he dsrbuons of he nsrumened log ax prce and he acual log ax prce. Ths phenomenon s very mporan and mrrors behavoural responses. Remember ha he nsrumen s a funcon of a measure of busness ncome o whch penson deducons have been added back. In he 9 h decle he dsrbuon of nsrumened log ax prces s much wder han ha for acual log ax prces. The oppose holds rue for he 10 h decle. Apparenly, self-employed belongng o he 10 h decle earn adjused ncomes ha place hem n he federal ax brackes. However, a large fracon of hese clam penson deducons and hereby swch ax bracke. In he 9 h decle, unadjused ncomes fall on boh sdes of he knk pon for federal axaon. However, when penson deducons have been made, few ax payers n he 9 h decle are lef n he uppermos brackes. 13

16 Log conrbuons gure 3. Log conrbuons o ax-favoured penson savngs accouns by decle. Boxes are bordered a he 25 h and 75 h percenles. The upper (lower horzonal lne s gven by he larges (smalles value ha s less (greaer han or equal o he hrd (frs quarle plus (mnus 1.5 mes he ner quarle range Log ax prce - nsrumen Log ax prce gure 4. Log ax prce nsrumen and log ax prce by decle. Boxes are bordered a he 25 h and 75 h percenles. The upper (lower horzonal lne s gven by he larges (smalles value ha s less (greaer han or equal o he hrd (frs quarle plus (mnus 1.5 mes he ner quarle range. 14

17 5. Regresson resuls 5.1 Baselne resuls The baselne regresson resuls are repored n Table 2. The frs hree columns show he fxed effecs OLS resuls wh dfferen ses of conrol varables ncluded n he regressons, whereas he hree rghmos columns sae he correspondng IV esmaes. When ncome conrols are added, n columns (2-(3, he OLS-esmaes of he lnear own prce elascy, P, ake on an unexpeced posve sgn. P s esmaed o be 0.4. The esmaed vrual ncome elascy M s szable, around 0.32, and suggess ha conrbuons o ax-favoured penson savngs accouns are a lnear normal good. A remarkable mplcaon of he OLS esmaes s ha he lnear compensaed prce elascy, whch s gven by he Slusky, c P relaonshp P P M s posve. Ths fndng s a odds wh sandard M consumer heory, whch predcs ha own compensaed elasces always should be nonposve snce he subsuon marx s negave semdefne. Table 2. Baselne regresson resuls. Dependen varable: Log conrbuons xed effecs OLS xed effecs IV (1 (2 (3 (4 (5 (6 Log ax prce (0.012*** (0.013*** (0.013*** (0.019*** (0.025*** (0.025*** Log vrual ncome (0.004*** (0.004*** (0.005*** (0.005*** Log oher ncome (0.002*** (0.002* (0.002*** (0.002** Conrol varables No No Yes No No Yes Tme dummes Yes Yes Yes Yes Yes Yes Observaons Number of ndvduals

18 Sandard errors n parenhess. *** denoes sgnfcance a a level of 1 %, ** a a level of 5% and * a a level of 10%. See Appendx Y for a descrpon of he full se of conrol varables. The pcure s, however, reversed when nsrumenal varables are used. As descrbed above, he nsrumens for he log ax prce and he log vrual ncome are consruced by removng he endogenous componen from he assessed busness ncome of he ndvdual and hen recompung hese wo varables. An appealng propery of he nsrumens s ha hey explan a consderable par of he varaon n he endogenous regressors. The frs sage - sascs of he excluded nsrumens are exremely hgh n boh frs sage regressons. 14 The mos srkng feaure of he IV regresson resuls s ha he prce elasces now ake on sgns ha are n accordance wh consumer heory. The lnear uncompensaed elascy, P, s esmaed o when ncome varables are ncluded n he regressons. The esmae of he vrual ncome elascy sll ndcaes ha conrbuons are a normal good. The magnude of he elascy has, however, drascally decreased and s now esmaed o 0.11 when he full se of conrol varables are added n column (6. The sharp dscrepancy beween he OLS and IV esmaes clearly pons o ha he reverse causaly problem oulned n secon 3.4 s a severe one: By deducng penson conrbuons he self-employed ndvdual smulaneously alers (usually rases her own ax prce. As gure 4 made clear, he dsrbuons of he endogenous ax prce regressor and s nsrumenal varable dffers, n parcular a hgher ncome levels. Obvously, when hs endogeney problem s unaddressed he esmaed prce and vrual ncome elasces are based upwards. Table 2 also reveals ha s crucal o conrol for he ncome varables. In he OLS case, he sgn of he prce elascy esmae s negave when he ncome varables are excluded (column 1 and n he IV case he esmaed elascy s consderably larger n absolue erms (column 4. On he oher hand, addng a hos of conrol varables (whch are all lsed n Appendx D makes lle dfference o he resuls. To some exen hs s explaned by he fac ha a majory of he conrol varables are raher me-nvaran n naure, renderng he denfyng varaon o be que small. rom Table 2 can also be seen ha he elascy esmaes for oher exogenous ncome are subsanally lower han he vrual ncome elasces. As a robusness check, I have also esmaed analogous models, where exogenous ncome has been ncluded n he compuaon 14 or he full model, column 6, he values of hese -sascs are 84,000 (frs sage for log ax prce and 1,700,000 (log vrual ncome. 16

19 of he vrual ncome measure. or he full model, correspondng o column (6, he response n log ax prces s hen somewha sharper, he coeffcen s -0.74, and he vrual ncome elascy s almos halved ( However, n ha seng one canno rule ou ha he ax prce coeffcen capures varaon ha works hrough own busness ncome. Wh some excepons (Veall (2001 and Ven and Wse (1988 he qualave resuls repored here resemble hose earler found n he leraure on how prvae penson savngs respond o margnal ax raes. 16 Quanavely, he obaned ax prce elascy esmaes are lower han hose recenly found by Power and Rder (2002. They esmaed a ax prce elascy of -2.0 on a sample of self-employed ndvduals n he U.S. 5.2 The dscree margn The heorecal framework descrbes he choce along he connuous margn. Noneheless, s of neres o sudy how he key ndependen varables relae o he dscree decson wheher or no o conrbue o ax-favoured penson savngs accouns. No a leas for he purpose of descrpve sascs. I have herefore esmaed fxed effecs lnear probably models on he complee populaon. The resuls from hs exercse are dsplayed n Table 3. Agan, when he endogenous varables are used o esmae he probably o conrbue (column 1 an unexpeced posve relaonshp beween he log ax prce and he dependen varables arses. If we nsead urn our aenon o a specfcaon where he nsrumens are regressed drecly on he probably o conrbue (column 2 he ax prce coeffcen exhbs expeced sgns. In fac, a comparson of columns (1 and (3 suggess ha he coeffcens for he log ax prce are smlar n absolue magnude for OLS and IV, bu ha he sgns of he wo coeffcens dffer! If we evaluae he mpled elascy a he mean value of he probably o conrbue (0.57 we oban an elascy of when explong nsrumenal varables. In he lgh of prevous leraure, hs s a modes elascy esmae. Table 3. Regresson resuls for he dscree margn. Dependen varable: An ndcaor varable for makng conrbuons. xed effecs OLS xed effecs IV (1 (2 (3 Log ax prce ull resuls can be provded upon reques. 16 Ths also holds rue for sudes ha have ncluded he endogenous margnal ax rae as a regressor, see e.g. Collns and Wyckoff (1988 who sudy ax-favoured reremen savngs on a sample of non-self-employed ndvduals n he U.S. A probable reason o why he endogeney problem s much more severe n my sudy s ha he deducon lms are consderably more generous for self-employed. 17

20 (0.004*** (0.005*** Log ax prce nsrumen (0.004*** Log vrual ncome (0.001*** (0.001*** Log vrual ncome nsrumen (0.001*** Log oher ncome (0.000*** (0.000*** (0.000*** Conrol varables Yes Yes Yes Tme dummes Yes Yes Yes Observaons Number of ndvduals Sandard errors n parenhess. *** denoes sgnfcance a a level of 1 %, ** a a level of 5% and * a a level of 10%. See Appendx D for a descrpon of he full se of conrol varables. 5.3 Comparson wh alernave esmaors Table 4 repors resuls from regressons where a random effecs IV esmaor and a pooled IV esmaor are employed. If he unobserved heerogeney,, s uncorrelaed wh he covaraes random effecs and fxed effecs esmaons should yeld smlar resuls. Table 4 ndcaes ha hs s no he case. The esmae of he ax prce elascy s now -0.89, whch can be compared wh for he fxed effecs case. 17 The vrual ncome elascy s esmaed o 0.225, whch s consderably larger han he fxed effecs esmae of A Hausman es forcefully rejecs he null hypohess ha he coeffcen parameer vecors generaed by he random effecs and fxed effecs esmaor are equal. When observaons from all years are pooled boh he ax prce elascy and vrual ncome elascy ncrease even more n absolue value. An advanage wh he wo alernave esmaors s ha hey allow us o oban a vew on he relaonshp beween he me-nvaran gender varable and conrbuons. Ineresngly, he 17 Here I le IV random effecs esmaor refer o wha n he economercs leraure s known as he G2SLS esmaor. Smlar resuls are obaned when he alernave esmaor, EC2SLS, s employed. See Balag and L (1992 for a descrpon and dscusson of hese wo esmaors. 18

21 coeffcen for he male dummy s posve. 18 Moreover, he esmaed coeffcens for he quadrac n age n Table 4 sugges ha he conrbued amoun o penson savngs ncreases n age bu a a decreasng rae. Table 4. Resuls from alernave esmaons. Dependen varable: Log conrbuons Random effecs IV Pooled IV (1 (2 Log ax prce (0.023*** (0.026*** Log vrual ncome (0.004*** (0.004*** Log exogenous ncome (0.001*** (0.002*** Male (0.009*** (0.006*** Age (0.003*** (0.002*** Age squared (0.000*** (0.000*** Observaons Number of ndvduals Sandard errors n parenhess. *** denoes sgnfcance a a level of 1 %, ** a a level of 5% and * a a level of 10%. See Appendx Y for a descrpon of he full se of conrol varables. 6. Concluson The purpose of hs paper has been o esmae he ax prce elascy and vrual ncome elascy of conrbuons o ax-favoured penson savngs accouns on a populaon of selfemployed ndvduals. To hs end I have exploed a unque oal daa base over he Swedsh populaon ha covers he years 1999 o A dsngushng feaure of hs sudy, n comparson wh prevous relaed works, s ha I have used several years of panel daa from a perod when no major ax reforms occurred. To denfy varaon n ax prces and vrual ncomes I have exploed he fac ha before-ax profs of he self-employed vares due o facors ha are ousde he ndvdual s conrol. When nsrumenal varables are used o address he problem ha ax prces are endogenous, I fnd ha he self-employed sgnfcanly ncrease her conrbuons o ax- 18 Conversely, he male dummy akes on he oppose sgn when smlar (non-repored esmaons are carred ou for he dscree margn. 19

22 favoured penson savngs accouns when ax prces decrease and vrual ncome ncreases. I oban a ax prce elascy of and a vrual ncome elascy of On he conrary, OLS produces esmaes wh sgns ha conflc wh sandard consumer heory. To sum up, hs sudy provdes clear evdence ha Swedsh self-employed aler her conrbuons o axfavoured penson savngs accouns o when margnal ax raes, and hereby ax prces, change. References Agell, J & P.A. Edn (1990 Margnal axes and asse porfolos of Swedsh housholds, Scandnavan Journal of Economcs 92(1, pp Bakja, J. (2000 Dsngushng ransory and permanen prce elasces of charable gvng wh pre-announced changes n ax law, Mmeo, Wllams College. Balag, B.H and Q. L (1992 A noe on he esmaon of smulaneous equaons wh error componens Economerc Theory 8, p Blomqus, N.S. (1989 Comparave sascs for uly maxmzaon models wh nonlnear budge consrans, Inernaonal Economc Revew 30(2, Collns, Jule H, and J.H. Wyckoff (1988 Esmaes of ax-deferred reremen savngs behavor, Naonal Tax Journal, pp eenberg, D. (1987 Are ax prce models really denfed : he case of charable gvng, Naonal Tax Journal 40(4, pp eldsen, M. & A. Taylor (1976 The ncome ax and charable conrbuons, Economerca 44(6, p lood, L. (2004 ormaon of wealh, ncome of capal and cos of housng n SESIM, mmeo. Gruber, J. & J. Poerba (1994 Tax ncenves and he decson o purchase healh nsurance: evdence from he self-employed Quarerly Journal of Economcs 199(3, pp Gruber, J. & J. Poerba (1996 Tax subsdes o employer-provded healh nsurance NBER Workng paper No Johannsson, I (2008 Prvae penson savngs: gender, maral saus and wealh evdence from Sweden n 2002, mmeo. Long, J.E. (1990 Margnal ax raes and IRA conrbuons Naonal Tax Journal 43(2, pp Long, J.E. (1993 Esmaes of ax-favoured reremen savng behavour of he selfemployed, Publc nance Revew 22(2, p

23 Kar, S. and T. Lyykänen (2004 A mehod o calculae he effecve ax rae on prvae penson savngs wh an applcaon o nnsh ax reform Governmen Insue for Economc Research, Helsnk, mmeo. OECD (2007 Pensons a a Glance. Publc Polces Across OECD counres edon. Organsaon for economc co-operaon and developmen, OECD. O'Nel, C.J. and R.G. Thompson (1987 Parcpaon n ndvdual reremen accouns: An emprcal nvesgaon Naonal Tax Journal 40, pp Mllgan K. (2002 Tax-preferred savngs accouns and margnal ax raes: evdence on RRSP parcpaon Canadan Journal of Economcs 35(3, pp Power, L. & M. Rder (2002 The effec of ax-based savngs ncenves on he selfemployed Journal of Publc Economcs 85(1, pp Poerba, J. (2002 Taxaon and Porfolo Srucure: Issues and Implcaons n L. Guso, M. Halassos, and T.Jappell, eds., Household Porfolos (MIT Press, 2001, Reece, W and K. Zeschang (1985 Conssen esmaon of he mpac of ax deducbly on he level of charable conrbuons, Economerca, 53, Slemrod, J. (1992 Do axes maer? Lessons from he 1980 s The Amercan Economc Revew 82(2, p Sundén, A. (2006 The Swedsh experence wh penson reform Oxford Revew of Economc Polcy 22(1, pp Veall, M (2001 Dd ax flaenng affec RRSP conrbuons?, Canadan Journal of Economcs 34(1, pp Ven, S.. and D.A. Wse (1988 The deermnans of IRA conrbuons and he effec of lm changes n Pensons n he U.S. Economy, ed. Z. Bode, J. Shoven and D.A. Wse (Chcago: Unversy of Chcago Press. 21

24 Appendces Appendx A. Compuaon of We have already saed ha P P, l (1 q (1 k. The margnal ax rae a he k :h segmen (1 q W of he ncome ax funcon, k, s compued accordng o he formula ( LTR TR *(1 RR P P (A.1 k k k k k k where LTR s he local ax rae, TR he federal ax rae, RR he reducon rae applyng o he sandard deducon and P a mandaory penson fee ha s deducble agans assessed ncome. or a gven muncpaly and year LTR s consan on all segmens of he ax funcon excep for he frs one, where s zero due o he sandard deducon. The average local ax rae has been hoverng around percen durng he perod. 19 TR s zero for segmens up o SEK 310,200 n Snce 1999 here are wo levels of TR, namely 0.2 and As he sandard deducon s phased n a lower ncome levels and hen s phased ou a hgher levels, RR could eher be negave or posve. The phase n rae was 0.25 beween 1999 and 2002 and 0.2 beween 2003 and or he whole perod of sudy he phase ou rae has been 0.1. The mandaory penson fee ( allmän pensonsavgf, P, s reaed as a par of he ncome ax sysem. Ths fee was leved on ncomes up o he lm for penson benefs n he publc penson sysem. In pracse here was no fscal connecon beween he fee and he publc penson benefs. Accordngly, whou any mplcaons for he penson benefs has been reduced durng he perod of sudy, from n 1998 o n Unl 1999, he local ax rae ncluded a church ax. 22

25 How o handle (1 q (1 q W n he expresson P, l (1 q (1 k s a more rcky ssue. (1 q W rom a legal pon of vew boh he specal ax leved on penson conrbuons ( särskld löneska, q, and he pay-roll ax ( egenavgfer, q W, should be seen as axes. However, n conras o q, q W generaes socal benefs, ncludng penson benefs, up o ceran moneary lms ha are deermned by he prce basc amouns and he ncome basc amouns. Here I do, however, rea q W as a pure ax. or he whole perod of sudy q whereas q W gradually declned somewha from n 1998 o n Appendx B. Imporan rules wh respec o ax-deducble penson conrbuons B1. Maxmum deducon lms rom 1999 and onwards, he maxmum deducon amouns o 35 percen of busness ncome, even hough s no allowed o exceed 10 basc amouns. or he whole perod, he ncome base for calculang he maxmum deducon s always busness ncome ne of oher deducons. The wo key deducons were sums allocaed for expansons [ avsänngar för expansonfond ] and ransformaon of earned ncome o capal ncome [ ränefördelnng ]. When calculang he conrbuon lm for a specfc ax year, he sole propreor may use he maxmum of he acual ax year ncome and he precedng ax year s ncome. B.2 Oher rules The man requremen for ax-preferenal reamen of penson capal s ha accumulaed asses are no allowed o be whdrawn before he age of Conrbuons o a ax-deferred savngs plan can eher be made n he form of purchases of radonal penson nsurance or deposs o a specal penson savngs accoun. The laer knd of savngs form, whch enables he ndvdual o have dsposal over her own volunary penson savngs porfolo, was nroduced n The yeld ax s pad by he nsurance companes or he fnancal nsuon ha admnsers he penson capal. I s calculaed by mulplyng 15 percen of 20 An neresng aspec of hs exreme llqudy from he pon vew of he self-employed ndvdual s ha penson asses are no dsranable -- n he case of a bankrupcy he penson wealh of he sole propreor s no affeced. Thus, rsk elmnaon n a more narrow sense han he more general precauonary savngs move mgh underle he nvesmen n penson nsurance or penson savngs accoun. 23

26 he sae lendng rae by he fund capal. The sock of penson asses was exemped from wealh axaon. Appendx C. Vrual ncome Le us defne N as he segmen of he ncome ax funcon no whch y ~ falls. As n he man ex, k s he segmen no whch W falls. Le f be he lower lm o he h segmen of he budge consran n he ( C, -plane. The segmen lms are defned by (c.f. Reece and Zeschang 1985: f 0 1 (C.1 f ~ l y bn l1, l [2, N] (C.2 Vrual ncome a segmen l s gven by he followng recursve formula: M N N N 1 ~ y ( b b ( ~ y b m (C.3 M l M l ( 1 p l p l 1 f l, l [2, N ] (C.4 Inserng p 1 (1, and (C.2 n (C.4 yelds equaon (5 n he man ex. l ( N l1 k 24

27 Appendx D. Descrpon of varables and summary sascs Table A.X Descrpve sascs Populaon condonal on Complee populaon conrbung Mean Sandard devaon Mean Sandard devaon Log conrbuons Share wh posve conrbuons Log ax prce Log ax prce - nsrumen Log vrual ncome Log vrual ncome - nsrumen Log oher ncome Male Age Age squared Chldren aged below Chldren aged beween 4 and Chldren aged beween 0 and Couny dummes: Sockholm Uppsala Södermanland Ösergöland Jönköpng Kronoberg Kalmar Goland Bleknge Skåne Halland Väsra Göaland Värmlands

28 Örebro Väsmanland Dalarna Gävleborgs Väsernorrland Jämland Väserboen Norrboen Type of educaon (dummes General programmes Educaon Humanes and ars Socal scences, busness and law Scence, mahemacs and compung Engneerng, manufacurng and consrucon Agrculure and and veernary Healh and welfare Servces Unknown Level of educaon (dummes Less han 9 years of schoolng Prmary or secondary educon 9-10 years Upper secondary educaon Pos-secondary educaon less han 2 years Pos-secondary educaon more han 2 years Posgraduae educaon Dummes for maral saus Sngle, never legally marred Marred man Marred woman, no cohabng wh he spouse Dvorced person and no remarred Wdow/wdower Marred woman, cohabng wh he spouse Regsered parner (men Regsered parner (women Year dummes: year year year year year year

29 year # observaons Appendx E. Compuaon of ~ The dependen varable n he regressons mrrors all deferrals ha have been made o axfavoured penson accouns durng he relevan ax year. However, when addng back he deduced amoun of conrbuons o he busness ncome measure s crucal no o add back conrbuons ha no have been deduced. Oherwse, a correlaon beween he error erm and he ndependen varable s lkely o occur. Whle usng he varable labels from he offcal Swedsh ax regsers I have defned, ~, as ~ ' aslspe' f ' aslspe' ' akupens' ~ max( ded lm,' akupens' oherwse The deducon lm, dedlm, s defned as ded lm 0.5 PBA mn(10 PBA,max( BASE, BASE 1, where BASE nake nakhb q nake nakhb q aslspe'. 'aslspe' s he ' ' ' ' W, (' ' ' ' ', deduced amoun for whch he busness owner has pad a specal wage ax, conrbued amoun repored by fnancal nsuons, PBA s he prce basc amoun, s assessed busness ncome from sole propreorshps, from parnershps. 'akupens' s he ' nake' ' nakhb' s assessed busness ncome 27