Are Taxes Capitalized in Bond Prices? Evidence from the Market for Government of Canada Bonds* Stuart Landon **

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1 PRELIINARY DRAFT Are Taxes Capalzed n Bond Prces? Evdence from he arke for Governmen of Canada Bonds* Suar Landon ** Deparmen of Economcs Unversy of Albera Edmonon, Albera Canada T6G 2H4 14 ay 2008 Absrac Ths paper nvesgaes he exen o whch corporae and personal ncome axes are capalzed n he prces of Governmen of Canada bonds. Ths s mporan o boh purchasers and ssuers of bonds snce he degree of ax capalzaon has mplcaons for marke bond yelds and afer-ax nvesmen reurns. The exen of he capalzaon of axes n bond prces may also affec esmaes of he erm srucure, has mplcaons for ax ncdence and can denfy he margnal nvesor n he bond marke or wheher one exss. The resuls ndcae ha he axes pad by fnancal-secor corporaons were almos compleely capalzed n bond prces durng he perod Ths suggess ha, durng hs perod, he margnal nvesor was a fnancal-secor corporaon, raher han an ndvdual, a non-fnancal corporaon or a ax-exemp eny, and ha bond prces moved n response o changes n corporae ax raes. For he perod , he capalzaon of corporae and personal ncome axes n bond prces s esmaed o be near zero, mplyng ha he margnal nvesor n hs perod faced a zero ax rae. The change n he paern of ax capalzaon n he early 1990s occurred a a me when here were nsuonal and regulaory changes n he marke for Governmen of Canada bonds ha augmened marke lqudy, ncreased ransparency, and lowered ransacons coss. *The auhor hanks Bev Dahlby and Ergee Ferede for provdng he corporae ncome ax rae daa. Helpful commens were provded by Consance Smh and semnar parcpans n he School of Economcs and Fnance a Vcora Unversy of Wellngon. **Auhor emal: Suar.Landon@ualbera.ca

2 1. Inroducon The degree of ax capalzaon n bond prces has mplcaons for bond yelds and afer-ax nvesmen reurns, so an undersandng of he mpac of axes on bond prces s of fundamenal mporance o purchasers of bonds, such as prvae nvesors and porfolo managers, and o bond ssuers, such as governmens and corporaons. As noed by Pye 1969 and Robchek and Nebuhr 1970, he capalzaon of axes n bond prces and, hus, bond yelds can have mporan consequences for esmaes of he erm srucure. An accurae specfcaon of he erm srucure s an mporan componen of models developed n recen years o explan cred spreads and o prce cred rsk dervaves and oher conngen clams. 1 The mpac of ax changes on bond prces s also mporan o ax ncdence and can be used o denfy he margnal nvesor n he bond marke and, hereby, o clarfy he role of dfferen ypes of marke parcpans n he deermnaon of bond prces. Snce ax raes generally dffer across nvesor ypes, f bond prces reflec he ax poson of one parcular ype of nvesor, hs could creae profable radng opporunes for oher nvesor ypes Green and Ødegaard Whch group ulmaely deermnes prces s an emprcal ssue Green and Ødegaard 1997, 611 abou whch no clear consensus has been reached Chalmers 1998, ackay, Prsman and Tan Ths paper presens emprcal evdence on he degree of ax capalzaon n Governmen of Canada bond prces. In so dong, makes several conrbuons. Unlke much of he leraure, ncorporaes daa on boh corporae and personal ncome ax raes and explcly examnes wheher, and o wha exen, hese axes have been capalzed n bond prces. As a resul, he analyss can assess wheher a parcular ype of ax has been capalzed n bond prces. Ths makes possble o deermne wheher a margnal nvesor exss and, f so, o denfy whch of he hree prncpal ypes of nvesors n bonds ndvduals, corporaons or non-axed enes s he margnal 1 ackay, Prsman and Tan 2000 sugges ha managers of fxed ncome porfolos have generally gnored he poenal effec of axes on he erm srucure even hough small changes n he erm srucure can have poenally large effecs on he value of fxed ncome porfolos. 1

3 nvesor. The use of acual ax daa also means ha s possble o drecly esmae he degree of ax capalzaon. Prevous sudes end o esmae mpled ax raes eher n a sngle perod or averaged over mulple perods raher han ncorporae ax rae daa drecly. The use of mpled ax raes makes more dffcul o relae esmaes of ax capalzaon o a parcular ax ype and o measure he degree of ax capalzaon. 2 The emprcal analyss ulzes daa on bond pars, whch makes unnecessary o esmae he enre yeld curve. 3 uch of he leraure uses an emprcal mehodology ha nvolves jon esmaon of he erm srucure and mpled ax raes see, for example, cculloch 1975, Jordan 1984, Lzenberger and Rolfo 1984a, Ehrhard, Jordan and Prsman 1995, Green and Ødegaard 1997, Elon and Green 1998, Elon, Gruber, Agrawal and ann 2001, Lu, Sh, Wang and Wu sspecfcaon of he erm srucure could poenally affec esmaes of he degree of ax capalzaon. Furher, o esmae he enre erm srucure, a large number of observaons s requred a each pon n me. Followng Green and Ødegaard 1997, he esmaon mehodology used here employs a non-lnear specfcaon of he bond prcng formula,. An alernave approach, used by Lzenberger and Rolfo 1984a and ackay, Prsman and Tan 2000, for example, employs a 2 I s possble o use mpled ax raes o denfy he margnal nvesor ype, bu he process ofen becomes que complcaed. For example, Lzenberger and Rolfo 1984a esmae mpled neres ncome ax raes assocaed wh dfferen pre-specfed capal gans ax raes, where hese capal gans ax raes are he raes ha apply o dfferen ypes of axpayers. Lzenberger and Rolfo hen compare her esmaes of he mpled neres ncome ax rae o he raes faced by acual axpayers for each pre-specfed capal gans ax rae. If he esmaed rae s close o ha of an acual nvesor ype, Lzenberger and Rolfo conclude ha hs ype of axpayer s lkely o be he margnal nvesor. An alernave ha does no use acual ax rae daa or esmae mpled ax raes s employed by ackay, Prsman and Tan They specfy four hypohecal ax brackes, one of whch corresponds o ax-exemp nvesors, whle anoher s close o he ax bracke faced by corporaons n Canada. Usng Canadan bond prce daa, ackay, Prsman and Tan 2000 esmae afer-ax yeld curves for each of hese four hypohecal ax brackes. If he yeld curve esmaed for a parcular ax bracke can explan acual bond prces, hey conclude ha hs s he ax bracke of he represenave nvesor. The resuls of ackay, Prsman and Tan show ha here exss a represenave nvesor, bu he ax bracke assocaed wh hs nvesor does no correspond o an acual ax bracke. 3 Anoher srand of he leraure whch also does no requre esmaon of he erm srucure of neres raes uses bond rples hree bonds from he same ssuer wh he same maury dae, bu dfferen coupons and arbrage ess. See Lzenberger and Rolfo 1984b, Ronn and Shn 1997, Elon and Green 1998 and ackay, Prsman and Tan 2000, for example. The applcably of hs mehodology s lmed by he small quany of daa avalable for bond rples. For example, here are only four rples ncluded n he daa se used n he presen sudy. 2

4 lnear verson of he prcng equaon ha ncorporaes he capal gan erm as an explanaory varable. Snce he capal gan erm s a funcon of he bond prce, hs lnear procedure necessaes he use of an nsrumenal varables esmaon echnque. A problem wh hs nsrumenal varables procedure s ha he denfcaon of approprae nsrumens s lkely o be dffcul, and he parameer esmaes may depend on he choce of nsrumens Jordan The analyss employs a relavely large prevously unused panel daase of Governmen of Canada bond prces. An advanage of Canadan daa s ha he ax code, as perans o fxedncome asses, s less complcaed han ha of he US ackay, Prsman and Tan, Ths grealy smplfes he emprcal analyss and makes easer for he emprcal specfcaon o accuraely reflec ax polcy. Furher, wh a smpler ax sysem, s easer for nvesors o deermne he ax mplcaons of dfferen nvesmens, so prcng errors based on ax confuson are less lkely. In addon, Governmen of Canada bonds are raded n a well developed secondary marke wh sgnfcan lqudy Gravelle Fnally, he sample ncorporaes 21 years of monhly daa, a sample perod ha s longer han he samples used n mos oher sudes and whch ncludes relavely large movemens n ax raes. I s ypcal n he leraure o esmae separae mpled ax raes for each pon n me generally each day or each monh whou akng no accoun ha axes n adjonng perods are lkely o be lnked for example, ax raes rarely change durng a year. Perod-by-perod esmaon also makes more dffcul o examne he mpac of changes n ax polcy on bond prces and o es wheher here have been sgnfcan shfs n behavour. The curren sudy dffers from mos of he leraure n ha uses me seres daa. 5 The use of a me seres of bond prce daa, n conjuncon wh explc daa on ax raes, recognzes ha axes may no always change from one 4 Ousandng Governmen of Canada bonds and debenures oaled C$87.4 bllon n percen of GDP, were C$272.7 bllon n percen of GDP, and peaked a C$320.1 bllon n percen of GDP. 5 Green and Ødegaard 1997 and Chenden and Hen 1999 also boh employ me seres daa. The laer use conegraon analyss o examne he relaonshp beween he yelds on axable and ax-exemp bonds, whle Green and Ødegaard 1997 esmae a srucural model of he erm srucure. 3

5 perod o he nex, makes possble o esmae he degree of ax capalzaon across he whole sample as well as for sub-perods, faclaes ess of srucural changes n bond marke behavour, and uses he varaon n ax raes o denfy he exen of ax capalzaon. The exsng evdence on he mpac of axes on bond prces and yelds s mxed. 6 A number of sudes fnd ha axes affec bond yelds, alhough hs effec s ofen small and, when he degree of capalzaon can be denfed, capalzaon s ypcally found o be less han complee see, for example, cculloch 1975, Van Horne 1982, Lzenberger and Rolfo 1984a, Heuson and Lasser 1990, Ehrhard, Jordan and Prsman 1995, Green and Ødegaard 1997 for he pre-1986 perod, and Elon and Green Oher auhors denfy sgnfcan ax effecs, bu fnd ha he esmaes of he magnudes of hese effecs are que varable Jordan 1984, Gay and Km In conras o hese sudes, Green and Ødegaard 1997, for he pos-1986 perod, show ha axes do no have a sgnfcan mpac on U.S. Treasury bond prces. The relaonshp beween corporae bond yelds and axes has receved far less aenon han he relaonshp beween axes and eher U.S. Treasury or U.S. muncpal bond yelds. In one of he frs sudes of he relaonshp beween corporae bond yelds and axes, Elon, Gruber, Agrawal and ann 2001 fnd, usng US daa for 1987 hrough 1996, ha a large proporon of sae corporae axes are capalzed n corporae bond yelds, and ha he ax effec s more mporan han defaul rsk. In a recen sudy, Lu, Sh, Wang and Wu 2007 confrm he fndngs of Green 6 Raher han analyzng ax capalzaon as relaes o naonal governmen bonds or corporae bonds, many of he sudes ha examne he relaonshp beween axes and bond prces yelds have done hs by addressng he US muncpal bond puzzle. Ths puzzle s he small spread beween he yelds on bonds ha earn axable neres and he yelds on US muncpal bonds whch are ax exemp for some groups of axpayers, so ha he afer-ax reurns on he ax-exemp muncpal bonds are greaer han he afer-ax reurns on axable bonds. See Green 1993, Chalmers 1998, Chenden and Hen 1999, and he papers ced heren. The mun bond puzzle s a phenomenon ha s pecular o he US ax sysem and he US muncpal bond marke s que dfferen from oher bond markes n ha he majory of US muncpal bonds are held by ndvduals 70 percen accordng o Ang, Bhansal and Xng 2007, a far greaer proporon han for mos oher ypes of bonds. Explanaons for he muncpal bond puzzle nvolve resrcons on arbrage, ransacon coss, and dfferences n defaul rsk see Chalmers 1998 and Erckson, Goosbee and aydew 2003, for example. 7 Guenher 1994 provdes evdence of a ax effec on he pre-ax yelds of US Treasury blls raher han bonds n an analyss of he major US ax changes of 1981 and However, he magnude of he esmaed effec s small relave o he effec ha would have been expeced f he margnal axpayer had been an ndvdual axpayer. 4

6 and Ødegaard 1997 wh respec o he absence of ax effecs n he US Treasury bond marke, bu fnd ha US corporae bonds wh larger coupons earn hgher reurns han low coupon corporae bonds, sgnfyng a sgnfcan ax effec, alhough he esmaed effec s small. Several sudes have examned ax capalzaon n bond yelds for non-us markes. The mul-counry sudy of Lzenberger and Rolfo 1984a shows ha axes have a sgnfcan mpac on he prces of bonds n Germany, Japan and he UK as well as he US and ha he mpled ax raes reflec he ax saus of he major holders of governmen bonds corporaons n Germany, Japan and he US, ndvduals n he UK. In a cross-counry sudy, Ejffnger, Huznga and Lemmen 1998 fnd ha whholdng axes have a sgnfcan mpac on governmen bond yelds n ndusralzed counres. An early sudy by ccallum 1973 shows ha he announcemen of he nroducon of a capal gans ax n Canada rased bond yelds, as would be expeced f axes are capalzed n bond prces. However, usng Canadan daa for , Brennan and Schwarz 1979 fnd ha he effec of personal ncome axes on bond yelds s slgh. ackay, Prsman and Tan 2000 confrm he resuls of Brennan and Schwarz, bu fnd ha, afer 1976, axes nduce a segmened equlbrum wh clenele effecs, especally beween 1981 and 1986 when her sample ends. 8 ackay, Prsman and Tan 2000 arbue he change n he laer par of her sample o he nroducon of he capal gans ax n 1972, large neres rae movemens, and defc fnancng 8 Cleneles form when dfferen sub-ses of nvesors, such as nvesors belongng o dfferen ax brackes, hold dfferen sub-ses of bonds, mplyng ha nvesors are no ndfferen across all bonds Schaefer Dybvg and Ross 1986 dsngush wo ypes of clenele effecs hose n quanes and hose n prces and quanes. Clenele effecs n quanes arse when here s a leas one margnal nvesor who holds or s ndfferen beween all bonds, bu oher ypes of nvesors hold only a subse of bonds. Clenele effecs n prces and quanes occur when no nvesor ype s ndfferen beween all bonds, so here s no prce vecor for whch some nvesor would be wllng o hold posve quanes of all bonds. In hs case, here does no exs a margnal nvesor. If a margnal nvesor exss, he erm srucure s deermned by he demand of ha nvesor ype. In he absence of a margnal nvesor, an esmae of he erm srucure usng all bond prces wll no reflec he demand of any sngle ype of nvesor. Impled ax raes esmaed n hs case may no apply o any parcular ype of nvesor Jordan 1984 and so may be of lle use. Arbrage n hs ype of equlbrum mus be mperfec due, for example, o resrcons on shor sellng. Prsman and Tan 1994, 303 noe ha, n Canada, shor sales are dffcul and cosly o mplemen and may consue he frcons needed o suppor an equlbrum wh clenele effecs. 5

7 by he Canadan governmen whch led o an ncrease n he supply of governmen bonds and araced more nvesors from dverse ax brackes o he bond marke. The resuls presened below ndcae ha fnancal secor corporae ncome axes were almos fully capalzed n he prces and yelds of Governmen of Canada bonds from 1986 when he sample begns o he early 1990s. Alhough movemens n corporae and personal ncome ax raes are correlaed o some exen, he resuls sugges ha personal ncome axes, unlke corporae axes, were no fully capalzed n bond prces. Ths resul s no surprsng as s conssen wh he much larger share of Governmen of Canada bonds held by corporaons han by ndvduals. Furher, as suggesed by Green and Ødegaard 1997, ndvduals are less lkely o be he margnal nvesor as hey face hgher ransacon coss. For he perod 1994 hrough 2006, he evdence mples ha neher corporae axes nor personal ncome axes are capalzed n bond prces. Ths resul s conssen wh he margnal nvesor durng hs perod beng an eny ha pays no ax. The change n he deny of he margnal nvesor and he degree of ax capalzaon does no appear o correspond o movemens n bond holdngs. However, n he early 1990s, he fnancal ndusry and he Bank of Canada nroduced nsuonal reforms o he operaon of he marke for Governmen of Canada bonds amed a mprovng marke lqudy, effcency and ransparency. These reforms are expeced o have reduced he rsk and ransacon coss of radng n hs marke and, as a consequence, may have nduced nvesors no subjec o ax o rade more acvely. Ths s conssen wh he suggeson of Shlefer and Vshny 1997 ha arbrage n fnancal markes may be less consraned when here s less rsk. The resuls obaned sugges ha here s a margnal nvesor who s ndfferen beween holdng all Governmen of Canada bonds, alhough no all ypes of nvesors would wan o hold all bonds. In he ermnology of Dybvg and Ross 1986, here exss a clenele n quanes, bu no 6

8 n prces and quanes. For boh he and perods, he resuls ndcae ha he margnal nvesor can be denfed wh a parcular ype of nvesor subjec o a parcular ype of ax a fnancal secor corporaon n he frs perod and a non-axpayng eny n he second. The nex secon oulnes he emprcal mehodology employed, whle Secon 3 descrbes he daa. Secon 4 presens he resuls and ndcaons of he robusness of he esmaes. The fnal secon provdes a dscusson of he resuls. 2. Emprcal ehodology The prce P A n perod of bond A, a bond wh a par-value of 100, coupon C A and perods o maury, s gven by: P A = C A 1 β τ d m= 1 m, + 100d, 100 P A d g, 1 where τ and τ g are he ax raes on neres ncome and capal gans, 9 respecvely, he β parameer represens he degree o whch axes are capalzed n he bond prce, and d m, β τ s he afer-ax dscoun facor n perod for he m h perod n he fuure he prce a me of an afer-ax clam of one dollar o be delvered m perods n he fuure, so, when r m s he m-perod pre-ax marke yeld, d m,β τ = 1 1+ r 1 m m. 10 The only dfference beween equaon 1 and he sandard bond prcng formula used n he 9 In some jursdcons, such as Canada, he capal gans ax rae s expressed as a fracon, φ g, of he ordnary ncome ax rae, so τ g =φ g τ, and he wo ax raes are no ndependen. 10 Noe, as s common n he leraure, s assumed ha he ax sysem reas capal gans and losses symmercally, ha axes are mposed when ncome s receved, and ha ax raes are known and consan hrough me. Ths las assumpon s conssen wh he assumpon n Shller and odglan 1979, 300 ha ax raes and ax laws relang o capal gans are, and are expeced o be, unchangng. Shller and odglan conend ha he alernave of modelng he me pah of expeced ax raes s smply oo dffcul. Furher, as n oher sudes ha examne he mpac of axes on bond yelds, he specfcaon gven n equaon 1 assumes ha nvesors plan o hold bonds o maury and so gnores he whole ssue of ax-mng opons as dscussed n, for example, Consanndes and Ingersoll Equaon 1 s conssen wh he axaon of bonds n Canada n ha coupon paymens and capal gans are boh axed when he correspondng ncome s receved. However, gnores he possble dfferenal ax reamen of premum and dscoun bonds. In Canada, he capal loss assocaed wh a premum bond can only be used o wre off a capal gan earned on anoher asse, no coupon ncome. 7

9 leraure, such as ha of Robchek and Nebuhr 1970 or Green and Ødegaard 1997, s he addon of he parameer β. An advanage of esmang β, raher han mpled ax raes as s done n much of he leraure, s ha, when usng me seres daa, he esmaon akes advanage of he nformaon conaned n observed movemens n ax raes hrough me. Re-wrng equaon 1, so ha he bond prce appears only on he lef-hand sde, yelds: P A C = A 1 m= 1 d m, d g, g d,. 2 Usng hs specfcaon, along wh daa on bond prces, coupons, ax raes, and he dscoun facors, would be possble o esmae β and deermne he exen o whch axes are capalzed n bond prces. A problem wh hs approach s ha requres daa on he dscoun facors assocaed wh he enre yeld curve he d m,β τ. An alernave, used n much of he leraure s o smulaneously esmae he ax effecs and an approxmaon o he yeld curve. A shorcomng of hs mehodology, as menoned above, s ha any errors n he esmaon or specfcaon of he yeld curve may bas he esmaes of he ax capalzaon parameers. I s no necessary o have nformaon on he enre yeld curve a every pon n me f here s a second bond Bond B wh he same maury dae and rsk characerscs as Bond A, bu a dfferen coupon. Followng equaon 2, he prce of hs second bond would be gven by: P B CB 1 β τ = m= 1 d m, d g g, g d,. 3 Snce boh bonds are dscouned by he same dscoun facor, s possble o use equaon 3 o subsue for m= 1 d m, β τ n equaon 2. Ths yelds: I s easy o modfy he prcng equaons o ncorporae accrued neres. However, hs modfcaon adds lle o he model as he accrued neres erms cancels ou of equaon 4. 8

10 C B P A C A P B C = B C A d g g d,,. 4 Equaon 4 ncorporaes only one pon on he yeld curve for each bond par, raher han he enre yeld curve, whch grealy smplfes esmaon. 12 Applcaon o Canada Equaon 4 can be used o esmae he exen of ax capalzaon n he prces of Governmen of Canada bonds. There are hree prncpal ypes of bondholders n Canada ndvduals, fnancal corporaons and non-axed enes penson funds and governmen agences, all of whom are axed dfferenly. Indvduals pay ax rae τ on coupon ncome and ax rae τ g on capal gans, wh τ g se as a proporon φ g of τ 0< φ g <1. Fnancal corporaons pay he same rae of ax τ c on coupon ncome and capal gans, 13 whle non-axed enes pay no ax on boh capal gans and coupon ncome. If a margnal nvesor exss, bond prces wll reflec he ax raes faced by ha nvesor. Thus, f he margnal nvesor s an ndvdual subjec o personal ncome axaon, so he personal ncome ax raes τ g and τ are capalzed n bond prces, β n equaon 4 would equal one. Alernavely, f fnancal-secor corporaons are he margnal nvesor, bond prces would reflec corporae ax raes. In hs case, s necessary o modfy equaon 4 so ha τ g and τ are replaced wh τ c and β s replaced by β c, he corporae ax capalzaon parameer. Wh full corporae ax capalzaon, β c would equal one. On he oher hand, f he margnal nvesor s a ax exemp eny 12 Van Horne 1982 also uses pars of bonds wh smlar maures. He chooses pars so ha one of he bonds n each par sells near par and he oher sells a a dscoun and uses he yeld o maury on he par bond as he dscoun rae n he prcng equaon for he dscoun bond. Heuson and Lasser 1990 use pars of bonds wh he same maury dae, bu have daa coverng only fve years. They employ a grd search o calculae he margnal ax rae ha equaes he afer-ax yeld-o-maury on each par. Chenden and Hen 1999 examne he yelds on bonds wh he same maures, bu use dfferen ypes of bonds, so he rsk characerscs of he bonds n each par are unlkely o be he same. 13 The corporae ax rae s generally dfferen from he ax raes pad by ndvduals on eher neres ncome or capal gans. Non-fnancal secor corporaons corporaons who do no rade n bonds as par of her busness pay ax rae τ c, bu pay only a fracon φ g of hs rae on capal gans he same proporon as pad by ndvduals. See Canada Revenue Agency 1984 for a dealed descrpon of he dfferences beween fnancal and non-fnancal corporaons. 9

11 such as a penson fund, he ax capalzaon parameers, β and β c, would boh be zero as ndvdual and corporae ax raes would have no mpac on bond prces. In he absence of a margnal nvesor, here s a segmened equlbrum n whch subses of axpayers hold only subses of bonds. In hs case, dfferen subses of bond prces wll reflec dfferen subses of ax raes and he esmaes of β and β c are lkely o le beween zero and one. As n Green and Ødegaard 1997, an error erm s added o he bond prcng equaons equaons 2 and 3. The addon of an error s jusfed because bond prce daa ypcally conan nose bd-ask spread, hn radng, and measuremen error.... Such observaon errors end o be random and have zero mean n a large sample ackay, Prsman and Tan 2000, 255, 263. Elon and Green 1998 also noe ha errors n bond prcng are common. The addon of an error o equaons 2 and 3, and he generaon of equaon 4 from hese wo equaons, causes he errors assocaed wh equaon 4 o be heeroscedasc. I s also possble ha he errors for he me seres of observaons for each bond par wll be correlaed as mgh he errors assocaed wh he observaons common o each me perod. As a resul, he repored sandard errors are adjused for wo-way cluserng by bond par and by me perod and heeroscedascy. 14 Ths s done usng he mehodology proposed n Cameron, Gelbach and ller 2006 and Thompson Daa In order o esmae equaon 4, prce and coupon daa are requred for bond pars, where each par consss of wo bonds ha have dfferen coupon raes, bu are dencal n erms of rsk and dae of maury. To ensure ha all he daa are characerzed by smlar rsk characerscs, bond prce daa for a sngle defaul rsk free ssuer he Governmen of Canada are employed. 14 Raher han cluser by bond par and observaon monh, snce ax raes generally reman consan for an enre year, s possble o esmae he sandard errors whle cluserng by bond par and year, whch allows he errors of all he observaons n a parcular year o be correlaed. Ths procedure ncreases he magnude of he esmaes of he sandard errors, bu no by enough o aler any of he conclusons. 10

12 These daa are aken from Canadan Bond Prces and FP Bonds Canadan Prces, boh publshed by he Fnancal Pos Corporaon. 15 The sample consss of 2190 las-busness-day-of-he-monh observaons on he bd prces of 94 bonds ha can be combned o form 49 bond pars. 16 As s ypcal n he leraure, only bonds wh more han 12 monhs o maury are ncluded n he sample. 17 All bonds n he sample are no callable, are denomnaed n Canadan dollars, are no real reurn bonds, are no exendable or exchangeable, and pay neres on a sem-annual bass. The bonds n each par may dffer n erms of amoun ssued and ssue year. 18 As hey are axed n a dfferen fashon han coupon bearng bonds, srp bonds and zero-coupon bonds are no ncluded n he daa se. The span of he daa s from 1986 o 2006, alhough some of he bonds maured durng he sample perod, whle ohers were newly ssued, so he bond prce daa form an unbalanced panel. 19 The number of monhly observaons for each bond par has an average of jus under 45, bu ranges from 2 o 112. The number of observaons per year vares from 45 o 203, and averages 104. The average coupons of he hgh and low coupon bonds n each par are jus under 12 and 8 percen, respecvely, so he average dfference beween he coupons of he bonds n each par s approxmaely 4 percenage pons. See Appendx A for addonal descrpve sascs. As he deny of he margnal nvesor s no known ex ane, wo ypes of ax daa are used 15 The characerscs of he bonds for example, amoun ssued, ssue year, callably, ec are gven n he Fnancal Pos publcaons: Governmen Bond Record and FP Bonds Governmen. 16 Nney-four bonds can be used o consruc 49, raher han 47, bond pars because here are four cases n whch hree bonds share he same maury dae, and so, for each of hese cases, wo separae pars can be formed from he observaons on hree bonds. 17 Ths s conssen wh he defnon of fxed-rae deb... as deb wh a remanng erm o maury of more han one year Harvey, 1999, 29n. Heuson and Lasser 1990, Elon and Green 1998 and Elon, Gruber, Agrawal and ann 2001 also, for example, do no use daa for bonds wh less han one year o maury. As n Elon, Gruber, Agrawal and ann 2001, a small number of observaons wh obvous prcng daa enry errors were elmnaed. For example, fve observaons were no used because he repored prce and yeld daa gave nconssen predcons by a small number of bass pons wh respec o wheher he bonds were radng a a dscoun or a premum. 18 The ssues of rsk dfferenals and dfferences n callably, whch have been ced as beng mporan n he US mun-bond-puzzle leraure Chalmers 1998 are no relevan here as he bond prce daa employed correspond o bonds ha are ssued by one ssuer and are no callable. 19 Whle observaons on bond prces are avalable from 1983, he Bank of Canada erm srucure daa used for r begns only n

13 o esmae he degree of ax capalzaon, daa on personal ncome ax raes, τ and τ g, and daa on corporae ax raes, τ c. The ax raes, τ and τ g, are se equal o he hghes personal ax raes on neres ncome and capal gans, respecvely, for a resden of Onaro, whle he combned federal and Onaro general corporae ax rae s used for τ c. 20 The raonale for usng he hghes margnal ax rae for τ and τ g s ha hgh ncome ndvduals are mos lkely o nves n bonds. The ax raes applcable n Onaro were employed because Onaro s he larges provnce n erms of boh GDP and populaon. Snce he federal governmen collecs he major share of boh personal and corporae ncome axes, he choce of provnce of resdence s lkely o have lle mpac on he resuls. The ax rae daa are presened n Table 1 and ploed n Fgure 1. The ax rae on neres ncome changed 14 mes durng he 21 year perod from 1986 o Snce τ g equals φ g τ, a large number of he 16 changes n he capal gans ax rae, τ g, were due o movemens n he ax rae on neres ncome, τ. However, he capal gans ax as a proporon of he ax rae on neres ncome φ g also changed four mes durng he sample perod, so he smple correlaon beween he wo ax rae seres s only.599. From a peak n 1994, he personal ncome ax rae on capal gans fell by 42 percen by 2001, whle he personal ax rae on neres ncome fell by only 13 percen over he same perod. The correlaon coeffcen beween he corporae ax rae and he personal ax rae on neres ncome s.68, whle he correlaon wh he capal gans ax rae s only.43. To esmae equaon 4, s necessary o assocae each observaon for each bond par wh one pon on he zero-coupon yeld curve r. The values for r were proxed usng esmaes 20 The personal ncome ax rae daa were aken from he acual Canadan federal and Onaro ncome ax forms for each year. These forms can be accessed a hp:// on he webse of he Canada Revenue Agency. The corporae ncome ax rae daa were provded by Bev Dahlby and Ergee Ferede. They obaned hese daa from varous ssues of The Naonal Fnances and Fnances of he Naon, boh publshed by he Canadan Tax Foundaon. 12

14 generaed by he Bank of Canada. 21 To ensure ha he daa for r and he bond prces are no conemporaneous, he value for r employed s for he busness day pror o he busness day on whch he bond prces are recorded Resuls Table 2 repors esmaes of he ax capalzaon parameers, β and. Esmaes of he parameer β are derved by esmang equaon 4 usng he personal capal gans τg and neres β c ncome τ ax raes. The βc parameer s esmaed by replacng τ and τ g n equaon 4 wh he corporae ax rae, τ c, and replacng β wh β c. As noed n Secon 2, f he margnal nvesor s a personal ncome axpayer, he ndvdual ax capalzaon parameer, β, would equal one. On he oher hand, f he margnal axpayer s a fnancal-secor corporaon, he ax capalzaon parameer assocaed wh he corporae ncome ax rae, β c, would equal one. If he margnal axpayer n he bond marke s an eny ha pays no ax, such as a penson fund or governmen agency, he coeffcens on he ax capalzaon parameers wll equal zero, so β = β = 0. Fnally, n he absence of a margnal nvesor, so no sngle ype of nvesor s ndfferen beween all bonds, he prces of sub-ses of bonds wll reflec he ax raes of sub-ses of nvesors. In hs case, one would expec he esmaes of boh β and β c o dffer from boh zero and one. Table 2 presens esmaes of he ax capalzaon parameers usng daa for he whole sample, 1986 hrough 2006, as well as for wo sub-perods and In hs c 21 Downloaded 1 June 2007 from hp:// For a descrpon of he mehodology used o generae hese daa, see Bolder, Johnson and ezler To mnmze he possbly of axnduced dsorons, hese yeld curve esmaes exclude observaons for bonds ha rade a hgh devaons from par Bank of Inernaonal Selemens, 2005, x, 3. For he sample perod employed, he Bank of Canada provdes zerocoupon yelds for every maury from 3 monhs o 300 monhs a hree monh nervals. The maury chosen o represen r for each monhly observaon s he maury ha s closes o he for ha observaon. 22 Ths s conssen wh he assumpon ha bond raders use only bond prce daa from he prevous day o generae esmaes of he dscoun rae. Noe ha he bonds ha form he bond pars n he sample used here are, mos lkely, only a fracon of he bonds used o esmae r, snce r s esmaed usng all he avalable bond daa wh he excepon noed n he prevous foonoe, no jus daa on bond pars. 13

15 sudy of he Governmen of Canada yeld curve, Johnson , 19 noes ha he perod beween he lae 1980s and he early 1990s had very dfferen characerscs from he lae 1990s and early 2000s. Some evdence suggess ha hs change was caused by nsuonal reforms o he operaon of he marke for Governmen of Canada bonds nroduced by he fnancal ndusry and he Bank of Canada n he early 1990s. 23 In he earler perod, has been suggesed ha many bonds were no lqud, ha here was a lack of ransparency n he bond marke, and ha raders used rules of humb and dosyncrac bond prcng formulas. The prevalence of hese characerscs declned afer he reforms Whngham and Johnson As he perod followng he early 1990s may have been characerzed by dfferen behavour or nsuons han he earler perod, may no be approprae o rea he enre sample as a sngle perod. For hese reasons, esmaes are provded for he wo sub-perods as well as for he full sample. 24 As shown n Par A of Table 2, over he whole sample, he esmaes of he personal ncome ax capalzaon parameer, β, s Ths parameer esmae s boh sgnfcanly dfferen from zero and one. The full sample esmae of he corporae ax capalzaon parameer gven n Par B of Table 2 s.5350, whch s closer o one han he ndvdual parameer, bu also sgnfcanly dfferen from boh zero and one. These resuls sugges ha no sngle ype of nvesor s he margnal nvesor for he enre sample perod. As can be seen from Table 2, he resuls for he wo sub-samples dffer srongly from each 23 See Branon 1995, Whngham , Halpern and Rumsey 1997, 2000, Gravelle 1999, Harvey 1999 and Chounard and Lalan Johnson suggess ha he exac pon a whch o spl he sample s unclear. The choce of break pon used here was made based on an examnaon of he nsuonal evdence as well as on he fac ha marke yeld dfferenals beween bonds wh he same maury dae, bu dfferen coupons, averaged less han 10 bass pons wh a sandard devaon of less han 3 bass pons for he years n he laer perod, bu averaged 28 bass pons wh a sandard devaon of up o 25 bass pons n he years of he earler perod. If he break pon beween he wo sub-samples s moved one year n eher drecon, he values gven n Table 2 are generally less han one sandard error from he new esmaes and never more han wo sandard errors. Alerng he wo sub-samples by one year n eher drecon would no cause any of he conclusons o change, so he precse pon a whch o spl he sample s no crcal. 14

16 oher as well as from he esmaes for he whole sample. 25 For he earler sub-sample, 1986 hrough 1993, he personal ncome ax capalzaon parameer, β, s.3190, whch s larger han he esmae for he whole sample, bu sll sgnfcanly dfferen from boh zero and one. On he oher hand, he corporae ax capalzaon parameer β c s esmaed o be Ths esmae s nsgnfcanly dfferen from one as well as sgnfcanly dfferen from zero and s also sgnfcanly dfferen from he esmae for β. These esmaes sugges ha, n he earler perod, fnancal-secor corporaons were he margnal nvesor n he bond marke, so ha changes n he corporae ax rae caused movemens n bond yelds durng hs perod. Esmaes of he wo ax capalzaon parameers β and β c for he sub-perod 1994 hrough 2006 mply ha neher corporae nor personal ncome axes are capalzed n bond prces. Boh esmaes of he ax capalzaon parameers are near zero and negave and, for each parameer, a es srongly rejecs he hypohess ha he ax capalzaon parameer equals one. These resuls sugges ha, n he more recen perod, he margnal nvesor n he bond marke s neher a corporaon nor an ndvdual. Raher, he resuls mply ha he margnal nvesor s an nvesor facng a zero ax rae, such as a penson fund or governmen agency Annual Esmaes of he Tax Coeffcens As an ndcaon of he robusness of he ax capalzaon parameer esmaes presened n Table 2, annual esmaes of he mpled personal and corporae ax raes are generaed by esmang equaon 4 separaely for each year of he sample. 27 Snce he ax raes τ and τ c are 25 A es ha he esmaed parameers are he same over he wo sub-samples rejecs he hypohess of parameer consancy for boh parameers. The -sascs for he srucural change ess of he ndvdual and corporae ax capalzaon parameers, β and β c, are and 8.32, respecvely. 26 Green and Ødegaard 1997 fnd negave esmaes of mpled ax parameers for he US n he pos-1986 perod and also nerpre hese esmaes as mplyng he absence of ax capalzaon n bond prces. 27 I s ypcal o esmae mpled ax raes for each observaon monh. Whle we have monhly daa, we do no have enough observaons o esmae he model for each monh. On he oher hand, snce neher τ nor τ c change durng any year of he sample, may be more effcen o esmae he mpled ax raes for each year han for each monh. 15

17 consan durng each year, hs procedure yelds esmaes of he mpled capalzed ax raes, β τ and β c τ c, raher han he ax capalzaon parameers β and β c, as he laer canno be denfed separaely when ax raes are consan. 28 The annual esmaes of β c τ c and β τ are llusraed n Fgures 2 and 3, respecvely. If a corporae axpayer s he margnal axpayer, he esmae of he mpled corporae ax rae β c τ c for each year should be nsgnfcanly dfferen from he acual corporae ax rae τ c for he same year. The esmaes presened n Fgure 2 ndcae ha, for sx of he egh years from 1986 hrough 1993, he esmaed mpled corporae ax rae s close o he acual corporae ax rae and fve of hese esmaes are nsgnfcanly dfferen from he acual rae. 29 From 1994 onwards, all he esmaes of he mpled corporae ax raes are close o zero, and all are sgnfcanly dfferen from he acual ax rae. Thus, he resuls n Fgure 2 are generally conssen wh he resuls of Table 2 whch mply ha corporae axes were capalzed n bond prces n he pre-1994 perod, bu had lle mpac on bond prces n he pos-1993 perod. 30 As can be seen n Fgure 3, he esmaes of he mpled personal ncome ax rae β τ all fall below he acual ndvdual ax rae τ, and are generally less han half of he acual rae. In all cases, he esmaed mpled ax rae s sgnfcanly dfferen from he value of he acual ax rae. As wh he mpled corporae ax rae, here s a dsnc fall n he esmaed mpled ndvdual ax rae n he early 1990s, and a subsequen sablzaon of he esmaes of hese raes near zero. 28 By usng daa on φ g, and nong ha τ g =φ g τ, s only necessary o denfy one mpled ax rae for ndvduals, β τ, raher han boh β τ and β τ g because β τ g =φ g β τ. I s he use of he daa for φ g whch allows he year-by-year esmaes of he corporae and ndvdual mpled ax raes o dffer. 29 Noe ha he esmaes presened n Fgures 2 and 3 are generaed for each year ndvdually and, as a consequence, each esmae s derved usng far fewer observaons a mnmum of 45 and a maxmum of 203 han he esmaes n Table 2. The varably of he esmaes could be due o he small number of observaons n each perod Green and Ødegaard The sandard errors llusraed n Fgures 2 and 3 are generaed usng wo-way robus-cluserng, he same mehod used o generae he sandard errors n Table The low esmaed mpled ax raes for 1989 and 1990 correspond wh a emporary spke n shor erm neres raes as well as a emporary declne n he percenage of ousandng Governmen of Canada markeable bonds held by charered banks, near-banks, lfe nsurance companes and oher fnancal nsuons. Ths percenage fell from an average of 20 percen n o 17 percen n 1989 and 1990, before rsng o 20 and 24 percen n 1991 and 1992, respecvely. 16

18 These annual esmaes are conssen wh he esmaes of Table 2 n ha hey mply ha ndvdual axpayers were no he margnal nvesor n he Governmen of Canada bond marke. The mpled ax raes of approxmaely zero for he pos-1993 perod n boh Fgures 2 and 3 ndcae ha he margnal nvesor durng hs perod had a ax rae of zero. 4.2 Robusness of he Esmaes 31 To assess he robusness of he resuls, several alernaves o he esmaon mehodology are consdered. Branon 1995, 14 and Jones and Fabozz 1992, 180 noe ha he mos acvely raded Governmen of Canada bonds are of nermedae maures, n he range of 3 o 10 years, so he model was esmaed usng only bonds wh from 36 o 120 monhs o maury. Whle hs reduces he number of observaons over he whole sample and n each of he wo sub-perods by almos half, he new esmaes of he ax capalzaon parameers and sandard errors dffer very lle from hose presened n Table 2 generally he esmaes dffer by less han one sandard error and none of he conclusons would change. The ax capalzaon parameers, β and β c, were also re-esmaed usng observaons from only one monh n each year, snce ax raes generally do no vary durng a year and, as a resul, here may be lle addonal nformaon generaed by usng more han one observaon for each calendar year. Observaons for he monh of June were chosen ex ane snce governmen budges are usually announced n arch or Aprl near he governmen fscal year-end of arch 31 and, hus, ax rae changes should be known by June. Usng June observaons only, he esmaes of he parameers and sandard errors are very smlar o hose repored n Table 2 none of he parameer esmaes change by more han wo sandard errors and cause none of he conclusons o change. 32 The margnal personal ncome ax raes used o generae he resuls n Table 2 nclude boh 31 Ths secon presens a summary of he robusness resuls. The esmaes underlyng hs summary are avalable from he auhor. 32 There are 183 June observaons n he full sample, , and 105 and 78 observaons n he and sub-perods, respecvely. 17

19 provncal and federal suraxes. Snce hese suraxes may be pad by only a small number of hgh ncome axpayers, he model was re-esmaed usng he hghes ax rae exclusve of federal and provncal governmen suraxes as he personal ncome ax rae. 33 Ths change yelded parameer esmaes ha were exremely close all whn one sandard error o hose repored n Table 2, ndcang ha he resuls are no parcularly sensve o he personal ncome ax raes employed. In 1985, he Canadan governmen nroduced a lfeme capal gans deducon for ndvduals. Ths deducon was capped a $100,000 n 1988 and elmnaed n 1994 Zeng 2002, bu could have had an mpac on he demand for bonds and, hus, on he esmaes of he ndvdual ax capalzaon parameer β for he earler sample sub-perod. To deermne wheher he capal gans deducon has mporan mplcaons for he resuls, he parameer β s esmaed for he perod 1986 hrough 1993 wh he capal gans ax rae se o zero, as would be he case f ndvdual axpayers were no consraned by he cap on he lfeme capal gans deducon. Whle hs change causes he esmae of β o fall, s sll sgnfcanly dfferen from boh zero and one. Non-fnancal corporaons pay ax a he corporae rae, bu, unlke fnancal corporaons, pay ax on only a proporon φ g of capal gans he same proporon as pad by ndvduals. Esmaes of equaon 4 usng he approprae ax rae for non-fnancal corporaons yelds esmaes of he ax capalzaon parameer ha are very close o hose presened for ndvduals n Table Ths resul mples ha, as wh ndvduals, non-fnancal corporaons are no he margnal nvesor n he marke for Governmen of Canada bonds. Ths s no surprsng as nonfnancal corporaons hold only one percen of ousandng markeable Governmen of Canada bonds Table 3. The sample employed ncludes boh on-he-run and off-he-run bonds. There may be dfferences n he marke lqudy and ransacons coss assocaed wh hese wo ypes of bonds. 33 The combned federal and provncal personal ncome surax averaged a lle over 5 percenage pons durng he sample perod and vared from approxmaely 2 o 9 percenage pons. 34 For he non-fnancal corporaons case, equaon 4 s modfed by replacng τ wh τ c and τ g wh φ g τ c. 18

20 These dfferences may be refleced n he prce daa and hs could have affeced he esmaes. To es f he mxure of on-he-run and off-he-run bonds n he sample s mporan o he resuls, he ax capalzaon parameers were re-esmaed wh daa only for bonds wh an ssue dae ha was a leas wo years n he pas. The new parameer esmaes are almos dencal o he esmaes gven n Table 2 whch s no surprsng as only a small percenage of he observaons n he sample correspond o bonds ssued n he prevous wo years. Fnally, o allow for possble ms-prcng and lqudy effecs, he specfcaon of he esmang equaon s modfed o allow he bond prce o dffer from he presen dscouned value of bond ncome n hree alernave ways by a consan parameer; by a consan parameer and a lnear funcon of he log of he ssue amoun of each bond; and by a consan parameer and a lnear funcon of he number of years snce he bond was ssued. See Appendx B for a dervaon of he modfed esmang equaon. Ths specfcaon s more flexble n ha allows for he sysemac over- or under-prcng of bonds as well as he dependence of prces on ssue amoun and years snce ssue, boh poenal proxes for bond lqudy. 35 If he bd prces employed are sysemacally based, hs bas should be refleced n he esmaed consan erm. Elon and Green 1998 sugges ha prces may also dffer from he presen value of paymens due o ransacon coss. In addon, hey argue ha llqud bonds should offer hgher yelds and fnd ha lqudy s a sgnfcan alhough no very large deermnan of he relave prces of US Treasury bonds. For he whole sample, and n boh sub-samples, he esmaes of β and β c for hese hree varans of he model are smlar o hose presened n Table 2 and n no a sngle case would here be a change n he general conclusons wh respec o he degree of ax capalzaon. Thus, he magnude of he esmaes repored n Table 2 do no appear o be he resul of a falure o accoun for errors n bond prcng or lqudy effecs. 35 The number of years snce ssue as a proxy for lqudy s suggesed by Green and Ødegaard

21 5. Concludng Commens Ths paper examnes he exen o whch corporae and personal ncome axes are capalzed n Governmen of Canada bond prces. Tax capalzaon effecs are mporan o nvesors snce hey can affec nvesmen reurns as well as esmaes of he erm srucure used o prce oher asses. Tax capalzaon effecs may also be nformave for polcymakers as hey provde nformaon abou ax ncdence and he role of dfferen marke parcpans n he deermnaon of bond prces. The fndngs descrbed above ndcae near complee capalzaon n bond prces of he fnancal secor corporaon ncome ax durng he perod Whle he esmaes are also conssen wh paral capalzaon of personal ncome axes, hs paral capalzaon may follow smply from he posve bu no perfec correlaon of corporae and personal ax raes. Tha our evdence suggess ha he margnal nvesor pad corporae axes, raher han personal axes, durng he perod s perhaps no surprsng gven he relavely small share of Governmen of Canada bonds held by personal ncome axpayers see Table 3. For he perod , he ax capalzaon parameer esmaes fall o near zero, whch suggess ha he margnal nvesor faces a zero ax rae, he ax rae of penson funds and governmen agences. In boh sub-perods, here appears o be a margnal nvesor ype, whch suggess he absence of ax-cleneles excep n quanes. The dfferen ax reamen of nvesorypes, and he exsence of a sngle-ype of margnal nvesor, mples ha here are frcons ha nhb arbrage n he Canadan bond marke. As ndvdual nvesors are no found o be he margnal nvesor n eher perod, changes n personal ncome axes are unlkely o have affeced bond yelds or equlbrum bond marke prces. The falure of bond prces o capalze eher personal or corporae axes n recen years means ha afer-ax bond reurns for ndvduals and corporaons wll change as ax raes change, 20

22 so he enre burden of ax changes s borne by he non-ax exemp holders of bonds, as opposed o bond ssuers. As a resul, ax changes should no affec governmen fnancng coss hrough he ax capalzaon channel. The esmaed degree of ax capalzaon also has mplcaons for esmaes of he yeld curve. Tax-relaed coupon effecs are consdered o be of suffcen mporance ha Bank of Canada esmaes of he Governmen of Canada yeld curve exclude observaons for bonds ha rade a large devaons from par Bank of Inernaonal Selemens, 2005, 21. The resuls presened here ndcae ha, n he recen pas, here has been lle ax capalzaon and so pre-ax yelds are largely nsensve o movemens n corporae or personal ncome ax raes. As a resul, a leas snce he md-1990s, yeld curve esmaes are unlkely o depend on ax raes or he coupons of he bonds ncluded n a parcular sample. 36 One possble explanaon for he declne n he degree of ax capalzaon afer 1993 s an ncrease n he proporon of bonds held by ax-exemp bondholders. However, he percenage of Governmen of Canada markeable bonds held by ruseed penson plans and socal secury funds acually fell, on average, from 21.8 percen n o 20.7 percen durng , as shown n Table 3. Furher, he holdngs of non-resdens, a group ha may also be less subjec o domesc axes, fell by an even larger amoun beween he wo perods, whle he holdngs of banks and oher axable fnancal nsuons acually rose. Ths evdence suggess ha he change n he degree of ax capalzaon was no caused by changes n he dsrbuon of bond holdngs across nvesor ypes. 36 Ths s conssen wh he suggeson of Elon and Green 1998, 1557, 1561: The nconsequenal ax and lqudy effecs ha we fnd sugges ha more bonds can be ncluded n erm srucure esmaon. arke parcpans commonly narrow he pool of bonds hey consder when esmang he erm srucure n order o use bonds hey beleve are unaffeced by ax and lqudy effecs. Our evdence mples ha a larger sample of bonds can be used o esmae he erm srucure, whch could lead o smaller esmaon error.... The lack of subsanal ax and lqudy effecs n he relave prces of bonds has mporan mplcaons for... praconers decdng whch bonds o nclude n her erm srucure esmaons for use by raders. 21

23 A second possble explanaon for he change n he exen of ax capalzaon s ha an ncrease n he quany of ousandng Canadan governmen deb made he marke more lqud, whch faclaed arbrage. Green and Ødegaard 1997, 628 sugges ha one of he reasons for he dsappearance of ax capalzaon n he US durng he md-1980s was ha he number of bonds and he range of maures ssued by he U.S. Treasury ncreased dramacally. The hgher degree of marke compleeness hs affords also makes easer o consruc arbrage posons and o explo quas-arbrage opporunes. However, rapd ncreases n Canadan Federal governmen deb began n he md-o-lae 1980s, long before he declne n he esmaes of he ax capalzaon parameer. 37 I s also possble ha changes o he exen of compeon n he fxed-ncome marke could have alered he degree of ax capalzaon as a more compeve marke may lower he cos of arbrage. However, he fxed ncome marke does no appear o have become more compeve n he early 1990s. As recenly noed by he Bank of Canada, Sandard measures of marke concenraon sugges ha he secondary marke for governmen secures, along wh oher secors of he domesc fxed-ncome marke, s hghly concenraed Bank of Canada, 2004, 8. The average marke share of he fve larges dealers n he secondary marke for Governmen of Canada bonds decreased somewha n he lae 1990s relave o he early 1990s, bu rose sharply n recen years Anderson and Lavoe 2004 wh no change n he mpled ax rae as ndcaed by Fgures 2 and 3. An alernave explanaon for he fall n he degree of ax capalzaon s ha here was a major change n ax polcy whch affeced behavour n he bond marke. For example, n he US bond marke, Green and Ødegaard 1997 found ha mplc ax raes were posve n he pre From a base of C$87 bllon n 1986, he quany of Governmen of Canada bonds ousandng rose o C$185 bllon n 1993, a rse of C$14 bllon per year on average, wh he ncrease n each year exceedng C$10 bllon. 22