Ineres Raes, Taxes and Corporae Financial Policies Roger H. Gordon, a Young Lee b a Universy of California, San Diego b Hanyang Universy, Seoul, Korea June, 2006 Absrac This paper invesigaes he combined effec of nominal ineres raes and axes on he use and maury srucure of corporae deb. The ne ax gain from use of corporae deb is proporional o nominal ineres raes, so ha behavioral responses should be larger when ineres raes are higher. For similar reasons, firms should shif owards more long-erm deb as longerm raes rise relaive o shor-erm raes. Our paper presens evidence consisen wh boh predicions, using corporae and personal ax reurn daa from he U.S. Saisics of Income. Roger H. Gordon: Tel: (858)-534-4828 Fax: (858)-534-7040, Deparmen of Economics 0508, Universy of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0508. Email: rogordon@ucsd.edu Young Lee: Tel: +82-2-2220-1023 Fax: +82-2-2296-9587, Deparmen of Economics and Finance, Hanyang Universy, 17 Haengdang-dong, Seongdong-gu, Seoul, Korea 133-291. Email: younglee@hanyang.ac.kr
1. Inroducion There has been a subsanial leraure examining boh heoreically and empirically he effecs of he ax srucure on corporae use of deb vs. equy finance. According o he heoreical leraure, deb finance should be encouraged o he degree ha more axes are saved on corporae ineres deducions han are owed on he resuling ineres income. Mos all pas papers on axes and corporae borrowinghough, ignore an imporan elemen in he heory. According o he heoryhe size of he ne ax savings per dollar of corporae deb is proporional o nominal ineres raes. Everyhing else equalhereforehe size of he ax incenives affecing use of corporae deb should be high in years such as he early 1980's in he U.S. when nominal ineres raes were high (around 14%), and should be very low in he years immediaely afer 2000 when a leas shor-erm nominal ineres raes were around 1%. If his variaion in ineres raes were saisically independen of he variaion in ax raes, hen prior esimaes could sill be unbiased, even if highly dependen on he sample period. However, we find below ha years when corporae ax raes were high relaive o personal ax raes, encouraging use of corporae deb, also ended o be years in which nominal ineres raes were low, weakening he esimaed effecs of any ax incenives. The pas neglec of variaion in ineres raes when esimaing he sensivy of use of corporae deb o ax incenives may be one explanaion why his pas leraure has no found much effec of axes on use of deb. For similar reasonshe erm srucure of ineres raes can affec a firm s choice of he maury of s deb srucure. This poin is developed formally in Gordon (1982) and Brick and Ravid (1985). 1 In paricularo he degree ha he long-erm ineres rae is higher han he shor- 1 Brick and Ravid (1991) exended he analysis o handle sochasic ineres raes. Boyce and Kaloay (1979) noed a relaed incenive o make bonds callable when corporae ax raes are relaively high. 1
erm raehe ax savings from use of long-erm deb increase relaive o he ax savings from an equivalen amoun of shor-erm deb. These incenives are sronger he larger he ax differenial. There are a few pas papers ha aemped o ake ino accoun he ineracion of axes and marke ineres raes on use of corporae deb. For example, Gordon (1982) esed hese predicions using aggregae ime-series daa for he U.S. While he poin esimaes were consisen wh he heory, 2 sandard errors were high based on weny-five observaions. There have also been a few aemps o es he effecs of he erm srucure of ineres raes on he maury srucure of deb using he largely cross-secional daa from Compusa. 3 Here he esimaed effec of ax incenives is commonly saisically insignifican or he wrong sign, given he heory. These sudies using Compusa daa suffer from he problem ha he proxies for he corporae ax rae can be picking up imporan nonax effecs on behavior. The aim of his paper is o reexamine he combined effecs of ineres raes and axes on corporae deb and deb maury, using he U.S. Saisics of Income Corporae Income Tax Reurns, building on he idenificaion sraegies developed in Gordon and Lee (2001). As repored below, we find ha esimaed ax effecs are large and significan saisically, in conras o he resuls in mos previous papers. In paricular, reducing he ax rae on corporae income by 10 percenage poins is forecas o reduce he fracion of capal financed wh deb by 3 percenage poins, given average ineres raes. 4 The resuls also show imporan effecs of he level of nominal ineres raes on he overall use of deb: given average ax incenives, we esimae ha an increase in marke ineres raes by 5 percenage poins should increase he 2 In paricularhe paper finds ha use of long-erm deb falls when he shor-erm ineres rae goes up, condional on he longerm ineres rae, while use of shor-erm deb is unaffeced, raising he raio of shor-erm o long-erm deb. Conversely, when he long-erm ineres rae increases, long-erm deb increases much more han shor-erm deb. 3 See Barclay and Smh (1995), Sohs and Mauer (1996), Guedes and Opler (1996), Harwood and Manzon (2000) and Newberry and Novack (1999). 4 The size of forecased effecshough, are proporional o nominal ineres raes, so vary subsanially by year. 2
fracion of capal financed wh deb by 5.4 percenage poins. In addion, we repor evidence ha he erm srucure of ineres raes has smaller bu saisically significan effecs on he maury srucure of corporae deb. The res of he paper is organized as follows. Secion 2 briefly examines he hypoheses and develops he empirical sraegy. The daa are described in secion 3, and regression resuls are repored in secion 4. The paper concludes wh a brief summary and discussion. 2. Theory and Specificaion The heoreical forecass for he combined effecs of ineres raes and axes on a corporaion s choice of an overall deb level, and of he erm srucure on he choice of long-erm vs. shorerm deb have been laid ou in he pas. 5 In order o moivae he paricular empirical specificaion we use, however, is helpful o summarize explicly he naure of he heoreical argumen. Consider he financial decisions made by a corporaion. Denoe s oal deb by D, s long-erm deb by D L, and s shor-erm deb by D S. Denoe he curren shor-erm nominal ineres rae by r S and he curren long-erm nominal ineres rae by r L. Owners of long-erm deb also receive an ex-pos capal gain (loss if negaive) of g ~ in a given ime period. We examine firs he incenives faced by he marginal shareholder whose preferences deermine he pricing of corporae equy. 6 Assume ha his marginal shareholder has a personal ax rae of m, while he marginal ax rae on corporae income (including any subsequen personal axes for his shareholder) is denoed by τ. By consrucionhis marginal 5 See, e.g., Gordon (1982) and Brick and Ravid (1985). 6 According o he model in Gordon and Bradford (1980)he ax raes faced by his "marginal" shareholder represen a weighed average of he ax raes faced by shareholders generally, weighed by heir asses imes he inverse of he degree of heir risk aversion. These implic ax raes characerize secury pricing generally. 3
invesor is jus indifferen beween invesing anoher dollar in he firm s equy and invesing insead in eher long-erm or shor-erm bonds. In paricularhe invesor's marginal indifference beween long-erm and shor-erm bonds implies ha (1) 1 m) r + (1 ) c = (1 m) r, ( L g g S where c g denoes he equilibrium cerainy-equivalen (preax) income generaed by he random capal gain on long-erm deb, while g is he capal-gains ax rae on his random reurn. We assume ha he objecive of he firm's managers when making financial decisions is o maximize he value of he firm. The specific financial choices we focus on are he fracions of he firm's capal o finance wh long-erm and shor-erm deb, denoed by d L and d S respecively. When choosing he opimal use of long-erm and shor-erm deb financehe firm rades off he resuling ax savings/dissavings wh any nonax coss arising from a use of deb differen from ha which would be chosen ignoring ax consideraions. Le hese nonax coss be denoed by C( d, d K, where K denoes he firm's capal sock. By making his funcion L S ) proporional o K, we assume ha financial choices will be he same regardless of he scale of he firmhough we relax his assumpion in he empirical work below. We also assume ha hese nonax coss are a convex funcion of boh d L and d S. In paricular, assume ha C LL > 0 and C SS > 0. 7 Inuively, firms face pressures o mach he ime paern of heir income and financial liabilieso avoid having o come up wh he funds o repay deb a a dae when hey are cash consrained and may be forced o sell nonliquid asses a a deep discoun. Shor-erm deb would hen be ideal o handle seasonal variaion in expenses vs. revenue, whereas long-erm deb is preferable in financing longer-lived asses. In addion, assume ha he cos of adding 7 We are no assuminghoughha he minimum nonax coss occur when d L = d S = 0. See Jensen and Meckling (1976) for discussion of he many compeing pressures ha affec a firm's opimal financial srucure, even ignoring axes. 4
more of one maury of deb is higher he more deb he firm has of he oher maury: C > 0, LS wh C C < C C. If all ha maers is oal deb, due for example o he risk of LS SL SS LL bankrupcy when oal deb exceeds firm valuehen C = C = C. 8 LS LL SS The value of he firm will adjus o leave his marginal invesor indifferen a he margin beween invesing furher in equy and shor-erm bonds. 9 The cerainy-equivalen nominal reurn from equy should herefore equal he reurn he invesor could have received insead from invesing he same funds in shor-erm bonds: {( 1 τ )[ f ( K)(1 ρ) ( d r + d r ) K C( d, d ) K ] + (1 )( π c d ) K} V L L S S L S g g L / = ( 1 m)r S, where he numeraor of he lef-hand side is he afer-ax income from equy, and he denominaor V is he inial marke value of equy. Here, f ( K)(1 ρ) is he cerainyequivalen preax income o he firm for any given capal sock K, where f (K) is he expeced reurn and ρ capures he equilibrium marginal cos of risk bearing. The inflaionary increase in he value of he firm's capal and he cerainy-equivalen loss from bearing he capal-gains risk on long-erm deb are no par of he corporae income ax base, so are axed only a he shareholder's capal-gains ax rae g. Noe ha by definion V = qk( 1 d L ds ), where q equals he raio of he marke value o he book value of equy. A he financial policies ha maximize firm value, q / d = q / d = 0. 10 Using equaion (1) o simplifyhe resuling firs-order condions are: (2a) τ m ) r /(1 τ ) = C ( d, d ) and ( L L S L L S 8 When nonax coss of deb depend jus on aggregae deb, however, we would forecas corner soluions for long-erm vs. shorerm deb, conrary o he daa. 9 Of course, boh reurns also equal ha on long-erm bonds, as follows from equaion (1). 10 In addion, a he opimal capal sock for he firm, q = 1. 5
(2b) τ m ) r /(1 τ ) = C ( d, d ). ( S S S L We hen solve hese wo equaions for he opimal values of d S and d L, finding in general ha * (3a) d d (( τ m) r /(1 τ ),( τ m) r /(1 τ )) L = L L S * S = S S L (3b) d d (( τ m) r /(1 τ ),( τ m) r /(1 τ ))., and Given our assumpions, use of any given maury of deb will be an increasing funcion of he firs argumen in equaions (3ab), and a decreasing funcion of he second argumen o he exen ha C > 0. LS In he empirical work, for simplicy we will focus on he case where he wo specificaions in equaions (3ab) are linear: 11 (4a) D K S = δ S + α S τ m) r 1 τ ( τ m)( r ) β L r S, and 1 τ ( S S D (4b) L ( τ m) r ( τ )( ) = δ + α L m r + β L rs L L L. K 1 τ 1 τ Togeherhese equaions imply ha he firm s overall deb/capal raio should saisfy D ( τ m) r ( τ ) (4c) = δ + S m r a + L S al. K 1 τ 1 τ The expeced signs of all coefficiens are posive, given he way each equaion is specified. In he special case where C = 0, only he own ineres raes maer, in which case β β = 0 and α = a for i = S, L. i i LS Noe ha virually all pas empirical ess for ax effecs on use of corporae deb looked jus for effecs of ( τ m ). By ignoring he ineracion wh ineres raes, resuls can be misleading, suggesing consan effecs over ime of axes on deb raher han effecs ha vary in size depending on nominal ineres raes. S = L 6
In general he desired level of he deb/capal raio and he desired maury srucure ignoring ax incenives, δ S and δ L, can vary by firm and over ime. In paricular, assume ha δ S X + ε = θ S S, while δ L Xθ L + ε L =. We will include in he vecor X a flexible funcion of he amoun of asses of he firm, a measure of he business cyclehis business-cycle measure ineraced wh he log(asses) of he firm in order o allow for a differing impac of he business cycle on small vs. large firms, and informaion on he asse composion of he firm s capal sock. 12 In addion, we include hroughou a dummy variable equal o 1 in all years following he 1986 Tax Reform Ac. Under he 1986 Tax Reform Ac, individuals could no longer deduc nonmorgage ineres paymens and passive business losses (which commonly arose due o large ineres deducions). For individuals for whom hese resricions became binding in 1986, increasing heir ne holdings of bonds (borrowing less) no longer resuled in any ax liabilies. To he exen such individuals play an imporan role in he marke, corporae deb should hen be more aracive han our figures sugges. We saw no way o capure hese effecs of he 1986 Tax Reform ha go beyond changes in ax raes, oher han hrough such a dummy variable. 13 3. Descripion of Daa Se Daa come from hree sources: SOI Corporae Reurns, SOI Individual Reurns, and he Individual Model File (IMF). 14 All informaion abou firms comes from he SOI Corporae Reurns, which are available for 51 years from 1950 o 2000. These daa repor summary 11 We also reparameerize he equaion so ha depends on he ineres rae for ha maury and he erm srucureo aid in he laer inerpreaion of he resuls. 12 The expecaion is ha firms use more long-erm deb o finance longer-lived asses. 13 This dummy variable also provides some conrol for oher elemens of he 1986 Ac, such as changes in he Alernaive Minimum Taxha are no oherwise conrolled for. 14 The IMF is a sraified sample of individual ax reurns in he Uned Saes, made available for research purposes by he IRS, and is available from 1964 unil 1993, excep for 1965. 7
informaion aken from he corporae income ax reurns each year, and cover all corporaions in he US ha file ax reurns. While no informaion is available by firm, for confidenialy reasons, aggregae informaion for key variables is repored separaely each year for beween en and foureen differen asse inervals. 15 Uns of observaion in our empirical analysis are hese asse caegories. As a resul, our dependen variables will be he average deb per firm of a given maury over average capal per firm among all firms in a given size caegory, so is a weighed average of he dependen variables in equaion (4a-c) for firms whin a given size caegory, weighing by he asses of each firm. Since he break poins beween asse-size caegories are no fixed in nominal (le alone real) erms, and since on occasion he number of asse size caegories changeshis daa se is no sricly a panel daa se. We herefore include deailed conrols for he effecs of asse size on firm behavioro conrol flexibly for any effecs of firm size per se on financial policy. In order o esimae equaions (4a-c)he firs variables we need o measure are he dependen variables, requiring daa on shor-erm deb, long-erm deb, and oal firm asses. The amoun of deb held by firms in each asse caegory is repored separaely for shor-erm and long-erm deb. Shor-erm deb equals he accouning book value of morgages, noes, and bonds payable in less han one year, while long erm deb maures in a year or more. Toal deb is simply he sum of he wo. The (accouning) book value of asses in each size caegory again is repored direcly in he SOI Tables. Noe, howeverha he heory assumes ha all long-erm deb pays a given long-erm ineres rae, and similarly for shor-erm deb. Long-erm bonds payable whin one year are lised as shor-erm deb, ye pay he long-erm rae. Since he firm can adjus oher shor-erm 15 The asse caegories change slighly over ime, bu a ypical breakdown is: (0, 0.025m), (0.025m, 0.05m), (0.05m, 0.1m), (0.1m, 0.25m), (0.25m, 0.5m), (0.5m, 1m), (1m, 2.5m), (2.5m, 5m), (5m, 10m), (10m, 25m), (25m, 50m), (50m, 100m), (100m, 250m), and ($>$250m), where ``m'' indicaes millions of (nominal) dollars. 8
deb a he margin o compensae for any residual long-erm deb, our exising specificaion should handle his whou problem. In addion, some long-erm deb conracs have a floaing ineres rae. These bonds have he nonax characerisics of long-erm deb bu generae ax incenives ied o he shor-erm ineres rae. To ha exen, higher shor-erm ineres raes can lead o more raher han fewer long-erm bonds. 16 The nex variable we need o measure is he marginal corporae ax rae for each size caegory of firm. I is no always easy o find exogenous variaion in ax incenives o use in idenifying he causal effecs of axes on corporae use of deb. One poenial source of exogenous variaion is changes in he ax law. The ime-series variaion in a leas he op sauory corporae ax rae largely comes from he 1986 Tax Reform Ac. Ye his ax reform was sufficienly comprehensive ha is difficul o isolae he effecs of corporae vs. personal ax raes per se on corporae financial decisions. 17 The corporae ax schedule is progressive, however, and he lower bracke raes did change frequenly during he sample period, variaion we make use of below. Anoher poenial source of idenificaion is variaion in marginal ax raes across firms a any dae. Since sauory ax schedules are shared by firms, cross-secional variaion in marginal corporae ax raes depends on variaion in he paricular economic circumsances of each firm. In noaionhe marginal corporae rae τ is a funcion of some economic circumsances, X: τ (X ). Ye any ax rae ha by consrucion is simply a funcion of X could be serving as a proxy for X in he empirical work, leading o a biased coefficien. 16 An addional quesion is hen under wha condions a firm borrows a a fixed rae or a floaing rae. Since we have no daa on his choice, we do no examine his quesion. 17 For example, nonmorage ineres deducions were phased ou under he legislaion, as were deducions for passive losses on invesmens in noncorporae firms (which commonly arose due o large ineres deducions). By severely resricing ineres deducions under he personal axhe Ac should induce firms o do more borrowing. In addionhe corporae and personal alernaive minimum ax became much more imporan, effecs ha are hard o capure in he empirical work. 9
Many pas papers, for example, use dummy variables for he presence of ax loss carryforwards and he size of nondeb ax shields as indicaors for cross-secional variaion in ax incenives. Ye firms wh losses (as proxied by having ax loss carryforwards) may be pressed o borrow for nonax reasons, since hey likely face immediae liquidy pressures. As a resul, firms wh ax loss carryforwards will likely be observed o borrow more, in spe of he fac ha heir ax incenives are o avoid use of deb, because his measure of ax incenives is serving as a proxy for immediae liquidy pressures. Similarly, firms wh large nondeb ax shields (mainly depreciaion) presumably have more angible asses, which provide good collaeral for deb, generaing a poenially posive associaion beween nondeb ax shields and use of deb, in spe of he ax implicaions. Oher aspecs of firm circumsances ha researchers have used in consrucing a measure of corporae ax raes include curren profs and he volaily of pas profs. 18 Againhese economic circumsances per se can easily affec a corporaion's desired use of deb for nonax reasons, making hard o inerpre he coefficien of such a measure of he corporae ax rae. 19 In Gordon and Lee (2001), we focused on hese idenificaion problems, using U.S. Saisics of Income Corporae Tax Reurns ha repor informaion on he average values of key enries in he balance shee and income saemens for firms in various asse size caegories in each year over an exended ime period, based on ax reurn daa. 20 Since he corporae ax schedule is progressive, and changes shape frequenly over ime, we focused on using his variaion in he shape of he corporae ax schedule o idenify ax effecs on corporae use of deb. The calculaed ax rae sill depends on he amoun of asses for a firm, bu we included a 18 For example, Graham (1996) uses daa on curren profs and he volaily of pas profs o simulae he effecive marginal corporae ax rae for a firmaking ino accoun many complicaions in he corporae ax provisions. 19 For example, firms wh high curren profs face as a resul fewer liquidy pressures, so likely borrow less. Firms wh more volaile profs ceeris paribus are worse cred risks, so would have a harder ime borrowing. 20 Shih (1996) also used SOI corporae reurns o conduc aggregae ime-series analysis of he deerminans of ineres expense / oal revenue. He found an associaion wh corporae ax raes, personal ax raes, ineres raes, and inflaion. No aemp was 10
flexible funcion of firm asses, e.g. f (X ), in he esimaion. As a resul, τ (X ) differs from f (X ) due o s ime variaion arising from changes in he ax law, providing an exogenous source of variaion. In his paper, following Gordon and Lee (2001), we se he marginal corporae ax rae for firms in size caegory i in year o τ ( θ K ), where τ (.) represens he sauory corporae ax schedule in year, θ is he average axable income per dollar of asses in his size caegory in ha year, as repored in he daa, and K is he average asses per firm. 21 The ax rae sill depends heavily on conrol for independen effecs of of K. 22 K, and corporae use of deb can easily vary depending on firm size. To K on firm deb, we added as conrols a very flexible funcion Various issues arise wh his measure of he corporae ax rae. One concern is ha average income/asses for firms in a given size caegory may have direc effecs on corporae deb decisions. In Gordon and Lee (2001), we used as an insrumen o correc for any poenial bias a ax rae ha depended insead on K imes a fixed number represening an average prof rae for all firms. Resuls were unaffeced, so we do no worry abou such endogeney here. Noe ha our daa include firms wh boh profs and losses. We inenionally do no make use of daa on wheher firms have profs or losses in esimaing he corporae ax rae, since his informaion can have independen effecs on corporae use of deb. Our daa also madehougho es wheher he size of hese ax effecs varied wh ineres raes, or wheher ineres raes affec use of deb, and no jus ineres expense. 21 If he marginal corporae ax rae differs when we use he minimum vs. maximum capal sock per firm whin a size caegory, hen we use a weighed average marginal ax rae, assuming a uniform disribuion of firms whin he asse inerval for ha size caegory. n 22 j The funcional form we chose was β j (ln K ). We repor resuls wh n=9, given ha powers of ln K up o his order j= 1 were saisically significan in some of he specificaions. 11
unavoidably include boh C and S corporaions. 23 Boh ypes of firms, however, face he same ax incenive o use deb if he firms face he same marginal ax rae, 24 so problems arise only o he exen ha S corporaions face a differen ax rae. Tha firms are observed o shif quickly beween C and S corporae saus as relaive ax raes change suggess ha he ax raes faced by C and S corporaions are very close. 25 The daa also include all indusries, so we are no in a posion o es for differenial responses by indusry. Personal income ax raes are calculaed using he Individual Model File, when available, and oherwise wh daa from he SOI Individual Reurns. The represenaive ax rae for income repored under he personal income ax is defined o equal he weighed average marginal ax rae, weighing by axable income. One complicaion in capuring he effecs of personal axes on ineres income is he role of pension funds and oher insuional saving, which o a firs approximaion face a zero marginal ax rae on ineres income. Assuming ha pensions are as likely o rebalance heir porfolios in response o a change in corporae financial policy as households are on he financial porfolios hey conrol direcly, we se m equal o he weighed average ax rae calculaed from personal ax reurns muliplied by he fracion of household asses held ouside of pensions and life insurance companies. We also need o measure he effecive personal ax rae on income from corporae equy. There is much debae in he ax leraure on he appropriae measure of he effecive ax rae on boh dividends and capal gains. 26 We follow convenional pracice here and se he personal 23 The daa also unavoidably include financial insuions as well as some pass-hrough enies (REIT s and RIT s). The SOI ables unforunaely do no include breakdowns simulaneously by indusry as well as by asse size. To he exen our ax measure is irrelevan for hese oher secors (as we expec)hen he coefficiens do in fac measure he effecs of ax incenives on he behavior of nonfinancial corporaions. 24 Ayers e al (2001) noeshoughha his argumen applies only o ouside deb: Unlike C corporaions, S corporaions have no ax incenive o borrow from heir shareholders. Ayers e al hen find similar effecs of axes on use of ouside deb for C and S corporaions. 25 For evidence on shifing beween C and S corporae saus, see e.g. Gordon and MacKie-Mason (1990). 26 See, e.g. Auerbach (1979), Bernheim (1991) and Consaninides (1983) for argumens ha hese effecive ax raes can be zero or even negaive. 12
ax rae on ne-of-corporae-ax equy income equal o +, where d denoes d m ( 1 d ) ag he aggregae dividend payou rae, 27 g denoes he op capal gains ax raes, while a measures he gains from deferral of capal gains unil realizaion and he ax exempion of capal gains a deah. Following Feldsein e al. (1983), we se a equal o 0.25. The nex key variables we need o measure are he shor-erm and long-erm ineres raes. Here, we used he 3-year Treasury bond rae as a proxy for long-erm ineres raes and he 3-monh Treasury bill rae for he shor-erm ineres rae. 28 This choice mers some discussion, since he coupon rae ha firms in fac face will boh be higher and vary by firm, due o he surcharge credors require o compensae for defaul risk. The key poin o noe is ha compeion among lenders should ensure ha he acual paern of repaymens has he same value o he lender as receiving he risk-free rae insead. The mirror image of his saemen is ha he cos of he acual paern of repaymens o he borrowers should have he same cos as paying he risk-free rae insead. We used he governmen ineres raes as proxies for he shorerm and long-erm risk-free ineres raes. 29 In addion, we need some conrol for business cycle effecs on use of deb. As one conrol, we used he raio of he Dow Jones Index o GDP, on he grounds ha behavior can change as soon as new informaion arrives abou changing economic rends, and no jus when hese changes maerialize. 30 We allowed he response o business cycles o vary by size of firm 27 Here, we used he acual dividend payou raio for Sandard and Poor's 500 firms. Resuls were no sensive o his choice. 28 As an alernaive o he 3-year rae, we also ried he 5-year rae and he 10-year rae. Resuls were lle affeced. We focused on he 3-year bond rae on he presumpion ha bonds end o be issued inially for en years, leading o an average remaining maury of 5 years, bu bonds are ofen repaid early. 29 We also ried using he AAA corporae bond rae and he shor-erm prime rae, on he grounds ha hese bonds approximaed defaul free securies, ye may have raes ha differ from hose on governmen bonds for oher reasons. (The adminisraive oversigh for corporae loans could be higher, ineres receips are subjec o sae income axes unlike governmen bond ineres, ec.) Resuls again were virually unchanged. We preferred using governmen bond raes, since even AAA bonds face some defaul risk ha can vary in size over ime. 30 To calculae he yearly value for he Dow Jones Index, we ook he average of he opening and closing price in each monh, hen averaged hese monhly figures for each year. We also ried using he percen change in real GDP as a cyclical conrol. Oher coefficiens were unchanged, bu he coefficien of his conrol was insignifican and he f was a b worse. 13
by ineracing his variable wh ln K. As addional business-cycle conrols, we included he inflaion rae and he unemploymen rae, since hese wo variables appear o be he key inpus o moneary policy according o Taylor s rule. 31 We also included conrols for he asse composion of he firm's capal sock. 32 Since SOI Individual Reurns are no available before 1954 and SOI Corporae Reurns do no repor shor-erm deb and he composion of asses in 1962 and 1966-1969, our sample consiss of 42 years from 1954 hrough 2000, excluding 1962 and 1966-1969. Wh abou welve asse caegories on average per year, we end up wh 489 observaions. Summary saisics are repored in Table 1. On average, long-erm deb has been 64% of he oal deb of US corporaionshough his share varied grealy across size of firm and across years. The share of long-erm deb in oal deb ends o increase wh firm size, as shown in Figure 1, as would be expeced based on he above heory, since large firms face higher corporae ax raes han do smaller firms and since long raes generally exceed shor raes. Nominal 3-year and 3-monh TB ineres raes varied grealy during he sample period, from a mere 1% o 14%. Figure 2 describes he variaion over ime in sauory corporae ax raes, comparing nominal axable corporae income in each year wh he resuling marginal corporae ax rae. As seen from he Figurehere is subsanial variaion boh whin each year and across years in marginal ax raes. Using he real raher han nominal axable income in his graph, e.g. correcing for inflaion, would lead o furher variaion in corporae ax raes across years. 4. Regression resuls 31 For he inflaion rae, we used he yearly percen change in he CPI. 32 The informaion available includes he fracion of he capal represened by depreciable asses, land, cash, and oher asses. 14
Since pas papers have ignored he effecs of ineres raes, we sar in column (1) in Table 2 wh a specificaion ha also ignores ineres raes: D K = a m ) + X B ( τ + ε. There are a number of differences beween his specificaion and ha repored in Gordon and Lee (2001). 33 The key difference is ha we excluded year dummies in order o idenify more clearly he role of ineres raes. While he previous paper found a highly significan coefficien of around 4.2he coefficien now is -1.11 and saisically insignifican. The sensivy of he esimaed coefficien o he inclusion of year dummies we ake as srongly suggesive of he imporance of ineres rae effecs. If he correcly specified variable is ( τ τ m ) rs /(1 ) TrS bu he variable coefficiens compare wh ha of T rs? Noe ha (5) TrS = T ( r + ΔrS ) = rt + TΔrS -Including T raher han T is included insead, how should s esimaed T rs is equivalen o including he firs erm on he righ-hand side of equaion (5) bu oming he second erm from he specificaion. If Δ rs and T are saisically independenhen here is no bias: he expecaion of he esimaed coefficien of T should simply equal r imes he rue coefficien. 34 However, if Δ rs and T are negaively correlaed, hen he coefficien of T is biased downwards due o his omed variable. In fache daa show ha he correlaion in he sample beween Δ rs and T is -0.37. The oher coefficiens in column (1) are as expecedhough. Consisen wh pas resuls, more deb is used o he exen ha he firms asses are longer erm. Firms also use more deb 33 This specificaion differs from hose in Gordon and Lee (2001) because five more years of daa are included, year dummies are no included, oher yearly variables are included inseadwo more powers of ln K are included as conrols, personal axes on equy income are included, and he ax variable has 1 in he denominaor. τ 15
during recessions. 35 As expeced, firms use more deb afer he 1986 Tax Reform, even afer conrolling for changes in ax raes. Column 2 provides a nonparameric es o see if he daa sugges an ineracion of he ax variable wh marke ineres raes. To do so, we inerac he ax variable wh dummy variables indicaing wheher he shor-erm ineres rae in ha year is in he boom, secondhird, or op quariles of s values during he full sample period. The predicion is ha all of hese coefficiens should be posive, and an increasing funcion of he size of nominal ineres raes. We find ha he coefficiens do increase monoonically wh he size of ineres raes. For all bu he lowes quarile hey are posive, and hose for he highes wo quariles (bu also he lowes quarile) are saisically significan. 36 A leas for years wh ineres raes in he highes wo quarileshe coefficien on he ax variable is broadly similar o he value in Gordon-Lee (2001). Why migh he esimaed effec of axes on use of deb have he wrong signhough, in years wh he lowes ineres raes? Noe ha for years when ineres raes are in he boom quarile, variaion in he expression suggesed by he heory, movemens in r S T rs, will be heavily dominaed by, e.g. he variable doubles if ineres raes are 2% raher han 1%. To capure he effecs of his omed variaion in he ineres raehe esimaed coefficien of T needs o be negaive, given he negaive correlaion beween T and r S. In he oher quarileshere could sill be a downward bias, bu variaion in T rs is more likely o be dominaed by differences in effecive ax raes across size caegories and over ime. 34 There should be no bias as well if year dummies are included, as in Gordon-Lee (2001). Neing ou year effecshe wo variables on he righ-hand side of equaion (5) become r( T T ) and ( T T ) ΔrS. These wo variables are uncorrelaed, implying no bias from oming he laer variable from he specificaion. 35 While overall deb levels are no affeced by he inflaion rae or he unemploymen rae, for any given he value of he Dow, firms shif away from shor-erm deb when he inflaion rae and he unemploymen raes are high, perhaps due o more uncerainy abou shor-erm flucuaions in moneary policy. 36 Noe ha we also repor in brackes Whe-correced robus sandard errors o address he possibily ha error erms whin asse caegory over ime can be correlaed. Error erms whin a year across asse caegories can also be correlaed. Robus sandard errors addressing as well his possible problem are ye larger, bu coefficien esimaes remain significan. 16
These coefficiens, even wh any downward bias, indicae nonrivial effecs of axes on use of deb during periods when nominal ineres raes are above average in value. During years wh high ineres raes for example, lowering he ax rae on corporae income from.46 o.36 would reduce he forecased fracion of capal financed wh deb by abou 1.1%, relaive o a sample mean of 26%. Similarly, holding ax raes a heir mean, increasing ineres raes from values in he lowes o values in he highes quarile increases he fracion of capal financed wh deb by over 7%. Column 3 hen repors he resuls from esimaing equaion (4c), ineracing he ax variable wh boh he shor-erm ineres rae and he difference beween long-erm and shorerm ineres raes. Here, we find ha he shor-erm ineres rae is srongly saisically significan, while he erm srucure has a moderaely large coefficien bu is no saisically significan. In years where he shor-erm ineres rae and he difference beween long raes and shor raes boh equal he sample meanhe implied coefficien on he ax variable self is 4.7 (=5.62*.741+1.03*.472), so implies larger effecs of axes han hose repored in column (2). 37 Cuing he ax rae on corporae income by en percenage poins lowers forecased deb levels by 1.0% of capal, whereas he same ax changes in a year wh he highes observed shor ineres rae (holding he erm srucure fixed) would raise deb levels by 2.3% of capal, and by only 0.2% of capal in years wh he lowes shor-erm ineres rae. In years wh he mean ax raes, raising he shor-erm ineres rae by 10 percenage poins would raise forecased deb levels by 3.0% of capal. 38 37 Noe ha his esimae is jus slighly larger han he esimae of 4.2 found in Gordon and Lee (2001), where year dummies implicly conrolled for ineres rae effecs. 38 Tha he resuls here show less sensivy o ineres raes han hose in column 2 again suggess more of a downward bias in years where ineres raes were in he boom quarile han in years when ineres raes were in higher quariles. 17
Column 4 repors esimaes for equaion (4a), explaining D L / K. Here, we find highly saisically significan effecs of he long-erm ineres raes, bu no effecs of he shor-erm rae, perhaps because of he use of floaing ineres raes on some of he long-erm deb. Column 5 repors comparable esimaes for equaion (4b), explaining D S / K. Here, we find highly saisically significan effecs of he shor-erm ineres raes. Againhe coefficien on he erm srucure is small and saisically insignifican. By consrucionhe sum of he coefficiens for a given independen variable in columns 4 and 5 equal ha in column 3. The small and saisically insignifican coefficiens on he erm srucure in columns (4) and (5) of Table 2 sugges ha C 0, in which case he nonax coss of addional shor-erm LS (long-erm) deb do no depend on he amoun of long-erm (shor-erm) deb ha he firm has. This suggess ha possible liquidy consrains when deb comes due, perhaps as a resul of asymmeric informaion, may be a more imporan consideraion han he hrea ha he firm faces bankrupcy risk when overall deb levels become oo high. 39 Table 3 shows ha our including a flexible conrol for firm size does have imporan effecs on he esimaed coefficiens of he ax variables. Whou conrols for firm size (column 1) or even including linear or quadraic funcions of ln( K ), all of he esimaed ax coefficiens are larger, suggesing ha he ax variables can easily serve as proxies for firm size whou due care. By including a 9 h order polynomial in ln( K ) for firm size, we are asking a lo of he daa, bu feel more confiden ha he esimaed coefficiens indeed capure effecs of he ax law. In paricular, whou such exensive conrols he resuls sugges ha ha ax effecs are roughly wice as large, and ha only he long-erm ineres rae maers. 39 See Myers and Majluf (1984) for a model of corporae finance focusing on such liquidy consrains arising from asymmeric informaion. 18
Table 4 repors he regression resuls separaely for large and small-firms. We use 10 million 1995 US dollar as he divider, which generaes wo sub-samples wh almos idenical size. The resuls generally confirm srong responsiveness of deb o axes. 40 For examplehe implied coefficien of he ax variable, evaluaed a average shor erm and long-erm ineres raes, is 3.5 in column (1) and 3.87 in column (4), in conras o 4.7 in column 3 of Table 2. 41 One inriguing new resulhough, is ha a high long-erm rae discourages small firms from aking on shor-erm debhe firs srong evidence for C > 0. I is unsurprising ha small firms need o worry more abou heir overall deb levels, given heir much higher failure raes. Our resuls above make use of boh cross-secional and ime-series variaion in he daa. In heoryhe expeced coefficien esimaes should be he same, regardless of he source of variaion. If he wo sources of variaion generae que differen esimaes, howeverhis could be a sympom of poenial biases due o eher inadequae conrols for nonax differences across firms of differen sizes or due o inadequae conrols across ime, e.g. for business cycle effecs. As a specificaion check, we reesimaed he above resuls using aggregae ime-series daa. Specifically, we consruced aggregae figures for each year by aking a weighed average of he daa for each size caegory, weighing by asses held by firms whin each size caegory. Raher han rying o esimae again he effecs of firm size, asse composion, and he ineracion of firm asses and business cycle effecs, we subrac LS X θˆ from he dependen variable, using he esimaes from he corresponding column in Table 2. 42 We did no subrac off he esimaed effecs of axes, however, in order o facilae he inerpreaion of he ax coefficiens based on purely ime-series variaion. We also leave in he business cycle conrol 40 Even hough he coefficien on he shor-erm ineres is no significan in he equaion for smaller firmshe large and saisically significan coefficien on he erm srucure sill implies srong posive effecs of he shor-erm rae and negaive effecs of he long-erm rae. 41 Tha boh esimaed effecs are slighly smaller han hose from Table 2 is no surprising. Wh less variaion in ax incenives whin each of hese subsamples, any downward bias due o measuremen error should be larger. 42 In hese caseshe cross-secional variaion is essenial o idenify he size of hese effecs. 19
variables, and he dummy variable for years afer he 1986 Tax Reform. These variables vary only wh ime, so remain well idenified even when we resric he sample o aggregae imeseries daa. Resuls are repored in Table 5, wh columns 1-3 in Table 5 corresponding o columns 3-5 in Table 2. Coefficien esimaes for D / K in he wo Tables are very close. Shor-erm deb is esimaed o be slighly more responsive o shor-erm ineres raes, and long-erm deb slighly less responsive o long-erm ineres raes in he ime-series esimaeshough neher difference is large relaive o he esimaed sandard errors. Taken ogeherhese resuls provide no clear evidence of any specificaion biases. As a furher es of he above specificaion, we examined he sensivy of he above resuls o he mehod used for defining he appropriae corporae ax rae for each size caegory. In he above resulshe assigned corporae ax rae, τ θ K ), equals he sauory ax rae ( calculaed using he average axable profs per dollar of asses for firms in each size caegory. Ye effecive ax raes can vary among firms in a size caegory due o variaion in he curren prof raes. 43 Ignoring his variaion should resul in a downward bias in he coefficien. 44 In principle, we would like o measure E τ ( θ K ) K ). To es he sensivy of our ( resuls o variaion in axable profs across firms whin a size caegory, we calculae Eτ θ (1 + σ~ ε ) K ), where ~ ε is a sandard normal variable while σ is a parameer we (( experimen wh. 45 Prior resuls implicly se σ = 0. 46 Column 1 of Table 6 repors resuls for 43 The average prof rae could be approximaely righ if here were unlimed averaging across many years. Bu wh he limed averaging provided by exising carryback and carryforward provisionsaxable prof raes will vary across firms. 44 Our calculaed ax rae jumps discreely when average profs in a size caegory cross ino a higher ax bracke, whereas he average marginal ax rae should increase smoohly as expeced profs increase. To compensae for he larger variaion in our calculaed ax raehe esimaed coefficien should be smaller. 45 This procedure is analogous o ha used by Graham (1986). Graham sared wh a firm s profs in a year and simulaed he degree o which profs are smoohed due o carryback and carryforward provisions. We sar wh average profs for firms in a given size caegory, and simulae how much axable profs vary across firms due o random variaion in prof raes no averaged ou due o exising carryback and carryforward provisions. 20
D / K when τ is calculaed using σ = 1, while column 2 repors resuls for σ = 2. 47 As expecedhe coefficiens on boh he shor-erm and he long-erm ineres raes are higher han hose repored in column 3 of Table 2, roughly doubling in size. Equivalen resuls are repored in columns 3 and 4 of Table 6 for D L / K, and in columns 5 and 6 for D S / K. In each case he coefficien of he ax erm imes he ineres rae of he same maury roughly doubles in size, while he coefficien of he erm srucure erm remains small and saisically insignifican. Using hese esimaes, we find ha increasing ineres raes by 5 percenage poins, assuming ha τ m =. 27 and ( 1 τ ) =. 48, should increase he fracion of capal financed wh deb by 5.4 percenage poins (e.g., going from 25.7% on average o 31.1%), based on he esimaes in column 2 of Table 6. A rise in r L by 200 basis poins, for any given value of r S, would increase ( D D ) K by 1.1 percenage poins using he resuls in columns 4 and 6 in L S / Table 6. The esimaed sensivy o ax raes is comparable. When r = 6.6%, r = 5.6%, and L S m = 24%, reducing τ by en percenage poins, i.e. from 46% o 36%, would reduce he fracion of capal financed wh deb by 3 percenage poins, using he coefficien esimaes in column 2 of Table 6. 48 The same ax change would lower D L / K by 1.9 percenage poins and D S / K by 1.1 percenage poins, using he esimaes in columns 4 and 6 in Table 6. 5. Summary and Discussions 46 Given he observed prof rae, however, we did allow dollar profs o vary whin a size caegory in proporion o he asses of each firm, assuming ha firm asses have a uniform disribuion whin he size caegory 47 Noe ha in each casehe resuling ax rae is a weighed average of all he differen ax brackes, weighing by he probabily ha he resuling axable income is in he appropriae range for ha bracke. We focus on resuls for σ = 2, since his degree of variaion is broadly consisen wh he fracion of asses reporing axable losses whin any given size caegory. 48 Noe ha his figure will differ across years, depending on he prevailing nominal ineres raes. 21
Consisen wh heoreical forecass, we provide empirical evidence ha boh he overall corporae use of deb and he maury srucure of his deb are affeced by he level and he erm srucure of nominal ineres raes. Inflaionary increases in ineres raes do have real effecs due o his ineracion wh he ax law. In paricular, our esimaes sugges ha he variaion in nominal ineres raes seen during our sample period is esimaed o have lead o a 14.1 percenage poin variaion in he fracion of capal financed wh deb, while a 200 basis poin increase in he long-erm ineres rae for any given value of he shor-rae is prediced o lead o 1.1 percenage poin variaion in he fracion of capal being financed wh long-erm raher han shor-erm deb. In addion, once he ineracion of axes wh ineres raes is aken ino accoun, esimaed effecs of axes on use of deb are found o be subsanial. In paricular, raising he effecive ax rae on corporae income from he minimum o he maximum value in our sample is forecas o raise he fracion of capal financed wh deb by 11.3 percenage poins during years wh average ineres raes, bu by much more during years wh high ineres raes and much less during years wh low ineres raes. Conrolling for ineres raes leads o larger esimaed effecs of axes on average, since in he daa ineres raes were negaively correlaed wh ax incenives. These ax effecs, of course, would be subsanially reduced if only real ineres paymens raher han nominal ineres paymens were deducible (and axable). The resuls herefore provide addional empirical evidence on he value of indexing he ax law appropriaely for inflaion. References 22
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Table 1. Summary Saisics Variable Noaion Sources Obs Mean s. dev. Min Max Corporae deb oal deb / asses SOI: Corporae Reurns 489 25.68 8.05 9.86 43.13 long-erm deb / asses SOI: Corporae Reurns 489 16.12 4.55 7.30 30.32 shor-erm deb / asses SOI: Corporae Reurns 489 9.56 3.98 0.79 17.34 long-erm deb / oal deb SOI: Corporae Reurns 489 64.01 7.24 49.00 93.51 Tax raes Corporae income ax rae including any subsequen personal axes on equy income Personal ax rae he fracion of household asses ouside of pensions and life insurance (Corporae personal ax raes) divided by (1 corporae ax raes) τ m ( τ m ) (1 τ ) Auhors calculaion using SOI: Corporae Reurns, Economic Repor of he Presiden (ERP) Auhors calculaion using SOI: Individual Reurns, FFA Auhors calculaion using SOI: Corporae Reurns, SOI: Individual Reurns, ERP, FFA 489 45.97 11.76 23.39 60.66 42 24.15 2.47 20.39 29.24 489 0.46 0.29 0.01 0.92 Ineres raes and oher yearly variables 3-year Treasury Bond rae r L ERP 42 6.65 2.85 1.63 14.44 3-monh Treasury Bill rae r S ERP 42 5.62 2.80 0.95 14.03 3-year 3-monh Treasury rae r L rs ERP 42 1.02 0.67-0.33 2.31 Consumer price index CPI ERP 42 0.60 0.36 0.19 1.23 weighed average of τ τ see source for τ 42 51.62 6.45 41.11 59.32 weighed average of τ m τ m see source for τ and m 42 27.47 4.93 18.59 35.28 Dow Jones index / GDP DowGDP GDP from ERP 42 0.71 0.33 0.27 1.27 Inflaion rae ERP 42 4.18 3.14-0.37 13.50 Unemploymen rae ERP 42 6.06 1.37 4.02 9.69 Corporae asses r Real asses per reurn A SOI: Corporae Reurns 489 375 1,041 0.02 4,803 Ne depreciable asses / asses SOI: Corporae Reurns 489 20.84 6.44 5.82 35.66 Land / asses SOI: Corporae Reurns 489 3.63 2.41 0.11 8.31 Cash / asses SOI: Corporae Reurns 489 9.77 4.45 2.80 28.69 Accoun receivable / asses SOI: Corporae Reurns 489 22.43 4.75 7.55 34.39 Inangible asses / asses SOI: Corporae Reurns 489 1.45 1.43 0.08 6.23 Noe: 1. Uns of he variables are percens excep for real asses per reurn and average Dow Jones index / GDP, for which uns are million US $ and a fracion, respecively. 2. Dow Jones indices are downloaded from www.forecass.org and The Flow of Funds Accouns in he Uned Saes are downloaded from he Federal Reserve Board s we se. 3. τ is he weighed average of τ whin a year, weighing by asses. Since firms wh larger asses face higher ax raeshe mean of τ is larger han he mean of τ. 25
Table 2. Baseline regressions, OLS Dependen variable (1) (2) (3) (4) (5) D / K D / K D / K D L / K D S / K -1.105 ( τ m ) (1.041) [1.416] ( τ m ) -2.928 (0.929)** (dummy for boom quarile of rs, ) [1.400]+ ( τ m ) 0.800 (1.020) (dummy for second quarile of rs, ) [1.470] ( τ m ) 2.850 (0.973)** (dummy for hird quarile of rs, ) [1.453]+ ( τ m ) 4.583 (1.050)** (dummy for op quarile of rs, ) [1.714]* 0.741 0.278 ( τ m ) rs (0.089)** (0.063)** [0.138]** [0.119]** ( τ 0.463 m ) rl (0.055)** [0.067]** ( τ ) /(1 ) ( ) 0.472 0.057-0.047 m τ rl rs (0.310) (0.199) (0.219) [0.290] [0.214] [0.269] DowGDP -3.342-0.888-2.856-0.850-2.006 (0.571)** (0.537)+ (0.528)** (0.325)** (0.373)** r DowGDP log( A ) -0.247-0.002-0.060 0.037-0.097 (0.117)* (0.107) (0.112) (0.069) (0.079) Dummy for pos 1986 1.732 2.267 2.298 1.731 0.567 (0.424)** (0.383)** (0.402)** (0.247)** (0.284)* Inflaion rae 0.068-0.012 0.013 0.065-0.052 (0.043) (0.038) (0.047) (0.029)* (0.033) Unemploymen rae 0.073 0.212 0.001 0.177-0.176 (0.089) (0.078)** (0.092) (0.057)** (0.065)** Ne dep. asses / oal asses 0.136 0.221 0.148 0.192-0.044 (0.049)** (0.043)** (0.046)** (0.028)** (0.032) Land / oal asses 0.836 0.477 0.992 0.781 0.211 (0.237)** (0.212)* (0.222)** (0.136)** (0.157) Cash / oal asses -0.293-0.225-0.270 0.237-0.507 (0.091)** (0.079)** (0.084)** (0.052)** (0.060)** Accouns receivable / oal asses -0.047-0.126-0.136-0.022-0.114 (0.054) (0.047)** (0.051)** (0.031) (0.036)** Inangible asses / oal asses 1.066 0.762 1.190 1.028 0.162 (0.175)** (0.155)** (0.143)** (0.088)** (0.101) Number of observaions 489 489 489 489 489 Adjused R 2 0.951 0.963 0.957 0.949 0.912 Sandard errors in parenheses. Whe-correced robus sandard errors assuming ha he observaions are independen across asse caegory bu no necessarily independen whin asse caegory in brackes. Consan erm and up o he 9 h polynomial in log of asses are included, bu no repored. + significan a 10% level; * significan a 5% level; ** significan a 1% level. 26
Table 3. Robusness o changes in firm-size conrols, OLS Dependen variables are he raio of oal, long-erm, or shor-erm deb o oal asses in percen. oal deb / asses ( τ ) r m S ( τ m ) ( rl rs ) (1) (2) (3) (4) whou firmsize 2 nd order 9 h order conrols wh log(asses) polynomial polynomial 1.283 1.308 1.296 0.741 (0.131) ** (0.126) ** (0.129) ** (0.089) ** [0.323] ** [0.321] ** [0.276] ** [0.138] ** 1.655 1.673 1.625 0.472 (0.472) ** (0.455) ** (0.470) ** (0.310) [0.509] ** [0.513] ** [0.482] ** [0.290] Adjused R 2 0.884 0.893 0.892 0.957 long-erm deb / asses ( τ ) r m L, ( τ m ) ( rl rs ) 0.664 0.661 0.635 0.463 (0.059) ** (0.058) ** (0.060) ** (0.055) ** [0.125] ** [0.120] ** [0.103] ** [0.067] ** 0.133 0.134 0.051 0.057 (0.230) [0.229] (0.229) [0.235] (0.232) [0.277] (0.199) [0.214] Adjused R 2 0.927 0.927 0.928 0.949 shor-erm deb / asses ( τ ) r m S ( τ m ) ( rl rs ) 0.619 0.646 0.661 0.278 (0.098) ** (0.090) ** (0.092) ** (0.063) ** [0.250] * [0.220] * [0.196] ** [0.119] * 0.858 0.878 0.940-0.047 (0.355) * [0.450]+ (0.324) ** [0.478]+ (0.335) * [0.384]* (0.219) [0.269] Adjused R 2 0.733 0.777 0.777 0.912 Sandard errors in parenheses. Whe-correced robus sandard errors assuming ha he observaions are independen across asse caegory bu no necessarily independen whin asse caegory in brackes. + significan a 10% level; * significan a 5% level; ** significan a 1% level. Each column repors he resuls of hree regressions for oal deb / asses, long-erm deb / asses, and shor-erm deb / asses. In each regressionhe same se of independen variables as in columns (3)-(5) of Table 2 is included in he regressions, bu no repored. Regression resuls wh up o he 3 rd polynomial in log of asses hrough wh up o he 8 h polynomial in log asses lie beween he resuls in columns (3) and (4), and are no repored. Resuls in column (4) of Table 3he same as columns (3)-(5) of Table 2, are repeaed for comparison. 27
Table 4. Large- vs. small-firms, OLS Dependen variables are he raio of oal, long-erm, or shor-erm deb o oal asses in percen. Sample Dependen variable (1) (2) (3) (4) (5) (6) asse caegories asse caegories wh real asses > 10m wh real asses < 10m D / K D L / K D S / K D / K D L / K D S / K ( τ m ) rs ( τ m ) rl ( τ m ) ( rl rs ) 0.521 0.252 0.734-0.010 (0.099) ** (0.065) ** (0.190) ** (0.124) [0.113] ** [0.040] ** [0.319] + [0.162] 0.269 0.744 (0.054) ** (0.122) ** [0.095] * [0.203] * 0.593 0.246 0.078-0.244-0.249-0.738 (0.201)+ (0.176) (0.213) (0.602) (0.400) (0.391) + [0.259]+ [0.231] [0.179] [0.488] [0.320] [0.476] Number of observaions 243 243 243 246 246 246 Adjused R 2 0.956 0.948 0.940 0.757 0.816 0.762 Sandard errors in parenheses. Whe-correced robus sandard errors assuming ha he observaions are independen across asse caegory bu no necessarily independen whin asse caegory in brackes. + significan a 10% level; * significan a 5% level; ** significan a 1% level. In each regressionhe same se of independen variables as in columns (3)-(5) of Table 2 is included in he regressions, bu no repored. 28
Table 5. Time series regressions, OLS, using weighed averages Dependen variables are yearly variaion in he raio of oal, long-erm, or shor-erm deb o oal asses unexplained by non-ax variables or non-yearly variables. (1) (2) (3) Esimaion mehod OLS OLS OLS Dependen variable D / K D L / K D S / K ( τ 0.733 0.440 m ) rs (0.210)** (0.117)** ( τ 0.292 m ) rl (0.117)* ( τ ) /(1 ) ( ) 2.110 1.151 0.666 m τ rl rs (0.729)** (0.401)** (0.406) DowGDP -2.652-1.384-1.268 (1.137)* (0.633)* (0.632)+ Dummy for pos 1986 2.762 1.703 1.059 (0.606)** (0.338)** (0.337)** Inflaion rae 0.203 0.156 0.047 (0.112)+ (0.062)* (0.062) Unemploymen rae -0.528-0.131-0.397 (0.219)* (0.122) (0.122)** Consan 1.140 1.866-0.726 (2.186) (1.217) (1.216) Number of observaions 42 42 42 Adjused R 2 0.781 0.810 0.668 Sandard errors in parenheses. + significan a 10% level; * significan a 5% level; ** significan a 1% level. Sample years are 42 years from 1954 o 2000 excep for 1962 and 1966-9. Dependen variables are he average values of he raio of deb o asses each year, correced for he effecs of he non-ax variables or non-yearly variables using coefficiens from column (3), (4), and (5) of Table 2. 29
Table 6. Sensivy o alernaive calculaion of corporae ax raes Dependen variables are he raio of oal, long-erm, or shor-erm deb o oal asses in percen. (1) (2) (3) (4) (5) (6) Dependen variable D / K D L / K D S / K Assumpion on σ σ = 1 σ = 2 σ = 1 σ = 2 σ = 1 σ = 2 ( τ m ) rs ( τ m ) rl ( τ m ) ( rl rs ) 1.259 1.932 0.472 0.806 (0.145) ** (0.212) ** (0.103) ** (0.150) ** [0.193] ** [0.295] ** [0.153] ** [0.244] ** 0.788 1.125 (0.089) ** (0.132) ** [0.119] ** [0.160] ** 0.820 0.970 0.072-0.137-0.039-0.018 (0.474)+ (0.681) (0.301) (0.442) (0.336) (0.483) [0.424]+ [0.671] [0.330] [0.524] [0.305] [0.420] Number of observaions 489 489 489 489 489 489 Adjused R 2 0.957 0.958 0.949 0.949 0.912 0.914 Sandard errors in parenheses. Whe-correced robus sandard errors assuming ha he observaions are independen across asse caegory bu no necessarily independen whin asse caegory in brackes. + significan a 10% level; * significan a 5% level; ** significan a 1% level. In each regressionhe same se of independen variables as in columns (3)-(5) of Table 2 is included in he regressions, bu no repored. 30
Figure 1. Raio of long-erm o oal deb, by firm asses, 1954-2000 54 90 58 55 59 57 56 60 61 55 54 58 57 56 61 64 long-erm deb / oal deb, % 80 70 60 56 59 60 54 63 55 61 58 54 59 64 54 60 57 100 65 100 58 58 56 55 63 99 59 93 98 99 94 61 60 56 55 57 65 64 9892 97 93 87 94 96 98 97 88 99 100 9795 96 91 94 94 96 95 99 98 99 89 98 57 63 77 93 9593 100 96 97 86 76 71 54 59 64 91 90 83 95 70 87 96 9590 88 99 61 92 78 75 100 898785 57 54 60 97 87 79 94 92 857080 8481 88 91 90 86 84 92 92 100 98 9793 94 86 90 58 88 71 89 96 72 82 63 87 92 82 54 61 89 59 59 57 57 58 59 648985 65 81 85 84 82 80 90 91 9591 93 83 64 78 88 63 61 60 75 74 91 86 79 86 10990 93 56 65 73 61 61 58 61 60 5955 63 57 61 63 63 58 57 63 63 7270 76 83 85 9290 87 83 89 86 72 76 89 78 8381 79 64 59 60 58 75 79 98 88 81 55 58 60 57 63 71 73 65 74 8280 84 90 88 91 96 95 94 82 74 80 77 8472 71 65 87 86 97 99 97 81 57 59 54 54 64 59 85 60 6454 56 77 58 70 60 71 60 1098 0 83 73 6554 64 64 63 73 78 76 7785 96 82 84 77 72 58 57 76 75 70 95 94 59 70 65 55 54 56 7056 65 8371 81 70 81 76 93 7574 71 71 72 80 8079 77 7370 78 73 7472 55 72 76 82 84 83 91 85 84 80 76 71 65 75 82 81 60 56 56 72 71 82 929088 75 70 6474 79 7592 93 77 86 55 80 61 55 557473 75 87 91 74 83 89 65 7473 75 72 56 77 73 73 77 78 8097 96 7978 7978 90 81 94 56 76 8280 7 6 74 95 54 55 89 81 91 99 98 90 63 83 79 92 86 84 7978 58 886 99 89 85 84 77 10 0 78 97 9893 85 60 59 100 96 95 88 87 94 57 87 65 63 71 7672 77 7573 78 70 79 80 74 81 82 86 93 9183 84 92 87 85 9488 95 96 97 89 10 0 90 98 99 50 55 56.025.05.1.25.5 1 2.5 5 10 25 50 100 250 500 4000 AsCPI Noe: Real asses per firm are on he x-axis, where log scale is used. The label is he year of he observaion. Source: Auhors calculaion using SOI Corporae Reurns. 31
Figure 2. US Corporae ax rae srucure, 1954-2000 Marginal ax rae 50 40 30 20 30 52 52.8 48 50 48 49.2 48 24.2 22 22 22.5 22 20 22 48 20 51 46 46 46 46 42.5 40 40 40 40 39 39 37 34 34 30 30 30 30 27.5 25 25 19 18 18 16.5 40 35 34 38 35 10 17 16 15 15 15 15 15 above 18,333 b 15 & 18,333 0 1954-1963 1964 1965-1967 Year 1968-1969 1970 1971-1974 1975-1978 1979-1981 1982 1983 1984-1986 1987 1988-1992 1993-2000 below 25 b 50 & 75 b 25 & 50 b 335 & 1,000 b 100 & 335 b 75 & 100 b 10,000 & 15,000 b 1,405 & 10,000 b 1,000 & 1,405 Taxable incomehousand dollars Noe: All figures represen nominal income. Source: Gordon and Lee (2001), updaed o year 2000. 32