Testing the Trade-off Theory of Capital Structure: A Kalman Filter Approach

Transcription

1 Tesng he Trade-off Theory of Capal Srucure: A Kalman Fler Approach Raul Susmel eparmen of Fnance C.T. Bauer College of Busness Unversy of Houson Houson, TX (713) rsusmel@uh.edu and Tan Zhao Invesco Am Capal Managemen LLC eparmen of Invesmen, Houson, TX (713) Tan.Zhao@nvescoam.com Sepember 2008 Absrac In hs paper, we use a Kalman fler n order o es he sandard dynamc rade-off model of capal srucure. In hs model, he observed realzed deb-equy rao s a weghed average of he unobservable arge deb-equy rao and las perod s realzed deb-equy rao. The use of he Kalman fler, however, allows us o drecly esmae he unobservable arge deb-equy rao. We fnd ha he rade-off model canno be rejeced for 32% o 52% of he frms n our sample a he sandard 5% level. We also use a regresson n order o es f our Kalman fler esmaed arge deb-equy raos are relaed o he fundamenal varables usually proposed n he corporae srucure leraure. Overall, we fnd suppor for our esmaes. We hank Ronald Snger and Ramon Rabnovch for her nsghful suggesons and advce. We also hank Abu Amn for a seres of helpful dscussons. 1

2 Tesng he Trade-off Theory of Capal Srucure: A Kalman Fler Approach Sepember 2008 Absrac In hs paper, we use a Kalman fler n order o es he sandard dynamc rade-off model of capal srucure. In hs model, he observed realzed deb-equy rao s a weghed average of he unobservable arge deb-equy rao and las perod s realzed deb-equy rao. The use of he Kalman fler, however, allows us o drecly esmae he unobservable arge deb-equy rao. We fnd ha he rade-off model canno be rejeced for 32% o 52% of he frms n our sample a he sandard 5% level. We also use a regresson n order o es f our Kalman fler esmaed arge deb-equy raos are relaed o he fundamenal varables usually proposed n he corporae srucure leraure. Overall, we fnd suppor for our esmaes. 2

3 1. Inroducon The hypohess ha arge deb-equy rao are employed by corporaons has been esed exensvely n he corporae srucure leraure. Graham and Harvey (2001) fnd ha 81% of frms use a specfc (or range of) arge deb-equy rao(s) when makng her deb decsons. Furhermore, Flannery and Rangan (2006) pon ou ha mos emprcal analyss of hs hypohess rely heavly on he rade-off heory, whch saes ha frms selec a arge deb-equy rao by radng off her cos and benefs of leverage. The workng verson of he rade-off heory allows for he adjusmen of he deb-equy rao over me, renderng a dynamc rade-off model. Hovakman, Opler, and Tman (2001), Srebulaev (2004), Flannery and Rangan (2006), and Kayhan and Tman (2007) fnd ha he dynamc rade-off model domnaes alernave models, such as: Myers (1984) peckng order model, Baker and Wurgler s (2002) marke mng model, and Welch s (2004) manageral nera model. They conclude ha frms acvely pursue arge deb-equy raos over me even hough marke frcons lead o an ncomplee adjusmen n any one perod. Fama and French (2002), however, do no fnd a clear cu domnan model. The rade-off model leraure recognzes ha he arge deb-equy rao s emprcally unobservable and, herefore, uses a reduced form equaon o drecly esmae he paral adjusmen parameer, whch s called he speed of adjusmen. Technques such as wo-sage esmaon, nsrumenal varables, and dynamc panels are used n order o work around he fac ha he deb-equy rao s unobservable and ge an esmae of he speed of adjusmen. Ye, as repored by Flannery and Hankns (2007), he esmaes obaned employng hese mehods exhb grea varaon. For example, Fama 3

4 and French (2002) repor annual esmaes of he paral adjusmen parameer from 7 o 18%, Robers (2002) repors annual esmaes close o 100% for some ndusres. These wde dfferences are arbued o economerc problems, among hem, unobservable varable ssues, heerogeneous panel, auocorrelaed and cross correlaed errors, shor panels, unbalanced panels, ec. In hs paper, we esmae he srucural dynamc rade-off model by employng he Kalman fler esmaon echnque. The man advanage of usng he Kalman fler s ha allows us o esmae he unobserved arge deb-equy rao drecly, hus, leadng o a smple es of he rade-off capal srucure heory. Wh hese esmaes, we es wheher he frm s realzed deb-equy rao s equal o a weghed average of he arge deb-equy rao and las perod s realzed deb-equy rao. Moreover, snce here s no consensus regardng he dynamc behavor of he arge deb-equy rao, he use of he Kalman fler echnque allows us o esmae he dynamc rade-off model under dfferen assumpons regardng he dynamcs of he unobservable deb-equy rao. In our analyss we use an auoregressve process, a random walk process, and a consan process and show her mpac on he resuls. We furher depar from he exan leraure by no usng panel daa esmaon, as s ofen done n he recen leraure. Insead, we esmae and es he srucural dynamc models for ndvdual frms. Ths focus on ndvdual frms allows us o sudy he percenage of frms for whch he dynamc rade-off model holds emprcally, as well as o esmae he speed of adjusmen for each frm. Our paper s closely relaed o Robers (2002), who also uses a Kalman fler model o esmae a dynamc rade-off model. He uses he Kalman fler o ndrecly 4

5 esmae he arge deb-equy rao hrough a se of economc varables, whle we use he Kalman fler o drecly esmae he arge deb-equy rao. A sgnfcan dfference beween our approach and Rober s (2002) s ha he emphaszes he speed of adjusmen and s deermnans, whle we emphasze esng he rade-off model. Our emprcal analyss ndcaes ha he dynamc rade-off model holds.e., canno be rejeced a he sandard 5% level- for 32% o 52% of he frms n our sample, dependng on he assumpons abou he arge deb-equy process used o esmae he Kalman fler. We also fnd ha for he model assumng an auoregressve arge debequy rao, he medan and he average quarerly speed of adjusmen are.161 and.276, respecvely. These numbers are close o he annual esmaes repored n Flannery and Rangan (2006). Confrmng prevous work, we fnd a huge cross-seconal varaon n he speed of adjusmen parameer. The emprcal 95% confdence nerval for he speed of adjusmen has as bounds.025 and.951. The nerquarle range, however, s no ha exreme, gong from.088 o.347. The res of he paper s organzed as follows. Secon 2 presens he model and he mehodology of our es of he dynamc rade-off model. Secon 3 presens he daa, Secon 4 presens he resuls and Secon 5 concludes. 2. The Model The dynamc rade-off model s based on he dea ha frms canno nsananeously acheve her arge leverage, raher hey adjus her realzed deb-equy raos over me. Thus, every me perod he frm uses he las perod s dfference beween he realzed deb-equy rao and s arge deb-equy rao n oder o acheve a 5

6 more desrable deb-equy rao n he nex perod. The dynamc rade-off heory s descrbed by he followng model: (,, 1 ) e, = +, γ (1) where, s frm s realzed deb-equy rao n perod,, s frm s arge debequy rao, s he dfference operaor, γ s he paral adjusmen coeffcen; 0 γ 1, and e, s a regresson error. Snce he arge deb-equy rao s unobservable, s no possble o drecly es he dynamc rade-off model n equaon (1) and s common o model he arge debequy rao,,, as a lnear funcon of a se of economc varables. The followng equaon complees he sandard emprcal seup for he rade-off model:, = β, (2) X, where he vecor X, conans a se of wdely suded varables n he leraure such as earnngs before axes, marke-o-book rao, margnal ax rae, Alman Z score, ndusry dummy varables, capal expendure, research and developmen expendures, ec. We emphasze ha equaon (2) s no par of he rade-off heory, snce he rade-off heory does no explcly model he arge deb-equy rao. Raher equaon (2) s an ad-hoc formulaon where some explanaory varables, whch are derved from dfferen heores and oher explanaory varables, ncluded because hey f he daa. (See, for example, Rajan and Zngales (1995), Fama and French (2002), Chen and Zhao (2005).) Subsung (2) no (1) yelds: γ β X + 1 γ ) + e, (3), =,, (, 1 whch s he sandard framework used n he leraure o esmae capal srucure models. 6

7 Noce ha he es of he rade-off heory would be sraghforward f an esmae of he arge deb-equy rao were avalable. Smply, rearrange equaon (1) o oban:, = + ( 1 γ ), 1 γ + e (4) Equaon (4) ells us ha f he sandard paral adjusmen verson of he rade-off model s correc, hen he realzed deb-equy rao s a weghed average of s lagged debequy rao and he arge deb-equy rao. If, s avalable, hen, o es he rade-off model n equaon (4) we only need o es ha he slope coeffcens n a lnear regresson of, agans, and, 1 (3) does no allow he researcher o es hs hypohess. add up o 1. Unforunaely, he usual esmaon of equaon As menoned above, gven ha he arge deb-equy rao s unobservable, many papers sudy he speed of adjusmen parameer, γ, assumng a common γ for all he frms (γ =γ for all ) by employng a panel regresson of realzed deb-equy rao on s one-perod lag as well as a vecor of varables X, ; see, for a recen example, Flannery and Hankns (2007). The esmaon of equaon (3), however, rases wo man problems: he denfcaon problem, and he frm heerogeney of he sample problem. The denfcaon problem arses because equaon (3) s a reduced form equaon ha depends on he correc specfcaon of equaon (2). I follows ha whle equaon (3) can be used o esmae he paral adjusmen coeffcen, γ, canno be used o esmae, drecly nor can be used o es he rade-off model. 1 In oher words, even when he coeffcens n equaon (3) are sascally sgnfcan, one may only nfer ha a lnear 1 Several papers conflc regardng he nerpreaon of he resuls from he esmaon of equaon (3). In parcular, a sgnfcan speed of adjusmen coeffcen can be obaned under dfferen heores. See, for example, Chen and Zhao (2005). 7

8 regresson of he realzed deb-equy rao on he lagged (observed) deb-equy rao and he drvng varables X, produces sgnfcan resuls. One canno draw any concluson regardng he valdy of equaons (1) and/or (2). Noe ha he unobservable may be esmaed n a second sep hrough he ndrec esmaon of β n equaon (3). Bu, we should keep n mnd ha a correc specfcaon of equaon (2) s crucal o draw vald nferences abou he rade-off model. Therefore, n ryng o avod hs possble msspecfcaon ssue, dfferen sudes assume he γ =γ for all, esmae γ β and focus aenon on γ. Tha s, hey do no esmae β or dynamc rade-off model., and hence do no drecly es he The frm heerogeney of he sample problem arses snce panel mehods are used o esmae equaon (3). Panel mehods assume a common γ for all frms (see, for example, he use of Fama-Macbeh s mehod n Fama and French (2002) or he use of fxed effecs n Flannery and Rangan (2006).) However, he sgnfcan cross-seconal varaon of deb-o-equy raos repored n he leraure clearly ndcaes ha assumng a common paral adjusmen coeffcen for all frms s a exremely resrcve assumpon. In hs paper we overcome boh problems by employng he Kalman fler echnque and, hus, esmang he unobservable arge deb-equy rao drecly. As wll become clear below, he arge deb-equy rao,,, can be drecly esmaed usng a Kalman fler. Frs, we assume ha, follows an AR(1) process. Ths assumpon leads o he followng sae-space model: = +, e, [ γ 1 γ ],, 1 (5A) 8

9 9 + = u u,2,1 2, 1, 1,, 1 0 γ γ φ, (5B) where e,, u 1,, and u 2, are ndependen normally dsrbued error erms. In he saespace model ermnology, equaon (5A) s called he measuremen equaon, whle equaon (5B) s called he sae equaon. The basc ool used o esmae sae-space models s a Kalman fler, whch s a recursve procedure ha esmaes he unobserved componen or he sae vecor. (See Hamlon (1994).) Robers (2002) also uses a Kalman fler o esmae he dynamc rade-off model, assumng ha he varables n equaons (1) and (2) are laen. In our approach, he only laen varable s,, whch allows us o drecly es he dynamc rade-off model. We use he followng unresrced form of model (5A)-(5B): + = 1,, 2 1,, ] [ e γ γ (6A) + = u u,2,1 2, 1, 2 1 1,, 0 γ γ φ (6B) We emphasze ha he only npu needed o esmae he srucural dynamc rade-off model (6A)-(6B) s he realzed deb-equy rao,,, and ha model (6A)-(6B) affords us he smulaneous esmaon of, and he parameersφ, γ 1 and γ 2, along wh he covarance marx for he error erms. Based on hese esmaes, we es he dynamc rade-off model drecly by esng ha 1 γ and 2 γ n equaon (4) add up o 1. Moreover, f he dynamc rade-off model s no rejeced, we can use equaons (6A) and (6B) o

10 esmae he arge deb-equy rao over me for each frm, along wh he frm s speed of adjusmen parameer, γ 1. Ths approach avods he problems assocaed wh endogeney, whch s a common problem n he emprcal models of capal srucure. For example, many of he economc varables ha deermne he arge deb-equy n equaon (2) are smulaneously deermned wh he frm s leverage. As poned ou by Robers (2002), gnorng he endogeney ssue leads o a well-known, bu seldom-addressed, basng of coeffcens n he sandard regresson framework. Fnally, noce ha model he dynamc rade-off model, descrbed n Equaon (2), allows for he arge leverage rao o change over me. Ths formulaon s conssen wh capal srucure heory ha poss ha he arge leverage for a frm changes over me as he characerscs of he frm change. (See, for example, Hennessy and Whed (2005) and Tman and Tsyplakov (2005).) Oher researchers, however, assume ha he arge levarage rao s consan. (See, Colln-ufresne and Goldsen (2001).) In spe of he dfferen assumpons, s commonly found ha observed leverage raos show mean reverson. Moreover, whle Marsh (1982), Auerbach (1985) and Opler and Tman (1995), among ohers, documen ha companes end o gradually adjus her capal srucures oward a arge level of leverage; Jallvand and Harrs (1984) fnd ha leverage raos are reasonably sable over me. More recenly, robez, Pensa, and Wanzenred (2007) fnd ha book leverage over he me perod of was que sable around.6, hough marke leverage ended o be more me-varyng. Robers (2002) presens esmaes employng a consan and a me-varyng process for he arge leverage and fnds ha he parameer esmaes are smlar n boh cases. 10

11 In lgh of he mxed evdence, we es he dynamc rade-off model under several assumpons. Frs, we assume ha he arge deb-equy rao follows an AR(1) process. Second, we assume ha he arge deb-equy rao s consan. Fnally, as a robusness check, we also assume a hrd scenaro, under whch he arge deb-equy rao follows a random walk process, makng he arge deb-equy rao compleely unpredcable based on prevous nformaon. 3. The aa Several defnons of he deb-equy rao are used n he leraure. In our analyss, we use he followng defnons: eb s he book value of he frm s long erm deb and Equy s he marke value of a frm s common sock. We use long-erm deb snce he rade-off heory argues ha he paral adjusmen s due o he exsence of ransacon coss or oher marke mperfecons. Shor-erm deb ends o be more flexble han long-erm deb, herefore, a paral adjusmen mechansm s no ha heorecally appealng. Moreover, snce we use quarerly daa, a lo of shor-erm dynamcs may be los beween quarers. 2 The use of book value deb vs. marke value deb s also a common ssue n he leraure. Marsh (1982) presens an early dscusson of hs ssue, fndng ha hs emprcal resuls are no sgnfcanly affeced by he measuremen choce. More recenly, robez, Pensa, and Wanzenred (2007) presen an updaed summary of he pros and cons of boh measures. Accordng o her dscusson, usng marke values may no reflec 2 Flannery and Rangan (2006) use hree defnons of deb, ncludng oal lables, long-erm deb plus shor-erm deb, and long-erm deb only. They fnd her resuls o be smlar across he dfferen deb defnons. 11

12 he underlyng changes naed by he frm s decson makers. They add ha from a more pragmac pon of vew, he marke value of deb s ofen no readly avalable and he calculaon of marke values of deb s cumbersome. They end-up referrng o he marke value of deb as quas-marke value and hey run her emprcal analyss wh book values and quas-marke values of deb. They conclude ha frms are more concerned wh book leverage raos han wh marke leverage raos. The emprcal leraure esmaes equaon (2) usng he followng varables: Volaly of cash flows, Produc unqueness, Tangble asses, Sze, Profably, Capal expendures, Marke-o-book rao, Z score, Capal expendure, Cash poson, Tax sheld, Tax raes, and Mgaon of free cash flow problem. In he Appendx, we presen he exac defnons of hese varables, along wh her respecve COMPUSTAT ems. We use hese varables o check he qualy of he Kalman fler esmaes of he arge deb-equy rao. Our sample consss of quarerly daa for he perod of 1985:I o 2005:IV. The daa s obaned from COMPUSTAT. All he frms n our sample have nnerruped observaons n he sample perod. 3 Followng he sandard pracce n he leraure, we exclude fnancals and regulaed ndusres. Our sample sze s 578 frms. Table I presens he unvarae sascs for he deb-equy rao for he frms n our sample. The average and medan deb-equy raos are.279 and.260. For close o 40% of he frms here s evdence of sgnfcan skewness, whle for 20% of he frms 3 We only use frms wh connuous observaons o avod he problems assocaed wh mssng daa. Robers (2002) fnds ha mssng daa mpac he magnude and sascal sgnfcance of he esmaes, bu no he drecon of assocaon beween varables. Snce he magnude and sascal sgnfcance of he ess s crucal for our es, we avod frms wh mssng daa. 12

13 here s evdence of sgnfcan excess kuross. For all frms, he deb-equy rao s hghly auocorrelaed, wh an average auocorrelaon coeffcen of.89. The null hypohess of no auocorrelaon of order 4 s rejeced for all frms by he LB(4) sascs for all sandard sgnfcance levels. Table II presens some descrpve sascs for he varables ha are ofen used n he leraure o explan he behavor of he deb-equy rao. 4. Emprcal Analyss As menoned above, mos emprcal works esmae of equaon (3) usng a panel daa echnque whch yelds he average speed of adjusmen. From a sascal pon of vew he panel seng s relavely powerful. I gnores, however, he heerogeney n he ndvdual frms parameers. Our choce of esmaon mehod allows us o es he radeoff heory for each frm, nsead of esng he rade-off heory only for he average frm. Frs, we conduc an unresrced esmaon of (6A) and (6B). Second, we conduc a resrced esmaon by mposng he resrcon ha γ 1 and γ 2 sum up o 1. Then, we consruc a lkelhood rao es sascs n order o es he dynamc rade-off model. For hs es, he null hypohess s H 0 : γ 1+ γ 2 =1. Noce, however, ha he rade-off model n equaon (6A) makes no sense when γ 1 s equal o zero. Therefore, we use a wo-sep process o decde wheher he dynamc rade-off model s approprae. Frs, we use a -es o es he null hypohess ha γ 1=0. If hs null hypohess canno be rejeced, he rade-off model can be rejeced drecly, 13

14 whou esng he null hypohess mpled n equaon (6A). Second, we do he above menoned lkelhood rao es o es he null hypohess of γ 1 and γ 2 summng up o 1. 4 Table III presens he resuls for he unresrced esmaon. In panel A, we fnd ha he rade-off model holds.e., canno be rejeced a he sandard 5% level- for 32% of he frms n our sample. Ths proporon ncreases o 52% for he consan scenaro for., case n whch We also esmae he speed of adjusmen for each frm n our sample. 5 For he, follows an AR(1) process, he medan and he average quarerly speed of adjusmen, γ 1, are.161 and.276, respecvely. These quarerly numbers, once compounded, are smlar o he panel daa annual esmaes repored by Jalvand and Harrs (1984), Al (2006) and Flannery and Rangan (2006), whch are n he.30 o.56 range; bu, he esmaes are low relave o he quarerly ndusry esmaes repored by Robers (2002). Confrmng Robers (2002), however, we fnd a bg varaon n he esmaed speed of adjusmen wh a 90% confdence nerval whose bounds are.951 and The nerquarle quarerly range s ( ), agan, once compounded, no ha far from he annual esmaes repored n he leraure. I s also possble o esmae γ 1 hrough γ 2, by mposng γ 1 +γ 2 =1, as ypcally done n he leraure when equaon (3) 4 Gven our small sample sze, 84 observaons, we expec o have relavely large sandard errors, whch wll lead o a larger number of non-rejecons of H 0, usng he sandard asympoc -values. We decded o use he 10% level.e., for he -ess n he frs-sep- nsead of he more sandard 5% level o es H 0. In a small smulaon, we found ha a he 10% level, he -es correcly rejeced 92% of he me H 0 : γ 1=0. 5 Noe ha we can drecly esmae he speed of adjusmen, γ 1, whle he leraure esmaes an unresrced γ 2 and hen mposes he resrcon γ 1=(1-γ 2 ) o ge an esmae of γ 1. 14

15 s esmaed. In hs case, he medan and average quarerly speed of adjusmen are.168 and.307, respecvely. For he case n whch, s consan he medan and he average quarerly speed of adjusmen are.117 and.094, respecvely. Agan, we fnd sgnfcan varaon n he esmaed speed of adjusmen wh a 90% confdence nerval whose bounds are.413 and.026. The nerquarle quarerly range s ( ). Agan, calculang γ 1 hrough γ 2, we ge a medan and an average quarerly speed of adjusmen equal o.110 and.129, respecvely. Observe ha he esmaes obaned under he consan scenaro for, are more sable han hose obaned under he AR(1) scenaro. I s, hus, mporan o es for how many frms he AR(1) case apples. Ths can be done wh he Wald es, wh he null hypohess H 0 : φ =0. We fnd ha hs hypohess s rejeced for 62% of he frms a he 5% level. Ths resul s no ha surprsng gven he emprcal dsrbuon repored n Table III, Panel A. In Panel B, Table III, we presen he esmaes of model (6A)-(6B), only for he frms for whch he rade-off heory canno be rejeced. Agan, for he AR(1) case scenaro for,, we fnd a good dsperson of esmaes; bu, n general, wh hgher esmaes for he speed of adjusmen, γ 1, and, as expeced, lower esmaes for γ 2. 6 For he consan case scenaro for,, we fnd more sable esmaes, whch are a lle b lower, bu overall smlar o he ones repored on Panel A. For more han half he sample we fnd evdence supporng he consan case scenaro for. 6 The nerquarle range for γ 2 s gven by ( ). I s a lle b msleadng, snce he range s ( ). 15

16 In Panel C, Table III, we presen he esmaes of model (6A)-(6B), only for he frms for whch he rade-off heory s rejeced. For he AR(1) case, he esmaes end o be more sable, showng an nerquarle range for γ 1 equal o (.258,.060), closer o he annual esmaes repored by he emprcal leraure. Agan, he esmaes for he consan case scenaro for, are more sable. Based on he resuls for he dynamc rade-off model for, presened n Table III, we conclude ha whle some sgnfcan proporon of frms use a arge deb-equy rao, he majory of he frms do no. Ths resul may be arbued o our use of he Kalman fler echnque. One way o check our esmaes of, s o see f hey are correlaed wh he sandard se of economc varables ha are proposed by he rade-off heory.e., he se of varables used n equaon (2). If he Kalman fler produced reasonable esmaes, hen hese esmaes should be hghly correlaed o he se of fundamenal varables only for he group of frms for whch he dynamc rade-off model canno be rejeced. Therefore, we run a cross-secon regresson verson of equaon (2) usng our Kalman fler esmaed deb-equy raos as he dependen varable and as he explanaory varables a se of fnancal varables. Tha s, we esmae: ^ = α + δ ' + ξ, (7) X where ^ s he Kalman fler esmaed deb-equy rao, X s he vecor of explanaory varables and ξ s he error erm. We esmae equaon (7) usng as explanaory varables Volaly of cash flows, Tangble asses, Frm sze (sales dvded by oal sales of sample), Profably (ne operang ncome), Alman s Z score, Capal expendures, Marke-o-book rao, Cash and shor-erm markeable secures, Tax shelds 16

17 (deprecaon and amorzaon), Income ax rae, and Mgaon of free cash problem (afer ax operang ncome). 7 The majory of he varables are scaled by oal asses see Appendx for exac defnons. Before esmang (7), we dvde he frms no wo groups. Group A ncludes he frms for whch he dynamc rade-off model canno be rejeced and Group B consss of all he frms for whch he dynamc rade-off model s rejeced. As explaned above, f we have correcly esmaed he rade-off model, hen he arge deb-equy rao esmaes for Group A should be explaned by he proposed se of economc varables, whle he arge deb-equy rao esmaes for Group B should be largely uncorrelaed wh any varables. 8 Table IV presens he resuls of boh regressons. I s lkely ha hese regressons suffer from mulcollneary, bu snce mulcollneary affecs he sandard errors of he coeffcens and no he coeffcens hemselves, we focus on he overall explanaory power gven by he R 2. For Group A, he se of explanaory varables explans 55% of he varably of he Kalman fler esmaed arge leverage. For Group B, however, he same varables only explan 8.2% of he varably of he Kalman fler esmaed arge leverage. The evdence n Table IV s que srong n favor of he Kalman fler esmaes of,. We fnd ha he Kalman fler esmaed arge deb-equy raos show a hgh correlaon wh he se of fundamenal varables only for he group of frms for whch he dynamc rade-off model canno be rejeced (Group A). 7 See Fama and French (2002), Robers (2002), Flannery and Rangan (2006), robez, Pensa, and Wanzenred (2007). 8 A non-zero correlaon may exs. For example, f he esmaed arge deb-equy s correlaed wh observed deb-equy rao. 17

18 Even hough we emphasze he jon explanaory power, a look a Table IV sheds some lgh on he relaon beween profably and he deb-equy rao. Fama and French (2002) pon ou ha he negave relaon beween profably and he debequy rao s sgnfcan scar for he rade-off heory. Table IV, however, shows ha he negave relaon beween profably and he deb-equy rao s only sgnfcan for he frm where he rade-off heory s rejeced. For he frms ha he rade-off heory s no rejeced here s a posve, hough no sascally sgnfcan relaon beween profably and he deb-equy rao. 5. Conclusons In hs paper, we presen a es of he dynamc rade-off model of capal srucure. We depar from he sandard esmaon echnque of he rade-off model, by drecly esmang a srucural model, nsead of he sandard reduced form equaon. Gven ha n he srucural rade-off model, he arge deb-equy rao s unobservable, he saespace represenaon s a naural model o es he dynamc rade-off model. We use a Kalman fler, whch allows us o drecly esmae he unobserved frm s arge debequy rao. Under he srucural model of he rade-off heory, he frm s observed, or realzed, deb-equy rao s a weghed average of las perod s realzed deb-equy rao and he frm s arge deb-equy rao. Wh he esmaed model parameers and he esmaed arge deb-equy rao, we sugges a smple es of he rade-off model. Ths es checks f he esmaed parameers n he srucural model foe each frm add up o one. 18

19 The focus on ndvdual frms allows us o drecly sudy he number of frms n whch he dynamc rade-off model canno be rejeced. In our sample of 578 frms, we fnd ha he rade-off model holds.e., canno be rejeced a he sandard 5% level- for 32% when we assume ha he arge deb-equy rao follows an AR(1) model. The model holds for as many as 52% when he arge deb-equy rao s assumed o be consan. We also esmae he speed of adjusmen for each frm. The medan and he average speed of adjusmen are.161 and.276, respecvely. These numbers are close o he annual esmaes repored n Flannery and Rangan (2006). Confrmng Robers (2002), we fnd a huge cross-seconal varaon n he speed of adjusmen parameer. The emprcal 95% confdence nerval for he speed of adjusmen has as bounds.025 and.951. The nerquarle range, however, s no ha exreme, gong from.088 o

20 References Al, A., 2006, How perssen s he mpac of marke mng on capal srucure?, Journal of Fnance, 61, Baker, M., and J. Wurgler, 2002, Marke mng and capal srucure, Journal of Fnance, 57, Chen, L., and X. Zhao, 2005, Profably, mean reverson of leverage srucure choces, Workng paper, Mchgan Sae Unversy. Colln-ufresne, P., and R. Goldsen, 2001, o cred spreads reflec saonary leverage raos? Journal of Fnance, 56, robez, W., P. Pensa, and G. Wanzenred, 2007, Frm characerscs, economc condons and capal srucure adjusmens, Workng Paper,. Unversy of Hamburg. Fama, E., and K. French, 2002, Tesng he rade-off and peckng order predcons abou dvdends and deb, Revew of Fnancal Sudes, 15, Fama, E., and J.. MacBeh, 1973, Rsk, reurn, and equlbrum: emprcal ess, Journal of Polcal Economy, 81, Faulkender, M., M. Flannery, K. Hankns and J. Smh, 2007, Are Adjusmen coss mpedng realzaon of arge capal srucure?, Workng Paper. Flannery, M. and K. Hankns, 2007, A heory of capal srucure adjusmen speed, Workng paper. Flannery, M., and K. Rangan, 2006, Paral adjusmen oward arge capal srucures, Journal of Fnancal Economcs, 79, Graham, J. R., and C. R. Harvey, 2001, The heory and pracce of corporae fnance: Evdence from he feld, Journal of Fnancal Economcs, 60, Hamlon, J.. (1994), Tme Seres Analyss, Prnceon, NJ: Prnceon Unversy Press. Hennessy, Chrsopher A, and T. M. Whed, 2005, eb ynamcs, Journal of Fnance, 60, Hovakman, A., T. Opler, and S. Tman, 2001, The deb-equy choce, Journal of Fnancal and Quanave Analyss, 36, Jallvand, A. and R. Harrs, 1984, Corporae behavor n adjusng o capal srucure and dvdend arges: An economerc sudy, Journal of Fnance, 39,

21 Kayhan, A. and S. Tman (2007). Frms' hsores and her capal srucures. Journal of Fnancal Economcs, 83, Lemmon, M., M. Robers, and J. Zender, 2007, Back o he begnnng: Perssence n he cross-secon of corporae capal srucure, Journal of Fnance, forhcomng. Marsh, P., 1982, The Choce beween equy and deb: an emprcal sudy, Journal of Fnance, 37, Myers, S. C., 1977, eermnans of Corporae Borrowng, Journal of Fnancal Economcs, 5, Myers, S. C , The Capal Srucure Puzzle, Journal of Fnance, 39, Rajan, R., and L. Zngales, 1995, Wha o We Know abou Capal Srucure? Some Evdence from Inernaonal aa, Journal of Fnance, 50, Robers, M., 2002, The dynamcs of capal srucure: An emprcal analyss of a parally observable sysem, Workng Paper, uke Unversy. Tman, S. and S. Tsyplakov, 2005, A dynamc model of opmal capal srucure, Workng paper, Unversy of Texas a Ausn. Srebulaev, I., 2004, o ess of capal srucure heory mean wha hey say? Workng Paper, London Busness School. Srebulaev, I., and B. Yang, 2006, The mysery of zero-leverage frms, Workng paper, Sanford Graduae School of Busness. Welch, I., 2004, Capal srucure and sock reurn, Journal of Polcal Economy, 112,

22 APPENIX: Varable efnons 1. Bankrupcy Coss and Cos of Fnancal sress Varables. Volaly of Cash Flows: Absolue Value of Change n Ne Income / Toal Asse COMPUSTAT defnon: aa69() aa69(-1) / aa 44. Produc Unqueness: Sellng Expenses / Toal Sales COMPUSTAT defnon: aa1 / (aa1+aa2). Tangble Asses: (PP&E) / Toal Asses COMPUSTAT defnon: aa42 / aa44 v. Frm Sze: Sales / Toal Sales of Sample COMPUSTAT defnon: (aa1+aa2) / Cross Seconal Sum of (aa1+ aa2) v. Profably: Ne Operang Income / Toal Asses COMPUSTAT defnon: (aa21-aa5)/ aa44 v. Z-Score: 3.3 EBIT / TA + Sales / TA Reaned Earnngs / TA Workng Capal/ TA COMPUSTAT defnon: 3.3x(aa21-aa5+aa31) / aa44 + (aa1+aa2) / aa44+1.4aa58 / aa (aa40-aa49)/aa44 v. Capal Expendure: Capal Expendures (+1) / Toal Asses (+1) COMPUSTAT defnon: aa90(+1) / aa44(+1) v. Marke o Book: (Toal Asses Book Equy + Marke Equy ) / Toal Asses COMPUSTAT defnon: (aa44 aa59 + aa61aa14) / aa44 COMPUSTAT defnon: (aa61aa14) / (aa44 aa49 aa51) v. Cash & Shor Term Markeable Secures COMPUSTAT defnon: aa36 2. Tax Varables 22

23 . Tax Sheld: (eprecaon and Amorzaon) / TA COMPUSTAT defnon: aa5 / aa44. Tax Rae: Income Tax Rae COMPUSTAT defnon: aa 6 / (aa6 + aa69) 3. Mgaon of Free Cash Flow Problem. Mgaon: Afer Tax Operang Income / Toal Asses COMPUSTAT defnon: (aa21 aa5) / aa44 23

24 TABLE I Unvarae Sascs for eb-equy Rao Max 3 rd Quan Medan 1 s Quan Mn Mean S ev Mean S. ev Skew Ex Kur Rho LB(4) LBS(4) Noes: S. ev: Sandard evaon. Skew: Skewness. Ex Kur: Excess Kuross. Rho: Frs-order auoregressve coeffcen. LB: Ljung-Box (1978) sasc for levels. I follows a χ 2 (4). LBS: Ljung-Box (1978) sasc for squared seres. I follows a χ 2 (4). 24

25 TABLE II Sascs for Frm Characersc Varables VCF Punque TangbA FSze Prof Zcore Mean Sd ev Medan Mnmum Maxmum Inerquarle h p h p Capex MB Cash TaxSh TaxRae Mgaon Mean Sd ev Medan Mnmum Maxmum Inerquarle h p h p Noes: VCF: Volaly of Cash Flows. Punque: Produc Unqueness. TangbA: Tangble Asses. FSze: Frm Sze. Prof: Profably. Zscore: Z-Score. Capex: Capal Expendure. MB: Marke o Book Value. Cash: Cash & Shor Term Markeable Secures. TaxSh: Tax Sheld. Tax Rae: Income Tax Rae. Mgaon: Mgaon of Free Cash Flow Problem See Appendx for daa defnons. 25

26 TABLE III srbuon of Unresrced Esmaes of Model (6A)-(6B) for he dfferen scenaros Panel A. All Frms AR(1) Scenaro Consan Scenaro γ S(γ 1 ) γ S(γ 2 ) φ S(φ ) Proporon of Rejecons of TM 68% Proporon of Rejecons of TM 48% Proporon of Rejecons of H 0 : φ =0 62% Panel B. Trade-off Model Frms AR(1) Scenaro Consan Scenaro γ S(γ 1 ) γ S(γ 2 ) φ S(φ ) Proporon of Rejecons of H 0 : φ =0 48% Panel C. Non Trade-off Model Frms AR(1) Scenaro Consan Scenaro γ S(γ 1 ) γ S(γ 2 ) φ S(φ ) Proporon of Rejecons of H 0 : φ =0 67% 26

27 TABLE IV Relaon beween Esmaed Targe eb-equy Rao and Fundamenal Varables Trade-off Non Rejeced Trade-off Rejeced Varable Coeff -sa Coeff -sa Inercep Volaly of Cash Flows Produc Unqueness Tangble Asses Frm Sze Profably Z-Score Capal Expend Marke-o-Book rao Cash & ST Secures Tax Sheld Tax Rae Mgaon R Ths Table presens he resuls from he followng pooled regresson:, = α + β X, + ε, where s he Kalman fler esmaed arge deb-equy rao for frm, assumng an AR(1) scenaro, and X, s he se of fundamenal varables for frm descrbed n he Appendx, and ε, s he error erm. The regresson s esmaed for wo groups: a group of frms (where he rade-off model canno be rejeced (Group A) and a group of frms where he rade-off model s rejeced. Noes: See Appendx for daa defnons. 27