An alternative test of the trade-off theory of capital structure

Transcription

1 365 Prmary submsson: Fnal acceptance: An alternatve test of the trade-off theory of captal structure Gorgo Canarella, Mahmoud ouray, Mchael J. Sullvan ABSTRACT The purpose of ths paper s to nvestgate the stochastc behavor of corporate debt ratos utlzng a balanced panel of,556 publcly traded U.S. frms durng the perod We partton the panel nto ten economc sectors and perform panel unt root tests on each sector employng book value and market value measures of debt rato. Frst-generaton panel unt root tests provde consstent evdence that debt ratos are mean revertng, whch supports the trade-off theory. However, these tests rely on the assumpton that the debt ratos are crosssectonally ndependent, but tests of cross-sectonal ndependence fal to uphold ths assumpton. Thus, utlzng a second-generaton panel unt root test that controls for cross-sectonal dependence, we uncover evdence showng that debt ratos are not mean revertng, whch contradcts the trade-off hypothess. We fnd that the recent macroeconomc developments trggered by the fnancal crss and the Great Recesson have consderable explanatory power over the dynamcs of the debt ratos. In fact, when we exclude the years of the recent global fnancal crss, the unt root hypothess s rejected n one half of the sectors. We nterpret these results as ndcatve that the recent global events may have produced n these sectors a structural change n the underlyng data generaton process (DGP). Overall, then, we fnd mxed evdence on the statonarty of debt ratos. KEY WORDS: JEL Classfcaton: panel unt root tests; captal structure theores; cross-sectonal dependence; debt rato G30; G3 Unversty of evada, Las Vegas - Lee Busness School, Unted States; Loyola Marymount Unversty, Unted States Introducton Snce the semnal work of Modglan and Mller (958), three man theores have been advanced to explan corporate captal structure: the trade-off theory, the peckng order theory, and the market-tmng hypothess. The trade-off theory s centered on the dea that frms have an optmal captal structure Correspondence concernng ths artcle should be addressed to: Mahmoud ouray Loyola Marymount Unversty - Accountng, LMU Drve Hlton 37, Los Angeles, Calforna 90045, Unted States E-mal: mnouray@lmu.edu that presupposes a target debt rato and explans ths target debt rato as a trade-off between tax and other benefts aganst fnancal dstress and other costs that are consequences of the use of debt (Bradley, Jarrell, & Km, 984; Graham & Harvey, 00; Harrs & Ravv, 99; Kraus & Ltzenberger, 973). The peckng order theory, however, postulates that the cost of fnancng ncreases wth asymmetrc nformaton and, therefore, predcts that a frm s debt rato smply reflects a herarchy of fnancng sources whereby nternal fnancng s preferred over debt, and debt s preferred over equty (Myers, 984; Myers & Majluf, 984). The market tmng theory speculates that captal structure decsons Vzja Press&IT

2 366 Vol. 8 Issue Gorgo Canarella, Mahmoud ouray, Mchael J. Sullvan are drven by frms attempts to tme the equty markets (Baker & Wurgler, 00). Tests of the trade-off theory attempt to measure the extent and speed of rebalancng a frm s debt rato towards the presumed target. Much of ths research fnds evdence supportng the trade-off theory (Almeda & Phlppon, 007; Flannery & Rangan, 006; Harrs & Ravv, 99; Hovakman, Opler, & Ttman, 00; Leary & Roberts, 005). Research that does not support the trade-off theory ncludes Lemmon, Roberts and Zender (008), Hovakman, Kayhan and Ttman (0). Recent surveys of captal structure theores nclude Baker and Martn (0) and Frank and Goyal (007). Much of the current research nvestgatng ssues related to captal structure s methodologcally based on structural modelng. That s, t manly explores the determnants of the observed captal structure. Recently, ths research has reled on a varety of econometrc technques, whch nclude, among others, logt and probt models (Bayless & Chaplnsky, 99; Helwege & Lang, 996; Hovakman et al., 00), the Fama-Mac- Beth two-step approach (Fama & French, 00; Flannery & Rangan, 006; Hovakman & L, 0; Welch, 004), structural equaton models (Chang, Lee, & Lee, 009; Ttman & Wessels, 988), non-lnear methods (Banerjee, Heshmat, & Whlborg, 000; Vlasuso & Mnkler, 00), cross-secton regressons (Frank & Goyal, 003; Hanousek & Shamshur, 0; Rajan & Zngales, 995), and Kalman flter technques (Zhao & Susmel, 008). Ths type of research has also beneftted from advances n tme seres and panel data econometrcs. For example, the determnants of frm debt ratos have recently been analyzed n a dynamc framework usng fxed-effect panel regressons (Flannery & Rangan, 006; Huang & Rtter, 009), fractonal dependent estmators (Elsas & Florysak, 0), generalzed method of moments (GMM) methods (Antonou, Guney, & Paudyal, 008; Faulkender et al., 0; Lemmon et al., 008), and dynamc panel threshold models (Dang, Km and Shn, 0; 04). A partcular concern about these models that has emerged n recent years s that they fal to nclude an assessment of the stochastc propertes of debt ratos and gnore the ssue of cross-sectonal dependence. The frst problem has been dscussed at length by Granger and ewbold (974) and exposes the econometrc results to the spurous regresson problem when data are non-statonary,.e., contan unt roots. The second problem s partcularly mportant n dynamc panel regressons. As noted by Phllps and Sul (003), ths substantally complcates the estmaton and nference n dynamc panel models. Phllps and Sul (003) address ths problem from a theoretcal perspectve and propose an approach that s based on a panel verson of the medan unbased estmator (Andrews, 993). The motvaton of ths study s twofold. Frst, unlke the vast bulk of the extant lterature that focuses on the determnants of corporate captal structure, we rely on recent developments n the econometrcs of non-statonary dynamc panel data. Specfcally, we approach the analyss of the trade-off theory by assessng the stochastc propertes of corporate debt rato from the perspectve of the panel unt root methodology. If the debt rato s represented by a statonary process, shocks affectng the seres are transtory, and the debt rato wll eventually return to ts target level. Thus, evdence of statonarty supports the trade-off theory, as t characterzes the dynamcs of captal structure as mean revertng. Ths stuaton, n turn, could be nterpreted as an ndrect sgnal of ndustry stablty. Conversely, f the debt rato evolves as a unt root process, shocks affectng the seres have permanent effects, shftng the corporate captal structure from one level to another, whch contradcts the trade-off theory. Second, we drectly address the queston of cross-sectonal dependence n panel unt root tests. The applcaton of unvarate unt root tests, such as the Augmented Dckey- Fuller (Sad & Dckey, 984) and the Phllps-Perron (Phllps & Perron, 988) tests, s somewhat commonplace n studes employng tme seres data. In contrast, the use of unt root tests for panel data s more recent (Im, Pesaran, & Shn, 003; Levn, Ln, & Chu, 00; Maddala & Wu, 999). It s by now a generally accepted argument that the commonly used unvarate unt root tests lack power n dstngushng the null hypothess of unt root from statonary alternatves, and utlzng panel data unt root tests s one way of ncreasng the power of unt root tests (Cho 00; Im et al., 003; Levn et al., 00). Panel unt root tests explot both the tme-seres (t =, T) and the cross-secton ( =, ) dmensons of the underlyng data, thereby havng more power and greater effcency than unvarate tme seres unt root tests (Baltag, 005). The tests share the null hypothess of unt root, but dffer COTEMPORARY ECOOMICS DOI: /ce

3 An alternatve test of the trade-off theory of captal structure 367 n the alternatve. The LLC test, proposed by Levn et al. (00), tests for the null hypothess of the unt root aganst a homogeneous statonary hypothess,.e., the autoregressve parameter constraned to be the same across cross-secton unts, whle the IPS test, suggested by Im et al. (003), and the Fsher type tests developed by Maddala and Wu (999) and Cho (00) test for the null hypothess of unt root aganst the heterogeneous alternatve,.e., the autoregressve parameter s allowed to vary across cross-secton unts. Surveys of panel unt root tests nclude, among others, Banerjee (999), Bretung and Pesaran (008), Guterrez (006), and Jang and Shn (005). Unfortunately, however, testng the unt root hypothess by employng panel data nstead of ndvdual tme seres s not wthout complcatons. In partcular, the panel unt root lterature has noted that n many emprcal applcatons t may be napproprate to assume that the cross-secton unts are ndependent. Observatons on frms, ndustres, regons and countres normally tend to be crosscorrelated and serally dependent (Bretung & Pesaran, 008). Thus, an mportant problem n panel unt root tests s whether the cross-sectons of the panel are ndependent. On ths ssue, the panel unt root lterature dstngushes between the frst-generaton tests, whch are developed on the assumpton of the cross-sectonal ndependence, and the second-generaton tests, whch account for the dependence that mght preval across the dfferent unts n the panel. If the data are crosssectonally dependent, the panel unt root lterature has demonstrated that the frst-generaton tests can generally be msleadng, n the sense that they expose the tests to sgnfcant sze dstortons. That s, the tests tend to reject the null hypothess of non-statonarty too often (see, for nstance, Cho, 00; Im et al., 003; Levn et al., 00; Maddala & Wu, 999). Moreover, Pesaran (007) demonstrates that panel unt root tests that do not account for cross-sectonal dependence when cross-sectonal dependences are ndeed present are serously based f the degree of cross-sectonal dependence s suffcently large. To date, only a few studes examne the corporate captal structure employng panel unt root tests. Chang, Lang, Su and Zhu (00) use quarterly data over the perod 996:Q4-007:Q3 from a panel of Tawanese electronc frms and fal to reject the null hypothess of unt root, except for the subsample of frms wth low proftablty. Bontemp and Golnell (00) utlze annual data from 5,079 Italan frms durng the perod and fnd evdence that favors the trade-off theory. Tasseven and Teker (009) employ annual data from 4 Turksh frms durng the perod and report fndngs that do not provde support for the trade-off hypothess. These studes employ frst-generaton panel unt root tests. Chang, Lang, Su and Zhu (00) make use of the LLC (Levn et al., 99) test, the IPS (Im et al., 003) test, and the Maddala and Wu (Maddala & Wu, 999) Fsher type tests. Bontemp and Golnell (00) apply the IPS test (Im et al., 003), whle Tasseven and Teker (009) employ the LLC (Levn et al., 99) and the Maddala and Wu (Maddala & Wu, 999) Fsher type tests. Thus, all three studes rely upon the assumpton of cross-sectonal ndependence. A large amount of the current research on panel data concentrates on how to address cross-sectonal dependence. The second-generaton tests, such as the Seemngly Unrelated Regressons Augmented Dckey-Fuller test (SURADF) developed by Breuer, Mcown and Wallace (00), and the Cross-Sectonally Augmented ADF test (CADF) proposed by Pesaran (007) address explctly the problem of cross-sectonal dependence. The SURADF test s based on a system of augmented Dckey-Fuller (ADF) equatons and estmates the autoregressve process by the Seemngly Unrelated Regresson Equatons (SURE) procedure;.e., t accounts for cross-sectonal dependence by drectly ncorporatng the varance-covarance matrx of the resduals of the equatons system n the estmaton process. The advantage of ths approach s that t allows dentfcaton of the cross-sectonal unts of the panel that contan a unt root (Lau, Baharumshah, & Soon, 03). The major drawback, however, s that f > T,.e., the number of cross-secton unts exceeds the number of tme perods, the SURE approach s not feasble. Ths lmtaton s also present n the robust verson of the non-parametrc panel unt root test proposed by Bretung and Das (005) to account for cross-sectonal dependence. In the panel data that we use n our emprcal analyss, the number of tme perods s sgnfcantly less than the number of cross-sectons. Ths fact, n turn, precludes the use of the SURADF test or the Bretung test n our emprcal analyss. Instead, we employ a second-generaton panel unt root test that allows for cross-sectonal dependence developed by Pesaran Vzja Press&IT

4 368 Vol. 8 Issue Gorgo Canarella, Mahmoud ouray, Mchael J. Sullvan (007), accountng for cross-sectonal dependence by mposng a common factor structure. Pesaran (007) suggests a cross-sectonally augmented Dckey-Fuller (CADF) test where the standard ADF regressons are augmented wth cross-sectonal averages of lagged levels and frst dfferences of the ndvdual seres. The data generatng process (DGP) s a smple dynamc lnear heterogeneous panel data model. The error term s assumed to have an dosyncratc component and an unobserved common factor structure accountng for cross-sectonal correlaton. There are a varety of reasons why cross-sectonal dependence may exst n an ndustry. Commonly, cross-sectonal dependence reflects the fact that frms n the same ndustry respond to unobserved common stochastc shocks and are lnked by unobserved common stochastc trends. Common shocks and common trends spread across all frms n an ndustry, thus engenderng the panel feature of cross-sectonal dependence. Monetary and fscal shocks frequently provde the channels that generate common stochastc shocks. For example, monetary shocks n the supply of money and fscal shocks n the supply of government debt affect the rate of nflaton and the structure of nterest rates, whch n turn nfluence the frm s cost of captal and the equlbrum of fnancal markets, leadng to changes n the fnancal constrants n the corporate sector and alternatve representatons of the corporate captal structure (Bokpn, 009; Frank & Goyal, 009). Furthermore, n a globalzed economy, shocks generated n one country are known to cross natonal borders (Lau, Baharumshah and Soon, 03). Ths phenomenon s especally true for ol shocks. The global fnancal crss s arguably one of the deepest exogenous shocks that recently affected the corporate sector. The credt supply shock (Dang et al., 04) orgnated by the subprme crss has affected the corporate demand for and supply of funds and, consequently, the captal structure. Common stochastc trends, however, are another source of cross-sectonal dependence, as they reflect the presence of corporate varables that tend to move together,.e., are contegrated n a VAR system (Granger, 98). Emprcal evdence, for nstance, has found that stable relatonshps exst at the ndustry level between measures of frm performance, such as sales or proftablty, and research and development expendtures (Chan, Lakonshok, & Souganns, 00) and between the market value added of the frm (MVA), an external measure of a frm s performance, and several nternal measures, such as earnngs per share (EPS), free cash flow per share (FCF), return on equty (ROE), return on assets (ROA), and economc value added per share (EVA) (Berner & Mouelh, 0). Ths study contrbutes to the emprcal captal structure lterature n several ways. Frst, as mentoned above, our methodologcal approach enables us to fll a gap n the exstng lterature by focusng on an alternatve stochastc process that mght be more consstent wth the long-run behavor of debt ratos. Exstng emprcal work has focused almost exclusvely on the relatonshps between corporate captal structure and ts determnants. Whle these studes have produced a great deal of evdence on the assocaton between captal structure and ts determnants, they have not been able to provde much evdence on the dynamcs of debt ratos. Our methodology s based on a panel unt root test that allows for alternatve assumptons of cross-sectonal dependency for captal structure adjustments. Surveys of panel unt root tests nclude, among others, Bretung and Pesaran (008), Banerjee (999), Guterrez (006), and Jang and Shn (005). Panel unt root tests explot both the tme-seres (t =, T) and cross-secton ( =, ) dmensons of the underlyng data, thereby havng more power and greater effcency than conventonal tme seres unt root tests (Baltag, 005). Ths type of analyss s not new n corporate fnance. Tppett (990), for example, models fnancal ratos n terms of stochastc processes, and Tppett and Whttngton (995) and Whttngton and Tppett (999) report emprcal evdence that the majorty of fnancal ratos exhbt random-walk behavor. A unt root process mposes no bounds on how a seres moves. If the debt rato really conforms to a random-walk process, then t s unpredctable. A presumpton of the trade-off theory s that managers make captal structure decsons based on a target debt rato and that shocks affectng the debt rato wll prove transtory. Ths mples that debt ratos are mean revertng towards a target level and follow a statonary dynamc. Conversely, f managers do not make decsons based on a target debt rato, shocks re- COTEMPORARY ECOOMICS DOI: /ce

5 An alternatve test of the trade-off theory of captal structure 369 sult n permanent shfts n the debt rato. In ths case, change n the debt rato evolves as a unt root, nonstatonary process, whch s consstent wth alternatve captal structure theores, such as the peckng order or the market tmng theores (Baker & Wurgler, 00; Myers & Majluf, 984). on-statonarty of the debt rato dffers from persstence. Persstence nvolves a slow process of adjustment to an optmal level, whle non-statonarty mples that debt ratos fluctuate randomly, drven only by stochastc shocks wthout a tendency to return to a mean. Therefore, non-statonarty mples that frm debt ratos exhbt a unt root, whle persstence suggests that frm debt ratos exhbt a near unt root. It s mportant to note that the dynamc partal adjustment models currently utlzed n the lterature are based on assumptons that captal structure adjustments are mean revertng and these adjustments are cross-sectonally ndependent across frms (Fama & French, 00; Flannery & Rangan, 006; Frank & Goyal, 003; Huang & Rtter, 009; Leary & Roberts, 005; Shyam-Sunder & Myers, 999; Welch, 004). Evdence on the stochastc propertes of the debt ratos also possesses welldefned mplcatons for econometrc modelng and forecastng. Falure to reject the unt root hypothess potentally mples that debt ratos exhbt a long-run contegratng relatonshp wth other frm-level data, whle rejectng the unt root hypothess mples that debt ratos exhbt only a short-term relatonshp wth other corporate seres. Rejectng or not rejectng the unt root hypothess, n turn, profoundly affects the forecastng process because forecastng based on a mean-revertng process proves qute dfferent from forecastng based on a random walk process. Second, we control for effects related to the economc sector when analyzng the stochastc propertes of debt ratos. We accomplsh ths by stratfyng the data nto ten sectors and examnng the stochastc propertes of debt ratos wthn each sector. Debt ratos have been found to exhbt sgnfcant dfferences across sectors (Bradley et al., 984; Lemmon et al., 008). Graham and Harvey (00) found that one thrd of ther sample had debt ratos lower than 0.0, and another thrd had debt ratos hgher than Ths stratfcaton s done because of dstnct dfferences n debt ratos across economc sectors, and the extent and speed of reverson of a frm s debt rato to ts target may vary by sector. Frm-level data for each sector are obtaned by parttonng a large panel of,556 U.S. publc companes durng the perod Because we partton the sample nto sectors, we employ the average debt rato for the sector as a benchmark. We frst examne the evoluton of the debt ratos over the entre sample perod The fnancal lterature, however, has recognzed that the turbulent and volatle macroeconomc envronment created by the recent fnancal crss and the resultng Great Recesson had severe effects on corporate fnancal polces (Campello, Graham, & Harvey, 00; Campello et al., 0; Duchn, Ozbas, & Sensoy, 00). Thus, t would seem prudent to evaluate the robustness of the panel unt root results wth the events of the global fnancal crss and the Great Recesson. To account for ths problem, we date the fnancal crss wth the year of the Lehman Brothers bankruptcy. We then construct a pre-crss sub-sample, , and nvestgate whether ths sample reducton has affected our fndngs. In ths respect, our paper adds to the nascent lterature that documents the negatve mpact of the recent fnancal crss on corporate debt ratos (Dang et al., 04). Thrd, we measure debt ratos usng both book values and market values. Book value and market value debt ratos are conceptually dfferent. Book measures are by defnton backward lookng because of ther relance on accountng data, whereas market values are generally held to be forward lookng. Therefore, dfferences between the movement of book value and market value debt ratos may be szeable (Barclay & Morellec, 006). Rajan and Zngales (995) and Welch (004) provde ndepth ratonale for analyzng both. The man fndngs of our paper can be summarzed as follows. Frst, we fnd that cross-sectonal dependence does matter and substantally affects the outcome of the tests. When we apply conventonal, frst-generaton panel unt root tests that are based on the assumpton of crosssectonal ndependence, we fnd results that lead to the rejecton of the unt root hypothess. Ths evdence s consstent wth mean reverson of debt ratos and, therefore, supports the trade-off hypothess. However, to determne f these frst-generaton tests are approprate, we utlze dagnostc tests developed by Pesaran (004) and Frees (995; 004). Second, we fnd strong evdence of sub- Vzja Press&IT

6 370 Vol. 8 Issue Gorgo Canarella, Mahmoud ouray, Mchael J. Sullvan stantal cross-sectonal dependence wthn our sample ndcatng that the assumpton of cross-sectonal ndependence s napproprate. Thrd, the Pesaran (007) panel unt root test that allows for cross-sectonal dependence consstently yelds results supportng the unt root hypothess, whch s nconsstent wth debt ratos beng mean revertng. Ths evdence s contradctory to the trade-off hypothess. Of course, the falure to formally reject a null hypothess of unt root does not, on ts own, rule out the exstence of some mportant structural change. Fourth, n lght of ths possblty, we fnd that the recent fnancal crss does matter and substantally affects the results of the tests. When the years of the recent fnancal crss are excluded from the analyss, the evdence of statonarty re-emerges n one half of the sectors. We nterpret these results as provdng some ndrect evdence that n one half of the sectors the recent global events have caused a structural break n the underlyng data generaton process (DGP). Thus, overall, our emprcal results provde only mxed evdence n favor of the trade-off theory. The rest of the paper s organzed as follows. Secton presents a smple dynamc lnear autoregressve model of the debt ratos and shows ts connectons wth panel unt root tests. Secton 3 descrbes the sample data and ther sources. Secton 4 gves a concse outlne of the procedures employed n ths study and presents the emprcal results. Conclusons are presented n Secton 5. Panel Unt Root Tests and the Corporate Debt Rato In ths secton, we outlne a dynamc panel model of corporate debt ratos that provdes a theoretcal background for the applcaton of panel unt root tests. Let d, t be the debt rato of frm, =, at tme t, t = T. The trade-off hypothess mples that devatons of the debt rato, d, t from the target debt rato, d for frm at tme t, are transtory. We assume the target debt rato s constant over tme and frms move towards ths target n the long run, consderng the trade-off between the margnal costs and benefts of rasng funds through ssues of debt and equty. Under ths hypothess, the debt rato d, s mean revertng, mplyng the followng statonary stochastc process for d d d, t = + ϑ () where k + = β jϑ j ε, t j= ϑ + () k + j j= wth β < and ε s a zero-mean whte nose process. Equatons () and () jontly mply the followng statonary autoregressve process, d k + = a + jd j j= β + ε where = k + a d β j. j= (3) Equvalently, equaton (3) can be gven the augmented Dckey-Fuller (ADF) representaton: k d = a + ρ d + α d + ε (4) j j= j where s the dfference operator, and + ρ = β j, j= k β j = α j α j for j =,..., k, and β = + ρ + α. Solvng equaton (4) for ρ = 0 reduces to the unt root process d = a + k α d + ε j j= j (5) Equaton (5) mples that when there s a shock ε at tme t, the debt rato changes n the long run by k α j. In other words, ths suggests the shock j= has a permanent effect, whch s nconsstent wth the trade-off hypothess. Under the null hypothess, H 0 : ρ = 0 for all, the stochastc process descrbng the debt rato has a unt root. Under the alternatve hypothess, H : ρ < 0 for some, the debt rato responds to shocks wth a mean-revertng process. Therefore, f the emprcal results provde evdence of a mean reverson of debt ratos, the trade-off hypothess s valdated. Conversely, f the results provde evdence of a unt root, the debt rato s not mean revertng, evdence that contradcts the trade-off hypothess. Fndng evdence of a unt root s generally consstent wth the peckng order or the markettmng theores. COTEMPORARY ECOOMICS DOI: /ce

7 An alternatve test of the trade-off theory of captal structure 37 Data We employ a panel of annual data on,556 publcly traded frms from the U.S. coverng all sectors of the economy for the perod Data are obtaned from the annual Compustat fles, yeldng a balanced panel of 35,784 frm-year observatons. These sample data nclude both fnancally sound frms and those n fnancal dstress to avod survval bas because the probablty of bankruptcy may have a sgnfcant mpact on a frm s fnancng decsons. A balanced panel bypasses the potental selecton effects that may emerge from specfc characterstcs of frms enterng and leavng the data wthn the sample perod. For ths reason, we restrct our perod of analyss to the perod and construct a balanced panel of,556 frms. A balanced panel s also a requrement of the econometrc technques employed n the analyss. We also stratfy the sample nto ten economc sectors, followng the Compustat economc sector (ECSEC) classfcaton scheme, and perform panel unt root tests on each sector utlzng our two alternatve debt rato measures. The ten sectors are (the number of frms s reported n parenthess): ) Materals (87); ) Consumer Dscretonary (40); 3) Consumer Staples (35); 4) Health Care (36); 5) Energy (8); 6) Fnancals (6); 7) Industrals (40); 8) Informaton Technology (449); 9) Telecommuncaton Servces (45); 0) Utltes (97). A summary descrpton of the ten sectors s presented n the Appendx. Frms n the Utltes and Fnancals sectors are ncluded despte ther atypcal captal structure, as they are analyzed ndependently from the rest of the sample. For example, a hgh debt rato s normal for fnancal frms, but the same hgh debt rato for non-fnancal frms may ndcate fnancal dstress. There s no wdespread consensus n the lterature regardng a sngle emprcal measure of captal structure, n partcular, whether the defnton of leverage should utlze book values or market values. A dscusson concernng the dfferent measures of leverage can be found n Ttman and Wessels (988) and Rajan and Zngales (995). Myers (977) and Fama and French (00) favor the use of book values, whle Welch (004) advocates the use of market values. Drobetz, Pensa and Wanzenred (007) dscuss the advantages and dsadvantages of each measure. We follow Rajan and Zngales (995) and defne leverage as the rato of fnancal debt to debt plus equty. We nclude short-term debt n the defnton of the debt rato as ts omsson may lead to an understatement of fnancal dstress rsk. We consder both the book and market values of equty because t s hghly possble that some frms operate wthn a book value framework rather than a market value framework, and vce versa. The book value of the debt rato BDR of frm at tme t s defned as follows: BDR LTD + STD = (6) LTD + STD + BVE where LTD s the book value of long-term debt (Compustat annual data tem 9), STD s the book value of short-term debt (Compustat annual data tem 34), BVE equals the book value of equty computed as the dfference between the value of total assets (Compustat annual data tem number 6), the sum of LTD s the book value of long-term debt (Compustat annual data tem 9) and STD s the book value of short-term debt (Compustat annual data tem 34). Alternatvely, the denomnator n equaton (6) equals TA, total assets (Compustat annual data tem 6). Smlarly, the market value of the debt rato MDR of frm at tme t s defned as follows: MDR LTD + STD r = (7) LTD + STD + MVE where MVE s the market value of equty, computed as η P where η s the number of shares outstandng (Compustat annual data tem 54) and P denotes the stock prce (Compustat annual data tem 99). In Table we report the pooled mean, standard devaton, and medan of the book and market value debt ratos for each of the ten economc sectors. Because we utlze ratos of varables, a transformaton of the varables to constant prces s not necessary. Our data reveals that there are consderable dfferences n these two measures of debt rato across most economc sectors. The average book value debt ratos are hgher than the correspondng market value debt ratos wth the excepton of Fnancals and Utltes and exhbt a hgher standard devaton than the market value debt ratos wth the excepton of Utltes. In the case of Utltes, however, the standard devaton of the book value debt rato (0.53) s not sgnfcantly dfferent from the standard devaton of the market value debt Vzja Press&IT

8 37 Vol. 8 Issue Gorgo Canarella, Mahmoud ouray, Mchael J. Sullvan Table. Descrptve statstcs Economc Sector Book value debt rato Market value debt rato Mean Std. dev. Medan Mean Std. dev. Medan Materals Consumer Dscretonary Consumer Staples Health Care Energy Fnancals Industrals Informaton Technology Telecommuncaton Servces Utltes ote: The table reports the mean, standard devaton and medan of the book value and market value debt rato for each of the ten economc sectors. All data are from the Compustat database. Debt ratos are calculated for,556 publcly traded U.S. corporatons from 997 to 00. The book value of the debt rato BDR of frm at tme t s defned as LTD + STD BDR =, where LTD LTD + STD + BVE s the book value of long-term debt, STD s the book value of short-term debt, and BVE equals the book value of equty. The market value of the debt rato MDR of frm at tme t s defned as LTD + STD MDR r =, where MVE LTD + STD + MVE s the market value of equty, computed as η P where η s the number of shares outstandng and P denotes the stock prce. Sectors are defned by the Compustat economc sector (ECSEC) classfcaton system. The ten sectors (number of frms n parenthess; Compustat economc sector code n brackets) are: ) Materals (87) [000]; ) Consumer Dscretonary (40) [000]; 3) Consumer Staples (35) [3000]; 4) Health Care (36) [3500]; 5) Energy (8) [4000]; 6) Fnancals (6) [5000]; 7) Industrals (40) [6000]; 8) Informaton Technology (449) [8000]; 9) Telecommuncaton Servces (45) [8600]; 0) Utltes (97) [9000]. rato (0.55). These fndngs are contrary to the argument that book debt ratos are less subject to uncontrollable frm factors, such as market prce varablty. We also fnd that the emprcal dstrbutons of each measure of debt rato are generally non-symmetrc. In each case, the mean s greater than the medan, mplyng that the dstrbuton s postvely skewed (longer tals to the rght). A number of frms demonstratng extremely leveraged postons are found n the sectors Materals, Consumer Dscretonary, Industrals, Informaton Technology, and Telecommuncaton Servces. Extreme leverage, defned as those debt ratos beyond two standard devatons, are left n the analyss to avod use of an arbtrarly selecton crteron. In cases where there was evdence of extreme values, the analyss also conducted wnsorzng of the top and bottom 5% of the data. Ths approach was used to elmnate any unexpected effects of outlers. There was no meanngful effect on the results. We do not report the wnsorzed results, but these are avalable upon request. Table reveals the potental problem of aggregatng all observatons as opposed to stratfyng them by sector. The four largest sectors n terms of the number of observatons (Informaton Technology, Consumer Dscretonary, Materals, and Health Care) account for approxmately 65% of the total number of observatons. The remanng sx sectors may have lttle, f any, mpact on parameter estmates and test results n an aggregated sample. Under these crcumstances, pooled regressons are lkely to prmarly reflect the behavor of only a few large sectors. COTEMPORARY ECOOMICS DOI: /ce

9 An alternatve test of the trade-off theory of captal structure 373 Emprcal Results We present the emprcal evdence n three stages. Frst, we perform the panel data statstcal analyss utlzng Fsher type tests (Cho, 00; Maddala & Wu, 999). These tests are nonparametrc and have the advantage of allowng for as much heterogenety across unts as possble. They belong to the frst generaton of panel unt root tests, whch nclude among others, Levn et al., (00), Im et al., (003), Harrs and Tzavals (999). The fndngs of these tests unformly favor the trade-off hypothess. However, the concern s that these tests are not robust n the presence of cross-sectonal dependence. In other words, these frst-generaton tests employ a methodology that ncorporates the often mplausble assumpton of cross-sectonal ndependence and fal to dscrmnate between statonarty wth cross-sectonal ndependence and non-statonarty wth cross-sectonal dependence. The power of the conventonal panel unt root tests s weakened by the presence of cross-sectonal dependence. Therefore, we next test ths assumpton of cross-sectonal ndependence utlzng the approaches suggested by Pesaran (004) and Frees (004). We fnd exhaustve evdence ndcatng the presence of heterogeneous cross-sectonal dependences among the tme seres, whch calls for an alternatve test methodology. Consequently, we utlze a second-generaton panel unt root test that accounts for cross-sectonal dependence based on the methodology of Pesaran (007). We conclude ths secton wth an assessment of the mpact of the recent fnancal crss on the results obtaned usng the full sample. Results of the panel unt root tests under the assumpton of cross-sectonal ndependence We frst mplement the Fsher type (Fsher, 93) unt root tests developed by Maddala and Wu (999) and Cho (00). The tests allow for heterogenety n the parameter estmates and combne the evdence on the unt root hypothess from the ndvdual unt root tests performed on each cross secton unt of the panel. The null hypothess n the Fsher type tests (and n the IPS tests) s the hypothess of unt root, and the alternatve s that of statonarty. Ths hypothess s reversed n the Hadrest, n whch the null hypothess s one of statonarty and the alternatve s the unt root (Hard, 000). From a meta-analyss perspectve, these tests combne the p-values of unvarate ndependent unt root tests usng the nverse ch-square, nverse normal, and nverse logt transformatons and are more powerful than the test proposed by Im et al. (003). The Maddala and Wu (999) test statstc s defned as follows: = ( ) P = ln (8) p where p s the p-value of the test statstc n cross-secton unt. P s the nverse ch-square test, dstrbuted ch-square wth degrees of freedom under the null hypothess of a unt root n each cross secton. Addtonally, Cho (00) proposes the Z, L, and P m tests, based on the combnaton of ndvdual p-values. Z s the nverse normal test, dstrbuted as a standard normal ( 0,), Z = = Φ ( ) p (9) where Φ s the standard normal cumulatve dstrbuton functon. The L test s represented as L = k L (0) 3( 5 + 4) where k = and L has a t dstrbuton π ( 5 + ) wth 5+4 degrees of freedom. L s referred to as the nverse logt test and has the logstc dstrbuton wth π mean 0 and varance. 3 L = p ln () p = The P m test s a modfed verson of the Maddala and Wu s (999) P test appled to large panels because n the lmt the P test statstc has a degenerate dstrbuton. P = ( ln ) m p = where E[ p ] = and var [ ln p ] = 4, whch converges to a standard normal dstrbuton. () We report the results of the Maddala and Wu (999) P test and Cho (00) Z test appled to the book value and market value debt ratos n Tables and 3. For robustness reasons, we report the test statstcs computed usng the p-values from both the Augmented Dckey-Fuller (ADF) and the Phllps- Vzja Press&IT

10 374 Vol. 8 Issue Gorgo Canarella, Mahmoud ouray, Mchael J. Sullvan Table. Fsher type panel unt root test results for book value debt ratos Economc Sector Fsher type ADF tests Fsher type PP tests P Z P Z Materals Consumer Dscretonary Consumer Staples (0.000) (0.000) (0.000) (0.064) Health Care Energy Fnancals Industrals Informaton Technology Telecommuncaton Servces (0.000) (0.000) (0.000) (0.0003) Utltes ote: See Table. The table reports the values of the P test statstc and Z test statstc for book value debt ratos for both the Augmented Dckey-Fuller (ADF) and the Phllps-Perron (PP) tests. The P statstcs s computed as P = ln( ) where p s the p-value of the test statstc n the cross-sectonal unt. P s the nverse ch-square test and s dstrbuted as a ch-square dstrbuton wth degrees of freedom under the null hypothess of a unt root n each cross-secton. The Z test statstc s the nverse normal statstc, s computed as Z = Φ ( p ) = appear n parenthess under the test statstcs. denotes sgnfcance at the % level; denotes sgnfcance at the 0% level. = and s dstrbuted as a standard normal ( 0,). The p-values p Perron (PP) tests conducted on each panel. In the Fsher type ADF unt root tests, we rely on the Akake nformaton crteron (AIC) as a lag selecton procedure and allow for a maxmum lag of 3. The AIC s defned as ( L L / T ) + ( k / T ), where LL s the log of the lkelhood functon wth k parameters estmated usng T observatons. In the Fsher type PP unt root test, the spectral regressons employ the Bartlett kernel n conjuncton wth the ewey-west bandwdth selecton. For economy of space, we do not report the results of the L and P m tests because they are unformly consstent wth the results of the P and Z tests. We do not nclude a tme trend because a tme trend s not consstent wth a long-run postve, non-acceleratng target debt rato. However, we do nclude an ntercept because the average debt rato s nonzero. We perform all tests usng the demeaned verson (.e., we subtract the cross-sectonal means from observed data to reduce the degree of contemporaneous correlaton) and, n the Fsher type ADF tests, we nclude one lag (to account for seral correlaton) chosen by AIC. Subtractng the crosssectonal means from the observed data s a strategy suggested by Levn et al. (00) and Im et al. (003) to address cases where dsturbances may be correlated across frms. COTEMPORARY ECOOMICS DOI: /ce

11 An alternatve test of the trade-off theory of captal structure 375 Table 3. Fsher type panel unt root test results for market value debt ratos Economc Sector Fsher type ADF tests Fsher type PP tests P Z P Z Materals Consumer Dscretonary Consumer Staples Health Care Energy Fnancals Industrals Informaton Technology Telecommuncaton Servces Utltes ote: See Table. The table reports the values of the P test statstc and Z test statstc for market value debt ratos for both p where p = the Augmented Dckey-Fuller (ADF) and the Phllps-Perron (PP) tests. The P statstcs s defned as P = ln( ) s the p-value of the test statstc n the cross-sectonal unt. P s the nverse ch-square test and s dstrbuted as a ch-square dstrbuton wth degrees of freedom under the null hypothess of a unt root n each cross-secton. The Z test statstc s the nverse normal statstc and s dstrbuted as a standard normal ( 0,), Z = Φ ( p ). The p-values appear n = parenthess under the test statstcs. denotes sgnfcance at the % level. The Fsher type meta-statstcs strongly ndcate that the unt root hypothess should be rejected n all cases at any conventonal sgnfcance level. Ths fndng ndcates that the behavor of equaton (4) n secton s consstent wth frms borrowng to gradually adjust toward ther target debt ratos. Random shocks have only a transtory effect on the debt rato. Ths evdence offers support for the trade-off hypothess and are consstent wth those of Harrs and Ravv (99) and Almeda and Phlppon (007), among others. For robustness, we have also computed the tests proposed by Im et al. (003), Harrs and Tzavals (999). The fndngs unformly confrm the results presented n Tables -3. In all economc sectors, the null hypothess of a panel unt root s rejected rather strongly. To save space, these results are not presented, but are avalable upon request. However, these frst-generaton Maddala and Wu (999) and Cho (00) tests are only vald under the assumpton of cross-sectonal ndependence, where the error terms are assumed to be ndependent across ndvdual cross-sectons. A weakness of the demeanng transformaton to overcome the problem of cross-sectonal dependence s the mplct assumpton that cross-sectonal dependence s homogeneous;.e., cross-sectonal de- Vzja Press&IT

12 376 Vol. 8 Issue Gorgo Canarella, Mahmoud ouray, Mchael J. Sullvan pendence s drven by a common factor that has a homogeneous effect on all frms n the ndustry, regardless of ther sze. Ths assumpton s hghly unrealstc for most practcal settngs because t gnores the heterogeneous mpact of short-run co-movements (common cycles) and long-run comovements (common trends) on the dynamcs of frms wthn the same ndustry (O Connell, 998). The presence of heterogeneous cross-sectonal dependences undermnes the power of the Maddala and Wu (999) and Cho (00) tests, leads to false rejectons of the null hypothess of the unt root, and may produce evdence of statonarty when the data are non-statonary. In the next secton, we address ths ssue by testng for cross-sectonal dependence usng the dagnostc tests proposed by Pesaran (004) and Frees (004). Results of the tests for cross-sectonal dependence Pesaran (004) proposes a general test for crosssectonal dependence referred to as the CD test. As demonstrated by Pesaran (004), the CD test apples to a large varety of panel data models. Ths ncludes statonary and non-statonary dynamc heterogeneous panel models havng a small T (years) and a large (frms), whch s the case for the sample panel data employed n ths study. The CD test apples to both balanced and unbalanced panels, s robust to parameter heterogenety and structural breaks n the slope coeffcents and error varance, and performs well n terms of sze and power. Under the null hypothess, the covarance matrx of the resduals s dagonal,.e., H 0 : ρ j = ρ j s = corr( ε, ε j t ) = 0 for j, and ε s ndependent and dentcally dstrbuted over tme perods and across cross-sectonal unts. Under the alternatve hypothess H : ρ j = ρ j s 0 for some j, ε s correlated across cross-sectons but uncorrelated over tme. Under the null hypothess of cross-sectonal ndependence, the CD test statstc s dstrbuted as a standard normal for a suffcently large. The CD test averages the par-wse correlaton coeffcents of the resduals obtaned from the ndvdual Augmented Dckey-Fuller (ADF) regresson equatons. We compute the CD test statstc for a balanced panel as follows: CD T = ( ) ( ˆ ε ˆ, ε j ) = j= + T ρ (3) where ˆ ε ˆ ε j t t= ρ ( ˆ ε, ˆ ε ) =, j T / T / ˆ ε ˆ ε j t t= t= and where εˆ and εˆ are estmated resduals from j t the Augmented Dckey-Fuller (ADF) regresson equatons. Under the null hypothess of cross-sectonal ndependence, the CD test statstc converges asymptotcally to the standardzed normal dstrbuton. A possble drawback of the CD test s that t nvolves the sum of the par-wse correlaton coeffcents of the resdual matrx, rather than the sum of the squared correlatons. Ths stuaton mples that the test s lkely to mss cases of cross-sectonal dependence where the sgns of the correlatons are alternatng (for example, where there are large postve and large negatve correlatons n the resduals) and cancel one another out n the averagng process. Ths outcome, however, s not the case n our fndngs. We computed the average absolute value of the off-dagonal elements of the cross-sectonal correlaton matrx of resduals. Ths approach can help dentfy cases of cross-sectonal dependence where the sgn of the correlatons alternates. The average absolute correlaton of the off-dagonal elements for the cross-sectonal correlaton matrx of resduals ranges from 0.73 (Consumer Staples) to (Materals) for the book value debt rato, and from 0.67 (Health care) to 0.36 (Telecommuncaton Servces) for the market value debt rato. These estmates further renforce strong evdence of crosssectonal dependence. Frees (995, 004) proposes a statstc that s not subject to ths shortcomng. The statstc s based on the sum of the squared correlaton coeffcents and s gven by: R AVE = ρ ( ˆ ε, ˆ ε j ) (6) ( ) = j= + where εˆ and εˆ j are the resduals obtaned from the same models estmated for the CD test. Frees (995, 004) demonstrates that a functon of R AVE follows a jont dstrbuton of two ndependent ch-square varables,.e. d = R T ) C AVE ( ( ) Q (7) AVE COTEMPORARY ECOOMICS DOI: /ce

13 An alternatve test of the trade-off theory of captal structure 377 Table 4. Results of the CD test for cross sectonal ndependence for both book value and market value debt ratos Economc Sector Book value debt rato Market value debt rato Materals (0.000) (0.000) Consumer Dscretonary (0.000) (0.000) Consumer Staples (0.000) (0.000) Health Care (0.000) (0.000) Energy (0.000) (0.000) Fnancals (0.000) (0.000) Industrals (0.000) (0.000) Informaton Technology (0.000) (0.000) Telecommuncaton Servces (0.000) (0.000) Utltes (0.000) (0.000) ote: See Table. The table reports the CD test statstc for a balanced panel computed as CD T T = ρ( ˆ ε, ˆ ε ) ( ) j = j= + ˆ ε ˆ ε j t t= where ρ ( ˆ ε, ˆ ε j ) =, and where εˆ / / and εˆ j t are estmated resduals from the Augmented Dckey-Fuller T T ˆ ˆ ε ε j t t= t= (ADF) regresson equatons. denotes sgnfcance at the % level. where Q =, T, T ( T 3) / a( T )[ χ ( T )] + b( T )[ χ T ( T 3)] (8) and where χ, T and χ, T ( T 3)/ are ndependent ch-square random varables wth T and T ( T 3) / degrees of freedom, respectvely, and where a ( T ) = 4( T + ) /( 5( T ) ( T + ) ) and b ( T ) = (5T + 6) /( 5T ( T ) ( T + ) ). The null hypothess s rejected f RAVE > ( T ) + Qq / where Qq s the approprate quntle of the Q dstrbuton. We report the fndngs of the two dagnostc tests n Tables 4 and 5. The outcomes of these tests clearly ndcate the presence of cross-sectonal dependence n both the book value and market value debt ratos. The tests strongly reject the null hypothess of cross-sectonal ndependence at any conventonal sgnfcance level. Ths stuaton casts doubt on the statstcal evdence n favor of statonarty by the Fsher type tests. In addton, the estmates of the resduals correlaton coeffcents present a wde range of varablty, suggestng that resdual correlaton s heterogeneous rather than homogeneous. For economy of space, the matrces of the estmates of resdual correlaton coeffcents are not reported, but are avalable on request. To summarze, the rejecton of the null hypothess of cross-sectonal ndependence mples that tests for the presence of a unt root n book value and market value debt ratos should take ths dependence nto account to produce unbased and relable test statstcs. These fndngs call nto queston any conclusons drawn from the Fsher type tests. The next secton ad- Vzja Press&IT

14 378 Vol. 8 Issue Gorgo Canarella, Mahmoud ouray, Mchael J. Sullvan Table 5. Results of the C AVE test for cross-sectonal ndependence for both book value and market value debt ratos Economc Sector Book value debt rato Market value debt rato Materals Consumer Dscretonary Consumer Staples Health Care Energy Fnancals Industrals Informaton Technology Telecommuncatons Servces Utltes ote: See Table. CAVE s a second cross-sectonal dependence test. The CAVE test statstc for a balanced panel s computed as C AVE = R AVE T ) d ( ( ) Q where εˆ and εˆ j are the resduals obtaned from the same Augmented Dckey-Fuller (ADF) regressons estmated for the CD test. RAVE follows a jont dstrbuton of two ndependent ch-square d varables,.e. C AVE = R AVE T ) ( ( ) Q where Q = a( T )[ χ, T ( T )] + b( T )[ χ, T ( T 3) / T ( T 3)], χ, T and χ, T ( T 3) / are ndependent ch-square random varables wth T and T ( T 3) / degrees of freedom, respectvely, a ( T ) = 4( T + ) /( 5( T ) ( T + ) ), and b ( T ) = (5T + 6) /( 5T ( T ) ( T + ) ). The null hypothess s rejected f R AVE > ( T ) + Qq / where Qq s the approprate quntle of the Q dstrbuton. The p-values are not avalable. The %, 5%, and 0% crtcal values for the Q test statstc for T=4 are 0.360, 0.84, and 0.84, and denoted,, and, respectvely. dresses ths ssue by applyng the test developed by Pesaran (007) that does not requre cross-sectonal ndependence. Results from the panel unt root tests under the assumpton of cross-sectonal dependence In ths sub-secton, we nvestgate the statonarty property of the two measures of debt rato by applyng the panel unt root test developed by Pesaran (007). The test assumes that cross-sectonal dependence s present n the data n the form of a sngle unobservable common factor. The test expands on the Im et al. (003) panel unt root test by augmentng the ADF regresson wth the cross-sectonal averages of lagged level, and contemporaneous and lagged cross-sectonal averages of the frst dfferences of the ndvdual seres. The test s a two-step procedure. Frst, Pesaran (007) proposes a test on the t-rato of the OLS estmate of β n the followng cross-sectonally augmented ADF (CADF) regressons COTEMPORARY ECOOMICS p d = α + β d + δ d + λ d + ϑ d + ϑ d + ε (9) j j t j j= j= p t j where d represents the debt rato of frm at tme t, ε denotes the regresson error term, p s the lag order of the model, and d = t d = =, d t = d are crosssectonal averages, ntended as a proxy for the unobserved common factor. The lagged terms d t and d act to flters out contemporaneous correlaton among 0 = d. The null hypothess of the test can be expressed as H : β 0 for all compared to the alternatve hypothess H : β 0 for some. Then, consstent wth Im et < al. (003), Pesaran (007) proposes a cross-sectonal augmented verson of the IPS test, whch s a smple average of the ndvdual CADF tests. = CIPS(, T ) = t (, T ) (0) where t (, T ) s the cross-sectonally augmented Dckey-Fuller statstc for the -th cross-sectonal unt, gven by the t-rato of the coeffcent of d n the CADF regresson defned by equaton (9). Under the DOI: /ce