Current vs. Permanent Earnings for Estimating Alternative Dividend Payment Behavioral Model: Theory, Methods and Applications

Transcription

1 Curren vs. ermanen Earnings for Esimaing Alernaive Dividend aymen Behavioral Model: Theory, Mehods and Applicaions Cheng Few Lee Rugers Universiy, USA Hong-Yi Chen Naional Cenral Universiy, Taiwan Alice Lee Sae Sree, USA Tzu Tai Rugers Universiy, USA 1

2 Curren vs. ermanen Earnings for Esimaing Alernaive Dividend aymen Behavioral Model: Theory, Mehods and Applicaions Absrac Marsh and Meron (1987) and Garre and riesley (000) have used aggregaed permanen insead of curren earnings o esimae aggregaed dividend behavior models which was developed by Linner (1956). Lee and rimeaux (1991) used permanen insead of curren ES o esimae Linner s dividend paymen behavior model for individual companies. Mos recenly, Lambrech and Myer (01) have heoreically shown ha permanen, insead of curren, ES should be used o esimae he dividend paymen behavior model for individual companies o avoid measuremen error and misspecificaion of he model. The main purposes of his paper are o: (1) heoreically explain why firms generally allocae permanen earnings and ransiory earnings beween dividends paymens and reained earnings; () develop alernaive mehods for decomposing curren earnings ino permanen and ransiory componens; (3) empirically esimae alernaive dividend paymen behavior models by using wo alernaive permanen ES esimaes for boh individual firms and pooled daa; and (4) es Lambrech and Myer s (01) heoreically resuls relaed o alernaive dividend paymen behavior models. We find ha he average long-erm payou raio is downward biased and he average esimaed inercep is generally upward biased when curren insead of permanen ES are used. We also find ha he combined model perform well o deal wih boh measuremen errors and specificaion errors in describing he dividend paymen behavior model. Keywords: Curren earnings; Curren ES; ermanen earnings; ermanen ES; Dividend behavior models; Specificaion analysis; arial adjusmen coefficien; Long-erm payou raio

3 1. Inroducion Earnings of a firm are allocaed o reained earnings or dividend paymens by a financial decision. Reained earnings are inernal sources of funds ha provide addiional financial capial for eiher he expansion of he firm or a financial reserve agains fuure coningencies. Dividends are generally disribued o sockholders o saisfy heir need for liquidiy or oher uses according o heir preference funcions. I is well-known ha earnings of a firm can be classified ino eiher permanen or ransiory componens. ermanen earning power creaes he permanen componen, and he ransiory componen is composed of income of a emporary naure. Modigliani and Miller (1958, 1961, l963, and 1966) have argued ha a firm s marke value is deermined by is permanen (expeced) earnings, no ransiory componens of income. The ransiory componen of a firm s earnings originaes from a emporary change in marke condiions, a emporary change in accouning mehod, or any oher nonpermanen change ha would cause earnings o flucuae over ime. Lalané and Jones (1979) discuss he imporance of unexpeced earnings of firms as signaling informaion in financial managemen and invesmen analysis. However, o he bes of our knowledge, no accepable mehod for decomposing curren earnings ino permanen (expeced) and ransiory (unexpeced) earnings has been previously developed. In addiion, forecass of dividends are imporan o boh securiy analyss and financial managers, and eiher condiional or uncondiional mehods are generally used o forecas dividend paymens. The mos popular condiional dividend-forecasing models are he parial-adjusmen model developed by Linner (1956) and he informaion conen model discussed by Ang (1975); several ohers are also available. Linner (1956) uses survey daa o develop he dividend paymen behavior model describing how 1

4 managers deermine heir dividend paymen. Lee e al. (1987) use parial adjusmen and adapive expecaion model o generalize Linner s dividend behavior model. Since hen, Linner s model has been widely used in finance research, such as Marsh and Meron (1987), Lee and rimeaux (1991), Garre and riesley (000), and Lambrech and Myer (01). Miller and Modigliani (1966) show ha curren earnings used o esimae cos of equiy capial is subjec o measuremen error problem. Therefore, using curren ES o esimae Linner s dividend behavior model migh be also subjec o measuremen error problem. Marsh and Meron (1987) have heoreically developed an aggregae dividend behavior model and empirically used S& 500 index as proxy o measure aggregae permanen earnings. However, hey did no explicily develop a mehod esimae permanen earnings. Garre and riesley (000) have generalized he Marsh and Meron model by including boh he S& 500 index and permanen earnings in heir dividend paymen behavior model. In addiion, hey proposed a common Kalman filer approach o esimae aggregae permanen earnings. To he bes of our knowledge, Lee and rimeaux (1991) is he firs paper ha empirically shows how curren ES can be decomposed ino permanen and ransiory ES. In addiion, hey used permanen insead of curren ES o esimae Linner s dividend paymen behavior model for individual companies. Mos recenly, Lambrech and Myer (01) have heoreically shown ha permanen insead of curren ES should be used o esimae he dividend paymen behavior model for individual companies. They also provide specificaion analysis o show how he dividend paymen behavior model can be misspecified if curren ES is applied. The main purposes of his paper are o: (1) heoreically explain why firms generally allocae permanen earnings and ransiory earnings beween dividends paymens and reained earnings; () develop alernaive mehods for decomposing curren earnings and dividends ino

5 permanen and ransiory componens; (3) empirically esimae alernaive dividend paymen behavior models by using wo alernaive permanen ES esimaes for boh individual firms and pooled daa; and (4) es Lambrech and Myer s (01) heoreically resuls relaed o alernaive dividend paymen behavior models. Secion 1 is he inroducion. Secion discusses heoreical deerminaion of firm s permanen and ransiory earnings and dividends. The relaionship beween accouning earnings and economic earnings is also discussed. Secion 3 discusses alernaive models for decomposing curren earnings and dividends ino permanen and ransiory componens, according o mehods proposed by Darby (197 and 1974), Lee and rimeaux (1991), and Garre and riesley (000). In Secion 4, empirical resuls of esing model discussed in Secion 3 are revealed in herms of individual firms and pooled daa. We also perform he empirical ess of Lambrech and Myer s (01) heoreical resuls of permanen ES and heir specificaion analysis of dividend paymen behavior model in erms of curren ES. Secion 5 provides a summary and some concluding remarks.. Theoreical deerminaion of firm s permanen and ransiory earnings and dividends In he evoluion of he consumpion funcion, which is one of he key conceps in Keynesian economics, several imporan heories were developed o explain how consumers adjus consumpion expendiures o accommodae changes in heir levels of income. One of hese heories is he permanen-income hypohesis developed by Friedman (1957). 1 The permanen-income hypohesis shows ha consumpion is no a funcion of curren income bu a funcion of permanen income. Toal income is composed of wo componens permanen income and ransiory income. Transiory income is no fully anicipaed and i may 1 When Friedman received he Nobel prize in economics, his work was cied as one of his major conribuions. 3

6 be posiive or negaive. Tha is, a prize would consiue a posiive ransiory income componen while a loss of income from emporary illness or layoff would consiue a negaive componen of ransiory income. Friedman explains ha hese ransiory elemens would no affec consumpion expendiures. The permanen-income hypohesis is applied o he finance heory, and a new heory of dividend paymens by business can be developed. The income of ineres here is he income of he business firm and dividends are analogous o consumer consumpion expendiures. The level of permanen income earned by a firm deermines he permanen dividends i can pay ou o sockholders. ermanen income is essenially an average of curren and pas earnings of he firm. Curren income, herefore, can be divided ino wo componens: E = E + E T (1) where E is he curren income per share of he firm, E is he permanen income per share of he firm, and E T is he ransiory income per share of he firm. Transiory income may be posiive or negaive, and curren income will differ from permanen income by he amoun of ransiory income. A business earns ransiory income, which is really unanicipaed earnings, from windfall profis from any sources. For example, oil companies earn ransiory income from he increased prices hey received from selling producs made from crude oil produced domesically. Firms incur negaive ransiory income if hey experience an uninsured caasrophic even such as he desrucion of a plan by a disaser of any kind or an unexpeced srike by employees. The ransiory componens of income, posiive and negaive, should cancel ou over he permanen-income ime horizon. Transiory componens, however, are always presen during shorer ime periods. Eisner (1967 and 1978) developed a permanen-income heory for invesmen decisions. If 4

7 firm invesmen essenially depends upon inernal sources of funds, he naure of reained earnings is an imporan facor affecing he decision o underake long-erm or shor-erm invesmen. Reained earnings can concepually be decomposed ino wo componens, permanen and ransiory. Dividends can also be divided ino wo similar componens: D = D + D T () where D is he curren dividends per share paid by he firm, D is he permanen dividends per share paid by he firm, and D T is he ransiory dividends per share paid by he firm. ermanen dividends are only one componen of dividends, and oal dividends may be larger han permanen dividends, depending upon he level of ransiory dividends. ermanen dividends are dividends ha he business firm sysemaically pays based on is permanen earnings, dividends paid ou of ransiory earnings would consiue exra dividends. Weson e al. (004) and ohers generally explain ha a firm may have one of hree dividend policies: (1) sable dollar amoun per share, () consan payou raio, or (3) a compromise lower regular dividend, plus exras. No maer wha policy is used, all income is eiher paid ou in dividends or reained by he business in he form of reained earnings: E (D + D T ) R = 0 (3) where R is he reained earnings per share of he firm. Transiory dividends are paid from ransiory income and are shor-run in naure. They are par of he shor-run measure of dividend yield. In conras, permanen dividends are paid from permanen earnings, are long-run in naure, and consiue all of he long-run measure of dividend yield. Miller and Scholes (198) have demonsraed ha shor-run and long-run dividend yield each have differen implicaions in esing he effeciveness of alernaive 5

8 dividend policies on securiy rae of reurn deerminaion. Our heoreical framework, decomposing income and dividend payou ino permanen and ransiory componens, elaboraes upon heir heoreical jusificaion of shor- and long-run dividend yield measuremens. Generally, ransiory earnings are no used for paymen of permanen dividends. However, ransiory dividends can come from eiher ransiory or permanen earnings. Differen sources of dividend paymen (i.e., permanen or curren income) may have differen implicaions in deermining a firm s dividend paymen behavior. This condiion provides he moivaion for examining boh permanen and curren earnings per share for describing a firm s dividend paymen behavior in he empirical secion of his work. In he nex secion, we will discuss alernaive mehods for decomposing curren ES ino permanen and ransiory ES componens. 3. Alernaive mehods for decomposing curren ES ino permanen- and ransiory-es componens In his secion, we will discuss four alernaive mehods o decompose curren ES ino permanen-es and ransiory-es componens. These four mehods are (1) Darby s (1974) mehod, () Lee and rimeaux s (1991) mehod, (3) Garre and riesley s (000) Kalman filer mehod, and (4) Lambrech and Myer s (01) mehod. 3.1 Darby s (1974) mehod We follow Darby s (1974) mehod o decompose curren ES ino permanen- and ransiory-es componens. Theoreically, he relaionship beween curren dividend and permanen earning can be defined as D E (4) i, i, i, 6

9 where D and Ei, are curren dividends and permanen earnings per share for i h firm in period respecively. In addiion, is a random variable wih mean zero and variance. Since E is no direcly observable, we assume ha curren expecaions are derived by modifying permanen expecaions in ligh of curren experience. Tha is, E (1 ) E (1 C) E, 0 1 (5) i, i i, i i, 1 i where λ i represens he weigh used o calculae he permanen ES and C represens he rend rae of ES growh. According o Darby (1974), he iniial value of permanen ES E i,0 and rend rae C can be derived from esimaing he ES rend regression ln E i, = a 1 + a + u (6) where u is he error erm. Afer a 1 and a are esimaed, E i,0 and C can be defined as E e, log(1 C) aˆ (7) aˆ1 i,0 To esimae he opimal weighs λ i, we firs subsiue esimaed E a i,0 and C e ˆ 1 ino Equaion (5) o compue alernaive E i, series for λ i =0, x, x, 3x,, 1 where x is he inerval of esimae for λ i ha eiher minimize sum of squared residuals or maximize adjused R squared of Equaion (4). 3. Lee and rimeaux s (1991) mehod Fama and Babiak (1968), Kmena (1986), and Lee e al. (1987) propose he adapive-expecaion model o deermine he permanen ES, E i, as E E (1 )( E E ) (8) i, i, 1 i i, 1 i, 1 7

10 Equaion (8) can be rewrien as: E (1 ) E E, 0 1 (9) i, i i, i i, 1 i By Koyck ransformaion, Kmena (1986) shows ha equaions (4) and (9) can derive: Di, 0 0 Ei, Di, 1 (10) where 0 (1 i ), 0 (1 i ), i. If λ i approaches zero, hen Ei, E, ha he permanen ES is equivalen o he curren ES. i. This implies By comparing Equaion (10) o Equaion (5), i is obvious ha Equaion (5) is a reduced form of Equaion (10) if C is equal o zero. To empirically esimae he permanen ES defined in Equaion (9), we can run he regression and obain he esimaed λ i which is equal o esimaed. Using esimaed λ i, curren ES, and iniial permanen ES described in Darby s mehod in Secion 3.1, we can esimae permanen ES in period. 3.3 Garre and riesley s (000) Kalman filer mehod Following Garre and riesley s (000) mehod, we define he relaionship among curren ES, E i,, permanen ES, E i,, and ransiory ES, E T i, as follows: E E E (11) T i, i, i, To complee he model, we need o specify equaion ha governs he evoluion of he u nobservable permanen ES: E E (1) i, i, 1 1 (13) 1 where he permanen ES, E i,, evolves as a random walk wih a changing rend, 8. To

11 exrac a measure of permanen ES, we rea measuremen equaion (11) and ransiion eq uaions (1) and (13) as defining an unobserved componens model and esimae i via h e Kalman filer. 3.4 Lambrech and Myer s (01) mehod Using he join deerminaion of manager s ren and cash dividend paymen o equiy holders, Lambrech and Myer (01) derive a Linner dividend paymen behavior in erms of permanen income as: where d a a d Y e, (14) d and d 1 are oal dividend payou a ime and -1 respecively; Y is he firm s permanen income a ime. Lambrech and Myer (01) argue ha permanen income Y is no observable bu heoreically could be esimaed from curren operaing profi and he marke s expecaion of fuure profis. They define permanen income Y as he rae of reurn on he sum of curren income and he presen value of all fuure income, ne of deb service, bu before rens. I is an annuiy paymen ha, given expecaions a ime, could be susained forever. If he profi margin follows he auoregressive process 1, hen permanen income Y can be simplified as : Y ( K (1 ) TD ), (15) i i, i i, i i i, 1 1i i where K i i, is oal operaing income wihou corporae ax for i h firm in period ; TDi, 1is he oal deb for i h firm in period -1; i is ineres rae; and i is he auoregression coefficien for operaing income of he firm i. In he limiing case where π follows a random See Appendix A for he deailed definiion of permanen income and is relaed implicaions. 9

12 walk (μ = 1), permanen income approaches K φ π ρtd 1, ha is, curren ne income, measured before rens bu afer ineres. Lambrech and Myer (01) have briefly discussed how corporae ax can affec permanen income defined in equaion (15), however, hey did no develop a closed form soluion for permanen income wih corporae ax. Therefore, heir permanen income defined in equaion (15) does no exacly follow he concep of eiher economics or accouning. Lambrech and Myer (01) claim ha he Linner model as radiionally esimaed can be defined as d b bte b d u, (16) where d d d 1 ; he curren repored earnings is TE p TD 1 ; p and are permanen and ransiory componens respecively. TD 1 is he componen neiher permanen nor ransiory componen of earnings. The coefficien b on lagged payous is inerpreed as (he negaive of) he speed of adjusmen (SOA) and he coefficien b 1 on earnings as he produc of he long-erm payou raio and he SOA. Under heir definiion of TD is he mos imporan erm in obaining he rue TE, 1 model as defined in equaion (54). According o Lambrech and Myer (01), he rue model is: SOA SOA (1 ) SOA 1 1 d TE SOAd TD e (17) where is he consan erm of dividend behavior model, i is generally used o measure he degree of relucance o cu dividend, is defined as percenage of earnings paid as cash dividend, =1/(1+ ). Therefore, he esimaes for he coefficiens from equaion (16) will be biased and inconsisen unless he omied variables TD -1 and are orhogonal o he included variables (Greene 10

13 (1993), p. 46). The omied variables are likely o be correlaed wih he included variables, given he definiion of he earnings variable TE and because d -1 is linked wih TD -1 hrough he budge consrain. The variance of he esimaes and of he error erms are also biased. Thus, he usual confidence inerval and hypohesis esing procedures can give misleading conclusions abou saisical significance. In pracice, however, he misspecificaion of he radiional Linner model in equaion (16) may no be all ha severe. Firs, corporae earnings or cash flows are highly persisen for maure, sable companies wih low earnings volailiy (see Dichev and Tang (009) and Frankel and Liov (009)). As 1 he erm in TD -1 in equaion (18) vanishes and he omied variable problem wih respec o TD -1 disappears. Second, he ransiory income componen may accoun for only a small par of he oal earnings TE of a maure company. Thus, he correlaion beween and TE may be small oo. In oher words, curren earnings TE may be highly correlaed wih permanen income when ransiory income is small. Of course, TE becomes a noisy measure of permanen income when ransiory income is volaile and imporan. The radiional Linner regression equaion (16) may herefore give quie differen resuls from he model specified in equaion (17). If approaches o 1, hen he problem associaed wih can be resolved by using Darby s approach o calculae permanen earnings. If does no approach o 1, hen equaion (17) can be modified as d b bte b d b TD u, (18) where TE is he esimaed permanen earnings in erms of equaion (5). Equaion (18) is obained by combining Lambrech and Myer s (01) heory and Darby s 11

14 mehod of esimaing permanen earnings. This specificaion solves boh specificaion errors and he ransiory componens of earnings. This new specificaion is he mos imporan conribuion of his research. Darby s mehod is relied upon opimal R-square searching for opimal i, while Lee and rimeaux s mehod relies only regression coefficien esimaes. Therefore, Lee and rimeaux s mehod is empirically easier o esimae permanen ES. We will use boh mehods o esimae permanen ES in he nex secion. Garre and riesley s (000) Kalman filer mehod is relaively resricive in esimaing permanen ES. Therefore, we will use only Darby s mehod, Lee and rimeaux s mehod, Lambrech and Myer s mehod, and he new mehod by combining Darby s mehod and Lambrech and Myer s mehod which is defined in equaion (18) for empirical invesigaion in nex secion. 4. Empirical resuls in esimaing wo alernaive dividend behavior models In his secion, we use ES and DS daa of 608 firms from Compusa, which has a leas 30 years consecuive daa by 011, o perform hese empirical sudies. The empirical sudies include (1) Darby s mehod and Lee and rimeaux s mehod, () Lambrech and Myer s mehod, and (3) combined model as defined in Equaion (18). ES, DS, and payou raio informaion for 608 firms are presened in Appendix C following he descending order of payou raios. In Appendix C, here are 605 firms wih posiive payou raios which are smaller han one. The payou raios of Weyerhaeuser Co and Rexam lc are and 1.005, respecively. The payou raio for Weyerhaeuser Co is larger han one because of paying special dividend $405 million in 010. The earnings per shares for Rexam lc are -0.83, -.37, -0.85, and -0.9 in 1996, 00, 003, and 009 respecively. However, his company paid dividends per shares 0.799, 1.348, 3.815, and for hese four years. This is he main reason ha his company 1

15 obained an average payou raio (1.005) above one. The payou raio of Dar Group Corp, which is lised in he las firm in appendix C, is The earnings per shares of Dar Group Corp are , -4.1, , -7.88, -8.73, in 1987, 1993, 1994, 1995, 1996, and 1997, respecively. However, his company uses a consan dividend payou (0.133) during Therefore, he average ES and DS are -0.0 and , respecively and average payou raio for his company is I is worhwhile o know ha his company bankrups in The appendix C shows ha average ES, DS, and payou raio are.490, , and , respecively. The sandard deviaion for ES, DS and payou raio are , , and , respecively. The skewness for ES, DS and payou raio are , 1.779, and , respecively. In addiion, he kurosis for ES, DS and payou raio are 0.665, , and , respecively. From hese saisics of ES, DS and payou raio, we conclude ha he saisical disribuions of hese hree variables are no normally disribued. Therefore, using he pooled daa o perform regressions migh resul in problems wih esing he significan esimaed coefficiens of regression. Hence, we believe ha using individual firms daa o esimae dividend behavior model can give more informaion han pooled ES and DS daa. Therefore, in his secion, we use boh individual firms daa and pooled daa o perform empirical sudies. 4.1 Darby s mehod and Lee and rimeaux s mehod Resuls from 608 individual regressions In his secion, we will use curren and permanen ES measures o esimae following wo alernaive dividend paymen behavior models as: D c c E c D u (19a) i, 0 1 i, i, 1 i, 13

16 D c c E c D u (19b) i, 0 1 i, i, 1 i, D c c E c D c D u (0a), ' 0 ' 1, ' i i i, 1 3 i, i, D c c E c D c D u (0b), ' 0 ' 1, ' i i i, 1 3 i, i, Following Equaion (11), he curren ES, E, can be decomposed ino permanen ES, E i,, and ransiory ES, E T i,. If we use Equaion (19a) insead of Equaion (19b) o esimae c 1, he esimaed c 1 will be subjec o errors-in-variable problem and he esimaed c 1 will be downward biased. Following Lee and Chen (013), we have analyzed he impac of his kind of errors-in-variable problem in appendix B in deails. We now analyze he biased associaed wih esimaed c 1 and c as follows: Case 1: Under he assumpion ha COV ( Ei,, Di, 1) 0, we can follow equaion (B10) in appendix B o obain he biased associaed wih esimaed c 1 and c as follows: plim cˆ c ( ) 1 1 c 1 1 E 1 and ( c ) 1 Di, Di, 1 Di, 1 plim cˆ c 0 ( ) Di, 1 Ei, 1 (1a) where E. T 1 is he variance of Case : Under he assumpion ha COV ( Ei,, Di, 1) 0, we can follow equaion (B.13) o obain he biased associaed wih esimaed c 1 and c as follows: plim cˆ c 1 1 c 1 1 b E 1 i, Di, E1 i, and 1 1 D i, 1 Ei, 1 R Ei, Ei, Di, 1 plim cˆ c c b (1 ) (1b) where b Di, 1 Ei, is he auxiliary regression coefficien of a regressing Di, 1on E, and R Ei, Di, 1 is he correlaion coefficien beween E and Di, 1. 14

17 Equaions (1a) and (1b) imply ha he esimaed c 1 are downward biased. Therefore, he esimaed inercep ĉ 0 as defined in Equaion (1c) is upward biased. c? D c E c D 0 i, 1 i, i, (1c) 1 Therefore, we need o deal wih his kind of errors-in-variable problem. Firs, we will use Darby s mehod o esimae permanen ES as defined in Equaions (4), (5), (6) and (7), and use Lee and rimeaux s mehod o esimae permanen ES as defined in Equaion (10). We hen use DS and boh curren ES and permanen ES o esimae equaions (19a), (19b), (0a), and (0b). From he opimal search of λ i by Darby s mehod, we esimae λ i for 608 firms and found ha here are 153 esimaed λ i equal o one and 45 esimaed λ i equal o zero. The esimaed λ i for oher 410 firms are beween 0 and 1. By using Lee and rimeaux s mehod, we find ha here are 580 esimaes of λ i eiher larger han zero or less han one. The oher 8 esimaes of λ i equal o zero. From he regression resuls of Equaions (19a) and (19b), we calculaed he averages of he esimaed inercep, he esimaed C 1 and he esimaed C and heir resuls are presened in columns 1,, and 3 of Table 1 (A). Similarly, he averages of he esimaed inercep, he esimaed C 1, he esimaed C and he esimaed C 3 in Equaions (0a) and (0b), can be found in columns 4, 5 and 6 of Table 1 (A). By comparing he average esimaed C 1 of Equaions (19a) and (19b) presened in Table 1 (A), we found ha he average esimaes of C 1 associaed wih permanen ES calculaed by boh Darby s mehod and Lee and rimeaux s mehod are significanly higher han hose esimaes associaed wih curren ES. Miller and Modigliani (1966) have shown ha here exiss errors-in-variable problem if he curren earnings insead of permanen earnings are used o esimae regression coefficien. Therefore, he regression coefficiens associaed wih curren ES insead of permanen ES are subjec o 15

18 errors-in-variable problem as presened in Equaions (1a) and (1b). In addiion, Almeida e al. (010) have used invesmen equaions o show how measuremen error can affec he esimaed regression coefficiens for invesmen equaions. Following he explanaion in Equaion (1c), we found ha he average inercep from Equaion (19a) is significanly larger han ha of Equaion (19b) by using Darby s mehod. From columns 4, 5 and 6 of Table 1(A), we found ha here are 9.7%, 10.86%, and 10.36% of esimaed C 3 significanly differen from zero a 5% significan level. This implies ha here exiss specificaion error in original Linner model for some companies. Table 1 (A). Individual Regression Resuls for Equaions (19a), (19b), (0a) and (0b) This able presens he summary of regression resuls for equaions (19a), (19b), (0a) and (0b). For he ime-series regression models (19a), (19b), (0a), and (0b), he dependen variable is he dividend per D Di, 1 share for firm i a year. Independen variables are he lag of dividend per share ( and Di, ), curren earnings per share ( ), and permanen earnings per share ( E ) for firm i a year. The independen variable, permanen earnings per share calculaed by Darby s mehod, is used in Equaions (19b) and (0b). The independen variable, permanen earnings per share calculaed by Lee and rimeaux s mehod, is used in Equaions (19b)* and (0b)*. Coefficiens presened are he cross-secional averages of esimaed coefficiens of he ime-series regressions. The cross-secional sandard deviaions of esimaed coefficiens of he ime-series regressions are in he parenhesis. The medians of esimaed coefficiens of he ime-series regressions are also presened. ercenage numbers show he percenage of significan esimaed coefficiens of he ime-series regressions a 95% significan level. 16 For equaions (19a) and (19b), he cross-secional averages of parial adjusmen coefficien and long-erm payou are also presened. The cross-secional averages of he number of observaions and R-square for each model are presened a he boom of able. Dependen Variable E Eq. (19a) Eq. (19b) Eq. (19b)* Eq. (0a) Eq. (0b) Eq. (0b)* D D D D D D Inercep

19 (0.3711) (.9668) (0.5354) (0.436) (3.1519) (0.7489) Median % 36.35% 34.05% 3.68% 31.09% 8.6% E (0.1365) (0.1108) Median % 5.96% E (.34) (0.947) (.4786) (0.3860) Median % 48.85% 6.01% 47.53% Di, (0.566) (0.607) (0.638) (0.3094) (0.3090) (0.318) Median % 75.33% 8.07% 84.05% 73.85% 76.48% Di, (0.3154) (0.198) (0.3199) Median % 10.86% 10.36% OBS R

20 Table 1(B). arial Adjusmen Coefficien and Long-Term ayou Raios This able presens he summary of parial adjusmen coefficien and long-erm payou raios for 608 firms. Each firm s parial adjusmen coefficien is equal o one minus are he coefficien of he lag of dividend per share ( Di, 1 ) in equaions (19a), (19b), and (19b)*. In equaion (19a), he long-erm payou raio of individual firm is equal o he coefficien of curren earnings per share ( ) divided by is parial adjusmen coefficien. In equaion (19b) and (19b)*, he long-erm payou raios of individual firm is equal o he coefficien of Darby s and Lee and rimeaux s permanen earnings per share ( E ) divided by heir parial adjusmen coefficien, respecively. The coefficiens presened are he cross-secional averages of parial adjusmen coefficiens and long-erm payou raios for 608 firms. The cross-secional sandard deviaions are in he parenhesis. The median, minimum, and maximum, skewness, kurosis values of esimaed coefficiens are also presened. Trimmed mean is calculaed by excluding 1% of sample s exreme value. Tha is, rimmed mean can be obained by aking ou 6 ouliers of esimaed coefficiens and hen calculaing he average of he remaining esimaed coefficiens. E Variable Eq. (19a) Eq. (19b) Eq. (19b)* arial adjusmen coefficien (0.566) (0.607) (0.638) Median Minimum Maximum Skewness Kurosis Trimmed Mean

21 Long-erm payou (0.9007) ( ).3635 Median Minimum Maximum Skewness Kurosis Trimmed Mean Table 1 (B) presens he disribuion informaion of parial adjusmen coefficiens and long-erm payou raio for 608 firms. We found ha hese wo parameers have a skewed disribued wih 6 ouliers. To deal wih his problem, we calculae median and rimmed average for boh average parial adjusmen coefficiens and long-erm payou raio. The ouliers of long-erm payou raios in equaion (19b) are , , , , , and for companies G & K Services Inc., Auomaic Daa rocessing Inc., Sepan Co., Echlin Inc., Goodrich Corp., And Marahon Oil Corp., respecively. Table 1(B) also indicaes ha he rimmed average of long-erm payou raios in erms of curren ES and permanen ES calculaed by Darby s mehod and Lee and rimeaux s mehod are 0.600, , and , respecively. This implies ha curren ES insead of permanen ES is measured wih error and esimaed regression coefficien is downward biased. I is worhwhile o know ha he average shor-erm payou raio is , which is presened in appendix C. The averages of parial adjusmen coefficiens in erms of curren ES and permanen ES calculaed by Darby s mehod and Lee and rimeaux s are similar regardless wheher regular 19

22 mean, median, or rimmed mean are used. Table. Alernaive ES and ayou Raios This able presens saisical analysis of λ i and permanen ES calculaed by boh Darby s and Lee and rimeaux s mehods. The payou raios calculaed by curren ES and wo alernaives permanen ES are also presened in Table. ES ayou ES λ i ayou ES λ i ayou Original Daa Darby s mehod Lee and rimeaux s mehod Mean Median Minimum Maximum Variance Sandard Deviaion Skewness Kurosis Table presens alernaive saisical informaion of curren and permanen ES, payou raio, and esimaed λ i by using eiher Darby s mehod or Lee and rimeaux s mehod. The average ES from curren earnings, permanen earnings by Darby s mehod, and permanen earnings by Lee and rimeaux s mehod are.490,.1867, and.3834, respecively. The average payou raios from curren earnings, permanen earnings by Darby s mehod, and 0

23 permanen earnings by Lee and rimeaux s mehod are , 0.444, and 0.37, respecively. The average esimaed λ i by using Darby s and Lee and rimeaux s mehods are and , respecively. This implies ha Lee and rimeaux s mehod for esimaing permanen earnings weighs more heavily on curren earnings han hose from Darby s mehod Resuls from pooled regression Table 3 presens he resuls from pooled regression by using boh curren and permanen ES calculaed by Darby s mehod and Lee and rimeaux s mehod. We found ha he resuls from pooled daa are similar o he rimmed mean presened in Table 1(B). In oher words, he esimaed inerceps using wo alernaive permanen ES measuremen are smaller han ha of using curren ES and he esimaed C 1 in erms of permanen ES is larger han ha of using curren ES. Table 3. ooled Regression Resuls for Equaions (19a), (19b), (0a) and (0b) This able presens pooled regression resuls for equaions (19a), (19b), (0a) and (0b). For he ime-series regression models (19a), (19b), (0a), and (0b), he dependen variable is he dividend per D Di, 1 share for firm i a year. Independen variables are he lag of dividend per share ( and Di, ), curren earnings per share ( ), and permanen earnings per share ( E ) for firm i a year. This able shows he coefficiens and sandard errors in he parenhesis. The independen variable, permanen earnings per share calculaed by Darby s mehod, is used in Equaions (19b) and (0b). The independen variable, permanen earnings per share calculaed by Lee and rimeaux s mehod, is used in Equaions (19b)* and (0b)*. ** denoes significan esimaed coefficiens a 99% significan level. In equaions (19a) and (19b), he parial adjusmen coefficien is equal o one minus are he coefficien of he lag of dividend per share ( Di, 1 E ). In equaion (19a), he long-erm payou raio is equal o he coefficien of curren earnings per share ( E ) divided by is parial adjusmen coefficien. In equaion 1

24 (19b), he long-erm payou raio is equal o he coefficien of permanen earnings per share ( E ) divided by is parial adjusmen coefficien. The numbers of observaions and R-square for each model are presened a he boom of able. Dependen Variable Eq. (19a) Eq. (19b) Eq. (19b)* Eq. (0a) Eq. (0b) Eq. (0b)* D D D D D D Inercep 0.188** ** ** ** ** ** (0.0077) (0.008) (0.0083) (0.0079) (0.0084) (0.0084) E 0.098** ** (0.000) (0.000) E ** ** ** 0.14** (0.003) (0.009) (0.0036) (0.0031) Di, ** ** ** 0.341** ** ** (0.0056) (0.0060) (0.0060) (0.0067) (0.0069) (0.0069) Di, 0.903** 0.457** 0.59** (0.0068) (0.0069) (0.0069) arial adjusmen coefficien Long-erm

25 payou OBS R Lambrech and Myer s mehod Since i is no available for an individual firm, we use a limiing definiion of Lambrech and Myers (01) mehod (see equaion (15)) o esimae permanen income and apply permanen income o es dividend paymen behavior models. More specifically, we esimae he following four dividend paymen behavior models: d a a TE a d e (a) i, 0 1 i, i, 1 i, d a a Y a d e (b) i, 0 1 i, i, 1 i, d a a TE a d a d e (3a) i, 0 1 i, i, 1 3 i, i, d a a Y a d a d e (3b) i, 0 1 i, i, 1 3 i, i, where d is oal dividend payou for firm i a ime, TE is ne income for firm i a ime, and Y is permanen income for firm i a ime defined as operaing income subraced by previous year ineres expenses. In addiion, Lambrech and Myers (01) show ha he Linner model may be subjec o he model misspecificaion. As indicaed in Equaion (17), he change of payou can be deermined by he ne income, he previous dividend payou, he ransiory income and he previous deb ousanding. We herefore es he model misspecificaion by using Equaion (4): 3

26 d a a TE a d a TD e (4) i, 0 1 i, i, 1 3 i i, 1 i, where is he ineres expenses for firm i a ime. Empirical resuls are presened in Tables 4 as follows: Table 4. Individual Regression Resuls for Equaions (a), (b), (3a), (3b) and (4) This able presens he summary of regression resuls for 5 regression models. For he ime-series regression models (a), (b), (3a), and (3b), he dependen variable is he oal dividend payou for firm i a year. For he ime-series regression model (4), he dependen variable is he change of oal dividend payou for firm i a year. Dependen variables are he lag of oal dividend payous ( di, 1 d ), ne income ( TE ), permanen income ( Y ), and oal ineres paymen for firm i a year. and Coefficiens presened are he cross-secional averages of esimaed coefficiens of he ime-series regressions. The cross-secional sandard deviaions of esimaed coefficiens of he ime-series regressions are in he parenhesis. ercenage numbers show he percenage of significan esimaed coefficiens of he ime-series regressions a 95% significan level. The cross-secional averages of he number of observaions and R-square for each model are also presened. Eq. (a) Eq. (b) Eq. (3a) Eq. (3b) Eq. (4) Dependen Variable d d d d d Inercep ( ) (47.915) ( ) ( ) ( ) Median % 14.71% 11.84% 11.57% 15.54% TE (0.1147) (0.181) (0.1014) Median % 58.39% 57.19% Y (0.0743) (0.0881) 4

27 Median % 71.40% di, (0.713) (0.801) (0.5000) (0.5078) (0.3586) Median % 94.05% 91.94% 91.07% 39.83% di, (0.467) (0.5891) Median % 3.73% TD i i, 1 (0.7949) Median % OBS R Table 4 presens he summary of regression resuls for models (a), (b), (3a), (3b), and (4). Table 4 shows ha he esimaed regression coefficiens associaed wih curren income and permanen income are 6.50% and 75.87% significanly differen from zero a 5% significan level, respecively. This able also shows ha he average R-square of Eq. (b) is higher han ha of Eq. (a). Similarly, he average R-square of Eq. (3b) is higher han ha of Eq. (3a). Such resuls sugges ha permanen earnings inroduced by Lambrech and Myers (01) do improve he power of dividend behavior models. In addiion, we find here are 5

28 5.45% of firms whose dividend payous can be deermined by heir ineres expenses. I indicaes ha here exiss a specificaion error in Linner s model in erms of curren earnings. The empirical resuls of Table 4 are based upon he measuremen of he permanen income, Y, equals K φ π ρtd 1. In his measuremen, we assume ha π follows a random walk (μ = 1). However, empirically we find ha π does no follow random walk and μ is no equal o one. Therefore, our empirical work can only rea as a qualiaive insead of quaniaive resuls. Hence, i is no meaningful o quaniaively calculae he average parial adjusmen coefficien and he average long-erm payou raio as we done in secion Combined model Resuls from 605 individual regressions In his secion, we will modify Equaion (18) in erms of ES and DS as follows: D b b E b D b I u (5a) i, 0 1 i, i, 1 3 i, 1 i, D b b E b D b I u (5b) i, 0 1 i, i, 1 3 i, 1 i, where D i, and D i,-1 are dividend per share for firm i a ime and -1, respecively; E i, and E i, are curren and permanen ES for firm i a ime ; I i,-1 is he ineres expense per share firm i a ime -1. lease noe ha equaions (5a) and (5b) are similar o equaions (19a) and (19b). In oher words, we add ineres expense per share variable o Equaions (19a) and (19b) o obain equaions (5a) and (5b). Since here are hree firms, Rexam lc., Telus Corp., and Warwick Valley Telephone Co., which do no have ineres expense daa, he oal sample used in equaion (5a) and (5b) conains 605 individual firms. We also esimae combined model as presen in equaions (5a) and (5b) in Table 5. The 6

29 empirical resuls of equaion (5a) show ha here are 5.3% esimaed b 1, 85.9% esimaed b, and.64% esimaed b 3 significanly differen from zero a 5% significan level, respecively. From empirical resuls of equaion (5b) by using Darby s mehod, we found ha here are 61.8% esimaed b 1, 69.09% esimaed b, and 1.16% esimaed b 3 significanly differen from zero a 5% significan level, respecively. From empirical resuls of equaion (5b) by using Lee and rimeaux s mehod, we found ha here are 49.09% esimaed b 1, 75.70% esimaed b, and.15% esimaed b 3 significanly differen from zero a 5% significan level, respecively. In addiion, we found ha he esimaed b 1 from permanen ES by using boh Darby s and Lee and rimeaux s mehods are larger han ha of curren ES and he esimaed inerceps using wo alernaive permanen ES measuremen are smaller han ha of using curren ES. Finally, we found ha abou % firms wih significan esimaed b 3 for boh equaions (5a) and (5b). Table 5. Individual Regression Resuls for Equaions (5a) and (5b) This able presens he summary of regression resuls for equaions (5a) and (5b). For he ime-series regression models (5a) and (5b), he dependen variable is he dividend per share D for firm i a year. Independen variables are he lag of dividend per share ( Di, 1), curren earnings per share ( E ), permanen earnings per share ( E ) and he lag of ineres expense per share ( Ii, 1) for firm i a year. The independen variables, permanen earnings per shares calculaed by Darby s and Lee and rimeaux s mehods, are used in Equaions (5b) and (5b)*, respecively. Coefficiens presened are he cross-secional averages of esimaed coefficiens of he ime-series regressions. The medians of esimaed coefficiens of he ime-series regressions are also presened. The cross-secional sandard deviaions of esimaed coefficiens of he ime-series regressions are in he parenhesis. ercenage numbers show he percenage of significan esimaed coefficiens of he ime-series regressions a 95% significan level. The cross-secional averages of he number of observaions and R-square for each model are presened a he boom of able. 7

30 Dependen Variable Eq. (5a) Eq. (5b) Eq. (5b)* D D D Inercep (0.3683) (.9797) (0.5490) Median % 3.89% 3.73% E (0.1114) Median % E (.57) (0.78) Median % 49.09% Di, (0.936) (0.943) (0.915) Median % 69.09% 75.70% Ii, (1.3754) (1.171) (1.813) Median

31 .64% 1.16%.15% OBS R The empirical resuls presened in Table 5 can be used o es wheher he companies annual ES is following he random walk or no. In addiion, hese resuls migh also be used o es wheher Lambrech and Myers s budge consrain is held for individual firm or no. Equaion (17) derived by Lambrech and Myers (01) is based upon he imporan budge consrain. Following heir paper, we explicily define he budge consrain as follows: d r ( K) TD 1 ( TD TD 1) (6) where d is oal dividend payou a ime, TD and TD 1 is he oal deb in period and -1, respecively; is ineres rae; r is managerial rens a ime ; ( K) is gross profi a ime. If deb is kep consan ( TD TD TD 1 0 ), he equilibrium payou and managerial ren policies simply spli ne income, ( ( K) TD 1) o payou and (1 )( ( K) TD 1) o managerial rens. Wih hese policies, payous and managerial rens follow ne income, always in he raio / (1 ). Because all fuure income will also be spli in his raio, ouside equiy, S ( V ( K) (1 ) TD 1), and he presen value of managerial rens, R (1 )( V ( K) (1 ) TD 1). Managers would of course like o reduce payous and ake more rens, bu canno do so wihou violaing he capial marke consrain. Managers pay ou no more han necessary, so he capial marke consrain pins down payous, rens, and values exacly. If he budge consrain does no hold, hen he erm associaed wih ineres expense will no necessarily exis. Even if he budge consrain holds and he annual ES follows a random walk, 9

32 hen he ineres expense per share iem will be dropped ou. Our empirical es shows ha almos all annual ES for 605 firms do no follow a random walk. Therefore, he empirical resuls presened in Table 5 imply ha here are only.64%, 1.16%, or.15% firms where budge consrains hold under he Lambrech and Myers heoreical model. Budge consrain presened in Equaion (6) implies ha only changes of deb are used o adjus he need of new funds. In oher words, here exiss no exernal equiy issued for he need of invesmen expansion for a firm. Higgins (1977, 1981, 008) have used similar budge consrain o calculae is susainable growh rae. However, his budge consrain imposes he opimal deb asse raio. Chen e al. (013) and Lee e al. (011) have expanded Higgins budge consrain by allowing new equiy issued as alernaive source of funds. Therefore, i may be more realisic o generalize he equaion (6) in erms of eiher Higgins or Chen e al. (013) budge consrains which have more explicily aken he growh rae variable ino he consrains Resuls from pooled regression Using pooled daa, we esimae boh equaions (5a) and (5b) and he empirical resuls are presened in Table 6. Table 6 shows us ha he esimaed b 0 and b 1 and b are similar o hose esimaed wihou ineres expense per share erm which can be found in Table 3. However, i is worhwhile o know ha he esimaed coefficien associaed wih ineres expense per share erm is no significanly differen from zero a a 5% significan level when he permanen ES is used. This migh imply ha he permanen ES no only can remove random flucuaion of ES bu can also remove pars of misspecificaion error which is shown by Lambrech and Myers. Table 6. ooled Regression Resuls for Equaions (5a) and (5b) This able presens pooled regression resuls for equaions (5a) and (5b). For he ime-series regression 30

33 models (5a) and (5b), he dependen variable is he dividend per share for firm i a year. D Independen variables are he lag of dividend per share ( Di, 1), curren earnings per share ( E ), permanen earnings per share ( E ) and he lag of ineres expense per share ( Ii, 1) for firm i a year. The independen variables, permanen earnings per shares calculaed by Darby s and Lee and rimeaux s mehods, are used in Equaions (5b) and (5b)*, respecively. This able shows he coefficiens and sandard errors in he parenhesis. ** denoes significan esimaed coefficiens a 99% significan level. The numbers of observaions and R-square for each model are presened a he boom of able. Dependen Variable Eq. (5a) Eq. (5b) Eq. (5b)* D D D Inercep 0.009** ** 0.139** (0.008) (0.0085) (0.0084) E 0.090** (0.000) E ** 0.156** (0.0033) (0.0030) Di, ** ** ** (0.0059) (0.0001) (0.0061) Ii, ** -.6E E-06 (0.0033) (3.7E-06) (3.6E-06) 31

34 OBS R Summary and concluding remarks Based upon he heories and mehods developed by Marsh and Meron (1987), Lee and rimeaux (1991), Garre and riesley (000), and Lambrech and Myers (01), in his paper, we performed boh heoreically analyses and empirical sudies. We invesigaed how firms generally allocae permanen earnings and ransiory earnings beween dividend paymens and reained earnings. Building on Friedman s permanen-income hypohesis, we firs showed how curren earnings can be decomposed ino permanen and ransiory componens in erms of mehods suggesed by Darby (197 and 1974). We hen used boh Darby s and Lee and rimeaux s mehods o decompose curren ES ino permanen and ransiory componens and performed empirical invesigaions. We found ha he average long-erm payou raio is downward biased and he average esimaed inercep is upward biased when curren insead of permanen ES are used. In addiion, we used Lambrech and Myers permanen earnings measuremen o esimae dividend behavior model. We found ha heir permanen earnings measuremen performs beer han he curren earnings measuremen. However, he permanen earnings measuremens from Lambrech and Myers mehod are difficul o be empirically measured in erms of accouning daa. Finally, we also empirically invesigaed he misspecificaion issue presened by Lambrech and Myers and found ha ineres expense per share migh be useful for esimaing dividend behavior model for some firms. Based upon he parial-adjused model and he adapive-expecaion model, and he 3

35 inegraion of hese models, we heoreically developed and empirically invesigaed boh currenand permanen-dividend payou behavioral models. We analyzed hese wo dividend behavior models by daa of individual firms and pooled daa. Empirical resuls show ha i is beer o use permanen ES, insead of curren ES o esimae dividend behavioral models. If we use curren ES insead of permanen ES, he esimaed inercep will be upward biased and he long-erm payou raio will be underesimaed. In fuure research, we will firs revise he permanen earnings measuremen developed by Lambrech and Myers o make i more plausible for using accouning daa o conduc empirical sudies for examining dividend behavior. Secondly, we will exend Marsh and Meron s (1987) and Garre and riesley s (000) heories and models from aggregae dividend behavior models o individual dividend behavior models o es eiher he signaling heory hypohesis or he free cash flow hypohesis for individual firms. 33

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