WHY ARE DIVIDENDS STICKY? A Dissertation CHUN-LI TSAI DOCTOR OF PHILOSOPHY. Major Subject: Economics

Transcription

1 WHY ARE DIVIDENDS STICKY? A Disseraion by CHUN-LI TSAI Submied o he Office of Graduae Sudies of Texas A&M Universiy in parial fulfillmen of he requiremens for he degree of DOCTOR OF PHILOSOPHY Augus 2005 Major Subjec: Economics

2 WHY ARE DIVIDENDS STICKY? A Disseraion by CHUN-LI TSAI Submied o he Office of he Graduae Sudies of Texas A&M Universiy in parial fulfillmen of he requiremens for he degree of DOCTOR OF PHILOSOPHY Approved by: Chair of Commiee, Commiee Members, Head of Deparmen, Dennis W. Jansen David Bessler Paula Hernandez-Verme Byeongseon Seo Leonardo Auernheimer Augus 2005 Major Subjec: Economics

3 iii ABSTRACT Why Are Dividends Sicky? (Augus 2005) Chun-Li Tsai, B.A., Naional Chengchi Universiy, Taipei, Taiwan; M.B.A., Naional Changhau Universiy of Educaion, Changhau, Taiwan Chair of Advisory Commiee: Dr. Dennis W. Jansen This disseraion invesigaes he sluggish adjusmen process of dividend paymen in he sock marke. Firs, I focus on he individual socks. A casual invesigaion of observed dividends for individual socks shows dividend adjusmens are sluggish and discree; his is no consisen wih he Linner s sylized fac (956) in which dividend adjusmens are assumed o change coninuously. Thus, I examine hree possible explanaions o accoun for dividend sickiness and discreeness: menu-coss (i.e. a consan adjusmen cos), decision-making delays, and dividend adjusmen asymmery. I rejec Dixi s menu-cos model as an appropriae specificaion for he sluggish adjusmen process of dividends. The empirical resuls imply ha decisionmaking delays and dividend adjusmen asymmery migh be possible explanaions for sicky and discree dividends on seleced individual socks. Second, I focus on he aggregae sock marke. I use a quadraic adjusmen cos model o examine wheher adjusmen coss can explain he slow adjusmen of aggregae dividends. The empirical resuls sugges ha adjusmen coss migh be a significan facor explaining he slow dividend adjusmen for S&P 500. The value of relaive weigh cos is relaed o he specificaion of arge dividend. If arge dividends

4 iv are relaed o earnings, hen he empirical resuls sugges ha he adjusmen coss are abou fory-fold more imporan han he deviaion cos beween he acual dividend and he arge level in deermining he dynamic dividend adjusmen process. If arge dividends are specified as proporion o he sock prices, he adjusmen coss are abou foureen-fold more imporan han he deviaion cos beween acual dividend and arge level when managers deermine he dividends.

5 v DEDICATION To my parens

6 vi ACKNOWLEDGMENTS I would like o hank my commiee members Dr. Dennis Jansen, Dr. Paula Hernandez-Verme, Dr. Byeongseon Seo and Dr. David Bessler for heir help and inspiraion in producing his disseraion. In paricular, I would like o express my deepes appreciaion o my advisor, Dr. Dennis Jansen. He has provided me wih help, suppor and encouragemen in my research. His invaluable assisance and guidance were crucial for he qualiy and imely compleion of my disseraion. I am especially indebed o Dr. Dennis Jansen for he knowledge ha was ransferred o me during he process. I am also very graeful for all he help and inspiraion I received from my family and all good friends. I could no have compleed my PhD program wihou heir encouragemen.

7 vii TABLE OF CONTENTS Page ABSTRACT.iii DEDICATION.. v ACKNOWLEDGMENTS. vi TABLE OF CONTENTS.. vii LIST OF FIGURES.....ix LIST OF TABLES.....x CHAPTER I INTRODUCTION... II LITERATURE AND THE EMPIRICAL MODELS Inroducion The Dixi Menu-Cos Model The Logi Model The Auoregressive Condiional Hazard Model III EMPIRICAL ANALYSIS ON INDIVIDUAL STOCKS: WHY ARE DIVIDENDS STICKY AND DISCRETE? Inroducion Daa Esimaing he Targe Dividend Series Empirical Resuls for he Menu-cos Model Empirical Resuls for he Decision-making Delays Empirical Resuls for he Dividend Adjusmen Asymmery Conclusions..45 IV THE ADJUSTMENT COST OF DYNAMIC BEHAVIOR OF DIVIDEND.47

8 viii CHAPTER Page 4. Inroducion The Quadraic Adjusmen Cos Model The Esimaion of an Euler Equaion Daa The Empirical Resuls Conclusions...73 V CONCLUSIONS REFERENCES APPENDIX.. 8 VITA.82

9 ix LIST OF FIGURES FIGURE Page 3. Sock price and acual dividend Targe dividend and acual dividend The difference beween acual dividend and arge dividend The gap percenage beween acual dividend and arge dividend Probabiliy of a dividend change Time series used in levels: sample 87:0-2003: Time series used in levels dividend and earnings (sock prices): sample 87:0-2003: Time series used in Log: sample 87:0-2003: Time series used in Log dividend and earnings (sock prices): sample 87:0-2003: Acual dividend and esimaed arge dividend (relaed o earnings) in levels: sample 87:0-2003: Acual dividend and esimaed arge dividend (relaed o sock prices) in levels: sample 87:0-2003:

10 x LIST OF TABLES TABLE Page 3. Menu-cos model esimaion Random walk es on arge dividends The average duraion beween changes of he dividends The Logi esimaion Log likelihood value for menu-cos and Logi model ACH(,0) esimaion (wih Z = ) Log likelihood value for alernaive models Tess for significance of decision delay in Logi specificaion Tess for significance of decision delay in ACH (,) model Tess for significance of gradual dividend adjusmen in Logi specificaion Tess for significance of gradual dividend adjusmen in ACH (, ) model Asymmeric Logi esimaes Tes for significance of asymmery in Logi specificaion Random walk es (Augmened-Dickey-Fuller es wihou lagged erms) Tes of he ime series daa in Augmened-Dickey-Fuller ess Johansen es for he coinegraion (log of dividends and log of earnings) Johansen es for he coinegraion (log of dividends and log of sock prices) Tes of Θ in Augmened-Dickey-Fuller es wih drif and rend

11 xi TABLE Page 4.5- The esimae of he Euler equaion in he case of D ry The esimae of he Euler equaion in he case of D r P The esimae of ϑ in he Euler equaion in he case of D ry The esimae of ϑ in he Euler equaion in he case of D r P The esimae of λ in he Euler equaion in he case of D ry The esimae of λ in he Euler equaion in he case of D r P = = = = = =

12 CHAPTER I INTRODUCTION In financial markes, he deerminans of dividend payou raes are sill no well undersood. However, dividend-smoohing behavior in he sock marke idenified by Linner (956) is fairly widespread. There have been several aemps in he lieraure o find and explain he observed paerns of dividend payou. Linner (956) lised some sylized facs of dividend policies he discovered in inerviews wih corporae managers. These sylized facs are summarized as follows: (i) Mos managers appeared o have in mind a arge dividend and a long-run arge payou raio when hey se dividends; (ii) Mos managers waned o avoid adjusing dividends; (iii) Many managers smooh dividend payous in erms of curren and pas earnings. Linner provided he firs empirical specificaion of corporae dividend policy--- he parial adjusmen process o describe dividend adjusmen behavior. This adjusmen process assumes managers adjus heir dividends o he arge levels. Linner (956), Fama and Harvey (968) found earnings were he mos imporan deerminan of a change in dividends, and herefore specified arge dividends as some percenage r (long-run arge payou raio) of earnings; Marsh and Meron (987) and Kao and Wu This disseraion follows he syle and forma of Journal of Moneary Economics. Linner (956) suggesed ha corporae dividend decisions can be explained by he following parial adjusmen process, d = b( d - d ) where b is he speed of adjusmen coefficien, 0 < b <, and d is he arge dividend.

13 2 (994) exended Linner s findings and proposed ha dividend payous are deermined by permanen earnings, ha is, arge dividends are specified as some percenage r of permanen earnings. From Linner s lis of sylized facs, dividend adjusmens are assumed o be coninuous wih respec o he sochasic variaions of he arge dividend, defined by eiher earnings or permanen earnings. However, even a casual invesigaion of observed dividends for individual socks shows ha dividend adjusmens are sluggish and discree. The claim ha dividends are smoohed over ime is hardly conroversial, bu few sudies examine he deerminans of dividend smoohing and even fewer focus on he discreeness of he dividend adjusmen process. Thus, he iniial moivaion of his research is o invesigae he facors ha could accoun for sicky and discree dividends for individual socks. Kumar and Lee (200) developed he firs empirical paper o invesigae a discree dividend adjusmen even hough arge dividends change coninuously. In his research, I examine hree oher possible explanaions o accoun for dividend sickiness: menu-coss, decision-making delays, and dividend adjusmen asymmery. The specificaions in Davis and Hamilon (2004) 2 are used o es hese alernaive explanaions. I focus on he discreeness of he dividend adjusmen process. Davis and Hamilon-ype models are appropriae o be applied o invesigae he sicky and discree dividend behavior for he individual socks because arge dividends change coninuously whereas acual dividends change only occasionally. 2 Davis and Hamilon (2004) originally proposed hese hree explanaions o es he sickiness of wholesale gasoline prices.

14 3 For he firs explanaion---menu-coss (i.e. a consan adjusmen cos) --- I use Dixi s menu-cos model. The idea is o see if he dynamic and discree dividend adjusmen behavior can be described by his specificaion wih a consan adjusmen cos 3. For he second explanaion--- decision-making delays--- I use he Logi specificaion and he ACH (Auoregressive Condiional Hazard) model 4. The Logi specificaion allows me o model he probabiliy of a dividend change, and he ACH model capures he probabiliy of a dividend change based on he pas duraions beween changes in dividends and oher explanaory variables. For he hird explanaion--- dividend adjusmen asymmery--- I use he Logi specificaion wih asymmery. In Chaper II of my disseraion, I provide a brief review of he lieraure and analyze he Dixi s menu-cos model, he Logi specificaion, and he ACH model. In Chaper III, I es hese hree explanaions for dividend sickiness on seleced individual socks. The empirical resul shows he adjusmen behavior of dividend is inconsisen wih he menu-cos model of Dixi (99). I find decision-making delays and dividend adjusmen asymmery migh be possible alernaive explanaions for seleced individual socks. The empirical resuls in Chaper III indicae he menu-cos model is no he appropriae specificaion in accouning for he dividend adjusmen process. In Chaper IV, I use an alernaive specificaion --- a quadraic adjusmen cos model--- o examine he quesion of wheher adjusmen coss can explain he slow adjusmen of dividends in 3 Davis and Hamilon (2004) used Dixi s menu-cos model o invesigae wheher his specificaion can describe he dynamic sicky and discree adjusmen of individual wholesale gasoline prices o coninuous changes in bulk spo gasoline prices. 4 ACH model proposed by Hamilon and Jorda (2002) was originally used o forecas he federal funds rae arges, which are discree-valued ime series.

15 4 he aggregae sock marke. I derive a dynamic dividend adjusmen process and apply a wo-sep mehodology o esimae he srucural parameers in he Euler equaion. The empirical resuls sugges adjusmen coss migh be a significan facor explaining he slow dividend adjusmen for S&P 500.

16 5 CHAPTER II LITERATURE AND THE EMPIRICAL MODELS 2.. Inroducion Corporae dividend policy is an imporan issue in he financial lieraure. Alhough mos researchers have recognized dividend smoohing in he sock marke, only a few sudies have invesigaed he deerminans of dividend smoohing. Linner (956) developed he parial adjusmen specificaion o explain he sluggish adjusmen of dividends. However, Linner s model is no consisen wih he discree dividends in mos socks, since i implied ha dividend adjusmens are coninuous wih respec o he sochasic variaions in arge dividends 5. Alhough i is known ha dividends are generally rigid and discree, few sudies in financial lieraure analyze he dynamic models of discree dividends; he primary reason for his being absence of he heory on he discreeness of dividends. Kumar and Lee s (200) paper was he firs o develop and empirically implemen a dynamic discree dividend model for proposing some deerminans of smoohing dividends. They showed ha dividend smoohing is posiively associaed wih he facors ha adversely impac of he invesor s demand. These facors include risk facors: higher earnings 5 Cyer, Kang, and Kumar (996) found he observed dividends are discree in mos firms; hey esimaed he average lengh, which socks remained unchanged dividends, is 6.5 quarers in he NYSE sample of 309 socks for he period

17 6 variance, lower liquidiy, and higher probabiliy of bankrupcy, as well as he lower expeced reurn on capial invesmen by he firm. The primary objecive of his research is o uncover he addiional deerminans of sicky and discree dividends. I accomplish his by analyzing he link beween he discree dividends and hree alernaive explanaions. These are menu-coss, decisionmaking delays, and dividend adjusmen asymmery. These hree explanaions originally were proposed by Davis and Hamilon (2004) o es he sickiness of wholesale gasoline price. Since he adjusmens of individual wholesale gasoline prices are also sicky and discree wih respec o coninuous changes in bulk spo gasoline prices, Davis and Hamilon-ype models seem appropriae o empirically examine he explanaions of sicky and discree dividends. I nex review he lieraure for he sock marke. The lieraure examines how managers se dividends. I connecs Davis and Hamilon s specificaions o he adjusmen behavior of dividend. The parial adjusmen process proposed by Linner (956) is he firs known empirical specificaion of corporae dividend decisions. However, i was based on a se of inerviews wih managers abou heir dividend policies. Thus, Garre and Priesley (2000) developed Linner s parial adjusmen equaion by deriving he manager s opimal sraegy of seing dividend wihin a heoreical specificaion.

18 7 In Garre and Priesley s specificaion, managers are assumed o minimize he quadraic cos funcion of dividend adjusmen 6. Managers are penalized for he deviaions of dividends from heir arge levels and he deviaions of dividend growh rae from a consan rae (α ). An agency cos beween managers and shareholders (Rozeff, 982) is incurred by he firm whenever he acual dividend is below he arge level ( d < d ). The agency cos is an implici cos and arises from he conflic beween managers and shareholders. Assuming ha managers hold a lower fracion of he socks han shareholders, when managers hold more reained earnings (managers pay dividends below arge dividends, d < d ), hey may use hese reained earnings o inves in projecs inefficienly. Thus, he agency coss arise. The posiive deviaions of acual dividends from he arge levels ( d > d ) also could make firms lose. When dividends are larger han arge dividends, and assuming ha exernal finance is cosly, higher dividend payous may cause firms o lose he opporuniy of reinvesing earnings on projecs paying above-marke raes of reurn. In Garre and Priesley s (2000) model, managers a each period are assumed o minimize he loss resuling from he deviaions of dividends from heir arge levels. Tha is, managers consider he deviaion cos of d - d when hey se he dividend. Thus, he deviaion beween he curren dividend and arge level should be an imporan facor influencing he probabiliy of a dividend change in he nex period. 6 The quadraic cos funcion is as following, 2 2 C = θ ( d - d ) + θ 2( d -α) where θ and θ 2 are he loss weighs in managers mind, d is observed dividend, d is arge dividend and α is one consan growh rae of dividend.

19 8 In addiion, Marsh and Meron (987) poin ou one of Linner s imporan sylized facs (956) in he sock marke; mos managers avoid making changes in dividends since he poenial coss could arise if managers change he dividends. There are some sources of poenial adjusmen coss managers migh face. For example, Garre and Priesly (2000) menioned a nonsable dividend policy could increase he uncerainies of managers decisions and herefore increase he managemen coss. Anoher source, dividends migh convey he informaion of he fuure sock price o invesors 7. Thus, managers are exremely relucan o cu dividends because hey are worried abou sending a bad signal o invesors. Furher, managers are slow o increase dividends because hey wan o minimize he probabiliy ha hey have o cu he dividends in he fuure. Garre and Priesly (2000) menioned a sable dividend policy could smooh invesors reacions. I can lower he likelihood of losing invesors confidences in he sock s fuure valuaions. According o he Dixi s model, he deviaion d - d and menu-coss (i.e. a consan adjusmen cos) are he wo mos imporan facors influencing he probabiliy of a dividend change in he nex period. Thus, he Dixi s funcional form seems reasonable for invesigaing he dynamic adjusmen process of dividend. I nex summarize why he Dixi s model is an appropriae specificaion of dividend payou for he individual socks. 7 There is a subsanial lieraure (Michaely, Thaler, and Womack,995; Kao and Wu, 994; and Healy and Palepu,988) showing ha he price of a firm s sock rises (falls) when he firm announces a dividend increase (decrease).

20 9 The Dixi s model is believed o be a proper specificaion o invesigae he dividend adjusmen process since i can saisfy four main aspecs of sock marke ha reflec he dividend policy of observed payou sraegies. Firsly, as noed earlier, in Garre and Priesley s specificaion, he opimal response of managers when seing dividends is o consider he loss of dividends deviaing from arge levels. One of he imporan elemens in he Dixi s model includes he difference beween he dividend and arge level. Secondly, he soluion of Dixi s model can conrol he discreeness of he dividend adjusmen even hough arge dividends change coninuously. Then he specificaion can capure he discreeness of he dividend adjusmen process. Thirdly, if dividends are smoohing, he es specificaion should concern he long-run horizon. The Dixi s model can solve he adjusmen loss of changing dividend by seing up he minimizaion problem for he enire ime horizon from curren period o infiniy. Fourhly, he adjusmen coss could arise when managers change he dividends. In he Dixi s menu-cos model, he adjusmen coss can be assumed o be consan when managers change he dividends. Managers sraegically choose he quarers a which o change dividend so as o minimize he oal adjusmen loss of changing dividends. I find in many respecs, he Dixi s framework appears consisen wih he feaures of dividend payous for he individual socks. Tha is, Dixi s model implies a paricular funcional form of manager s behavior on seing dividends. This research uses Dixi s model as he saring poin o invesigae he paerns managers could use on deciding dividends. In Dixi s specificaion, he deviaion d - d helps predic a dividend change. Hence, all he oher specificaions (Logi specificaion,

21 0 and ACH model), which are used o examine decision-making delays and dividend adjusmen asymmery for sicky dividends (Davis and Hamilon, 2004), also include he deviaion erm d - d. These specificaions allow me o inerpre wheher hese explanaions are consisen wih he behavior of dynamic dividend adjusmens. To es he above hree explanaions, I use hree mehods. The remainder of his chaper describes hese models as follows. In secion 2.2, I give a descripion of Dixi s menu-cos model (99). In secion 2.3, I describe he Logi model. In secion 2.4, I describe he ACH model The Dixi menu-cos model In he Dixi s model, managers are assumed o minimize he oal loss resuling from he deviaion cos of dividends from arge levels and he consan adjusmen cos of changing dividends. Since he adjusmen coss arise when mangers change he dividend, managers choose quarers, 2... in which o change dividend so as o minimize he following adjusmen loss funcion of dividends: E 0 { [( i β 2 β ( - ) + i e k d d d g e ]} i= i i (2.) wih d ( 0) = d ( 0) given and d d ( ) = σdb( ) Le d i denoe he previous dividend deermined by managers, B () is a sandard Brownian moion. σ is he sandard deviaion of he change in he arge dividends, d ( ). β is he discoun facor, and g is he lump-sum adjusmen cos (called he

22 , 2 menu cos in his model) when dividends change a quarers.... The parameer k scales he quadraic uni cos of deviaing from he arge dividend d. Since managers are assumed o wai o change a dividend in order o avoid he adjusmen coss, hey choose o eiher keep dividends unchanged or se dividends as he arge levels wih respec o he variaions of arge dividends a each period. If he arge dividend evolves sochasically, hen here are wo poins, one is below arge dividend and anoher is above, a which managers will change he dividends. Dixi (99) and Hansen (999) showed he soluion in Eq. (2.2), which managers change he dividend and se acual dividend equal o arge dividend, d = d ( i), when d d b i - i = happens - i in any quarer i, wih he opimal maximal deviaion b given by b = 6 g k 4 2 σ (2.2) From Eq. (2.2), some saic comparaive economic inuiion in he sock marke can be obained. Firs, if he menu coss increase, i is more cosly o adjus he dividends. Then he range of inacion widens, managers could pospone he decision on changing a dividend. Second, if k, which scales he quadraic uni cos of deviaing from d, is larger, hen he adjusmen loss of being ou of arge dividend is greaer and herefore, he zone becomes more narrow. Suppose mangers deermine wheher o adjus he dividends by following he above policy, hen he probabiliy ha he dividend changes beween quarer and + can be esimaed by he following,

23 2 Prob( d - d + > b) (2.3) Davis and Hamilon (2004) derived he probabiliy of d - d + > b. I is labeled [ ] h d, d, and can be approximaed by (see Appendix) - - h[ d, d ]= d d b - Φ ( ) + - ( d d + b Φ ) (2.4) σ σ where Φ is he cumulaive disribuion funcion of a sandard normal variable. In he observed discree-ime daa on dividends, le x = if he dividend changes in quarer and zero oherwise. The log of he likelihood of observing he sample {, 2,..., } hen given by T { + logh(, ) ( + )log[ h( d, ]} x x xt is x d d + x d ) (2.5) = 0 b, σ in Eq. (2.4) are chosen o maximize he log of he likelihood in Eq (2.5). The parameer esimaes of b and σ imply an esimae of he expeced ime inerval beween changes in he dividends and can be used o judge wheher his menu-cos model is an appropriae specificaion of he dividend process The Logi model The Logi specificaion is used o examine he possible explanaions based on a decision-making delay and on dividend adjusmen asymmery. In he Logi model, Eq. (2.6), he probabiliy of a dividend change a +, h+, depends on a vecor of variables Z which are used o forecas he probabiliy o a dividend change. Hence,

24 3 ' eδ Z h+ = ' (2.6) eδ Z + where δ is he parameers muliplying Z. Given his probabiliy h+, I can evaluae he log likelihood funcion. Le = if dividend changes in quarer and zero oherwise. The parameer vecor δ is esimaed by maximizing he likelihood funcion given in Eq. (2.7), T - { log (- )log(- } x+ h+ + x+ h+ ) (2.7) = 0 x 2.4. The auoregressive condiional hazard model Since dividends are generally discree for individual socks, he disadvanage of using he radiional Logi model is ha significan serial correlaion could arise. The discreeness of dividend also implies ha he lagged ime inerval beween dividend changes may be relevan for he iming of he nex dividend change. Thus, I use an alernaive model, he Auoregressive Condiional Hazard specificaion (ACH), o model he serial dependences and lagged ime inervals in discree-valued dividend series. This model was proposed by Hamilon and Jorda (2002). I can remove he serial correlaion properies in he dynamics of he limied dependen dividend variable. In addiion o aking accoun of he expeced duraion of dividend changes, his model also incorporaes updaed explanaory variables, which may help forecas he probabiliy of a dividend change. The ACH model was developed originally from he ACD (Auoregressive Condiional Duraion) model proposed by Engle and Russell (998). In Engle and

25 4 Russel s ACD (m, r) specificaion, le n describe he cumulaive number of dividend changes, un denoes he lengh of quarers beween he nh and (n+)h ime a which managers change he dividend payous. ψ n represens he expecaion of un given pas observaions un-, un-2... u as he following equaion, m ψ = α j n- j + β ψ n u j n j j= j= r (2.8) For example, he ACD (, ) model forms he expecaion ψ n as he following 2 n-2 n- ψ = α un + βα un-2 + β α un β α u + β α u (2.9) n where u is he average lengh of quarers observed beween changes in dividends. Engle and Russell (998) denoed he probabiliy of a divided change in quarer + as h = ψ n ( ) + (2.0) Hamilon and Jorda (2002) proposed he ACH specificaion ha can generalize he ACD model, in which he probabiliy of a dividend change a period + is funcion of linearly on expeced duraions ψ n () and oher variables Z. Le n () denoe he number of imes manager has been observed o change dividends of quarer. Then Eq. (2.) is one general expression of ACH model, h + = ψ n( ) ' + ξ Z (2.) where h+ is he hazard rae, ha is, i is he probabiliy of a dividend change in quarer +, Z denoes a vecor of oher variables which can help predic he probabiliy of a dividend change in quarer + and hese variables are known a ime.

26 5 I is imporan o confirm ha he hazard rae h+ is no ouside of (0, ). Hence, Hamilon and Jorda proposed (2002) he following funcion Eq. (2.3) o smooh ransiion such ha he following hazard rae always lies in [ 0,], h + = ' [ + ξ ] λ ψ n( ) Z (2.2) The denominaor in Eq. (2.2) is specified by he following, ' If [ ] + n( ) ξ Z ψ, ' If [ + ξ Z ] < + < n( ) 0 ' hen, [ ] = ( ) Z λ ψ n ξ ψ, where 0 0. ' If [ ξ Z ] + + n( ) 0 λ ψ ψ, where ( ψ = ( ψ ' n( ) hen, [ ] n( ) ξ Z ' 2 n( ) ' ' hen, λ[ ψ ξ ] =. + [ ψ + ξ ] ' + ξ Z -) + ξ Z -) + Z 000 ( ) ( ) Z ( 2.3) n Therefore, I have one differeniable smooh funcion for he ransiion of values beween. and.000 for Eq. (2.2). The numerical procedure can selec a value of h+ inside of (0, ). Given he hazard rae in Eq. (2.2), he log likelihood funcion is esimaed. In he observed discree-ime on dividends, le x = if he dividend changes in quarer and zero oherwise. The log of he likelihood of observing he sample {, 2,..., } hen given by n x x xt is 2

27 6 T - { log + ( )log(- } L( θ ) = x+ h+ x+ h+ ) = 0 (2.4) where θ is he vecor of parameers o influence he probabiliy of a dividend change in Eq (2.2). This vecor of parameers is esimaed by maximizing Eq. (2.4). I use he ACH model o examine if decision-making delays can explain he sluggish adjusmen of dividends.

28 7 CHAPTER III EMPIRICAL ANALYSIS ON INDIVIDUAL STOCKS: WHY ARE DIVIDENDS STICKY AND DISCRETE? 3.. Inroducion In his chaper, I use Dixi s model as he saring poin o invesigae possible explanaions for he observed paerns of dividends. Three alernaive explanaions are esed. These are menu-coss, decision-making delays, and dividend adjusmen asymmery. The Dixi s menu-cos model is used o see if dynamic dividend adjusmen can be explained in erms of menu-coss (i.e. a consan adjusmen cos). In he second explanaion--- decision-making delays--- I use he Logi specificaion and he ACH model. In he hird explanaion--- dividend adjusmen asymmery--- I use he Logi specificaion wih asymmery o invesigae i. I firs describe he economic inuiion behind hese hree explanaions. The firs explanaion is associaed wih adjusmen coss; he poenial coss managers face when hey change dividends. The adjusmen coss in his chaper are assumed o be consan and invarian o he magniude of he change in dividends. Such coss are labeled menucoss in Dixi s model. In response o a change in he arge dividend, managers eiher make no change in dividends or else adjus dividends o he arge, hus increasing an

29 8 adjusmen cos. If i is cosly o adjus dividends, managers migh keep dividends unchanged for a subsanially run of periods, before inacing a change. A second possible explanaion for dividend sickiness is a decision-making delay in dividend adjusmen. This explains he discreeness of dividend adjusmen. This delay migh be a lieral ime-lag in decision-making. If managers need a lengh of ime o process informaion abou he sochasic arge dividend, hen dividend sickiness migh resul. This is jus a decision delay and differs from he menu-cos model, in which managers are concerned wih he physical cos of changing dividend. A hird possible explanaion for dividend sickiness is ha managers are concerned wih he responses of invesors. An increase in dividends may reduce he funds available o managers, and herefore remove agency coss (Cruchely and Hansen, 989; Easerbrook, 984). Managers are more likely o increase dividends and hence reduce he agency loss when acual dividend is less han arge dividend ( d < d ), since higher dividends can send a good signal o invesors. Managers are supposed o be relaively more relucan o cu dividends when d > d, since hey are worried abou invesors confidence in he sock s fuure valuaions. Asymmeric dividend adjusmen explains dividend sluggishness since i reflecs sraegic consideraions abou invesors response o a dividend adjusmen. Alhough his asymmeric specificaion is conrary o he assumpion of Dixi s model, here is significan evidence for asymmeric dynamic adjusmen of dividends on seleced individuals socks. I firs selec six socks o examine wheher he hree explanaions can accoun for sicky and discree dividend. I furher compare he predicions of a dividend change

30 9 among he Dixi s model, he alernaive Logi, and he ACH specificaion. I hope o shed ligh on which of he here explanaions mos accuraely describe he sicky and discree dividend process for he individual socks. The res of his chaper is organized as follows. In secion 3.2, describes he daa used in his chaper. In secion 3.3, esimaes he arge dividends. In secion 3.4, repors he empirical resuls for he menu-cos model. In secion 3.5, uses he Logi and he ACH model o invesigae he decision-making delays. In secion 3.6, uses he Logi model o invesigae he asymmeric dividend adjusmen. In secion 3.7, presens he main conclusion Daa The daa used in his chaper are exraced from Compusa. The variables are composed of quarerly dividends, and sock prices 8. I resric my sample o six socks, GE, NY Times, Duquesne Ligh Holdings INC (Duquesne), MEG Energy INC (MEG), Murphy Oil Corp (Murphy), and Midland Co (Midland) 9. I invesigae wheher any of hese hree explanaions lised above can accoun for dividend sickiness in each of hese 8 In order o deal wih sock splis, all he variables are deflaed by he defaul cumulaive adjusmen facor of Compusa. 9 Since he arge dividends in managers mind are unobservable and here has been difficuly in measuring hem precisely, I selec only he socks whose parameer esimaes are consisen wih he menu-cos model. The empirical resuls for 5 oher individual socks eiher did no converge or did no produce reasonable esimaes in he menu-cos model.(sock Exxon, Bank of NY, Bank of America, Piedmon Naural Gas Co, Inernaional Paper Co., Carpener Technology Corp, Handleman Co., Genuine Par Co., Air Producs & Chemical INC., INTL Business Machine Corp, Moorola INC, CMS Energy Corp, PG&E Corp, General Mills INC, Dow Chemical)

31 20 socks. Figure 3. plos he dividends and sock prices of hese six socks. I is found ha he dividends are rigid and discree Esimaing he arge dividend series To complee his analysis, my firs sep is o esimae he arge dividends. Previous sudies including Marsh and Meron (987), Kao and Wu (994), Kumar and Lee (200) specified arge dividends as proporion o he permanen earnings as in Eq. (3.). d = ry P (3.) Here d is he arge dividend and defined as a percenage r of permanen earnings, Y P. Linner called r he long run arge payou raio, and suggesed he raio is consan; 0 r <. Marsh and Meron (987) employed he sock price as a measure of permanen earnings. Thus, I follow Marsh and Meron (987) and assume sock price is a proxy for a sock s permanen earnings. The long run arge payou raio, r, is esimaed as he consan average markup of dividends over he permanen earnings 0. Tha is, T rˆ = d (3.2) T i= p where T is he number of quarers over he samples in each sock. 0 Kumar and Lee (200) also used he same mehod o esimae he long-run arge payou raio.

32 2 The esimaes of rˆ are repored in he firs row of Table 3.. Then, he arge dividends are esimaed by Eq. (3.3), ˆ d = rˆ P (3.3) For a preliminary analysis of dividend payous, Figures 3.2 plos he dividends wih corresponding arge dividends esimaed by Eq. (3.3). Figures 3.3 plos he deviaion beween he acual and arge dividends, d d. Targe dividends are assumed o follow a random walk in he Dixi s menu-cos model. Hence, he Augmened Dickey-Fuller es wihou lagged erms, Eq. (3.4), is used o examine. d ˆ = ς dˆ + - ε (3.4) Eq. (3.4) is employed o es he null hypohesis of ς = 0. As shown in Table 3.2, for all he socks, he null hypohesis canno be rejeced a he 5% level of significance. Hence, he resuls show arge dividends I esimaed by Eq. (3.3) are consisen wih he assumpion of he Dixi s menu-cos model in which arge dividends are assumed o follow a random walk.

33 22 Sock GE Sock MEG PRICE($) Acual Dividend($) PRICE($) Acual Dividend($) Sock NY Times Sock Murphy PRICE($) Acual Dividend($) PRICE($) Acual Dividend Sock Duquesne Sock Midland PRICE($) Acual Dividend($) PRICE($) Acual Dividend($) Fig. 3.. Sock price and acual dividend

34 23 Sock GE Sock MEG Targe Dividend($) Acual Dividend($) Sock NY Times Tarege Dividend($) Acual Dividend($) Sock Murphy Targe Dividend($) Acual Dividend($) Targe Dividend($) Acual Dividend($) Sock Duquesne Sock Midland Targe Dividend($) Acual Dividend($) Targe Dividend($) Acual Dividend($) Fig Targe dividend and acual dividend

35 24 Sock GE Sock MEG DIFFERENCE($) Sock NY Times DIFFERENCE($) Sock Murphy DIFFERENCE($) DIFFERENCE($) Sock Duquesne Sock Midland Difference($) DIFFERENCE($) Fig The difference beween acual dividend and arge dividend

36 25 Table 3. Menu-cos model esimaion Sock GE NY Times Duquesne MEG Murphy Midland rˆ bmle (0.0575) 0.37 (0.0288) (0.029) (0.065) (0.0058) (0.0575) σ MLE (0.0348) (0.099) (0.02) (0.0523) (0.0020) (0.0348) σ direc bdirec b 2 σ 2 MLE MLE log L Obs Noes: Asympoic Sandard errors are in he parenheses. Aserisk () denoes saisically significan a he 0% level. Double-aserisk () denoes saisically significan a he 5% level. Tri-aserisk () denoes saisically significan a he % level. Table 3.2 Random walk es on arge dividends Sock Lag Order ADF -saisic Criical Value GE NY Times Duquesne MEG Murphy Midland Noe: Criical values are a 5% significance level.

37 Empirical resuls for he menu-cos model I firs use he Dixi s menu-cos model o forecas he quarers in which a manager would change his dividend payou. The Dixi s model is summarized as following, E 0 { [( i β 2 β ( - ) + i e k d d d g e ]} i= i i (3.5) wih d ( 0) = d ( 0) given and d d ( ) = σdb( ) Managers change he dividend and se acual dividend equal o arge dividend, d( i ) = d ( i), when d - d = b happens in any quarer i ( by he soluion of Dixi i i 99; Hansen, 999). Davis and Hamilon (2004) derived he probabiliy of a dividend change beween quarer and + as h[ ] d, d, - - h[ d, d ]= d d b d - d + b Φ ( ) + - Φ ( ) (3.6) σ σ where d denoes he acual dividend payou, and d as he arge dividend, Φ is he cumulaive disribuion funcion of a sandard normal variable. σ is he sandard deviaion of he change in he arge dividends, b is he opimal maximal deviaion beween acual and arge dividend. Le - d - d be he gap beween dividend and arge level, and T is _ T = he average markup for each sock. I replaced d - d in Eq (3.6) wih -, he value _ of he deviaion of he acual dividend from he arge level. In Eq. (3.7), le x = if he

38 27 dividend changes in quarer and zero oherwise. I choose b and σ in Eq (3.6) so as o maximize he following Eq. (3.7) T - { + logh(, ) ( + )log[ h( d, ]} x d d + x d ) (3.7) = 0 Table 3. shows he resuls of he menu-cos model esimaion for six socks. The maximum likelihood esimaes of b and σ are repored in he second and hird rows in Table 3.. The b esimaes range beween among he six socks. The σ values, he sandard deviaion of change in he arge dividends, vary beween per quarer. The empirical resuls imply ha he srucure inerpreaion of he esimaed coefficiens is no so consisen wih he dividend daa, since hese esimaed values b, σ seem oo large. Hence I examine he plausibiliy of he esimaed value of b and σ. In order o examine he plausibiliy of he esimaed parameer,bmle, I direcly esimae bdirec by finding he median absolue value of he change in dividend for hose quarers when managers adjus heir dividends. The resuls are repored in he fifh row of Table 3.. I also direcly esimae he parameer σ, which corresponds o he sandard deviaion of changes in d. The direc esimaor σ direc can be inferred by he sandard deviaion of d d and are repored in he fourh row of Table 3.. These σ MLE esimaed by menu-cos model are larger han hose values of σ direc in five of he six socks. This migh be a problemaic resul for he suiabiliy of he menu-cos model. I inerpre ha his problem comes from he difficuly in forecasing he arge dividends. Since arge dividends are unobservable, sock prices are used as he

39 28 proxies of esimaing arge dividends. However, sock prices are relaively more volaile han acual dividends. In oher words, he esimaed arge dividend ˆ d could flucuae more han rue arge dividend d. If he proxy of managers arge dividends, ˆ d, differs from he rue arge dividends d ˆ (d = d + u, u is he measuremen error), his migh accoun for an overly large esimaed value forσ MLE. Anoher issue on he plausibiliy of he parameer b, he bmle esimaed by menu-cos model are also significanly larger han hose b calculaed by median absolue value of change in dividends in all he six socks. In order o fi he observed infrequency of dividend changes, Davis and Hamilon (2004) needed o assume ha boh he uncerainy abou fuure arge dividends (σ ) and he amoun by which i changes he dividend (b ) are quie large in he Dixi s model. If his model impues much more uncerainy abou he arge dividends han is warraned by he daa, hen i migh accoun for much larger dividend changes han he managers acually make. σ direc and bdirec can be inferred direcly from he daa oher han he frequency of dividend adjusmen, Davis and Hamilon (2004) concluded hese inferred values are an order of magniude smaller han he srucure esimaes σ MLE and bmle. 2 However, I find ha he raios b MLE are accepable numbers given a menu-cos σ 2 MLE inerpreaion of seing dividend, alhough he level of bmle is much lager han can be reconciled wih he observed magniude of dividend changes, and he level of σ MLE is also much larger han can be reconciled wih he difficuly in esimaing he rue arge

40 29 dividends. These raios are repored in he sixh row of Table 3.. The value of σ 2 implies an esimae of he expeced ime inerval beween changes in he dividends and can be used o judge wheher his menu-cos model is an appropriae specificaion of he dividend process. Managers wan o find he opimal boundary a which a dividend changes so as o minimize he oal loss in Eq. (3.5). Hansen(999) solved E [ T d(0) (0) = 0] d b 2 MLE MLE, he expeced lengh of a cycle which is defined as he ime inerval unil reseing he dividend as he following, 2 E [ T d(0) (0) 0] b d = = (3.8) σ 2 Hence, he parameer esimaes of b and σ imply an esimae of he expeced ime inerval of changing dividend. I is also a measure of he expeced frequency of changing dividend. From he resuls of menu-cos model esimaion in Table 3., he b MLE values are below 2 quarers in one of six socks, beween 2 and 2.5 quarers in wo σ 2 2 MLE 2 socks, and he value of b MLE for Murphy is , for Midland is 4.002, and for σ 2 MLE Duquesne is I also esimae direcly he average ime inervals beween changes in he dividends from he daa for each sock. Table 3.3 shows he direc average duraion in erms of quarer, u direc and he difference from he esimaed lengh of a Davis and Hamilon (2004) found ha he parameer esimaes imply a raio of b ha is reasonable 6σ 2 given a menu-cos inerpreaion of pricing gasoline, alhough boh esimaed levels of b and σ are much larger han he direc esimaors of b and σ.

41 30 b 2 cycle σ 2 MLE MLE. I find he direc average duraion, u direc, is larger han he esimaed expeced b 2 ime inerval of one cycle, σ 2 MLE MLE, in all six socks. The difference is larger han.5 quarers in five socks. I inerpre ha alhough managers face he adjusmen cos, g when hey rese he dividend, i sill leads o non-rigid dividend changes. Tha resul implies ha menu-cos model canno describe he sluggish adjusmen process of dividends properly. Table 3.3: The average duraion beween changes of he dividends Sock GE NY Times Duquesne MEG Murphy Midland u direc difference Noes: u direc is he average ime inerval direcly esimaed beween changes in he dividend. The difference is defined as u direc - b 2 MLE σ 2. MLE Alhough adjusmen cos of changing dividends is probably an imporan facor in accoun for sicky dividends, he Dixi s model appears o be inconsisen wih he dividend daa. Possible explanaions for he inconsisency are: () The arge dividends esimaed by sock prices seem more volaile han he rue arge dividends. Tha causes he inconsisency beween dividend adjusmens and he srucure inerpreaion of he esimaed coefficiens in he Dixi s model. (2) Managers ake he adjusmen coss of changing dividends ino accoun on deciding a dividend change. However, he adjusmen coss migh no be consan. They could be posiively relaed wih he

42 3 magniude of deviaion beween changes in he dividends. (3) From he implicaion of agency cos issues wih respec o dividend policy, dividend adjusmen could be symmeric. However, he asymmeric dividend adjusmens in he sock marke arise due o he dividend signal issues. The dividend daa canno be compleely consisen wih he symmeric adjusmen policy of he Dixi s soluion. Thus, hese above reasons could cause ha Dixi s model canno describe he dividend adjusmen process properly. To analyze dynamic dividend adjusmen saisically, I use wo oher heoreical models, which can handle he dynamics of discree changes of dividends. One is Logi specificaion; anoher is ACH model ha akes he duraion beween changes in he dividends ino accoun. I nex compare he performances among hese hree models. Comparison resuls among models I firs compare he menu-cos model wih he Logi specificaion. As in he Dixi s model, he difference beween acual and arge dividend is an imporan elemen influencing he probabiliy of a dividend change. Hence, I firs consider a Logi model in which he probabiliy of a dividend change depends on he same variable d d as in he Dixi s model. Moreover, d d is aken he absolue values in Eq. (3.9), since he dividend change is assumed o be symmeric as in menu-cos model, in which opimal boundary is symmeric. Thus, his specificaion in he Logi model I have: Z (, ) ' = d d (3.9)

43 32 Table 3.4 presens he resuls of he Logi model esimaion [wih Eq (3.9)] for he six socks. If he coefficien of he absolue value of he difference is posiive, ha means once he acual dividend ges far away from he arge dividend, managers migh more likely o adjus he dividends. The resuls show ha he gap is posiively correlaed wih he probabiliy of a dividend change in five of six socks, alhough he es values are no saically significan. The values of he log likelihood funcion wih he Logi model are compared wih hose for he Dixi s menu-cos model [Eq. (3.6) and Eq. (3.7)] and are repored in Table 3.5. I find he values of he log likelihood are quie close, bu he resuls show ha he Dixi s model seems o perform beer a describing he dividend daa han he Logi specificaion. Table 3.4 The Logi esimaion Sock GE NY Times Duquesne MEG Murphy Midland Cons (0.2595) (0.393) (0.3838) (0.3838) (0.374) (0.3045) Z (4.0089) (6.5593) (2.348) (2.348) (8.84) (7.3866) log L Obs Noe: Asympoic Sandard errors are in he parenheses. Aserisk () denoe saisically significan a he 0% level. Double-aserisk () denoes saisically significan a he 5% level. Tri-aserisk () denoes saisically significan a he % level.

44 33 Table 3.5 Log likelihood value for menu-cos and Logi model Sock Menu Cos Logi GE NY Times Duquesne MEG Murphy Midland Noe: Aserisk () denoes he beer model based on Log likelihood value. The comparison resuls are consisen wih he resuls if I look a he Bayesian crierion (SBC) suggesed by Schwarz(978). I nex compare he performance of he ACH model, he Logi and he Dixi s model. To mainain he consisency wihin a wo-parameer model on he comparison o he Dix and Logi specificaion, I esimae he ACH (, 0) model wih Z =. Tha is, I solve Eq. (2.8) for m =, r = 0 ; I only ake he mos recen duraion of dividend change ino accoun. This condiion is subsiued ino Eq. (2.2). The hazard rae wih Z = can be wrien as, h + = λ α u [ n( ) + ] (3.0) where α denoes one parameer for ranslaing he previous duraion beween changes in he dividends and a hazard rae. Tha is, he probabiliy of a dividend change in quarer +, h+, depends linearly on he mos recen lagged duraion un( ) and Z =. The resul of ACH (, 0) model wih Z = [Eq (3.0)] is repored in Table 3.6. α is allowed o be negaive for obaining he convergence in he ACH model, indicaing negaive serial correlaion. In Table 3.6, α shows negaive numbers in hree socks (sock NY Times, MEG and Murphy). Tha is, if a manager adjuss he dividend payou

45 34 in he previous quarer, hen he probabiliy of changing dividend in his curren period is a lile less. Table 3.7 repors he comparison resuls among hese hree models, I find he ACH (, 0) model is he bes specificaion for hree of hese six socks. The menu-cos model is also he bes for hree of six socks. The Logi specificaion does no ou perform he oher wo specificaions. The overall resuls sugges adjusmen coss and he duraions beween changes in he dividends could help describe he observed dividend process. Table 3.6 ACH(, 0) esimaion (wih Z = ) Sock GE NY Times Duquesne MEG Murphy Midland Cons.379 (.699) (0.832) (2.0276) (2.0286) (3.9863) (4.303) α (0.4549) (0.0867) (0.4003) (0.5067) (0.3075).72 (0.9520) log L Obs Noe: Asympoic Sandard errors are in he parenheses. Aserisk () denoe saisically significan a he 0% level. Double-aserisk () denoes saisically significan a he 5% level. Tri-aserisk () denoes saisically significan a he % level. Table 3.7 Log likelihood value for alernaive models Sock Menu Cos Logi ACH GE NY Times Duquesne MEG Murphy Midland Noe: Aserisk() denoes he bes model based on Log likelihood value. The comparison resuls are consisen wih he resuls if I look a he Bayesian crierion (SBC) suggesed by Schwarz(978).

46 Empirical resuls for he decision-making delays Decision-making delays arise when managers need a lengh of ime o deermine he dividend change in response o an observed gap beween he acual and arge dividend. For insance, he sochasic srucure of arge dividend may lead o managers needing more ime decide he dividend payou. In such a case, he former quarers gap may conain addiional predicive power for a dividend change. This differs from he menu-cos model, in which he curren quarer s gap d d is he only facor influencing he probabiliy of a dividend change a quarer +. The Logi specificaion and he ACH model offer a convenien framework for invesigaing he role of addiional explanaory variables. Subsequenly, I now ouline he use boh models o invesigae he oher explanaory variables besides d d as facors ha migh influence he decision o a dividend change. If here are delays in manager s abiliy o process informaion, he former quarer s gap beween dividend and arge level can predic he probabiliy of a dividend change in quarer +. Dividend adjusmens are deermined quarerly, and here are four quarers in a year. Thus, I examine he relaion beween decision delays a period, 2 and he probabiliy of a dividend change a +. The former gaps, d i d i =,2 are added ino Z in he Logi and he ACH (, ) model 2 for examining he i 2 The ACH (, ) model is specified as he following h =, where = α β + ' ) ( ) + n u n ψ n( λ[ ψ + ξ Z ] n( ) ψ ( )