Dividend Policy: An Empirical Analysis

Dividend Policy: An Empirical Analysis Author(s): Eugene F. Fama and Harvey Babiak Source: Journal of the American Statistical Association, Vol. 63, No. 324 (Dec., 1968), pp. 11321161 Published by: American Statistical Association Stable URL: http://www.jstor.org/stable/2285874 Accessed: 16/09/2010 06:38 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=astata. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected].

American Statistical Association is collaborating with JSTOR to digitize, preserve and extend access to Journal of the American Statistical Association.

http://www.jstor.org

DIVIDEND POLICY: AN EMPIRICAL ANALYSIS* EUGENE

F. FAMA AND HARVEY University ofChicago

BABIAIK

Startingwiththe "partial adjustmentmodel" suggestedby Lintner [10, 11], this paper examinesthe dividendpoliciesof individualfirms. The Lintnermodel,in whichthe changein dividendsfromyear t-1to year t is regressedon a constant,the level of dividendsfort-1,and the level of profitsfor t, explains dividend changes for individualfirms fairlywell relativeto othermodels tested. But a model in whichthe constanttermis suppressedand the level of earningsfort-1is added, providesthe best predictionsof dividendson a yearof data not used in fittingthe regressions. Thoughthe dividendpolicyof individualfirmsis certainlya subject of economicinterest,perhaps much of the noveltyof the paper is methodological:specifically,the way in which a validation sample, simulations,and predictiontestsare used to investigateresultsobtained froma pilot sample. To avoid spuriousresultsthat could followfrom the externsive dividend data-dredging involvedin finding"good-fitting" models,onlyhalfof the available firmsare used in the originalsearch, the remainingfirmsservingas a check on the findings.In addition, theirstatisticalproperties since the models tested are autoregressive, cannot always be evaluated analytically.This problemis surmounted to someextentby usingsimulationsto studytheresultsand conclusions obtainedfromthe data forindividualfirms.The noveltyin thisuse of simulationsis that theyare directedtowardscheckingspecificempirical results rather than establishingthe propertiesof some general model.Finally,the conclusionsdrawnfromthe regressionanalysisand fromthe simulationsare again checkedby usingthe variousmodelsto predictdividendchangesfora inewyear of data. The coherencein the resultsobtained with these various tests justifiesstrongconclusions withrespectto the "best" dividendmodelsand theirproperties.

T

1. INTRODUCTION

His paper studies the determinantsof dividend payments by individual firms.The startingpointis the workof Lintner [10, 11], recentlyextended by Brittain [2, 3]. Lintner'smodel is an application of the partial adjustment model (cf. [16]). For any year t the targetdividends(D*) forfirmi are related to profits(Eit) accordingto

Dit

rXEt

I

whereri is the firm'stargetratio of dividendsto profits.In any givenyear the firmwill only partiallyadjust to the targetdividendlevel, so that the change in dividendpaymentsfromyear t-1 to year tis assumedto be ADt -Dit

D,t_1= a} + ci(Dg -

I1) + ui, (2) an errortermn. Suband uitis whereci is the "speed-of-adjustment coefficient" -

* We have benefittedfromthe commentsof P. Browni,Z. Griliches,H. Thornber,A. Zeilner,and especially H. Robertsand R. Roll. The studywas financedwithfundsgrantedto the GraduateSchool ofBusiness,University ofChicago,by the Ford Foundationand by a grantfromthe National ScienceFoundation.

1132

1133

DIVIDEND POLICY: AN EMPIRICAL ANALYSIS

stitutionof (1) into (2) yields1 ADit

a-1+ ciriEit-ciDi,t_1 + uit,

(3)

ADt=

ai + #1iDi,_?+ /2iEit +

(4)

or Ut4

whereac = ai, li =- ci,and2i=1ciri. AlthoughLintnerand Brittaindevelop (4) to explain dividend decisionsof individualfirms,most of theirempiricalworkinvolves aggregatedata. In this study the model will be applied to data forindividualfirms.The problemwill be approached as follows: (a) Most of the behavioral models consistentwith (4) implythat the current dividendis a functionof currentand past earnings.Section 2 providesa rough test of this postulated distributedlag effect. (b) Sections 3 and 4 are concernedmoredirectlywithtesting(4) as a description of dividendchanges. Issues that arise in estimatingthe coefficients of (4) will be considered,and alternativemodelswill be examined. (c) In Section 5 Monte Carlo experimentswill be used to study statistical propertiesofthe variousdividendmodelsthat cannotbe examinedanalytically. (d) Finally, in Section 6 a new year of data will be used to compare the predictions of the "best" regressionmodels with those of various "naive" forecastingprocedures. 2. DIVIDENDS AND DISTRIBUTED LAGS: A PRELIMINARY TEST

Most dividend models implicitlyassume that the current dividend payments of the firmare a distributedlag functionof currentand past profits. Before examiningmodels that assume specificlag structures,it is appropriate to test whetherthe data lend any supportto the notion of a lagged response. Table 1 providesdistributionsby sign of ADit, conditionalon the signs of the per share profitschanges AEit (Panel A), AEit and AEi ,tl (Panel B), and AEit,AEi,t-l and AE&,t2 (Panel C). The table is taken frompooled annual data on 392 major industrialfirmsforthe 19 years 1946-64.2 Table 1 seems to provideevidencefora distributedlag relationshipbetween profitsand dividendchanges. In Panel A when AEit>O, in 65.8 per cent of the cases ADit>O. In Panel B when both AEit and AEi,t-l are positive,the proportionof positive dividend changes is 74.8, while when AEit is positive but AEi,t-l is negative,thereare only 54.1 per cent dividendincreases.Finally,in Panel C, in 80.7 per celntof the cases wheretherewere threeconsecutiveincreasesin annual profits,the currentdividend per share was also increased;on the otherhand, two successiveprofitsincreasesprecededby a decreaseresulted I Lintnerwas led to the partial adjustmentmodel (2) as a resultof interviewswiththe managementsof 28 firms.But the partialadjustmentmodelis not the onlybehavioraljustificationof (4). For a discussionsee [2, pp.

27-311.

2 The basic data fileconsistsof annual financialstatementinformation on 900 major industrialfirmsforthe period 1946-64,as reportedon the Compustattapes of the Standard StatisticsCorporation.Our sample includes only the 392 firmsforwhich19 years of completedata on all variablesneeded in the varioustests are available. The profitsvariablein Table 1 is net incomeper share (incomeafterdepreciationand taxes dividedby an adjusted measureofnumberof sharesoutstanding).The reportednumberofsharesoutstandingis adjusted to eliminatethe effectofstockdividendsand splits.

1134

AMERICAN

STATISTICAL

ASSOCIATION

DECEMBER

JOURNAL,

1968

0-21 0)

Lf t-O C')\ 0U

*

HQ

O c\n

0o 0 O HO 0

Lf-N

_

-I.

___

mc\

-P t

~

CC) CC c3 J4 00

\O Q0 1 -l

\.D -O 0

~~~~~~~~~ HH HX

<

0~-

.iok

o Xrn cc HHcG~j"IO

0

0\) kG i(N

t- ('0

ccco0 0 ~~~~~~_I (Y-

X

o

0

Z

0

SS HtA

H tN

H

k

4

t\

GJ

ONH

ONc)NLrn

LC'

)

?4nn cc c ONCX)

0

hC\j \r

akG

g

m

H

t-kO L

HX

CHU

Sr

.,

ccO

_ f\O HkOw

40

o

'

-

am

Sa

X

O

H 4

C)

n

t

H~~~~~~~~~~~~~~~~~~~~~~ -4 >

4

__.___

xH

~ ~

~

~

+

,

0

-_

~

, . __vCj0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

W

H

+

n >a

S

c ' ccc

cc

nn

m

~ N-r

'

0 0

n C W

Q cr0 C

, '4

H

I'

\. _ H -

H :

1

F

9

|

H

V -O NO m 0 c ) c N H H HCH)H H ON H .)OONt-kG H. . cc 0 H. N cL(N

e

4-:

BS;H

H

C t00\?

< r4

H

H

H

H-4

(N CCN

t-ONO

n O0z

cc H kG ON 0)0)0) ON sy H HHo ,) ,c.c.) cocC)Ccn cYccc\

X

vcO

7

ON\N

NH

CO

-f0)

ko,--,'

0,\

X~~~~C\ C\j al

>

N | |~~-P

|

~~~~~~~~~~~~~~~~~~~~~4 ~ ~ ~

H

4

0 kG

O 'f;~~~~~~~~~~~~jccW\ m~~0 ls ~~~~~H+? 0 O~~~~~~~~nC

EH 1 1 $

H C\J

\ cc Hi ON ccc _-

(\1

O

\,, (Y3 m

-

\ONk

wP

14

4

H

K

(/

Lf'\ cnE

cct-w',

t--LCY)



?

P

(2) R2

(3)

(4)

(5)

A

A

(6)

(7)

(8)

NA

(P2)

A2

A (P)

.464

-.513

-3.85

.165

4.58

.165

.146

1.24

o4o

1.4o

.10

.246

.25

.360

-.698 -.6o4

-5.55 -4.67

.122 .138

2.87 3.65

*.50

.461

-.4q6

-3.70

.16o

4.29

.75 .90

.580 .673

-.427 -.352

-3.03 -2.57

.187 .213

5.44 6.56

P

.468

-.513

-4.15

r4

c_r(P)

.206

.139

2.15

.168 .o46

5.00 3.37

ot

.10

.217

-.708

-6.48

.121

2.75

m

.25 .50

.287 .444

-.6oi -.502

-5.02 -3.64

.139 .16o

3.28 4.26

.75 .90

.61o .751

-.415 -.363

-2.83 -2.43

.187 .218

5.83 7.62

o cq

P 3(P)

.502 .16o

-.o04 .158

- .05 1.23

-.561 .164

-3.87 1.26

.176 .051

4.20 1.41

o

.10

.287

-.200

-1.58

-.774

-5.51

.112

2.59

.25

.399

-.112

- .98

-.675

-4.70

.145

3.21

v

..50

.508

-.oo6

-

-.534

-3.69

.172

3.96

s::

*.75

.620

.o98

-_.454

-3.00

.207

5.o6

.90

.701

.162

1.36

-.365

-2.53

.238

6.12

P

.508

.002

- .o6

-.56o

-4.13

.i82

4.59

0r(P)

.194

.*345

1.20

.159

1.89

.073

3.22

.10

.266

-.260 -.130

-.779 -.666

.122

.354

-1.58 - .99

-6.44

.25

-4.82

.143

2.33 3.03

.50 .75

.502

-.011 .110

- .05

a)

-.54o -.444

-3.77 -2.89

.169 .205

3.94 5.34

pq

.90

-.376

-2.50

.236

7.06

q

.654 .763

.230

.0?4 .81

.74 1.47

* The modelis

AD t

+ iDgc

i

+162Et

+ st.

The data are generatedby (11) and (12) with X=.1 in (12). Thus the populationvalues of the coefficients are

a = O,fi= -.45

andB2 =.15.

OfAi, with a mean value of -.493 and a median of -.471, is centeredto the leftofthe truevalue 3 =-.45. On the otherhand, the samplingdistributionof /2 is centeredto the rightof the true value g2= .15, with a mean of .160 and a a median of .155. Panel B Table 4 presentsresultsforthe same model as Panel A but forthe

1146

AMERICAN

STATISTICAL

ASSOCIATION

JOURNAL,

DECEMBER

1968

case where all random variables are generated by stable 0 =1.7 rather than normaldistributions.This changehas littleeffecton the samplingdistributions of the regressioncoefficients. The mean values of the coefficients are close to those forthe normal model in Panel A, and the fractilesof the cross-sectional distributionsare similar.On the other hand, the cross-sectionaldistributions of the "t" values for the coefficientsare much more disperse in the stable O= 1.7 case. For example,forthe normal model of Panel A Table 4 the interquartilerangeofthe distributionoft(Al) is 1.63,whereasforthe stable modelof Panel B it is 2.23. Thus when the disturbancesare generatedby a stable distributionwith0= 1.7, the distributionsof the ordinaryleast squares regression are well-behaved(in the sense ofbeingclose to those obtainedwhen coefficients the disturbancesare normal), but inferencesbased on the normal regression modelwillbe misleading.The problemarisesfromthe factthat the estimatesof the standarderrorsof the regressioncoefficients computedunderthe normality assumptionare downwardbiased estimatesofdispersionwhenthe disturbances are stable withcharacteristicexponent0 < 2.10 The simulationssummarizedin Table 4 are forX= 0 in (12), i.e., no earnings trend. But during 1946-64 a majorityof firmshad positive earningstrends. The resultsforX -.1, summarizedin Panels A and B of Table 5, indicate that any such trendeffectsare minor;the cross-sectionaldistributionsof coefficient estimatesand their"t" values in Table 5 are close to those forthe corresponding modelsin Panels A and B of Table 4. c. The ConstantTerm The simulationssummarizedin Tables 4 and 5 also provideevidence on the effectsof estimatingthe dividend model with a constanttermwhen the population value of the constantis 0. Some of the pertinentresultsare presented in Table 6, along withcorrespondingresultsforthe Compustat firmdata from Panels A and D ofTable 2. In severalrespectsthe simulationsreproducefairly well the resultsforthe firmdata. As in the firmdata, includingthe constantin the estimatingequation in the simulationsleads to an increasein the values of ofDt-1,goes adjusted Rf2.In the firmdata the averagevalue of Ai,the coefficient from-.317 to -.366 when the constantis added to the model. In the simulations,includingthe constant seems to increase the downwardbias of j1; the 10 Considerthemodel yt

= St

+

ut

t =1, 2,,

,an

wherethe xg are fixednumbersand the ut are independentdrawingsfroma symmetricctable distributionwith 0 I x , thena(A) is a decreasingfunctionof0 for0 > 1. Thus if we applystandardnormalregression theory(i.e., assume O=2) whenin fact

is made and Di,64

0, ?'

0

REGRESSION MODELS Model

Predicted

R1

ai

R2

a.A mi.

1965 Dividend

+ gli

Di,d64 +

li

Di,d64 +

2i A

Change

ali

Di,64

+2i

Ei, 65

R4

li

D i,64

+ 02i

Ei,65

a

+

R6

3i

+ 32i Ei,65

i Di,64

+

65-Di

64)

Equals

A 2i Ei, 65 + 93i Ai 65

R3

R5

(Di

Eid65

+

ki

D i,64

R7

Best

of

Rl-R6

R8

Best

of

R:,

R9

Best

of

R3, R4 or R6 (i.e.,

2i

Ei,65

for each

Ai,65

3i Ei64 '3i

Ei,64

individual

R2 or R5 (i.e.,

firm

with constants) without

constants)

absoluteerror, andinterdecile ranges) meansquareerror, and theinterquartile For each crimodels. forjudgingthepredictive of the various dividend power errorare used, makinga teriontwo versionsof the standardizedprediction totalofeightsummary ofthe models.If forthe momentwe excomparisons theregression cludethesummary modelsR7-R9,in fiveofthesecomparisons and R6 ranksno modelR6 producesthe minimum value ofthetestcriterion, onthe intheremaining In theregressions lowerthanfourth threecomparisons. firmdata thebestmodel,in termsofaverageR2,was R5, the modelwiththe constantand laggedearnings variable.In thepredictions R6, thesamelagged model with the is best. constant but earnings suppressed, This negativeresultwithrespectto theimportance oftheconstanttermis models.R3 (theLinttestsfortheotherregression supported bytheforecasting nermodelwiththeconstantsuppressed) Rl (thesamemodelwith outperforms of ofdistributions theconstant)insixoutofeightofthesummary comparisons R2 in every modelR4 outperforms prediction errors.The constant-suppressed drawnfromthesimTheseresultsconfirm theearlierconclusions comparison. ulations(whichwereconcerned withmodelsRl, R3,R5 andR6). In thesimulamodelsledto a slightincrease theconstant termintheregression tions,including inR2,thoughthedatagenerating processdidnotinvolvetheconstant. modelswiththe The evidenceuniformly offirms, suggests that,fora majority ofdividendchangesthanmodels constant suppressed providebetterpredictions in whichthevalueoftheconstantis leftcompletely free.But froma Bayesian thepaperhas considered ourtreatment oftheconstantthroughout viewpoint, casesofdiffuse and dogmaticpriorbeliefs.If we had chosen onlytheextreme

1158

AMERICAN

STATISTICAL

ASSOCIATION

JOURNAL;

DECEMBER

1968 0 m

0

n

r-4

ON

C%jr-4t-- _-ten 0 M a,\a\ --t-t Co n

m

o

C\j n

rA

n

r--4

t t-\,D

0.

.

.

V2

r-4

w

0 ri Lr\ 4-) C.)

.

---t .

CO

1- 8 IF r-4i t-

c\j m N

c\j N

ON.Z n

r-4 CO CO Oj

A A ri ri A ri A ri

I-A00 \7 cnlo Co %loCo cn 10 . . . . . . .

.

.

0 r-,

0 In 8co0

t- 0 CC r4\,Q\,On

cncncn--t--t-4---tm A li li A A li A

r-"

r-4 0 r-4r-4

C\iCYNrt-r-4n 0 c\j n_:t

m t- ---t 0 C\j

(T\f-4(T\M\D (T\Ckja\ \0 \.0\0 \.0 tl-\10

ko

Coko 4 m f-4 f-4f-4

0

0

0 z

Cd F4

c\j

CC

4

Co

LC\

14

CQ

r-4 r-4

0 r-i

r-I c\j 0 Co

c\j0 n (7 n 0 t-A 1; A

---t n "o

nnnnnnn

t- c\ C'i

Co 0 ---tt-_:t r-iCO CO 'IO m n mlzil m CY)m cn ce) A A 4 A 4 ri A 11

0

t-

N o,\Co

t--( n r

oi

t-

Lf-\\o Lc\--t

4 a\ Co Co -:t Lc\--t Lc\ Lc\-:t

r

M 0 Fl

10 0 c\j-:t -4 t-co m 0 C! A C C 11

0c) r-4t- Co ---t--t r-4 m M r-4N r-i0 (\j N r-i ri 11 A A A A r4 A A

0 IV

0

0 C

C\j---t-I C\j C\jM-:t 0 (7\0 C'i cm (7\ 0 c\jm \D Co n tl-n n t- t-

r-4

1; AA

Co -4 0\

Co \7

LC\ r-iVN(7\0

0 tt-_:t

( ci c c c c c ci ci 4 c c A ci ci c c c ci ci ci ci ci

E-4 Do 0

Co

(7\ r-i

r-i n

Lrl\t- r-i ---t (Y)

t-

t- n

A Cd Ca

ON C\j

t- 0

--t

---t_:t m

c\jm CMc\jCQCQN A 4 ri rAri ri A A

Lr\ m _:t c\j A 4 ri A A

Om -r:t r-I c\jm A A A A ri A A A A

*r_, Co (7\m -t -t -t tA A A A A

0 CON ---tt.----tt- t- N CO C (7\Co 00 t-\D Lr\ tri ri ri ri ri ri ri ri ri

r-i0 m N (7\ a\ a\ Co Co n ri ri A A C;

t- 0 t- t-\D N (ON Co m t- CO\D t- \D n\D \.0 Lr\ A A A A A A A A A

-0 '5 -0

z

0

44 E-4 C)

CC)\.0 0 _:t

r-I 0

r-Ir-40 0 0 0 0 0 0 000000000

It C\i

ONc\j c\jci ri C M

E..,

4

---l- Wri L

t4

r-I0 C%j --,tr-IN r-Ir-ICY) 000000000

cm\j Cor-i

aj \'o C\iCo 0 \D 00 Co u-\CY,) 00 CY,) (31\ &O\D CY-) CY-)C0 A A C; C; A A C.; (4 c A A c Lr\ C\j

m

mcq C;

cYl)8 00

m CY,)

00 -:t cm t-- Lr\ C\j Lr,\CY,)\10 s \D c\j---tCs \D 00 00 --l- t- c\j Ll-Lr\ r4 ockolr-4 cnoo QO M 0 M--t - t--aD-4-Co U-\CY,) CY") -4 CY,,)CY',)CY",) CY,") A A A A c c A A ci 01iA c c 4 c c

-:t 87\,o\o 0 Q 4 r-i A r4 rA

m ci 0 \,Dcm0*0ONm (gy) Co 0 m 0 Co 00 (31\ c\j0 r-ir-4c\j (31\ (31\ (31\ (31\ 0 (31\ A r-iA r-ir-Ir-i

Ckl 0'\

Oj 00 c\j \'o "X8

cy\\3\s&s CY,) CY,) cn CY)CY')

R-l

2ml

0-4

0

0

-.t

N 0

0

&\'o

0

%O\10ko ,0 V.,\..D

IR rp--,,-4 LR'A 4 (MR

T Aq pap-FATp st a7)e MZTJ JOJ JOlae U0T40T.P9xa V 'Laulacl

S

-4 04\'o r. t- CY)

16

CZc c 4

ON0:3 ONr-i N C\j c\jo C; c c c A

r4

c\j

r-420 Lr\ 0

m4q

0\,O\o m m m m m n 0 0 (31\ (31\ 0 0 (31\ 0 (31\ 10 H A r-i r-Ir-i C4

-A C8 t- T ro,4 (r:-)4N

.4

0

4-

4

r-Ir-4 I r-I r-4r-4r-4r-40,\ r-Ir-Ir-4r-4i IC\ ko "Iollo \-o 10 \10 %0 %0 \10 CY') Cy-) Cy-) CY,) Cy-)Cy-) CY,) CY')CY')CY') cn CY')

ce

\D \10 10 \0

121

r-IR P A P

(rV)bj W.TT-j aoj

4% R

Aq P9PTATP ST T .10.1.xq UOT.oTpeacT

4) -C 1.4 IC-d'

Co

Cd 9.

4-

DIVIDEND

POLICY:

AN EMPIRICAL

-ANALYSIS

1159

theBayesianroute,we wouldhavebeenforcedto admitthatoura priorifeelingsconcerning the constantwouldhave been summarized by a distribution closelybutnotcompletely concentrated aboutzero.Imposingsucha priordistribution onthedatawouldguarantee thattheposterior distribution oftheconstantwas also closelyconcentrated about zero.Sinceit wouldruleout wild valuesoftheestimatedconstant, thisapproachcouldlead to evenbetterpredictionsofdividendchangesthansimplysuppressing theconstant. The prediction testsalso confirm theearlierconclusions withrespectto the relevantmeasureofearnings to be usedin dividendmodel.Followingthe suggestionsofBrittain[2,3], R2 andR4 containbothnetincomeanddepreciation as explanatory variables;following Lintner[11], Ri and R3 containonlynet income.Forsixofeightofthesummary measuresofprediction error, modelRl is betterthanR2, and R3 outperforms R4 insevenofeightcomparisons. Thus, formostfirmsthe depreciation variableadds littleto the prediction of dividends. ofdividendchangesbe improved Can predictions byusingthemodelthathas The resultsformodelsR7-R9in Table 13indicate thehighestRI foreachfirm? that the answeris negative.R9 producesthe minimum predictionerrorin column(10) Panel B, but in the remaining seven tests modelsR7-R9 are dominated by oneoftheothermodels(usuallyR6). In mostoftheteststhenaivemodelN2 (samedollarchange)performs well models.Whentestingmanynaive models, relativeto the variousregression oneis likelyto findby chancealoneat leastone thatperforms however, well. ofN2 is easyto find.For theCompustat The reasonforthegoodperformance firmsthe averagechangein net incomefrom1964-65was verycloseto the so wellin yearswhenthiswasnot changefrom1963-64.N2 wouldnotperform thecase. Finally,the foursummarymeasures(averageabsoluteerror,meansquare ofpreand interdecile error,and theinterquartile ranges)ofthedistributions not of equal value. The primaryconcernhereis dictionerrorsare certainly whichofthevariousdividendmodelsworksbestfora largemadetermining itis unreasonable to expectthatanygivenmodelwillbe appropjorityoffirms; If a modelworkswellformostfirmsbut is completely inriateforall firms. thisis thebestwe can expect.We certainly do not fora fewfirms, appropriate errorsofthefewfirms forwhich wantto giveheaviestweightto theprediction But sincethesefirms themodelexamined is completely arelikely inappropriate. themeansquareerrorcriterion to havethelargestprediction errors, givesthem and interdecile heaviestweight.For ourpurposestheinterquartile rangesproofpredistributions vide a morerepresentative pictureofthe cross-sectional dictionerrors producedby eachmodel,butthesealso havetheirshortcomings. Anyinterfractile rangecriterion putsheavyweightonjusttwopointsofthedistribution. The averageabsoluteerrorcriterion providesa muchmoreeven ofind'ividual errors thaneithermeansquareerrororinterweighting prediction fractile ranges. modelsR7-R9) by size The rankings ofthemodels(excluding thesummary ofaverageabsoluteerrorare as follows.

1160

AMERICAN

ASSOCIATION

STATISTICAL

JOURNAL,

DECEMBER

1968

Rank

1

2

3

4

5

6

7

8

9

10

11

Mi & (AD) Mi =IQ(AD)

R6 R6

R3 R3

R5 R5

Rl Rl

N2 N2

R4 R4

R2 R2

N4 N4

N5 N3

N3 N5

Nl Ni

It is clear that forthis criterionthe rankingsof the various models do not depend much on whetherthe predictionerrorsare measuredin units of standard deviation of dividendchangesor in units of the interquartileranges. 7. CONCLUSIONS

The regressionson thefirmdata, the simulations,and thepredictiontestsprovide consistentevidenceon dividendmodelsforindividualfirms.The two variable Lintnermodel (4), includinga constantterm,Dt-,, and Et, performswell relativeto othermodels;in general,however,deletingthe constantand adding the lagged profitsvariable Et-, leads to a slightimprovementin the predictive powerofthe model. In applyingdividendmodelsto the data of mostfirms,net incomeseemsto providea bettermeasureof profitsthan eithercash flowor net income and depreciationincluded as separate variables in the model. Finally, in the modelstestedhere,serial dependencein the disturbancesdoes not seem to be a seriousproblem. REFERENCES

[1] Barnard,G. A., Jenkins,G. M., and Winsten,C. B., "LikelihoodInferenceand Time Series,"Journalof theRoyal StatisticalSociety,Series A (General), Vol. 125 (1962), 321-72. [2] Brittain,JohnA., CorporateDividendPolicy (Washington:The BrookingsInstitution, 1966). [3] Brittain,JohnA., "The Tax Structureand CorporateDividend Policy," American EconomicReview(May, 1964), 272-87. [4] Fama, Eugene F., "The Behavior of Stock Market Prices," Journalof Business (January,1965), 34-105. [5] Fama, Eugene F., and Roll, Richard, "Some Propertiesof SymmetricStable Distributions,"Journal of the American StatisticalAssociation (September, 1968). Theory(New York: JohnWileyand Sons, 1964). [6] Goldberger,ArthurS., Econometric [71 Griliches,Zvi, "DistributedLags: A Survey",Econometrica(January,1967), 16-49. Biometrika [8] Kendall, M. G., "Note on Bias in the Estimationof Autocorrelation," (1954), 403-04. Analysis(Amsterdam:NorthHolland [9] Koyck,L. M., Distributed Lags and Investment PublishingCo., 1954). [10] Lintner,John,"The Determinantsof CorporateSaving," in Savingsin theModern Economy,edited by W. W. Heller (Minneapolis: Universityof Minnesota Press, 1963), 230-55. [11] Lintner,John,"DistributionofIncomesofCorporationsamongDividends,Retained Earningsand Taxes," AmericanEconomicReview(May, 1956), 97-113. [12] Malinvaud, Edmond, "Estimation et Prevision dans les Modeles Rconomiques de StatistiqueVol. 29, No. 2 (1961), Revuede l'InstitutInternational Autoregressifs," 1-32. (Amsterdam:North Hol[131 Malinvaud, Edmond, StatisticalMethodsof Econometrics land PublishingCo., 1966), Chs. 13-15. [14] Mandelbrot,Benoit,"The Variationof CertainSpeculativePrices,"JournalofBusir?ess(October,1963), 394-419.

DIVIDEND POLICY: AN EMPIRICAL ANALYSIS

1161

Merton H., and Modigliani, Franco, "Dividend Policy, Growth and the [15] MVJiller, Valuationof Shares,"Journalof Business (October,1961), 411-33. [16] Nerlove,Marc, Distributed Lags and DemandAnalysis(Washington:U.S.D.A. AgricultureHandbook No. 141, 1958). [17] Roll, Richard,"The EfficientMarket Model Appliedto U. S. TreasuryBill Rates," unpublishedPh.D. thesis, Graduate School of Business, Universityof Chicago, March, 1968. [18] Thornber,Hodson, "Finite Sample Monte Carlo Studies: An AutoregressiveIllustration,"JournaloftheAmericanStatisticalAssociation(September,1967), 801-18. in the 'Partial Adjust[19] Waud, Roger N., "Small Sample Bias Due to Misspecification ment'and 'AdaptiveExpectations'Models," JournaloftheAmericanStatisticalAssociation(December,1966), 1130-52. [20] White,JohnS., "AsymptoticExpansionsforthe Mean and Variance of the Serial Biometrika(1961), 85-94. CorrelationCoefficient," [21] Wise, John,"Linear EstimatorsforLinear RegressionSystemsHaving InfiniteReMathesidual Variances," unpublishedpaper presentedto the Berkeley-Stanford matical EconomicsSeminar(October,1963). [221 Zellner,Arnold,and Tiao, George C., "Bayesian Analysisof the RegressionModel withAutocorrelated Errors,"JournaloftheAmericanStatisticalAssociation(September,1964), 763-78.