Tilburg University

Modelling dividend behavior

Hempenius, A.L.

Publication date:1984

Link to publication in Tilburg University Research Portal

Citation for published version (APA):Hempenius, A. L. (1984). Modelling dividend behavior. (Ter discussie FEW; Vol. 84.30). Unknown Publisher.

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30:S "TER DISCUSSIE"

No. 84.30

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MODELLING DIVIDEND BEHAVIOR

A.L. Hempeniu5

~ SUBFACULTEIT DER ECONOMETRIE

MODELLING DIVIDEND BEHAVIOR

A.L. Hempenius, Tilburg University,The Netherlands.~

Abstract

Cash dividend is a nonnegative variable with positive probability ofbeing zero for a substantial proportion of firms in less properoustimes. In this note it is shown that Heckman's (1979) model for acensored variable is appropriate.

1. Introduction

In studying a dataset on corporate figures published by a Dutch bank(NMB (1983)) one observes 21 losses among the 204 profit figures for34 corporations over the period 1977-1982. A loss ~ a given periodleads invariably to zero dividends in the same period. About the samenumber of cases, 18, show no dividend while there is a positive profit.

r,intner's (1956) well-known lagged adjustment model, which is alsomentioned in finance textbooks, see e.g. Levy and Sarnat (1982), handlesthis phenomenon of zero dividend payments poorly. The lagged adjustmentmodel is:

Dt - ~1 } S2Dt-1 } S3Pt , (1)

with D dividends and P profits. Inclusion of a substantial fractionof zero and negative profits in the data results in an estimated modelwith poor forecasting ability because from zero and negative profitsno (cash) dividends are paid in practice (which this model cannot predict)and because dividends of regular years are predicted less satisfactory(because of the inclusion of the irregular years).

Lintner (1956) did his testing on aggregate data, for which theproblem does not arise, and Fama and Babiak (1968), using firm data,do not mention the problem (possibly because it did not exist).

Maddala (1983, p.162) suggests a"model of friction" in order totake into account the sticky character of dividends. Although there isa positive probability of zero dividends in his model, the assumptionof known limits at which the jumps take place, is not realistic.

A better model may be obtained by using Heckman's (1979) model fora censored variable. Although there is then only one jump in the

~ address: Tilburg University, c~o A.L. HempeniusP.O. Box 901535000 LE Tilburg, The Netherlands

-z-

model's dividend variable, this is hardly serious if one is interested

in the behavior of the average firm. There is only one value at whichjumps take place for all firms at the same value: that of zero dividends;this is the critical value.

2. The model

Denoting by xt the vector of variables influencing potential dividendDt for period t, one has for the equation describing potential dividend:

g(Dt) - fl(xt) f et , (2)

with g( ) a known function and st an error term. One observes only zero

and positive dividends. The firm concerned decides to pay a positive

dividend over period t only if its profit is "large enough", say if ~

~Pt ? Pt ,

with P~ the critical value of profit in period t: dividend is censored

for values of Pt ~ Pt. The critical value Pt depends on a vector of

variables zt :

Pt - f2 (zt) f ut ,

with ut an error term.The complete dividend decision may then be described as follows:

(3)

(4)

Dt ~ 0, if Pt ~ f2(zt) t ut ; (5a)

Dt - 0, if Pt ~ f2(zt) f ut .

For the zero dividend observations one does not observe the potentialvalue of Dt according to the potential dividend function (2). Forpositive dividend observations it follows from (5a) and (2):

E[ g(Dt) I Dt~ 0] - E[ g(Dt) I ut ~ Pt - f2 ( zt) ]

- fl (xt) f E[ Etl ut ~ Pt - f2 (zt)] .

(5b)

(6)

A selectivity problem exists if the last expectation is unequal tozero, which is, for example, the case if the et and ut have nonzerocontemporaneous covariances. (This is so if xt and zt both containthe observed value of the same variable with random measurement error.)Heckman (1979) solves this problem by assuming a bivariate normaldistribution forf~t, ut) and estimating E[ Etlut ~ Pt - f2(zt)] .

t

-3-

3. Some remarks

The sluggish character of observed dividend polices suggests theinclusion of lagged observed dividend Dt-1, into xt of (2). It may

happen that Dt-1 - 0, when estimating fl( ) from the potential D-

values (Dt ~ 0). A specification like (1) can handle such a case.Note that a double logarithmic specification cannot. (An exponential

specification again can.)Note that one may force E[etlut ~ Pt - f2(zt)] to near-zero by being

still more selective in the sample analyzed, i.e. in such a way that

the condition ut ~ Pt - f2(zt) is nearly nonrestrictive. This is the

case for prosperous firms, which will have a large value of Pt - f2(zt).

Of course, such a selection procedure assumes enough degrees of freedom

left, as may be the case in a pooled time series cross section analvsis~

see e.g. Hempenius (1984).As final remark it is noted that in Heckman's (1979) two-stage

estimation procedure Var(ut) may be identified for the above model,

because of the presence of a variable with coefficient equal to one (Pt).

-4-

REFERENCES

1. Fama, Eugene F. and Harvey Babiak, 1968,"Dividend policy:an empirical analysis'; Journal of the American StatisticalAssociation, 63, 1132-1161.

2. Levy, Haim and Marshal Sarnat, 1982, Capital investment andfinancial decisions (Prentice-Hall).

3. Lintner, John, 1956, Distribution of incomes of corporations

among dividends, retained earnings and taxes, American Economic

Review, 46, 97-113.

4. Heckman, James J., 1979, Sample selection bias as a specification

error, Econometrica 47, 153-161.

5. Hempenius, A.L., 1984, "Divided policy of large Dutch corporations",Discussion paper no. 84.19 of the Department of Economics,Tilburg University.

6. Maddala, G.S., 1983, Limited-dependent and qualitative variablesin econometrics (Cambridge University Press).

7. Nederlandse Middenstandsbank, 1983, Aandelenanalyses.

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O1. F. BoekemaL. Verhoef

02. R. H. VeenstraJ. Kriens

03. J. KriensJ.Th. van LieshoutJ. RoemenP. Verheyen

04. P. Meys

05. H.J. Klok

06. J. GlombowskiM. Kriiger

07. G.J.C.Th. van Schijndel

08. F. BoekemaL. Verhoef

09. M. Merbis

10. J.W. VelthuijsenP.H.M. Ruys

11. A. KapteynH. van de StadtS. van de Geer

12. W.J. Oomens

13. A. KapteynJ.B. Nugent

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15. H. GremmenTh. van Bergen

16. M.D. Merbis

17. H.J. Klok

18. D. ColasantoA. KapteynJ. van der Gaag

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26. B.R. Meijboom

27. P. KooremanA. Kapteyn

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O1. P. KooremanA. Kapteyn

02. Frans BoekemaLeo Verhoef

03. J.H.J. Roemen

04. M.D. Merbis

05. R.H. VeenstraJ. Kriens

06. Th. Mertens

07. P. BekkerA. KapteynT. Wansbeek

08. B.R. Meijboom

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