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Managerial objectives and firm dividend policy: A behavioral theory and empirical evidence
JaJmuLoF Journal of Economic Behavior & Organization Vol. 31 (1996) 157-174
ELSEVIER
Managerial objectives and firm dividend policy: A behavioral theory and empirical evidence1 Richard Cyert*, Sok-Hyon Kang, Praveen Kumar Graduate School of Industrial Administration, Cameige Mellon University, Schenley Park, Pittsburgh, PA 15213-3890, USA Received 3 August 1994
Abstract We construct a dynamical model of firm dividend policy based on some basic ingredients of the behavioral theory of the firm, in particular, uncertainty avoidance and sequential decision-making by self-seeking managers. We characterize the optimal dividend policy and show that comparative statics on this policy generate restrictions on the relation of the likelihood of future dividend changes with respect to current real and financial variables such as investments, dividends, and technological parameters that govern the evolution of economic earnings of the firm, such as the variance and persistence of the systematic shocks on capital productivity. These relations are then empirically tested on NYSE dividend data. The empirical results are supportive of the predictions from the behavioral model. Specifically, current investment, dividend payouts and the return on capital appear to have significant impact on the likelihood of future dividend changes, as do the variance and persistence of capital productivity shocks. In particular, idiosyncratic fii risk is found to have a negative relation to the likelihood of dividend charges. Finally, these variables are shown to impact the likelihood of dividend increases and decreases asymmetrically, a distinction emphasized by the behavioral model. JEL classification: C30; C35; L20 Keywords:
Dividends
* Corresponding
smoothing;
Uncertainty
avoidance;
Firm risk
author.
‘We thank Franklin Allen, Sugato Bhattacharyya, Douglas Gale, James Poterba, Chester Spatt, and Shyam Sunder for helpful conversations on related issues. We are esspecially grateful to three anonymous referees and the editor Richard Day for suggestions that have significantly improved the paper. All remaining shortcomings are our own. 0167-2681/96/$15.00 0 1996 Elsevier Science B.V. All rights reserved PII SO167-268 1(96)00897-9
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1. Introduction From a theoretical viewpoint, firm dividend policy would be irrelevant (and uninteresting) in a Miller and Modigliani (1961) world of perfect capital markets. From an empirical point of view, however, certain systematic features about the dividend payout behavior of U.S. corporations have intrigued economists, and inspired considerable speculation. For instance, it is a puzzle why firms historically paid a significant fraction of their earnings as dividends even under tax regimes where such payouts imposed a substantial tax liability on shareholders (Black, 1966, Feldstein and Green, 1983). Furthermore, the observed systematic connection between unexpected changes in dividend payouts and their stock prices has focused attention on the possible signaling role of dividends in a world where managers are better informed (relative to outsiders) of their firm’s economic prospects (Bhattacharyya, 1979, Miller and Rock, 1985, Kumar, 1988).2 Over the years, a stylized fact has emerged that firms systematically smooth dividend payouts. In a seminal paper, based on extensive interviews with firm managers, Linter (1956) pointed to deliberate dividend smoothing by firms and suggested four hypotheses regarding the behavioral rules followed by firm managers with respect to dividend policy: (Hl) Managers attempted to attain some long term payout ratio between dividends and economic earnings; (H2) In setting dividends they focus on the change in the existing payouts and not the level, per se; (H3) Dividend changes are likely to follow large unanticipated and non-transitory changes in economic earnings; and, (H4) Managers avoid raising dividends if they stand a good chance of being reversed in the near future. Linter (1956) then attempted to formalize certain salient aspects of these hypotheses through a (reduced form) model in which the dividend process is a function of current period earnings and lagged dividends. The Linter model was found to perform well in explaining aggregate corporate dividend behavior in the inter-war and postwar years (Linter, 1963). However, Linter also tested other firm-specific variables such as gross and net investments, but found that they did not add to the explanatory power of the basic model. Fama and Babiak (1968) tested the Linter model on individual firm data and also found that investment-related variables and lagged earnings did not add to much. Using aggregate, industry- and firm- level data, Brittain (1966) found that individual tax rates improved the explanatory power of the model in few cases, but the improvements were minor. Marsh and Merton (1986, 1987)) also used a dividend process based on the Linter model, but in their version stock price was used as a proxy for the firm’s (unobservable) permanent earnings. Finally, by using firm-level data, Pettit (1972), and Laub (1972) pointed out that at the micro level dividend payouts by firms are “sticky,” i.e. they have a tendency to remain unchanged for non-trivial lengths of time, and charged by discrete amounts. While these empirical patterns regarding dividend payouts have been well documented, the reasons underlying them are still not well understood. As Marsh and Merton (1986) put it, dividend policy is an issue where, “the literature has not arrived at even a local sense of closure.” In this paper we show that the behavioral theory of the firm (Cyert and March, 1993) can provide the missing explanation through an operational model which incorporates ‘Miller (1986) presents an excellent survey of the research related to the dividend controversy.
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salient factors that concern management in its formulation of dividend policy. It is consistent with the management rules actually observed by Linter (1956) and generates refutable predictions about dividend smoothing. In Section 2 we show how Linter’s managerial rules are related to the behavioral theory of the firm, and reformulate the manager’s problem as one of dynamic optimization. The strategy implied by this formulation is described in Section 3 and is consistent with the behavioral theory. This provides a basis for interpreting the pragmatic Linter rules as proxies for sophisticated strategies that have no possibility of implementation in the business environment. The optimal strategy implies dividend smoothing based on the conditional probability of future dividend changes in a way that differs from Linter’s approach in which smoothing arises due to the partial adjustment of dividends toward the desired payout ratio. Our analysis is in accordance with the stylized fact that dividend payouts are discrete (Fama and Babiak, 1968, Laub, 1972, Pettit, 1972). Moreover, the model generates refutable predictions on the relation of the likelihood of future dividends to financial and technological variables. In Section 4, we present an empirical test of our theory. We find that all the factors identified by the behavioral model appear to have a significant influence on dividend smoothing as interpreted in this paper. Moreover, these factors also appear to influence the probabilities of dividend increases and decreases asymmetrically, a distinction emphasized by the behavioral model. We also find that the persistence and riskiness of firms’ earnings play a significant role in dividend policy. Specifically, firms with more persistent earnings tend to make more frequent increases and decreases in dividends, and more risky firms tend to increase dividends less often but decrease them more often. Interestingly, firms idiosyncratic risk turns out to be more important than the systematic risk in terms of influence on dividend smoothing.
2. A behavioral
model of dividend policy
A central feature of the (behavioral) hypothesis of uncertainty avoidance (Cyert and March, 1993) is that organizations, and in particular managers, attempt to avoid the requirement of correctly anticipating events in the distant future by using decision rules that emphasize sequential reaction or adaption to possibly short-run feedback from changes in the firm’s economic environment. More concretely, firms tend to impose standard operating procedures, industry conventions and other types of uncertaintyabsorbing contracts on their environment. This, however, does not imply that firms are able to eliminate uncertainty; only that management frames the decision-making problems in a manner that makes dealing with uncertainty more tractable. Specifically, in relation to the formulation of firm dividend policy, uncertainty avoidance is suggestive of the following basic features:3 ‘The reader is referred to Cyert and March (1993) for a more detailed discussion of the concept of uncertainty avoidance and its relation to other features of business decision-making emphasized by the behavioral theory of the firm.
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1. Firms focus on the dividend adjustments in response to (possibly short-run) changes in the environment, such as changes in earnings prospects. 2. The levels of dividends are not optimized per se on the basis of some long-run optimization model. The levels are usually set according to industry conventions, firm history, etc. 3. Firms maintain simple rules of thumb in relation to acceptable dividend adjustments. For example, the adjustments may be required to be such so as to leave the adjusted dividends in the neighborhood of some pre-set payout ratio. 4. Shareholder/investor attitudes toward given dividend adjustments may change or shift over time as their information sets and net worth evolve over time. Rather than attempting to predict such shifts in shareholder responses, firms will avoid making adjustments that will be very likely to be readjusted in the near future. We observe that while (l)-(4) are derived from the notion of uncertainty avoidance, they appear in conformance with the behavioral observations regarding managerial dividend policy formulation actually made by Linter: (l)-(3) are consistent with Linter’s hypotheses (Hl)-(H3) and (4) is consistent with (H4). Indeed, (l)-(4) can also be suitably adapted to form the basis of a behavioral model of other instruments of financial policy, such as capital structure choice. The notion of uncertainty avoidance relating to dividend policy does not, however, rule out the use of optimization frameworks to study dividend policy formulation. Rather, the behavioral considerations explicated in (l)-(4) impose a certain structure on management decision-making with regard to dividend policy. This structure utilizes the objectives of the management and the specification of their decision spaces and leads us to an analytically tractable decision-theoretic framework for studying the formulation of dividend policy in an inter-temporal model. And the optimal strategies implied by our formulation serve two useful purposes. First, these policies generate precise refutable predictions regarding dividend smoothing, and these refutable predictions are then empirically tested. Secondly, these optimal policies can be usefully interpreted as the basis for the pragmatic proxies actually observed by Linter (1956). We consider an infinite horizon economy, populated by a large number of firms, each endowed with a risky productive technology. The net economic earnings of a typical firm follow a stochastic process specified by
where Yf are the net economic earnings at time t, I,_, is the investment at time f - 1, and 0, is the realization of a random variable representing the stochiastically evolving systematic (non-transitory) capital productivity of the firm. More specifically, {O,} is a stationary Markov process with the support 0 (a subset of the extended reals), with the transition distribution G(B,+i 10,). The distribution has the property that G(. 10’) strictly first order stochastically dominates G(. 10”) if 0’ > 0”. This formalizes the notion of positive but imperfect serial correlation. For convenience we will refer to 8, as the capital productivity of the firm in period t. We will also assume that F is a strictly increasing and a strictly concave function.
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All investment outlays have to be internally generated, and for simplicity, we also assume that the typical firm can carry no surplus cash. These assumptions are made only to allow us to focus on the nature of the optimal dividend policy. The form of the optimal dividend policy that is derived below will be robust to relaxing this assumption as long as there is some constraint on the firm’s ability to borrow and lend at the same rate of interest.4 Then, let Q > 0 be the dividend payout at time r. The stated restrictions imply that, I, = Y, - D,.
(2)
The dividend payouts are the discretion of firm managers. Uncertainty avoidance rules (2) and (3) suggest that management, in setting dividends, focuses on the change in existing payouts, and moreover, dividends are set to maintain some stable proportionality with non-transitory earnings. Then let, at any stage, D-1 and Y-t generically denote the previous period’s dividend level and net economic earnings, and let Y be the current net earnings. The possible dividend payouts at the current stage are then given by the correspondence r : R x R+ + R+, where, l’(Y,D-I)
= {O,D-I
-f-(Y,D-I),D-,,D-I
+f+(Y,D-I)}.
(3)
Heref-,f+ : R x R, ---) R++, are continuous, and bounded mappings of current earnings and previous dividends, and will be interpreted shortly. Thus, at any stage, the managers may choose to eliminate dividend payouts completely (E); cut the previous period’s dividends (C); maintain the previous period’s earnings (M), or increase them (H). Consistent with the foregoing, the dividend innovation (D - D-1) is designed to maintain some relation to a desirable payout ratio (D/Y) by suitably defining dividend innovation functionsf andft. We notice that f ~ and ff can be specialized to yield the deterministic form of the dividend innovation rule used by Linter (1956), viz. D, = D,_l+ @((D/Y)Y, - D,_I ). Note, however, that since f -, f’ are time-independent, every element of I? may not be feasible in the light of the restriction that dividend payouts must be non-negative. Then consider the correspondence F(Y, D_,) = {w E lT(Y, D-,)
1w > 0, w 5 Y}
(4)
r then encapsulates both the non-negativity restriction on D, and the budget constraint (2). To understand the content of these restrictions better, consider how r behaves with respect to some of its arguments. The mapping r is non-decreasing in some argument x if x’ > x” implies that F(x”) C F(x’). Then given the maintained assumptions, r is nondecreasing in Y. And it is non-increasing in D-1 if f+(Y, DLl) L f’(Y,D_l) (and f-(Y, DL,) < f-(Y, D-1)) for D\, > D-1. Associated with each decision is a current (short term) individual cost or reward for managers. The managers receive a short run payofl of u”, uH for maintaining and increasing dividends, respectively. Consistent with rule (4), we assume that the payoffs *his is a very mild condition. The literature on the economics of information shows that firms will generally be constrained from borrowing (or can borrow only at increasingly high rates of interest) if there is asymmetric information in the capital markets, i.e. managers are better informed about the firm’s prospects relative to outsiders.
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from cutting or eliminating dividends depend on the previous period’s dividend. Then let uf, i = C, M, H, denote the payoffs if the dividends have been cut at the current stage and the decision i was taken at the previous stage. Similarly for u?, if the dividends have been eliminated in the current stage. The plausible ordinal ordering of these payoffs is ZAP< UC < u”’ < u”, for all i; and, Ug < u$ < ~4: (“the market punishes for inconsistency”), and a similar ordering holds among the of-‘. For sake of tractability, we do not model the origin of these managerial rewards and costs in a general equilibrium framework. It is plausible to argue, however, that a part of managerial caution against dividend cuts is their negative impact on the firm’s stock price. This negative impact is presumably costly for managers since it either leads to a non-transitory increase in the cost of raising capital for the firm, and/or makes management more vulnerable against hostile take-over bids. Both these factors can affect executive compensation. It is therefore important to note that uncertainty avoidance in dividend policy becomes a serious issue only if there are some imperfections in the capital markets in the sense of violating some subset of Miller and Modigliani’s (1961) perfect market assumptions.’ In light of these payoffs, the budget constraint imposed by rule 2 on the firm sets up an interesting dilemma for managers vis-a-vis dividend payouts. If managers increase dividends today (relative to the previous period), then they reap immediate rewards. However, this reduces investable surplus and increases the risk that next period’s earnings realization would force the firm to cut dividends. We now proceed to characterize the optimal dividend policy in the managerial problem set up above.
3. Optimal dividend
policy
To express the managerial decision problem compactly, let v : R -+ {u”, u”, UC, $, i = E, C, M, H} be a function expressing the manager’s short run payoffs from the current dividend decision. The manager then optimizes an infinite horizon decision problem written as follows: max 4cW,,D,-1)
(5)
s.t., (i) Do = 0, (ii) IO = & where 6 < 1 is a discount factor, and the expectations in (5) are taken over the risky capital productivity. It is important to note that as formulated the model implies that previous dividends affect the current dividend in two ways. First, to the extent that the size of dividend payouts may affect the firm’s investable surplus in imperfect capital markets, past dividends influence current earnings which, of course, impact current dividend payouts. Second, and more directly, uncertainty avoidance rule (3) above 5 Suppose to the contrary that capital markets were fricrionless and there were no informational asymmetries. The Miller and Modigliani (1961) analysis would then imply that the firm’s market value is independent of dividend policy in which case it would be difficult to justify managerial caution against dividend cuts.
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implies that current dividends are pegged to past dividends, and this is reflected in the feasible dividend payout set F. Similarly, past earnings also impact current dividend indirectly through an impact on past investments which influence current earnings. Given the structure imposed on the capital productivity process and managerial preferences, the program (5) can be studied through stationary dynamic programming methods. Then let 19be the current realization of the capital productivity. For notational ease, let s generically denote the state-vector (Y, 8, D-t), with the implied state spaces S = R x R, x 0. Also, we will let s(x) denote the state vector s with x deleted (for e.g. s(O) = (Y,D_t) etc.). Then6 Theorem 1. (i) There exists a boundedfunction V : S + R such that, at any stage, given any ES, the optimal dividend policy satisfies the functional equation V(F(Y
- w, O’), O’,w)dG(B’
10) 1
(ii) Moreover, V is non-decreasing in I: and 19,and non-increasing in D-1 .The second part of Theorem 1 formally verifies the intuition that, at any stage, the manager is better off with a lower previous dividend (D-l), in a dynamic consistency sense, since a smaller D-1 lowers the probability of a current dividend cut relative to the previous period’s payout. A similar argument holds for the welfare improving role of higher Yand 8, in light of the fact that F is an increasing function, and that {e,} are positively correlated. To further characterize the optimal dividend policy, we impose a regularity condition on the value function V(s). This function will be said to satisfy the monotonicity condition if for any (Y,8), and every D’, > D”,, the difference is non-decreasing in Y and 0. Note that, from (I’(.@,),&) - V(s(D-,),D!!,)) Theorem 1 (ii), this difference is negative. Thus, the monotonicity condition implies the plausible restriction that for the firm managers, the relative disadvantage of arriving at any stage with a large previous dividend payout is lessened through higher current earnings and a higher realization of the capital productivity. If the monotonicity condition is operative, then the optimal dividend policy (the solution to Eq. (5)) can be intuitively characterized as follows (recall that ~(6’~)= (Y,, Dr_l)). there exist stationary functions Theorem 2. Under the monotonicity condition, ~+3+, e507@- : R x R+ + 0 such that, at any stage, the solution w: to Eq. (5) may be written as
W:(St) =
H
if 0, > 4’(s(O,))
M C
if 6(s(&)) < 4 < 4’(s(&)) if f$“(s(&)) < 19,< 4-(s(&))
E
if 6 I~‘(s(&))
(7)
The optimal dividend payout policy can be expressed in terms of a specification of threshold levels of the current capital productivity of the firm. These threshold levels are functions of the current period’s earnings and the previous period’s dividend payout. ‘Proofs of the results described
below are available from the authors on request
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Dividends are increased if the current productivity is greater than a pre-specified threshold level, maintained if it falls between this and a lower threshold level and cut and eliminated for successively lower regions of the current productivity realization. In this model, dividends will be increased with positive probability because the manager trades with the discounted costs of tomorrow (u;, u$):’ off high payoffs of today (8) Conversely, dividends will certainly be cut if D-1 does not belong to the feasible set l?.
4. Comparative
statics refutable predictions
With a suitable transformation, however, the optimal policy of Theorem 2 allows convenient comparative statics on the stationary transition probability on dividend changes, conditional on the current productivity, investments and dividends. These comparative statics are of substantial interest since they form the basis of the refutable predictions of the model that will be empirically tested below. To state these comparative statics in a concise fashion, let 1-t (E Y-t - D-r ) generically denote the previous investment at any stage. Then using the fact that the earning function F is strictly increasing in Z-1, we may restate the optimal policy of Theorem 2 as follows: Corollary 1. Under the monotonic@ condition, there exist stationary functions pP : R: + 0 such that at any stage t, the optimal dividend policy is
w* = *
H M C 1E
if if if if
Bt > ,O+(Zt_t,D,_t) P-(ZrPt,DrPt) < 8, I P+(Z,-I,%,) PO(LI,~,~I) < 6 I P-(LI,&I) 6 5 ,@(L,,&,)
’
p’, p”,
(8)
Corollary 1 then restates the optimal dividend policy in terms of an expanded state space that includes information on It-t (or really Y,_t, since D,_t is already incorporated in the earlier defined state). There is a one-to-one link between the functions 4+, 4’, 4- defined in Theorem 2 and the functions p+, p”, ,F defined in Corollary 1. However, the statement in Corollary 1 is more directly related to the comparative statics we are interested in. These comparative statics in turn depend on the following result. Corollary 2. The functions ,@, p”, and p- are non-increasing in IL,. They are nondecreasing in D-1 if(V(s(D_,), DL,) - V(s(D_,), D”,)) is decreasing in (D’, - D”,), for any (Y, a). Intuitively, the functions +!J+,4’, & are non-increasing in current earnings Y i.e. with higher earnings, managers are more likely to increase dividends or less likely to cut them. But the one-to-one relationship between the p and the &functions then implies similar properties for the p-functions. The intuition for the role of D-, follows along similar lines, given the sufficient condition stated in Corollary 2 which is equivalent to requiring that V(Y, 8, D-1) be concave in D-1. ‘The montonicity condition rules out such high degree of uncertainty avoidance that management dividends, rather than increasing them, even for very favorable capital productivity realizations.
maintains
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Corollary
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1 implies that for any given (Y,_t , D,_, ,0,-l), fiob(Q > Dt-1 IZr-I,&I,&I)
= 1 - G(P+(LI,ZLI)
fiob(Q < %I
= G(Pp(Zt-l,Dr-~)Iet-,)
IZ,-I,%I,&I)
Iet-,) .
(9)
Equation (9) represents the transition probabilities of dividend increases and decreases at the next stage, given the current period investment, dividends and productivity, consistent with the managers following the optimal dividend policy (8) in period r. Then Eq. (9) and Corollary 1 yield the following: Proposition
1.
(Effects of Investments
D,_, , and Ii_, > I,-, ,
For any given &t, (i) (ii)
and Dividends)
Prob(Q
> XI
I Z~_lrDr-rrO,-t)
> Pmb(D,
>&I
I Zr-t,Dr-trOr-r)
Prob(&
< &I
I Ii_,,&l,
I l+W,
< &I
I L1,D,pl,fLl).
Also, for any D:_, > %I,
given
0,-r,
and
f&t)
(Ii-,, Dip,)
and
(Z,_,,D,_,)
such
Prob(D, > D:p, I I;-,&,
et-,) I Rot@,
> %I
I It-l,
fiob(D,
et-,) 2 Rob@,
< XI
I Llr Dt-1,
< D:_, I I;-,&,
that
&I, &,) et-,).
(1O)
Ii-, = Z1_-t,
(111
Thus, the probability of dividend increases at the next stage is itself non-decreasing in current investments and non-increasing in current dividends. Using Corollary 2, it is also a straightforward consequence of the positive serial correlation in (0,) that, other things being the same, the likelihood of next period dividend increases (decreases) is itself increasing (decreasing) in the current productivity. Proposition
2.
(Effects of Capital Productivity
Changes)
For any (Y,_t, D,_,), for Oi_, > q_, 6) (ii)
Prob(D, > D,-I
I LI,&I,~‘,_,)
2 Rob@,> RI
I LI,&I,~-,)
Prob(Dr < %I
I Ll,hl,e:_,)
5 Prob(D, <&I
I LI,%I,$,).
cl21
Propositions 1 and 2 are deriving an ordering over the conditional probabilities of time t dividend payouts and their relation to period (t - 1) dividend payouts, based on the period (t - 1) period information set. But the optimal payout policy in Theorem 2 depends only on current and one-period lagged variables. Hence, I,-,, D,_, , and (3-1 are sufficient to completely describe these transition probabilities from the perspective of the period (t - 1) period information set. The next comparative statics result relates the transition probability of dividend changes to variations in the persistence of the capital productivity. To make the argument more precise, suppose that we parameterize the transition distribution G(6’ I 0) as follows
8, = pet-, + V,
(13)
where V, is an i.i.d random variable on the support [-cc, fee], and 0s is drawn from a known distribution and p < 1 for stationarity. Then a larger (smaller) p coefficient may be
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interpreted as a greater (smaller) persistence of the 8, process. Intuitively, one expects that with greater persistence, the threshold productivity levels for dividend increases (i.e. 4’(.) and p’(.)) would be reduced, and that for dividend cuts (or elimination) increased, since the manager would be more certain of a good (bad) state following a good (bad) state. Again, this intuition needs to be sharpened somewhat, as in the following Proposition. Proposition 3.
(Effects of Persistence
in Capital Productivity)
Suppose that (0,) follows the process (13). Suppose that,R < 0 < ,!J’ for every (I,_, , Dt_1). Let Prob’(D, 1It-l, D,_1,0,_~) denote the transition probability for pI, i = 1,2. And, similarly let @, p;, i = 1,2, denote the functions specified in Corollary 1 for the respective transition distributions. Finally, suppose that p1 > ~2, Then for every (Ll,Kl),
P:(LlJLl)
also exist functions
(9
L
P,'(Ll&l)>
@(Z_l, 0,-l),
Prob’(Dt > %I
e(Z,_l ,Dt-l)
and
P;(LI,&I)
Prob’(D,
P;&I,&I),
there
/ LI,&I,&I)
> Prob*(D, > D,_I 1 I,_,, D,_,,B,_l) (ii)
2
such that
if &1 2 8(Zr+l, D),
< D,+I I L,rDt-I,&,)
2 Prob*(D, < D,_] 1 I,_, , D,_!, O,_,) if 8,-l I @(It_,, D). Proposition 3 verifies that, under appropriate scaling of p+ and p-, the threshold productivity values for dividend increases (decreases) are lower (higher) for a firm with greater persistence in systematic capital-shock productivity. In general, this characterization cannot be extended in a straightforward manner to a comparison of the appropriate transition probabilities since we are essentially comparing different probability measures over nested sets. However, Proposition 3 identifies conditions for which this ordering is unambiguous. Under the sufficient condition of this Proposition, the transition probability of dividend changes is unambiguously higher for firms with more persistent (systematic) productivity shocks, since the probability of both dividend increases and decreases is higher. The foregoing comparative statics illustrate relationships between the (transition) probability of dividend changes and factors that affect the transition distribution of earnings in a first order stochastic dominance sense. However, one can also explore the role of the variance of these shocks. It is convenient to do this within the parameterization defined by Eq. (13). Suppose that V, in Eq. (13) are i.i.d. normally distributed with mean zero and variance o’,. There is an intuition that a risk-averse manager would respond to exogeneous increases in a; by increasing dividends less frequently (i.e. by raising the threshold productivity level for a dividend increase), and decreasing dividends more frequently. In fact, the relevant risk aversion condition can be specified by writing the value function from the management decision problem (cf. Theorem 1) as V(s; o$) to make explicit the (implicit) dependence of this function on the variance parameter. Then, the manager is cautious if for any s(D_1 ), and any D-1 > D-1, the difference (V(s(D_l), D-1; 2) - V(s(D_l), D\,; a:)) is non-decreasing in a;. In other words, the relative disadvantage of having paid previously high dividends is higher (or is exacerbated) for more variable productivity shocks.
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Proposition 4. (Effects of the Variance of Capital Productivity) Suppose that the manager is cautious. Let $, /3,:, i = a, b, denote the functions specified in Theorem 2 when v is Normal (0, o:(a)) and Normal (0, d,(b)), respectively. Suppose that a:(a) > at(b). Then /3,‘(Z_i,D_i) > ,@(Z_i,D_i) and &(Z_i,D_i) 2 &(Z_i,D_i) for every (Z_i,D_i). The point is that for a cautious manager, a higher current dividend payout is a riskier gamble (for future welfare) under high variance distributions of the capital productivity process. Thus, Proposition 4 says that conditional on any (Z-1, D-i,&,), the highervariance firm manager will increase (decrease) dividends with a smaller (larger) probability than the low-variance firm manager. There is a strong presumption from Proposition 4 that under managerial cautiousness the conditional likelihood of dividend increases (decreases) is smaller (larger) for the higher variance firms. Finally, note also that our framework can be extended to include the role of non-systematic capital productivity risk. Specifically, suppose that (1) was extended as follows: y, = F(Z,-I 14) + Et
(14)
where {G} are i.i.d. shocks, and E(O,+kcr) = 0 for every t, and every integer k. In perfect capital markets the distribution of transitory shocks should play no role, since the investment/financing decisions would depend only on the realization of the systematic productivity shocks. In imperfect capital markets, however, the distribution of the transitory shocks could also be relevant. In particular, if the ct are i.i.d. normal with zero and variance $, then one can also derive a relation similar to that in Proposition 4, with managerial cautiousness defined in terms of the idiosyncratic risk gf. 5. Empirical
tests
The principal implications of the model in the preceding section are that, at any stage, dividends are increased, maintained or decreased by relating the true (or realized) productivity to the threshold levels as defined in Theorem 2. Since we do not observe the threshold levels described in Theorem 2 but only whether dividends are changed or not, we investigate whether the firms’ propensity to change (increase or decrease) dividends is influenced by the said factors. Consider the following equation for the probability of dividend increases and decreases. p(‘)i,~ =
QO +
al
[ei,r-11
+
W[zi,r-ll
+ a3[Di,t-l]
+
Q4[Pi,t-I] (15)
+
~5[(au),,-,l
+ Q6[(g<)ir-l]
+
Ui,r.
Here P(.)i, is specified to be either the probability of increasing dividends denoted as [P(H), ,] 0; that of decreasing dividends as [P(L), ,] for firm i. With this specification, the theoretical model makes the following predictions: 1. When the dependent variable is the transition probability of dividend increases, then the coefficients al and (~2 should be positive, while ~3 should be negative. And these coefficients should have the opposite sign if the dependent variable is the transition probability of dividend decreases. (Propositions 1 and 2) 2. The coefficient a4 should be positive for both the probability of dividend increases and decreases. (Proposition 3)
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3. When the dependent variable is the probability of dividend increases, then the coefficients as and fl6 should be negative. When the dependent variable is the probability of dividend decreases, then the theoretical model is indeterminate on the sign of the risk-variable coefficient. Only with a presumption of strong managerial caution should these coefficients be positive. (Proposition 4) In terms of the empirical implementation of Eq. (15) an immediate issue is how to define P(.)i,t, and the suitable time frame for t. Since most firms declare quarterly dividends, we can estimate Eq. (15) as a binary choice model on quarterly dividend data. Such an approach, however, is problematic for several reasons. First, since dividends are sticky, changes in technological factors in the current quarter are not likely to result in an immediate adjustment in the following quarter. Second, as noted by Marsh and Merton (1987) dividend changes are usually made in the last fiscal quarter and not as often in other quarters. The sluggishness of dividends and apparent seasonality thus favor the use of annual rather than quarterly dividends. The use of binary model on annual data, on the other hand, could result in a loss of information because many firms change quarterly dividends more than once a year. We thus define P(.)i,, as the sample frequency of quarterly dividend changes in a year, and estimate Eq. (15) using an OLS regression.8 Specifically, the probability of dividend increase in year t is calculated as:
where r(H), I is the number of firm i’s quarterly dividend increases in year t, and ni,r is the number of dividends in year t. Since our tests will distinguish between dividend increases and decreases, we also define the sample frequency of dividend decreases as P(L),,, = where r(L)it is the total number of quarterly dividend decreases in year t. dL)i,tl%r~ Appendix A displays the regression model and precise definition of the regressors. We employ the firms’ stock return as a proxy for Q,, the capital productivity in year t, following Marsh and Merton’s (1986, 1987) argument that in a rational capital market stock price should be positively related to the economic earnings. Similarly, we interpret the residual variance of the firm’s stock return to represent the idiosyncratic variance of the firm’s capital productivity [(a,)J and the market risk of the firm’s stock return to be a proxy for the systematic variance of the firm’s capital productivity, [(a,)J. As for the proxy for the persistence coefficient, we follow the parameterization (13) and estimate the following AR(l) model of earnings-per-share (EPS) of firm i. yi.I =
Pi
+
PI y!.r-
I + Vi.1
(17)
where Y,,, is the EPS of time f (adjusted for stock splits and stock dividends), vt is a stochastic error with mean zero, and p; is a proxy for the persistence coefficient of firm i.9
*We also estimated Eq. (15) using the logit model on an annual basis but obtained virtually identical results to those of the OLS. Details of the logit estimation are available from us. ‘The persistence coefftcient could also be estimated using stock returns, consistent with its use as a proxy for @,_I. We, however, calculate p, using earnings because stock rate of return is not expected to have a significant degree of persistence (autocorrelation) over time. The level of stock return should nevertheless capture a significant portion of the firm’s realized productivity (0,-t) at any given time. As an empirical matter, there is evidence that stock returns are autocorrelated.
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We assume that the three variables [((T~)~,,], [(a,)i,t], and [pi] are intertemporal constants, and hence estimate them using all the available data for firm i.” Since dividend and financing policies may be jointly determined endogenously, we control for the influence of external financing by including the EQUITY variable (percentage change in the number of common shares in year t adjusted for stock split and stock dividends). All time-subscripted explanatory variables are lagged by one period to measure the impact of current period changes in the technological parameters on the likelihood of next stage dividend increases and decreases. The investment (Zi,r-r) and lagged dividend variable (Di,t-t ) are normalized by the standard deviation of the respective variables.” 6. Data and results We use the quarterly dividend data of NYSE firms for the period 1946-87, taken from the CRSP files. In brief, the sample consists of 726 firms for which all variables in Eq. (15) can be estimated during the 1946-87 period.” The total number of sample quarterly dividends is 39,858, out of which dividends were increased in 6,558 cases (16.7%) decreased in 523 (1.3%) cases, and were unchanged for the remainder (82%). Consistent with the specification of Eq. (15) the quarterly dividend data were converted into 8,5 17 firm-year intervals. i3 The results are displayed in Table 1. Panel A contains the estimated parameters of Eq. (IS), while Panels B and C respectively, report the descriptive statistics and the correlation matrix for the variables in the regression.14 In Panel A, two sets of regression results are reported, one for the probability of dividend increases and the other for that of dividend decreases. The numbers in parentheses are standard errors reflecting White’s (1980) heteroskedasticity correction.‘5 ‘sAlthough in principle p, oV, and or can vary over time, there is not enough degree of freedom to estimate these variables as time-varying parameters, “Although no contemporaneous regressors appear in the model, there is no presumption that they are unimportant. For example, to the extent that quarterly dividends in year t are affected by the productivity shocks realized in the same year, the model can be enhanced by including contemporaneous stock returns as an additional explanatory variable. As stock returns in period r should be orthogonal to the variables predetermined in t ~ 1 form the standpoint of market efficiency, the absence of 6’, is not likely to bias the regression coefficients in a predictable way. Similarly, higher order lags can also be introduced in Eq. (15). As the firms’ speed of reaction is not well-known in the literature, the data do not permit us to pinpoint precisely the timing of the dividend changes. “Further details of the sample selection procedures are available from the authors on request. ‘sWe include extra or special dividends to calculate P(.),,, although such a treatment did not have a material impact on our results. The incidence of special dividends is rare, accounting for 1.05% of the sample dividends. 14We do not estimate (15) on a firm-by-firm basis as in Linter (1956) and Fama-Babiak (1968) because of the small number of time-series observations relative to the large number of regressors. (The mean length of the dividend data is 14 years.) Restricting the number of time-series observations could lead to a smaller sample and a survival bias. “In any given year r, there could be contemporaneous cross-sectional correlation in the regression disturbances u,., due to common shocks. In view of the small number of time-series observations (and the large number of cross-sections), we assess the extent of cross-sectional correlation by allowing for the following simple equi-covariance structure: for firms i and j E(u,,,, u~,,_~) = S, if k = 0, E(ui,,, u,,,_k) = 0 if k # 0, for time t. The sample standard errors are larger for some variables and smaller for others, but the overall results are not materially different.
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Table 1 Panel A - Least squares estimates of the relation between the probability and firm-specific factors
of dividend increases and decreases
726 NYSE Firms, 1946-87 P(.)i,r = (~0 + (~1 [oi,t-~] + QT[~~,,-I] Estimated parameters (asymptotic
+
a~[Di,t-~]
+
al[pi]
+a~[~u,,]
Dependent variable[P(.),,,]
R,,-t Lagged capital productivity
(+)
I&-I Lagged investment
(+)
Di,,- I Lagged dividends
(-1
PI Earnings
(+)
a7[EQUITYi,t+,]
+ ui,t
W),,,l Parameter estimate +0.2640 (0.0095) +0.9979 (0.0593) +0.0295 (0.0016) -0.0205 (0.0014) f0.0327 (0.0050) PO.2634 (0.1438) -1.3012 (0.0778) +0.0255 (0.0178) 0.169
persistence (-) risk (-) risk
(+)
EQUITY,,,- I
+
Dividend decrease
PW,,,l
Intercept
0c.i Firm-specific
~[oc,t]
a
Dividend increase Predicted sign
cv,i Systematic
+
standard errors in parentheses)
Percent change in equity base Adjusted R2
Predicted sign
Parameter estimate -0.0109 (0.0038) -0.1447 (0.0243) -0.0110 (0.0009) f0.0084 (0.0008) f0.0073 (0.0021) -0.0409 (0.0606) +0.2130 (0.0369) -0.0043 (0.0055) 0.064
(-) (-) (+) (+) (?) (?) (-)
See Appendix A for variable definitions. Each period t represents one year’s quarterly dividends for firm i. The sample size used to estimate the regression is 8,517 firm-years for 726 firms. a The standard errors reflect White’s (1980) heteroskedasticity correction. Panel B - Descriptive
Mean Std. Dev. Min. Max.
sample statistics
P(H)t.,
P(L),.,
Q,>,-I
Ii,,- I
Q-I
P,
~V,l
g<,r
EQUITY,,,+ I
0.1674 0.1691 0.0000 1.0000
0.0132 0.0649 0.0000 1.0000
0.0138 0.0302 -0.1534 0.3996
1.0087 1.1261 -6.1211 6.0942
1.8566 1.4216 0.0000 11.5833
0.0287 0.1072 PO.9250 3.1616
0.0509 0.0152 0.0014 0.1324
0.0869 0.0273 0.0365 0.3611
0.7227 0.3572 -0.5489 2.7407
Panel C - Sample correlation
P(L),,, Bi,,GI I,+ I R-1 PI g”.l a<,,
EQUITY,,,- I Correlation
-0.1168 0.2307 0.2437 PO.0953 0.1817 -0.0868 PO.2362 0.0090
exceeding
matrix
-0.1117 -0.1674 0.1132 -0.0582 -0.0084 0.0761 0.0017
0.0204 is significant
0.1969 PO.0365 0.0562 0.0395 -0.0186 0.0168
0.2458 0.1941 PO.0649 -0.1886 -0.0133
at the 5% level.
PO.2462 PO.3272 -0.2176 0.0458
0.0461 -0.1368 -0.0310
0.5526 -0.0400
-0.0073
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The results reported in Table 1 appear consistent with the predictions of the model. In brief, the coefficients for lagged stock returns (the proxy for lagged capital productivity), lagged investment, and dividends have the signs predicted above. And these estimates are highly significant in the statistical sense. Furthermore, the coefficients for persistence and idiosyncratic risk also have the signs predicted by the model, and the estimates are, again, highly significant. We now highlight some particularly interesting features of the estimates. The coefficients of the lagged returns indicate that dividend increases (decreases) are more likely to occur following favorable (unfavorable) realizations of the capital productivity. This result is consistent with Proposition 2, and the notion that stocks return are a good indicator of the change in the permanent or non-transitory earnings of the firm (Marsh and Merton, 1987). Observe also that the size of (~1 is smaller when the dependent variable is the transition probability of dividend decreases, compared to the case where the dependent variable is the transition probability of dividend increases. Thus, there appears to be a downward rigidity in dividends in that a given percentage change in investment returns is more likely to increase dividends in the following period than decrease them. Next, the impact of the lagged investment I,_ 1, and lagged dividends D,_l on the transition probability of dividend change is consistent with the predictions of the model. In this connection we recall that lagged investment has not been found to have significant explanatory power in the Linter model. It is also interesting to observe that the coefficient of the persistence (pi) is positive for both P(H) and P(L), as is consistent with Proposition 3. This suggests that managers will both increase and decrease dividends more often with greater persistence in the capital productivity. With regard to capital productivity risk, dividend increases are less likely, other things remaining the same, for firms with greater capital productivity risk. Interestingly, firms with greater capital productivity risk are also more likely to decrease dividends, other things remaining the same. Finally, the idiosyncratic earnings risk appears to have a stronger impact on the likelihood of dividend changes relative to systematic risk. The coefficient of the lagged percentage change in common shares (EQUITY,,,_,) is positive, but only marginally significant. Thus, the evidence is weak for the hypothesis that dividend decisions are significantly associated with external equity financing. This result is in sharp contrast to the evidence of significant influence of the investments through internal funding. In summary, the results indicate a significant influence of current capital productivity, dividend levels and lagged investment on the likelihood of future dividend changes. Moreover, earnings persistence, and firm risk also appear to have a considerable impact on the decision to change dividends. And the directional effects of these factors are consistent with the empirical implications of the behavioral model described in Section 2. Finally, we also performed several checks to examine the robustness of our findings. First, we performed non-parametric tests to assess the influence of outliers, and found that the results were consistent with those reported in Panel A.16 Second, we ‘6Details are available upon request. Briefly, we assign each firm’s P(H)s into five portfolios ranked by the independent variable of Eq. (15), namely, p,. cr,,, and o,,,, and assess whether the size of P(H)s and P(L)s are as predicted.
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experimented with several different specifications of Eq. (15) to explore alternative explanations of our findings. In the original Linter model, the earnings variable appears as a contemporaneous explanatory variable. Thus, it is plausible to assume that the lagged investment variable appears significant in our model only to the extent that the lagged earnings are correlated with contemporaneous earnings. To investigate this possibility, we re-estimated Eq. (15) by including the current period earnings as an additional explanatory variable, and indeed, the coefficient of current period earnings turned out to be significant. The R2 improvement, however, was marginal, an increase of 1.3% from 16.9% to 18.2%. Moreover, the lagged investment variable continued to be highly significant, as did the lagged stock returns, the lagged dividends and the systematic and firm risk variables. We also estimated Eq. (15) by specifying the investments (r) and dividends (D) variables in first difference not in levels. The R2 declined to 13.9%, but all the variables remained highly significant. Next, we also tested for the possible impact of industry effects on the estimates since the functions f- and f + are managerial payoffs could be industry-specific. I7 We have thus re-estimated the model by including industry dummies based on the two-digit SIC classification. The result were, however, virtually unchanged. Along similar lines, we have also included two variables, namely, earnings-price ratio (E/P) and firm size (log of market value of equity), both of which can be viewed as a proxy for future growth opportunity/maturity of the firm. Neither of these variables were statistically significant nor did they alter our results in Table 1.
7. Conclusions This paper argues that selected basic features of the behavioral theory of the firm (Cyert and March, 1993) can be successfully adopted to develop a decision-theoretic model of the firm dividend policy. Using some basic implications of uncertainty avoidance, a decision-theoretic model of dividend payouts was constructed wherein managers trade off short term gains from increasing payouts with associated future increased probabilities of suffering costs of dividend cuts. The optimal dividend policy in this model was characterized in a manner that allows derivation of restrictions on the probability of future dividend changes (increases and decreases, separately) in terms of the current observable firm-specific real and financial variables, and also technological factors such as the persistence of the firms’ non-transitory earnings, and the variance of their systematic and idiosyncratic earnings shocks. The fact that the empirical results show significant influence of the cited factors on the probability of future dividend change allows us to conclude that the ideas underlying uncertainty avoidance can be usefully exploited to put structure on the decision problem relating to derivation of other aspects of financial policy (such as capital structure) as well.
‘71ndeed, the literature also suggests significant payout policy differences by industry (Brittain, 1966). It may also be argued that significant industry differences in investment patterns affect the speed of dividend adjustments.
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Appendix A. Variable Definition ‘(‘)i,t
= aO + aI [@i,t-11 + &2[li,t-1] +a5
‘(‘)i,t = di,t
=
Ii,r =
oi,t =
fl =
gu,i =
g,,i =
EQUITYi,,_i
ia,il + a6
[a<$] +
a7
+ CQ[D+l]
+ cyq[pi]
[EQUITY,,,_, 1+ ui,,
P(H),,,[P(L),,,]: number of quarterly dividend increases [decreases] dividend by the number of quarterly dividends in year I, including zero dividends. capital productivity: average monthly stock return in year r, continuously compounded. investment (from internal funds):(Y, - DI)/u(Y,D,)’ where Y, is earnings in year t, D, is dividends of year t, and o(Yt - Dl) is the sample standard deviation of ( Yl - Dl). dividends of year I deflated by a(D,), the sample standard deviation of dividends. earnings persistence of firm i: the coefficient pi of the AR(l) model Yi,r = Iii + PiYip + %,f> where Y, is the annual earnings-per-share adjusted for stock splits and stock dividends. systematic risk firm i: pipmm,where /?i is the slope coefficient of the market model regression of the firm i’s stock returns, and Ok is the sample standard deviation of the CRSP value-weighted monthly market return (estimated over the full sample period of firm i). idiosyncratic risk of firm i: sample standard deviation of the market model disturbances (estimated over the full sample period of firm i). = percentage change in the number of common shares in year t, adjusted for stock splits and stock dividends.
References Bhattacharyya, S., 1979, Imperfect information, dividend policy and the bird in the hand fallacy, Bell Journal of Economics, 10, 259-270. Black, F., 1966, The dividend puzzle, Journal of Portfolio Management, Winter, pp. 5-8. Brittain, J., 1966, Corporate Dividend Policy, (The Brookings Institute, Washington, DC). Cyert, R. and J. March, 1993, A Behavioral Theory of the Firm, (Prentice-Hall, Englewood Cliffs, NJ). Fama, E. and H. Babiak, 1968, Dividend policy: An empirical analysis, Journal of American Statistical Association, 63, 1132-l 161. Feldstein, M. and J. Green, 1983, Why firms pay dividends, American Economic Review, 73, 312-328. Kumar, P., 1988, Shareholder-manager conflict and the information content of dividends, Review of Financial Studies, 1, 111-136. Laub, M., 1972, Some aspects of the aggregate problem in dividends earnings relationships, Journal of American Statistical Association, 67, 792-805. Linter, J., 1956, Distribution of incomes of corporations among dividends, retained earnings and taxes, American Economic Review, 46, 97-l 13. Linter, J., 1963, The determinants of corporate savings, In: W. Heler, Ed., Savings in the Modem Economy, (University of Minnesota Press, Minneapolis, MN). Marsh, T. and R. Merton, 1986, Dividend variability and the variance bounds tests for the rationality of stock markets, American Economic Review, 76, 483-498.
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Marsh, T. and R. Merton, 1987, Dividend behavior for the aggregate stock market, Journal of Business, 60, I-40. Miller, M., 1986, Behavior rationality in finance: The case of dividends, Journal of Business, 59, S451-S468. Miller, M. and K. Rock, 1985, Dividend policy under asymmetric information, Journal of Finance, 40, 1031-1051. Miller, M. and F. Modigliani, 1961, Dividend policy, growth and valuation of shares, Journal of Business, 34, 411433. Pettit, R., 1972, Dividend announcements, security finance and capital market efficiency, Journal of Finance, 31, 993-1000. White, H., 1980, Heteroskedasticity-consistent covariance matrix and a direct test of heteroskedasticity, Econometrica, 48, 8 17-838.
ELSEVIER
Managerial objectives and firm dividend policy: A behavioral theory and empirical evidence1 Richard Cyert*, Sok-Hyon Kang, Praveen Kumar Graduate School of Industrial Administration, Cameige Mellon University, Schenley Park, Pittsburgh, PA 15213-3890, USA Received 3 August 1994
Abstract We construct a dynamical model of firm dividend policy based on some basic ingredients of the behavioral theory of the firm, in particular, uncertainty avoidance and sequential decision-making by self-seeking managers. We characterize the optimal dividend policy and show that comparative statics on this policy generate restrictions on the relation of the likelihood of future dividend changes with respect to current real and financial variables such as investments, dividends, and technological parameters that govern the evolution of economic earnings of the firm, such as the variance and persistence of the systematic shocks on capital productivity. These relations are then empirically tested on NYSE dividend data. The empirical results are supportive of the predictions from the behavioral model. Specifically, current investment, dividend payouts and the return on capital appear to have significant impact on the likelihood of future dividend changes, as do the variance and persistence of capital productivity shocks. In particular, idiosyncratic fii risk is found to have a negative relation to the likelihood of dividend charges. Finally, these variables are shown to impact the likelihood of dividend increases and decreases asymmetrically, a distinction emphasized by the behavioral model. JEL classification: C30; C35; L20 Keywords:
Dividends
* Corresponding
smoothing;
Uncertainty
avoidance;
Firm risk
author.
‘We thank Franklin Allen, Sugato Bhattacharyya, Douglas Gale, James Poterba, Chester Spatt, and Shyam Sunder for helpful conversations on related issues. We are esspecially grateful to three anonymous referees and the editor Richard Day for suggestions that have significantly improved the paper. All remaining shortcomings are our own. 0167-2681/96/$15.00 0 1996 Elsevier Science B.V. All rights reserved PII SO167-268 1(96)00897-9
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1. Introduction From a theoretical viewpoint, firm dividend policy would be irrelevant (and uninteresting) in a Miller and Modigliani (1961) world of perfect capital markets. From an empirical point of view, however, certain systematic features about the dividend payout behavior of U.S. corporations have intrigued economists, and inspired considerable speculation. For instance, it is a puzzle why firms historically paid a significant fraction of their earnings as dividends even under tax regimes where such payouts imposed a substantial tax liability on shareholders (Black, 1966, Feldstein and Green, 1983). Furthermore, the observed systematic connection between unexpected changes in dividend payouts and their stock prices has focused attention on the possible signaling role of dividends in a world where managers are better informed (relative to outsiders) of their firm’s economic prospects (Bhattacharyya, 1979, Miller and Rock, 1985, Kumar, 1988).2 Over the years, a stylized fact has emerged that firms systematically smooth dividend payouts. In a seminal paper, based on extensive interviews with firm managers, Linter (1956) pointed to deliberate dividend smoothing by firms and suggested four hypotheses regarding the behavioral rules followed by firm managers with respect to dividend policy: (Hl) Managers attempted to attain some long term payout ratio between dividends and economic earnings; (H2) In setting dividends they focus on the change in the existing payouts and not the level, per se; (H3) Dividend changes are likely to follow large unanticipated and non-transitory changes in economic earnings; and, (H4) Managers avoid raising dividends if they stand a good chance of being reversed in the near future. Linter (1956) then attempted to formalize certain salient aspects of these hypotheses through a (reduced form) model in which the dividend process is a function of current period earnings and lagged dividends. The Linter model was found to perform well in explaining aggregate corporate dividend behavior in the inter-war and postwar years (Linter, 1963). However, Linter also tested other firm-specific variables such as gross and net investments, but found that they did not add to the explanatory power of the basic model. Fama and Babiak (1968) tested the Linter model on individual firm data and also found that investment-related variables and lagged earnings did not add to much. Using aggregate, industry- and firm- level data, Brittain (1966) found that individual tax rates improved the explanatory power of the model in few cases, but the improvements were minor. Marsh and Merton (1986, 1987)) also used a dividend process based on the Linter model, but in their version stock price was used as a proxy for the firm’s (unobservable) permanent earnings. Finally, by using firm-level data, Pettit (1972), and Laub (1972) pointed out that at the micro level dividend payouts by firms are “sticky,” i.e. they have a tendency to remain unchanged for non-trivial lengths of time, and charged by discrete amounts. While these empirical patterns regarding dividend payouts have been well documented, the reasons underlying them are still not well understood. As Marsh and Merton (1986) put it, dividend policy is an issue where, “the literature has not arrived at even a local sense of closure.” In this paper we show that the behavioral theory of the firm (Cyert and March, 1993) can provide the missing explanation through an operational model which incorporates ‘Miller (1986) presents an excellent survey of the research related to the dividend controversy.
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salient factors that concern management in its formulation of dividend policy. It is consistent with the management rules actually observed by Linter (1956) and generates refutable predictions about dividend smoothing. In Section 2 we show how Linter’s managerial rules are related to the behavioral theory of the firm, and reformulate the manager’s problem as one of dynamic optimization. The strategy implied by this formulation is described in Section 3 and is consistent with the behavioral theory. This provides a basis for interpreting the pragmatic Linter rules as proxies for sophisticated strategies that have no possibility of implementation in the business environment. The optimal strategy implies dividend smoothing based on the conditional probability of future dividend changes in a way that differs from Linter’s approach in which smoothing arises due to the partial adjustment of dividends toward the desired payout ratio. Our analysis is in accordance with the stylized fact that dividend payouts are discrete (Fama and Babiak, 1968, Laub, 1972, Pettit, 1972). Moreover, the model generates refutable predictions on the relation of the likelihood of future dividends to financial and technological variables. In Section 4, we present an empirical test of our theory. We find that all the factors identified by the behavioral model appear to have a significant influence on dividend smoothing as interpreted in this paper. Moreover, these factors also appear to influence the probabilities of dividend increases and decreases asymmetrically, a distinction emphasized by the behavioral model. We also find that the persistence and riskiness of firms’ earnings play a significant role in dividend policy. Specifically, firms with more persistent earnings tend to make more frequent increases and decreases in dividends, and more risky firms tend to increase dividends less often but decrease them more often. Interestingly, firms idiosyncratic risk turns out to be more important than the systematic risk in terms of influence on dividend smoothing.
2. A behavioral
model of dividend policy
A central feature of the (behavioral) hypothesis of uncertainty avoidance (Cyert and March, 1993) is that organizations, and in particular managers, attempt to avoid the requirement of correctly anticipating events in the distant future by using decision rules that emphasize sequential reaction or adaption to possibly short-run feedback from changes in the firm’s economic environment. More concretely, firms tend to impose standard operating procedures, industry conventions and other types of uncertaintyabsorbing contracts on their environment. This, however, does not imply that firms are able to eliminate uncertainty; only that management frames the decision-making problems in a manner that makes dealing with uncertainty more tractable. Specifically, in relation to the formulation of firm dividend policy, uncertainty avoidance is suggestive of the following basic features:3 ‘The reader is referred to Cyert and March (1993) for a more detailed discussion of the concept of uncertainty avoidance and its relation to other features of business decision-making emphasized by the behavioral theory of the firm.
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1. Firms focus on the dividend adjustments in response to (possibly short-run) changes in the environment, such as changes in earnings prospects. 2. The levels of dividends are not optimized per se on the basis of some long-run optimization model. The levels are usually set according to industry conventions, firm history, etc. 3. Firms maintain simple rules of thumb in relation to acceptable dividend adjustments. For example, the adjustments may be required to be such so as to leave the adjusted dividends in the neighborhood of some pre-set payout ratio. 4. Shareholder/investor attitudes toward given dividend adjustments may change or shift over time as their information sets and net worth evolve over time. Rather than attempting to predict such shifts in shareholder responses, firms will avoid making adjustments that will be very likely to be readjusted in the near future. We observe that while (l)-(4) are derived from the notion of uncertainty avoidance, they appear in conformance with the behavioral observations regarding managerial dividend policy formulation actually made by Linter: (l)-(3) are consistent with Linter’s hypotheses (Hl)-(H3) and (4) is consistent with (H4). Indeed, (l)-(4) can also be suitably adapted to form the basis of a behavioral model of other instruments of financial policy, such as capital structure choice. The notion of uncertainty avoidance relating to dividend policy does not, however, rule out the use of optimization frameworks to study dividend policy formulation. Rather, the behavioral considerations explicated in (l)-(4) impose a certain structure on management decision-making with regard to dividend policy. This structure utilizes the objectives of the management and the specification of their decision spaces and leads us to an analytically tractable decision-theoretic framework for studying the formulation of dividend policy in an inter-temporal model. And the optimal strategies implied by our formulation serve two useful purposes. First, these policies generate precise refutable predictions regarding dividend smoothing, and these refutable predictions are then empirically tested. Secondly, these optimal policies can be usefully interpreted as the basis for the pragmatic proxies actually observed by Linter (1956). We consider an infinite horizon economy, populated by a large number of firms, each endowed with a risky productive technology. The net economic earnings of a typical firm follow a stochastic process specified by
where Yf are the net economic earnings at time t, I,_, is the investment at time f - 1, and 0, is the realization of a random variable representing the stochiastically evolving systematic (non-transitory) capital productivity of the firm. More specifically, {O,} is a stationary Markov process with the support 0 (a subset of the extended reals), with the transition distribution G(B,+i 10,). The distribution has the property that G(. 10’) strictly first order stochastically dominates G(. 10”) if 0’ > 0”. This formalizes the notion of positive but imperfect serial correlation. For convenience we will refer to 8, as the capital productivity of the firm in period t. We will also assume that F is a strictly increasing and a strictly concave function.
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All investment outlays have to be internally generated, and for simplicity, we also assume that the typical firm can carry no surplus cash. These assumptions are made only to allow us to focus on the nature of the optimal dividend policy. The form of the optimal dividend policy that is derived below will be robust to relaxing this assumption as long as there is some constraint on the firm’s ability to borrow and lend at the same rate of interest.4 Then, let Q > 0 be the dividend payout at time r. The stated restrictions imply that, I, = Y, - D,.
(2)
The dividend payouts are the discretion of firm managers. Uncertainty avoidance rules (2) and (3) suggest that management, in setting dividends, focuses on the change in existing payouts, and moreover, dividends are set to maintain some stable proportionality with non-transitory earnings. Then let, at any stage, D-1 and Y-t generically denote the previous period’s dividend level and net economic earnings, and let Y be the current net earnings. The possible dividend payouts at the current stage are then given by the correspondence r : R x R+ + R+, where, l’(Y,D-I)
= {O,D-I
-f-(Y,D-I),D-,,D-I
+f+(Y,D-I)}.
(3)
Heref-,f+ : R x R, ---) R++, are continuous, and bounded mappings of current earnings and previous dividends, and will be interpreted shortly. Thus, at any stage, the managers may choose to eliminate dividend payouts completely (E); cut the previous period’s dividends (C); maintain the previous period’s earnings (M), or increase them (H). Consistent with the foregoing, the dividend innovation (D - D-1) is designed to maintain some relation to a desirable payout ratio (D/Y) by suitably defining dividend innovation functionsf andft. We notice that f ~ and ff can be specialized to yield the deterministic form of the dividend innovation rule used by Linter (1956), viz. D, = D,_l+ @((D/Y)Y, - D,_I ). Note, however, that since f -, f’ are time-independent, every element of I? may not be feasible in the light of the restriction that dividend payouts must be non-negative. Then consider the correspondence F(Y, D_,) = {w E lT(Y, D-,)
1w > 0, w 5 Y}
(4)
r then encapsulates both the non-negativity restriction on D, and the budget constraint (2). To understand the content of these restrictions better, consider how r behaves with respect to some of its arguments. The mapping r is non-decreasing in some argument x if x’ > x” implies that F(x”) C F(x’). Then given the maintained assumptions, r is nondecreasing in Y. And it is non-increasing in D-1 if f+(Y, DLl) L f’(Y,D_l) (and f-(Y, DL,) < f-(Y, D-1)) for D\, > D-1. Associated with each decision is a current (short term) individual cost or reward for managers. The managers receive a short run payofl of u”, uH for maintaining and increasing dividends, respectively. Consistent with rule (4), we assume that the payoffs *his is a very mild condition. The literature on the economics of information shows that firms will generally be constrained from borrowing (or can borrow only at increasingly high rates of interest) if there is asymmetric information in the capital markets, i.e. managers are better informed about the firm’s prospects relative to outsiders.
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from cutting or eliminating dividends depend on the previous period’s dividend. Then let uf, i = C, M, H, denote the payoffs if the dividends have been cut at the current stage and the decision i was taken at the previous stage. Similarly for u?, if the dividends have been eliminated in the current stage. The plausible ordinal ordering of these payoffs is ZAP< UC < u”’ < u”, for all i; and, Ug < u$ < ~4: (“the market punishes for inconsistency”), and a similar ordering holds among the of-‘. For sake of tractability, we do not model the origin of these managerial rewards and costs in a general equilibrium framework. It is plausible to argue, however, that a part of managerial caution against dividend cuts is their negative impact on the firm’s stock price. This negative impact is presumably costly for managers since it either leads to a non-transitory increase in the cost of raising capital for the firm, and/or makes management more vulnerable against hostile take-over bids. Both these factors can affect executive compensation. It is therefore important to note that uncertainty avoidance in dividend policy becomes a serious issue only if there are some imperfections in the capital markets in the sense of violating some subset of Miller and Modigliani’s (1961) perfect market assumptions.’ In light of these payoffs, the budget constraint imposed by rule 2 on the firm sets up an interesting dilemma for managers vis-a-vis dividend payouts. If managers increase dividends today (relative to the previous period), then they reap immediate rewards. However, this reduces investable surplus and increases the risk that next period’s earnings realization would force the firm to cut dividends. We now proceed to characterize the optimal dividend policy in the managerial problem set up above.
3. Optimal dividend
policy
To express the managerial decision problem compactly, let v : R -+ {u”, u”, UC, $, i = E, C, M, H} be a function expressing the manager’s short run payoffs from the current dividend decision. The manager then optimizes an infinite horizon decision problem written as follows: max 4cW,,D,-1)
(5)
s.t., (i) Do = 0, (ii) IO = & where 6 < 1 is a discount factor, and the expectations in (5) are taken over the risky capital productivity. It is important to note that as formulated the model implies that previous dividends affect the current dividend in two ways. First, to the extent that the size of dividend payouts may affect the firm’s investable surplus in imperfect capital markets, past dividends influence current earnings which, of course, impact current dividend payouts. Second, and more directly, uncertainty avoidance rule (3) above 5 Suppose to the contrary that capital markets were fricrionless and there were no informational asymmetries. The Miller and Modigliani (1961) analysis would then imply that the firm’s market value is independent of dividend policy in which case it would be difficult to justify managerial caution against dividend cuts.
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163
implies that current dividends are pegged to past dividends, and this is reflected in the feasible dividend payout set F. Similarly, past earnings also impact current dividend indirectly through an impact on past investments which influence current earnings. Given the structure imposed on the capital productivity process and managerial preferences, the program (5) can be studied through stationary dynamic programming methods. Then let 19be the current realization of the capital productivity. For notational ease, let s generically denote the state-vector (Y, 8, D-t), with the implied state spaces S = R x R, x 0. Also, we will let s(x) denote the state vector s with x deleted (for e.g. s(O) = (Y,D_t) etc.). Then6 Theorem 1. (i) There exists a boundedfunction V : S + R such that, at any stage, given any ES, the optimal dividend policy satisfies the functional equation V(F(Y
- w, O’), O’,w)dG(B’
10) 1
(ii) Moreover, V is non-decreasing in I: and 19,and non-increasing in D-1 .The second part of Theorem 1 formally verifies the intuition that, at any stage, the manager is better off with a lower previous dividend (D-l), in a dynamic consistency sense, since a smaller D-1 lowers the probability of a current dividend cut relative to the previous period’s payout. A similar argument holds for the welfare improving role of higher Yand 8, in light of the fact that F is an increasing function, and that {e,} are positively correlated. To further characterize the optimal dividend policy, we impose a regularity condition on the value function V(s). This function will be said to satisfy the monotonicity condition if for any (Y,8), and every D’, > D”,, the difference is non-decreasing in Y and 0. Note that, from (I’(.@,),&) - V(s(D-,),D!!,)) Theorem 1 (ii), this difference is negative. Thus, the monotonicity condition implies the plausible restriction that for the firm managers, the relative disadvantage of arriving at any stage with a large previous dividend payout is lessened through higher current earnings and a higher realization of the capital productivity. If the monotonicity condition is operative, then the optimal dividend policy (the solution to Eq. (5)) can be intuitively characterized as follows (recall that ~(6’~)= (Y,, Dr_l)). there exist stationary functions Theorem 2. Under the monotonicity condition, ~+3+, e507@- : R x R+ + 0 such that, at any stage, the solution w: to Eq. (5) may be written as
W:(St) =
H
if 0, > 4’(s(O,))
M C
if 6(s(&)) < 4 < 4’(s(&)) if f$“(s(&)) < 19,< 4-(s(&))
E
if 6 I~‘(s(&))
(7)
The optimal dividend payout policy can be expressed in terms of a specification of threshold levels of the current capital productivity of the firm. These threshold levels are functions of the current period’s earnings and the previous period’s dividend payout. ‘Proofs of the results described
below are available from the authors on request
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Dividends are increased if the current productivity is greater than a pre-specified threshold level, maintained if it falls between this and a lower threshold level and cut and eliminated for successively lower regions of the current productivity realization. In this model, dividends will be increased with positive probability because the manager trades with the discounted costs of tomorrow (u;, u$):’ off high payoffs of today (8) Conversely, dividends will certainly be cut if D-1 does not belong to the feasible set l?.
4. Comparative
statics refutable predictions
With a suitable transformation, however, the optimal policy of Theorem 2 allows convenient comparative statics on the stationary transition probability on dividend changes, conditional on the current productivity, investments and dividends. These comparative statics are of substantial interest since they form the basis of the refutable predictions of the model that will be empirically tested below. To state these comparative statics in a concise fashion, let 1-t (E Y-t - D-r ) generically denote the previous investment at any stage. Then using the fact that the earning function F is strictly increasing in Z-1, we may restate the optimal policy of Theorem 2 as follows: Corollary 1. Under the monotonic@ condition, there exist stationary functions pP : R: + 0 such that at any stage t, the optimal dividend policy is
w* = *
H M C 1E
if if if if
Bt > ,O+(Zt_t,D,_t) P-(ZrPt,DrPt) < 8, I P+(Z,-I,%,) PO(LI,~,~I) < 6 I P-(LI,&I) 6 5 ,@(L,,&,)
’
p’, p”,
(8)
Corollary 1 then restates the optimal dividend policy in terms of an expanded state space that includes information on It-t (or really Y,_t, since D,_t is already incorporated in the earlier defined state). There is a one-to-one link between the functions 4+, 4’, 4- defined in Theorem 2 and the functions p+, p”, ,F defined in Corollary 1. However, the statement in Corollary 1 is more directly related to the comparative statics we are interested in. These comparative statics in turn depend on the following result. Corollary 2. The functions ,@, p”, and p- are non-increasing in IL,. They are nondecreasing in D-1 if(V(s(D_,), DL,) - V(s(D_,), D”,)) is decreasing in (D’, - D”,), for any (Y, a). Intuitively, the functions +!J+,4’, & are non-increasing in current earnings Y i.e. with higher earnings, managers are more likely to increase dividends or less likely to cut them. But the one-to-one relationship between the p and the &functions then implies similar properties for the p-functions. The intuition for the role of D-, follows along similar lines, given the sufficient condition stated in Corollary 2 which is equivalent to requiring that V(Y, 8, D-1) be concave in D-1. ‘The montonicity condition rules out such high degree of uncertainty avoidance that management dividends, rather than increasing them, even for very favorable capital productivity realizations.
maintains
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1 implies that for any given (Y,_t , D,_, ,0,-l), fiob(Q > Dt-1 IZr-I,&I,&I)
= 1 - G(P+(LI,ZLI)
fiob(Q < %I
= G(Pp(Zt-l,Dr-~)Iet-,)
IZ,-I,%I,&I)
Iet-,) .
(9)
Equation (9) represents the transition probabilities of dividend increases and decreases at the next stage, given the current period investment, dividends and productivity, consistent with the managers following the optimal dividend policy (8) in period r. Then Eq. (9) and Corollary 1 yield the following: Proposition
1.
(Effects of Investments
D,_, , and Ii_, > I,-, ,
For any given &t, (i) (ii)
and Dividends)
Prob(Q
> XI
I Z~_lrDr-rrO,-t)
> Pmb(D,
>&I
I Zr-t,Dr-trOr-r)
Prob(&
< &I
I Ii_,,&l,
I l+W,
< &I
I L1,D,pl,fLl).
Also, for any D:_, > %I,
given
0,-r,
and
f&t)
(Ii-,, Dip,)
and
(Z,_,,D,_,)
such
Prob(D, > D:p, I I;-,&,
et-,) I Rot@,
> %I
I It-l,
fiob(D,
et-,) 2 Rob@,
< XI
I Llr Dt-1,
< D:_, I I;-,&,
that
&I, &,) et-,).
(1O)
Ii-, = Z1_-t,
(111
Thus, the probability of dividend increases at the next stage is itself non-decreasing in current investments and non-increasing in current dividends. Using Corollary 2, it is also a straightforward consequence of the positive serial correlation in (0,) that, other things being the same, the likelihood of next period dividend increases (decreases) is itself increasing (decreasing) in the current productivity. Proposition
2.
(Effects of Capital Productivity
Changes)
For any (Y,_t, D,_,), for Oi_, > q_, 6) (ii)
Prob(D, > D,-I
I LI,&I,~‘,_,)
2 Rob@,> RI
I LI,&I,~-,)
Prob(Dr < %I
I Ll,hl,e:_,)
5 Prob(D, <&I
I LI,%I,$,).
cl21
Propositions 1 and 2 are deriving an ordering over the conditional probabilities of time t dividend payouts and their relation to period (t - 1) dividend payouts, based on the period (t - 1) period information set. But the optimal payout policy in Theorem 2 depends only on current and one-period lagged variables. Hence, I,-,, D,_, , and (3-1 are sufficient to completely describe these transition probabilities from the perspective of the period (t - 1) period information set. The next comparative statics result relates the transition probability of dividend changes to variations in the persistence of the capital productivity. To make the argument more precise, suppose that we parameterize the transition distribution G(6’ I 0) as follows
8, = pet-, + V,
(13)
where V, is an i.i.d random variable on the support [-cc, fee], and 0s is drawn from a known distribution and p < 1 for stationarity. Then a larger (smaller) p coefficient may be
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interpreted as a greater (smaller) persistence of the 8, process. Intuitively, one expects that with greater persistence, the threshold productivity levels for dividend increases (i.e. 4’(.) and p’(.)) would be reduced, and that for dividend cuts (or elimination) increased, since the manager would be more certain of a good (bad) state following a good (bad) state. Again, this intuition needs to be sharpened somewhat, as in the following Proposition. Proposition 3.
(Effects of Persistence
in Capital Productivity)
Suppose that (0,) follows the process (13). Suppose that,R < 0 < ,!J’ for every (I,_, , Dt_1). Let Prob’(D, 1It-l, D,_1,0,_~) denote the transition probability for pI, i = 1,2. And, similarly let @, p;, i = 1,2, denote the functions specified in Corollary 1 for the respective transition distributions. Finally, suppose that p1 > ~2, Then for every (Ll,Kl),
P:(LlJLl)
also exist functions
(9
L
P,'(Ll&l)>
@(Z_l, 0,-l),
Prob’(Dt > %I
e(Z,_l ,Dt-l)
and
P;(LI,&I)
Prob’(D,
P;&I,&I),
there
/ LI,&I,&I)
> Prob*(D, > D,_I 1 I,_,, D,_,,B,_l) (ii)
2
such that
if &1 2 8(Zr+l, D),
< D,+I I L,rDt-I,&,)
2 Prob*(D, < D,_] 1 I,_, , D,_!, O,_,) if 8,-l I @(It_,, D). Proposition 3 verifies that, under appropriate scaling of p+ and p-, the threshold productivity values for dividend increases (decreases) are lower (higher) for a firm with greater persistence in systematic capital-shock productivity. In general, this characterization cannot be extended in a straightforward manner to a comparison of the appropriate transition probabilities since we are essentially comparing different probability measures over nested sets. However, Proposition 3 identifies conditions for which this ordering is unambiguous. Under the sufficient condition of this Proposition, the transition probability of dividend changes is unambiguously higher for firms with more persistent (systematic) productivity shocks, since the probability of both dividend increases and decreases is higher. The foregoing comparative statics illustrate relationships between the (transition) probability of dividend changes and factors that affect the transition distribution of earnings in a first order stochastic dominance sense. However, one can also explore the role of the variance of these shocks. It is convenient to do this within the parameterization defined by Eq. (13). Suppose that V, in Eq. (13) are i.i.d. normally distributed with mean zero and variance o’,. There is an intuition that a risk-averse manager would respond to exogeneous increases in a; by increasing dividends less frequently (i.e. by raising the threshold productivity level for a dividend increase), and decreasing dividends more frequently. In fact, the relevant risk aversion condition can be specified by writing the value function from the management decision problem (cf. Theorem 1) as V(s; o$) to make explicit the (implicit) dependence of this function on the variance parameter. Then, the manager is cautious if for any s(D_1 ), and any D-1 > D-1, the difference (V(s(D_l), D-1; 2) - V(s(D_l), D\,; a:)) is non-decreasing in a;. In other words, the relative disadvantage of having paid previously high dividends is higher (or is exacerbated) for more variable productivity shocks.
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167
Proposition 4. (Effects of the Variance of Capital Productivity) Suppose that the manager is cautious. Let $, /3,:, i = a, b, denote the functions specified in Theorem 2 when v is Normal (0, o:(a)) and Normal (0, d,(b)), respectively. Suppose that a:(a) > at(b). Then /3,‘(Z_i,D_i) > ,@(Z_i,D_i) and &(Z_i,D_i) 2 &(Z_i,D_i) for every (Z_i,D_i). The point is that for a cautious manager, a higher current dividend payout is a riskier gamble (for future welfare) under high variance distributions of the capital productivity process. Thus, Proposition 4 says that conditional on any (Z-1, D-i,&,), the highervariance firm manager will increase (decrease) dividends with a smaller (larger) probability than the low-variance firm manager. There is a strong presumption from Proposition 4 that under managerial cautiousness the conditional likelihood of dividend increases (decreases) is smaller (larger) for the higher variance firms. Finally, note also that our framework can be extended to include the role of non-systematic capital productivity risk. Specifically, suppose that (1) was extended as follows: y, = F(Z,-I 14) + Et
(14)
where {G} are i.i.d. shocks, and E(O,+kcr) = 0 for every t, and every integer k. In perfect capital markets the distribution of transitory shocks should play no role, since the investment/financing decisions would depend only on the realization of the systematic productivity shocks. In imperfect capital markets, however, the distribution of the transitory shocks could also be relevant. In particular, if the ct are i.i.d. normal with zero and variance $, then one can also derive a relation similar to that in Proposition 4, with managerial cautiousness defined in terms of the idiosyncratic risk gf. 5. Empirical
tests
The principal implications of the model in the preceding section are that, at any stage, dividends are increased, maintained or decreased by relating the true (or realized) productivity to the threshold levels as defined in Theorem 2. Since we do not observe the threshold levels described in Theorem 2 but only whether dividends are changed or not, we investigate whether the firms’ propensity to change (increase or decrease) dividends is influenced by the said factors. Consider the following equation for the probability of dividend increases and decreases. p(‘)i,~ =
QO +
al
[ei,r-11
+
W[zi,r-ll
+ a3[Di,t-l]
+
Q4[Pi,t-I] (15)
+
~5[(au),,-,l
+ Q6[(g<)ir-l]
+
Ui,r.
Here P(.)i, is specified to be either the probability of increasing dividends denoted as [P(H), ,] 0; that of decreasing dividends as [P(L), ,] for firm i. With this specification, the theoretical model makes the following predictions: 1. When the dependent variable is the transition probability of dividend increases, then the coefficients al and (~2 should be positive, while ~3 should be negative. And these coefficients should have the opposite sign if the dependent variable is the transition probability of dividend decreases. (Propositions 1 and 2) 2. The coefficient a4 should be positive for both the probability of dividend increases and decreases. (Proposition 3)
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3. When the dependent variable is the probability of dividend increases, then the coefficients as and fl6 should be negative. When the dependent variable is the probability of dividend decreases, then the theoretical model is indeterminate on the sign of the risk-variable coefficient. Only with a presumption of strong managerial caution should these coefficients be positive. (Proposition 4) In terms of the empirical implementation of Eq. (15) an immediate issue is how to define P(.)i,t, and the suitable time frame for t. Since most firms declare quarterly dividends, we can estimate Eq. (15) as a binary choice model on quarterly dividend data. Such an approach, however, is problematic for several reasons. First, since dividends are sticky, changes in technological factors in the current quarter are not likely to result in an immediate adjustment in the following quarter. Second, as noted by Marsh and Merton (1987) dividend changes are usually made in the last fiscal quarter and not as often in other quarters. The sluggishness of dividends and apparent seasonality thus favor the use of annual rather than quarterly dividends. The use of binary model on annual data, on the other hand, could result in a loss of information because many firms change quarterly dividends more than once a year. We thus define P(.)i,, as the sample frequency of quarterly dividend changes in a year, and estimate Eq. (15) using an OLS regression.8 Specifically, the probability of dividend increase in year t is calculated as:
where r(H), I is the number of firm i’s quarterly dividend increases in year t, and ni,r is the number of dividends in year t. Since our tests will distinguish between dividend increases and decreases, we also define the sample frequency of dividend decreases as P(L),,, = where r(L)it is the total number of quarterly dividend decreases in year t. dL)i,tl%r~ Appendix A displays the regression model and precise definition of the regressors. We employ the firms’ stock return as a proxy for Q,, the capital productivity in year t, following Marsh and Merton’s (1986, 1987) argument that in a rational capital market stock price should be positively related to the economic earnings. Similarly, we interpret the residual variance of the firm’s stock return to represent the idiosyncratic variance of the firm’s capital productivity [(a,)J and the market risk of the firm’s stock return to be a proxy for the systematic variance of the firm’s capital productivity, [(a,)J. As for the proxy for the persistence coefficient, we follow the parameterization (13) and estimate the following AR(l) model of earnings-per-share (EPS) of firm i. yi.I =
Pi
+
PI y!.r-
I + Vi.1
(17)
where Y,,, is the EPS of time f (adjusted for stock splits and stock dividends), vt is a stochastic error with mean zero, and p; is a proxy for the persistence coefficient of firm i.9
*We also estimated Eq. (15) using the logit model on an annual basis but obtained virtually identical results to those of the OLS. Details of the logit estimation are available from us. ‘The persistence coefftcient could also be estimated using stock returns, consistent with its use as a proxy for @,_I. We, however, calculate p, using earnings because stock rate of return is not expected to have a significant degree of persistence (autocorrelation) over time. The level of stock return should nevertheless capture a significant portion of the firm’s realized productivity (0,-t) at any given time. As an empirical matter, there is evidence that stock returns are autocorrelated.
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We assume that the three variables [((T~)~,,], [(a,)i,t], and [pi] are intertemporal constants, and hence estimate them using all the available data for firm i.” Since dividend and financing policies may be jointly determined endogenously, we control for the influence of external financing by including the EQUITY variable (percentage change in the number of common shares in year t adjusted for stock split and stock dividends). All time-subscripted explanatory variables are lagged by one period to measure the impact of current period changes in the technological parameters on the likelihood of next stage dividend increases and decreases. The investment (Zi,r-r) and lagged dividend variable (Di,t-t ) are normalized by the standard deviation of the respective variables.” 6. Data and results We use the quarterly dividend data of NYSE firms for the period 1946-87, taken from the CRSP files. In brief, the sample consists of 726 firms for which all variables in Eq. (15) can be estimated during the 1946-87 period.” The total number of sample quarterly dividends is 39,858, out of which dividends were increased in 6,558 cases (16.7%) decreased in 523 (1.3%) cases, and were unchanged for the remainder (82%). Consistent with the specification of Eq. (15) the quarterly dividend data were converted into 8,5 17 firm-year intervals. i3 The results are displayed in Table 1. Panel A contains the estimated parameters of Eq. (IS), while Panels B and C respectively, report the descriptive statistics and the correlation matrix for the variables in the regression.14 In Panel A, two sets of regression results are reported, one for the probability of dividend increases and the other for that of dividend decreases. The numbers in parentheses are standard errors reflecting White’s (1980) heteroskedasticity correction.‘5 ‘sAlthough in principle p, oV, and or can vary over time, there is not enough degree of freedom to estimate these variables as time-varying parameters, “Although no contemporaneous regressors appear in the model, there is no presumption that they are unimportant. For example, to the extent that quarterly dividends in year t are affected by the productivity shocks realized in the same year, the model can be enhanced by including contemporaneous stock returns as an additional explanatory variable. As stock returns in period r should be orthogonal to the variables predetermined in t ~ 1 form the standpoint of market efficiency, the absence of 6’, is not likely to bias the regression coefficients in a predictable way. Similarly, higher order lags can also be introduced in Eq. (15). As the firms’ speed of reaction is not well-known in the literature, the data do not permit us to pinpoint precisely the timing of the dividend changes. “Further details of the sample selection procedures are available from the authors on request. ‘sWe include extra or special dividends to calculate P(.),,, although such a treatment did not have a material impact on our results. The incidence of special dividends is rare, accounting for 1.05% of the sample dividends. 14We do not estimate (15) on a firm-by-firm basis as in Linter (1956) and Fama-Babiak (1968) because of the small number of time-series observations relative to the large number of regressors. (The mean length of the dividend data is 14 years.) Restricting the number of time-series observations could lead to a smaller sample and a survival bias. “In any given year r, there could be contemporaneous cross-sectional correlation in the regression disturbances u,., due to common shocks. In view of the small number of time-series observations (and the large number of cross-sections), we assess the extent of cross-sectional correlation by allowing for the following simple equi-covariance structure: for firms i and j E(u,,,, u~,,_~) = S, if k = 0, E(ui,,, u,,,_k) = 0 if k # 0, for time t. The sample standard errors are larger for some variables and smaller for others, but the overall results are not materially different.
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Table 1 Panel A - Least squares estimates of the relation between the probability and firm-specific factors
of dividend increases and decreases
726 NYSE Firms, 1946-87 P(.)i,r = (~0 + (~1 [oi,t-~] + QT[~~,,-I] Estimated parameters (asymptotic
+
a~[Di,t-~]
+
al[pi]
+a~[~u,,]
Dependent variable[P(.),,,]
R,,-t Lagged capital productivity
(+)
I&-I Lagged investment
(+)
Di,,- I Lagged dividends
(-1
PI Earnings
(+)
a7[EQUITYi,t+,]
+ ui,t
W),,,l Parameter estimate +0.2640 (0.0095) +0.9979 (0.0593) +0.0295 (0.0016) -0.0205 (0.0014) f0.0327 (0.0050) PO.2634 (0.1438) -1.3012 (0.0778) +0.0255 (0.0178) 0.169
persistence (-) risk (-) risk
(+)
EQUITY,,,- I
+
Dividend decrease
PW,,,l
Intercept
0c.i Firm-specific
~[oc,t]
a
Dividend increase Predicted sign
cv,i Systematic
+
standard errors in parentheses)
Percent change in equity base Adjusted R2
Predicted sign
Parameter estimate -0.0109 (0.0038) -0.1447 (0.0243) -0.0110 (0.0009) f0.0084 (0.0008) f0.0073 (0.0021) -0.0409 (0.0606) +0.2130 (0.0369) -0.0043 (0.0055) 0.064
(-) (-) (+) (+) (?) (?) (-)
See Appendix A for variable definitions. Each period t represents one year’s quarterly dividends for firm i. The sample size used to estimate the regression is 8,517 firm-years for 726 firms. a The standard errors reflect White’s (1980) heteroskedasticity correction. Panel B - Descriptive
Mean Std. Dev. Min. Max.
sample statistics
P(H)t.,
P(L),.,
Q,>,-I
Ii,,- I
Q-I
P,
~V,l
g<,r
EQUITY,,,+ I
0.1674 0.1691 0.0000 1.0000
0.0132 0.0649 0.0000 1.0000
0.0138 0.0302 -0.1534 0.3996
1.0087 1.1261 -6.1211 6.0942
1.8566 1.4216 0.0000 11.5833
0.0287 0.1072 PO.9250 3.1616
0.0509 0.0152 0.0014 0.1324
0.0869 0.0273 0.0365 0.3611
0.7227 0.3572 -0.5489 2.7407
Panel C - Sample correlation
P(L),,, Bi,,GI I,+ I R-1 PI g”.l a<,,
EQUITY,,,- I Correlation
-0.1168 0.2307 0.2437 PO.0953 0.1817 -0.0868 PO.2362 0.0090
exceeding
matrix
-0.1117 -0.1674 0.1132 -0.0582 -0.0084 0.0761 0.0017
0.0204 is significant
0.1969 PO.0365 0.0562 0.0395 -0.0186 0.0168
0.2458 0.1941 PO.0649 -0.1886 -0.0133
at the 5% level.
PO.2462 PO.3272 -0.2176 0.0458
0.0461 -0.1368 -0.0310
0.5526 -0.0400
-0.0073
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The results reported in Table 1 appear consistent with the predictions of the model. In brief, the coefficients for lagged stock returns (the proxy for lagged capital productivity), lagged investment, and dividends have the signs predicted above. And these estimates are highly significant in the statistical sense. Furthermore, the coefficients for persistence and idiosyncratic risk also have the signs predicted by the model, and the estimates are, again, highly significant. We now highlight some particularly interesting features of the estimates. The coefficients of the lagged returns indicate that dividend increases (decreases) are more likely to occur following favorable (unfavorable) realizations of the capital productivity. This result is consistent with Proposition 2, and the notion that stocks return are a good indicator of the change in the permanent or non-transitory earnings of the firm (Marsh and Merton, 1987). Observe also that the size of (~1 is smaller when the dependent variable is the transition probability of dividend decreases, compared to the case where the dependent variable is the transition probability of dividend increases. Thus, there appears to be a downward rigidity in dividends in that a given percentage change in investment returns is more likely to increase dividends in the following period than decrease them. Next, the impact of the lagged investment I,_ 1, and lagged dividends D,_l on the transition probability of dividend change is consistent with the predictions of the model. In this connection we recall that lagged investment has not been found to have significant explanatory power in the Linter model. It is also interesting to observe that the coefficient of the persistence (pi) is positive for both P(H) and P(L), as is consistent with Proposition 3. This suggests that managers will both increase and decrease dividends more often with greater persistence in the capital productivity. With regard to capital productivity risk, dividend increases are less likely, other things remaining the same, for firms with greater capital productivity risk. Interestingly, firms with greater capital productivity risk are also more likely to decrease dividends, other things remaining the same. Finally, the idiosyncratic earnings risk appears to have a stronger impact on the likelihood of dividend changes relative to systematic risk. The coefficient of the lagged percentage change in common shares (EQUITY,,,_,) is positive, but only marginally significant. Thus, the evidence is weak for the hypothesis that dividend decisions are significantly associated with external equity financing. This result is in sharp contrast to the evidence of significant influence of the investments through internal funding. In summary, the results indicate a significant influence of current capital productivity, dividend levels and lagged investment on the likelihood of future dividend changes. Moreover, earnings persistence, and firm risk also appear to have a considerable impact on the decision to change dividends. And the directional effects of these factors are consistent with the empirical implications of the behavioral model described in Section 2. Finally, we also performed several checks to examine the robustness of our findings. First, we performed non-parametric tests to assess the influence of outliers, and found that the results were consistent with those reported in Panel A.16 Second, we ‘6Details are available upon request. Briefly, we assign each firm’s P(H)s into five portfolios ranked by the independent variable of Eq. (15), namely, p,. cr,,, and o,,,, and assess whether the size of P(H)s and P(L)s are as predicted.
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experimented with several different specifications of Eq. (15) to explore alternative explanations of our findings. In the original Linter model, the earnings variable appears as a contemporaneous explanatory variable. Thus, it is plausible to assume that the lagged investment variable appears significant in our model only to the extent that the lagged earnings are correlated with contemporaneous earnings. To investigate this possibility, we re-estimated Eq. (15) by including the current period earnings as an additional explanatory variable, and indeed, the coefficient of current period earnings turned out to be significant. The R2 improvement, however, was marginal, an increase of 1.3% from 16.9% to 18.2%. Moreover, the lagged investment variable continued to be highly significant, as did the lagged stock returns, the lagged dividends and the systematic and firm risk variables. We also estimated Eq. (15) by specifying the investments (r) and dividends (D) variables in first difference not in levels. The R2 declined to 13.9%, but all the variables remained highly significant. Next, we also tested for the possible impact of industry effects on the estimates since the functions f- and f + are managerial payoffs could be industry-specific. I7 We have thus re-estimated the model by including industry dummies based on the two-digit SIC classification. The result were, however, virtually unchanged. Along similar lines, we have also included two variables, namely, earnings-price ratio (E/P) and firm size (log of market value of equity), both of which can be viewed as a proxy for future growth opportunity/maturity of the firm. Neither of these variables were statistically significant nor did they alter our results in Table 1.
7. Conclusions This paper argues that selected basic features of the behavioral theory of the firm (Cyert and March, 1993) can be successfully adopted to develop a decision-theoretic model of the firm dividend policy. Using some basic implications of uncertainty avoidance, a decision-theoretic model of dividend payouts was constructed wherein managers trade off short term gains from increasing payouts with associated future increased probabilities of suffering costs of dividend cuts. The optimal dividend policy in this model was characterized in a manner that allows derivation of restrictions on the probability of future dividend changes (increases and decreases, separately) in terms of the current observable firm-specific real and financial variables, and also technological factors such as the persistence of the firms’ non-transitory earnings, and the variance of their systematic and idiosyncratic earnings shocks. The fact that the empirical results show significant influence of the cited factors on the probability of future dividend change allows us to conclude that the ideas underlying uncertainty avoidance can be usefully exploited to put structure on the decision problem relating to derivation of other aspects of financial policy (such as capital structure) as well.
‘71ndeed, the literature also suggests significant payout policy differences by industry (Brittain, 1966). It may also be argued that significant industry differences in investment patterns affect the speed of dividend adjustments.
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Appendix A. Variable Definition ‘(‘)i,t
= aO + aI [@i,t-11 + &2[li,t-1] +a5
‘(‘)i,t = di,t
=
Ii,r =
oi,t =
fl =
gu,i =
g,,i =
EQUITYi,,_i
ia,il + a6
[a<$] +
a7
+ CQ[D+l]
+ cyq[pi]
[EQUITY,,,_, 1+ ui,,
P(H),,,[P(L),,,]: number of quarterly dividend increases [decreases] dividend by the number of quarterly dividends in year I, including zero dividends. capital productivity: average monthly stock return in year r, continuously compounded. investment (from internal funds):(Y, - DI)/u(Y,D,)’ where Y, is earnings in year t, D, is dividends of year t, and o(Yt - Dl) is the sample standard deviation of ( Yl - Dl). dividends of year I deflated by a(D,), the sample standard deviation of dividends. earnings persistence of firm i: the coefficient pi of the AR(l) model Yi,r = Iii + PiYip + %,f> where Y, is the annual earnings-per-share adjusted for stock splits and stock dividends. systematic risk firm i: pipmm,where /?i is the slope coefficient of the market model regression of the firm i’s stock returns, and Ok is the sample standard deviation of the CRSP value-weighted monthly market return (estimated over the full sample period of firm i). idiosyncratic risk of firm i: sample standard deviation of the market model disturbances (estimated over the full sample period of firm i). = percentage change in the number of common shares in year t, adjusted for stock splits and stock dividends.
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