Ambiguity, Risk, and Dividend Payout Policy∗

Jay Dahya† Richard Herron‡ Yehuda Izhakian§

July 18, 2017

Abstract

We study the effect of ambiguity—Knightian uncertainty—on dividend payout policy.

We find that firm-level risk decreases and delays dividends, while firm-level ambiguity

increases and accelerates dividends. These findings can be explained by the attrac-

tiveness of investment opportunities, which potentially increases in risk and leaves less

capital for dividend payout. In contrast, since ambiguity leads investors to overweight

the likelihoods of bad outcomes and underweight the likelihoods of good outcomes, the

attractiveness of investment opportunities decreases in ambiguity. Consistent with this

positive effect of ambiguity on dividends, we find that dividend initiation announce-

ment returns increase in ambiguity.

Keywords: Ambiguity, Knightian Uncertainty, Dividends.

JEL Classification Numbers: D81, D83, G35.

∗We appreciate helpful comments and discussions by Yakov Amihud, Ryan Davies, MichaelGoldstein, Shingo Goto, Jasmina Hasanhodzic, Laurie Krigman, Andrew Lo, Gordon Phillips,Jerome Taillard, and Jaime Zender. We thank seminar and conference participants at Babson Col-lege, the University of Rhode Island, the 7th International Conference of the Financial Engineeringand Banking Society, and the 2017 Financial Management Association European Conference.†Baruch College, City University of New York, One Bernard Baruch Way, New York, NY 10010,

United States. Office 646-312-3511. Fax 646-312-3451. Jay.Dahya@baruch.cuny.edu.‡Babson College, 326 Tomasso Hall, Babson Park, MA 02457-0310. Office 781-239-3835. Fax

781-239-5004. rherron1@babson.edu.§Stern School of Business, New York University; and Baruch College, City University of New

York, One Bernard Baruch Way, New York, NY 10010, United States. Office 646-312-3465. Fax646-312-3451. yud@stern.nyu.edu.

I Introduction

Dividend payout policy decisions are among the most important in the life of the firm and de-

pend heavily on the firm’s future prospects. These prospects are largely driven by investment

opportunities, which are subject to two dimensions of uncertainty: risk and ambiguity. Risk

is the uncertainty of outcomes, while ambiguity—Knightian uncertainty—is the uncertainty

of probabilities.1 Risk and ambiguity bear different implications for evaluating investment

opportunities and for dividend payout policy.

Consider a manager who must choose between retaining earnings to fund an investment

opportunity or distributing earnings as dividends (or share repurchases). Suppose that the

probabilities associated with the outcomes of an investment opportunity are well understood,

perhaps based on experience or previous investments. When the expected return compen-

sates appropriately for risk, the decision to retain earnings for investment is straightforward

and delays dividend distribution. In contrast, suppose that the probabilities associated with

the outcomes of the investment opportunity are uncertain. Such uncertainty makes retention

to invest less attractive, and thus makes the manager less likely to delay dividend distribu-

tion. Previous studies focus mainly on the effect of firm-level risk on dividend payout and

find a negative effect (e.g., Chay and Suh, 2009; Hoberg and Prabhala, 2008; Hoberg et al.,

2014). To best of our knowledge, we are the first to focus on the implication of firm-level

ambiguity for dividend payout.

Firms may also distribute earnings as share repurchases. The relation between repur-

chases and uncertainty can be explained similarly. Firms with profitable, appropriately

compensating, risky investment opportunities delay and decrease repurchases, while firms

with ambiguous investment opportunities hasten and increase repurchases. We focus on

1Risk is a condition where outcomes are a priori unknown, but the odds of all possible outcomes areperfectly known. Ambiguity is a condition where not only are outcomes a priori unknown, but also theodds of outcomes are unknown or not uniquely assigned. Knight (1921) defines the concept of (Knightian)uncertainty as distinct from risk and as conditions under which the set of events that may occur is a prioriunknown, and the odds of these events are either not unique or unknown.

1

dividend payouts rather than repurchases for the following reasons. First, as opposed to re-

purchases, regular dividends are not driven by extra cash, temporary earnings, or (perceived)

equity mispricing. Second, dividends are less confounded by capital structure decisions, ei-

ther in isolation or in response to employee stock options. Third, dividend level and timing

are clearly observable, so market responses can be attributed exclusively to dividend initi-

ations. Regardless, our empirical findings are qualitatively similar with either dividends or

repurchases.

We derive our hypotheses from a two-period stylized model of the optimal decision be-

tween investment and dividend payout in the presence of risk and ambiguity. The intuition

of our model is that higher risk is accompanied by higher expected returns, which may ap-

propriately compensate for that risk. In turn, this encourages retention and investment, and

delays the return of capital. In contrast, since higher ambiguity leads firms and investors to

overweight the likelihoods of bad outcomes and underweight the likelihoods of good outcomes

(e.g., Izhakian and Yermack, 2017), higher ambiguity reduces the perceived attractiveness of

investment opportunities (i.e., a lower perceived expected return). This behavior accelerates

the return of capital via dividends.

Notably, risk and ambiguity act through different channels in our model. Risk affects

investor expected utility through the utility of each outcome. Ambiguity affects expected

utility through the perceived probability of each outcome (i.e., through the way individuals

interpret uncertain probabilities). In related work, Shefrin and Statman (1984) examine the

effect of managers’ perceived probabilities on dividend payout policy through the lens of

prospect theory (Kahneman and Tversky, 1979). They explain dividend payout policy by

self-control and probability weighting derived by mental accounting. However, they do not

explore the effect of ambiguity.2

We test two main hypotheses, derived from the two-period stylized model of a firm

2Later, Tversky and Kahneman (1992) introduce ambiguity into prospect theory through non-additiveprobabilities.

2

that chooses between dividend distribution and investment. The first hypothesis is that

the propensity to pay dividends decreases in firm-level risk. The second hypothesis is that

the propensity to pay dividends increases in firm-level ambiguity. We find robust empirical

support for both hypotheses. In particular, we find that firm-level risk negatively affects

dividend payout timing and level, and firm-level ambiguity positively affects dividend payout

timing and level. These effects of risk and ambiguity are distinct from one another in both

the cross section and time series.

We test two additional hypotheses about the effect of ambiguity and risk on dividend

payout policy. First, that dividend initiation announcement cumulative abnormal returns

(CARs) decrease in firm-level risk. Second, that dividend initiation announcement CARs

increase in firm-level ambiguity. The intuition of these two hypotheses is that investors

condition their response to dividend initiation announcements by how appropriate they con-

sider the initiation. Firms with profitable, appropriately compensating, risky investment

opportunities should retain and invest, so dividend initiation announcement CARs decrease

in firm-level risk. Conversely, firms with ambiguous investment opportunities should pay-

out dividends, so dividend initiation announcement CARs increase in firm-level ambiguity.

We find robust statistical support for the positive relation between ambiguity and dividend

initiation announcement returns, although the risk relation point estimates are negative.

To estimate equity risk and ambiguity, we follow Izhakian and Yermack (2017). Namely,

we estimate risk as the volatility of daily returns and ambiguity as the volatility of daily

return probability distributions, estimated from intraday data. This ambiguity measure-

ment is based on Izhakian’s (2017) model of decision making under ambiguity. This model

separates ambiguity from risk, separates tastes from beliefs, and delivers a risk-independent

measure of the extent of ambiguity.3 In particular, it provides a theoretical framework for

3Other decision-making frameworks do not allow for the extent of ambiguity to be measured in isolationof tastes for ambiguity or risk. For example, in Gilboa and Schmeidler (1989) the set of priors captures bothambiguity and aversion to ambiguity. In Schmeidler (1989) capacities also capture ambiguity and aversionto it. In contrast, Izhakian’s (2017) model separates ambiguity and aversion to it.

3

measuring ambiguity by the volatility of probabilities, analogous to measuring risk by the

volatility of returns. Extensive tests by Brenner and Izhakian (2016) address concerns that

our ambiguity measure captures other well-known dimensions of uncertainty. Nevertheless,

our own robustness tests show that the same is true in the context of dividend payout policy.

We find that ambiguity and volatility measure distinctly separate aspects of financial un-

certainty. The effect of our ambiguity measure is also robust to the inclusion of alternative

measures of uncertainty (i.e., volatility of mean returns, volatility of volatility returns, and

dispersion of analyst price forecasts) and various market microstructure measures (i.e., effec-

tive bid-ask spreads and illiquidity). These alternative measures do not reduce the economic

or statistical significance of the positive relation between ambiguity and dividend payout

policy.

Our approach of measuring firm-level risk by the volatility of daily equity returns is simi-

lar to Chay and Suh (2009) measurement of firm-level risk by the volatility of monthly stock

returns. Hoberg and Prabhala (2008) decompose risk into systematic and idiosyncratic com-

ponents and Hoberg et al. (2014) measure firm-level risk by “fluidity”, which they propose

as a measure of product-market competition. Our risk findings are consistent with all three

sets of authors. As well, our results are robust to Hoberg et al.’s (2014) fluidity measure.

Our empirical tests use quarterly firm-level data over 1993 to 2016 and provide robust

support for our model’s predictions. The cross-sectional logit and Tobit tests show that

firms with higher ambiguity have a higher propensity to pay dividends and among firms

that already pay dividends those with higher ambiguity tend to pay higher dividends as a

fraction of either earnings or total assets. Controlling for the propensity to pay dividends,

our event studies show that dividend initiation announcement CARs increase in firm-level

ambiguity. With respect to dividend payout level, we find that in the cross-section larger

shocks to ambiguity are associated with larger shocks to dividend payout level. Finally, our

survival regression tests demonstrate that non-dividend paying firms with higher ambiguity

are quicker to initiate dividends and that dividend paying firms with lower ambiguity are

4

quicker to omit dividends.

Consistent with our stylized model, the empirical results show that risk has the opposite

effect of ambiguity. In particular, the cross-sectional regression tests show that firms with

higher risk have a lower propensity to pay dividends and among firms that already pay

dividends those with higher risk tend to pay lower dividends as a fraction of either earnings

or total assets. The survival regression tests demonstrate that non-dividend paying firms

with higher risk are slower to initiate dividends and that dividend paying firms with higher

risk are quicker to omit dividends. Controlling for the propensity to pay dividends, our

regression tests show that dividend initiation announcement CARs decrease in firm-level

risk, but these results are not statistically significant.

Unlike previous studies, we show that dividend payout policy is driven by both firm-level

ambiguity and risk, which are first-order determinants of the attractiveness of investment

opportunities. We show that our empirical findings cannot be attributed to other known

determinants of dividend payout policy. Throughout, we control for the standard dividend

payout predictors from Fama and French (2001) and DeAngelo et al. (2006), and find that

our results are robust. In addition, we demonstrate robustness to a host of alternative expla-

nations, including free cash flows, agency conflicts, clienteles, illiquidity, and product market

fluidity (Hoberg et al., 2014). Our results are also consistent with the negative relation

between dividends and investment opportunities that Fama and French (2001) identify with

U.S. data, Brav et al. (2005) support with surveys, and Denis and Osobov (2008), and Von

Eije and Megginson (2008) confirm around the world.4

We proceed as follows. Section II establishes a stylized model and develops the hypothe-

ses. Section III describes the sample selection and variable definitions. Section IV tests

the hypotheses about the effect of ambiguity and risk on dividend payout policy. Section V

expands this analysis and Section VI concludes.

4DeAngelo et al. (2008) provide an exhaustive survey of the dividend literature.

5

II Model

II.A The decision theoretic model of ambiguity

We distinguish the concepts of risk and ambiguity (Knightian uncertainty) by using the

theoretical framework of expected utility with uncertain probabilities (EUUP) established in

Izhakian (2017).5 EUUP considers two tiers of uncertainty, one with respect to outcomes and

the other with respect to the probabilities of these outcomes. It assumes two differentiated

phases of the decision-making process, one for each of these tiers. In the first phase, the

investor forms her perceived probabilities for all events that are relevant to her decision. In the

second phase, she assesses the expected value (utility) of each alternative using her perceived

probabilities and chooses accordingly. Ambiguity—the uncertainty about probabilities—

dominates the first phase, while risk—the uncertainty about consequences—dominates the

second phase.

5The concept of Knightian uncertainty can be viewed as underpinning two branches of literature. Thefirst is the “unawareness” literature, which assumes that decision-makers may not be aware of a subset ofevents (e.g., Karni and Vierø, 2013). The second is the ambiguity literature, which assumes that the setof events is perfectly known but their probabilities are either not unique or are unknown (e.g., Schmeidler,1989; Gilboa and Schmeidler, 1989). These two literatures can be viewed as overlapping when dealing withmonetary outcomes (real numbers). In this case, the “uncertain”—risky and ambiguous—variable is definedby a measurable function from states into the real numbers such that there is no real monetary outcome thatthe decision-maker is not aware of. The decision-maker may not be aware of some events (the so-called blackswans), which affects the uncertainty about the probabilities of some outcomes. This uncertainty, however,is already accounted for by ambiguity—the uncertainty about the probabilities of outcomes.

Parameter uncertainty assumes the set of events is known and the nature of the probability distribution isknown, but the parameters governing the distribution are unknown and the decision-maker maximizes utilityusing posterior parameters that generate a set of priors, which can be viewed as reflecting both information(beliefs) and tastes for ambiguity (e.g., Coles and Loewenstein, 1988; Coles et al., 1995). Thus, parameteruncertainty may be viewed as a special case of ambiguity, in which the nature of the probability distributionsis known. In this view, model uncertainty is also a special case of ambiguity. This class of models assumesan uncertainty about the true probability law governing the realization of states, and a decision-maker, withher concerns about misclassification, looks for a robust decision-making process (e.g., Hansen et al., 1999;Hansen and Sargent, 2001).

Other studies take an empirical view of model uncertainty (or model risk). In this perspective, whileestimating an empirical model, there is uncertainty about the true set of predictive variables. To accountfor such a model misspecification, a Bayesian (predictive distribution) approach may be taken by assigningeach set of variables (or model) a posterior probability (e.g., Pastor and Stambaugh, 2000; Avramov, 2002;Cremers, 2002).

6

To formally define the uncertain payoff X, let (S, E ,P) be a probability space, where S

is a state space, E is a σ-algebra of subsets of the state space (i.e., a set of events), P ∈ P

is a probability measure, and the set of probability measures P is convex. An algebra Π of

measurable subsets of P is equipped with a probability measure, denoted ξ. The uncertain

outcome is then given by the “uncertain” variable, X : S → R. Denote by ϕ (x) the

(uncertain) marginal probability (density function or probability mass function) associated

with the (uncertain) cumulative probability P ∈ P of outcome x. The expected marginal

and cumulative probability of x, taken using the second-order probability measure ξ, are

then respectively defined by

E [ϕ (x)] ≡∫Pϕ (x) dξ and E [P (x)] ≡

∫P

P (x) dξ, (1)

and the variance of the marginal probability is defined by

Var [ϕ (x)] ≡∫P

(ϕ (x)− E [ϕ (x)]

)2dξ. (2)

With these definitions in place, the expected outcome and the variance of outcomes are

computed using the expected probabilities. That is,

E [X] ≡∫

E [ϕ (x)]xdx and Var [X] ≡∫

E [ϕ (x)](x− E [x]

)2dx. (3)

Notice that double-struck capital font designates expectation or variance of outcomes with

respect to expected probabilities, while regular straight font designates expectation or vari-

ance of probabilities with respect to second-order probabilities.

Investors have distinct preferences concerning risk and ambiguity. As usual, preferences

concerning risk are modeled by a bounded, strictly-increasing and twice-differentiable utility

function U : R+ → R. Risk aversion takes the form of a concave U (·), risk loving takes the

form of a convex U (·), and risk neutrality takes the form of a linear U (·). We normalize U

7

to U (k) = 0, where k is the investors’ reference point. Like Tversky and Kahneman’s (1992)

cumulative prospect theory, EUUP assumes that investors have a reference point, relative

to which returns are classified as either unfavorable (loss) or favorable (gain).

As investors are sensitive to ambiguity, they do not compound the set of priors P and the

prior ξ over P in a linear way (compounded lotteries), but instead they aggregate these prob-

abilities in a non-linear way, reflecting their aversion to ambiguity. Preferences concerning

ambiguity are defined by preferences over mean-preserving spreads in probabilities and mod-

eled by a strictly-increasing and twice-differentiable function over probabilities, Υ : R+ → R,

called the outlook function. Similar to risk, ambiguity aversion takes the form of a concave

Υ (·), ambiguity loving takes the form of a convex Υ (·), and ambiguity neutrality takes the

form of a linear Υ (·). In EUUP, ambiguity aversion is exhibited when an investor prefers the

expectation of an uncertain probability of each payoff over the uncertain probability itself.6

Suppose that the decision to save one unit of wealth is made at the beginning of the

period, and the outcome, which is the only source of wealth, occurs at end of the period. In

EUUP, the expected utility of this investment opportunity can be approximated by7

W (X) ≈∫x≤k

U (x) E [ϕ (x)]

(1− Υ′′ (1− E [P (x)])

Υ′ (1− E [P (x)])Var [ϕ (x)]

)︸ ︷︷ ︸

Perceived Probability of Unfavorable Outcome

dx+ (4)

∫x≥k

U (x) E [ϕ (x)]

(1 +

Υ′′ (1− E [P (x)])

Υ′ (1− E [P (x)])Var [ϕ (x)]

)︸ ︷︷ ︸

Perceived Probability of Favorable Outcome

dx.

6Recall that risk aversion is exhibited when an investor prefers the expected outcome of the uncertainoutcome over the uncertain outcome itself.

7This functional representation is obtained by taking the Taylor expansion of the dual represen-tation of EUUP, proposed by Izhakian (2017). The reminder of this approximation is of order

o(∫

E[|ϕ (x)− E [ϕ (x)]|3

]xdx

)as

∫|ϕ (x)− E [ϕ (x)]| dx → 0, meaning that the accuracy of the approx-

imation is equivalent to the accuracy of the cubic approximation, o(E[|x− E [x]|3

]), in which the fourth

and higher absolute central moments of outcomes are of strictly smaller order than the third absolute centralmoment as |x− E [x]| → 0, and are therefore negligible.

8

Notice that when investors are ambiguity neutral (Υ (·) is linear), investors compound prob-

abilities linearly and Equation (4) collapses to the conventional expected utility. In contrast,

when the investors are ambiguity averse (Υ (·) is concave), they do not aggregate proba-

bilities linearly and the perceived probabilities are affected by the intensity of aversion to

ambiguity. In this case, investors overweight the probabilities of the unfavorable outcomes

and underweight the probabilities of favorable outcomes.

The advantage of EUUP is that ambiguity preferences are applied exclusively to prob-

abilities such that ambiguity aversion is defined as aversion to mean-preserving spreads in

probabilities. Conceptually, the perceived probability of a given outcome can be viewed as

the unique certain probability values that the investor is willing to accept in exchange for

its uncertain probability (i.e., a certainty equivalent probability).

The notion of mean-preserving spreads in probabilities in Equation (4) can be used to

derive a measure of ambiguity (Izhakian, 2017, Theorem 6). This measure, defined by the

expected volatility of probabilities, is formally given by

f2 [X] ≡∫

E [ϕ (x)] Var [ϕ (x)] dx. (5)

The measure f2 (mho2) can be used either in a continuous state space with infinitely many

outcomes or in a discrete state space with finitely many outcomes. Unlike other measures of

ambiguity, which are outcome-dependent (and thus risk-dependent) and consider only the

variance of a single moment of the distribution (e.g., the variance of the variance or the

variance of the mean), our measure is outcome-independent (and thus risk-independent) and

accounts for the variance of all the moments of the outcome distribution.8 Furthermore, our

8Sometimes the literature takes the volatility of volatility or the volatility of the mean as measures ofambiguity. The measure of ambiguity f2 is broader than either of these measures in that it accounts forboth, as well as for the volatility of all higher moments of the probability distribution (e.g., skewness andkurtosis) through the variance of probabilities. As opposed to the volatility of the volatility and the volatilityof the mean, the measure f2 is outcome- and risk-independent, as it does not depend upon the magnitudesof outcomes but only upon their probabilities. Furthermore, f2 solves some major issues that arise from theuse of only the volatility of the volatility or only the volatility of the mean as measures of ambiguity. For

9

measure of ambiguity can be employed in empirical studies using stock data (e.g., Brenner

and Izhakian, 2016; Izhakian and Yermack, 2017).

To observe the distinct impact of ambiguity and ambiguity aversion on the value of an

investment opportunity, consider a binomial asset with low payoff (L) and high payoff (H).

Suppose that the reference point k satisfies L ≤ k ≤ E [X] < H.9 By Equation (4), the value

of this asset in terms of expected utility is

W (X) ≈ U (L) E [ϕ (L)]

(1− Υ′′ (1− E [P (H)])

Υ′ (1− E [P (H)])Var [ϕ (L)]

)+ (6)

U (H) E [ϕ (H)]

(1 +

Υ′′ (E [P (H)])

Υ′ (E [P (H)])Var [ϕ (H)]

).

Expected utility in this functional representation is assessed using the investor’s perceived

probabilities. Ambiguity and ambiguity aversion are modeled in Equation (6) through the

investor’s marginal perceived probabilities. Consider the high payoff, H. The expression

Q(H) ≈ E [ϕ (H)]

(1 +

Υ′′ (E [P (H)])

Υ′ (E [P (H)])Var [ϕ (H)]

)(7)

is the marginal perceived probability of this outcome occurring.10 This marginal perceived

probability is a function of the degree of ambiguity, measured by Var [ϕ (H)], and the in-

vestor’s attitude toward ambiguity, captured by −Υ′′(·)Υ′(·) . For an ambiguity-averse investor

with −Υ′′(·)Υ′(·) > 0, a higher aversion to ambiguity or a higher degree of ambiguity results in

lower marginal perceived probabilities of good states and higher marginal perceived proba-

bilities of bad states. This in turn implies a lower expected utility.

example, two equities could have constant volatility but different degrees of ambiguity, or two equities couldhave constant means but different degrees of ambiguity.

9We assume that the expected outcome is greater than the reference point; otherwise, a rational decisionmaker would not consider the investment opportunity.

10Note that, since every P ∈ P is additive, 1 − E [P (L)] = E [P (H)]. In this case, the variance ofthe probabilities of L is equal to the variance of the probabilities of its complementary event H, so thatVar [ϕ (L)] = Var [ϕ (H)].

10

II.B Dividend decisions

To study the effect of ambiguity and risk on dividend payout, we employ the EUUP frame-

work to develop a stylized static model, as in Miller and Modigliani (1961) and Baker and

Wurgler (2004). We consider a one-period decision by a manager who is free of agency con-

flicts and maximizes the expected utility of investors, who are risk and ambiguity averse.

As such, this manager can be viewed as a representative investor. We assume a standard

structure, where the only variation is the specification of probabilities. As in Baker and

Wurgler (2004), we model investment and payout decisions directly through the investor’s

utility function, rather than through the cost of capital. Note that the cost of capital is

determined by risk and ambiguity preferences, which are formed by the investor’s utility

function.

Suppose that at date 0 the firm has a free cash available in the amount C. At date 0,

the manager decides between a liquidating dividend D0 = C and a risky and ambiguous

investment opportunity (a project). Suppose that the project’s net return can be either +g

in the high state or −g in the low state, where g > 0. If the manager accepts the project,

then at date 1 the firm pays out a liquidating dividend DH = C (1 + g) or DL = C (1− g) in

high or low states of the investment, respectively. The manager’s decision is solely about the

free cash and does not involve new funds, which may effect the optimal capital structure of

the firm (Izhakian et al., 2017). The expected utility incorporates both risk and ambiguity

preferences; for simplicity, we assume neutral time preferences.

11

By Equation (6), the objective function of the utility-maximizing investors is

max

{U (D0) , [1−Q(H)] U (DL) + Q(H)U (DH)

}(8)

s.t.

DH = DL = 0, if D0 = C;

DH = C(1 + g), if D0 = 0;

DL = C(1− g), if D0 = 0;

g > 0,

where Q(H) is defined in Equation (7). This objective function simplifies to an inequality,

implying that the firm pays a date 0 dividend when the following condition is met

U (C) > (1−Q(H)) U (C(1− g)) + Q(H)U (C(1 + g)) . (9)

Suppose that the project become riskier (g increases). The concavity of U (risk aversion)

implies that, when Q(H) is sufficiently high or when risk aversion is sufficiently low such

that

Q(H) >U′ (C(1− g))

U′ (C(1− g)) + U′ (C(1 + g))(10)

the right hand side (RHS) of Equation (9) becomes greater as g increases.11 This implies

the following.

Hypothesis 1 The propensity to pay dividends decreases in firm-level risk.

The intuition of this hypothesis is as follows. When the perceived probability of the high

payoff is relatively high, an increase in risk is accompanied by an increase in (perceived)

expected payoff. For moderately risk-averse investors, this increase in (perceived) expected

11 This condition is obtain by differentiating the RHS with respect g.

12

payoff provides adequate compensation for the higher risk. The investors in this case would

prefer the risky investment over the dividend payout. Hypothesis 1 of a negative effect of risk

on dividend payout is consistent with Chay and Suh (2009), Hoberg and Prabhala (2008),

and Hoberg et al. (2014). It is important to note that we do not assume that risk is the

variance of either payoffs or returns, since we do not assume that either utility is quadratic

or returns are normally distributed. We expect that the propensity to pay dividends is also

subject to investors’ risk aversion. However, since we are not aware of a verified methodology

to elicit risk aversion from stock data, we focus on the effect of risk.

Suppose now that risk is constant and ambiguity increases (the volatility of probabili-

ties increases). By Equation (7), since Υ (·) is concave (ambiguity aversion, −Υ′′(·)Υ′(·) > 0),

this results in a lower perceived probability Q(H) of state H, implying that the RHS of

Equation (9) becomes smaller. This implies the following.

Hypothesis 2 The propensity to pay dividends increases in firm-level ambiguity.

The intuition of this hypothesis is as follows. When the ambiguity of the project increases,

the perceived probability of the high payoff decreases and the perceived probability of the

low payoff increases, such that the (perceived) expected payoff decreases. This makes the

project less attractive and investors would prefer the dividend payout over the ambiguous

investment. The effect of aversion to ambiguity is similar. Higher ambiguity aversion reduces

the (perceived) expected payoff of the project, which makes it less attractive. As with risk

aversion, since we are not aware of a verified methodology to elicit ambiguity aversion from

stock data, we focus on the effect of ambiguity.

Two additional observations about value changes around dividend initiations can be

derived from Equation (9). The difference between the left hand side (LHS) and the RHS of

Equation (9) is the date 0 expected utility the firm provides as a dividend payer versus the

expected utility the same firm provides as a dividend nonpayer. When the LHS is larger,

initiating a dividend increases investor expected utility and firm value. Conversely, when the

13

RHS is larger, initiating a dividend decreases both investor expected utility and firm value.

The CAR around dividend initiation announcement may capture this change in expected

utility.

Hypothesis 3 Dividend initiation announcement CAR decreases in firm-level risk.

Hypothesis 4 Dividend initiation announcement CAR increases in firm-level ambiguity.

III Data

The primary data sources for our analysis are Compustat for historical information on divi-

dend payout and firm fundamentals, Intraday Trade and Quote (TAQ) data for estimation

of firm-specific degree of ambiguity, and Center for Research in Security Prices (CRSP)

data for estimation of firm-specific risk. For a given firm, we require Compustat data and

stock price information in TAQ and CRSP, which leaves us with a sample of 8109 firms

with 208,837 quarterly observations from 1993 to 2016 for which we can extract joint infor-

mation on ambiguity, risk, and dividend payout policy.12 Our empirical investigation looks

at dividend payout at quarterly resolution, as most dividend payout decisions are made on

a quarterly basis, including initiation and omission decisions. Our results throughout are

qualitatively similar using annual data.

III.A Dividends

Our dividend measures are based on common cash dividends, which the quarterly Compustat

database reports as cumulative millions of U.S. Dollars paid fiscal year-to-date. To recover

quarterly dividends, we use dividends as reported in the first fiscal quarter, or as the quarterly

12We omit the first two quarters of 1993 because we require two-quarter lags of both ambiguity and risk.We omit the fourth quarter of 2016 because the Compustat fundamental data are not yet available for allfirms.

14

change in fiscal year-to-date dividends otherwise. We consider a firm a dividend payer in

a given quarter if dividends are strictly positive and a dividend nonpayer otherwise. We

consider a firm a dividend initiator in a given quarter if it is a dividend payer, but was not

a dividend payer in any of the previous eight quarters. Conversely, we consider a firm a

dividend omitter in a given quarter if it is a dividend nonpayer, but was a dividend payer

in all of the previous eight quarters.13 To further test the propensity to pay dividends, we

also look at dividend payout levels using the dividend payout ratio, computed as the ratio

of common cash dividends to quarterly net income.

We follow Fama and French (2001) and Skinner (2008) to determine net share repur-

chases. For firms that use the treasury stock method, we measure net share repurchases as

the positive quarterly change in treasury stock. Otherwise, we use the positive portion of

repurchases of common and preferred stock net of new issues of common and preferred stock.

We consider a firm a repurchaser if net share repurchases are strictly positive in a quarter

or in any of the preceding eight quarters.14

III.B Estimating ambiguity and risk

We estimate ambiguity of a firm’s equity to proxy for firm-level ambiguity.15 The intuition is

that equity ambiguity represents the uncertainty in future outcome probabilities of a firm’s

projects. Similarly, equity risk represents the uncertainty in future outcomes of a firm’s

projects. We employ Izhakian and Yermack’s (2017) empirical method to estimate the

degree of ambiguity using intraday stock trading data from the TAQ database. We compute

the degree of ambiguity, given in Equation (5), for each stock each month and use the trailing

13Our results are qualitatively similar if we instead use a four-quarter threshold for dividend initiation andomission.

14Allowing a two-year window to identify repurchasers is consistent with Skinner (2008).15Because they are based on stock returns data, both risk and ambiguity measure uncertainty about the

firm’s equity. Consistent with Hoberg and Prabhala (2008), for simplicity, we report results with equity-based uncertainty measures. Our results are qualitatively similar when using unlevered stock returns datato generate risk and ambiguity.

15

three-month moving average. We handle risk the same way and use the trailing three-month

moving average.16

We compute monthly firm-level ambiguity using the following procedure.17 We suppose

the existence of a representative agent with a set of priors over intraday returns. The observed

intraday returns on the underlying asset are assumed to be a realization of one specific prior.

That is, every day is characterized by a different distribution of returns, and the set of these

distributions over a month represents the agent’s set of priors. Assuming that stock returns

are normally distributed, the degree of ambiguity of return rj on equity j can be measured

by

f2 [rj] =

∫E [φ (rj;µj, σj)] Var [φ (rj;µj, σj)] drj, (11)

where φ (rj;µj, σj) stands for the normal probability density function of rj conditional upon

the mean µj and the variance σ2j .

To estimate the set of possible probability distributions of returns using TAQ data, we

sample the price of the stock every five minutes from 9:30 until 16:00. The decision to use

five-minute time intervals is motivated in part by Andersen et al. (2001), who show that

this time interval is sufficient to eliminate microstructure effects. In cases where there is no

trade at a specific time interval, we take the volume-weighted average of the closest trading

prices. Using these prices, we compute five-minute returns for a maximum of 78 intraday

returns on any given day. We ignore returns between closing and next-day opening prices,

thereby eliminating the impact of overnight price changes and dividend distributions. For

each stock, we drop all trading days with fewer than 15 different five-minute time intervals,

16The results are qualitatively similar if we instead use the last ambiguity and risk observation in eachfiscal quarter.

17We emphasize that our empirical tests use a measure of the degree of ambiguity, defined by Equation (5),which is distinct from aversion to ambiguity. The former, which is a matter of beliefs (or information), isestimated from the data, while the latter, which is a matter of tastes, is endogenously determined by theempirical estimations.

16

and we drop all trading months with fewer than 15 intraday return distributions. In addition,

we winsorize extreme five-minute returns (i.e., plus or minus 10 % log returns), as many of

these are mistaken orders that the stock exchange later cancels.

Each day for each stock we compute the time-normalized mean µj and variance σ2j of

five-minute returns.18 We follow French et al. (1987) and adjust the variance of returns

for non-synchronous trading as Scholes and Williams (1977) propose.19 We assume that

intraday returns are normally distributed, and for each stock j we construct the set of priors

Pj, where each prior Pj within the set Pj is defined by a pair of µj and σj.

The set Pj of (normal) probability distributions of each stock j for a given month consists

of 15 to 22 different probability distributions. To compute the monthly degree of ambiguity

of a given asset, specified in Equation (11), we represent each daily return distribution by

a histogram. We divide the range of daily returns into 160 intervals (bins) from −40 % to

40 %, each of width 0.5 %. For each day, we compute the probability of the return being in

each bin, as well as the probability of the return being lower than 40 % and the probability

of the return being higher than 40 %. Using these probabilities, we separately compute the

mean and the variance of probabilities for each of the 162 bins, assigning equal weights

to each probability distribution in the set Pj (i.e., all histograms are equally likely). This

is equivalent to assuming that the daily ratiosµjσj

are student’s-t distributed.20 Then we

18This normalization is applied since for less liquid stocks the return is obtained over time intervals longerthan 5 minutes.

19The Scholes and Williams (1977) adjustment for non-synchronous trading suggests that the volatility of

returns takes the form σ2t =

1

Nt

Nt∑i=1

(rt,i − E [rt,i])2

+ 21

Nt − 1

Nt∑i=2

(rt,i − E [rt,i]) (rt,i−1 − E [rt,i−1]). We also

test our model without the Scholes and Williams correction for non-synchronous trading. The results areessentially the same.

20 When µσ is Student’s t-distributed, cumulative probabilities are uniformly distributed. See, for example,

Proposition 1.27 of Kendall and Stuart (2010). This is consistent with the idea that the representativeinvestor does not have any information indicating which of the possible probability distributions is morelikely, and thus she acts as if she assigns an equal weight to each possibility.

17

estimate the degree of ambiguity of each stock j for each month by the discrete form

f2 [rj] =1

π

(0.01

w

)1+ 1π2

E[Φ (rj,0;µj, σj)

]Var[Φ (rj,0;µj, σj)

]+

160∑i=1

E[Φ (rj,i;µj, σj)− Φ (rj,i−1;µj, σj)

]×

Var[Φ (rj,i;µj, σj)− Φ (rj,i−1;µj, σj)

]+

E[1− Φ (rj,160;µj, σj)

]Var[1− Φ (rj,160;µj, σj)

]

, (12)

where Φ (·) stands for the cumulative normal probability distribution, r0 = −0.40, w =

ri − ri−1 = 0.005, r160 = 0.40, and 1π

(0.01w

)1+ 1π2 scales the weighted-average volatilities of

probabilities to the bins’ size.21 This scaling, which is analogous to Sheppard’s correction,

has been tested to verify that it minimizes the effect of the selected bin size on the values of

f2.

Brenner and Izhakian (2016) empirically rule out the concern that f2 may capture other

well-known “uncertainty” factors including skewness, kurtosis, variance of variance, vari-

ance of mean, downside risk, mixed data sampling measure of volatility forecasts (MIDAS),

investors’ sentiment, among several others. Their tests also rule out the concern that ob-

served returns are generated by a single (additive) probability distribution. In unreported

results, we confirm this with a weak correlation of −0.10 between monthly ambiguity and

risk. As expected, when aggregating risk and ambiguity over quarters, their correlation rises

to −0.43 in Table II. Our robustness tests further rule out concerns that f2 may capture

other well-known uncertainty factors, as well as market-microstructure factors.

Along with ambiguity, risk serves as the most important explanatory variable in our

analysis. We compute risk with standard methods, using daily returns adjusted for dividends

obtained from the CRSP database. Since probabilities are uncertain, volatilities can be

viewed as computed using the expected probabilities of outcomes (see Izhakian, 2017). For

each individual stock j in a given month t, we calculate the standard deviation, Stdj,t, of

21We find that this scale improves Izhakian and Yermack’s (2017) scale of 1w ln 1

w

in the sense that it reduces

the sensitivity of the estimated f2 to the selection of the bin’s size.

18

the stock’s daily returns over that month, again applying the Scholes and Williams (1977)

correction for non-synchronous trading and a correction for heteroscedasticity (see French

et al., 1987).

III.C Other explanatory variables

In addition to ambiguity and risk, our empirical models include the control variables of Fama

and French (2001) and DeAngelo et al. (2006). In particular, we proxy growth opportunities

with quarterly asset growth rates and market-to-book asset ratios. The quarterly asset

growth rate is the quarterly change in the book value of total assets relative to the book

value of total assets. The market-to-book asset ratio (Market/Book) is the market value

of total assets at the end of each quarter divided by the corresponding book value of total

assets. We proxy profitability with Return on Assets, which is operating income before

depreciation divided by the book value of total assets. We proxy size with the natural log of

the market value of equity. We follow DeAngelo et al. (2006) and proxy firm life cycle as the

ratio of earned to contributed equity, which is retained earnings divided by the book value

of common equity (Retained Earnings/Book Equity).

We also include the ratios of research and development (R&D) and capital expenditures

to the book value of total assets. These allow us to explore whether firms with high ambiguity

invest less in either research and development or capital expenditures. Quarterly Compustat

reports both R&D and capital expenditures as fiscal year-to-date. To recover R&D, we take

R&D as reported in the first fiscal quarter, or as the change in R&D relative to the previous

quarter otherwise. We follow the same approach to generate quarterly capital expenditures.

As well, we follow Hovakimian et al. (2001) and replace missing R&D values with zeros. We

winsorize all ratios, ambiguity, and risk by 5 % in each tail.

19

III.D Summary statistics

Table I presents summary statistics for the full sample from 1993 to 2016, as well as separately

for dividend payer and dividend nonpayer firms. The first row provides the first support for

Hypothesis 2 of a positive relation between ambiguity and dividend payout. The average

degree of ambiguity is higher for payers at 0.043 and lower for nonpayers at 0.026. With a

sample of 208,837 firm-quarter observations and a standard deviation of ambiguity of 0.019,

the difference in ambiguity between the two samples is statistically significant at the 0.1 %

level. Tables I and II report one-quarter lags of ambiguity and risk because we use one-

quarter and two-quarter lags of ambiguity and risk throughout to reduce reverse causality

concerns.

The second row provides the first support for Hypothesis 1 of a negative relation between

risk and dividend payout. The average risk of dividend nonpayers is statistically higher

than that of dividend payers at 0.034 and 0.013, respectively. Risk over the entire sample is

0.028 on average, consistent with the extant literature (e.g., Chay and Suh, 2009, Table 1).

Notice that the averages of both ambiguity and risk are higher than the medians because

by definition both are left-censored at zero. Nevertheless, as with the averages, median

ambiguity is higher and median risk is lower for dividend payers relative to nonpayers.

The remaining summary statistics in Table I are consistent with the dividend literature

(Fama and French, 2001; DeAngelo et al., 2006). The fraction of payers is in line with the

literature at 0.289. Computing the ambiguity variable requires stocks with sufficient trade

data, which could slightly bias the sample towards larger firms, which are more likely to pay

a dividend. Consistent with the literature, the Market/Book ratio is larger for nonpayers

than for payers (i.e., 2.309 vs. 1.931). Conversely, Return on Assets, log(Market Equity),

and Retained Earnings/Book Equity are all larger for dividend payers than for nonpayers

(i.e., 0.036 vs. 0.003, 7.473 vs. 5.676, and 0.470 vs. −1.116, respectively).

[Table I]

20

Table II presents the correlations of the key variables.22 Ambiguity is negatively corre-

lated with risk at −0.43. Again this correlation rises from −0.10 to −0.43, when moving

from monthly observations to quarterly averages of monthly observations. The positive cor-

relation of 0.41 between ambiguity and dividend payers indicator variable is consistent with

Hypothesis 2. The other notable positive correlations with ambiguity are Return on Assets

at 0.33 and log(Market Equity) at 0.67. Two notable negative correlations are with Capital

Expenditures at −0.02 and R&D at −0.24, which support our intuition that firms with high

ambiguity make less investment through either Capital Expenditures or R&D.

[Table II]

IV Empirical findings

We start by investigating the effect of ambiguity and risk on the selected payout method.

We use a multinomial logit test of the choice of no payout, repurchases only, or dividends.

The first two columns in Table III describe the findings of Model 1, which includes only

one-quarter lags of ambiguity and risk, as well as year fixed effects. The last two columns

describe Model 2, which adds the standard predictors suggested by Fama and French (2001),

DeAngelo et al. (2006), and Skinner (2008). In both models the base category is firms that

are neither dividend payers nor share repurchasers. Both models cluster standard errors by

two-digit industry. Both models show a significantly positive effect of ambiguity on dividends

with point estimates that are at least three times as large as the positive effect of ambiguity

on repurchases only. All standard predictors enter with the expected signs.

We focus on dividends rather than repurchases since dividend decisions are less con-

founded by extra cash, temporary earnings, (perceived) mispricing, and capital structure

decisions, and are clearly observable. Furthermore, Fama and French (2001) show that

22For robustness, we also compute correlations among the different variables for each firm and examinethe average correlations and p-values across firms. The findings are qualitatively similar.

21

many repurchases are made by firms that also pay dividends, so the bulk of repurchase deci-

sions are associated with dividend decisions. Regardless, our results are qualitatively similar

if we replace dividends with repurchases.

[Table III]

IV.A Dividend payout

To test Hypotheses 1 and 2, we first look at the fraction of payers by dependent sorts on

ambiguity and risk. Panel A of Figure 1 first sorts into risk quintiles each year, then sorts into

ambiguity quintiles within each risk-year quintile. Panel A demonstrates that the fraction

of payers monotonically increases in ambiguity quintiles within each risk quintile. Panel B

repeats this analysis, but first sorts into ambiguity quintiles each year, then sorts into risk

quintiles within each ambiguity-year quintile. As before, the fraction of dividend payers is

negatively related to risk and positively related to ambiguity. In both panels, for all quintiles

of risk and ambiguity the differences between high and low quintiles of the dependent sorts

are statistically significant. The findings in Figure 1 support Hypotheses 1 and 2 and show

that dividend payment is negatively related to risk, positively related to ambiguity, and that

the two reactions are distinct.

[Figure 1]

To verify these findings, we conduct cross-sectional regression tests using Fama and Mac-

Beth (1973) methodology with quarterly first-stage logit regressions.23 Table IV reports the

time-series means of these quarterly cross-sectional logit regression coefficients using Newey

and West (1987) standard errors to correct for serial correlation to eight quarterly lags. Re-

call that ambiguity is determined using intraday returns and is independent of overnight

23Although not reported in tables, the findings hold in panel logit and linear probability models, witheither firm or two-digit industry fixed effects.

22

returns. Thus, there is no mechanical relation between ambiguity and dividends. However,

it could still be the case that dividend payout affects risk and ambiguity contemporaneously.

To address this causality concern, we lag both ambiguity and risk in our tests throughout.

Column 1 includes only the one-quarter lag of ambiguity to confirm the positive effect of

firm-level ambiguity on dividend payout in Tables I and II and Figure 1. To identify the

economic significance of ambiguity, we use an odds-ratio interpretation. With respect to am-

biguity, the interquartile range of the one-quarter lag of ambiguity is 0.0277 (not reported

in tables). Accordingly, the odds ratio of an interquartile rise is exp(71.67× 0.0277) = 7.28,

implying an economically sizable effect of a 628 % increase in the odds of paying a dividend.

Column 2 in Table IV replaces the one-quarter lag of ambiguity with the one-quarter lag

of risk, again to verify the negative effect of firm-level risk on dividend payout that appears

in Tables I and II and Figure 1. The effect of risk on the propensity to pay dividends is of

the same order of magnitude as the effect of ambiguity, but in the opposite direction. The

coefficient of the one-quarter lag of risk is similar in magnitude at −83.05. The interquar-

tile range of the one-quarter lag of risk is 0.0271 (not reported in tables) and suggests an

odds-ratio 0.105, which is an economically sizable effect of a 89.5 % decrease in the odds of

paying a dividend. Column 3 includes the one-quarter lags of both ambiguity and risk. Both

coefficient point estimates remain economically meaningful and statistically significant, pro-

viding a unique perspective on the dividend decision. Column 4 adds the standard predictors

from Fama and French (2001) and DeAngelo et al. (2006), and shows that both ambiguity

and risk point estimates remain economically meaningful and statistically significant. The

standard predictors all enter with the expected signs. For ambiguity, the odds ratio of an

interquartile rise is 2.33 and for risk it is 0.478. For a frame of reference, the other strongest

dividend determinant in Column 4 is log(Market Equity), which has an odds ratio of 2.16

for an interquartile rise.

Columns 5 to 8 in Table IV repeat the analyses of Columns 1 to 4 with two-quarter

lags of ambiguity and risk. The point estimates and statistical significance are qualitatively

23

similar to their one-quarter lag counterparts. Ambiguity increases a firm’s propensity to pay

dividends and risk decreases a firm’s propensity to pay dividends. In both cases, the effects

are economically sizable with interquartile changes leading to large changes in the propensity

to pay dividends.

The economic significance of ambiguity and risk can also be identified by the improve-

ment in model fit after introducing ambiguity and risk relative to the empirical model with

the standard predictors, as indicated by the average pseudo R2s of cross-sectional logit re-

gressions.24 Columns 1 and 2 of Table IV show that by itself each ambiguity and risk has

meaningful explanatory power. Alone ambiguity and risk have average pseudo R2s of 0.181

and 0.165, respectively. Including only the standard predictors yields an average pseudo R2

of 0.254 (not reported in tables). Column 4 adds the one-quarter lags of both ambiguity

and risk to the standard predictors to yield an average pseudo R2 of 0.288, a meaningful

increase in explanatory power. Columns 5 to 8 repeat this progression with the two-quarter

lags of ambiguity and risk. In all models both ambiguity and risk considerably increase the

explanatory power. Consistent with the model, the results in Table IV show that both risk

and ambiguity have an economically sizable effect on the propensity to pay dividends that

are distinctly different from each other and not explained by the standard predictors.

[Table IV]

The inclusion of ambiguity also improves the explanatory power of the models in the sense

that it reduces prediction errors. This improvement is robust to the inclusion of risk. Figure 2

depicts this improvement visually as time-series plots of the prediction errors. Panels A

and B present absolute prediction errors and Panels C and D present squared prediction

errors. All models include the standard predictors and use the coefficients estimated in the

24Pseudo R2s cannot be interpreted independently or compared across datasets, but they are valid anduseful in evaluating multiple models predicting the same outcomes on the same dataset (Long and Freese,2006). The results are qualitatively similar if we compare average adjusted R2s from Fama and MacBeth(1973) regressions with quarterly first-stage ordinary least squares regressions.

24

previous quarter. In Panels A through D, including ambiguity almost uniformly improves

the prediction errors.

[Figure 2]

Table V statistically tests prediction error improvement. All regressions include the

standard predictors from Fama and French (2001) and DeAngelo et al. (2006) with different

combinations of the one-quarter lags of ambiguity and risk. Panel A tests absolute prediction

error improvement using quarterly logit regressions with coefficients estimated in the previous

quarter. The reported values are the means of quarterly means of absolute prediction errors.

Column 1 reports the mean of quarterly means of absolute prediction errors from models

with only the standard predictors. Column 2 adds the one-quarter lag of ambiguity and

Column 5 reports the paired t-test of Column 2 minus Column 1. Column 5 demonstrates

an economically meaningful improvement of 0.0102, which is a 3.51 % improvement relative

to 0.291 in Column 1. A closer look at the prediction error improvement on a quarter-by-

quarter basis shows an absolute prediction error improvement in each of the 93 quarters

in the sample. This improvement is qualitatively consistent with the average pseudo R2

improvements in Table IV.

Column 3 of Panel A replaces the one-quarter lag of ambiguity with the one-quarter lag

of risk, and Column 4 includes the one-quarter lags of both ambiguity and risk. Column 6

reports the paired t-test of Column 4 minus Column 3. Again, the paired t-test of the

absolute prediction error improvement is statistically significant and economically meaningful

across the whole sample, as well as quarter-by-quarter, which is consistent with Chay and

Suh (2009) and Hoberg et al. (2014). Ambiguity improves the absolute prediction error by

0.00499, which is a 1.78 % improvement on the average absolute prediction error of 0.281 of

the model with the standard predictors plus risk in Column 3. As well, ambiguity improves

prediction error in 91 of the 93 quarters in the sample. Panel B repeats these tests with the

squared prediction errors, demonstrating a similar improvement. These improvements are

25

economically meaningful. Consistent with our model, both ambiguity and risk make unique

a contribution.

[Table V]

IV.B Dividend initiation

Our tests so far focus on Hypotheses 1 and 2, which address the effect of risk and ambi-

guity on the manager’s decision to pay a dividend. Increasing investor expected utility, as

determined by the firm’s market value of equity, motivates the manager to set dividend pol-

icy based on firm-level ambiguity and risk. We now turn to explore firm valuation changes

around dividend initiation announcements. These valuation changes are the foundations for

Hypotheses 3 and 4, which state that dividend initiation announcement CARs decrease in

risk and increase in ambiguity.

The market will not react to a fully anticipated dividend. To screen for dividend initi-

ation anticipation and isolate the effect of ambiguity on dividend initiation announcement

CARs, we consider only a firm’s first dividend initiation announcement in the CRSP daily

database. This leaves us with 452 dividend initiation announcements. Ambiguity affects

market response through two opposing channels. On one hand, the propensity to pay divi-

dends increases in ambiguity, so the market more strongly anticipates dividend initiation as

ambiguity increases; thus announcement returns decrease in ambiguity. On the other hand,

the expected utility gain from dividend initiation increases in ambiguity; thus, announce-

ment returns increase in ambiguity. To address these two opposing channels, we include

ambiguity and ambiguity interacted with propensity to pay dividends. The interaction term

identifies the market response to ambiguity conditional upon the propensity to pay dividends.

The propensity to pay dividends is the fitted probability from a quarterly logit model with

the coefficients estimated in the previous quarter. To better disentangle these two chan-

nels and prevent collinearity between ambiguity and the propensity to pay dividends, we

26

estimate the propensity to pay dividends with only the standard predictors (Asset Growth

Rate, Market/Book, Return on Assets, log(Market Equity), and Retained Earnings/Book

Equity). Table VI reports these findings. Columns 1 and 2 use market-adjusted returns and

Columns 3 and 4 use a single-factor market model, both with a value-weighted CRSP index.

Starting with five-day market adjusted returns in Column 1, we find that announcement

abnormal returns decrease in both ambiguity and the propensity to pay dividends, but in-

crease in ambiguity conditional on the propensity to pay dividends. For any given propensity

to pay dividends, the market response increases in ambiguity. Column 2 shows that this re-

lation is robust to a seven-day event window. Columns 3 and 4 show that this relation

is robust to CARs from a market-model. This positive effect of ambiguity, conditional on

the propensity to pay dividends, on dividend initiation announcement CARs is consistent

with Hypothesis 4 and not driven by event window choice or abnormal return definition.

In results not reported, the coefficient point estimates on the risk-propensity to pay divi-

dends interactions are negative, but we fail to find any statistically significant support for

Hypothesis 3.

[Table VI]

V Extensions

The hypotheses we test so far derive from our formal model. Next, we present several

empirical extensions.

V.A Dividend payout ratios

Our first empirical extension is for a firm with multiple projects that faces a decision about

the level of dividend payout rather than whether or not to pay a dividend. A firm with

multiple risky and profitable projects is expected to accept more of these projects and pay

27

less dividends. A firm with multiple ambiguous and profitable projects is expected to reject

more of these projects and pay higher dividends. To capture the extent of dividend payment,

we use the dividend payout ratio, which is the ratio of common cash dividends to net income

each quarter.25

We test the effect of ambiguity and risk on dividend payout ratio using Fama and Mac-

Beth (1973) regressions with quarterly first-stage Tobit regressions.26 To account for negative

or excessively positive dividend payout ratios, we left censor dependent variables at zero and

right censor dependent variables at one.27 Table VII reports the time-series means of quar-

terly cross-sectional regression coefficients with Newey and West (1987) standard errors to

correct for serial correlation to eight quarterly lags. Table VII follows the same progres-

sion as Table IV, first including the one-quarter lags of ambiguity and risk separately, then

together, then alongside the standard predictors.

Column 1 of Table VII includes only the one-quarter lag of ambiguity, which enters

with a positive coefficient of 21.75 that is significant at the 0.1 % level. The interquartile

range of the one-quarter lag of ambiguity is the same as in Table IV and the effect of an

interquartile rise is 21.75 × 0.0277 = 0.603, which is economically sizable. An interquartile

increase in ambiguity increases the dividend payout ratio from zero to just over one half.

Column 2 replaces the one-quarter lag of ambiguity with the one-quarter lag of risk, which

enters with a negative coefficient of −28.45 that is significant at the 0.1 % level. This implies

that the effect on dividend payout ratio of an interquartile rise in risk is −0.772, which is

similar in magnitude to ambiguity. Column 3 adds back the one-quarter lag of ambiguity

to include both measures and shows that their economic and statistical significance remain

25The results throughout are qualitatively similar using the ratio of common cash dividends to book valueof total assets. The dividend payout ratio, however, better captures the decision to payout or reinvest sincereinvestment is made from retained earnings.

26The results are qualitatively similar using linear panel models with either two-digit industry or firm fixedeffects.

27The results are qualitatively similar if we do not right censor dependent variables, right censor dependentvariables at five, or replace negative dependent variables with one (Julio and Ikenberry, 2004).

28

qualitatively similar. Column 4 adds the standard predictors. Although the literature is less

clear on dividend payout ratio determinants, we include the standard predictors from Fama

and French (2001) and DeAngelo et al. (2006), which all enter with the expected signs and are

statistically significant. In particular, dividend payout ratios increase in profitability, size,

and life cycle, and decrease in growth opportunities (Asset Growth Rate and Market/Book).

Again, with the addition of the standard predictors the point estimates for the one-quarter

lags of ambiguity and risk decline in magnitude, but remain economically sizable. The effect

of an interquartile rise in the one-quarter lag of ambiguity is 0.185 and the effect of an

interquartile rise in the one-quarter lag of risk is −0.303.

Columns 5 to 8 of Table VII repeat the analyses of Columns 1 to 4, but with the two-

quarter lags of ambiguity and risk. Again the results are qualitatively similar and both

ambiguity and risk have meaningful effects on dividend payout ratios.

[Table VII]

V.B Ambiguity shocks

We next explore how shocks to firm-level ambiguity and risk affect future dividend payout

decisions. Table VIII reports the related findings. The dependent variable is the forward

four-quarter change in the natural log of one plus common cash dividends, which allows

ample time for managers to adapt payout policy to shocks to ambiguity and risk. We use

the natural log of dividend levels, rather than dividend payout ratios, to focus on changes in

dividend levels in isolation of changes in net income. This removes concerns that the results

are due to changes in net income, rather than explicit changes in payout policy. As our main

independent variables, we consider lagged one- to four-quarter changes in ambiguity and

risk. To focus on firms with meaningful changes in dividend payout, we limit our analysis to

firm-quarters that are dividend payers, although firms may decrease or omit dividends over

the following four quarters. The results are qualitatively similar if we do not restrict these

29

tests to firm-quarters that are dividend payers. We directly address dividend initiation and

omission decisions with survival models in Table IX. Table I shows that 0.289 of 208,837

firm-quarters are dividend payers. Requiring forward four-quarter changes in dividends and

lagged three-quarter and four-quarter changes in ambiguity and risk further reduces the

sample. All regressions are Fama and MacBeth (1973) regressions with quarterly first-stage

ordinary least squares regressions. Standard errors use the Newey and West (1987) correction

for serial correlation out to eight lags.

Column 1 of Table VIII relates future four-quarter log changes in dividend levels to

lagged four-quarter changes in ambiguity and risk. Changes of both ambiguity and risk enter

Column 1 with the expected signs, consistent with the results above. The 1.860 coefficient

of the one-quarter change in ambiguity suggests that a one unit rise in ambiguity relates to

a 186.0 % rise in dividend payout. In the sample of dividend payers with sufficient leads,

the interquartile range of one-quarter changes in ambiguity is 0.105 (not reported in tables),

implying that the interquartile rise in ambiguity changes leads to a 1.95 % dividend increase.

This effect is of the same order of magnitude as changes in risk. The interquartile range of

one-quarter changes in risk is 0.00597 (not reported in tables), implying a −1.05 % dividend

change. Both of these changes are sizable relative to in interquartile range of forward four-

quarter change in dividends of 10.7 % (not reported in tables).

Column 2 of Table VIII repeats the changes analysis including the standard predictors.

The findings are similar. Columns 3 to 8 repeat the analyses in Columns 1 and 2 with

lagged two-, three-, and four-quarter changes in ambiguity and risk. The findings confirm

our results in changes as well as levels.

[Table VIII]

30

V.C Survival analysis

Our next extension is a survival analysis of time to first dividend initiation and omission.

We conjecture that firms with high risk tend to more slowly initiate and more quickly omit

dividends, and that firms with high ambiguity tend to more quickly initiate and more slowly

omit dividends. Table IX presents a Cox proportional hazard survival model to test this

conjecture.28 Columns 1 and 2 test time to first dividend initiation, and Columns 3 and 4

test time to first dividend omission. All regression tests include year fixed effects and cluster

standard errors by industry.

Column 1 of Table IX presents a survival model using the one-quarter lags of ambiguity

and risk, again to mitigate concerns of reverse causality, and the standard predictors. The

risk coefficient of −1.758 is smaller in magnitude than the ambiguity coefficient of 11.14. In

the sample of not-yet dividend payers, the interquartile range of the one-quarter lag of risk

is 0.00898, which leads to an odds ratio of 0.984, indicating that an interquartile rise in the

one-quarter lag of risk leads to a 1.57 % decrease in the odds of first dividend initiation. The

interquartile range of the one-quarter lag of ambiguity is 0.0295, which leads to an odds ratio

of 1.39, or a 38.9 % rise in the odds of first dividend initiation. For a frame of reference, in

this sample, the interquartile range of Return on Assets is 0.0654, which leads to a 30.3 % rise

in the odds of first dividend initiation. Column 2 repeats this analysis with the two-quarter

lags of ambiguity and risk, and finds qualitatively similar results, although the one-quarter

lag of risk is no longer statistically significant.

Columns 3 and 4 of Table IX repeat the analysis for first dividend omissions rather than

first dividend initiations. The results are consistent with our results throughout. Firms

with higher risk are quicker to omit a dividend and firms with higher ambiguity are slower

to a omit a dividend. For the dividend omission analysis, the ambiguity coefficients are

larger than their dividend initiation analysis counterparts and the risk coefficients are now

28Our results are qualitatively similar if we instead use exponential or Weibull hazard models.

31

significantly positive. For the sample of dividend payers that have not yet omitted, the

interquartile range of the one-quarter lag of ambiguity is nominally the same as the whole

sample at 0.0295. With a coefficient of −20.5, an interquartile rise in the one-quarter lag

of ambiguity has an odds ratio of 0.546, which is similar to the magnitude of the ambiguity

effect on first dividend initiation. This is also of similar order of magnitude of the effect

of the one-quarter lag of risk. For the one-quarter lag of risk, the interquartile range is

0.00898, resulting in an odds ratio of 1.08. The results in Column 4 for the two-quarter lags

of ambiguity and risk are similar in statistical and economic significance.

In all, the survival model results provide additional support to Hypotheses 1 and 2, and

show that our results hold in both the cross section and time series.

[Table IX]

V.D Alternative explanatory measures

Our analysis so far focuses on ambiguity, risk, and the standard predictors that Fama and

French (2001) and DeAngelo et al. (2006) show are the fundamental determinants of div-

idend payout policy. However, there could be alternative explanations for our findings of

a positive relation between ambiguity and dividend payout policy. First, it could be that

ambiguity proxies other uncertainty or market-microstructure measures. These other uncer-

tainty measures include the volatility of the mean returns, the volatility of the volatility of

returns, bid-ask spread, analyst dispersion, and product market fluidity. Since the bid-ask

spread also proxies liquidity, we also add Amihud’s (2002) illiquidity measure. Second, it

could be that ambiguity proxies other determinants of dividend payout policy that Fama

and French (2001) and DeAngelo et al. (2006) do not address.

These other dividend payout policy determinants include free cash flows (Jensen, 1986),

agency costs (Easterbrook, 1984), dividend clienteles (Allen et al., 2000; Becker et al., 2011),

and stock liquidity (Banerjee et al., 2007). Table X tests whether ambiguity proxies for the

32

first set of alternative uncertainty or market-microstructure measures. Figure 3 tests for the

second set of alternative explanations with dependent portfolio sorts rather than regression

tests. We use this approach because several of these dividend payout policy determinants

are more likely to be ordinal than cardinal.

To test for the first set of alternative explanations, Table X presents Fama and Mac-

Beth (1973) regressions of the propensity to pay dividends with first-stage quarterly logit

regressions and second-stage Newey and West (1987) time-series standard errors adjusted for

serial correlation to eights quarterly lags. These tests in Table X mirror those in Table IV.

Columns 1 to 6 in Table X add the alternative uncertainty and market-microstructure mea-

sures one at a time, and Column 7 includes all alternative measures together. We draw

two major conclusions from these results. First, across all seven columns, the economic and

statistical significance of the one-quarter lags of both ambiguity and risk are the same as

without the alternative measures (i.e., the same as in Column 4 of Table IV). The coeffi-

cient on the one-quarter lag of ambiguity is notably stable and explains a unique aspect of

dividend payout policy that is not explained by any of the alternative measures. Second,

when including the exception of product market fluidity, most of the alternative measures are

either not statistically significant or not stable. The most promising alternative measure is

Analyst Dispersion, however its availability significantly limits the samples in Columns 5 and

7 and its economic significance is small with an interquartile range of 0.00657, which implies

an odds ratio of only exp(2.413× 0.00657) = 1.02. In all, the tests in Table X indicate that

the relation between ambiguity, risk, and dividend payout policy are robust to alternative

measures of uncertainty and controls for market microstructure. Untabulated results with

dividend payout ratio tests that mirror those in Table VII are qualitatively similar.

[Table X]

To test for the second set of alternative explanations, Figure 3 replicates Panel A of

Figure 1 with proxies for each alternative dividend payout policy determinant to show that

33

the effect of ambiguity is unique. Each year, first we sort observations into quintiles on

each of these alternative explanatory variables, then we sort into ambiguity quintiles within

each alternative explanatory variable-year quintile and plot the fraction of firms that pay

dividends. To address Jensen’s (1986) free cash flow hypothesis, Panel A of Figure 3 sorts

first on operating cash flow, then on ambiguity. To address Easterbrook’s (1984) agency

cost hypothesis, Panel B sorts first on the Entrenchment Index (Bebchuk et al., 2009), then

on ambiguity. The Entrenchment Index is just one of many firm-level governance proxies,

so Panel C sorts first on fraction of institutional ownership, then on ambiguity. To the

extent that institutional owners form a dividend clientele (Allen et al., 2000), Panel C also

addresses dividend clientele concerns. Finally, to further address liquidity concerns, Panel D

sorts first on effective bid-ask spreads, Panel E sorts first on Amihud’s (2002) illiquidity, and

Panel F sorts first on market value of equity. In all cases, the fraction of dividend payers

monotonically increases in ambiguity, even after controlling for the alternative dividend

payout policy determinants. Further, in all cases the variation in dividend payout policy

explained by ambiguity is at least as large as the variation explained by the alternative

determinants. In figures not shown, the results are qualitatively similar with dividend payout

ratios instead of dividend payers, as well as the remaining alternative uncertainty and market-

microstructure variables in Table X.

[Figure 3]

VI Conclusion

This paper studies the importance of ambiguity—Knightian uncertainty—in decisions about

dividend payout policy. The impact of risk on the dividend payout has motivated sev-

eral prior studies. Our contribution involves the introduction of a second dimension of

uncertainty—ambiguity—alongside the traditional measure of volatility. Consistent with

34

previous studies, we find that the propensity to pay or to initiate a dividend decreases in

firm-level risk, as does the level of dividend payout. Moreover, risk delays dividend initiations

and accelerates dividend omissions.

Conversely, we find that the propensity to pay dividends and the level of dividend payout

increase in ambiguity. As well, ambiguity accelerates dividend initiation and delays dividend

omission. The attractiveness of available investment opportunities can explain these findings.

The attractiveness of investment opportunities potentially increases in risk, leaving less capi-

tal for dividend distribution. In contrast, ambiguity causes firms and investors to overweight

the likelihoods of bad outcomes and underweight the likelihoods of good outcomes, which

decreases the attractiveness of investment opportunities and accelerates dividend payout.

35

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39

0 .2 .4 .6 .8Mean of Dividend Payer for Portfolio

Risk Q5

Risk Q4

Risk Q3

Risk Q2

Risk Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

Panel A: Dependent sorts on risk, then ambiguity

0 .2 .4 .6 .8Mean of Dividend Payer for Portfolio

Ambiguity Q5

Ambiguity Q4

Ambiguity Q3

Ambiguity Q2

Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Risk Q1

... Q5

... Q4

... Q3

... Q2Risk Q1

... Q5

... Q4

... Q3

... Q2Risk Q1

... Q5

... Q4

... Q3

... Q2Risk Q1

... Q5

... Q4

... Q3

... Q2Risk Q1

Panel B: Dependent sorts on ambiguity, then risk

Figure 1: Fraction of dividend payersThis figure plots the fraction of dividend payers by portfolios based on dependent sorts on ambiguityand risk. Portfolios are based on quintiles formed each year. Sample is Quarterly CRSP-CompustatMerged from 1993 to 2016. Dividend Payer is an indicator variable for firms that pay a dividend in aquarter. Dividends are common cash dividends from Compustat. Ambiguity and Risk follow Izhakianand Yermack (2017).

40

.2.2

5.3

.35

1995q1 2000q1 2005q1 2010q1 2015q1Quarter

Absolute Error from Standard Predictors

Absolute Error from Standard Predictors plus Ambiguity

Panel A: Absolute errors from regressions with stan-dard predictors versus absolute errors from regres-sions with standard predictors plus ambiguity.

.2.2

5.3

.35

1995q1 2000q1 2005q1 2010q1 2015q1Quarter

Absolute Error from Standard Predictors plus Risk

Absolute Error from Standard Predictors plus Ambiguity and Risk

Panel B: Absolute errors from regressions with stan-dard predictors plus risk versus absolute errors fromregressions with standard predictors plus ambiguityand risk.

.1.1

2.1

4.1

6.1

8

1995q1 2000q1 2005q1 2010q1 2015q1Quarter

Squared Error from Standard Predictors

Squared Error from Standard Predictors plus Ambiguity

Panel C: Squared errors from regressions with stan-dard predictors versus squared errors from regres-sions with standard predictors plus ambiguity.

.1.1

2.1

4.1

6

1995q1 2000q1 2005q1 2010q1 2015q1Quarter

Squared Error from Standard Predictors plus Risk

Squared Error from Standard Predictors plus Ambiguity and Risk

Panel D: Squared errors from regressions with stan-dard predictors plus risk versus squared errors fromregressions with standard predictors plus ambiguityand risk.

Figure 2: Errors from propensity to pay dividends regressionsThis figure plots the quarterly means of errors from propensity to pay dividends regressions. Propensityto pay dividends regressions are quarterly logit regressions, where the dependent variable is a dividendpayer indicator variable and coefficients are estimated in the preceding quarter. All regressions include thestandard predictors. Panels A and B plot the quarterly means of absolute errors. Panels C and D plot thequarterly means of squared errors. Sample is Quarterly CRSP-Compustat Merged from 1993 to 2016. Thestandard predictors are asset growth rate, market/book, return on assets, natural log of market equity,and retained earnings/book equity. Ambiguity and Risk follow Izhakian and Yermack (2017). Ambiguity,risk, and all non-payout ratios are winsorized at 5 % in each tail.

41

0 .2 .4 .6 .8Mean of Dividend Payer for Portfolio

OCF Q5

OCF Q4

OCF Q3

OCF Q2

OCF Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

Panel A: Dependent sorts on op-erating cash flow, then ambiguity

0 .2 .4 .6 .8Mean of Dividend Payer for Portfolio

E Index=5

E Index=4

E Index=3

E Index=2

E Index=1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

Panel B: Dependent sorts on En-trenchment Index, then ambigu-ity

0 .2 .4 .6 .8Mean of Dividend Payer for Portfolio

IO Q5

IO Q4

IO Q3

IO Q2

IO Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

Panel C: Dependent sorts onfraction of institutional owners,then ambiguity

0 .2 .4 .6 .8Mean of Dividend Payer for Portfolio

Spread Q5

Spread Q4

Spread Q3

Spread Q2

Spread Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

Panel D: Dependent sorts on bid-ask spreads, then ambiguity

0 .2 .4 .6 .8Mean of Dividend Payer for Portfolio

Illiquidity Q5

Illiquidity Q4

Illiquidity Q3

Illiquidity Q2

Illiquidity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

Panel E: Dependent sorts on illiq-uidity, then ambiguity

0 .2 .4 .6 .8Mean of Dividend Payer for Portfolio

Market Equity Q5

Market Equity Q4

Market Equity Q3

Market Equity Q2

Market Equity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

... Q5

... Q4

... Q3

... Q2Ambiguity Q1

Panel F: Dependent sorts onmarket value of equity, then am-biguity

Figure 3: Alternative dividend payout policy determinantsThis figure plots the fraction of dividend payers by portfolios based on dependent sorts on alternative divi-dend payout policy determinants, then ambiguity. Portfolios are based on quintiles formed each year. Sam-ple is Quarterly CRSP-Compustat Merged from 1993 to 2016. Dividend Payer is an indicator variable forfirms that pay a dividend in a quarter. Dividends are common cash dividends from Compustat. Ambigu-ity follows Izhakian and Yermack (2017). Operating Cash Flow is operating income before depreciationminus taxes plus depreciation minus interest minus change in net working capital. Entrenchment Indexfollows Bebchuk et al. (2009). Institutional Ownership is fraction of equity owned by filers of SEC Form13F. Bid-Ask Spread is effective bid-ask spread. Amihud Illiquidity follows Amihud (2002). MarketEquity is quarter closing share price times shares outstanding (millions U.S. Dollars).

42

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0.4

67

0.2

31

12.7

48

0.0

00

0.0

00

0.0

00

Rep

urc

has

er0.

693

1.0

00

0.4

61

0.7

94

1.0

00

0.4

04

0.6

52

1.0

00

0.4

76

Rep

urc

has

es/N

etIn

com

e0.

135

0.0

00

80.4

59

0.3

52

0.0

00

23.0

16

0.0

47

0.0

00

94.2

98

Ass

etG

row

thR

ate

0.00

80.0

09

0.0

83

0.0

12

0.0

10

0.0

63

0.0

06

0.0

07

0.0

90

Mar

ket/

Book

2.20

01.6

90

1.3

96

1.9

31

1.6

01

1.0

51

2.3

09

1.7

45

1.5

01

Ret

urn

onA

sset

s0.

013

0.0

27

0.0

55

0.0

36

0.0

37

0.0

29

0.0

03

0.0

21

0.0

60

log(

Mar

ket

Equ

ity)

6.19

66.1

19

1.9

11

7.4

73

7.3

83

1.8

25

5.6

76

5.6

44

1.6

88

Ret

ain

edE

arn

ings

/Book

Equ

ity

-0.6

570.2

34

2.5

70

0.4

70

0.7

11

1.3

64

-1.1

16

-0.0

06

2.7

94

Cap

ital

Exp

end

itu

res/

Ass

ets

0.01

30.0

08

0.0

14

0.0

14

0.0

10

0.0

13

0.0

13

0.0

08

0.0

14

R&

D/A

sset

s0.

016

0.0

00

0.0

25

0.0

05

0.0

00

0.0

12

0.0

20

0.0

05

0.0

28

Ob

serv

atio

ns

208,

837

60,3

96

148,4

41

43

Tab

leII

:C

orre

lati

ons

Sam

ple

isQ

uar

terl

yCRSP-C

ompustatMerged

from

1993

to20

16.

Am

big

uit

yan

dR

isk

foll

owIz

hakia

nan

dY

erm

ack

(2017).

Div

iden

dP

ayer

isan

ind

icat

orva

riab

lefo

rfi

rms

that

pay

ad

ivid

end

ina

qu

arte

r.D

ivid

end

s/N

etIn

com

eis

div

iden

ds

div

ided

by

net

inco

me.

Div

-id

end

sar

eco

mm

onca

shd

ivid

end

sfr

omCompustat.

Rep

urc

has

eris

anin

dic

ator

vari

able

for

firm

sth

at

(net

)re

pu

rchase

share

sin

aqu

arte

ror

any

ofth

ep

rece

din

gei

ght

qu

arte

rs.

Rep

urc

has

es/N

etIn

com

eis

rep

urc

has

esd

ivid

edby

net

inco

me.

Rep

urc

hase

sare

posi

tive

chan

ges

intr

easu

ryst

ock

,if

firm

use

str

easu

ryst

ock

met

hod

,ot

her

wis

ep

osit

ive

por

tion

ofre

pu

rch

ase

sm

inu

sis

sues

.A

sset

Gro

wth

Rat

eis

chan

gein

book

valu

eof

tota

las

sets

div

ided

by

book

valu

eof

tota

las

sets

.M

arke

t/B

ook

isto

tal

ass

ets

min

us

book

valu

eof

equ

ity

plu

sm

arke

tva

lue

ofeq

uit

y,al

ld

ivid

edby

tota

las

sets

.R

etu

rnon

Ass

ets

isop

erat

ing

inco

me

bef

ore

dep

reci

ati

on

div

ided

by

tota

las

sets

.M

arke

tE

qu

ity

isqu

arte

rcl

osin

gsh

are

pri

ceti

mes

shar

esou

tsta

nd

ing

(mil

lion

sU

.S.

Dol

lars

).R

etain

edE

arn

ings/

Book

Equ

ity

isra

tio

ofre

tain

edea

rnin

gsto

book

equ

ity.

Cap

ital

Exp

end

itu

res/

Ass

ets

isca

pit

alex

pen

dit

ure

sd

ivid

edby

tota

lass

ets.

R&

D/A

sset

sis

rese

arch

and

dev

elop

men

td

ivid

edby

tota

las

sets

(mis

sin

gR

&D

rep

lace

dw

ith

zero

).A

mb

igu

ity,

risk

,an

dall

non

-pay

ou

tra

tios

are

win

sori

zed

at5

%in

each

tail

.

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(1)

On

e-qu

arte

rla

gof

Am

big

uit

y1.

00(2

)O

ne-

qu

arte

rla

gof

Ris

k-0

.43

1.0

0(3

)D

ivid

end

Pay

er0.

41-0

.27

1.0

0(4

)D

ivid

end

s/N

etIn

com

e0.

01-0

.01

0.0

31.0

0(5

)R

epu

rch

aser

0.15

-0.0

50.1

40.0

01.0

0(6

)R

epu

rch

ases

/Net

Inco

me

0.00

-0.0

00.0

00.0

50.0

01.0

0(7

)A

sset

Gro

wth

Rat

e0.

07-0

.14

0.0

3-0

.00

0.0

00.0

01.0

0(8

)M

arke

t/B

ook

-0.0

50.0

6-0

.12

-0.0

0-0

.06

0.0

00.0

91.0

0(9

)R

etu

rnon

Ass

ets

0.33

-0.3

20.2

80.0

10.1

30.0

00.3

7-0

.17

1.0

0(1

0)lo

g(M

arke

tE

qu

ity)

0.67

-0.4

00.4

30.0

10.1

60.0

00.2

10.1

30.4

41.0

0(1

1)R

etai

ned

Ear

nin

gs/B

ook

Equ

ity

0.29

-0.2

50.2

80.0

10.1

40.0

00.2

0-0

.18

0.5

40.3

91.0

0(1

2)C

apit

alE

xp

end

itu

res/

Ass

ets

-0.0

2-0

.04

0.0

40.0

00.0

20.0

00.1

40.0

40.1

90.1

10.1

31.0

0(1

3)R

&D

/Ass

ets

-0.2

40.2

0-0

.27

-0.0

1-0

.12

-0.0

0-0

.20

0.4

0-0

.59

-0.2

3-0

.46

-0.1

81.0

0

Ob

serv

atio

ns

208,

837

44

Table III: Choice of payout method

This table presents multinomial logit regressions of payout choice. The base category is observations thatare neither a repurchaser nor a dividend payer. Repurchaser Only is a repurchaser, but not a dividendpayer. Dividend Payer may also be a repurchaser. Sample is Quarterly CRSP-Compustat Merged from1993 to 2016. Dividend Payer is an indicator variable for firms that pay a dividend in a quarter. Dividendsare common cash dividends from Compustat. Repurchaser is an indicator variable for firms that (net)repurchase shares in a quarter or any of the preceding eight quarters. Repurchases are positive changesin treasury stock, if firm uses treasury stock method, otherwise positive portion of repurchases minusissues. Ambiguity and Risk follow Izhakian and Yermack (2017). Asset Growth Rate is change in bookvalue of total assets divided by book value of total assets. Market/Book is total assets minus book valueof equity plus market value of equity, all divided by total assets. Return on Assets is operating incomebefore depreciation divided by total assets. Market Equity is quarter closing share price times sharesoutstanding (millions U.S. Dollars). Retained Earnings/Book Equity is ratio of retained earnings to bookequity. Ambiguity, risk, and all non-payout ratios are winsorized at 5 % in each tail. Standard errors areclustered by industry based on two-digit SIC Code.

(1) (2)Payout Method Payout Method

Repurchaser Only Dividend Payer Repurchaser Only Dividend Payer

One-quarter lag of 18.11∗∗∗ 61.89∗∗∗ 11.65∗∗∗ 29.96∗∗∗

Ambiguity (11.38) (23.19) (6.73) (7.55)

One-quarter lag of -0.668 -28.17∗∗∗ 0.611 -16.37∗∗∗

Risk (-1.93) (-12.24) (1.57) (-7.91)

Asset Growth Rate -0.689∗∗∗ -3.344∗∗∗

(-5.95) (-22.14)

Market/Book -0.0782∗∗∗ -0.396∗∗∗

(-6.24) (-8.68)

Return on Assets 1.001 7.713∗∗∗

(1.81) (6.59)

log(Market Equity) 0.0470 0.371∗∗∗

(1.91) (7.37)

Retained 0.0411∗∗∗ 0.261∗∗∗

Earnings/Book Equity (14.56) (6.39)

Year Fixed Effects Yes Yes Yes Yes

Observations 208,837 208,837Pseudo R2 0.124 0.162

t statistics in parentheses∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

45

Table IV: Propensity to pay dividends

This table presents Fama and MacBeth (1973) regressions with quarterly first-stage logit regressions, wherethe dependent variables are dividend payer indicators. Sample is Quarterly CRSP-Compustat Merged from1993 to 2016. Dividend Payer is an indicator variable for firms that pay a dividend in a quarter. Div-idends are common cash dividends from Compustat. Ambiguity and Risk follow Izhakian and Yermack(2017). Asset Growth Rate is change in book value of total assets divided by book value of total as-sets. Market/Book is total assets minus book value of equity plus market value of equity, all divided bytotal assets. Return on Assets is operating income before depreciation divided by total assets. MarketEquity is quarter closing share price times shares outstanding (millions U.S. Dollars). Retained Earn-ings/Book Equity is ratio of retained earnings to book equity. Ambiguity, risk, and all non-payout ratiosare winsorized at 5 % in each tail. Standard errors use Newey and West (1987) correction for serialcorrelation to eight quarterly lags.

Dividend Payer

(1) (2) (3) (4) (5) (6) (7) (8)

One-quarter lag of 71.67∗∗∗ 55.96∗∗∗ 30.56∗∗∗

Ambiguity (12.70) (12.02) (4.95)

One-quarter lag of -83.05∗∗∗ -41.11∗∗∗ -27.20∗∗∗

Risk (-10.75) (-7.15) (-7.47)

Two-quarter lag of 73.40∗∗∗ 57.10∗∗∗ 31.88∗∗∗

Ambiguity (12.54) (12.13) (5.17)

Two-quarter lag of -82.78∗∗∗ -40.81∗∗∗ -27.26∗∗∗

Risk (-10.96) (-7.30) (-7.92)

Asset Growth Rate -2.563∗∗∗ -2.506∗∗∗

(-14.57) (-13.96)

Market/Book -0.324∗∗∗ -0.316∗∗∗

(-12.61) (-12.46)

Return on Assets 6.568∗∗∗ 6.650∗∗∗

(6.83) (7.09)

log(Market Equity) 0.306∗∗∗ 0.297∗∗∗

(9.56) (9.03)

Retained 0.231∗∗∗ 0.227∗∗∗

Earnings/Book Equity (7.75) (8.02)

Observations 208,837 208,837 208,837 208,837 208,837 208,837 208,837 208,837Average Pseudo R2 0.181 0.165 0.230 0.288 0.186 0.167 0.234 0.289

t statistics in parentheses∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

46

Table V: Errors from propensity to pay dividends regressions

This table presents the means of quarterly means of errors from propensity to pay dividends regressions andpaired t-tests of differences. Panel A reports means of quarterly means of absolute errors. Panel B reportsmeans of quarterly means of squared errors. Sample is Quarterly CRSP-Compustat Merged from 1993 to2016. Errors are residuals from propensity to pay dividends regressions. Propensity to pay dividendsregressions are quarterly logit regressions, where the dependent variable is a dividend payer indicatorvariable and coefficients are estimated in the preceding quarter. All regressions include the standardpredictors. The standard predictors are asset growth rate, market/book, return on assets, natural log ofmarket equity, and retained earnings/book equity. Dividend Payer is an indicator variable for firms thatpay a dividend in a quarter. Dividends are common cash dividends from Compustat. Ambiguity andRisk follow Izhakian and Yermack (2017). Ambiguity, risk, and all non-payout ratios are winsorized at5 % in each tail.

Panel A: Means of quarterly means of absolute errors

(1) (2) (3) (4) (5) (6)

StandardPredictors

StandardPredictors

plusAmbiguity

StandardPredictors

plusRisk

StandardPredictors

plusAmbiguity

andRisk

(2) minus (1) (4) minus (3)

Absolute Error 0.291∗∗∗ 0.281∗∗∗ 0.281∗∗∗ 0.276∗∗∗ 0.0102∗∗∗ 0.00499∗∗∗

(91.23) (75.67) (77.89) (69.64) (14.26) (10.85)

Quarters 93 93 93 93 93 93Quarterswith Improvement 93 91

t statistics in parentheses∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

Panel B: Means of quarterly means of squared errors

(1) (2) (3) (4) (5) (6)

StandardPredictors

StandardPredictors

plusAmbiguity

StandardPredictors

plusRisk

StandardPredictors

plusAmbiguity

andRisk

(2) minus (1) (4) minus (3)

Squared Error 0.143∗∗∗ 0.139∗∗∗ 0.137∗∗∗ 0.136∗∗∗ 0.00435∗∗∗ 0.00142∗∗∗

(86.95) (74.61) (72.59) (68.01) (14.27) (9.33)

Quarters 93 93 93 93 93 93Quarterswith Improvement 91 85

t statistics in parentheses∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

47

Table VI: Dividend initiation announcements

This table presents event studies of first dividend initiation announcements. Cumulative abnormal returns(CARs) are centered on dividend declaration announcements, which are the firms’ first in CRSP. Mar-ket adjusted returns and market model returns use a value-weighted CRSP index. Five- and seven-dayCARs are (-2,+2) and (-3,+3), respectively. Sample is Quarterly CRSP-Compustat Merged from 1993to 2016. Ambiguity and Risk follow Izhakian and Yermack (2017). Propensity to Pay is predicted prob-ability from quarterly logit regressions with the standard predictors, where the dependent variable is adividend payer indicator variable and coefficients are estimated in the preceding quarter. The standardpredictors are asset growth rate, market/book, return on assets, natural log of market equity, and retainedearnings/book equity. Dividend Payer is an indicator variable for firms that pay a dividend in a quar-ter. Dividends are common cash dividends from Compustat. Ambiguity, risk, and all non-payout ratiosare winsorized at 5 % in each tail. Propensity to Pay and Ambiguity are at least 90 days before dividendinitiation announcement date.

Market Adjusted Returns Market Model Returns

(1) (2) (3) (4)(-2,+2) CAR (-3,+3) CAR (-2,+2) CAR (-3,+3) CAR

One-quarter lag of -0.810 -0.938 -0.766 -0.736Ambiguity (-1.91) (-1.91) (-1.83) (-1.55)

Propensity to Pay -0.142∗∗∗ -0.149∗∗ -0.147∗∗∗ -0.148∗∗

(-3.46) (-3.09) (-3.62) (-3.13)

One-quarter lag of 2.178∗ 2.480∗ 2.228∗∗ 2.334∗

Ambiguity × Propensity to Pay (2.54) (2.47) (2.65) (2.43)

Constant 0.0672∗∗∗ 0.0699∗∗∗ 0.0637∗∗∗ 0.0606∗∗

(3.80) (3.36) (3.64) (2.98)

Observations 452 452 452 452R2 0.036 0.028 0.037 0.027

t statistics in parentheses∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

48

Table VII: Dividend payout ratios

This table presents Fama and MacBeth (1973) regressions with quarterly first-stage Tobit regressions,where the dependent variables are dividend payout ratios censored on [0, 1]. Sample is Quarterly CRSP-Compustat Merged from 1993 to 2016. Dividend Payer is an indicator variable for firms that pay adividend in a quarter. Dividends are common cash dividends from Compustat. Ambiguity and Riskfollow Izhakian and Yermack (2017). Asset Growth Rate is change in book value of total assets dividedby book value of total assets. Market/Book is total assets minus book value of equity plus market valueof equity, all divided by total assets. Return on Assets is operating income before depreciation dividedby total assets. Market Equity is quarter closing share price times shares outstanding (millions U.S.Dollars). Retained Earnings/Book Equity is ratio of retained earnings to book equity. Ambiguity, risk,and all non-payout ratios are winsorized at 5 % in each tail. Standard errors use Newey and West (1987)correction for serial correlation to eight quarterly lags.

Dividends/Net Income

(1) (2) (3) (4) (5) (6) (7) (8)

One-quarter lag of 21.75∗∗∗ 14.53∗∗∗ 6.663∗∗∗

Ambiguity (14.54) (13.47) (5.85)

One-quarter lag of -28.45∗∗∗ -15.28∗∗∗ -11.18∗∗∗

Risk (-9.94) (-8.20) (-7.02)

Two-quarter lag of 22.00∗∗∗ 14.80∗∗∗ 6.920∗∗∗

Ambiguity (14.04) (13.57) (6.02)

Two-quarter lag of -28.00∗∗∗ -14.82∗∗∗ -10.92∗∗∗

Risk (-9.71) (-8.00) (-7.09)

Asset Growth Rate -0.623∗∗∗ -0.601∗∗∗

(-8.02) (-7.55)

Market/Book -0.0852∗∗∗ -0.0830∗∗∗

(-14.22) (-14.63)

Return on Assets 5.003∗∗∗ 5.036∗∗∗

(8.74) (8.88)

log(Market Equity) 0.0585∗∗∗ 0.0570∗∗∗

(8.93) (8.44)

Retained 0.0929∗∗∗ 0.0921∗∗∗

Earnings/Book Equity (11.35) (11.62)

Observations 208,837 208,837 208,837 208,837 208,837 208,837 208,837 208,837Average Pseudo R2 0.174 0.178 0.231 0.297 0.176 0.177 0.230 0.297

t statistics in parentheses∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

49

Table VIII: Dividend changes

This table presents Fama and MacBeth (1973) regressions with quarterly first-stage ordinary least squaresregressions, where the dependent variables are forward four-quarter log changes in dividends. Sample isQuarterly CRSP-Compustat Merged from 1993 to 2016. This sample includes only firms that pay dividendsat the start of the four-quarter change period, but allows firms to decrease or omit dividends. Dividends arecommon cash dividends from Compustat. Ambiguity and Risk follow Izhakian and Yermack (2017). AssetGrowth Rate is change in book value of total assets divided by book value of total assets. Market/Book istotal assets minus book value of equity plus market value of equity, all divided by total assets. Return onAssets is operating income before depreciation divided by total assets. Market Equity is quarter closingshare price times shares outstanding (millions U.S. Dollars). Retained Earnings/Book Equity is ratio ofretained earnings to book equity. Ambiguity, risk, and all non-payout ratios are winsorized at 5 % in eachtail. Standard errors use Newey and West (1987) correction for serial correlation to eight quarterly lags.

50

Forward Four-quarter Change in log(1 + Dividends)

(1) (2) (3) (4) (5) (6) (7) (8)

One-quarter change 1.860∗∗∗ 1.695∗∗∗

of Ambiguity (4.05) (3.54)

One-quarter change -1.515∗∗∗ -1.343∗∗∗

of Risk (-3.43) (-3.42)

Two-quarter change 1.819∗∗∗ 1.663∗∗

of Ambiguity (3.51) (3.10)

Two-quarter change -0.992 -0.894of Risk (-1.46) (-1.77)

Three-quarter change 2.269∗∗∗ 2.009∗∗∗

of Ambiguity (3.72) (3.41)

Three-quarter change -1.926∗ -1.637∗∗

of Risk (-2.25) (-2.66)

Four-quarter change 2.293∗∗∗ 1.904∗∗

of Ambiguity (3.52) (2.99)

Four-quarter change -1.805∗ -1.641∗

of Risk (-2.00) (-2.47)

Asset Growth Rate 0.813∗∗∗ 0.807∗∗∗ 0.806∗∗∗ 0.804∗∗∗

(5.55) (5.51) (5.50) (5.24)

Market/Book 0.0135∗ 0.0130∗ 0.0123∗ 0.0128∗

(2.18) (2.12) (2.00) (2.06)

Return on Assets 1.426∗∗∗ 1.392∗∗∗ 1.460∗∗∗ 1.427∗∗∗

(7.83) (7.93) (7.91) (7.57)

log(Market Equity) 0.0134∗∗∗ 0.0149∗∗∗ 0.0145∗∗∗ 0.0143∗∗∗

(3.47) (3.55) (3.44) (3.57)

Retained 0.0143∗∗∗ 0.0141∗∗∗ 0.0152∗∗∗ 0.0154∗∗∗

Earnings/Book Equity (3.99) (4.00) (4.08) (4.22)

Observations 54,504 54,504 54,504 54,504 53,215 53,215 51,981 51,981Average R2 0.011 0.045 0.012 0.046 0.014 0.049 0.016 0.051

t statistics in parentheses∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

51

Table IX: Survival analysis

This table presents Cox proportional hazard regressions of first dividend initiation and omission. A firminitiates a dividend when it becomes a dividend payer after not being a dividend payer all of the precedingeight quarters. A firm omits a dividend when it stops being a dividend payer after being a dividend payerany of the preceding eight quarters. Dividend payers pay a strictly positive dividend in a quarter. Sampleis Quarterly CRSP-Compustat Merged from 1993 to 2016. Dividends are common cash dividends fromCompustat. Ambiguity and Risk follow Izhakian and Yermack (2017). Asset Growth Rate is change inbook value of total assets divided by book value of total assets. Market/Book is total assets minus bookvalue of equity plus market value of equity, all divided by total assets. Return on Assets is operatingincome before depreciation divided by total assets. Market Equity is quarter closing share price timesshares outstanding (millions U.S. Dollars). Retained Earnings/Book Equity is ratio of retained earningsto book equity. Ambiguity, risk, and all non-payout ratios are winsorized at 5 % in each tail. Standarderrors are clustered by industry based on two-digit SIC Code.

First Dividend Initiation First Dividend Omission

(1) (2) (3) (4)

One-quarter lag of 11.14∗∗ -20.49∗∗∗

Ambiguity (3.12) (-4.86)

One-quarter lag of -1.758 8.790∗∗∗

Risk (-1.80) (9.04)

Two-quarter lag of 10.82∗∗∗ -19.86∗∗∗

Ambiguity (3.80) (-4.48)

Two-quarter lag of -0.449 6.843∗∗∗

Risk (-0.41) (5.60)

Asset Growth Rate -0.706 -0.712 0.241 0.0365(-1.01) (-1.00) (0.48) (0.07)

Market/Book -0.00395 -0.00757 0.0360 0.0408(-0.10) (-0.21) (0.51) (0.60)

Return on Assets 4.051∗∗∗ 4.100∗∗∗ -6.356∗∗∗ -6.693∗∗∗

(3.87) (3.96) (-5.00) (-5.41)

log(Market Equity) 0.0315 0.0428 -0.220∗∗∗ -0.239∗∗∗

(0.68) (1.02) (-5.75) (-6.42)

Retained 0.0203 0.0216 -0.0505 -0.0500Earnings/Book Equity (1.69) (1.84) (-1.63) (-1.72)

Year Fixed Effects Yes Yes Yes Yes

Observations 116,338 116,338 35,352 35,352

t statistics in parentheses∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

52

Table X: Alternative uncertainty measures

This table presents Fama and MacBeth (1973) regressions with quarterly first-stage logit regressions,where the dependent variables are dividend payer indicators. Sample is Quarterly CRSP-CompustatMerged from 1993 to 2016. Dividend Payer is an indicator variable for firms that pay a dividend in aquarter. Dividends are common cash dividends from Compustat. Ambiguity and Risk follow Izhakianand Yermack (2017). Volatility of Mean is variance of daily return means (computed from 5-minutereturns) over the month. Volatility of Volatilty is variance of daily return variance (computed from 5-minute return) over the month. Bid-Ask Spread is effective bid-ask spread. Amihud Illiquidity followsAmihud (2002). Analyst Dispersion is variance among analyst stock-price forecasts. Product MarketFluidity follows Hoberg et al. (2014). Asset Growth Rate is change in book value of total assets dividedby book value of total assets. Market/Book is total assets minus book value of equity plus market valueof equity, all divided by total assets. Return on Assets is operating income before depreciation dividedby total assets. Market Equity is quarter closing share price times shares outstanding (millions U.S.Dollars). Retained Earnings/Book Equity is ratio of retained earnings to book equity. Ambiguity, risk,and all non-payout ratios are winsorized at 5 % in each tail. Standard errors use Newey and West (1987)correction for serial correlation to eight quarterly lags.

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Dividend Payer

(1) (2) (3) (4) (5) (6) (7)

One-quarter lag of 34.13∗∗∗ 32.87∗∗∗ 33.62∗∗∗ 33.00∗∗∗ 33.05∗∗∗ 28.15∗∗∗ 35.77∗∗∗

Ambiguity (5.25) (4.93) (5.80) (4.70) (4.05) (3.97) (3.48)

One-quarter lag of -27.43∗∗∗ -26.96∗∗∗ -26.12∗∗∗ -33.31∗∗∗ -41.88∗∗∗ -19.82∗∗∗ -33.35∗∗∗

Risk (-8.09) (-7.69) (-8.03) (-7.39) (-7.35) (-6.61) (-7.46)

One-quarter lag of 25.12∗∗ 66.16∗

Volatility of Mean (2.85) (2.63)

One-quarter lag of 106094.6∗∗ -387977.1∗

Volatility of Volatility (2.63) (-2.33)

Bid-Ask Spread 25.30∗∗ 7.972(2.67) (0.99)

Amihud Illiquidity 397.5∗∗∗ 199.3(5.82) (1.93)

Analyst Dispersion 2.413∗∗ 3.350∗∗∗

(2.92) (3.81)

Product Market -0.167∗∗∗ -0.180∗∗∗

Fluidity (-13.67) (-23.99)

Asset Growth Rate -2.543∗∗∗ -2.555∗∗∗ -2.522∗∗∗ -2.553∗∗∗ -2.875∗∗∗ -2.311∗∗∗ -2.482∗∗∗

(-14.60) (-14.54) (-14.19) (-14.09) (-10.62) (-9.97) (-6.70)

Market/Book -0.320∗∗∗ -0.321∗∗∗ -0.329∗∗∗ -0.323∗∗∗ -0.464∗∗∗ -0.236∗∗∗ -0.405∗∗∗

(-13.68) (-13.28) (-13.19) (-15.67) (-27.85) (-10.71) (-17.05)

Return on Assets 6.597∗∗∗ 6.569∗∗∗ 6.708∗∗∗ 6.746∗∗∗ 7.965∗∗∗ 3.610∗∗ 5.937∗∗∗

(6.63) (6.69) (6.64) (5.45) (6.94) (3.15) (4.46)

log(Market Equity) 0.299∗∗∗ 0.299∗∗∗ 0.338∗∗∗ 0.348∗∗∗ 0.379∗∗∗ 0.350∗∗∗ 0.461∗∗∗

(10.38) (10.64) (13.06) (11.30) (13.69) (17.28) (16.58)

Retained 0.227∗∗∗ 0.229∗∗∗ 0.228∗∗∗ 0.261∗∗∗ 0.483∗∗∗ 0.174∗∗∗ 0.356∗∗∗

Earnings/Book Equity (7.29) (7.45) (7.33) (6.61) (8.35) (5.70) (5.35)

Observations 208,837 208,837 208,817 183,660 105,321 154,297 75,538Average Pseudo R2 0.291 0.290 0.291 0.295 0.365 0.294 0.379

t statistics in parentheses∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

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