How often do managers withhold information?
December 1, 2015
Abstract
We estimate and test a model of voluntary disclosure in which a manager’s
information set is uncertain (Dye 1985; Jung and Kwon 1988). In this model, a
manager makes his disclosure decision to maximize the market price, but sometimes,
for exogenous reasons, he cannot or is not willing to disclose. We offer a flexible
framework to measure the prevalence of unobservable disclosure frictions and the
quality of managers’ private information. More broadly, the method can be used to
test for voluntary disclosure in datasets featuring an option to withhold. We also
develop theory-based tests for detecting whether a firm is reporting strategically.
At the firm level, we reject strategic reporting for between 1/3 to 2/3 of the sample
of firms. Finally, estimating the model with quarterly management guidance, we
document that firms face a disclosure friction between 30% to 46% of the time.
Conditional on not facing a friction, firms strategically withhold between 4.3% to
20.7% of the time. To aid policymakers, these estimates predict that the level
of voluntary forecasts will increase by 2.6% to 13.5% in a counter-factual world
without strategic information withholding.
Keywords: persuasion, voluntary, disclosure, structural estimation.
JEL Classification: D72, D82, D83, G20.
1
Introduction
Disclosure theory postulates that managers will reveal some of their private informa-
tion if they (i) may truthfully disclose information, (ii) choose to do so if it increases the
market price, but (iii) are subject to a disclosure friction that may prevent costless communication. The theory helps explain why information flows into the capital market even
before regulated accounting numbers are released (Ball and Brown 1968), why voluntary
disclosures account for a large portion of returns (Beyer, Cohen, Lys and Walther, 2010)
and provides a theoretical foundation for the role of mandatory disclosure rules (Coffee
1984; Porta, Lopez-de Silanes and Shleifer 2006).
Despite its wide appeal, the theory faces continued open challenges to its defining
assumption, namely, that observed disclosures are truly voluntary as predicted by the
theory or reflect legal obligations to report both good and bad news. For example, to
give two well-known empirical facts, Lev and Penman (1990) find that markets respond
negatively to withholding of earnings forecasts and Lang and Lundholm (2000) document
that managers release more positive voluntary disclosures prior to new capital issues. On
the other hand, other studies report that most disclosure are related to litigation concerns that might specifically target firms that report strategically (Skinner 1994; Francis,
Philbrick and Schipper 1994).1
One problem when trying to test disclosure theory is that it is extremely capable to
rationalize many features of the data. A disclosure friction is hard to observe empirically,
so a direct test of the theory is difficult. In models with uncertainty about a reporting
friction (Dye 1985; Jung and Kwon 1988), the friction must be assumed to be unobservable
to outsiders to prevent unraveling, thus a test that relies on a contemporaneous proxy
for the friction is incompatible with the theory.2 Indirect evidence about the theory is
1
We have only picked here two examples of an extensive empirical literature; see Beyer, Cohen, Lys
and Walther (2010) for a review of this literature.
2
Other voluntary disclosure theories share the same challenges. In the costly disclosure model of
Verrecchia (1983), the link between competitive disclosure costs and observable characteristics of an
industry is ambiguous (Wagenhofer 1990; Darrough 1993; Corona and Nan 2013; Cheynel and Ziv 2015).
1
elusive as well. If the frequency of disclosure frictions is low, the unraveling theorem of
Milgrom (1981) predicts that both good and bad news will be voluntarily disclosed and
can rationalize high levels of disclosure that occasionally feature bad news. Alternatively,
if frictions occur with high frequency, the theory can rationalize low levels of disclosure, so
that the frequency of disclosure, on its own, provides limited evidence about the theory.
In this paper, we develop an alternative structural approach to estimating and testing
the basic voluntary disclosure model from Dye (1985) and Jung and Kwon (1988). Such an
approach carries benefits and costs. On the benefit side, the approach allows us to recover
the decision problem solved by the managers and quantify the magnitude of the disclosure
friction, which by nature is unobserved and hence impossible to quantify in a model free
approach. We design an estimation procedure that relies on an unexploited implication
of disclosure theory: the frequency of disclosure and the type of news disclosed should be
connected: a situation in which bad news are disclosed should be symptomatic of (near-)
unraveling, implying that frictions are low and disclosure frequency is high. Together,
our estimation approach recovers, at the firm level, the probability of a disclosure friction
(between 30% to 46%), as well as the fraction of non-disclosures due to strategic motives
(4.3% to 20.7%). These estimates, while themselves interesting, also enable us to perform
counter-factual analysis of the potential impact of policies designed to reduce the incidence
of strategic information disclosure.3 In particular, our estimates suggest that the level
of voluntary forecast will increase by 4.3% to 13.5% in a counter-factual world without
strategic information disclosure and economically significant relative to the median firm’s
disclosure frequency of 48%.
On the cost side, the analysis requires some auxiliary assumptions that need not be
satisfied by all models in disclosure theory. We estimate only classes of models with uncertainty about a disclosure friction: these are models in which the manager sometimes
3
The only comparative exercise we are aware of that quantifies the effect of policy interventions on
information withholding is Jin, Luca and Martin (2015) which looks at how educational interventions to
receivers about senders’ strategies change the amount of unraveling in equilibrium.
2
does not disclose for exogenous reasons - as in Dye (1985) and Jung and Kwon (1988),
hereafter, DJK. Nevertheless, we also develop two generalizations of this model, which
involve 1) an exogenous probability of disclosure and 2) serially-correlated information
endowment (Einhorn and Ziv 2008). A second notable cost is that the relationships predicted by the theory are non-linear and, therefore, one cannot estimate the econometric
model by ordinary least-squares. To minimize complexity, we derive a simple closed-form
estimator of the friction and remain as close as possible to classic theoretical models.
Further, the methods used here are commonly-used and not intended as an econometric
contribution. Our hope is to remove any barriers to entry to using these methods in
empirical accounting research by offering a detailed step-by-step account of their implementation.
For our empirical application, we use quarterly management forecasts from US firms.
Having noted this, however, any voluntary disclosure setting for which we observe either
quantitative disclosure or market reactions is suitable for the method. We propose two
estimation methods that present different perspectives on the problem. First, we estimate
the model with the generalized method of moments (GMM) using for the estimation
several interpretable moments predicted by the theory. GMM is a robust and relatively
simple method, that delivers both estimates and a test statistic, the J test, which measures
the distance between the theoretical moments and the data. Second, we estimate the
model using maximum likelihood estimation (MLE); MLE can be interpreted as a special
case of moment estimation involving the set of moments corresponding to first-order
condition of the likelihood function. Asymptotically, MLE is the most efficient estimator
but, typically, at the cost of greater sensitivity to distributional assumptions.
In terms of ease of use, both GMM and MLE are very standard techniques and, as
we illustrate, one or the other can be simpler to implement depending on the desired
assumptions. Our GMM procedure is sufficiently robust to be used with pooled samples
(one set of parameters imposed on multiple firms) despite high levels of heterogeneity.
3
By contrast, our MLE procedure assumes a time-varying friction to capture stickiness
in forecasts. If frictions are sufficiently persistent, after a disclosure, the probability of a
disclosure friction in the next period is low and therefore the managers will be more likely
to disclose again. Further, given unfavorable realized earnings, the market will update
that the managers was (most likely) not subject to the friction, thus predicting more
disclosure in the next period.
Related literature. Our approach is closely related to a number of recent studies, which focus on the estimation of biases in reported earnings. Beyer, Guttman and
Marinovic (2014) estimate a dynamic misreporting model. In their model, the manager
can bias a mandatory report for a cost but the market cannot recover the true signal
because of noise in the accounting system (Fischer and Verrecchia, 2000; Dye and Sridhar, 2004). Both Zakolyukina (2014) and Terry (2014) estimate structural models where
agents consider the dynamic consequences of manipulation. Zakolyukina (2014) estimates
her model using observed accounting violations, recovering current choice of manipulation
as a trade-off between current benefits and an increase in the long-term probability of an
accounting restatement. Terry (2014) focuses on the effect of misreporting on firm’s dynamic investment policy, measuring that reporting incentives appear to cause significant
distortions to investment.
Two recent studies have examined properties of voluntary disclosure within a structural model. Cheynel and Liu-Watts (2015) and Bertomeu, Beyer and Taylor (2015)
estimate the implied disclosure cost in the classic Verrecchia (1983). Their primary focus, however, is not on the Dye-Jung-Kwon but it is possible that, as part of future efforts,
more general models may involve estimating and separating both types of friction.
Lastly, several studies focus on a structural model of reversals, that is over-reporting
of earnings must reverse when cash flows occur, to identify misreporting.
Two examples in this strand are Gerakos and Kovrijnykh (2013) and Nikolaev (2014).
The first paper shows that biases in reported earnings map into a second-order auto-
4
correlation in accruals. As we do, they apply their methodology to the cross-section
of firms to test for strategic manipulation. The second paper estimates a structural
model of reversals from its moment conditions to recover the link between manipulation
and observed reversals. In this prior literature, discretion takes the form of a bias to
earnings. By contrast, our study focuses on disclosures that are entirely voluntary. To
our knowledge, the only study that implements a test of an earnings forecast model is
Chen and Jiang (2006); however, they focus on how analysts weight information when
making forecasts.
There is also an extensive theoretical literature on voluntary disclosure drawing on the
original model of Dye (1985).4 One prediction in the case of multi-dimensional disclosures
is the use of sanitation strategies, in which all unfavorable information is withheld (Shin
1994, 2003); we did not examine such types of disclosures here for two reasons: first,
we cannot easily identify a multi-dimensional distribution of private signals and, second,
disclosures that take the form of a lower bound, as predicted by sanitation, are very rare.
Other studies predict that disclosure can interact with other features of the environment.
For example, in Indjejikian (1991), Huddart, Hughes and Brunnermeier (1999), Bertomeu,
Beyer and Dye (2011), the amount of information released is a function of the price
discovery in the market. Dye and Sridhar (1995) and Acharya, Demarzo and Kremer
(2011) show that, given correlation between firms’ information, firms’ disclosure can be
positively correlated to other firms’ disclosures. These extensions offer possible future
steps for the methods developed here.
The remainder of the paper is organized as follows. We describe in Section 2 the
modeling framework and estimation strategy. Section 3 reports the data and our main
GMM estimation results. Section 4 describes extensions to the basic framework and
4
There is also a large literature providing empirical evidence about management forecasts. This
approach can be much more comprehensive as to the factors that relate to forecasts, such as crosssectional differences in litigation risk (Brown, Hillegeist and Lo, 2005) or shocks to stock prices (Sletten,
2012). By contrast, our purpose here is to identify and measure one possible first-order, unobservable,
economic primitive of forecasts.
5
estimation results from MLE. Finally Section 5 concludes.
2
The empirical model
2.1
Method of moments
We follow the setting and notation of Dye (1985) and Jung and Kwon (1988), hereafter
DJK. For expositional purposes, we describe the analysis in the context of a single firm
making earnings forecasts, referring to a disclosure as a forecast and the realized number
as earnings. In this section, we derive theoretical moments, that is, restrictions on the
data implied by DJK that will allow us to estimate and test the model.
In each period t = 1, . . . , T , the manager has an expectation xt about end-of-period
earnings. There is a probability p0 ∈ (0, 1) that the manager faces a disclosure friction.
When facing the friction, the manager cannot or does not wish to disclose. For example,
in the original formulation of Dye (1985), this is motivated by assuming that the manager
does not receive information and cannot disclose that he is uninformed. However, other
motivations yield the same equation: for example, when subject to the friction, the manager may not care about the short-term stock price or, alternatively, may face prohibitive
disclosure costs.5
With probability 1 − p0 , the manager is not subject to the friction and may either
truthfully disclose a forecast (dt = 1) or withhold that information (dt = 0). Forecasts
are netted out of the market expectation (i.e., they are defined as forecast surprises) and
we assume that xt /σ follows a standard normal distribution with p.d.f φ(.) and c.d.f.
Φ(.) with σ > 0. In the absence of the friction, the manager discloses strategically
to maximize the post-disclosure market price, which we assume is linear in the market
5
For example, Edmans, Goncalves-Pinto, Wang and Xu (2014) show that, in months in which the
CEO has vesting equity, he releases more news. This attracts attention to the stock increasing trading
volume, which allows the CEO to cash out his equity in a more liquid market. Indeed, they find that
these news releases lead to significant increases in the stock price and trading volume in a 16-day window,
but the effect dies down over 31 days, consistent with a temporary attention boost.
6
expectation about xt .6
In the unique equilibrium of this game, managers with xt ≥ y0 disclose, where a
manager observing y0 is indifferent between disclosing and not disclosing. From Equation
(7) in Jung and Kwon (1988), specialized to normal distributions, the threshold satisfies
p
(y0 /σ) =
−
1−p
Z
y0 /σ
Φ(x)dx,
(1)
−∞
and we can define z0 = y0 /σ is the standardized threshold.
Equation (19) defines an implicit relation z0 = Z(p0 ) that maps the probability of any
friction to a standardized disclosure threshold. The function Z(.) is increasing, because
a higher probability of the friction p makes it more likely that the firm was subject to
the friction and did not strategically withhold. This increases the non-disclosure price
causing more firms to withhold information.
Equation (19) is not yet in a form suitable for empirical analysis, because we observe
a sample of forecast (dt , dt xt )Tt=1 but do not directly observe the true parameters (p0 , σ).
However, noting that the model implies that dt = 1xt ≥y0 , we can formally derive several
moment restrictions.
First, the expected probability of a disclosure predicted by the model is E(dt ) which,
since dt = 1 if and only if (a) the manager is not subject to the friction, which has
probability p0 , and (b) xt is greater than y, which has probability Φ(−Z(p0 )), implies
E(dt ) = (1 − p0 )Φ(−Z(p0 )).
(2)
The left-hand of this moment can be estimated using the sample frequency of a forecast
6
The theory can be (fairly easily) extended to risk-averse investors, but we feel uncomfortable using
risk-aversion to fit the model. First, voluntary disclosures contain, for the most part, firm-specific risks
that might be diversified away, in which case the systematic component will not affect the disclosure
threshold (Cheynel 2012). Second, in a setting with constant absolute risk-aversion, the risk-aversion
of the representative investor declines fast in the number N of potential investors (at rate 1/N , see,
e.g., Dye 2010); hence, empirically, it is unlikely that risk-aversion would change the results unless we
appealed to extremely high levels of individual risk-aversion. Note, finally, that the predictions of DJK
do not depend on whether the manager is risk-averse.
7
dˆ and yields an implied estimated value for p0 . Of course, the greater the observed
frequency, the lower the probability of the friction.
Second, we examine the prediction of the model for E(dt xt ), which is intended to
extract information from both forecast frequency and the expected forecast.7 Note that
E(dt xt ) = E(dt )E(xt |xt /σ ≥ Z(p0 )) is the conditional expectation of a truncated normal,
implying
E(dt xt ) = (1 − p0 )φ(Z(p0 ))σ0 .
(3)
ˆ over all
The left-hand side of this equation can be estimated by the sample average dx
observed forecasts and zeros for periods without a forecast. If, say, we observe a large
average sample forecast, the moment condition requires that either (a) the probability of
the friction is high, so that only managers with very good news would optimally disclose,
or that (b) the volatility of the private information is large, which reduces the level of
the expectation relative to the ex-ante variance.
After substituting the sample moments, equations (8)-(9) form a system of two equations in two unknowns. The method of moments estimator (p̂, σ̂) of the parameters (p0 , σ)
is defined as the solution to the system of equations



dˆ = (1 − p̂)Φ(−Z(p̂))
.
(4)


ˆ = (1 − p̂)φ(Z(p̂))σ̂
dx
A valid solution (with positive σ̂) requires the sample average forecasts to be positive,
ˆ ≥ 0. It can be verified that this equation has, at most, a unique solution, implying
or dx
that the parameters of interest are parametrically identified.
7
Throughout, we remain as close as possible to the generalized method of moments (GMM) in Hansen
(1982) which (in its standard form) requires the same number of observations for each moment. This
implies that we cannot use the conditional expectation of forecasts E(xt |dt = 1) since, unlike the frequency
moment, it is calculated using fewer observations. However, loosely speaking, the unconditional moment
E(dt xt ) should contain at least as much information as E(xt |dt = 1) in order to identify p and σ.
8
One complication in (4) is that finding a solution requires solving a non-linear equation. However, the solution can be very closely approximated as a closed-form expression
of the sample moments that can be plugged in any statistical package. Setting
p̂a = 0.9dˆ2 − 1.9dˆ + 1
and
ˆ
dx
,
σ̂a =
max(0, −0.35dˆ2 + 0.77dˆ − 0.02)
(5)
(6)
ˆ a − dx/σ̂|
ˆ
the maximum approximation error |p̂a − p̂| and |dx/σ̂
remains below .01 for all
p̂ ∈ [0, 1], which implies that we can use these approximations as very good substitutes
for the correct estimator (p̂, σ̂). Equation (5)-(6) also imply an approximation for the
q
ˆ
ˆ 8
d)
ˆ
standard-error of p̂ given by 1.85(1 − d) d(1−
.
T
From equation (4), we can also estimate and approximate the probability of strategic
withholding q0 = (1 − p0 )Φ(Z(p0 )) with
q̂ = (1 − p̂)(1 − Φ(−Z(p̂)) = 1 − p̂ − dˆ .
| {z }
(7)
ˆ
ˆ
≈q̂a =0.9d(1−
d)
In equation (7), if the friction is very small, unraveling to full disclosure predicts that
nearly all information is reported; vice-versa, if the friction is very large, no manager
will be reporting strategically. The maximum level of strategic reporting is attained
for intermediate values of the friction.9 This observation has an important consequence:
because strategic withholding is not a monotonic function of the disclosure frequency, one
√
To prove this, note that, from the central limit theorem, T (dˆ− E(dt )) → N (0, V ar(dt )). From (5),
ˆ where b(x) = 0.9x2 − 1.9x + 1 which, applying the delta method, yields
p̂a = b(d)
√
T (p̂ − p) → N (0, (b0 (E(dt )))2 V ar(dt ) .
|
{z
}
8
≈3.4(1−E(dt ))3 E(dt )
9
It is uncertainty about the friction, not its level, that determines strategic withholding. This feature
of strategic models is relatively transparent in the original DJK, yet lost to empirical studies that use
frequency of disclosure as a proxy for discretionary disclosure. Note that the same aspect is also true in
models of noise trading, where the maximum level of information asymmetry is attained when there is
maximal uncertainty about the noise trade (Bertomeu, Beyer and Dye 2011).
9
cannot use disclosure frequency as a proxy for the unconditional probability of strategic
disclosure.
2.2
Generalized method of moments
The method of moment estimator in equation (4) uses two moment conditions to estimate two parameters and, typically, will find parameter values that perfectly fit all the
moments. The generalized method of moments (GMM) is an extension of this method,
which may involve more moment restrictions than parameters. The over-identifying restrictions can be used to incorporate more predictions of the model; further, GMM admits
a test statistic, the J test, that can be used to test whether the over-identifying restrictions
are satisfied by the data.
To develop multiple over-identifying restrictions, we use information from realized
earnings et where, to lighten notation, we write et in earnings surprise with unconditional
mean zero. Assume that (x̃t , ẽt ) ∼ N ((µ0 , 0)0 , V0 ) are jointly normally distributed with
positive definite variance V0 and such that the manager’s expectation may involve a
bias µ0 .10 The two moments in equations (8) and (9) can be written E(g1,t ) = 0 and
E(g2,t ) = 0, where
g1,t = dt − (1 − p)Φ(−Z(p)),
(8)
g2,t = dt (xt − µ) − σ(1 − p)φ(Z(p))).
(9)
Next, we incorporate an additional moment meant the capture the variability of observed forecasts. Trying to explain this variability is important given that the method-ofmoment estimator defined earlier may generate a variance σ that seemingly contradicts
10
We allow for the possibility that management forecasts are biased relative to earnings (Fischer and
Verrecchia 2000; Stocken and Verrecchia 2004; Indjejikian and Matějka 2009; Caskey, Nagar and Petacchi
2010). We define bias in forecasts as bf ≡ Et [xt ] − µt and bias in earnings as be ≡ Et [et+1 ] − µt . In
essence, these biases are firm fixed-effects, and they might account for the possibility that managers
manipulate the forecast strategically, given the unverifiable nature of management forecasts (Rogers and
Stocken 2005), or that managers exhibit behavioral biases.
10
the observed dispersion of forecasts. Specifically, we use the theoretical prediction
E(dt (xt − µ)2 ) =
E(dt )
| {z }
(1−p)Φ(−Z(p))
× E(((xt − µ)2 |(xt − µ)/σ ≥ z).
|
{z
}
φ(Z(p))
φ(Z(p))
σ 2 (1+Z(p) Φ(−Z(p)) −( Φ(−Z(p)) )2 )
In this equation, E((xt − µ)2 |(xt − µ)/σ ≥ z) is greater when forecasts vary more (σ is
high) or when forecasts are observed less often (p is high). This equation can be rewritten
as the moment E(g3,t ) = 0 where
g3,t = dt (xt − µ)2 − σ 2 (1 − p)(Φ(−Z(p)) + Z(p)φ(Z(p)) −
φ(Z(p))2
).
Φ(−Z(p))
(10)
Lastly, we use the implied forecast error by the model, using the implication E(dt (xt −
et − µ)) = 0. This yields the moment restriction E(g4,t ) = 0 where
g4,t = dt (xt − et − µ).
For each observation, we define the stacked moment vector gt = (g1,t
(11)
g2,t
g3,t
g4,t )0 .
The generalized method of moment involves obtaining an estimator θ̂ = (p̂, σ̂, µ̂) for the
true parameters θ0 = (p0 , σ0 , µ0 ) obtained by minimizing the following objective function
θ̂ ∈ arg min
(
1X
1X 0
gt ) W (
gt ),
T
T
(12)
where W can be any invertible weighting matrix.
Hansen (1982) shows that the most efficient estimation can be achieved by choosing
W to be a consistent estimator of Ω−1 , where Ω = V ar(gt ), the variance of the moments.
The logic of this procedure is similar to generalized least-squares and sets a lower weight
on moments that are more noisy. To implement the estimation, we run the estimation
with W equal to the identity matrix, recover (inefficient but consistent) estimates of
P 0
the parameters and use this first-stage estimation to compute W −1 = 1/T
gt gt as the
11
sample variance matrix (which is a consistent estimator of Ω). Then, we compute efficient
estimates using this new weighting matrix in equation (12). The J-test statistic, defined as
T × Obj, follows, asymptotically, a chi-square distribution with degrees of freedom equal
to the difference between the number of moments (4) and the number of parameters (3).
3
Empirical application
3.1
Data description
While the method is applicable to any voluntary disclosure, management forecasts are a
natural setting where one might look for evidence of the theory. First, Dye (1985) built the
original theory with explicit reference to management forecasts, noting that such forecasts
are made before actual earnings are fully realized and reflect private information held by
management. Second, managers may face shareholder lawsuits or penalties within a short
horizon, especially if the realized earnings number is very different from the forecast.11
Third, managers decide whether to issue a forecast and the data features observable
periods with or without forecasts, which is precisely what the theory aims to predict.
Fourth, forecasts are a primary channel through which markets receive information but,
to this date, some strong disagreements persist as to whether they are truly voluntary,
thus offering a good setting to “test” the theory.
The starting sample is all firms present in the I/B/E/S earnings announcement (EA)
database and with fiscal periods ending between January 1st and December 31st 2014
and non-missing identifiers, which totals 222, 149 observations and 10, 701 unique firms.
The starting period is set after Regulation Fair Disclosure, a one-time regulatory event
which significantly increased the observed frequency of management forecasts for reasons
11
Although in a different framework, Gigler and Hemmer (2001) make the general point that voluntary
disclosures are confirmed by realized earnings; their setting nests traditional voluntary disclosure theory
in the case where this confirmatory value is perfect. Similarly, our view is that a realized short-term
earnings number helps making the voluntary disclosure credible.
12
outside of the model. We drop all observations with missing EA or lagged EA date,
because we need to know both dates to construct the window for management forecasts
and analyst consensus.
We use raw earnings per share (EPS). The raw EPS is the actual variable being
forecasted by management and, further, prior research has shown that forecast tend to
be relatively invariant with scale (Cheong and Thomas, 2011). As we unadjust adjusted
analyst EPS forecasts to measure the market consensus, we require the adjustment factor
used by I/B/E/S, which we define as the ratio between raw and adjusted EPS. For cases
in which adjusted EPS is zero, we use the most recent adjustment factor or, if none exists,
the latest, dropping firms for which the adjustment factor cannot be calculated. We drop
all observations without an adjustment factor, which yields a preliminary sample of EAs
with 217, 366 observations and 10, 337 unique firms. The data selection process is detailed
further in Table 1.
Management forecasts are obtained from the I/B/E/S company-issued guidance (CIG)
database. We retain only adjusted EPS forecasts, and use the mid-point for range forecasts and the nominal value for point or open-ended forecasts; we do not include verbal
forecasts without a point or range estimate.12 Since CIG reports adjusted EPS forecasts, we recover unadjusted forecasts using the adjustment factor calculated earlier. For
each forecast made for a particular quarter, we drop all forecasts made after the fiscal
quarter end and forecasts made before the prior earnings announcements; this removes
pre-announcements as well as long-term forecasts. Then, for each forecasted period, we
retain the earliest forecast. About 96% of the forecasts in the sample are within five days
of an earnings announcement. Note that the theory does not specifically speak about
bundled versus unbundled settings, so that we have not made any active data selection
12
We have also examined other construction of the expected information contained in the forecasts,
using upper or lower ends of the range, re-adjusting range forecasts as a function of the verbal information
given in CIG - e.g., using the top quartile of the range if CIG with a CIG code indicating “toward the
upper end” - or adding (subtracting) a standard-error of earnings given an open-ended upper (lower)
forecast. These modifications had very minor effects on forecast errors and the estimates of the model.
13
on this criterion in our baseline empirical model.
Forecasts are matched to earnings announcements using the I/B/E/S ticker. We
calculate a consensus by averaging over all analyst EPS forecasts issued between the last
two prior earnings announcements, with a 91 days window if an earnings announcement
date is missing. We drop all observations for which the consensus measure is missing,
either because analyst coverage is scarce or no analyst has updated a forecast. EPS
and forecasts are standardized by the firm-level standard-error of EPS and, to remove
any potential systematic industry-level bias, we normalize all forecasts at the industry
level by subtracting the average forecast error within the firm’s Fama-French 48 industry
classification.
We remove all firms that have less than 20 earnings announcements date. This yields
a full sample with 120, 445 earnings announcements, of which 21, 208 were preceded by
a forecast, from a total of 3, 317 unique firms, of which 1, 464 have made at least one
forecast. To estimate the model by firm, we require firms with sufficient time-series
variation in forecasting behavior. We require a firm to have at least four forecasts and at
least one period without a forecast. This yields a restricted sample with 42, 406 earnings
announcements, of which 20, 311 were preceded by a forecast, from a total of 1, 086 unique
firms.
Table 2 reports some additional descriptive statistics for the full and restricted samples. Since about half of the firms in the full sample do not issue management forecasts,
the frequency of disclosure is higher in the restricted sample (one in five quarters) than in
the restricted sample (one in two quarters). Firms in the restricted sample tend to have
lower assets ($5.6b versus $11.9b in the full sample) and slightly greater market capitalization ($6.69b versus $5.6b in the full sample). The average book-to-market is 0.58 in the
restricted sample versus 0.74 in the full sample. For the other variables, averages in the
full and restricted samples are similar. Another interesting fact is that we already appear
to see descriptive evidence against strategic disclosure applied to the entire cross-section
14
of firms: the average forecast surprise is very small, at 1 cent per share. So, either the
entire cross-section of firms is featuring unraveling with a very low friction (which contradicts the observed frequency of disclosure) or, as we shall empirically evaluate, selective
disclosure does not fit all firms in the sample.
Table 3 presents multivariate descriptives on the restricted sample, with an objective
to measure the type of heterogeneity present in the data and guide our empirical implementation. We only provide this analysis on the restricted sample, since this is the
primary sample that is directly estimated. We use a logistic regression with dependent
variable an indicator equal to one when there is a management forecast during a firmquarter (and zero otherwise) on various observable characteristics measured at the date
of the earning announcement in the prior quarter. In specifications (1)-(5), most of the
variables are significant but, overall, disclosure behavior appears to be primarily related
to firm fixed effects. In particular, the pseudo R2 is .311 with only firm fixed effects,
versus 0.026 using other variables and 0.054 when adding industry fixed effects. Once
we incorporate firm fixed effects, other variables add very little incremental R2 , barely
increasing it to 0.324.13 This preliminary analysis suggests that additional controls add
little over firm-level estimates and we therefore choose, for our baseline, to use firm-level
estimates.
We also found in (6)-(7) that another factor, whether a firm has disclosed in the
prior quarter, captures a large portion of heterogeneity; in fact, stickiness may be even
more important than firm-level heterogeneity. One problem with stickiness is that it is
endogenous to the model, as it is related to past realizations of the predicted variable. For
this reason, we develop a complete theoretical treatment in later sections; note, also, that
stickiness is less important (about .1 extra R2 ) when already using firm-level estimates.
13
The pseudo R2 does not correct for the degrees of freedom, so we may be overfitting the model. In
untabulated analysis, we also ran an OLS version of this analysis and the adjusted R2 is very similar, thus,
showing the importance of firm fixed effects. Further, in the logistic estimates, most of the individual
firm fixed effects are statistically significant.
15
3.2
GMM Estimates
For each firm, we estimate the probability of the friction p, the variance of the manager’s information σ and the bias µ using the outlined GMM procedure. We report the
average and standard errors of the distribution of parameter estimates, as well as selected
quantiles. The restricted sample includes only firms for which we have enough forecasts
to consistently estimate the optimal weighting matrix (at least four forecasts and one
period without a forecast).
In Panel A of Table 4, the friction occurs in 40% of all quarters but, consistent with
Tables 2 and 3, there is a large amount of cross-sectional variation in the friction. The
median is about 33% and half of the firms range between 7% and 72%.14 The standarderror of the manager’s private signal σ is .31, or half of the total uncertainty of .64
(the standard-error of the EPS surprise in Table 2). The average firm-level bias is very
small, as expected given that we have netted out average bias by industry. Perhaps more
surprisingly, we do not find a very large cross-sectional variation in the bias, with half of
the firms lying between minus 12 cents and 4 cents of EPS.
Compared to the friction, the probability of strategic withholding is relatively flat,
and remains between 15% and 25% for most firms. Panel A reports for the restricted
sample: the average probability of strategic withholding is 13.21%. We conduct a J test
based on the over-identifying restriction implied by the model. The test rejects at a
5% significance level the hypothesis that the firm does not behave according to DJK for
29.34% of the sample. This level of rejection, significantly greater than the expected 5% if
the DJK model were to apply to all firms, implies that we can reject the joint hypothesis
that DJK applies to the entire population.
In Panel B of Table 4, we report descriptives for the subsample in which DJK is
14
We also computed the standard error on each firm-level estimate to check whether this reported
standard error is likely driven by error in the firm-level estimate or cross-sectional heterogeneity. The
latter explanation appears more plausible, given that the standard error on the estimated p̂ is on average
about 5%.
16
not rejected, or 708 firms out of 1,002. These firms tend to have a marginally smaller
friction (35%) and manager standard-error, as well as a negative biases. The probability
of withholding is very similar at 13.5%.
Next, we conduct various pooled estimates, assuming common parameters for firms
over the entire sample, firms with similar past disclosures, firms with similar financial
characteristics (Table 5) or firms in the same Fama French 48 industry classification
(Table 6).15
In Panel A of Table 5, column (1) estimates a single set of parameters for the restricted
sample. The estimated probability of the friction is 26.6% and the manager’s variance
is 0.027. The pooled variance tends to be low partly because, when imposed parameter
values common to all firms, most managers are being identified by the model as being very
poorly informed. The pooled model implies a higher probability of strategic withholding,
at 22%. The J-test statistic implies that the DJK model is rejected at the 5% level,
but not at the 1% level. In columns (2)-(4), we parse the sample as a function of past
disclosure history, to capture serial correlation in disclosure behavior by separating firms
that have disclosed in the previous quarter (2), did not disclose for a single quarter (3)
or did not disclose for more than one quarter (4). As expected, the probability of the
friction increases from column (2) to column (4). The probability of strategic withholding
appears is the greatest, at 20.83%, after missing a single quarter, relative to around 10%
for firms that disclosed in a previous quarter or have not disclosed for multiple periods.
In columns (5)-(8), we parse the sample in terms of financial characteristics, choosing
the two ratios that appear to be the most strongly related to disclosure in Table 3. We
classify firm-quarters as to whether they are above or below the median on book-to-market
and debt-to-assets, denoting H (resp. L) as an above (resp. below) median firm-quarter.
15
The pooled estimates allow us to re-examine the economic variables associated to forecasts, although
they do carry a caveat. Pooled estimates ignore firm-level heterogeneity which creates misspecification
in the econometric model; this causes problems in the interpretation of a joint pooled coefficient and in
the conclusions from the J-test statistic given that a rejection is likely to be caused by heterogeneity in
the data, rather than a fundamental breakdown in the theoretical restrictions.
17
We document that book-to-market and debt-to-assets appear to be positively related to
the friction. One candidate explanation for this result is that high book-to-market (value)
firms tend to rely less on capital markets since they expand less and highly leveraged firms
rely on debt capital, which depends less on short-term fluctuations in the stock price and
may involve other communication channels. Note that the model is rejected at the 5%
level except for firms with low book-to-market and debt to assets.
Since we pool observations, we may now estimate the full sample, in Panel A of Table
5, without requiring a special treatment of firms with few forecasts. Results in the full
sample are very similar, and exhibit a higher probability of the friction in columns (1)-(4).
In column (4), we find that firms that have not made a forecast for at least two quarters,
are very unlikely to strategically withhold information (at about 2%). Comparing to
the restricted sample, we also find much more variation in the probability of strategic
withholding for each characteristic in columns (5)-(8); this probability is 7% for firms
with high book-to-market and debt-to-assets but increases to 18% for firms with low
book-to-market and debt-to-assets.
Table 6 reports additional pooled estimates by industry. In the restricted sample, the
probability of strategic withholding is very stable across industries, at around 20%, and in
contrast to the friction which varies from .14 to .61. We can reject the DJK model at a 5%
except in the case of nine industries: Trading, Mining, Food Products, Beer and Liquor,
Entertainment, Medical Equipment Candy & Soda, Real Estate and Shipbuilding. In
the full sample, we find much more variation in the probability to strategically withhold,
from 5% in Pharmaceutical Products to 22% in Computers. The full sample exhibits
more rejections, and three additional industries, Entertainment, Food Products and Beer
and Liquor, are now rejected under the J test.
18
3.3
Exogenous disclosure
We examine next a version of the baseline model that combines both voluntary, following DJK, and an involuntary (exogenous) disclosure. This extended model is meant
to incorporate shocks that may require the manager to disclose, such as a threat of litigation or a duty to update (Jagolinzer 2009; Dye 2011). To remain as simple as possible,
we assume that, when not subject to the friction, the manager discloses with probability
h > 0, a parameter that we estimate.16 A benefit of this approach is that the variable h
offers an alternative channel that explains observed disclosure behavior and thus offers a
generalized approach to evaluating the DJK model - that is, from h = 0 (pure DJK) to
h = 1 (disclosure is never strategic).
The moments associated to the extended model are now given as follows:
g1,t = dt − (1 − p)((1 − h)Φ(−Z(p)) + h),
(13)
g2,t = dt (xt − µ) − σ(1 − p)(1 − h)φ(Z(p))),
(14)
g3,t = dt (xt − µ)2
−σ 2 (1 − p)((1 − h)(Φ(−Z(p)) + Z(p)φ(Z(p)) −
g4,t = dt (xt − et ) − µ(1 − p)((1 − h)φ(Z(p)) + h).
φ(Z(p))2
) + h), (15)
Φ(−Z(p))
(16)
We report the firm-level estimates in Table 7. The parameter estimates for the friction,
the variance and the bias are very similar to Table 4 (which corresponds to h set to zero).
We also find that there is a very high estimated probability of exogenous disclosure,
at about 56%, and about one third of the sample is estimated to be non-strategic, at
h = 1, which broadly matches the rejection rates of the DJK model in Table 4. When
incorporating this additional parameter, the probability of strategic withholding is much
16
The model can accommodate more sophisticated versions of litigation costs but, since our objective
here is not to build an endogenous model of litigation (Caskey, 2014), we have chosen to remain as
close as possible to the baseline and use the estimation procedure to illustrate the incremental effect of
involuntary disclosures.
19
lower, at an average of 5.7% with a disclosure friction occurring 46% of the time.
3.4
Alternative implementations
We next examine in Table 8 alternative implementations of the estimation procedure.
In Column (1), we consider a version of the model in which managers are assumed to be
truthful, that is, we do not de-bias the forecasts by industry and set the firm-level bias to
zero. To be coherent with this perspective, we also omit the moment condition E(g4,t ) = 0
that was associated to the estimation of a bias. This variation is meant to be literally
faithful to the assumption made in DJK that forecasts are truthful and, empirically, Table
2 also suggests that the average quarterly bias is very close to zero.17 Nevertheless, we
find that the theory is rejected much more often when assuming a zero bias, at 64.87%
versus 29.34% in the baseline, implying that the presumption of a (typically negative)
bias is critical to rationalize the model for about one third of the sample.18 We also find
a modest decrease in the probability of strategic withholding, at 12.67%.
In Columns (2) and (3), we scale total earnings by lagged total assets (calculated at
the lagged quarter) and market capitalization (calculated one day before the lagged earnings announcement), keeping all other implementation choices in the baseline unchanged.
These two alternative methods of scaling are commonly-used in corporate finance and
accounting but, for our purpose, tend to add significant unmodelled noise in the estimation. Indeed, we find significantly higher rejection rates, at levels equal to 51.85% for
total assets and 47.84% for market capitalization. The cause of this result is that the
scaling does create substantial time-series variability in the observed forecasts, but very
17
This restriction is somewhat demanding, since it assumes that the manager does not misreport and
has an expectation that well-calibrated (i.e., is not optimistic). A less literal reading of DJK would
note that the variable x̃ corresponds to the manager’s posterior belief, which may or may not match the
market belief.
18
Absent a formalization of a more complete theory (which goes beyond our current objective), we
cannot make strong claims about the expected sign of the bias. For example, expectations management
may cause the manager to prefer positive earnings surprises (in part relative to the forecast) as a signal
of growth or other soft information (Cianciaruso and Sridhar 2015); this type of model would induce the
manager to be negatively biased as can be frequently observed in the data.
20
little variability in realized biases. This causes the estimation procedure to predict very
small biases for most firms which yields results similar to those in Column (1).
In Columns (4) and (5), we explore the performance of the model for unbundled
forecasts only, defined as forecasts that occurs at least five days after the earnings announcement day. There are advantages and disadvantages to restricting to unbundled
forecasts. An obvious advantage is that such forecasts are isolated from the earnings announcement, which allows us to recover a forecast-specific consensus and market reaction.
In Column (4), we compute the analyst consensus during the window between the lagged
earnings announcement day and the unbundled forecast day. In Column (5), we switch
from the EPS surprise to the raw 3-day contemporary return (an alternative measure of
investor surprise), omitting the bias and the moment corresponding to the bias.19 Another advantage of unbundled forecasts is that they typically convey unexpected news
and are unlikely to be driven by a social norm to issue forecasts. On the other hand,
the fit within DJK is less evident, as unbundled forecasts can be timed during the entire
period and the market does not immediately know that a forecast has been withheld. A
related notable disadvantage is that, when they are not the first forecast (the most common case), it might not be appropriate to examine them in isolation of a prior bundled
forecast.
In both columns, unbundled forecasts are more infrequent and consistent with a higher
friction, at .72. In Column (4), the manager’s private information appears similar to the
bundled case and, for the market return analysis, the standard-error of the manager’s
posterior is 4% of market return. The probability of strategic withholding is 10.45% with
raw EPS surprise and 10.58% with returns. We also find that the rejection of DJK is
slightly less, at 23.45% with raw EPS and 23.79% with returns. Interestingly, these results
are not only similar with each other but also roughly consistent with those obtained in
the baseline setting.
19
We also performed the same analysis with market-adjusted returns, and the results are very similar.
21
In Column (6), we offer a preliminary exploration of annual forecasts, defined as
forecasts made between six and twelve months before a fiscal year end and for the entire
fiscal year. To be part of the sample, we require a firm to have at least ten annual earnings
announcement. We conjecture that annual forecasts may feature a higher probability of
being uninformed (in the DJK interpretation) but do not find this to be true in our
sample: there is a higher frequency of earnings announcements that come with an annual
forecasts, and the estimated friction is lower, at 30%. On other dimensions, we find
that the probability of strategic withholding is marginally higher, at 14.32% and the
probability that the model is rejected at the 5% level for one firm is similar to the baseline,
at 27.25%. At a conceptual level, we did not find any deep reason as to why the theory
should apply to certain voluntary forecasts and not others; speaking to this, column (6)
suggest differences as to the estimated parameters but no fundamental difference as to
the firm-level relevance of the theory.
4
Forecast stickiness
4.1
Serially-correlated friction
We extend the model to a multi-period setting, using index t for the time period;
the resulting empirical model offers a foundation for a dependence on past disclosure as
previously illustrated in columns (2)-(4) of Table 5. Our empirical model is an implementation of Einhorn and Ziv (2008), thereafter EZ.20 This model shows that stickiness can
be recovered endogenously within DJK, without appealing to any exogenous commitment
ability or penalty, under the (plausible) assumption that the friction is serially-correlated.
Formally, in each period t, the following random variables realize. As before, the
20
The empirical model is faithful adaptation of Einhorn and Ziv (2008), with one difference: they also
assume that there may be a non-zero disclosure cost. We have omitted this cost because we want to
focus our estimation procedure on the DJK model and conducting horse race between the DJK model
and Verrecchia (1983) would take us too far from our original question.
22
manager’s private information xt and the next-period earnings et are jointly normal with21



  


2
µ0   σ0
ρ0 σ0 ϕ0 
(xt , et ) ∼ N 

  , 
.
2
 0

ρ
σ
ϕ
ϕ
0 0 0
0


|
{z
}
(17)
V0
Within this formulation, one more restriction is needed to impose that the manager’s
information is his posterior expectation (as assumed in GMM). Specifically, if xt = E(et ),
it must be the case that et = xt + ut , where ut is noise, implying that cov(et , xt ) = ϕ20 .
This requires to set ρ0 = ϕ0 /σ0 . This restriction is similar in nature to Chen and Jiang
(2006) and Lundholm and Rogo (2014) who use it to test for overconfidence in analyst
forecasts. Further along, we will relax this restriction (estimating ρ0 as a free parameter)
to observe whether management forecasts appear to feature a volatility different from
that predicted by posteriors.
In addition, there is a process θt ∈ {0, 1} where θt = 1 indicates that the manager
is subject to the DJK friction in period t. The random variable θt follows a stationary
Markov chain with transition matrix


k1 1 − k1 
K=
.
k2 1 − k2
(18)
That is, if (not) subject to the friction at date t, the manager is subject to the friction
at date t + 1 with probability (k2 ) k1 .
We maintain the assumptions made in DJK.22 When not subject to the friction, the
manager chooses the disclosure dt ∈ argmaxd Et (et |d, dxt ) to maximize the current price
21
As before, we net out the market expectation before a forecast is made, so that xt and et are written
as forecast and market surprises.
22
In particular, we maintain the assumption that managers maximize short-term price as used in DJK,
as well as EZ and other multi-period studies, such as Shin (2003). Unfortunately, a model that involves
forward-looking concerns (reputations) by the manager for future prices is neither conceptually, nor
computationally, trivial. Recent work on this problem, for example, focuses on two periods (Beyer and
Dye 2012; Guttman, Kremer and Skrzypacz 2014).
23
and investors do not observe the friction but form a Bayesian expectation pt = Et (θt ),
where Et (.) represents the expectation conditional on all forecasts di , di xi and realized
earnings ei prior to periods i < t. At one extreme, setting k1 = 1 = 1 − k2 yields forecasts
that are completely sticky and, at the other extreme, k1 = k2 = p0 yields the model
estimated earlier.
Note that EZ does not pre-assume that firms pre-commit to disclose in advance or
that managerial concerns for their reputation enforces disclosure behavior: the manager
maximizes short-term price and stickiness emerges endogenously as a result of the timevarying market response to disclosure behavior.23
For a given market belief pt , an analogue to equation (19) holds
pt
(y0,t /σ0 ) =
−
1 − pt
Z
y0,t /σ0
Φ(x)dx,
(19)
−∞
implying that the disclosure threshold y0,t is time-varying and, is intuitive, varies with
market beliefs pt .
EZ further show that pt is updated each period as24
pt+1 =



k2
if dt = 1
(20)

 α(pt )k1 + (1 − α(pt ))k2 if dt = 0
where
α(pt ) =
pt
.
pt + (1 − pt ) Pr(xt ≤ y0,t |et )
(21)
To explain the updates (20) and (21), note that if the manager discloses in period t,
then the market knows that the manager was not subject to the friction, that is, θt = 0.
23
In their survey of upper management, Graham, Harvey and Rajgopal (2005) note that the act of
disclosing information sets a precedent before investors whereby investors tend to expect more disclosure
from a firm that has frequently disclosed in the past versus one that has remained silent. EZ is entirely
consistent with this explanation because a disclosure changes market beliefs about the friction.
24
See Appendix equation (A3), p. 584, in Einhorn and Ziv (2008).
24
pt+1
pt+1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
1
3
5
7
-2
-1
0
1
2
Realized earnings et
Nb. of periods with no disclosure
Figure 1. Time-series variation in disclosure
From the transition matrix (18), the probability of being subject to the friction must be
k2 in period t + 1. If the manager does not disclose in period t, then the market knows
that either the manager was subject to the friction, which conditional on realized earnings
et and non-disclosure, has probability α(pt ) or was not subject to the friction, which has
probability 1 − α(pt ).
Before we lay out the estimation procedure, let us briefly illustrate how EZ can explain
any level of serial correlation in forecasts. Assume that k1 > k2 , which means that the
friction is persistent. For exposition purposes, let us (for now) assume that we do not
condition on earnings so that αt =
pt
.
pt +(1−pt )Φ(Z(pt ))
Let us denote pk as the market prior after exactly k periods of non-disclosure, then,
it is readily seen that pk+1 = α(pk )k1 + (1 − α(pk ))k2 ∈ (pk , k1 ) is strictly increasing, so
that the market becomes more convinced that the manager is uninformed after repeated
periods of non-disclosure. This is illustrated in the left-hand side of Figure, with σ0 = 1,
k1 = .7 and k2 = .2: in the first period after a disclosure, the market believes that the
manager is subject to the friction with probability p0 = k2 = .2 after one period, the
new market beliefs is p1 = .44 as the manager is more likely to have been subject to the
25
friction in both periods and, after two periods of non-disclosure p2 = 0.56. This reduces
the probability of disclosure from 59% in a period following a disclosure to 27% after only
two periods of non-disclosure.
In the general model with observed earnings, realized earnings also play an important
role in the updating function (21). Specifically, as illustrated on the left panel of Figure
1 (with ϕ0 = .7, pt = k2 and ρ0 = .6), high realized earnings make it more likely that
the manager did not disclose because of the friction. Hence, high earnings imply that,
in future periods, the firm is perceived as a high friction firms and becomes less likely to
disclose. In this example, for an increase from a half standard-deviation below mean to
a half standard-deviation above mean, the probability of disclosure decreases from 36%
to 29%.
4.2
Maximum Likelihood Estimation
The multi-period updating belief of market beliefs makes it convenient to use a different
econometric approach to conduct the estimation. Maximum likelihood estimation (MLE)
is a method in which we use the likelihood function of a sequence observations and it allows
us to input directly the theoretical market beliefs into the likelihood of each observation,
in order to write the likelihood of a time-series of observations. The primary benefit
of MLE is that it implicitly selects moments (the first-order condition on the likelihood
function) that minimize the asymptotic variance of the estimators and it can be simpler
to implement than GMM if the theoretical moments are not in closed-form (as in EZ).
On the other hand, MLE is sensitive to misspecification and, for this reason, we conduct
it only at the firm-level.
To illustrate the method, let us consider first a simplified version, imposing p0 = k1 =
k2 to replicate the pure DJK model estimated earlier with GMM. Recall that, for a given
firm, there is a sample {dt , dt xt , et } where dt is a binary variable equal to one if there is
a forecast at date t, dt xt is the forecast, and et is the following realized earnings. In the
26
pure DJK model, the likelihood of the sample is
T
Y
L(p, σ, µ) =
[g(et ) (p + (1 − p) H (Z(p)|et )]1−dt [(1 − p) f (xt , et ))]dt ζt ,
(22)
t=1
where g is the marginal probability density of et , H(.|et ) is the cumulative distribution
of xt conditional on realized earnings et . and ζt is a binary variable equal to one if xt −µ ≥
σZ(p).
In the likelihood function L, for each observation (dt , dt xt , et ), the first term in brackets
g(et )(p + (1 − p)Ht (Z(p)|et )) captures the likelihood of observing realized earnings et and
non-disclosure. The second term in brackets (1 − p)f (xt , et ) captures the likelihood of
realized earnings et and disclosure xt . In addition, as captured by the binary variable ζt ,
the likelihood of observing an observation below the theoretical threshold σZ(p), which
imposes the bound
σ ≥ min(x)/Z(p).
(23)
This bound is key for understanding how MLE reconciles with DJK observations in
which very bad news are voluntarily disclosed, that is, when min(x) is a large negative
number. A forecast dt xt must always be above the disclosure threshold σZ(p). So, to
meet this bound, the estimation relies on all three parameters (p, σ, µ). First, a lower
probability of the friction p tends to shift the model toward unraveling (full disclosure),
increasing disclosure by reducing Z(p). Second, a higher σ implies that the manager has
more precise information and the market reacts more strongly to a non-disclosure; in turn,
this will also decrease the disclosure threshold. Third, a decrease in the bias µ reduces
the predicted disclosure threshold. While they can explain low disclosures, these three
parameters also penalize the likelihood function: a low p requires frequent disclosures, a
high σ requires volatile forecasts and a low µ requires low signed forecast errors.
The likelihood function in equation (24) is easily adapted to k1 6= k2 by replacing p
with pt (k1 , k2 ) given by the updating equations (20). To implement the estimation with
27
a finite sample, we further set p0 =
k2
1−k1 +k2
which is the steady-state probability of not
being informed in the Markov chain.
To interpret the estimated parameters, we examine two moments of special interest.
First, we compute the steady-state probability of being subject to the friction, which we
denote by p∞ . That is,
(p∞ , 1 − p∞ ) = (p∞ , 1 − p∞ )K.
This probability measures the importance of the friction and lies in-between k1 and k2 .
This parameter reveals how often the manager does not disclosure for reasons unrelated
to his information about the firm’s future earnings. Second, we define v∞ as the steadystate probability that the manager withholds information for strategic reasons, namely,
when the information is unfavorable. We compute it by simulating histories of 1000
periods given the MLE estimate, and recovering the probability as the average frequency
of strategic withholding realized in the simulated histories.
Lastly, as for the case of GMM, we also estimate an extension of this model, assuming
that with probability h, the manager discloses for exogenous reasons when not subject
to the friction. This modification is even more important in the MLE model that it was
in the GMM model, because it can now explain why some firms may make disclosures
below the threshold. The likelihood function is altered to
L(p, σ, µ, h) =
T
Y
1−dt
[g(et ) (pt + (1 − pt ) (h + (1 − h)H (Z(pt )|et ))]
[(1 − p) (h + (1 − h)ζt f (xt , et ))]dt .
t=1
(24)
4.3
MLE estimates
In Table 9 , we present the results of maximum likelihood estimation. Panel A presents
the results with the baseline model without exogenous disclosure. We find high levels of
persistence in the friction, that is, the probability of remaining subject to the friction is,
on average, 67%, versus 16% after a period without the friction (e.g., a quarter following a
forecast). The standard-deviation of the managers’ private information, at .43, implying
28
that the manager knows in advance about 61% of the standard-deviation of the realized
earnings innovation (at 0.70). Overall, the friction occurs about one quarter out of three.
The implied probability of strategic disclosure is somewhat lower than in the comparable
GMM model, at 9.94%, because the serial correlation in the friction allows the market to
learn about the manager’s type and (comparatively) reduces the ability of an informed
manager to strategically withhold.
In Panel B of the same Table, we estimate the MLE model including an exogenous
probability of disclosure h. The estimates for the process of the friction (k1 , k2 ) are similar
to Panel A. On the other hand, we find that including an estimate h affects the estimates
of other parameters. First, in this generalized model, we find a slightly lower standarderror on the manager’s information and on realized earnings, because this model relies
less on noise to fit the predicted restrictions. The probability of the friction is now higher,
at 42.86%. We also estimate that more than half of the sample does not appear to be
making any voluntary disclosure (ĥ = 1). The average probability of mandatory disclosure
is very high, at 76%, which makes the estimated probability of strategic withholding is
only about 2.6%.
We also conduct a likelihood ratio test, taking as our null hypothesis that h = 0 or,
“there is no mandatory disclosure.” Under the null, the difference between two times the
log-likelihood in Panel B and the log-likelihood in Panel A follows a χ2 distribution with
one degree of freedom. We can reject this null hypothesis for about 2/3 of the sample
(65.7%) at the 5% level. As expected, rejection rates are significantly greater than under
GMM because our implementation of MLE requires disclosure theory to explain the data
more closely (i.e., does not impose only the economic moments). Also, note that the null
of the test is different from the J test: we are testing here whether the fit is improved
whether the addition of some exogenous disclosure improves the statistical model.
In Table 10, we re-estimate the model without the restriction to Bayesian posterior
expectations, that is, estimating ρ0 in (17) as a free parameter. This extended model has
29
various possible interpretations. For example, it may be that the manager simply reports
a private signal, letting the market form a posterior expectation or that the manager
puts too much weight on his private signal, thus leading to excess volatility in forecasts
(which we interpret as overconfidence). For expositional purposes, and as in Chen and
Jiang (2006), we refer to this model as “overconfidence.”
In Panel A, we report the estimates of the model with h = 0. We find a higher
level of persistence than in Table 9, and the model predicts that the standard-error in the
manager’s forecast is very close to that in realized earnings (albeit lower). This increase in
the standard-error of forecasts, relative to Table 9, does suggest that there is some amount
of excess volatility in forecasts relative to the Bayesian model. The average estimated
correlation ρ is at 57%, which is lower than a baseline ratio of ρ∗ = 0.53/0.61 = 86% if all
firms were identical to the average firm and did not experience overconfidence.25 Hence,
this suggests that forecasts and realized earnings correlate far less than expected by
Bayesian posteriors. About 29.44% of firms feature a variance in forecasts that is greater
than the variance in realized earnings, which is anomalous outside of the overconfident
model. As a more formal test, we conduct a likelihood ratio test using the null hypothesis
“ρ = σ/ϕ” at the 5% level by comparing the log likelihood in Table 9 Panel A to the
log likelihood in Table 10 Panel A. This hypothesis is rejected for most of the sample
(81.14%).
In Panel B, we re-estimate model when including h as a free parameter. Interestingly,
one important effect of including the estimation of h is to reduce the estimated overconfidence. The standard-error of the manager’s information is much lower than in Panel
A, with an average σ̂ at 0.36. The estimated correlation remains very similar (slightly
higher), at ρ̂ = 0.66 on average. In the model with overconfidence, the estimated probability of mandatory disclosure is lower, although still very high, at 63%. Estimates of the
25
For expositional simplicity, we ignore in this calculation the distribution of estimates; when we
calculate the exact predicted ratio as the average of all σi /ϕi , we find the even higher number of about
one which is much higher than the estimated 57%.
30
probability of the friction and of the probability of strategic disclosure are very similar
to the model in Table 9, implying that including overconfidence in the statistical model
is primarily important to estimate the manager’s information precision when not subject
to the friction, not the process for the friction.
We compute the two likelihood ratio tests conducted earlier. In the model with estimated h, we can only reject “ρ = σ/ϕ” at the 5% level for one third of the firms (33.93%),
much lower than the estimated 81.14% in Table 9. We also conduct the likelihood ratio
test of “h = 0” and find a very similar frequency of rejections, at about 2/3 of the sample
(64.89%).
5
Conclusion
In this paper, we develop a simple empirical methodology to structurally estimate and
tests models of voluntary disclosure with uncertain frictions, as in Dye (1985) and Jung
and Kwon (1988). The estimation procedure can incorporate various important features,
such as disclosure biases, involuntary disclosure and (endogenous) stickiness in observed
disclosure patters. The structural parameters recover the inputs of the decision problem
faced by a manager when choosing whether or not to disclose, and offer researchers to
test the internal validity of the theory. To our knowledge, our study is the first to offer
an estimation procedure that is fully derived from theoretical predictions.
Applying the model to quarterly management forecast data, we find that strategic
withholding is uncommon. Depending on samples and specification, we find the unconditional incidence of strategic withholding is often not more than 13%, but as low 2.6%
in our most general statistical model.
The structural approach also offers stricter tests of the theory, and we find that from
1/3 to 2/3 of the firms do not appear to disclose in a manner consistently with disclosures
being purely voluntary. We interpret these observations more broadly, as limited evidence
31
suggesting that strategic short-term price manipulations are unlikely to be a first-order
consideration. Because forecast withholding is likely less risky than other forms of quarterly accrual manipulations, this result may, more generally, indicate that managers do
not care about short-term prices as much as usually assumed.
Yet, as an important caveat to interpreting our results, we do not claim to have
found evidence against the theory in any setting, nor do we claim to have tested any
possible version of disclosure theory. In this respect, our objective is mainly to test for
potential limitations of a theory in order to both improve it and identify other settings
where it may apply. Indeed, several research directions may offer promising paths for
extended theories. First, recent laboratory evidence suggests that subjects might not
disclose according to the predictions of disclosure theory (Jin, Luca and Martin 2015),
suggesting modifications of the equilibrium concept. Second, it is an open question as to
whether long-term information may not be managed; in particular, one may possibly find
greater levels of manipulation in such long-term forecasts. Other types of disclosures,
such as contract disclosures and other press releases or MD&A, may offer valuable other
settings where the theory may apply. The method developed here is applicable as long
as there is an option to withhold and there is data about either a market reaction or a
quantitative disclosure. Third, we have estimated the standard models of disclosure of
Dye (1985) and Jung and Kwon (1988), as well as Einhorn and Ziv (2008), as they have
been proposed and used in the literature. These models offer the natural first step to
take theory to data, and we needed to first evaluate their ability to explain empirical
facts. However, their failure may be tied to their simplicity and further insights may be
obtained by extending these models to incorporate features such as costs, real decisions,
litigation deterrence, long-term managerial objectives, managerial learning or earnings
manipulation, among other possibilities.
32
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36
Table 1. Sample selection
This table summarizes the sample selection criteria. Earnings announcements (EA) and management forecasts (MF) are
obtained from I/B/E/S. Firms in our sample must be present in the CRSP and Compustat database using the IBES ticker,
gvkey and permno matching tables from WRDS. The restricted sample is used for all models involving firm-level estimates. For
pooled estimates, we use the full sample, which includes firms regardless of their number of MF.
I/B/E/S EA sample 2004-2014
Non-missing current or prior announcement date
Non-missing adjustment factor
Earnings announcements (EA) Management forecasts (MF)
EA Obs
Unique firms
MF Obs
Unique firms
224,647
10,898
219,832
10,592
219,673
10,524
37
I/B/E/S CIG sample 2004-2014
Non-missing EAs
MF after prior EA date and before period end date
Keep earliest MF
Merged I/B/E/S EA and CIG
Non-missing analyst consensus
Non-missing CRSP
Non-missing Compustat
At least 20 EA Obs
Full sample
At least 3 MF obs
At least one period without MF
Restricted sample
219,673
161,845
150,167
149,653
120,343
120,343
39,662
39,246
39,246
10,524
7,723
6,505
6,489
3,312
3,312
1,017
1,002
1,002
37,268
36,458
29,174
25,865
2,968
2,807
2,301
2,301
25,865
25,169
24,765
24,754
21,208
21,208
20,475
20,059
20,059
2,301
2,181
2,120
2,118
1,464
1,464
1,017
1,002
1,002
Table 2. Descriptive statistics
This table reports descriptive statistics of firms in our sample. The full sample is the sample of all firms, covered by I/B/E/S with
at least 20 earnings announcements during the period Jan. 1st 2004-Dec. 31st 2014 and which can be matched to Compustat
and CRSP. The restricted sample restricts the sample to firms with at least 3 MF. Forecast and earnings surprises are computed
as the difference with the consensus, scaled by the standard error of raw EPS. Forecast surprises have also been netted of an
average industry bias, using the Fama-French 48 industry classification. Firm characteristics are obtained from Compustat and
measured at the lagged earnings announcement date. Except for total assets, balance sheet variables are scaled by total assets.
Market capitalization is obtained from CRSP and measured as the closing price (variable prc) multiplied by the number of
shares outstanding (variable shrout) one day before the lagged earnings announcement.
38
Full sample
Min
Median
Max
Mean
Restricted sample
SD
Min Median
Max
29%
0.53
29.68
0.61
0.22
0.85
0%
-12.00
-53.23
-55.12
-11.86
-104.92
0%
0.31
0.28
0.04
0.00
0.00
100%
15.80
2,876
18.70
14.28
31.04
51%
0.42
0.41
0.01
0.01
-0.01
30%
0.52
0.61
0.61
0.22
0.64
Firm characteristics
Number of quarters
38
7
Total assets (TA)
11,929 81,595
Market Capitalization (MCAP) 5,618 20,193
Book to Market
0.74
2.06
Debt/TA
55%
27%
R&D/TA
2%
4%
CAPEX/TA
3%
5%
20
3
1
-77.18
0%
-1%
-15%
42
1,403
1,004
0.51
54%
1%
1%
44
2,573,126
600,970
215.14
426%
210%
130%
40
7,872
6,769
0.59
48%
2%
3%
Forecast characteristics
Forecast frequency
Management forecast (raw)
Realized EPS (raw)
Forecast surprise
Forecast error
EPS surprise
Mean
SD
18%
0.42
0.85
0.01
0.01
-0.05
9%
-12.00
-14.15
-55.12
-11.86
-9.28
48%
0.33
0.33
0.05
0.00
0.03
98%
15.80
22.16
18.70
14.28
31.04
6
20
38,437
9
22,976
4
2.20 -62.13
23%
1%
2%
0%
3%
-6%
44
1,341
1,441
0.44
48%
1%
2%
44
911,120
600,970
215.14
230%
48%
76%
Table 3. Multivariate analysis
This table reports the results of a logistic regression where the dependent variable is an
indicator equal to one in the presence of a management forecast (zero otherwise) during a
quarter-firm observation. All variables are measured at the quarter prior to the quarter to
be forecasted, except for Market capitalization which is calculated with the closing price
and number of shares one day after the earnings announcement preceding the forecasted
quarter. The variables R&D, Capital expenditures and financing CF are divided by total
assets. We dropped observations with missing R&D. Industry fixed effects are calculated
using the Fama-French 48 industry classification.
TA
-0.93
(0.88)
MCAP
2.07**
(0.76)
Book-to-Market
-0.07***
(0.02)
Debt/TA
-1.42***
(0.06)
R&D/TA
2.62***
(0.65)
Capital Exp./TA 3.25***
(0.43)
Lag Disclosure
Industry FE
Firm FE
Pseudo R2
Obs.
No
No
0.022
23,434
0.49
(0.89)
0.97
(0.78)
-0.06***
(0.02)
-1.06***
(0.06)
-1.30
(0.77)
2.86***
(0.48)
Yes
No
0.035
39,246
Yes
No
0.051
23,434
39
-20.8***
(4.31)
-1.11
(2.53)
-0.13***
(0.03)
-2.03***
(0.15)
-2.81**
(1.72)
3.60***
(0.71)
No
Yes
0.288
39,246
No
Yes
0.31
23,434
2.71***
(0.03)
No
Yes
0.46
38,191
Table 4. Firm-level GMM estimates
This table reports the results from the GMM estimation, run separately for each firm. In Panel A,
we use the restricted sample, that is, firms covered by I/B/E/S with 20 or more EAs, at least one
quarter without a MF and at least four MFs. Firms for which the optimal weighting matrix could not
be estimated (5% of the sample) were classified as rejections. In Panel B, we report estimation results
only for firms that pass the J-test.
Panel A: Restricted sample
Friction
ρ
Precision
σ
Bias
µ
Strategic withholding
J test rejections at 5%
Unique firms
v
average point estimate
(standard error)
0.40
(0.33)
0.31
(0.43)
0.00
(0.24)
13.21%
29.34%
1,002
10%
0.02
25%
0.07
quantiles
50%
0.34
75%
0.69
90%
0.87
0.00
0.08
0.21
0.39
0.58
-0.23
-0.12
-0.04
0.04
0.10
Panel B: Sample of Firms Not Rejected by J-Test
Friction
ρ
Precision
σ
Bias
µ
Strategic withholding
Unique firms
v
average point estimate
(standard error)
0.35
(0.27)
0.27
(0.46)
-0.05
(0.27)
13.50%
708
40
10%
0.08
25%
0.13
quantiles
50%
0.26
75%
0.52
90%
0.79
0.03
0.12
0.23
0.39
0.53
-0.23
-0.13
-0.05
0.02
0.08
Table 5. Pooled GMM estimates, by disclosure history and characteristics
This table reports the results from the GMM estimation on pooled samples. Panel A uses the full samples of firms covered by I/B/E/S with 20 or
more earnings announcements. Panel B uses the restricted samples of firms covered by I/B/E/S with 20 or more earnings announcements, at least
one quarter without a forecast and at least four forecasts. Model (1) pools all firm-quarters in the sample. Models (2)-(4) pool firm-quarters that
were preceded by a forecast (1), a single period without a forecast (3) and two or more quarters without a forecast (4). Models (5)-(8) pool firmquarters with above-median book-to-market and debt to assets (5), above-median book-to-market and below-median debt to assets (6), below-median
book-to-market and above-median debt to assets (7) and below-median book-to-market and debt to assets (8).
Panel A: Restricted sample
41
Friction
ρ
Precision
σ
Bias
µ
Strategic withholding
J test p-value
Obs.
v
(1)
All obs.
(2)
Disclosers
0.045
(0.001)
0.108
(0.019)
0.001
(0.003)
(3)
1 quarter
miss
0.443
(0.011)
0.000
(0.031)
0.011
(0.016)
(4)
>1 quarter
miss
0.817
(0.004)
0.000
(0.030)
0.004
(0.015)
(5)
High BTM
High Debt
0.394
(0.006)
0.000
(0.018)
-0.014
(0.008)
(6)
High BTM
Low Debt
0.239
(0.004)
0.000
(0.017)
-0.050
(0.007)
(7)
Low BTM
High Debt
0.288
(0.005)
0.153
(0.013)
-0.037
(0.006)
(8)
Low BTM
Low Debt
0.187
(0.004)
0.210
(0.014)
-0.006
(0.006)
0.266
(0.002)
0.027
(0.008)
0.004
(0.004)
22.3%
0.016
39,246
11.10%
0.000
19,977
20.83%
0.000
3,000
8.51%
0.000
14,289
21.6%
0.000
9,420
22.0%
0.000
10,273
22.4%
0.000
10,212
21.0%
0.207
9,341
Panel B: Full sample
Friction
ρ
Precision
σ
Bias
µ
Strategic withholding
J test p-value
Obs.
v
(1)
All obs.
(2)
Disclosers
0.054
(0.001)
0.095
(0.017)
-0.019
(0.003)
(3)
1 quarter
miss
0.509
(0.010)
0.000
(0.030)
-0.038
(0.016)
(4)
>1 quarter
miss
0.955
(0.001)
0.000
(0.024)
0.033
(0.014)
(5)
High BTM
High Debt
0.855
(0.003)
0.000
(0.017)
-0.020
(0.010)
(6)
High BTM
Low Debt
0.662
(0.004)
0.000
(0.013)
-0.036
(0.008)
(7)
Low BTM
High Debt
0.703
(0.004)
0.093
(0.010)
-0.045
(0.007)
(8)
Low BTM
Low Debt
0.559
(0.003)
0.111
(0.009)
0.003
(0.006)
0.686
(0.002)
0.000
(0.006)
0.009
(0.004)
13.8%
0.003
120,343
12.4%
0.000
21,109
19.4%
0.000
3,622
2.2%
0.000
84,737
6.8%
0.000
31,877
14.6%
0.000
28,558
13.1%
0.001
28,336
18.0%
0.133
31,572
Table 6. Pooled GMM estimates, by industry
This table reports the results from the GMM estimation on samples, pooled by industry using the Fama-French 48 industry classification. The full sample includes firms covered by I/B/E/S with 20
or more earnings announcements. The restricted samples of firms covered by I/B/E/S with 20 or more earnings announcements, at least one quarter without a forecast and at least four forecasts.
Standard-errors (SE) were computed using the optimal weighting matrix (Hansen 1982). Four industries, defense, fabricated products, precious metals and tobacco products had too few forecasts to be
estimated. Hide indicates the probability that information is voluntarily withheld.
42
Industry
Agriculture
Aircraft
Almost Nothing
Apparel
Automobiles and Trucks
Banking
Beer & Liquor
Business Services
Business Supplies
Candy & Soda
Chemicals
Coal
Communication
Computers
Construction
Construction Materials
Consumer Goods
Electrical Equipment
Electronic Equipment
Entertainment
Food Products
Healthcare
Insurance
Machinery
Measuring and Control Equipment
Medical Equipment
Non-Metallic and Metal Mining
Personal Services
Petroleum and Natural Gas
Pharmaceutical Products
Printing and Publishing
Real Estate
Recreation
Restaurants, hotels, motels
Retail
Rubber and Plastic Products
Shipbuilding
Shipping Containers
Steel Works Etc
Textiles
Trading
Transportation
Utilities
Wholesale
Friction
0.65
0.55
0.38
0.23
0.62
0.39
0.65
0.20
0.38
0.27
0.38
0.54
0.38
0.19
0.53
0.35
0.39
0.34
0.15
0.39
0.48
0.44
0.44
0.22
0.19
0.31
0.55
0.33
0.39
0.34
0.31
0.24
0.61
0.31
0.24
0.27
0.19
0.27
0.23
0.14
0.54
0.28
0.40
0.31
SE
0.06
0.05
0.03
0.01
0.03
0.03
0.07
0.00
0.02
0.10
0.02
0.05
0.03
0.01
0.03
0.02
0.02
0.02
0.01
0.03
0.02
0.03
0.02
0.01
0.01
0.01
0.07
0.02
0.02
0.02
0.03
0.06
0.04
0.02
0.01
0.03
0.03
0.03
0.02
0.03
0.02
0.02
0.03
0.01
Precision
0.21
0.15
0.01
0.00
0.11
0.06
0.05
0.13
0.04
0.10
0.08
0.00
0.00
0.42
0.00
0.07
0.00
0.22
0.07
0.09
0.00
0.09
0.03
0.11
0.25
0.00
0.15
0.04
0.20
0.23
0.03
0.20
0.09
0.12
0.00
0.30
0.72
0.03
0.14
0.19
0.14
0.25
0.13
0.20
Restricted
SE
0.07
0.10
0.08
0.04
0.06
0.06
0.05
0.02
0.05
0.04
0.05
0.13
0.12
0.02
0.06
0.06
0.05
0.04
0.03
0.05
0.05
0.05
0.07
0.03
0.03
0.04
0.10
0.04
0.06
0.04
0.07
0.06
0.10
0.04
0.02
0.10
0.23
0.07
0.07
0.07
0.07
0.02
0.05
0.04
Bias
-0.01
-0.04
-0.01
-0.10
-0.07
-0.10
-0.04
-0.03
0.00
-0.05
-0.03
-0.10
-0.02
-0.04
-0.10
-0.01
-0.01
-0.05
-0.08
-0.05
-0.08
-0.01
-0.02
-0.03
-0.04
0.07
-0.03
0.01
-0.03
0.00
0.01
0.04
-0.19
-0.09
-0.01
-0.06
-0.01
-0.07
-0.02
-0.15
-0.08
-0.07
-0.01
-0.03
SE
0.04
0.06
0.03
0.02
0.04
0.03
0.02
0.01
0.03
0.03
0.02
0.06
0.06
0.01
0.04
0.02
0.02
0.02
0.01
0.03
0.03
0.02
0.04
0.01
0.01
0.02
0.05
0.02
0.02
0.02
0.03
0.03
0.06
0.02
0.01
0.03
0.03
0.03
0.02
0.03
0.03
0.01
0.03
0.02
J-test p-value
0.01
0.03
0.00
0.00
0.00
0.00
0.05
0.00
0.00
0.22
0.00
0.04
0.03
0.00
0.00
0.00
0.00
0.00
0.00
0.04
0.05
0.00
0.00
0.00
0.00
0.30
0.06
0.00
0.00
0.00
0.00
0.15
0.00
0.00
0.00
0.00
0.39
0.00
0.00
0.00
0.19
0.00
0.00
0.00
Hide
0.15
0.18
0.22
0.22
0.16
0.22
0.15
0.21
0.22
0.22
0.22
0.18
0.22
0.21
0.19
0.22
0.22
0.22
0.20
0.22
0.20
0.21
0.21
0.22
0.21
0.22
0.18
0.22
0.22
0.22
0.22
0.22
0.16
0.22
0.22
0.22
0.21
0.22
0.22
0.19
0.19
0.22
0.22
0.22
Obs.
88
131
366
1,018
412
489
84
6,196
683
24
909
128
395
2,559
501
492
860
672
3,843
292
643
409
640
1,693
1,433
1,557
87
642
559
1,009
304
62
290
956
3,709
216
43
301
480
85
1,503
935
380
1,168
Friction
0.84
0.89
0.82
0.38
0.89
0.96
0.86
0.47
0.60
0.90
0.70
0.82
0.90
0.39
0.80
0.74
0.59
0.68
0.46
0.83
0.76
0.81
0.90
0.52
0.41
0.64
0.88
0.65
0.92
0.89
0.52
0.86
0.76
0.55
0.47
0.61
0.82
0.39
0.63
0.59
0.88
0.80
0.92
0.65
SE
0.03
0.02
0.01
0.01
0.01
0.00
0.03
0.01
0.02
0.02
0.01
0.03
0.01
0.01
0.01
0.01
0.02
0.02
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.02
0.02
0.00
0.00
0.03
0.02
0.03
0.01
0.01
0.03
0.03
0.03
0.02
0.04
0.01
0.01
0.01
0.01
Precision
0.20
0.11
0.00
0.00
0.09
0.00
0.07
0.09
0.00
0.00
0.06
0.00
0.00
0.27
0.00
0.01
0.00
0.15
0.03
0.03
0.00
0.00
0.03
0.03
0.10
0.00
0.09
0.04
0.09
0.13
0.02
0.15
0.08
0.08
0.00
0.17
0.26
0.02
0.09
0.00
0.07
0.12
0.10
0.13
Full
SE
0.07
0.09
0.07
0.04
0.05
0.05
0.05
0.01
0.05
0.08
0.04
0.12
0.09
0.03
0.05
0.05
0.04
0.04
0.02
0.05
0.06
0.04
0.05
0.02
0.03
0.04
0.10
0.03
0.05
0.03
0.06
0.04
0.10
0.03
0.01
0.09
0.06
0.06
0.06
0.12
0.06
0.03
0.04
0.03
Bias
-0.01
-0.03
0.00
-0.10
-0.08
-0.08
-0.07
-0.03
0.01
-0.01
-0.03
-0.11
-0.02
-0.01
-0.10
0.00
-0.01
-0.04
-0.07
-0.03
-0.09
0.02
-0.04
0.01
0.00
0.07
-0.01
0.01
-0.01
0.02
0.01
0.03
-0.19
-0.09
-0.01
-0.04
0.02
-0.07
-0.01
-0.14
-0.06
-0.04
0.00
-0.02
SE
0.04
0.06
0.03
0.02
0.04
0.04
0.03
0.01
0.03
0.04
0.02
0.07
0.06
0.01
0.04
0.02
0.02
0.02
0.01
0.04
0.04
0.03
0.05
0.01
0.01
0.02
0.05
0.02
0.03
0.02
0.03
0.03
0.06
0.02
0.01
0.04
0.02
0.03
0.02
0.07
0.03
0.02
0.02
0.02
J-test p-value
0.01
0.01
0.00
0.00
0.00
0.00
0.05
0.00
0.00
0.04
0.00
0.01
0.02
0.00
0.00
0.00
0.00
0.00
0.00
0.02
0.01
0.00
0.00
0.00
0.00
0.26
0.05
0.00
0.00
0.00
0.00
0.14
0.00
0.00
0.00
0.00
0.16
0.00
0.00
0.07
0.18
0.00
0.00
0.00
Hide
0.07
0.05
0.08
0.22
0.05
0.02
0.07
0.20
0.17
0.05
0.13
0.09
0.05
0.22
0.09
0.12
0.17
0.14
0.20
0.08
0.11
0.09
0.05
0.19
0.21
0.16
0.06
0.15
0.04
0.05
0.19
0.07
0.11
0.18
0.20
0.16
0.08
0.22
0.16
0.17
0.05
0.09
0.04
0.15
Obs.
197
719
1,715
1,497
1,764
11,544
260
12,053
1,175
301
2,310
390
3,141
3,856
1,450
1,542
1,428
1,602
7,611
1,321
1,701
1,608
4,634
3,777
2,232
3,587
366
1,476
5,625
7,735
496
476
481
1,790
6,116
476
305
387
1,266
272
7,438
4,306
3,896
2,825
Table 7. Firm-level GMM estimates with exogenous disclosure
This table reports the results from the GMM estimation with a probability each period that a firm not
subject to the friction discloses regardless of the information. The estimation is run separately for each
firm. We conduct the estimation only in the restricted sample, that is, firms covered by I/B/E/S with
20 or more EAs, at least one quarter without a MF and at least four MFs. Because the model is exactly
identified (four moments and four moments), we do not report a J test rejection.
Friction
ρ
Precision
σ
Bias
µ
Exogenous Disclosure
h
Strategic withholding
Unique firms
v
average point estimate
(standard error)
0.46
(0.32)
0.34
(0.40)
-0.02
(0.25)
0.56
(0.43)
5.73%
1,002
43
10%
0.04
25%
0.13
quantiles
50%
0.47
75%
0.75
90%
0.89
0.03
0.13
0.25
0.40
0.65
-0.19
-0.10
-0.02
0.05
0.12
0.00
0.12
0.69
1.00
1.00
Table 8. Firm-level GMM estimate Robustness Tests
This table reports the results from the GMM estimation with other data preparation and estimation
assumptions. In Column (1), the model is estimated assuming that no signal is biased, omitting the
industry-level debias and the bias moment. In Columns (2) and (3), EPS are standardized by lagged
total assets and market capitalization one day before the forecast, respectively. In Column (4), the
model is estimated using unbundled forecasts only and using the analyst consensus obtained by analyst
forecasts during the window after the prior earnings announcement and the management forecast date.
In Column (5), we use 3-day market returns centered around the unbundled forecast date as a measure
of surprise. In Column (6), we use forecasts made for an entire year, and at least six months before fiscal
year end. Firms with singular variance-covariance matrix were classified as J test rejections.
Friction
ρ
Manager SE
σ
Bias
µ
Strategic withholding
J-test rejections α = 5%
Unique firms
v
(1)
No
bias
0.43
(0.34)
(2)
Scaling
TA
0.53
(0.39)
(3)
Scaling
MCAP
0.52
(0.39)
(4)
Unbundled
EPS
0.72
(0.24)
(5)
Unbundled
CAR
0.72
(0.04)
(6)
Annual
only
0.30
(0.30)
0.15
(0.41)
0.08
(0.15)
0.07
(0.14)
0.34
(0.52)
0.04
(0.12)
0.37
(0.49)
0.00
(0.02)
0.00
(0.01)
-0.04
(0.19)
10.06%
51.85%
1,001
10.15%
47.84%
999
10.45%
23.45%
243
12.67%
64.87%
1,002
44
-0.14
(0.40)
10.58%
23.79%
248
14.32%
27.25%
477
Table 9. Firm-level MLE estimates
This table reports the results from the MLE estimation, run separately for each firm. We uses the restricted samples of
firms covered by I/B/E/S with 20 or more EAs, at least one quarter without a MF and at least four MFs. Panel A reports
the estimates using the basic model. Panel B reports the estimates using the extended model in which an exogenous
probability of mandatory disclosure is estimated conditional on not being subject to the friction.
Panel A: Voluntary Disclosure Only
Friction
(after uninformed period)
Friction
(after informed period)
Manager SE
k1
Earnings SE
φ
Bias
µ
k2
σ
k2 /(1 − k1 + k2 )
v
Stationary friction
Strategic withholding
Unique firms
average point estimate
(standard error)
0.67
(0.30)
0.16
(0.21)
0.43
(0.30)
0.70
(0.28)
-0.18
(0.41)
32.65%
9.94%
1,002
10%
0.15
25%
0.49
quantiles
50%
0.79
75%
0.92
90%
0.97
0.00
0.01
0.06
0.23
0.40
0.12
0.21
0.36
0.58
0.82
0.28
0.42
0.64
0.90
1.12
-0.54
-0.25
-0.09
0.00
0.08
Panel B: Voluntary and Mandatory Disclosure
Friction
(after uninformed period)
Friction
(after informed period)
Manager SE
k1
Earnings SE
φ
Bias
µ
Mandatory Disclosure
h
Stationary friction
Strategic withholding
LRT of null h = 0, α = 5%
Unique firms
k2
σ
k2 /(1 − k1 + k2 )
v
average point estimate
(standard error)
0.72
(0.26)
0.21
(0.22)
0.37
(0.25)
0.58
(0.31)
-0.01
(0.26)
0.76
(0.37)
42.86%
2.60%
65.7%
1002
45
10%
0.30
25%
0.60
quantiles
50%
0.83
75%
0.91
90%
0.96
0.03
0.06
0.12
0.27
0.53
0.10
0.19
0.31
0.50
0.73
0.24
0.37
0.55
0.75
0.94
-0.18
-0.08
-0.01
0.06
0.12
0.00
0.60
1.00
1.00
1.00
Table 10. Firm-level MLE estimates with Overconfidence
This table reports the results from the MLE estimation, run separately for each firm and estimating the covariance between
the manager’s information and realized earnings. We uses the restricted samples of firms covered by I/B/E/S with 20 or
more EAs, at least one quarter without a MF and at least four MFs. Panel A reports the estimates using the basic model.
Panel B reports the estimates using the extended model in which an exogenous probability of mandatory disclosure is
estimated conditional on not being subject to the friction.
Panel A: Voluntary Disclosure Only
average point estimate
(standard error)
Friction
(after uninformed period)
Friction
(after informed period)
Manager SE
k2
Earnings SE
φ
Correlation
ρ
Bias
µ
Stationary friction
Strategic withholding
LRT of ρ = σ
, α = 5%
φ
Unique firms
k1
σ
k2
1−k1 +k2
v
0.72
(0.30)
0.12
(0.18)
0.53
(0.45)
0.61
(0.29)
0.57
(0.35)
-0.24
(0.48)
30.00%
9.90%
81.14%
1,002
10%
25%
quantiles
50%
75%
90%
0.17
0.57
0.86
0.95
0.98
0.00
0.02
0.05
0.14
0.37
0.13
0.22
0.42
0.68
1.09
0.26
0.39
0.58
0.80
0.97
0.00
0.24
0.69
0.87
0.95
-0.74
-0.38
-0.10
0.01
0.09
Panel B: Voluntary and Mandatory Disclosure
average point estimate
(standard error)
Friction
(after uninformed period)
Friction
(after informed period)
Manager SE
k2
Earnings SE
φ
Correlation
ρ
Bias
µ
Mandatory disclosure
h
Stationary friction
Strategic withholding
LRT of ρ = σ
, α = 5%
φ
LRT of h = 0, α = 5%
Unique firms
k1
σ
k2
1−k1 +k2
v
0.73
(0.27)
0.18
(0.03)
0.36
(0.29)
0.57
(0.28)
0.66
(0.31)
-0.04
(0.28)
0.63
(0.27)
40.00%
2.61%
33.93%
64.89%
1,002
46
10%
25%
quantiles
50%
75%
90%
0.30
0.60
0.83
0.93
0.97
0.03
0.05
0.11
0.22
0.46
0.11
0.18
0.31
0.46
0.66
0.24
0.37
0.54
0.74
0.91
0.02
0.52
0.76
0.89
0.96
-0.24
-0.10
-0.02
0.05
0.12
0.00
0.00
0.93
1.00
1.00