How Does More Frequent Reporting Reduce Information … · While many factors enter into the...
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How Does More Frequent Reporting Reduce Information
Asymmetry?∗
Robert Stoumbos†
Columbia Business School
July 25, 2017
Abstract
In countries around the world, policymakers are debating the costs and benefits of switching
from semiannual to quarterly reporting. This study contributes to that debate by examining the
mechanism that drives quarterly reporting’s reduction of information asymmetry. Using U.S.
data, I show that Amihud (2002) illiquidity, a common information asymmetry proxy, grows by
10.7% over the intervening period between two quarterly earnings announcements. This suggests
that cutting a semiannual period into two quarters cuts the growth time in half, leading to lower
information asymmetry in the period’s second half. I confirm this in international settings, where
I find switching from semiannual to quarterly reporting reduces Amihud (2002) illiquidity by
up to 5.3% in the second half of each semiannual period.
∗This paper formed part of my dissertation at Yale School of Management. I am grateful to the members ofmy dissertation committee, Jake Thomas (chair), Frank Zhang, Shyam Sunder, and Marina Niessner, for theirguidance, support, and encouragement. I also thank participants at the Carnegie Mellon University Emerging ScholarsSymposium and at workshops at Columbia University, Emory University, London Business School, Carnegie MellonUniversity, University of Toronto, University of British Columbia, George Washington University, and Yale University.I also thank Benedikt Downar, Juergen Ernstberger, Aytekin Ertan, Zeqiong Huang, Steve Karolyi, Peter Kelly, AlinaLerman, Thomas Steffen, Heather Tookes, Huai Zhang, and my fellow PhD students for their helpful comments. Igratefully acknowledge financial support from the Yale School of Management. All errors and omissions are my own.†Contact E-mail: [email protected].
1 Introduction
How does information asymmetry between informed and uninformed traders evolve from
one earnings announcement to the next? There is no clear prediction based on existing theory.
The classic Kyle model predicts a constant level of information asymmetry between earnings
announcements, because the informed trader reveals private information at a constant rate (Kyle,
1985). In the accounting literature, we seem to accept this prediction, except we expect leaks
to cause a brief jump in asymmetry right around the earnings announcement itself (e.g., Kim
and Verrecchia, 1994).1 But more recent theory shows that information asymmetry is unlikely
to remain constant between announcements. By extending the Kyle model to include multiple
informed traders and the arrival of new private information over time, Bernhardt and Miao (2004)
demonstrate that information asymmetry could rise or fall between earnings announcements in
different circumstances. Whether it tends to rise or fall in the real world is an empirical question.
In this paper, I show that information asymmetry increases monotonically during the entire period
from one earnings announcement to the next. This finding is important because it has real
implications for the reporting frequency debate, which is taking place around the world.
While the United States has required quarterly reporting since 1970, there is no global
consensus over the optimal reporting frequency. Many countries, including most of Europe, only
require semiannual reports. There is even disagreement within reporting jurisdictions. In 2004, the
European Union rejected proposed legislation to require quarterly financial reports (Euromoney
Institutional Investor PLC, 2004),2 and the Singapore Exchange recently commissioned a study to
reconsider local quarterly reporting requirements (Yahya, 2016). Even some in the United States
have questioned the wisdom of quarterly reporting (Benoit, 2015), prompting the SEC to consider
its pros and cons at length during a 2015 meeting (Higgins, 2016). In the face of this uncertainty,
we as academics should help real-world decision-makers—both regulators and firms—determine
appropriate reporting frequency policies.
1Kim and Verrecchia (1994) say the following in their conclusion (page 59): “[L]ogically market-makers are likelyto increase spreads in anticipation of an earnings announcement, to guard against investors acting on the informationbefore it is disclosed publicly (e.g., ‘leaks’). This suggests that spreads temporarily widen around announcements.As this advantage dissipates, spreads fall back to the level that prevailed before the announcement was anticipated.”
2The EU instead settled on a compromise, requiring narrative quarterly statements in addition to firms’ regularsemiannual reports. But in 2013 the EU decided that quarterly reporting was too costly and both revoked thisrequirement and prohibited EU member states from requiring quarterly reports for their own firms (Wagenhofer,2014).
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While many factors enter into the reporting frequency decision, this paper focuses on
the relationship between reporting frequency and information asymmetry. This relationship is
important, since lower information asymmetry is one of the academic literature’s few proposed
benefits of more frequent reporting.3 Practitioners also consider lower information asymmetry an
important benefit. Keith Higgins, a former Director of the SEC Division of Corporate Finance,
cites increased insider trading as a major cost of maintaining lower reporting frequencies (Higgins,
2016), and other commentators worry that these low frequencies aggravate information asymmetry
between informed and uninformed investors (Malmqvist, 2014; Szopo, 2014). These commentators
find this information asymmetry to be unfair, because they believe the firm already has more-
frequent internal reports that it could easily publish. Aside from potential unfairness, greater
information asymmetry is costly because it likely increases the firm’s cost of capital (Amihud and
Mendelson, 1986; Diamond and Verrecchia, 1991).
I am not the first to explore the relationship between reporting frequency and information
asymmetry. Prior literature shows that more frequent reporting reduced average information
asymmetry between informed and uninformed investors during the nineteen-fifties, sixties, and
early seventies (Fu et al., 2012), but this literature has not explored the mechanism that drove
this reduction. Managers and regulators need the mechanism to predict how the magnitude of
the reduction has changed since the early seventies, and how it might change for different firms
across different settings. This will help them accurately weigh the information asymmetry benefit
against any costs when deciding future reporting frequency changes.4 The mechanism will also
reveal whether the information asymmetry reduction comes with its own hidden costs, or whether
there is some easier way to achieve the reduction without increasing reporting frequency at all.
In this paper, I determine the mechanism. Higher reporting frequencies reduce the
average level of information asymmetry because information asymmetry grows over time between
earnings announcements, and a higher reporting frequency reduces the time that is available for
this interannouncement growth to occur. (In the rest of the paper, I refer to the information
asymmetry growth between earnings announcements as “interannouncement growth”.) Figure
3The other proposed benefits are improved price discovery (Butler et al., 2007; Arif and De George, 2015) andlower cost of capital (Fu et al., 2012).
4The costs of more frequent reporting include greater managerial myopia (Gigler et al., 2014; Kraft et al., 2015;Ernstberger et al., 2015) and compliance costs (Verdi, 2012).
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Figure 1: Illustration of Interannouncement Growth and Reporting Frequency
1 provides an illustration. It depicts a hypothetical firm’s information asymmetry path over
time when it reports quarterly versus when it reports semiannually. Under interannouncement
growth, information asymmetry grows between earnings announcements. These announcements
then cause information asymmetry to fall again, because they publicly reveal some of the informed
traders’ private information. The growth between announcements combined with the drop after
each new announcement creates a sawtooth pattern over time. Notice that there is less time for
interannouncement growth when the firm reports quarterly than when it reports semiannually. As
a result, a switch from semiannual to quarterly reporting reduces average information asymmetry.5
In this paper, I show graphical and statistical evidence that interannouncement growth occurs. I
also use a difference-in-differences design to show that interannouncement growth is the mechanism
at work when quarterly reporting reduces information asymmetry.
I first demonstrate that interannouncement growth occurs in the United States. Plots
visually demonstrate that the Amihud (2002) illiquidity measure, my proxy for information
asymmetry, follows interannouncement growth’s predicted sawtooth pattern from one earnings
5The purpose of this figure is to illustrate that interannouncement growth is sufficient for quarterly reporting toreduce average information asymmetry. To make this as clear as possible, it implicitly makes simplifying assumptionsthat my actual tests do not require. My tests do not require information asymmetry to be the same for semiannualand quarterly reporters absent any interannouncement growth. Nor do they require the information asymmetry levelto be the same each quarter. Nor do they require interannouncement growth to be linear.
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announcement to the next.6,7 Regressions confirm that this growth between announcements is
statistically significant. I estimate that Amihud (2002) illiquidity increases by 0.161% (t=39.24) for
each additional day without a new earnings announcement. Assuming two quarterly announcements
are 63 trading days apart, this estimate translates to an increase of around 10.7% from right
after the first earnings announcement to right before the second. Additional regressions show
that this increase in information asymmetry occurs throughout the entire period between earnings
announcements, and not only for a brief period right before each announcement.
I next turn to international settings, where firms report both semiannually and quarterly,
to estimate the effect on information asymmetry when a firm cuts interannouncement growth time
in half by switching from semiannual to quarterly reporting. My test is a difference-in-differences
made possible because, as shown in Figure 1, the decision to report quarterly does not affect
interannouncement growth in the first and third quarters. Thus, I can use these quarters to control
for cross-sectional differences in Amihud (2002) illiquidity from other factors. The difference-in-
differences compares the semiannual and quarterly reporters’ change in information asymmetry from
the first to the second quarter and from the third to the fourth quarter. This test estimates the
average second- and fourth-quarter Amihud (2002) illiquidity reduction that comes from quarterly
reporting’s reduction of interannouncement growth.
I estimate this difference-in-differences in three international settings. The first consists of
five large European countries where semiannual reporting is the norm, but many firms voluntarily
report quarterly. My regression includes firm-year fixed effects, which allow it to be well-identified
even for voluntary adopters.8 The other two settings, Singapore and Japan, both began to require
quarterly reporting in the first half of the 2000s. I estimate that the decision to report quarterly
reduces the average level of Amihud (2002) illiquidity by 5.3% (t=10.04) for European firms, 2.9%
(t=2.11) for Singaporean firms, and 1.1% (t=1.51) for Japanese firms. Robustness tests show that
these results are not driven by a violation of the parallel trends assumption.
In additional analyses, I first demonstrate that these results hold when I use the bid-
6Amihud (2002) illiquidity is my main information asymmetry proxy because it measures the price impact oftrades, which is the construct examined by Kyle (1985) and Bernhardt and Miao (2004).
7The Amihud (2002) illiquidity plots in Figure 2 look remarkably similar to the hypothetical pattern in Figure1, with Amihud (2002) illiquidity increasing until the earnings announcement and falling right after.
8This is true as long as the unobservables associated with adoption have the same effect on Amihud (2002)illiquidity in quarters one and three as in quarters two and four.
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ask spread as my information asymmetry proxy. I then explore how other disclosures affect
interannouncement growth, showing that the growth is less pronounced for firms with more analyst
forecasts and 8-K filings between earnings announcements. Finally, I show that interannouncement
growth occurred both before and after decimalization, and before and after the financial crisis.
Finding evidence of interannouncement growth is an important contribution. Not only does
it provide us with a better understanding of how accounting affects capital markets, it also has
implications for the reporting frequency debate, which is an important policy issue. Specifically, it
gives us three main insights.
First, interannouncement growth implies that more frequent reporting’s reduction of
information asymmetry provides a good reason to increase reporting frequencies. This was not
clear beforehand, because the two other likely possible mechanisms behind the reduction would
not justify more frequent reporting. These alternative mechanisms either generate additional costs
that may outweigh the benefits from reducing information asymmetry, or they suggest an easier
way to get the same reduction without increasing reporting frequency at all.9 In contrast, reducing
interannouncement growth does not generate any obvious additional costs, and the easiest way to
reduce it is by increasing reporting frequencies. So the drop in information asymmetry that comes
from reducing interannouncement growth provides a good reason to report more frequently.
Second, knowledge of interannouncement growth can help regulators and managers make
decisions about hypothetical reporting frequency changes. Based on this study, practitioners
can now expect higher reporting frequencies to provide a greater benefit to firms with steeper
interannouncement growth slopes. Because of interannouncement growth, practitioners can also
expect the marginal benefit from reduced information asymmetry to get smaller and smaller with
each reporting frequency increase.10 The decreasing marginal benefit suggests that information
asymmetry alone may not justify moving all the way to continuous reporting. If future research
finds that more frequent reporting’s marginal costs hold constant or increase as reporting frequency
increases, then these marginal costs would eventually outweigh the marginal benefits from lower
asymmetry.
Finally, existing theory shows that information asymmetry could rise or fall over time,
9In Section 5.1, I describe these alternative mechanisms and their implications in more detail.10In Section 5.2, I describe how the marginal information asymmetry reduction gets smaller with each reporting
frequency increase.
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depending on the circumstances. This paper increases our understanding of capital markets by
showing that it in fact rises over time. Future models should produce rising information asymmetry
between earnings announcements in order to better reflect the real world.
The rest of this paper proceeds as follows: Section 2 reviews related literature; Section
3 describes the three settings I use for the international tests, as well as my data sources;
Section 4 contains research designs and results for my main tests; Section 5 discusses some of
interannouncement growth’s policy implications; Section 6 contains additional analyses; and Section
7 concludes.
2 Literature Review
2.1 Literature on Information Asymmetry Patterns
Based on existing theory, how might we expect information asymmetry to evolve between
earnings announcements? Ex ante, it is unclear.
Beginning with the classic Kyle (1985) model, we have an informed trader who must decide
how to trade on her private information before a terminal date. With each trade, the informed
trader moves the stock price closer to its fundamental value, but she does not fully reveal her
information because uninformed trading camouflages her trades. In equilibrium, the informed
trader takes advantage of this camouflage and spreads her trades over time such that she gradually
reveals her private information at a constant rate. This results in a constant level of information
asymmetry. Therefore, if the Kyle model’s assumptions held in the real world, we could expect a
constant level of information asymmetry between earnings announcements.11
But what if there are multiple informed traders, and what if they receive new private
information over time? Bernhardt and Miao (2004) extend Kyle’s model to allow for these
possibilities. This extension adds two new considerations: (1) the arrival rate of new information
and (2) competition between informed investors, where more competition induces these investors to
trade more aggressively and in turn impound their information into prices more quickly. Depending
on whether the arrival of new information or the aggressiveness of informed trading dominates, this
11Back and Pedersen (1998) extend Kyle (1985) so that the single risk-neutral insider receives a continuous flow ofnew private information over time. They find that the intuition in Kyle (1985) extends to this setting: informationasymmetry does not change deterministically over time.
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model can produce any information asymmetry path between earnings announcements: an increase,
a decrease, or no change. Since any path is possible, whether information asymmetry increases or
decreases between earnings announcements is an empirical question.12
Stepping away from the finance literature, the accounting literature seems to assume that
information asymmetry holds constant at some normal level for most of the quarter, and then
spikes for a brief period before the earnings announcement. For example, Kim and Verrecchia
(1994) express this intuition, reasoning that pre-announcement asymmetry is likely higher because
of leaks.13 Their hypothesis is reasonable given previous findings in Lee et al. (1993) and Skinner
(1993) (both cited by Kim and Verrecchia (1994)) that information asymmetry is higher in a short
window before the earnings announcement than after.14 Later studies of the bid-ask spread and
price impact of trades within the ten days before and after the earnings announcement generally
corroborate this finding (Amiram et al., 2016; Chae, 2005; Affleck-Graves et al., 2002; Yohn, 1998;
Krinsky and Lee, 1996).15,16 However, my results show that this intuition is incorrect. I find
that information asymmetry increases steadily throughout the entire period between earnings
announcements, not just for a brief period right before each earnings announcement. This
distinction is important in the reporting frequency context. If there were no interannouncement
growth and information asymmetry only increased briefly before each announcement, we would
not expect the time between announcements to directly affect average information asymmetry.
Doubling the reporting frequency would cut the information content of each earnings announcement
in half, so while it would double the number of pre-announcement jumps in information asymmetry,
it would likely cut the size of each jump in half. The net effect would cancel out.
A prominent result that may seem similar to mine at first blush comes from Patell and
12Aside from Bernhardt and Miao (2004), most other extensions of the Kyle model produce decreasing informationasymmetry over time (e.g., Holden and Subrahmanyam, 1992, 1994; Foster and Viswanathan, 1996; Back et al., 2000;Caldentey and Stacchetti, 2010), though most of these models do not include new private information arrivals overtime.
13See footnote 1.14An even earlier paper, Morse and Ushman (1983) (also cited by Kim and Verrecchia (1994)), found no significant
difference in spreads before and after the earnings announcement for a small sample of 375 announcements.15One paper, Acker et al. (2002), examines bid-ask spreads over a much longer window: 125 days before and after
the earnings announcement. Unlike my results, they find that bid-ask spreads decrease in the period leading up tothe earnings announcement, hit a trough on the day of the announcement, and then recover slowly back to “normallevels.” They find these results in a sample of 195 London Stock Exchange firms selected from the lowest 40% of firmsby size within the FT-All Share Index between 1986 and 1994.
16In a demonstration of their dynamic microstructure model on a sample of 16 stocks, Easley et al. (2008) showadditional consistent results for the probability of informed trading (PIN) before and after the earnings announcement.But due to their small sample, they do not test for significance.
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Wolfson (1979, 1981), who find that average implied volatilities to option expiration increase
in the period leading up to the earnings announcement.17 But their result does not actually
anticipate interannouncement growth, because it relates to average volatility to option expiration
rather than daily volatility. In fact, both papers hypothesize that daily volatility holds constant
apart from a brief spike around the earnings announcement. They expect that this spike causes
the average implied volatility to increase in the days leading up to the announcement, because the
announcement period itself becomes a larger fraction of the remaining time until option expiration.
In contrast, interannouncement growth does not predict a brief information asymmetry spike around
the announcement, but rather predicts that asymmetry will grow over time between announcements.
2.2 Reporting Frequency Literature
The literature has generally established that more-frequent reporting reduces the average
level of information asymmetry. In a difference-in-differences, Fu et al. (2012) show that the
U.S.’s reporting frequency increases during the nineteen-fifties, sixties, and early seventies caused
information asymmetry to fall.18 They suggest this asymmetry reduction might come from an
increase in total public information, but do not search further for the underlying mechanism.
They do not consider interannouncement growth—not even implicitly, since they test reporting
frequency’s effect on the mean of information asymmetry over the entire year. Had they been
testing for interannouncement growth, they would have focused on the second and fourth quarters,
the only periods when it predicts a decrease.
Apart from the decrease in information asymmetry, the literature has identified a few other
benefits from more frequent reporting. Fu et al. (2012) find that more frequent reporting reduces
a firm’s cost of capital. The reduction in information asymmetry likely contributes to this result
(Amihud and Mendelson, 1986; Diamond and Verrecchia, 1991). Butler et al. (2007) find that stock
prices reflect accounting information more quickly when firms voluntarily increase their reporting
17Rogers et al. (2009) find the same implied volatility pattern as Patell and Wolfson (1979, 1981) around earningsforecasts bundled with earnings announcements.
18Cuijpers and Peek (2010) find consistent evidence for European firms that voluntarily increase their reportingfrequencies. There are two papers that do not find this result. The first is Kubota and Takehara (2016), whichexamines quarterly reporting adoption on the Tokyo Stock Exchange. Consistent with my own insignificant results inthe Japanese setting, they conclude that the reporting frequency increase likely did not cause information asymmetryto fall. The second paper, Kajüter et al. (2015), finds no evidence that increased reporting frequency in Singaporecaused a decrease in information asymmetry. This may be due to the sample restrictions they adopt for their tests.
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frequencies. But they find no effect when the frequency increase is involuntary, suggesting that the
relationship may not be causal. On the other hand, Arif and De George (2015) find evidence that
more frequent reporting reduces mispricing.
The literature has also identified costs associated with more frequent reporting. Theory
suggests that higher reporting frequencies can cause managers to myopically prefer short-term
performance gains at the expense of overall firm value (Gigler et al., 2014). Recent empirical
evidence supports this prediction, showing that more-frequent reporting leads to lower investment
and higher real earnings management (Kraft et al., 2015; Ernstberger et al., 2015). In addition
to increased myopia, Verdi (2012) suggests that more-frequent reporting may increase compliance
costs, agency costs, monitoring costs, and proprietary costs. Gigler and Hemmer (1998) suggest
that it may also reduce managers’ incentives to make voluntary disclosures.
3 Research Settings and Data
3.1 International Research Settings
Because my difference-in-differences design (described in detail in Section 4.2) does not
require an exogenous change in reporting frequency, I can perform it with both voluntary and
involuntary adopters of quarterly reporting. The important thing is to find settings that have both
semiannual and quarterly reporters. In my international tests, I examine three such settings. The
first is a set of European countries where quarterly reporting is voluntary, and many firms have
chosen to voluntarily adopt it. The second is Singapore, which began to require quarterly reporting
for a subset of its firms beginning in 2003. The third is Japan, where the Tokyo Stock Exchange
began requiring quarterly reporting in 2004.
The European Union (EU) contains a number of countries that do not require quarterly
reporting. According to Link (2012), the five of these countries with the largest number of firms are
the United Kingdom, France, Germany, the Netherlands, and Denmark.19 These are the countries
from which I draw my sample, because I expect them to have the most even mix of semiannual
and quarterly reporters. Each contains firms that switched from semiannual to quarterly reporting
19While German national law does not require firms to report quarterly, the prime listing segment of the DeutscheBorse requires quarterly reporting for firms that register on it. This does not affect the interpretation of my results.
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during the sample period, which runs from 1993 to 2015.
This sample has one confounding factor that might work against my results. In 2004, the
EU adopted the Transparency Directive, which required all semiannual reporters on EU-Regulated
Markets to produce Interim Management Statements (IMS’s) halfway through each semiannual
period. These IMS’s did not need to include financial statements, such as balance sheets or income
statements. Rather, they were only required to include an explanation of material events and
transactions, as well as a “general description” of the financial performance and position of the
company since the last semiannual report (European Commission, 2004). My data, which comes
from Worldscope, only identifies firms as quarterly reporters if they report earnings-per-share each
quarter. So even though every firm provides IMS’s for part of the sample period, I still classify firms
as semiannual reporters if their IMS’s do not report the quarter’s earnings. If any of the remaining
disclosures in these IMS’s were useful, treating them as if they were not would bias against finding
the predicted results in my tests. But since this bias works against my predictions, it does not
affect my overall inferences.
My second setting, Singapore, introduced a quarterly reporting requirement in 2003 for
some firms. According to Listing Rule 705(2) of the Singapore Exchange, all firms that had a
market capitalization greater than S$75 million on March 31, 2003 had to file quarterly reports.
Starting on December 31, 2006, this requirement has been extended to all firms whose market
capitalizations have grown since 2003 to exceed the S$75 million threshold. This extension gave
these firms a year to comply, so they did not have to begin reporting quarterly until their 2008
fiscal years. From then on, the requirement kicked in for any firm whose market capitalization grew
to exceed S$75 million. As a result, there are many firms that switch from semiannual to quarterly
reporting throughout the sample period.
On April 1, 2004, Japan’s Tokyo Stock Exchange began requiring firms listed on its First
and Second Sections to disclose quarterly reports (Kubota and Takehara, 2015). Even though there
initially was no punishment for failing to comply with this requirement, most firms began reporting
quarterly immediately after the rule went into effect.
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3.2 Data
For my U.S. sample, earnings announcement dates come from Compustat, and daily security
data comes from CRSP. The U.S. sample runs from 1993 to 2015. I only include years after 1992
because CRSP’s NYSE bid and ask data are not continuously available until December 28, 1992. I
drop earnings announcements when the next quarter’s announcement occurred before it or on the
same day. I also drop earnings announcements where the earnings announcement date is before the
balance sheet date, because I assume this represents a data error. Finally, I drop firm-days when
two SEC filing deadlines have passed without a new earnings announcement from Compustat.20
For continuous variables, I either take the logarithm of the variable or I Winsorize at the 1% and
99% levels to reduce the influence of outliers.
Panel A of Table 1 shows yearly averages of Size, measured as the logarithm of market
value of equity at the firm-day level. It also shows yearly averages of log(Price Impact), calculated
for each firm-day as the logarithm of Amihud (2002) illiquidity (i.e, as log(
|return|$ volume of trades
), where
dollar volume is in terms of millions of dollars). Panel A shows that log(Price Impact) has dropped
steadily over time.
The main U.S. test relies on cross-sectional variation on each calendar-day in the time
since the firm’s most recent earnings announcement. Panels B and C show the extent of this
variation. Panel B shows that eighty-eight percent of the firm-years have a fiscal year that ends
in either March, June, September, or December, so differences in the most recent quarter-end only
contribute a little of the needed variation. Panel C shows that there is a reasonable amount of
variation at the firm-quarter level in the number of trading days between quarter-end and the
earnings announcement. This is the source of most of the variation in the number of days since the
most recent earnings announcement.
International data comes from Datastream and Worldscope, both provided by Thomson
Reuters. The European sample goes from 1992 to 2015. It starts in 1992 because that is when the
European firms’ earnings announcement dates first become available in the data. The Singaporean
sample goes from October 27, 2000—the date when bid and ask data is first available for Singapore—
20In untabulated robustness checks, I further restrict both the U.S. sample and the international samples (describedbelow) by dropping the bottom 5% of observations by stock price within each sample. The results with this samplerestriction are the same as those presented in the paper.
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to the end of 2015. For the Japanese sample, a preliminary check showed that bid and ask data was
not available before February, 2001, so my Japanese sample begins then. My full Japanese sample
runs from February, 2001 to September, 2008, a period that contains the Tokyo Stock Exchange’s
implementation of its quarterly reporting requirement in 2004. In the international samples, I only
include firm-years that I could identify as either reporting quarterly or semiannually. I also drop
any firms that are listed on exchanges located outside of the country (or, in the case of Europe,
countries). Finally, I drop earnings announcements if they occur on the balance sheet date or if
they occur before the earnings announcement of an earlier quarter. For continuous variables, I
again either take the logarithm of the variable, or I Winsorize at the 1% and 99% levels to reduce
the influence of outliers.
Panel A of Table 2 shows the number of semiannual reporters and quarterly reporters in
each year of the European sample. The number of quarterly reporters generally increases over time,
though there are fluctuations from year to year as firms list and delist. The table also shows average
log(Price Impact) each year. It is much larger than in the U.S. sample, indicating that European
firms have lower liquidity. Interestingly, the quarterly reporters in later years have higher values
of log(Price Impact) than the semiannual reporters do. As previously noted, firms voluntarily
adopt quarterly reporting in this setting. Because quarterly reporting reduces average information
asymmetry (Fu et al., 2012), this might indicate that firms are more likely to choose quarterly
reporting when asymmetry is higher. The table also shows that the quarterly reporters tend to be
larger than the semiannual reporters.
Panel B shows the same table for the Singaporean sample. The number of quarterly
reporters jumps in 2003, which is consistent with the adoption of mandatory quarterly reporting
for large firms that year. It jumps again in 2008, when the quarterly reporting requirement was
extended to more firms. Unlike in Europe, the quarterly reporters have lower log(Price Impact) than
the semiannual reporters do. Because adoption in this sample was mandatory, this is consistent
with the finding that quarterly reporting reduces information asymmetry.
Panel C shows this table for Japan. Few firms reported quarterly before the mandated
change, which took place on April 1, 2004. The table shows that almost all of the firms switched
soon after the time of the mandate.
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4 Main Empirical Tests
4.1 Main U.S. Tests
Amihud (2002) illiquidity is my main proxy for information asymmetry because it measures
the price impact of trades, which is the construct examined by the models in Kyle (1985) and
Bernhardt and Miao (2004).21 Conceptually, the price impact is the amount the stock price moves
in response to trading volume, and it increases when the information advantage of informed traders
increases (Kyle, 1985). Goyenko et al. (2009) compare Amihud (2002) illiquidity to the price impact
measured using intraday data, and they find that Amihud (2002) illiquidity measures the intraday
price impact well. In additional analyses, I show that the results below also hold when I use the
bid-ask spread as my information asymmetry proxy.
Interannouncement growth predicts that Amihud (2002) illiquidity will increase between
earnings announcements and fall after each new announcement in a sawtooth pattern. This
sawtooth is easy to see in visual representations of the data. Panel A of Figure 2 plots average
Amihud (2002) illiquidity in the 45 trading days before and after the earnings announcement for
the entire U.S. sample. To create the figure, I measure log(Price Impact) for each firm-day as
the logarithm of the Amihud (2002) illiquidity measure, |return|$ volume of trades (where dollar volume is in
terms of millions of dollars). The Amihud (2002) illiquidity measure is highly skewed; taking the
logarithm reduces the influence of outliers. I then subtract the mean value of log(Price Impact) for
the market on each observation’s calendar day to get Abnormal log(Price Impact). Finally, I plot the
average Abnormal log(Price Impact) in event time for each of the 45 trading days before and after
all earnings announcements in the sample.22 Consistent with interannouncement growth, Abnormal
log(Price Impact) increases gradually over the period leading up to the earnings announcement, and
falls after the announcement’s release.
In Panel B of Figure 2, I produce the same plot in a wider window that includes the 80
trading days before and after each earnings announcement. This plot clearly shows the sawtooth
21Consistent with the literature, I measure Amihud (2002) illiquidity throughout the paper as |return|$ volume of trades
.I recognize that the numerator and denominator have different scales, so in untabulated robustness tests I measureAmihud (2002) illiquidity as |∆ market capitalization|
$ volume of trades(i.e., the change in firm market value for every dollar of trading).
All of my results hold with this alternate measure.22For each plot, I only include an earnings announcement’s observations if the data needed to make the plot is
available on both the first and last day of the window. This ensures that the composition of firms in the plot doesnot change over the window.
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pattern predicted by interannouncement growth. In the data, information asymmetry grows over
time between the earnings announcements—which occur on event days -63 (approximately), 0, and
+63 (approximately)—and then falls after each new announcement’s release.
In order to better line up the three consecutive earnings announcements in event time,
Panel B only plots Abnormal log(Price Impact) in the 80 trading days before and after the second
quarter announcement, rather than the announcements of all four quarters.23 Even so, the adjacent
announcements do not always occur on days -63 and +63, which is why the information asymmetry
drop around these event days does not look as deep as it does around day 0.
I next show that the growth in information asymmetry between earnings announcements is
statistically significant after controlling for other factors. The regression takes the following form:
log(Price Impact)iyt = αiy + αt + βDays Since EAiyt + γControlsiyt + εiyt.
Each observation is a firm-day, with i indexing firms, y indexing calendar years, and t indexing
calendar days. I calculate log(Price Impact), my information asymmetry proxy, for each firm-day
as log(
|return|$ volume of trades
)(i.e., the logarithm of the daily Amihud (2002) illiquidity measure), where
dollar volume is in terms of millions of dollars. Taking the logarithm allows me to interpret my
coefficients as percentage changes. Days Since EA is the number of trading days since the firm’s
most recent earnings announcement (it resets to zero on each new earnings announcement day).
Interannouncement growth predicts that information asymmetry increases between announcements,
so the coefficient on Days Since EA, β, should be positive.
The regression includes firm-year fixed effects, where a year is a calendar year, which fully
control for fixed differences across firm-years. This means that firm-specific trends from year to year
are accounted for. It also includes calendar day fixed effects to control for aggregate fluctuations
that affect all of the firms over time. I cluster standard errors at both the firm and day levels to
account for correlation in the errors arising from within-firm autocorrelation and common daily
shocks.
In the Controls vector, I control for Size, the logarithm of the firm-day’s market value of
23While the number of days between the fourth quarter announcement and the first and third quarterannouncements varies across firm-years, the lag between the second quarter announcement and the first and thirdquarter announcements is generally about a quarter, or 63 trading days.
14
equity. Because turnover and return volatility are associated with liquidity (Stoll, 1978), I control
for Turnover, measured as the logarithm of one plus the fraction of the firm’s shares outstanding
traded that day, and Volatility, measured as the logarithm of one plus the standard deviation
of returns over the twenty trading days before the firm-day. Turnover also acts as a proxy for
investor attention—if attention wanes after the earnings announcement, then noise trading may
fall, causing liquidity to decrease. My measurements of Size, Turnover, and Volatility closely follow
prior literature (Leuz and Verrecchia, 2000; Fu et al., 2012). In particular, Turnover is measured
in accordance with the most common specification used in the literature (Bamber et al., 2011):
measuring trading activity as a percentage of shares outstanding is natural (Lo and Wang, 2000),
and taking the logarithm counteracts high skewness to the right (Ajinkya and Jain, 1989).
I also include Midpoint, measured as the logarithm of the midpoint between the bid and
the ask, because I expect trading to mechanically move prices more when prices are lower, given
that bid and ask quotes must be in one-penny increments. I include an indicator for the three-day
earnings announcement window (Earnings Window). I also include an indicator for the period after
the fourth-quarter earnings announcement (Annual Report), since it tends to have lower values of
Days Since EA, and the annual report may cause a larger reduction in information asymmetry than
the other quarterly reports. I include an indicator (Late Filing) that turns on when more trading
days than expected have passed since the quarter-end without an announcement.24 Amihud (2002)
illiquidity may be higher when the earnings announcement is late, since a late announcement is
usually an indication of bad news (Chambers and Penman, 1984). Finally, I include an indicator for
days that occur within five trading days before the earnings announcement (One Week Before) and
another for days that occur within five trading days after (One Week After). These two controls
make sure that the period around the earnings announcement, which may have greater information
leaks and noise trading, is not driving my results.25
Panel A of Table 3 contains the results for this test. Consistent with interannouncement
growth, the coefficient on Days Since EA is significantly positive. On average, each additional
day without a new earnings announcement comes with with a 0.161% increase (t=39.24) in the
24I estimate the expected filing date to be the median seasonal earnings announcement delay from the previousthree years (Cohen et al., 2007).
25In untabulated robustness checks, I re-perform this paper’s tests (both U.S. and international) while excludingfrom the sample the 11-day window around the earnings announcement. Results throughout the paper are robust tothis exclusion. It causes one substantive change, which I discuss in Section 6.1.
15
firm’s Amihud (2002) illiquidity. If a quarter (approximately 63 trading days) passes between two
earnings announcements, then this regression predicts a 10.7% increase in Amihud (2002) illiquidity
from just after the first announcement to just before the second one.
The controls tend to have sensible coefficients with the notable exception of Volatility,
which ought to be positively related to Amihud (2002) illiquidity. The negative coefficient on
Volatility flips to a positive sign in untabulated robustness tests when firm and year fixed effects
are used rather than firm-year fixed effects. Additional untabulated robustness checks show that
removing the Volatility control from the paper’s Amihud (2002) illiquidity tests does not change
any of the results. The coefficients on Size and Turnover are both consistent with prior literature.
The coefficient on Midpoint is negative, as expected. The coefficient on Earnings Window is
negative, consistent with the sharp drop around the earnings announcement shown in Figure 2.
The coefficient on Annual Report is insignificant. Contrary to my expectations, the coefficient
on Late Filing is negative. The coefficients on One Week Before and One Week After are both
significantly negative.
Panel B of Table 3 demonstrates that interannouncement growth occurs throughout the
entire interval between earnings announcements. Column (1) shows results from a regression like
the one in Panel A, except I include an indicator that turns on for days between quarter-end and
the earnings announcement date (Post Quarter-end), and I interact this indicator with Days Since
EA. The uninteracted Days Since EA coefficient remains significantly positive, demonstrating that
a brief information asymmetry spike right before the earnings announcement does not drive the
result. Instead, interannouncement growth occurs before the books close at quarter-end. In fact,
it is greater before quarter-end than after, since the coefficient on the interaction between Days
Since EA and Post Quarter-end is significantly negative. This seems to indicate that most of the
informed traders’ private information is not coming from insider leaks. If it were, I would expect
interannouncement growth to become more pronounced after the books close at quarter-end, when
the managers become more certain about recent performance.
Column (2) of Panel B uses a piecewise regression to show that interannouncement growth
occurs throughout the quarter. I create three indicators: One that turns on for the first 20 trading
days after the earnings announcement (1st Month), one that turns on for the days between the 21st
trading day and the 40th trading day after the earnings announcement (2nd Month), and one that
16
turns on for all days from the 41st trading day on (3rd Month). I then interact these indicators with
Days Since EA to see how the slope varies in each month. Column (2) reveals that the relationship
between Amihud (2002) illiquidity and Days Since EA is significantly positive in all three months
after the earnings announcement, consistent with interannouncement growth occurring throughout
the period between announcements.
Column (3) of Panel B corroborates that information asymmetry monotonically increases
between earnings announcements, without assuming linearity. Instead of regressing Amihud (2002)
illiquidity on Days Since EA, I regress it on an indicator that turns on for all days greater than 20
trading days after the previous earnings announcement (Greater Than 1 Month) and another that
turns on for all days greater than 40 trading days after the previous earnings announcement (Greater
Than 2 Months). The coefficients on both of these indicators are significantly positive, showing
a monotonic increase in information asymmetry. This is again consistent with interannouncement
growth occurring throughout the period between earnings announcements.
4.2 Main International Difference-in-Differences Test
I now estimate the amount that information asymmetry falls in response to the interan-
nouncement growth reduction brought about by a switch from semiannual to quarterly reporting.
I use a difference-in-differences design to obtain this estimate. The U.S. has required quarterly
reporting since 1970, so I use international settings with both semiannual and quarterly reporters
to perform this test.26
Figure 3 illustrates the logic behind the difference-in-differences. The figure shows a
hypothetical firm’s interannouncement growth when the firm reports semiannually versus when
it reports quarterly. Notice that interannouncement growth only causes higher information
asymmetry for the semiannual reporter in the second and fourth quarters, but not in the first
and third quarters.27 Therefore, in order to estimate the effect of a switch from semiannual to
quarterly reporting, I must estimate the drop in average information asymmetry during the second
and fourth quarters. A naïve test would cross-sectionally compare the second- and fourth-quarter
Amihud (2002) illiquidity of semiannual and quarterly reporters. But this cross-sectional difference26I describe these settings in Section 3.1.27For the difference-in-differences, a “quarter” is bounded by the previous earnings announcement and the next
earnings announcement, as depicted in Figure 3.
17
would also contain the effects of any other factors that differ between these two groups of firms. I
perform a difference-in-differences to remove the effects of these other factors from the estimate.
The difference-in-differences compares the semiannual and quarterly reporters’ change in
Amihud (2002) illiquidity from the first to the second quarter and from the third to the fourth
quarter.28 As depicted in Figure 3, I expect this change to be lower for quarterly reporters than
for semiannual reporters because of interannouncement growth (i.e., I expect B – A < D – C). The
difference-in-differences controls for any effects from other factors that differ between semiannual
and quarterly reporters. As depicted in the figure, a firm’s decision to report semiannually or
quarterly does not affect interannouncement growth in the first and third quarters, so any cross-
sectional difference in Amihud (2002) illiquidity during these quarters comes from factors other
than interannouncement growth. As long as these other factors have the same effect in quarters
one and three as in quarters two and four, a difference-in-differences subtracts out their impact,
leaving an estimate of the effect from reducing interannouncement growth.
The regression equation for the difference-in-differences is as follows:
log(Price Impact)iyt = αiy + αt + β0Q2 or Q4iyt + β1Quarterlyiy ×Q2 or Q4iyt
+γControlsiyt + εiyt. (1)
Each observation is a firm-day, with i indexing firms, y indexing years, and t indexing calendar
days. For this regression, I define a year to run from the earnings announcement of the previous
fiscal year’s last period to the earnings announcement of the current fiscal year’s last period.29
In other words, I treat the four quarters shown in Figure 3 as a year. This ensures that all four
quarters get the same designation as either a semiannual or a quarterly reporter.
Q2 or Q4 is an indicator that turns on for days that occur between the first and second
quarter earnings announcements or the third and fourth quarter earnings announcements. In other
words, Q2 or Q4 turns on during the second and fourth quarters in Figure 3. Of course, semiannual
reporters do not have first or third quarter announcements, so I estimate the day that these interim
28This research design is similar to the one used in Hu (2016).29More precisely, I define firm-years to run from two days after the earnings announcement of the previous fiscal
year’s last period to the day after the earnings announcement of the current fiscal year’s last period. I include theday after the earnings announcement in the same period as the day of the earnings announcement in keeping withthe convention of treating the day after the earnings announcement as part of the earnings announcement window.
18
announcements would have occurred if the firm were to report quarterly, and I turn on the Q2 or
Q4 indicator for days after this estimated announcement date.
To estimate when an interim earnings announcement would have occurred, I first count the
number of trading days for each quarterly reporter from the beginning of the fiscal semester to the
date of the interim quarter’s earnings announcement.30 For example, for the first semester of a
calendar-year firm, I would count the number of trading days from January 1st to the date of the
first quarter earnings announcement. Once I have calculated this interval for each fiscal semester of
each quarterly reporter, I take the median for each firm across the years when it reports quarterly.
For the semiannual reporting years of each of these firms, I then use this median to create estimates
of what the first and third quarter earnings announcement dates would have been if the firm had
reported quarterly that year.31 For example, say that a particular firm has a median of 90 trading
days between the beginning of the fiscal semester and the interim earnings announcement for years
when it reports quarterly. For the years when the firm reports semiannually, I estimate that a first
or third quarter earnings announcement would have happened on the 90th trading day of the fiscal
semester. So for the first semester of these semiannual reporting years, the Q2 or Q4 indicator will
be zero from the day after the second semester earnings announcement to the 89th day of the fiscal
semester, and will be one from the 90th day of the fiscal semester to the day of the first semester
earnings announcement.
The Quarterly variable in the regression is an indicator that turns on when the firm-year is
a quarterly reporter. Reporting frequency is recorded by Worldscope at the annual level under the
variable WC05200. If WC05200 indicates that a firm reports quarterly, but the firm-year has no
first-quarter or third-quarter observations, then I exclude the observations for that firm-year from
the sample. If the firm only reports annually, I also exclude the observations for that firm-year.
The regression also includes both firm-year and calendar day fixed effects. The firm-year
fixed effects control for the difference between the semiannual and quarterly reporters’ Amihud
(2002) illiquidity during quarters one and three. This controls for differences arising from factors
30Here and elsewhere in the paper, I define the first fiscal semester as the first two fiscal quarters of the year, andthe second fiscal semester as the last two fiscal quarters.
31For firms that never switch to quarterly reporting, I use the median interval for the entire sample to make thisdetermination. This is 92 trading days in the European sample, 93 trading days in the Singaporean sample, and 91trading days in the Japanese sample. In all three samples, there is very little variation in the median from year toyear.
19
other than interannouncement growth. Note that Quarterly does not enter the regression equation
on its own, since a firm’s decision to report quarterly is fixed for a given firm-year. This means
that the test is well-identified for firms that voluntarily adopt quarterly reporting, as long as the
unobservables that caused the firm to adopt have the same effect on Amihud (2002) illiquidity in
quarters one and three as in quarters two and four. I cluster standard errors at both the firm
and day levels to account for correlation in the errors arising from within-firm autocorrelation and
common daily shocks.32
The Q2 or Q4 indicator captures the average change in Amihud (2002) illiquidity from
the first to the second quarter and from the third to the fourth quarter for semiannual reporters.
The interaction between the Q2 or Q4 indicator and the Quarterly indicator is my variable of
interest, and it captures the difference-in-differences. In other words, the interaction term coefficient
estimates the difference between the quarterly and semiannual reporters’ change in Amihud (2002)
illiquidity from the first to the second quarter and from the third to the fourth quarter. I expect
this coefficient to be negative, because I expect a lower change for the quarterly reporters than the
semiannual reporters.
In the regression, I include controls for Size, Turnover, Volatility, Midpoint, Earnings
Window, One Week Before, and One Week After, which have the same definitions as in Section
4.1.33 I also control for First Semester, an indicator that turns on between the year-end earnings
announcement of the previous year and the second quarter/first semester earnings announcement
of the current year.
Results are in Table 4. The Quarterly by Q2 or Q4 interaction term’s coefficient estimates
that quarterly reporting reduces Amihud (2002) illiquidity in the second and fourth quarters by
5.3% (t=-10.04) for European firms and 2.9% (t=-2.11) for Singaporean firms. This is consistent
with quarterly reporting reducing information asymmetry because it reduces interannouncement
growth. While the coefficient is negative for the Japanese sample, it is insignificantly different
from zero. It could be that the true coefficient is actually negative, or it could be that there is
no interannouncement growth in Japan.34 If the latter is true, this should not be taken as strong
32Clustering at the firm-quarter level, rather than the firm level, does not change the significance of the results.33The results are the same, and generally more significant, when I omit these controls.34In support of the former explanation, when I repeat the U.S. test in Panel A of Table 3 using the Japanese sample
(untabulated), I find a significant positive relationship between Days Since EA and log(Price Impact). So it may bethat the difference-in-differences just lacks power. I also find a significant postive relationship between Days Since
20
evidence against interannouncement growth elsewhere, since common asset pricing patterns—such
as those based on size and momentum—do not exist in Japan (Fama and French, 2012; Chui
et al., 2010), and accounting measures explain significantly less of firm market value in Japan
than in the U.S. (Ely and Pownall, 2002). Also, Harris and Darrough (1989) note that the vast
majority of Japanese firms provide management forecasts of earnings, and they find evidence that
these forecasts are value-relevant. If these management forecasts preempt much of the earnings
announcement’s information, then the switch to quarterly reporting may not have much of an
effect on interannouncement growth, since most of the growth would occur between management
forecasts rather than between earnings announcements.
For both Europe and Singapore, the coefficient on Q2 or Q4 is significantly positive,
consistent with semiannual reporters’ information asymmetry increasing from quarters one and
three to quarters two and four. The illustration in Figure 3 predicts that quarterly reporting will
undo this increase, which means the negative coefficient on the interaction term should have the
same magnitude as the positive coefficient on Q2 or Q4. This appears to be true for the European
sample. Both the positive coefficient on Q2 or Q4 and the negative coefficient on the interaction
term have a magnitude of about 0.05, and their sum is insignificantly different from zero with a
t-statistic of 0.18. But the Singaporean sample’s Q2 or Q4 coefficient has double the magnitude
of its interaction term coefficient, and the sum of the two coefficients is significantly positive. This
suggests that the Singaporean firms have some trend other than interannouncement growth that
causes Amihud (2002) illiquidity to increase over the fiscal year. As long as this other trend is
parallel for the semiannual and quarterly reporters, then the difference-in-differences controls for
it, and the coefficient on the interaction term identifies the effect from interannouncement growth.
I test for parallel trends in the next subsection.
4.3 Testing Parallel Trends Assumption in International Test
To gain comfort that interannouncement growth drives the result in the previous subsec-
tion’s difference-in-differences, I need to show that the result is not driven by other information
asymmetry trends over the course of the fiscal year.
Such other trends might exist. For instance, there could be a trend based on seasonality.
EA and log(Price Impact) when I repeat this test for the European and Singaporean samples (also untabulated).
21
If most of a firm’s business is concentrated at the end of its fiscal year, there may not be much
information asymmetry early in the year because there is little new information to begin with.
When business activity picks up at the end of the year, there would be new information to gather,
leading to higher information asymmetry. Thus information asymmetry would increase over the
course of the fiscal year. In the previous subsection, I found evidence that Singaporean firms have
some trend other than interannouncement growth that causes information asymmetry to increase
from the first and third quarters to the second and fourth quarters. If such a trend is not parallel
between the semiannual and quarterly reporters, it may drive the difference-in-differences results.
But if it is parallel, then the difference-in-differences is well-identified.
Figure 4 illustrates how non-parallel trends could drive Table 4’s result. Panel A shows the
schematic from Figure 3. It depicts interannouncement growth for a semiannual and a quarterly
reporter, with the implicit assumption that the firms have parallel underlying Amihud (2002)
illiquidity trends over time.35As before, the change in Amihud (2002) illiquidity from the first to
the second quarter and from the third to the fourth quarter is larger for the semiannual reporter
than the quarterly reporter (i.e., Bi – Ai < Di – Ci for i ∈ {1, 2}), and this inequality is caused by
interannouncement growth. But Panel B shows that, even without interannouncement growth, the
same inequality can come from an Amihud (2002) illiquidity trend that increases more over time for
semiannual reporters than for quarterly reporters (i.e., Panel B still predicts that Bi – Ai < Di –
Ci for i ∈ {1, 2}, even without interannouncement growth). So Table 4’s results could come from
this difference in trends rather than from interannouncement growth. Fortunately, a comparison of
Panels A and B suggests another difference-in-differences that can test for this difference in trends.
If the underlying trend for semiannual reporters increases faster than for quarterly reporters, as in
Panel B, then a difference-in-differences should find that Amihud (2002) illiquidity grows more from
the first half of the year to the second half for semiannual reporters than for quarterly reporters
(i.e., A2 – A1 < C2 – C1 and B2 – B1 < D2 – D1). In contrast, if the underlying trends
are parallel over time and interannouncement growth drives the result in Table 4, as in Panel A,
then I should find that the change from the first half of the year to the second half is the same for
semiannual and quarterly reporters (i.e., A2 – A1 = C2 – C1 and B2 – B1 = D2 – D1).
35More precisely, Panel A implicitly assumes that there are no underlying trends affecting Amihud (2002) illiquidity,other than interannouncement growth. But the analysis would be the same if the semiannual and quarterly reportershad a trend that increased Amihud (2002) illiquidity by the same amount for both each quarter.
22
Based on this logic, I perform another difference-in-differences to test the parallel trends
assumption. The regression takes the following form:
log(Price Impact)iyt = αiy + αt + β0Second Half-yeariyt
+β1Quarterlyiy × Second Half-yeariyt + γControlsiyt + εiyt.
Second Half-year is an indicator that equals 1 for days in quarters three and four (the firm-year’s
second half-year), and 0 for days in quarters one and two (the firm-year’s first half-year). Quarterly
is defined the same as in Section 4.2, and the regression includes the same controls and fixed-
effects as that section’s regression other than First Semester, which I omit because it has perfect
collinearity with Second Half-year. I continue to cluster standard errors at both the firm and day
levels.
If semiannual and quarterly reporters have parallel underlying Amihud (2002) illiquidity
trends over time, then β1 would equal zero. This would indicate that interannouncement growth
drives Table 4’s difference-in-differences result. On the other hand, if semiannual and quarterly
reporters have different underlying trends, then β1 will be different from zero. If β1 is negative,
then this difference in trends may be responsible for the results in Table 4. A negative β1 would
indicate that quarterly reporters have a lower Amihud (2002) illiquidity trend than semiannual
reporters, which would give quarterly reporters a lower change from the first to the second quarter
and from the third to the fourth quarter, even without interannouncement growth. On the other
hand, a positive β1 would indicate a difference in trends that works against interannouncement
growth.
In Table 5, the coefficient on the interaction between Quarterly and Second Half-year
is insignificantly different from zero for the European, Singaporean, and Japanese samples, so
the test does not reject the parallel trends assumption. This increases my confidence that
interannouncement growth drives the result in Table 4’s difference-in-differences.
23
5 Policy Implications
5.1 Reducing Information Asymmetry is a Good Reason to Report More
Frequently
This paper provides evidence that interannouncement growth is the mechanism through
which more frequent reporting reduces information asymmetry. Establishing this mechanism is
important for decision-makers. If managers and regulators do not know how a higher reporting
frequency reduces information asymmetry, they cannot know whether the reduction provides a
good reason to report more frequently. This is especially true, given that neither of the two other
likely possible mechanisms justifies a higher reporting frequency.
The first of these other possible mechanisms is as follows: more frequent reporting may
reduce information asymmetry by simply increasing total public information, as suggested by Fu
et al. (2012). Unlike interannouncement growth, which focuses on the timing of the disclosures,
this explanation imagines an increase in the overall level of public information.36 More frequent
reports may increase this level by providing a finer breakout of firm performance into shorter time
intervals, which would make it easier to spot trends. If informed traders were already aware of
these trends, then the finer breakout would decrease information asymmetry. But if more-frequent
reporting only reduced information asymmetry through this channel, then firms could achieve the
reduction without increasing reporting frequency at all. Rather than adopt quarterly reporting, a
semiannual reporter could just continue reporting semiannually and break firm performance out
by quarter within each semiannual report. This would reveal the trends and reduce information
asymmetry without incurring the costs of more frequent reporting.
The second alternative is that quarterly reporting may reduce information asymmetry by
reducing private research.37 When there is less time to discover private information before it
becomes public, there may be a lower benefit to searching for it. This could in turn reduce
the amount of private research conducted. But while reducing private research would reduce
asymmetry, it would also likely reduce price discovery.38 The costs from less efficient prices could
36This is clear because Fu et al. (2012) examine reporting frequency’s effect on information asymmetry’s mean overthe entire year, and not just the second and fourth quarters. Interannouncement growth only predicts a reductionduring the second and fourth quarters.
37This mechanism is also suggested in Cuijpers and Peek (2010).38This would happen if private research yields private information about the future as well as about the current
24
outweigh the benefits from this channel’s information asymmetry reduction.
In contrast to these two mechanisms, reducing interannouncement growth does not generate
any obvious additional costs, and the easiest way to reduce it is by increasing reporting frequency.
So the drop in information asymmetry—and any resulting cost of capital reduction—caused
by lower interannouncement growth provides a good reason to report more frequently. Unlike
interannouncement growth, neither of the other two mechanisms predict my results, because neither
say anything about how information asymmetry evolves over time. A change in the total amount
of public information or private research would change the overall level of information asymmetry,
even if there were no interannouncement growth.
Finding evidence of interannouncement growth helps decision-makers, both managers and
regulators, as they weigh trade-offs to determine an optimal reporting frequency. The costs of more
frequent reporting include increased managerial short-termism and disclosure costs (Gigler et al.,
2014; Kraft et al., 2015; Ernstberger et al., 2015; Verdi, 2012). Evidence of interannouncement
growth demonstrates that the information asymmetry reduction is a countervailing benefit to
weigh against these costs. This finding also informs decision-makers that firms with steeper
interannouncement growth slopes benefit more from increasing reporting frequencies. Finally,
interannouncement growth implies that the marginal benefit from reducing information asymmetry
gets smaller with each reporting frequency increase. I discuss this decreasing marginal benefit in
the next subsection.
The academic literature identifies two other possible benefits from more frequent reporting:
improved price discovery (Butler et al., 2007; Arif and De George, 2015) and lower cost of capital
(Fu et al., 2012). Among the possible benefits, the information asymmetry reduction is particularly
important. This is because the evidence on improved price discovery is mixed—Butler et al. (2007)
find that it only improves for firms that voluntarily increase their reporting frequencies—and some
of the cost of capital reduction likely comes from the reduction in information asymmetry.
quarter’s performance. If quarterly reporting reduces private research, then it may reduce the speed with whichnews that will affect future earnings gets incorporated into the price, even as it increases the speed with which pastperformance gets incorporated into the price through more timely public reports.
25
5.2 Interannouncement Growth Implies a Decreasing Marginal Benefit
One of interannouncement growth’s implications is that the marginal information asymme-
try reduction diminishes with each increase in reporting frequency. With this diminishing marginal
benefit, if there is even a small constant cost to prepare each financial report, then at some point this
cost will outweigh the marginal benefit from lower information asymmetry. So while the presence
of interannouncement growth implies that the information asymmetry reduction is beneficial, it
also implies that the benefit decreases at higher reporting frequencies.
To see this, suppose that information asymmetry, x, is simply equal to the amount of time
since the earnings announcement, t (i.e., x(t) = t). If there is an interval of length T between
earnings announcements, then average information asymmetry is 1T
´ T0 x(t)dt = 1
2T . Doubling the
reporting frequency cuts T in half, which in turn cuts average information asymmetry in half. At
the same time, if there is a fixed cost, c > 0, to produce each financial report, then doubling the
reporting frequency doubles report preparation costs. Suppose that t is in terms of trading days,
with 250 days in a year. Also suppose that the preparation cost per report is c = 1, and that the
cost of information asymmetry is equal to average information asymmetry during the year. Then
the annual costs across different reporting frequencies are as follows:
Reporting Interval Information Report Total
Frequency Between Asymmetry Preparation Annual
Per Year Reports (T ) Cost (12T ) Cost Cost
Once 250 125 1 126
Twice 125 62.5 2 64.5
Four Times 62.5 31.25 4 35.25
Eight Times 31.25 15.625 8 23.625
Sixteen Times 15.625 7.8125 16 23.8125
Notice the decreasing marginal benefit. Moving from one report per year to two decreases the
information asymmetry cost by 62.5, moving from two to four decreases it by 31.25, and so on. At
the same time, the marginal increase in report preparation costs is doubling. So even though the
preparation cost is less than 1% of the information asymmetry cost when the firm reports annually,
doubling the number of reports quickly moves the two costs towards each other. Among the options
26
presented, costs are lowest when the firm reports eight times per year.
As reporting frequency grows, the marginal information asymmetry reduction will even-
tually become vanishingly small. If the marginal costs from increasing reporting frequencies are
constant or growing, then they will eventually outweigh the marginal benefit from lower asymmetry.
As shown in the example, it is not unreasonable to expect the marginal cost to increase as reporting
frequency doubles, since there are twice as many new reports to prepare after each doubling. So
while reducing information asymmetry through the interannouncement growth channel could justify
switching from semiannual to quarterly reporting, it probably cannot justify moving all the way to
continuous reporting.
6 Additional Analysis
6.1 Repeating U.S. Tests with Bid-Ask Spreads
I next re-perform the previous tests using the bid-ask spread as my measure of information
asymmetry. Both the U.S. and international results are robust when I switch to this measure.
Panel A of Figure 5 plots the bid-ask spread in the forty-five trading days before and after
the earnings announcement for the entire U.S. sample. In creating this plot, I follow the same steps
as I did for the plot in Panel A of Figure 2. Consistent with interannouncement growth, the plot
shows that bid-ask spreads increase over time and then drop right after a brief spike during the
earnings announcement. Panel B of Figure 5 extends the window to include eighty trading days
before and after the earnings announcement, which includes the previous and subsequent earnings
announcements in the window.39 The pattern shown in Panel A repeats over time, with information
asymmetry again rising between each earnings announcement.
I next repeat the U.S. regressions described in Section 4.1 with bid-ask spreads on the
left-hand side rather than Amihud (2002) illiquidity.40 These results are in Table 6. In Panel
A, I regress the bid-ask spread on Days Since EA, defined as in Section 4.1, and controls. The
coefficient on Days Since EA is significantly positive, which is consistent with interannouncement
growth and with the results when Amihud (2002) illiquidity is on the left-hand side (see Panel A of39As in Panel B of Figure 2, the window is centered on the second quarter earnings announcement.40Specifically, the left-hand side variable in these regressions is log(Spread), which is calculated for each firm-day
as log(
100 ∗ ask−bid(ask+bid)/2
).
27
Table 3). On average, each additional day without a new earnings announcement is associated with
a 0.03% increase (t=16.61) in the firm’s bid-ask spread. If a quarter (approximately 63 trading
days) passes between earnings announcements, then this regression predicts a 1.9% increase in the
bid-ask spread from right after the first earnings announcement to right before the second.
The controls tend to have sensible coefficients. The coefficients on Size, Turnover, and
Volatility are all consistent with prior literature. The coefficient on Midpoint is negative, which is
to be expected since it enters into the denominator in Bid-Ask Spread. The coefficient on Earnings
Window is positive, consistent with the spike around the earnings announcement shown in Figure 5.
The coefficient on Annual Report is significantly positive. The coefficient on Late Filing is negative,
but insignificantly different from zero. The coefficients on One Week Before and One Week After
are both positive.
Panel B of Table 6 repeats the tests in Panel B of Table 3 with bid-ask spreads on the left-
hand side instead of Amihud (2002) illiquidity. Again, the results reveal that interannouncement
growth occurs throughout the entire period between earnings announcements. Column (1)
shows results from the regression that interacts Post Quarter-end with Days Since EA. The
significant positive coefficient on the uninteracted Days Since EA variable demonstrates that
interannouncement growth occurs before the books close at quarter-end. This indicates that leaks
right before the earnings announcement do not drive the positive coefficient on Days Since EA in
the main specification.
Column (2) shows results from the piecewise regression, which examines how the slope
on Days Since EA varies from month to month. While the relationship between bid-ask spreads
and Days Since EA is significantly positive during the second and third months after the earnings
announcement, it is negative during the first month. The first month’s negative coefficient likely
comes from the large drop in bid-ask spreads right after the earnings announcement, which can
be seen in Figure 5. In support of this hypothesis, untabulated results show that this coefficient
becomes significantly positive when I re-perform this test with the 11-day window around the
earnings announcement excluded from the sample.
Column (3) regresses bid-ask spreads on the indicators Greater Than 1 Month and Greater
Than 2 Months. The coefficients on both indicators are significantly positive, again indicating that
information asymmetry grows monotonically between earnings announcements.
28
6.2 Repeating International Results with Bid-Ask Spreads
In this section, I repeat my international tests with the bid-ask spread as my information
asymmetry proxy. Table 7 presents results for the same difference-in-differences test as in Section
4.2, except that bid-ask spreads are on the left-hand side. As before, the variable of interest is the
interaction between Quarterly and Q2 or Q4. The test estimates that bid-ask spreads in quarters
two and four are 1.3% lower (t=-5.12) when European firms report quarterly and 1.5% lower (t=-
3.48) when Singaporean firms report quarterly. While the coefficient is negative for the Japanese
sample, it is again insignificantly different from zero.
For both Europe and Singapore, the coefficient on Q2 or Q4 is significantly positive, which
is consistent with interannouncement growth. But as with the Singaporean sample in the Amihud
(2002) illiquidity tests, this coefficient’s magnitude is different from that of the interaction term’s
coefficient, suggesting that there are trends other than interannouncement growth during the year.
As before, these trends do not affect the difference-in-differences estimate as long as they are parallel
for semiannual and quarterly reporters.
Table 8 presents results for the parallel trends test, which is the same as in Section 4.3,
except that bid-ask spreads are on the left-hand side. The coefficient on the interaction between
Quarterly and Second Half-year is insignificantly different from zero for the Singaporean and
Japanese samples. This indicates that there is no significant difference between the underlying
bid-ask spread trends of semiannual and quarterly reporters in these countries.
The positive coefficient on the European sample’s interaction term is significant at the
10% level, indicating a more-positive underlying trend for quarterly reporters than semiannual
reporters. This difference in trends works against interannouncement growth, meaning that the
European sample’s interaction term coefficient in Table 7 is likely biased towards zero. So while
this difference in trends affects the accuracy of Table 7’s estimate, it also provides evidence that
interannouncement growth drives the result.
6.3 Other Public Information and Interannouncement Growth
If the information released by the earnings announcement causes information asymmetry
to fall, then other public information should cause it to fall too. Indeed, Amiram et al. (2016)
29
show that analyst forecasts cause a drop in information asymmetry. If the analyst forecast—or
any other disclosure, for that matter—contains information about earnings, then some of this drop
should reduce the accumulation of earnings-related information asymmetry. When more of these
disclosures occur between earnings announcements, the accompanying drops should reduce the total
amount of interannouncement growth during the quarter. Therefore, I should find that firms with
more interannouncement disclosures have lower interannouncement growth slopes when I regress
information asymmetry on the number of days since the earnings announcement.
The prediction is less clear when a disclosure comes out during the earnings announcement
itself. If all of the disclosure’s information relates to next quarter’s earnings, then it likely reduces
information asymmetry throughout the entire period between the current earnings announcement
and the next one. A reduction that lasts for the entire period might not affect the rate of
interannouncement growth—it might just reduce the intercept of information asymmetry and leave
the slope unchanged. On the other hand, if some of the disclosure’s information is unrelated
to next quarter’s results, it could create a drop in information asymmetry during the earnings
announcement that does not last until the next announcement. Because such a drop would reverse
between the two announcements, it would increase the total growth in information asymmetry over
the period. In other words, the initial drop during the announcement would reduce the intercept,
and the reversal during the quarter would increase the slope. Therefore, I expect disclosures
that occur during the earnings announcement to increase the interannouncement growth slope, if
anything.
I test these two hypotheses by examining the effects of analyst forecasts and 8-K filings on
interannouncement growth. The regression takes the following form:
log(Price Impact)iyt = αiy + αt + β0Days Since EAiyt + β1EA Disclosure Countiq
+β2Non-EA Disclosure Countiq
+β3Days Since EAiyt × EA Disclosure Countiq
+β4Days Since EAiyt ×Non-EA Disclosure Countiq
+γControlsiyt + εiyt.
30
Each observation is a firm-day, with i indexing firms, y indexing calendar years, t indexing calendar
days, and q indexing fiscal quarters as bounded by earnings announcements. The regression again
puts my information asymmetry proxies on the left-hand side. On the right-hand side, it interacts
Days Since EA, defined as in the main specification (see Section 4.1), with EA Disclosure Count,
which counts the number of disclosures on the day of and the day after the most recent earnings
announcement, as well as with Non-EA Disclosure Count, which counts the number of disclosures
during the current interval between two earnings announcements (not including disclosures during
the earnings announcement windows themselves).41 I run two seperate sets of specifications,
where the disclosures are either analyst forecasts42 or 8-K filings.43 Since I expect disclosures
between earnings announcements to reduce the interannouncement growth slope, I expect β4 to be
negative. And since I expect disclosures during the earnings announcement to either increase the
interannouncement growth slope or leave it unchanged, I expect β3 to be non-negative. As in the
main specification in Section 4.1, the regression includes firm-year fixed effects and calendar day
fixed effects, and I cluster standard errors at both the firm and day levels. The Controls vector is
also the same as the one in the main specification.
Table 9 contains the results. As predicted, β4 is significantly negative in all specifications.
In other words, the interannouncement growth slope is less steep when there are more analyst
forecasts (columns (1) and (2)) and 8-K filings (columns (3) and (4)) during the period between
two earnings announcements. Also as predicted, β3 is significantly positive in the 8-K specification
(columns (3) and (4)), meaning that 8-K filings during the earnings announcement increase the
steepness of the interannouncement growth slope. On the other hand, β3 is insignificant in columns
1 and 2, indicating that more analyst forecasts during the earnings announcement do not increase
the slope. Perhaps this occurs because analyst forecasts only provide information about the next
earnings announcement. As discussed above, this could lead to no change in the interannouncement
growth slope when the number of forecasts during the earnings announcement increases.
41By “current” interval, I mean the interval that contains the firm-day observation. By “earnings announcementwindow,” I mean the day of and the day after an earnings announcement.
42The analyst forecasts come from I/B/E/S. If an analyst makes multiple forecasts on the same day, then I countit as a single forecast.
438-K filing data comes from EDGAR. All public companies were required to post their filings on EDGAR beginningon May 6, 1996, so the sample period for the 8-K specification of this test begins on that date.
31
6.4 U.S. Results Hold in Different Periods
The main U.S. results run from 1993 to 2015, a period that includes the decimalization of
bid and ask quotes and the rise of high-frequency trading. In Table 10, I re-run the main U.S.
regression separately for the years 1993 to 2001, 2002 to 2007, and 2007 to 2015.44 The NYSE,
AMEX, and NASDAQ switched to decimal prices in 2001, so the first period shows the results
before decimalization. The second period is between the implementation of decimalization and the
financial crisis. The last period is post-crisis, and is also a period characterized by the prominence
of high-frequency trading. With either log(Price Impact) or log(Spread) on the left-hand side, the
coefficient on Days Since EA is significantly positive in all of these periods.
7 Conclusion
In this paper, I propose and find evidence for a mechanism that explains the negative
relationship between information asymmetry and reporting frequency. Information asymmetry
between informed and uninformed investors grows steadily until a new earnings announcement
causes it to fall again. This creates a sawtooth pattern that I call interannouncement growth.
More frequent reporting reduces a firm’s average information asymmetry by reducing the time
available for interannouncement growth to occur. In univariate plots and multivariate regressions,
I provide evidence for interannouncement growth in the United States. I estimate that Amihud
(2002) illiquidity, my main proxy for information asymmetry, grows by 10.7% over the period
between two quarterly earnings announcements. I then move to international settings to estimate
the effect when firms switch from semiannual to quarterly reporting. I estimate that quarterly
reporting’s reduction of interannouncement growth causes Amihud (2002) illiquidity to fall by up
to 5.3% on average in the second half of each semiannual period.
Interannouncement growth has direct implications for the reporting frequency debate. First
of all, it implies that more frequent reporting’s information asymmetry reduction provides a
good reason to increase reporting frequency. This is because reducing interannouncement growth
does not generate any obvious additional costs, and the easiest way to reduce it is to report
44More specifically, I include firm-days based on the year in which the previous earnings announcement occurred.So if the previous earnings announcement for a firm-day observation in January of 2002 was in December of 2001,the observation would be included in the 1993 to 2001 sample.
32
more frequently. Interannouncement growth also implies that not all (and perhaps none) of the
information asymmetry reduction comes from breaking firm performance out into shorter time
intervals in the financial reports. This means firms cannot achieve the entire reduction by simply
reporting more about current performance trends—they need to actually increase their reporting
frequencies. In addition, by explaining the drop in information asymmetry, interannouncement
growth makes it less likely that more-frequent reporting reduces private research, which would be
costly since less private research means slower price discovery.
In order to determine optimal reporting frequencies, regulators and managers need to
know the mechanism behind the information asymmetry reduction. Without knowing this
mechanism, they cannot know how the reduction might vary across firms, or how it might change
with further increases in reporting frequency (e.g., from quarterly to monthly reporting). This
study tells practitioners that higher reporting frequencies more-greatly benefit firms with steeper
interannouncement growth slopes. Interannouncement growth also implies that the marginal benefit
from reducing information asymmetry gets smaller and smaller with each reporting frequency
increase, and vanishes as the reporting frequency becomes large. As a result, information
asymmetry alone likely cannot justify continuous reporting.
More generally, interannouncement growth increases our understanding of how accounting
affects capital markets. Theory shows that information asymmetry could rise or fall over time,
depending on the circumstances. By showing empirical evidence of interannouncement growth,
this paper shows that information asymmetry in fact rises, and this rise is interrupted by each
earnings announcement. Future theoretical models should reproduce this pattern in order to better
reflect the real world.
33
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Figure 2: Average Price Impact of Trades Around the Earnings Announcement
This graph plots my information asymmetry proxy around the earnings announcement. My proxy is log(Price Impact),which I measure as the logarithm of the Amihud (2002) illiquidity measure, |return|
$ volume of trades(where dollar volume
is in terms of millions of dollars). For the plots, I remove market effects by subtracting the mean log(Price Impact)for the market that day; I call the difference the Abnormal log(Price Impact). For Panel A, I then plot the meanAbnormal log(Price Impact) in event time during the 45 trading days before and after the earnings announcement.Panel B widens the window to 80 trading days before and after the earnings announcement in order to show thatthe pattern repeats from quarter to quarter. For the Panel B plot, I restrict the sample to windows centered on thesecond quarter earnings announcement. This reduces cross-sectional variation in the lag between adjacent quarters’announcements, which makes the announcements line up better in event time. (While the number of days between the4th-quarter announcement and the 1st- and 3rd-quarter announcements varies across firm-years, the lag between the2nd-quarter announcement and the 1st- and 3rd-quarter announcements is generally about a quarter, or 63 tradingdays.) For both graphs, I only include a firm-quarter’s observations if both the first and last day of the window arenot missing.
Panel A: 91 Trading Days Around Earnings Announcement
−.1
5−
.1−
.05
0.0
5M
ean
Abn
orm
al lo
g(P
rice
Impa
ct)
−40 −20 0 20 40Days Relative to Earnings Announcement
Panel B: 161 Trading Days Around 2nd-Quarter Earnings Announcement
−.1
5−
.1−
.05
0.0
5M
ean
Abn
orm
al lo
g(P
rice
Impa
ct)
−100 −50 0 50 100Days Relative to Earnings Announcement
39
Figure 3: Illustration of Logic Behind Difference-in-Differences Test
This visual aid illustrates the logic behind the difference-in-differences test in Table 4. It showsa hypothetical firm’s interannouncement growth when the firm reports semiannually versus whenit reports quarterly. Switching from semiannual to quarterly reporting reduces the time availablefor interannouncement growth, reducing information asymmetry in the second and fourth quarters,but not in the first and third quarters. I estimate the second- and fourth-quarter informationasymmetry reduction with a difference-in-differences that compares the semiannual and quarterlyreporter’s change in Amihud (2002) illiquidity from the first (third) quarter to the second (fourth)quarter. The semiannual reporter’s change is D – C, and the quarterly reporter’s change is B –A. Interannouncement growth predicts that B – A < D – C.
40
Figure 4: Illustration of Logic Behind Parallel Trends Test
This visual aid illustrates the logic behind my test of the parallel trends assumption, which is crucial to the difference-in-differences test described in Figure 3. (Table 5 contains the results of this parallel trends test.) Panel A containsthe schematic from Figure 3, which shows interannouncement growth for a semiannual and a quarterly reporter.The schematic also assumes that the semiannual and quarterly reporters have parallel underlying Amihud (2002)illiquidity trends over time. As in Figure 3, Bi – Ai < Di – Ci for i ∈ {1, 2}. Panel B shows that this inequality,Bi – Ai < Di – Ci , can also result from an underlying Amihud (2002) illiquidity trend that increases more overtime for semiannual reporters than for quarterly reporters, even in the absence of interannouncement growth. But ifPanel B is true, then I should also find that A2 – A1 < C2 – C1 and B2 – B1 < D2 – D1. In contrast, underPanel A’s assumptions—where the underlying trends are parallel over time and interannouncement growth drives theBi – Ai < Di – Ci inequality—I should find that A2 – A1 = C2 – C1 and B2 – B1 = D2 – D1.
Panel A: Amihud (2002) Illiquidity with Parallel Trends and Interannouncement Growth
Panel B: Amihud (2002) Illiquidity without Parallel Trends or Interannouncement Growth
41
Figure 5: Average Bid-Ask Spread Around the Earnings Announcement
Panels A and B in this figure are created the same way as the plots in Panels A and B of Figure 2, except they plotthe mean Abnormal log(Bid-Ask Spread). I measure the bid-ask spread for each firm-day as 100 ∗ ask−bid
(ask+bid)/2 .
Panel A: 91 Trading Days Around Earnings Announcement
−.0
20
.02
.04
Mea
n A
bnor
mal
log(
Bid
−A
sk S
prea
d)
−40 −20 0 20 40Days Relative to Earnings Announcement
Panel B: 161 Trading Days Around 2nd-Quarter Earnings Announcement
−.0
4−
.02
0.0
2.0
4M
ean
Abn
orm
al lo
g(B
id−
Ask
Spr
ead)
−100 −50 0 50 100Days Relative to Earnings Announcement
42
Table 1: U.S. Sample Descriptive Statistics
Panel A shows the average Size, which is the logarithm of a firm-day’s market value of equity, and the averagelog(Price Impact), which is calculated for each firm-day as log
( |return|$ volume of trades
)(where dollar volume is in terms
of millions of dollars), each year during the years covered by the sample. Panel B counts the number of firm-yearobservations with each year-end month. Panel C shows the percentage of firm-quarter observations by fiscal quarter(i.e., Q1 through Q4) with different ranges of trading days between the quarter end and the earnings announcement.
Panel A: Price Impact Over Timelog(Price
Year Size Impact)1993 18.62 -2.651994 18.61 -2.531995 18.67 -2.781996 18.85 -3.061997 18.97 -3.281998 18.96 -3.201999 18.96 -3.262000 18.99 -3.252001 18.85 -3.092002 18.88 -3.212003 19.15 -3.892004 19.58 -4.582005 19.73 -4.832006 19.88 -5.092007 19.98 -5.262008 19.64 -4.362009 19.43 -4.202010 19.83 -4.952011 19.98 -5.072012 20.01 -5.152013 20.25 -5.582014 20.42 -5.842015 20.35 -5.61
Panel B: Number of Firm-Year Observations by Year-EndMonth
Year-End Month N %1 4,592 3.152 1,526 1.053 7,518 5.164 1,881 1.295 1,853 1.276 9,800 6.727 1,848 1.278 1,808 1.249 8,629 5.9210 2,515 1.7311 1,371 0.9412 102,417 70.27
Panel C: % of Firm-Quarters by Number of Trading DaysBetween Quarter End and Earnings Announcement
Percentage of Firm-QuartersDays Before EA Q1 Q2 Q3 Q4
0-9 3.23 3.23 2.98 1.0010-19 41.42 41.33 39.96 18.5820-29 39.24 39.04 40.13 23.6630-39 14.59 14.51 15.72 23.7140-49 0.98 1.18 0.83 12.9350-59 0.22 0.33 0.17 8.52≥60 0.32 0.38 0.20 11.59Total 100 100 100 100
43
Table 2: International Sample Descriptive Statistics
This table shows the number of firm-year observations, the average Size (the logarithm of a firm-day’s market valueof equity), and the average log(Price Impact) (calculated for each firm-day as log
( |return|$ volume of trades
), with “dollar”
volume in terms of millions of euros, etc.) each year during the years covered by the sample. I calculate theseaverages separately for semiannual and quarterly reporters. Panel A shows the European sample, Panel B shows theSingaporean sample, and Panel C shows the Japanese sample.
Panel A: European SampleSemiannual Quarterly
log(Price log(PriceYear N Size Impact) N Size Impact)1992 943 4.53 1.55 34 8.10 -1.441993 1572 4.40 1.40 43 7.90 -1.271994 1771 4.59 1.46 49 7.79 -1.041995 1851 4.60 1.60 60 7.52 -0.661996 1812 4.83 1.48 64 7.61 -0.631997 1753 5.01 1.33 66 7.94 -1.091998 1973 4.79 1.85 107 7.11 0.041999 2194 4.65 2.70 245 6.29 2.892000 2209 4.66 2.72 383 6.21 3.172001 2187 4.16 2.61 502 5.68 3.902002 2217 3.77 3.05 671 4.89 5.502003 2309 3.72 3.30 651 5.03 5.222004 2291 4.00 2.80 638 5.47 4.412005 2486 4.02 2.58 630 5.73 3.802006 2709 4.06 2.63 647 5.92 3.922007 2860 4.14 2.76 694 5.97 4.182008 2807 3.71 3.99 707 5.54 5.552009 2676 3.45 4.27 706 5.21 6.012010 2548 3.75 3.69 698 5.46 5.452011 2395 3.88 3.51 723 5.54 5.392012 1929 3.61 3.14 719 5.52 5.322013 1768 3.64 2.77 669 5.74 4.942014 1794 3.83 2.67 591 6.14 4.542015 1893 3.95 2.86 582 6.34 4.45
44
Panel B: Singaporean SampleSemiannual Quarterly
log(Price log(PriceYear N Size Impact) N Size Impact)2000 82 5.09 6.16 6 6.79 3.182001 404 4.35 7.03 8 6.40 3.422002 409 4.26 6.76 31 5.58 5.032003 297 3.68 7.00 167 5.72 4.122004 302 3.60 7.85 225 5.80 4.152005 333 3.43 8.45 252 5.75 4.312006 361 3.51 7.85 280 5.90 3.932007 361 4.09 5.95 316 6.11 3.542008 285 3.46 8.75 436 5.35 5.782009 238 3.09 9.16 480 5.00 5.842010 230 3.28 8.61 499 5.30 5.322011 210 3.20 8.92 516 5.24 5.832012 195 3.14 8.78 529 5.18 5.652013 187 3.41 7.76 535 5.35 5.062014 181 3.48 8.03 545 5.36 5.352015 165 3.49 8.57 539 5.21 5.86
Panel C: Japanese SampleSemiannual Quarterly
log(Price log(PriceYear N Size Impact) N Size Impact)2001 3227 9.44 0.52 7 14.12 -5.602002 3505 9.28 0.47 13 13.53 -4.812003 3452 9.24 0.11 99 11.17 -2.112004 1423 9.24 -0.41 1916 9.82 -0.992005 355 9.34 -1.00 3357 10.07 -1.982006 201 9.42 -0.70 3696 10.07 -1.622007 62 10.10 -1.86 3926 9.81 -1.352008 40 10.79 -2.49 3825 9.50 -0.52
45
Table 3: Interannouncement Growth in the U.S., with Amihud (2002) Measure
Panel A: Interannouncement Growth of Information Asymmetry
Each observation is a firm-day. The left-hand-side variable is the log(Price Impact), which is calculated for eachfirm-day as log
( |return|$ volume of trades
)(i.e., the logarithm of the daily Amihud (2002) illiquidity measure), where dollar
volume is in terms of millions of dollars. Days Since EA, the variable of interest, is the number of trading dayssince the firm’s most recent earnings announcement. Size is the logarithm of the firm-day’s market value of equity.Turnover is the logarithm of one plus the fraction of the firm’s shares outstanding traded that day. Volatility is thelogarithm of one plus the standard deviation of returns over the twenty trading days before the firm-day. Midpointis the logarithm of the bid-ask spread’s midpoint. Earnings Window is an indicator for the three-day earningsannouncement window. Annual Report is an indicator for the period after the fourth-quarter earnings announcement.Late Filing is an indicator that turns on when more trading days than expected have passed since the quarter-endwithout an announcement. (I estimate the expected filing date as the median seasonal earnings announcement delayfrom the previous three years.) One Week Before is an indicator for days that occur within five trading days beforethe earnings announcement and One Week After is an indicator for days that occur within five trading days after.The regression includes firm-year fixed effects and calendar day fixed effects. Standard errors are clustered at boththe firm level and the calendar day level. T-statistics are in parentheses. *** p<0.01, ** p<0.05, * p<0.1.
(1) (2)VARIABLES log(Price Impact) log(Price Impact)
Days Since EA 0.00234*** 0.00161***(59.75) (39.24)
Size -0.768***(-37.20)
Turnover -12.59***(-15.02)
Volatility -2.674***(-22.27)
Midpoint -0.752***(-32.56)
Earnings Window -0.0131***(-2.873)
Annual Report -0.00183(-1.026)
Late Filing -0.0309***(-10.89)
One Week Before -0.00800***(-4.458)
One Week After -0.0747***(-36.89)
Observations 27,926,439 25,418,852R-squared 0.864 0.880Firm-Year FE YES YESDay FE YES YESClusters by Firm & Day YES YES
46
Panel B: Interannouncement Growth Throughout the Quarter
Post Quarter-end is an indicator that turns on for days between the end of the fiscal quarter and that quarter’searnings announcement date. 1st Month, 2nd Month, and 3rd Month are indicators that turn on when Days SinceEA is, respectively, between 0 and 20 trading days, between 21 and 40 trading days, and greater than 40 tradingdays. Greater Than 1 Month is an indicator that turns on when Days Since EA is greater than 20 trading days,and Greater than 2 Months is an indicator that turns on when Days Since EA is greater than 40 trading days. Allother variables are defined the same as in Panel A, and the regressions include the same controls as in Column (2) ofPanel A. The regressions include firm-year fixed effects and calendar day fixed effects. Standard errors are clusteredat both the firm level and the calendar day level. T-statistics are in parentheses. *** p<0.01, ** p<0.05, * p<0.1.
(1) (2) (3)VARIABLES log(Price Impact) log(Price Impact) log(Price Impact)
Days Since EA 0.00222***(25.94)
Post Quarter-end 0.0488***(9.187)
Days Since EA x Post Quarter-end -0.00131***(-10.31)
Days Since EA x 1st Month 0.00155***(10.50)
Days Since EA x 2nd Month 0.00184***(24.90)
Days Since EA x 3rd Month 0.00160***(35.11)
Greater Than 1 Month 0.0395***(24.71)
Greater Than 2 Months 0.0304***(18.48)
Observations 25,418,852 25,418,852 25,418,852R-squared 0.880 0.880 0.880Controls YES YES YESFirm-Year FE YES YES YESDay FE YES YES YESClusters by Firm & Day YES YES YES
47
Table 4: Difference-in-Differences Using International Settings, with Amihud (2002) Measure
Each observation is a firm-day. The left-hand-side variable is log(Price Impact), which is calculated for each firm-dayas log
( |return|$ volume of trades
)(i.e., the logarithm of the daily Amihud (2002) illiquidity measure), where “dollar” volume
is in terms of millions of euros, etc. Q2 or Q4 is an indicator for days that either occur between the first and secondquarter earnings announcements or the third and fourth quarter earnings announcements. (The semiannual reportershave estimated hypothetical earnings announcement dates for quarters one and three; see Section 4.2.) Quarterly is anindicator that turns on for firm-years that report quarterly. Size, Turnover, Volatility, Midpoint, Earnings Window,One Week Before, and One Week After have the same definitions as in Table 3. First Semester is an indicator thatturns on between the year-end earnings announcement of the previous year and the second quarter/first semesterearnings announcement of the current year. The regression includes calendar day fixed effects and firm-year fixedeffects. I cluster standard errors by firm and by calendar day. T-statistics are in parentheses. *** p<0.01, ** p<0.05,* p<0.1.
(1) (2) (3)Europe Singapore Japan
VARIABLES log(Price Impact) log(Price Impact) log(Price Impact)
Q2 or Q4 0.0545*** 0.0652*** -0.0169***(11.37) (4.743) (-2.666)
Quarterly x Q2 or Q4 -0.0534*** -0.0287** -0.0107(-10.04) (-2.107) (-1.505)
Size -0.920*** -1.324*** -0.756***(-15.86) (-15.94) (-11.27)
Turnover -18.97*** -27.66*** -10.98***(-2.881) (-13.15) (-8.383)
Volatility -2.887*** -2.657*** -7.260***(-10.09) (-7.073) (-17.49)
Midpoint -0.349*** -1.186*** -0.710***(-6.209) (-13.20) (-10.27)
Earnings Window -0.140*** -0.139*** -0.0585***(-12.38) (-12.17) (-10.78)
First Semester 0.0173** -0.0218 0.0778***(2.177) (-1.069) (8.041)
One Week Before -0.0161*** 0.00906 0.00782*(-4.560) (1.055) (1.849)
One Week After -0.122*** -0.166*** -0.0405***(-24.63) (-17.19) (-8.789)
Observations 6,518,086 1,113,323 3,064,532R-squared 0.913 0.821 0.862Firm-Year FE YES YES YESDay FE YES YES YESClusters at Firm & Day YES YES YES
48
Table 5: Test of Parallel Trends Assumption, with Amihud (2002) Measure
Each observation is a firm-day. The left-hand-side variable is log(Price Impact), which is calculated for each firm-dayas log
( |return|$ volume of trades
)(i.e., the logarithm of the daily Amihud (2002) illiquidity measure), where “dollar” volume
is in terms of millions of euros, etc. Second Half-year is an indicator that equals one for days in quarters 3 and 4, andzero for days in quarters 1 and 2. Quarterly is an indicator that turns on for firm-years that report quarterly. Size,Turnover, Volatility, Midpoint, Earnings Window, One Week Before, and One Week After have the same definitionsas in Table 3. The regression includes calendar day fixed effects and firm-year fixed effects. I cluster standard errorsby firm and by calendar day. T-statistics are in parentheses. *** p<0.01, ** p<0.05, * p<0.1.
(1) (2) (3)Europe Singapore Japan
VARIABLES log(Price Impact) log(Price Impact) log(Price Impact)
Second Half-year -0.0611*** -0.0357* -0.0499***(-11.78) (-1.785) (-4.921)
Quarterly x Second Half-year 0.00426 -0.0145 0.00594(0.575) (-0.740) (0.508)
Size -0.922*** -1.325*** -0.755***(-15.91) (-15.92) (-11.24)
Turnover -18.99*** -27.67*** -10.98***(-2.881) (-13.14) (-8.384)
Volatility -2.896*** -2.655*** -7.260***(-10.10) (-7.063) (-17.49)
Midpoint -0.346*** -1.185*** -0.711***(-6.177) (-13.19) (-10.26)
Earnings Window -0.169*** -0.165*** -0.0471***(-13.36) (-15.06) (-9.258)
One Week Before -0.0214*** -0.00255 0.0146***(-6.392) (-0.307) (3.430)
One Week After -0.128*** -0.158*** -0.0461***(-25.36) (-16.97) (-10.28)
Observations 6,518,086 1,113,323 3,064,532R-squared 0.913 0.821 0.862Firm-Year FE YES YES YESDay FE YES YES YESClusters at Firm & Day YES YES YES
49
Table 6: Interannouncement Growth in the U.S., with Bid-Ask Spread
Panel A: Interannouncement Growth of Information Asymmetry
The tests in this table are the same as in Panel A of Table 3, except the left-hand-side variable is log(Spread), whichis calculated for each firm-day as log
(100 ∗ ask−bid
(ask+bid)/2
). T-statistics are in parentheses. *** p<0.01, ** p<0.05, *
p<0.1.
(1) (2)VARIABLES log(Spread) log(Spread)
Days Since EA 0.000180*** 0.000304***(11.08) (16.61)
Size -0.237***(-26.21)
Turnover -1.604***(-16.30)
Volatility 1.168***(31.67)
Midpoint -0.419***(-43.75)
Earnings Window 0.0576***(41.97)
Annual Report 0.00637***(6.036)
Late Filing -0.00169(-1.155)
One Week Before 0.00887***(10.44)
One Week After 0.00141*(1.721)
Observations 31,032,772 28,725,843R-squared 0.868 0.875Firm-Year FE YES YESDay FE YES YESClusters by Firm & Day YES YES
50
Panel B: Interannouncement Growth Throughout the Quarter
The tests in this table are the same as in Panel B of Table 3, except the left-hand-side variable is log(Spread), whichis calculated for each firm-day as log
(100 ∗ ask−bid
(ask+bid)/2
). T-statistics are in parentheses. *** p<0.01, ** p<0.05, *
p<0.1.
(1) (2) (3)VARIABLES log(Spread) log(Spread) log(Spread)
Days Since EA 0.000319***(8.657)
Post Quarter-end -0.00628***(-2.656)
Days Since EA x Post Quarter-end 8.04e-05(1.465)
Days Since EA x 1st Month -0.000149***(-2.697)
Days Since EA x 2nd Month 0.000156***(5.448)
Days Since EA x 3rd Month 0.000232***(12.58)
Greater Than 1 Month 0.00602***(9.022)
Greater Than 2 Months 0.00735***(10.04)
Observations 28,725,843 28,725,843 28,725,843R-squared 0.875 0.875 0.875Controls YES YES YESFirm-Year FE YES YES YESDay FE YES YES YESClusters by Firm & Day YES YES YES
51
Table 7: Difference-in-Differences Using International Settings, with Bid-Ask Spread
The tests in this table are the same as in Table 4, except the left-hand-side variable is log(Spread), which is calculatedfor each firm-day as log
(100 ∗ ask−bid
(ask+bid)/2
). T-statistics are in parentheses. *** p<0.01, ** p<0.05, * p<0.1.
(1) (2) (3)Europe Singapore Japan
VARIABLES log(Spread) log(Spread) log(Spread)
Q2 or Q4 0.00404** 0.0214*** -0.0118***(2.245) (5.062) (-3.419)
Quarterly x Q2 or Q4 -0.0128*** -0.0151*** -0.00384(-5.115) (-3.477) (-0.995)
Size -0.215*** -0.317*** 0.0658*(-9.057) (-8.827) (1.925)
Turnover -1.278*** -2.557*** -0.289***(-3.599) (-9.829) (-3.344)
Volatility 0.534*** 0.740*** 2.323***(10.95) (5.088) (18.32)
Midpoint -0.298*** -0.457*** -0.337***(-12.83) (-11.13) (-9.893)
Earnings Window 0.00387* -0.0156*** 0.0149***(1.765) (-4.959) (4.494)
First Semester 0.00905*** -0.00361 0.0326***(2.669) (-0.604) (6.139)
One Week Before 0.00143 2.81e-05 0.00855***(0.882) (0.0118) (3.560)
One Week After -0.00497*** -0.0190*** -0.00427*(-3.184) (-7.237) (-1.757)
Observations 8,984,194 1,502,046 3,423,133R-squared 0.842 0.848 0.626Firm-Year FE YES YES YESDay FE YES YES YESClusters at Firm & Day YES YES YES
52
Table 8: Test of Parallel Trends Assumption, with Bid-Ask Spread
The tests in this table are the same as in Table 5, except the left-hand-side variable is log(Spread), which is calculatedfor each firm-day as log
(100 ∗ ask−bid
(ask+bid)/2
). T-statistics are in parentheses. *** p<0.01, ** p<0.05, * p<0.1.
(1) (2) (3)Europe Singapore Japan
VARIABLES log(Spread) log(Spread) log(Spread)
Second Half-year -0.0111*** -0.00650 -0.0109**(-4.734) (-1.023) (-2.045)
Quarterly x Second Half-year 0.00674* -0.0100 -0.00460(1.880) (-1.470) (-0.760)
Size -0.215*** -0.318*** 0.0656*(-9.069) (-8.819) (1.918)
Turnover -1.279*** -2.558*** -0.289***(-3.596) (-9.834) (-3.339)
Volatility 0.532*** 0.741*** 2.323***(10.93) (5.091) (18.32)
Midpoint -0.298*** -0.456*** -0.337***(-12.88) (-11.10) (-9.883)
Earnings Window 0.00282 -0.0223*** 0.0219***(1.547) (-7.577) (7.196)
One Week Before 0.00207 -0.00233 0.0125***(1.353) (-1.001) (5.330)
One Week After -0.00619*** -0.0179*** -0.00739***(-4.001) (-6.903) (-3.156)
Observations 8,984,194 1,502,046 3,423,133R-squared 0.842 0.848 0.626Firm-Year FE YES YES YESDay FE YES YES YESClusters at Firm & Day YES YES YES
53
Table9:
How
Other
Disc
losuresCha
ngeInterann
ounc
ementGrowth
Thistableuses
theU.S.sam
ple.
EA
Dis
clos
ure
Cou
ntcoun
tsthenu
mbe
rof
disclosureson
theda
yof
andtheda
yafterthemostrecent
earnings
anno
uncement,
and
Non
-EA
Dis
clos
ure
Cou
ntcoun
tsthenu
mbe
rof
disclosuresdu
ringtheinterval
betw
eentw
oearnings
anno
uncements.The
disclosure
iseither
anan
alyst
forecast
(for
EA
/Non
-EA
Fore
cast
Cou
nt)or
an8-K
filing(for
EA
/Non
-EA
8-K
Cou
nt).
Allothe
rvaria
bles
arede
fined
thesameas
inTa
ble3an
dTa
ble6.
The
regression
includ
esfirm-yearfix
edeff
ects
andcalend
arda
yfix
edeff
ects.Stan
dard
errors
areclusteredat
both
thefirm
levelan
dthecalend
arda
ylevel.
T-statis
ticsarein
parenthe
ses.
***p<
0.01,*
*p<
0.05,*
p<0.1.
(1)
(2)
(3)
(4)
VARIA
BLE
Slog(Pr
iceIm
pact)
log(Sp
read
)log(Pr
iceIm
pact)
log(Sp
read
)
DaysSinceEA
0.00182***
0.000319***
0.00174***
0.000312***
(41.62)
(15.80)
(36.03)
(12.77)
EAFo
recast
Cou
nt-0.00138***
-0.00478***
(-2.838)
(-12.84)
Non
-EA
Forecast
Cou
nt-0.00383***
-0.000826***
(-16.34)
(-5.308)
DaysSinceEA
xEA
Forecast
Cou
nt-8.35e-07
6.22e-06
(-0.107)
(1.644)
DaysSinceEA
xNon
-EA
Forecast
Cou
nt-3.88e-05***
-5.52e-06***
(-10.60)
(-2.839)
EA8-K
Cou
nt-0.0325***
-0.0110***
(-11.23)
(-6.154)
Non
-EA
8-K
Cou
nt-0.0110***
-0.00204***
(-14.77)
(-4.892)
DaysSinceEA
xEA
8-K
Cou
nt0.000540***
0.000197***
(9.912)
(7.219)
DaysSinceEA
xNon
-EA
8-K
Cou
nt-0.000198***
-3.37e-05***
(-13.65)
(-4.288)
Observatio
ns25,327,036
28,598,837
22,374,647
24,588,220
R-squ
ared
0.880
0.875
0.879
0.860
Con
trols
YES
YES
YES
YES
Firm
-YearFE
YES
YES
YES
YES
Day
FEYES
YES
YES
YES
Clustersby
Firm
&Day
YES
YES
YES
YES
54
Table10
:Interann
ounc
ementGrowth
ofInform
ationAsymmetry
intheU.S.D
uringDifferentPe
riods
Thistableuses
theU.S.sam
ple.
The
regression
specificatio
nsin
thistablearethesameas
inPa
nelA
ofTa
ble3an
dTa
ble6,
except
that
thesamplepe
riods
are
restric
tedin
each
regression
—either
from
1993
to2001,2
002to
2007,o
r2008
to2015.T-statis
ticsarein
parenthe
ses.
***p<
0.01,*
*p<
0.05,*
p<0.1.
1993
to20
0120
02to
2007
2008
to20
15(1)
(2)
(3)
(4)
(5)
(6)
VARIA
BLE
Slog(Pr
iceIm
pact)
log(Sp
read
)log(Pr
iceIm
pact)
log(Sp
read
)log(Pr
iceIm
pact)
log(Sp
read
)
DaysSinc
eEA
0.00
149*
**0.00
0150
***
0.00
172*
**0.00
0506
***
0.00
171*
**0.00
0446
***
(30.69
)(6.832
)(23.19
)(12.38
)(20.09
)(13.51
)Size
-0.764
***
-0.188
***
-0.710
***
-0.206
***
-0.884
***
-0.353
***
(-27
.43)
(-19
.01)
(-20
.47)
(-13
.05)
(-21
.82)
(-16
.72)
Turnover
-22.82
***
-3.004
***
-9.822
***
-1.301
***
-7.907
***
-0.851
***
(-27
.32)
(-37
.05)
(-17
.51)
(-22
.77)
(-6.81
4)(-7.97
5)Vo
latility
-1.225
***
1.58
9***
-3.911
***
1.11
1***
-3.459
***
0.55
3***
(-14
.41)
(32.98
)(-26
.76)
(16.47
)(-16
.38)
(9.116
)Midpo
int
-0.740
***
-0.466
***
-0.885
***
-0.454
***
-0.546
***
-0.284
***
(-25
.82)
(-43
.58)
(-24
.23)
(-26
.99)
(-12
.78)
(-13
.18)
Earnings
Windo
w-0.070
6***
0.01
37**
*0.02
11**
*0.06
93**
*0.02
02**
0.10
7***
(-18
.02)
(14.01
)(4.228
)(27.23
)(2.435
)(49.17
)Ann
ualR
eport
0.00
166
0.00
133
-0.001
520.01
40**
*-0.006
77**
0.00
477*
**(0.678
)(1.030
)(-0.44
5)(5.570
)(-2.03
1)(2.877
)La
teFilin
g-0.022
6***
-0.007
43**
*-0.027
8***
0.00
0671
-0.045
5***
0.00
290
(-5.50
1)(-3.91
2)(-5.58
8)(0.233
)(-8.29
1)(1.001
)One
WeekBefore
-0.009
49**
*0.00
0967
-0.000
108
0.01
49**
*-0.013
9***
0.01
24**
*(-4.17
2)(0.990
)(-0.03
27)
(7.329
)(-3.82
9)(8.452
)One
WeekAfter
-0.069
6***
-0.000
698
-0.072
2***
-0.000
553
-0.081
9***
0.00
840*
**(-29
.33)
(-0.73
5)(-20
.15)
(-0.28
4)(-19
.69)
(6.071
)
Observatio
ns9,59
2,05
512
,085
,947
7,35
9,24
17,81
7,43
48,46
7,49
58,82
2,41
0R-squ
ared
0.86
60.77
80.86
90.74
40.88
20.87
5Firm
-YearFE
YES
YES
YES
YES
YES
YES
Day
FEYES
YES
YES
YES
YES
YES
Clustersby
Firm
&Day
YES
YES
YES
YES
YES
YES
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