Preemption and Forecast Accuracy:
A Structural Approach∗
Job Market Paper
[Download the most recent version]
Fanny Camara†
January 26, 2016
Abstract
This paper examines how competition affects information provided by experts. I estimate a
timing game played by financial analysts who produce earning forecasts. Over time, both the
exogenous information available to the market and the information privately observed by each
analyst become more precise. In choosing when to release their forecasts, analysts weigh whether
to wait for more precise information in order to forecast more accurately, or to preempt their
competitors by reducing the informational advantage enjoyed by rivals who have yet to issue
their forecasts. I assess the informational value of professional forecasters. I find that financial
analysts produce 40% of the information on future earnings made available to investors during the
forecasting period. I perform a counterfactual experiment with fixed forecast dates to quantify
the extent to which preemption affects forecast delay and forecast accuracy. Preemption reduces
forecast delays substantially: without preemption, the average analyst would disclose her forecast
eight days after the date observed in the data. Because earlier forecasts use less information,
preemption diminishes the average forecast accuracy by 24%.
Keywords: Structural Estimation, Preemption, Timing Game, Earning Forecasts, Information
Economics
JEL: C18, C57, D83, D84, G14, L15
∗
I am deeply indebted to Margaret K. Kyle, Marco Ottaviani , and Jesse M. Shapiro for their invaluable
guidance and support. I am also grateful to Christian Hellwig, Andrew Foster, John Friedman, Augustin
Landier, Laura Lasio, Ernest Liu, Christopher Malloy, Mathias Reynaert, and Paul Scott for insightful comments. Finally this paper has benefitted from discussions with seminar audiences at Bocconi, Mines ParisTech,
and Brown. Errors and opinions are mine.
†
Toulouse School of Economics, 21 allée de Brienne, 31015 Toulouse Cedex 6, France; fanny.camara@tse-fr.eu.
1
1
Introduction
Experts play an important role in markets with information problems. For example,
consumers may rely on expert assessments of the quality of a new car, firms may base their
investment decisions on the forecasts of macroeconomic variables produced by central
banks, and investors may adjust their portfolios in response to the forecasts of financial
analysts. However, strategic interactions between competing experts can affect the quality
of the information they provide to the market, and distort market outcomes as a result.
This paper examines the distortions that may result from mis-timing the release of
information in the presence of competition. Specifically, I study financial analysts who
issue forecasts on the earnings of public companies. These analysts are experts, who invest
significant effort to acquire information about the companies they follow. If experts are
rewarded for the informational content of their forecasts, the timing of the forecast release
is a critical decision for the analyst. By waiting, she acquires more precise information
and forecasts more accurately. However, forecasts already issued by her rivals become
public information, thereby reducing her own information advantage.
This paper is the first to develop a methodology to quantify the distortions generated
by strategic interactions between competing experts. I use this methodology to estimate
the extent to which preemption affects the delay and the accuracy of quarterly Earning Per Share (EPS) issued by sell-side analysts (analysts employed by brokerage firms).
Amid growing regulatory efforts to curb concentration in the brokerage industry (Regulation of National Market System (2005) in the US, Markets in Financial Instruments
Directive (2007) in the EU), this work can help determine the optimal level of competition
needed to ensure the efficient functioning and the liquidity of capital markets. In addition, this paper is the first to develop a structural method to quantify the contribution
of professional forecasters to the information available to the market.
When experts cannot choose the timing of their forecasts, economic theory suggests
that having more experts forecasting a given outcome improves forecast accuracy for two
reasons. First, as the number of experts who collect conditionally independent signals
increases, their aggregated information becomes more precise. Second, the theoretical
literature on persuasion suggests that competition disciplines experts to report their
2
private information truthfully either by confronting experts with misaligned preferences
(Gentzkow and Kamenica, 2011; Krishna and Morgan, 1999; Milgrom and Roberts, 1986)
or by increasing the amount of feedbacks that the market receives about the state of the
world (Gentzkow and Shapiro, 2006; Camara and Dupuis, 2015).
In contrast, competition among experts has ambiguous effects on accuracy when experts are free to time their forecasts. On the one hand, tougher competition implies that
a higher number of experts collect and process information. On the other hand, when the
payoff of each expert is tied to the relative informational content of her forecast, strategic
interactions between analysts results in sub-optimal forecast timing. The mechanism is
the following: Each disclosed forecast becomes public information. The expert who issues
an early forecast reduces the informational advantage that her competitors, who have not
yet released their forecasts, have on the market. Experts anticipate that earlier forecasts
reduce the value of their private information and react by issuing their predictions before
the time they would have chosen in the absence of competitors.
Assessing the impact of strategic interactions between analysts on forecast accuracy
constitutes an empirical question of particular relevance for earning forecasts since economic efficiency depends crucially on their accuracy. First, analysts play an important
role in reducing the asymmetry of information between insiders and outsiders which, to
the extent that inside trading hurts investors’ confidence in securities markets (Ausubel,
1990), stimulates investment. Second, since earning forecasts are used as inputs by credit
rating agencies to rate firms’ debts (Fong et al., 2014), accurate earning forecasts increase
the reliability of credit ratings and have positive spillover effects on financial stability. Finally, sell-side analysts lower the cost for investors of acquiring information and, therefore,
improve the liquidity of securities markets (Groysberg et al., 2007).
In this paper, I quantify the informational loss in earning forecasts that preemption
generates. To do so, I generalize the game studied by Guttman (2010) to N players
to model the timing decisions of sell-side financial analysts who forecast the quarterly
Earning Per Share (EPS) of public companies. Motivated by the works of Irvine et al.
(2007) which provides empirical evidence that brokerage firms give early access to research
to clients who generate significant commission revenues – a practice called tipping – and
Cowen et al. (2003) which documents that research firms who employ financial analysts
3
sell research as a stand-alone product, I assume that analysts indirectly capture the
benefits of the information that they produce by selling their forecasts to their private
clients before disclosing them to the market. The willingness-to-pay of the client for the
analyst’s information corresponds to the trading gain that he can make by exploiting
his informational advantage over the market. Exogenous public information about the
future realization of the EPS – which can take the form of financial reports issued by
the company – arrives continuously over the forecasting period. At the beginning of the
game, the analyst receives a signal whose precision depends on her initial ability. As time
goes by, she accumulates more private information at a rate determined by her learning
ability. The time when the informational advantage of the analyst over the market reaches
its maximum increases with the magnitude of her learning ability relative to her initial
ability.
When a unique analyst covers the stock, she maximizes her payoff by issuing her
forecast when the precision of her private information relative to the public information
reaches its maximum. Hereafter, I refer to this level of precision (and the corresponding timing) as the unconstrained optimal. When multiple analysts cover the stock, the
equilibrium timing profile is such that each analyst chooses the date that maximizes the
relative precision of her private information under the constraint that no later analyst
finds it profitable to deviate from the equilibrium timing by undercutting previous forecasters. Unlike the dynamic timing game studied by Fudenberg and Tirole (1985), this
game features players who receive one-shot payoffs that depend only on the history of the
game before their moves and not on the actions of players who move after them. This
implies that players have no incentive to influence the timing of subsequent movers. As
a result, I define preemption not as a deviation from a precommitment equilibrium but
as a deviation from the unconstrained optimum. More specifically, the analyst is said to
preempt her competitors when she chooses to issue her forecast at a time when the accuracy of the public information is lower than the level that maximizes her informational
advantage over the market. It is worth noting that, besides preemption, competition reduces forecast delays for a purely mechanical reason: each disclosed forecast increases the
precision of the public information and thus decreases the time each subsequent analyst
has to wait to reach the point when her informational advantage is maximized.
4
At equilibrium, analysts with similar ratios of initial to learning ability which command similar optimal unconstrained timing, tend to engage in a preemption which results
in clustered forecasts. The intuition is the following. Consider a scenario with two analysts, in which the informational advantage of analyst A (she) is maximized for a public
precision yA , while the informational advantage of analyst B (he) is maximized when the
public information reaches the level of precision yB . Denote by f A (yA ), the precision of
the private information of analyst A that corresponds to the public information yA . Define similarly f B (yB ) for analyst B. Assume that the abilities of both analysts are similar
so that the difference between yA and yB is small with yA < yB , and yB < yA + f A (yA ).
Assume further that the difference between yA and yB is small enough that analyst B
is better off by timing his forecast right before yA rather waiting for analyst A to issue
her forecast in yA . If analyst B believes that analyst A will release her forecast when
the public signal reaches the precision yA , he has incentives to undercut analyst A and
issues his forecast in yA − . Analyst A anticipates that she will be preempted by B if she
waits until the public precision reaches the level yA to issue her forecast. She reacts by
releasing her forecast at an even earlier date when the public precision, y ∗ , is such that B
is indifferent between undercutting A and forecasting immediately after her at a level of
public precision y ∗ + f A (y ∗ ). As a result of the preemption race between both analysts,
A forecasts before her optimal unconstrained timing and the two forecasts are clustered
in time (B forecasts immediately after A). At equilibrium, analysts who differ enough in
terms of initial to learning ability ratios issue unclustered forecasts at their unconstrained
optimal levels of public precision. The multiple players version of the timing game does
not admit a unique equilibrium. However all the equilibria of the game have the property
that analysts who issue unclustered forecasts do it when the precision of the public signal
reaches their unconstrained optimal level. This feature of the game, that is invariant
across equilibria, is at the core of the identification strategy.
I estimate the structural parameters that govern the arrival process of public information as well as the initial and learning abilities of the analysts. This allows me to
assess the informational value of financial analysts – which the contribution of financial
analysts to the accuracy of investors’ expectations about future earnings – and the level
of heterogeneity in the precision of analysts’ private information. Finally I quantify the
5
extent to which preemption affects accuracy and forecast delay. To do so, I perform a
counterfactual experiment in which the forecasts’ dates are fixed so as to maximize the
relative precision of each forecast under the constraint that no analyst issues her forecast
before the public signal reaches her unconstrained optimal precision.
I estimate that analysts produce 40% of the information available to investors which
supports the widespread perception that analysts are major market information intermediaries (Bradshaw, 2011). I find that preemption creates sizable informational losses:
the accuracy of the average forecast in the counterfactual scenario without preemption
is 24% larger than the estimated accuracy of the actual average forecast. In terms forecast errors, the loss in accuracy caused by preemption translates into an average absolute
forecast error that 18% larger than the one that would occur in the absence of preemptive
incentives. In terms of forecast timing, I estimate that preemption reduces the average
forecast delay by 8 days, bringing the average forecast delay to 2 days after the report of
the EPS of the previous quarter. I find that, at the beginning of the forecasting period,
the higher number of disclosed forecasts in the actual data swamps the negative effect on
accuracy of the sub-optimal timing so that preemption actually increases the amount of
information produced by analysts and disclosed to investors during the first week of the
forecasting period. However after this period, preemption reduces the accuracy of the
information made available to the market. The overall effect of preemption on welfare is
ambiguous and depends on how much investors value access to information at the very
beginning of the forecasting period.
While the literature on EPS forecasts is large and has explored the questions of herding (Gleason and Lee, 2003; Hong et al., 2000), forecast bias (Hong and Kacperczyk, 2010;
Hong and Kubik, 2003; Lim, 2001), forecast accuracy (Fang and Yasuda, 2004; Mikhail
et al., 1997), and the market reaction to earning forecasts (Park and Stice, 2000; Stickel,
1992), I focus on timing which has received much less attention.
The existing empirical literature on timing has mostly focused on the informativeness
of early forecasts versus late forecasts, the informational content being measured by the
stock price response to the forecasts (Cooper et al., 2001) or a combination of accuracy,
price response, and boldness of revisions (Keskek et al., 2014). More closely related to
this paper, Kim et al. (2011) explores the determinants of the timing of forecast revisions.
6
They find that the characteristics that predict later revisions also predict lower forecast
errors. Their reduced-form approach does not enable them to distinguish whether late
forecasters outperform early forecasters because they receive better private information
later in the forecasting period or whether they simply benefit from the information revealed by previously issued forecasts.
Gul and Lundholm (1995) were the firsts to study a game of forecast timing. The
authors develop a model that rationalizes the clustering (in value) of the forecasts issued
by two experts. Since the informational environment that they consider does not include
exogenous information, after the first expert issues her forecast, the second expert has no
further incentives to wait and releases her forecast immediately. This feature makes the
model unfit to rationalize the forecasting behavior of financial analysts who typically wait
for more exogenous public information even when they are the last forecasters. Guttman
(2010) considers a richer informational environment in which exogenous information arrives continuously during the forecasting period. He further assumes that experts time
their forecasts so as to maximize the market value of their private information. These
two features make the timing game that he studies better tailored to financial analysts.
This paper also contributes to the literature on structural estimation of timing games.
To the best of my knowledge, only two papers quantify the efficiency loss arising from
competition when timing is endogenous. Schmidt-Dengler (2006) estimates the effects of
both preemption and business stealing on the timing of MRI adoption by hospitals and
find that competition affects adoption times mostly through business stealing. Takahashi
(2013) estimates a dynamic exit game played by movie theaters. He finds that strategic
interactions cause theaters to delay exit by 2.7 years relative to the profit-maximizing
date. While these papers have focused on traditional questions in industrial organization
(namely technology adoption and exit), this work constitutes the first attempt to estimate
an equilibrium timing model to recover the informational cost of preemption in a financial
setting.
The remainder of the paper is organized as follows: Section 2 provides some background on sell-side analysts and relevant regulations. Section 3 describes the data. Section 4 presents reduced-form evidence on the effects of competition on timing and accuracy. Section 5 explains the model used for timing decisions. Section 6 reports the
7
details of estimation and identification. Section 7 presents the results of the structural
estimation. Section 8 concludes.
2
Background on Sell-Side Analysts and Regulatory
Context
The job of a sell-side analyst consists in providing investment reports about publicly
listed companies to retail and institutional investors (for example pension plans or mutual funds). Investment reports typically include a review of the firm’s business model,
short-term earning forecasts, projections of stock price, and “buy”, “sell”, or “hold”
recommendations. In order to produce those reports, analysts study the companies’ financial and operating data, assess firms’ competitive environments, and gather additional
insights on future performance through meetings with firm management1 and discussions
with traders and sales staff who provide them with information on trading volumes and
planned future purchases. For the specific task of producing earning forecasts, analysts
build financial models to predict future revenues and costs that use as inputs the information that they have gathered.
Securities firms who employ sell-side analysts generate revenue by underwriting public
offerings, charging trading commissions, and selling research as a stand-alone product
(Cowen et al., 2003). Trading commissions usually take the form of fees charged by
brokerage houses to handle trades and to provide clients with investment advice based on
the research produced by sell-side analysts. In addition, securities companies commonly
practice “tipping”. Tipping consists in providing select institutional clients with access
to investment reports before their public disclosure. Institutional clients compensate the
company indirectly through trading commissions.
Since the early 2000s, the introduction of regulatory measures to tackle the issue
of conflict of interests and promote competition has changed substantially the relative
importance of those sources of research funding. The implementation of the Sarbanes1
Since 2000, the Fair Disclosure Regulation prohibits firms from privately communicating value-
relevant information to analysts which may have reduced the analysts’ ability to collect private information from firm management
8
Oxley Act of 2002 has weaken the linkage between underwriting activities and research
by mandating securities firms to build a Chinese Wall between their investment banking
and research departments and by precluding firms from tying analysts’ compensations
to specific investment banking transactions. In an effort to promote competition in the
market for brokerage services, the UK’s Financial Services Authority issued new guidelines (CP176) in 2003 prescribing the unbundling of research and execution commissions.
Similar regulations have later been adopted by the US where the Securities and Exchange
Commission (SEC) implemented the Regulation of National Market System (NMS) in
2005 and by the EU which adopted the concept of best execution as part of the Markets in
Financial Instruments Directive (MiFID) in 2007. These regulatory changes have limited
the extent to which brokerage houses can rely on underwriting and bundled trading commissions to finance their research activities and have increased the relative importance of
tipping or direct sales of investment reports as sources of research funding.
3
3.1
Data and Descriptive Statistics
Data Sources
I use data on quarterly forecasts of Earning Per Share (EPS) of publicly listed U.S.
companies from the Institutional Brokers’ Estimate System (I/B/E/S) detail history
dataset. The dataset contains the value of the forecasts, the date and time at which each
forecast is issued, the identity of the financial analyst who issues the forecast, the identity
of the brokerage house for which the analyst works, the realization of the EPS, and the
date at which the realization of the EPS is announced publicly. I use data on stock prices
and stock returns from the Center for Research in Security Prices (CRSP) database.
3.2
Sample Definition
In line with the previous literature on EPS forecasts, I focus on forecasts issued for typical
fiscal quarters i.e. quarters ending in March, June, September, and December. These
represent more than 85% of the forecasts. I exclude forecasts released before the beginning
of the fiscal quarters, forecasts released after the end of the fiscal quarter, as well as all
9
forecasts pertaining to stock-quarter whose previous quarterly EPS is announced with a
delay of more than 90 days. I select forecasts issued from the beginning of 2010 through
the end of 2014.2 After all exclusions, the sample contains a total of 392,846 quarterly
EPS forecasts for 3,412 stocks issued by US companies. The companies are distributed
across 371 industries as defined by the Standard Industrial Classification code (SIC).
3.3
Brokerage Houses
The data contain EPS forecasts issued by analysts working for 333 brokerage houses
(summarized in Table A3). In a typical quarter, the average brokerage house employs 12
analysts and covers 94 stocks from companies distributed across 34 industries. I measure
the size of a brokerage house by the number of analysts employed. Bigger brokerage
houses offer higher compensations and positions that are perceived as more prestigious.
Following the literature and notably Hong and Kacperczyk (2010), I use the size of the
brokerage house for which the analyst works as a measure of her career success. An
analyst employed by a big brokerage house will hereafter be referred to as high status
analyst. I define a big brokerage house as a house whose size is above the 90th percentile
of brokerage house size distribution i.e. a house which employs at least 33 analysts. On
average, a big brokerage house employs 54 analysts and covers 449 companies distributed
over 144 industries. Big brokerage houses issue about 51% (201,452) of the quarterly
forecasts in the sample. In a given quarter, 47% of the analysts in the sample work
for big brokerage houses. The typical company covered by a big brokerage house has a
bigger market capitalization ($11.6 million) than those covered by a smaller brokerage
house ($7.3 million).
2
I focus on recent data to avoid the issue of selective ex-post deletion of inaccurate forecasts docu-
mented by (Ljungqvist et al., 2009). As evidenced by the reaction of Thomson Financial, which issued
in 2007 a confidential guidance to select clients regarding the integrity of its I/B/E/S historical detail
recommendations database, the publication of this influential paper has disciplined the Thomson to
produce more reliable data since then.
10
3.4
Analysts
The data contain the quarterly EPS forecasts of 4,262 sell-side analysts (Table A5). On
average, the Experience of the analyst, measured as the number of years passed since
she has entered the database, is 7 years. Her average Tenure, measured by the time she
has spent working for the same brokerage house, is close to 3.5 years. I use the term
Stock Experience to refer to the number of years the analyst has covered a specific stock.
The typical forecaster has a stock-specific experience of nearly 4 years. I measure the
industry-specific experience, referred to as Industry Experience, as the number of years
the analyst has covered the industry. The typical analyst has followed the same industry
for almost 5 years. Roughly half of the analysts are classified as high status, as explained
in Section 3.3. During a given quarter, the typical forecaster covers 11 stocks distributed
over 5 industries. In the following, I will use the term Stock Workload to refer to the
number of stocks that an analyst covers during a quarter and Industry Workload to refer
to the number of industries that the analyst covers.
3.5
Stocks
Table A4 summarizes the key statistics for stock coverage, market capitalization, return
volatility, number of recommendations, and dispersion of the recommendations. The average firm in the sample has a market capitalization of $5.8 million and is covered by 8
analysts. Bigger companies are covered by more analysts: those above the 90th percentile
of the market capitalization distribution are covered by an average of 17 analysts. To
measure the level of interest investors attribute to different companies, I collect the number of recommendations issued by analysts on each stock (# of Recommendations). The
recommendations are translated by I/B/E/S into a five-point scale from 1 (= strong buy)
to 5 (= strong sell). I compute the standard deviation of the recommendations received
by each stock (Recommendation Dispersion) to measure the degree of disagreement between analysts about the future earnings of the companies. For each stock-quarter pair,
I define the variable Volatility as the average daily variance of the stock returns over the
year that ends at the beginning of the quarter.
11
3.6
Forecast Timing
34 days
1. First day
57 days
2. EPS
of fiscal quarter pre-announcement
3. Analyst’s
4. Last day of
forecasts
fiscal quarter
Forecasting Period
Figure 1: Fiscal Quarter
Table A6 presents the descriptive statistics for the forecast delays. A fiscal quarter
lasts 91 days. The realization of the EPS marks the end of the forecasting period and is
announced with an average delay of about 34 days. For each company, the variable EPS
Report Delay measures the average report delay of the EPS over the period 1984-2010. I
use this variable to capture the commitment of each company to transparent and efficient
financial reporting. Since analysts usually wait for the report of the EPS of the previous
quarter – the EPS pre-announcement – to issue their forecasts, I define the forecasting
period as the time span between the date of the EPS pre-announcement and the end of
the fiscal quarter.
Following the announcement of the EPS pre-announcement, the average analyst waits
5 days before issuing her forecast. Half of the forecasts are issued within 1 day after the
announcement of the previous quarters’ EPS but 10% of the forecasts are issued more
than 13 days after this date.
Analysts seldom revise their forecasts. In 84% of the cases, the analyst issues a unique
forecast that she never revises during the forecast period. When the analyst does decide
to revise her forecast, she does so only once in more than 85% of the cases.
4
4.1
Reduced-Form Evidence
Forecast Delay
In this section, I explore the relationship between competition and forecast delay. I
use the stock coverage which is the number of analysts who cover the stock during a
12
given quarter as a measure of competition. I show that, after controlling for stock and
analyst characteristics, analysts issue their forecasts earlier on stocks which receive larger
coverage. The empirical result that analysts react to tougher competition by timing their
forecasts earlier supports the conjecture that competition creates preemption incentives.
Figure 9 plots the relationship between forecast delay and stock coverage.
In order to identify the determinants of forecast delay, I estimate a continuous time
proportional Cox model to fit the hazard rate that a forecast is issued at a given day
during the forecasting period3 . I denote by λt,i,s,q,y the hazard rate that the forecast on
stock s in quarter q of year y is issued at time t by analyst i. I allow the hazard rate to
depend on analyst characteristics, Wi,s,q,y , and stock characteristics, Zs,q,y :
λt,i,s,q,y = λ0 (t) exp(βj + βq + βy + β0 Coverage + βW Wi,s,q,y , βW + βZ Zs,q,y )
(4.1)
The vector of analyst characteristics, W , contains the various measures of the analyst’s
experience, the status of the analyst, and her workload. The vector of stock characteristics, Z, includes the market capitalization, the volatility of past returns, the EPS report
delay, the number of recommendations, and the dispersion in recommendations. I add
quarter dummies, βq , to account for the fact that estimates for the last quarter of the year
are likely to be followed more closely by investors. I add industry dummies βj , to capture
the difference in forecast delays between industries perceived as more or less attractive
to investors. I also include year dummies, βy . λ0 (t) is the baseline hazard function.
Results
Table 1 displays the results of the cox proportional hazard regression. Table A1 shows
the predicted CDF of the forecast delay and the shifts in the predicted CDF induced by
an increase of one standard deviation of the various explanatory variables. The model
predicts that the typical analyst issues her forecast by the end of the first day of the
forecasting period with a probability of 62%. By the end of the first month following
the EPS pre-announcement, the typical analyst has issued her forecast with a predicted
probability of 92%. The most interesting result concerns the impact of coverage on
forecast delay: the model predicts that increasing the stock coverage by one standard
deviation (7 analysts) increases the probability that each analyst discloses her forecast
3
The choice of a continuous-time model is motivated by the high frequency of the forecast data.
13
by the end of the first day following the EPS pre-announcement by 3.3%.
The total and the stock specific experiences, the status of the analyst, as well as the
two measures of workloads have significant impacts on forecast delays. Analysts who
have followed a stock for a longer period as well as analysts working for bigger brokerage
houses issue their forecasts earlier. An analyst with a stock experience one standard
deviation larger than the average is 2.8% more likely to issue her forecast by the end of
the first day of the forecasting period and a high status analyst is 2.8% more likely to
issue her forecast on the first day than her low status counterpart. More surprisingly,
analysts with longer total experience issue their forecasts later. However the magnitude
of this effect is small: a one standard deviation increase in the total experience translates
into a modest .01% decrease in the probability of a first day forecast. Analysts who follow
more stocks and more industries during the quarter disclose their forecasts earlier. This
can reflect the fact that more competent analysts are assigned more stocks to cover.
Stocks issued by companies with larger market capitalization, stocks that receive more
recommendations, and stocks for which analysts issue less divergent recommendations
receive later earning forecasts. All those characteristics correlate with less uncertainty
regarding the realization of the future EPS. Their estimated negative impacts on timeliness is consistent with the idea that analysts maximize the value of their forecasts for
investors by prioritizing stocks for which public information is scarce.
4.2
Forecast Accuracy
In this section, I investigate how competition affects forecast accuracy. More specifically,
I assess the extent to which the analyst learns from the information disclosed in previously
issued forecasts by estimating the impact of the order of the forecast on its precision. I
also evaluate how competitive pressure affects the quality of the information produced
by analysts, beyond what analysts can learn from observing the disclosed forecasts of
their opponents, by estimating the impact of stock coverage on forecast accuracy after
controlling for forecast order.
I measure forecast accuracy by using the inverse of the absolute forecast errors. As
shown in table A2, forecasts are positively biased. This finding is consistent with the rich
14
Table 1: Determinants of Forecast Delay
Dependent Variable: Hazard rate of forecast release
a
Coef.
Std. Err.
Experience
-.0020∗∗∗
.0006
.0005
Stock Experience
.0127∗∗∗
.0008
.0000
Industry Experience
-.0001
.0008
.9147
High Status Analysts
.0508∗∗∗
.0049
.0000
Stock Workload
.0108∗∗∗
.0007
.0000
Industry Workload
.0054∗∗∗
.0014
.0002
Market Capitalization
-.0007∗∗∗
.0002
.0003
Volatility
3.844
2.432
.1140
EPS Report Delay
.0044∗∗∗
.0004
.0000
# of Recommendations
-.0054∗∗∗
.0006
.0000
Recommendation Dispersion
.0244∗∗∗
.0092
.0082
Coverage
.0048∗∗∗
.0007
5.18e-11
Quarter Fixed Effects
Yes
Year Fixed Effects
Yes
Industry Fixed Effects
Yes
Nbr of Obs
201,843
∗
p < .1,
a
∗∗
p < .05,
∗∗∗
p < .01
clustered at stock level
15
P. Value
literature on earning forecasts’ bias which documents that analysts issue overly optimistic
forecasts partly because of self-selection (McNichols and O’Brien, 1997) – analysts are
more likely to cover stocks they are enthusiastic about – and partly because of incentives
to please managers (Francis and Philbrick, 1993), to secure equity underwriting deals
(Lin and McNichols, 1998), and to generate trading commissions. Since I want to uncover
the determinants of the precision of the information produced by analysts and not the
determinants of their biases, I use centered forecast errors to measure accuracy. To do
so, I estimate the determinants of the bias and I subtract the predicted bias from the
forecast error for every stock-analyst pair. Table A2 shows the summary statistics for
the uncentered and centered absolute forecast errors.
The average centered absolute forecast error is about .11, while the median forecast
error is much smaller, .048, which reflects the fact that the distribution of forecast error is
very skewed to the right. Figure 10 shows the relation between forecast error and forecast
delay broken down by order. For given forecast delays, forecasts released first are noisier
than forecasts released by following analysts.
I use the following model to the estimate the effect of coverage, order, and forecast
delay on the absolute forecast error of analyst i, on stock s, issued in quarter q of year y:
F Ei,s,q,y = αj +αq +αy +α1 Coverage+α2 Order Index+α3 Delay+αW Wi,s,q,y +αZ Zs,q,y +i,s,q,y
(4.2)
Where: αj is the industry fixed effect; αq is the quarter fixed effect; αy is the year
fixed effect; W is the vector of analyst characteristics; and Z is the vector of stock
characteristics. Delay is the number of days after the EPS pre-announcement.
The variable Order Index is constructed in the following way. I sort the analysts who
cover a given stock by forecasting time from the earliest analyst to the latest one4 . The
rank tends to be lower on stocks covered by less analysts creating a downward bias for
the estimate of the effect of forecast order for stocks covered by few analysts. In order
to construct a measure of forecast order that is robust to variation in stock coverage, I
divide the rank by the total number of forecasts issued on the stock, using the following
formula:
4
When more than one forecast are issued at the same time, I assign them the same rank
16
Order Indexi,s,q,y = 100
Ranki,s,q,y − 1
Coverages,q,y − 1
Results
Results are displayed in Table 2. I find that the order of the forecast has a positive
impact on forecast accuracy: an increase of the magnitude of one standard deviation (=
30) in the order index decreases the forecast error by .004 which is about 4% of the mean
absolute forecast error. This constitutes empirical evidence that analysts do incorporate
in their forecasts the information disclosed through previously issued forecasts. However,
after controlling for the order, the forecast delay itself has no significant effect on the
precision of the forecasts. Since the timing of the forecast is endogenous, it is difficult
to interpret this result. The insignificant impact of forecast delay may suggest that
the amount of exogenous information that analysts receive over the forecasting period
is modest. Alternatively, it may reflect the fact that analysts who receive more precise
private information at the beginning of the forecasting period issue their forecasts earlier.
I find that the impact of coverage on forecast accuracy is negative: each additional analyst
covering the stock increases the absolute forecast error by a quantity corresponding to
1.3% of the mean absolute forecast error. This result is consistent with the idea that
competition produces accuracy loss, possibly through suboptimal timing.
Among analyst characteristics, only the status of the analyst has a significant effect
on the accuracy of the forecast. As intuition suggests, analysts who hold prestigious
positions in big brokerage houses deliver more accurate forecasts.
Among stock characteristics, the volatility of stock returns and the market capitalization are found to increase forecast errors. This means that earnings are harder to predict
for highly volatile stocks and for stocks issued by bigger companies. Analysts are found
to issue more accurate forecasts for the earnings of companies that report their EPS later,
confirming the earlier conjecture that companies that disclose their EPS late have less
volatile earnings.
17
Table 2: Determinants of Forecast Accuracy
Dependent Variable: Centered Absolute Forecast Error (×103 )
a
Coef.
Std. Err.
Experience
.066
.182
.716
Stock Experience
.006
.152
.970
Industry Experience
-.053
.182
.770
High Status
-1.575∗∗
.666
.018
Stock Workload
-.017
.152
.910
Industry Workload
.124
263.637
.637
Share of High Status Analysts
1.956
12.267
.873
Market Capitalization
.249∗
.136
.066
Returns Volatility
38.028∗∗∗
6.707
.000
EPS Report Delay
-.865∗∗
.398
.030
# of Recommendations
-.364
.384
.343
Recommendation Dispersion
9.851
9.082
.278
Order Index
-.162∗∗∗
.030
.000
Coverage
1.601∗∗
.659
.015
Delay
.131
.088
.134
Intercept
115.951∗∗∗
38.963
.003
Quarter Fixed Effects
Yes
Year Fixed Effects
Yes
Industry Fixed Effects
Yes
Nbr of Obs
286,469
∗
P. Value
p < .1, ∗∗ p < .05, ∗∗∗ p < .01
Note: The variable Share of High Status Analysts measures the percentage of high status analysts who cover the stock.
a
clustered at stock level
18
4.3
Discussion
The reduced form approach provides evidence that coverage correlates negatively with
forecast delay and forecast accuracy. Both findings suggest that competition might create preemptive incentives. However this reduced-form approach does not permit to make
causal inferences. Since analysts have discretion to choose which stocks they follow, the
negative correlation between coverage and accuracy may reflect the fact that analysts
are more likely to cover companies which provide less public information on their future earnings. This selection pattern would be consistent with analysts maximizing the
market value of their private information. Similarly the relationship between coverage
and forecast delay may merely reflect the fact that analysts prefer to cover companies
that release public information earlier during the fiscal quarter. Moreover, this approach
does not allow to identify what share of the accuracy loss can be imputed to less precise
exogenous public information at the time of the forecasts’ releases and to less precise
private information contained in the forecasts.
In order to quantify the distortion in timing and accuracy caused by preemption, I
build a structural approach that uses the equilibrium conditions of a timing game that I
present in section 5 to recover the parameters that govern the public learning as well as
the accuracy of the analysts’ private information.
5
5.1
Model
Setup
Consider a stock covered by n analysts in a continuous time framework. Each analyst
has to issue her forecast of the future realization of the EPS, x, at some time, t, during
the forecasting period, [0, T ]. The EPS, Π, is a random variable which follows a common
knowledge distribution N (µ0 , σ0 ). At the end of the forecasting period, the company
reports the realization of its EPS, π.
19
5.2
5.2.1
Information Structure
Exogenous Public Information
During the forecasting period, investors and analysts receive some exogenous public information on the company’s future earnings. This information can take the form of reports
of disclosures of accounting information, or announcements of any events that affect the
future performance of the company such as a merger, a technological breakthrough made
by the company, the appointment of a new CEO, or the results of clinical trials for a
pharmaceutical firm. Over time, the market receives a continuous stream of exogenous
public signals so that the precision of the exogenous public information, denoted f˜(t), increases in a differentiable manner: for all t1 < t2 , f˜(t1 ) < f˜(t2 ). Formally, the cumulative
exogenous public signal at instant t is represented by:
st = π + t
with t ∼ N (0,
1
)
f˜(t)
In practice analysts never wait until the last day of the forecasting period to issue their
forecasts. To guarantee that the model predicts realistic outcomes, I assume that the
precision of the exogenous public signal becomes arbitrarily large at the end of the forecasting period which suppresses all incentives for analysts to issue their forecasts at the
very end of the fiscal quarter.
lim f˜(t) = +∞
t→T
5.2.2
Private Information
At the beginning of the forecasting period, analyst i receives a private signal whose
precision is determined by her initial ability, αi . As time progresses, the accuracy of the
analyst’s private information increases as she builds on publicly released information to
refine her forecast. At instant t, the cumulative private signal of analyst i is represented
by:
sit = π + i
with it ∼ N (0,
1
) and yt = f (t)
f i (yt )
it is independent of the realization of the EPS, π. Moreover, analysts receive conditionally
independent signals: for all i 6= j, it ⊥ jt . The function f i (yt ) captures the precision
of the private information that analyst i has accumulated when the precision of the
20
public information (f (t)) reaches yt . f (t) corresponds to the sum of the precision of the
exogenous public information, f˜(t), and the precision of the private information disclosed
through the forecasts issued by t. Formally:
X
f (t) = f˜(t)+
f i (f (ti )) where ti denotes the time at which analyst i issues her forecast
i | ti <t
I use the following functional form for f i ():
f i (yt ) = αi + β i log(yt ) with yt = f (t)
β i captures the learning ability of the analyst. Positive values of β reflect the fact
that professional analysts are able to draw predictions from the public information that
are more precise than the investors’ beliefs about the future realization of the earning. I
assume that the marginal cost of converting public information into additional private is
increasing, which translates into a concave relationship between private and public precision. This assumption captures the fact that when there is little remaining uncertainty
about the future earning, the analyst finds it more difficult to improve on the public
signal5 .
5.3
Forecast
Analyst i issues a forecast equals to her posterior after observing the public signal st and
her private signal sit :
xit = wti sit + (1 − wti ) st
(5.1)
The weight, wti , that she allocates to her private signal is an increasing function of the
relative precision of her private information:
wti =
5.4
1/f (t)
1/f (t) + 1/f i (yt )
and yt = f (t)
Analyst Payoff
Guttman (2010) shows that when the analyst sells her forecasts to a single investor
6
before disclosing it publicly, her payoff is an increasing function of the precision of her
5
6
The computing power needed to process big data might be prohibitively large
which can be regarded as represented a group of investors not large enough for their trading decisions
to affect the price of the stock
21
private information relative to the public information:
U i (t) = log(
f i (t) + f (t)
)
f (t)
(5.2)
This result hinges on the following assumptions. The initial and the learning abilities
of the analyst are common knowledge. The market contains a continuum of investors
with a CARA utility function. Each investor decides how to allocate her initial wealth
between a safe asset with zero returns and a risky asset which corresponds to the stock of
the firm. Each investor is small enough that her trade does not affect the market price.
The supply of the stock is exogenous and constant. The willingness-to-pay for observing
the analyst’s forecast ahead of the market corresponds to the amount that equalizes her
expected utility if she remains uninformed to her expected utility if she acquires the
analyst’s information. The extra profit that the investor can make by using the forecast
of the analyst is determined by the relative informational content of the forecast. Since
the analyst is a monopolist on her private information, she extracts the entire the surplus
of her client.
5.5
5.5.1
Equilibrium Timing
Single-Analyst Case
The analyst issues her forecast at the time t that maximizes the relative precision of her
forecast. Since f (.) is invertible, for the analyst, choosing the optimal time is equivalent
to choosing the optimal precision of the public information at which to issue her forecast.
From now on, I refer to the precision of the public signal at which the analyst chooses to
issue her forecast when she is the only analyst who covers the stock as her unconstrained
optimum which I denote by yuc . yuc is such that:
i
yuc
= arg max U i (y) with U i (y) = log(
y≥0
f i (y) + y
)
y
It follows that:
i
= max{0, exp(1 −
yuc
22
αi
)}
βi
(5.3)
Since the payoff function is single-peaked, the unconstrained optimum is always
unique. Figure 2 shows the precision of the public signal at which the analyst chooses to
issue her forecast in the single-analyst case.
U
1
yuc
f (t)
Figure 2: Unconstrained Optimum
5.5.2
Two-Analyst Case
When an analyst issues her forecast, the precision of the public signal increases in a
discrete way. The size of the jump corresponds to the precision of her private signal. At
time t, the precision of the public information, denoted f (t), corresponds to the sum of
the precision of the exogenous public information and the informational content of the
forecasts – i.e. the precision of the private information of the analyst at the time she
issues her forecast – issued by t. Formally:
f (t) = f˜(t) +
X
f i [f (ti )]
i=1,2|ti ≤t
By increasing the precision of the public signal through her forecast, the analyst reduces the informational value of her opponent’s signal. The dependence of one analyst’s
payoff on the timing of the other analyst’s forecast generates a strategic interaction between competing analysts.
Intuitively, when analysts differ enough in terms of initial and learning abilities, each of
them forecasts at her unconstrained optimum. However, when analysts are more similar,
23
their unconstrained optima are also similar. In this case, they engage in a preemption
race and cluster their forecasts in time.
To see this, assume that the unconstrained optimal timings of analysts 1 and 2 are t1 <
1
2
1
2
1
).
| < f 1 (yuc
− yuc
such that |yuc
< yuc
t2 , with corresponding optimal public precisions yuc
1
If analyst 1 forecasts at t1 the public precision increases by a quantity f 1 (yuc
). It follows
that analyst 2 cannot reach her unconstrained optimal payoff by forecasting after analyst
1
1
1
2
1
1
)], analyst 2 finds it profitable to
+ f 1 (yuc
) > U 2 [yuc
. If U 2 (yuc
) > yuc
+ f 1 (yuc
1 since yuc
preempt analyst 1 by forecasting right before t1 . In turn, analyst 1 prefers to forecast right
before analyst 2 as long as t is such that U 1 (f˜(t)) > U 1 {f˜(t) + f 2 [f˜(t)]}. Both analysts
preempt each other until the precision of the public signal is such that one analyst becomes
indifferent between undercutting her opponent and forecasting immediately after her.
In the following, I present a more formal argument. First, it is useful to introduce the
concept of indifference interval. Denote J ≡ f 2 [f (τ1 )] the precision of the private signal
of analyst 2 when the public signal reaches a precision equal to f (τ1 ). Assume that J
is such that analyst 1 is indifferent between forecasting when the precision of the public
signal is f (τ1 ) and forecasting when the precision is f (τ1 ) + J:
f (τ1 ) is such that U 1 [f (τ1 )] = U 1 [f (τ1 ) + J]
(5.4)
If 5.4 holds, analyst 1 is said to admit an indifference interval of lower end f (τ1 ) and
length J. Since U 1 (.) is single-peaked and f 2 (.) is increasing, the indifference interval is
unique. The indifference interval exists as long as, at the beginning of the forecasting
period, analyst 1 is better off by forecasting immediately after analyst 2 rather than
forecasting first:
U 1 [f (0)] < U 1 {f (0) + f 2 [f (0)]}
(5.5)
Figure 3 shows an example of indifference interval.
Using the concept of subgame perfect equilibrium, Guttman (2010) shows that the
equilibrium timing is the following:
• At the very beginning of the forecasting period, if both analysts are better off
24
U
J ≡ f 2 (f (τ1 ))
f (τ1 )
f (t)
f (τ1 ) + J
Figure 3: Indifference Interval
issuing their forecasts immediately rather than waiting for their opponent to issue
her forecast and quickly follow suit, then both analysts forecast at time 0. Formally,
if U i [f (0)] ≥ U i {f (0) + f −i [f (0)]} for all i ∈ {1, 2}, then t1 = t2 = 0.
• If U i [f (0)] < U i {f (0) + f −i [f (0)]} for analyst i and U −i [f (0)] ≥ U −i {f (0) +
f i [f (0)]}, analyst −i forecasts at time 0 and analyst i forecasts immediately afi
i
ter if f (0) + f −i [f (0)] > yuc
and forecasts at tiuc = f −1 (yuc
) otherwise.
• If U i [f (0)] < U i {f (0) + f −i [f (0)]} for both analysts, the analyst with the smallest
lower end of indifference interval (f (τi ) < f (τ−i )) forecasts first. She forecasts at a
time t = min{τ−i , tiuc }.
– If the first analyst forecasts at τ−i , her competitor forecasts immediately after.
– If the first analyst chooses her unconstrained optimal time tiuc , then her competitor also chooses his unconstrained optimal time whenever it is feasible i.e.
−i
i
i
whenever yuc
≥ yuc
+ f i (yuc
) otherwise he forecasts immediately after analyst
i.
When one analyst forecasts immediately after the other, the equilibrium is said to be
clustered in timing. Otherwise the equilibrium is said to be unclustered. In an unclustered
equilibrium, both analysts always issue their forecasts at their unconstrained optima.
Figure 4 shows an example of unclustered equilibrium where analyst 1 (blue) forecasts
25
1
2
first at yuc
while analyst 2 (red) forecasts second at yuc
. Figure 5 shows an example of
clustered equilibrium where analyst 1 (blue) forecasts first at f (τ2 ) and analyst 2 (red)
forecasts immediately after the first analyst.
U
1
)
f 1 (yuc
1
yuc
2
yuc
f (t)
Figure 4: Two Analysts, Unclustered Equilibrium
U
f 1 [f (τ2 )]
f (t)
1
2
f (τ2 ) yuc
yuc
Figure 5: Two Analysts, Clustered Equilibrium
5.5.3
n-Analyst Case
When more than two analysts compete, it is no longer possible to derive a closed-form
solution for the equilibrium and the game generally admits multiple equilibria. Depending
on the degree of heterogeneity in analysts’ abilities, the game can present a non-clustering
equilibrium pattern, a combination of clusters of several forecasts separated in time with
26
other clusters of forecasts or with single non-clustered forecasts, or a fully clustered
pattern in which all forecasts are issued at the same time. In the following, I present the
algorithm that I use to find the equilibria of the game for an arbitrary number n (n > 2)
of analysts.
The precision of public signal increases exogenously over time as well as endogenously
after each forecast. At any instant t, the precision of the public signal depends on the
history of forecasts issued before t. I denote by ti the timing chosen by analyst i. The
precision of the public signal at t is:
X
f (t) = f˜(t) +
f i (f (ti ))
i | ti <t
I introduce the concept of a k-degree indifference interval with respect to an ordered
sequence of forecasts by k analysts. I denote by τSi k the lower end of a k-degree interval
for analyst i with respect to the ordered sequence of forecasts Sk = {s1 , s2 , ..., sk }, where
sk is the identity of the analyst who is the k th to forecast in the sequence. The jump
in precision after the sequence of forecasts Sk corresponds to the sum of the precisions
of the private signals disclosed in the successive forecasts. I define the upper end of the
indifference interval, denoted τ iSk , as follows:
τ iSk
=
k
X
f sl (f sl−1 (τSi k )) with f s0 (τSi k ) = f˜(τSi k )
l=1
τSi k
is such that analyst i is indifferent between being the first to forecast in τSi k and
forecasting right after the sequence of forecasts described in Sk .
τSi k
is such that U i (f (τSi k )) = U i (f (τSi k ) + τSi k )
To find the set of subgame perfect equilibria of the game, I consider all possible orders
of moves (= n!). For a given order of moves M = {m1 , m2 , ..., mn } where mk is the identity
of the analyst who is the k th to forecast, I derive a timing profile σ̃ = (y m1 , ..., y mn ) such
that no analyst would find it profitable to forecast before her prescribed timing. This
timing profile is such that analysts issue their forecasts no later than when the precision
of the public signal reaches the lower ends of the indifference intervals of the following
analysts.
27
After analyst mn−1 forecasts in y mn−1 , the last analyst, mn , chooses to forecast at the
public precision y mn such that:
mn
, y mn−1 + f mn−1 (y mn−1 )}
y mn = min{yuc
For any integer k such that 1 ≤ k < n, after the forecast of analyst mk−1 in y mk−1 ,
analyst mk chooses the public precision y mk such that:
mk
mk
= {mk , mk+1 , ..., ml }
, {f (τSmml k )}nl=k+1 } with Sm
y mk = min{yuc
l
ml
The timing profile σ̃ constitutes a subgame perfect equilibrium if there is no profitable
right-deviation. A right-deviation for analyst mk consists in forecasting after y mk . When
the timing profile commands that analyst mk forecasts at or after her unconstrained opmk
, she cannot find it profitable to delay her forecast. When the timing
timal timing yuc
profile commands that she forecasts before her unconstrained optimum, she has no incentives to delay her forecast if and only if she cannot gain by forecasting immediately
after tmk = f −1 (y mk ) when other analysts follow the timing strategies prescribed by σ̃.
When y mk = τSmml k , there is no profitable right-deviation for analyst mK , whenever:
ml
U mk (y mk ) ≥ U mk (y mk + τ mml k+1 )
Sml
The off-equilibrium beliefs and the corresponding strategies off the equilibrium path
are the following: If analyst mk has not issued her forecast when the precision of the
public signal reaches y > y mk , her competitors who have not yet issued their forecasts
believe that she is going to forecast immediately. As long as y + f mk (y) < y mk+1 , analyst
mk+1 waits until the precision of the public information approaches y mk+1 . As soon as
y + f mk (y) ≥ y mk+1 , analyst mk+1 responds by forecasting immediately and following
analysts ({ml }nl=k+2 ) quickly follow suit by forecasting in the order prescribed by the
equilibrium strategy. If analyst mn−1 issues her forecast at a precision of the public
mn
signal y < y mn−1 analyst mn issues her forecast in max{yuc
, y + f mn−1 (y)}. For all
k 6= n − 1, if analyst mk deviates by issuing her forecast before her prescribed timing,
the precision of the public signal at which her competitors issue their forecasts is left
unaffected.
28
6
Estimation: Description and Identification
6.1
Notation
A period refers to a given quarter in a given year. I observe S stocks and N analysts.
I use the subscript s ∈ {1, .., S} for all variables that differ across period-stock pairs,
the subscript i ∈ {1, ..., N } for variables that differ across analysts, and the subscript
q ∈ {1, ..., Q} to index variables that differ across periods. The variable ns,q denotes the
number of analysts who cover the stock s in period q. For each stock, s, Qs is the number
of quarters for which I observe at least one forecast. T corresponds to the time span
between the beginning and the end of the forecasting period. ti,s,q denotes the time at
which analyst i issues her forecast on stock s at period q. If the forecast is issued during
a time cluster, I index the forecasting time by c (= tci,s,q ), otherwise the forecast receives
the index uc (= tuc
i,s,q ).
6.2
Specification
Precision of the Public Signal
I impose the following functional form on the precision of the exogenous public signal:
1
1
t
+Γ
f˜s,q (t) = +
κ exp(σ0 )
T −t
I accommodate stock heterogeneity by allowing the parameters σ0 , which corresponds to
the variance of the EPS, and Γ, which captures the arrival rate of exogenous public information, to vary across stocks. Specifically, I allow σ0 to be stock and period specific and
I parametrize Γ as an exponential function of Zs,q . Choosing an exponential formulation
guarantees that the predicted precision of exogenous public information takes on positive
values.
0
Γ(Zs,q ; γ) = exp(Zs,q γ)
∈ [0, +∞)
Precision of the Private Signal
f i (yi,s,q ) = α(Wi,s,q ; δ) + β(Wi,s,q ; η) log(κ yi,s,q )
29
I allow the precision of the private signal to be analyst and stock specific by using the
following functional forms for α and β:
0
α(Wi,s,q ; δ) = exp(Wi,s,q δ)
0
β(Wi,s,q ; η) = exp(Wi,s,q η)
∈ [0, +∞)
∈ [0, +∞)
Moreover, I introduce the scaling parameter, κ, to allow the model to fit forecast
errors of a wider range of magnitudes. The optimal unconstrained public precision at
which the analyst issues her forecast becomes:
i,s,q
yuc
=
6.3
α(Wi,s,q ; δ)
1
exp(1 −
)
κ
β(Wi,s,q ; η)
Identification
I aim to recover the parameters that govern the public learning (Γ), which I define as the
precision of public information that the market would accumulate over time in the absence
of financial analysts, the initial precision of the exogenous public information (σ0 ), and
the analysts’ initial (α) and learning (β) abilities using data on EPS realizations (π), EPS
forecasts (x), and forecast timing t.
The intuition behind the identification of the parameters of the model is the following:
The accuracy of both the public signal and the private signal received by the analyst at
the time she issues her forecast jointly determine the magnitude of her forecast error. The
public learning does not affect the equilibrium precision of public information at which
analysts issue their forecasts but it affects the calendar time of the forecasts releases: the
model predicts that analysts issue their forecasts earlier when they cover companies that
release more precise exogenous information about their performances so that the uncertainty surrounding their future earnings is resolved faster. It follows that the variation
across stocks in the calendar time of the forecast releases identifies the parameters that
govern the precision of the exogenous public information (f˜). Since I observe a time
series of EPS for each stock, I can infer the initial precision of the public signal from
30
the empirical variance of the EPS. Once σ0 is recovered, the public learning, Γ, can be
obtained by inverting f˜.
For a given precision of exogenous public information, the precision of the analyst’s
private information can be recovered from the accuracy of her forecast. In turn, the
precision of the private information of the analyst depends on both the precision of her
initial signal, α, and her learning ability, β. I use the variation across analysts in forecast
release time to separately identify the two dimensions of analysts’ abilities. To see this,
notice that, even though the timing game admits multiple equilibria, a common feature
of all the equilibria of the game is that analysts who issue unclustered forecasts always
do so when the precision of the public signal reaches their unconstrained optima. From
the optimality condition 5.3, I can derive a one-to-one relationship between the precision
of the public information at the time of the forecast and the two dimensions of analysts’
abilities, α and β.
6.4
Estimation Algorithm
I use the time series of EPS realizations for each stock to compute the nonparametric
estimate of the variance of the EPS for stock s in period q, σ̂0s,q , which corresponds to
the empirical counterpart of σ0s,q .
Pq
σ̂0s,q
=
q 0 =0
(πs,q0 − π̄s,q )2
nq
The starting period 0 corresponds to the first quarter of 1984, the first year for which
EPS data are available in the I/B/E/S database. π̄s,q is the empirical mean of the EPS
of stock s computed over the period ranging from 0 to q. nq is the number of quarters
from 0 to q.
Let δ0 be the initial guess of values of the vector of parameters δ of the initial ability,
α. Given δ0 , the algorithm generates a sequence of estimates of {θk = (ηk , γk ) : k ≥ 1}
where the k-stage estimates correspond to the values of θ that maximize the likelihood
of observing the vector of forecast values, x, and forecast times, t, given the realization
of the EPS π:
31
θk = arg max L(x | t , π; θk , δk−1 )
(6.1)
θ
L(x | t, π; θk , δk−1 ) =
Qs ns,q
S Y
Y
Y
s=1 q=1 i=1
1
p
φ[(xi,s,q − πs,q )/σ(ti,s,q | θk , δk−1 )]
σ(ti,s,q | θk , δk−1 )
with
σ(ti,s,q | θk , δk−1 ) =
1
fθk (ti,s,q ) + fθik (yi,s,q )
with yi,s,q = fθk (ti,s,q )
and
fθk (ti,s,q ) =
1
1
ti,s,q
+ s + Γ(Zq,s |γk )
+
κ σ̂0
Ts,q − ti,s,q
X
fθlk (fθk (tl ))
l | tl <ti,s,q
fθik (yi,s,q ) = α(Wi,s,q ; δk−1 ) + β(Wi,s,q ; ηk ) log(κyi,s,q )
The parameters {δk : k ≥ 1} are obtained recursively as:
δk = ψ(tuc ; θk )
(6.2)
ψ(.) is derived from the optimality condition 5.3:
ψ(tuc ; θk ) = arg min
δ
X
−1
[tuc
i,s,q − fθk (
tuc
1
exp(1 − α(Wi,s,q ; δ)/β(Wi,s,q ; ηk ))]2
κ
The two steps, 6.1 and 6.2, are repeated until the algorithm reaches convergence.
Formally the stopping criterium is: |δk − δk−1 | < , with very small (.0001).
The estimator ϑ̂ ≡ (θ̂, δ̂) is consistent. Its asymptotic distribution is:
√
M (ϑ̂ − ϑ0 ) ∼ N (0, Avar(ϑ̂))
Where
M=
Qs ns,q
S Y
Y
Y
ms,q,i
s=1 q=1 i=1
With asymptotic variance:
M
1 X
Avar(ϑ̂) =
M m=1
Where
∂g(xm , πm ; ϑ̂)
ϑ0
!−1
M
1 X
g(xm , πm ; ϑ̂)g(xm , πm ; ϑ̂)0
M m=1

ψ(tuc
m ; θ̂)
!
M
1 X ∂g(xm , πm ; ϑ̂)
M m=1
ϑ0


g(xm , πm ; ϑ̂) = 
L(xm | πm ; θ̂, δ̂)
50
For implementation, I bootstrap the data 50 times to get {θ̂b }50
b=1 , {δ̂b }b=1 , and
{σ̂0,b }50
b=1 , and I calculate their standard errors.
32
!−1
6.5
Data Selection and Scaling
The model assumes that analysts issue a unique forecast during the fiscal quarter. This
assumption is consistent with the empirical observation that analysts who issue quarterly
earning forecasts seldom revise their forecasts (84% of the observed forecasts are never
revised). I estimate the parameters of the model on a selected subsample of the data that
excludes stocks for which at least one analyst has revised her forecast.
After all exclusions, the data contain 70,770 forecasts issued by 3,430 analysts on
2,224 stocks. Table A8 summarizes the characteristics of the stocks and the analysts
that compose the subsample used for the structural estimation. In the structural sample,
stocks are issued by smaller companies (the average market capitalization is 2.2 in the
subsample compared with 5.7 in the full sample), they consequently receive less recommendations (6 versus 7 on average) and are covered by fewer analysts (6 versus 8 on
average). The selected sample also features analysts who tend to be less experienced,
to cover less stocks and to be slightly less likely to work for big brokerage houses. For
numerical reasons7 , I exclude very late forecasts, i.e. forecasts issued less than two weeks
before the end of the quarter, which represent less than 1% of the sample.
The variance of the centered forecast errors is 0.0149 which corresponds to an average
precision of the forecast equal to 67. To achieve better numerical performance, I fix the
scale of the model, κ, to
1
20
in order to let the upper bound of range of the optimal
unconstrained public precision be close enough to the nonparametric estimate of the
variance.
The variable time, t, is continuous and corresponds to the number of minutes since the
date of the EPS pre-announcement. The length of the forecasting period, T , corresponds
to the number of minutes between the EPS pre-announcement and the end of the fiscal
quarter. Table 3 shows the summary statistics for both variables. I consider that the
analyst issues an unclustered forecast, if no other analyst issues a forecast during the day
of her forecast release. According to this definition, 33% of the observed forecasts are
unclustered.
7
For forecasts issued at the very end of the forecasting period, the ratio
t
T −t
which for scaling reasons affects the performance of the estimation algorithm.
33
takes very large values,
Table 3: Length of Forecasting Period and Forecast Delay (structural sample)
Variable
Obs
Mean
Std. Dev.
P25
P50
P75
P90
P95
Length of the forecasting period (in days)
70,770
56.824
11.783
53
59
65
69
71
# days since EPS pre-announcement
70,770
2.159
4.073
1
1
2
5
9
7
Results
7.1
Precision of initial belief on EPS
At the beginning of the forecasting period, analysts and investors share common beliefs
about the future realization of the EPS. Their common best initial prediction of the EPS
corresponds to the historical mean of the company earnings. The precision of their initial
belief is determined by the historical variance of the EPS. Table A9 shows the summary
statistics for the estimates of the variance of the EPS, σ̂0s,q .
As shown in Table 4, the variance of the EPS is smaller for bigger companies, probably
because bigger companies are more likely to be long-established with profits that vary
less over time than those of younger companies. The variance is also smaller for stocks
that receive more recommendations, which seems to indicate that analysts make safe bets
by recommending stocks of companies for which there is little uncertainty regarding the
future profitabilities. I also find that companies that report their EPS later in the fiscal
quarter have earnings that are more stable over time; those companies might choose to
report late precisely because investors can infer their EPS before the official report with
a high level of accuracy. As expected, the volatility of the stock returns is positively
correlated with the volatility of the EPS.
7.2
Exogenous Public Information
There are two sources of public information in the model. The first is purely exogenous:
over time the market learns about the future earning of the company. The exogenous
public information can take the form of the disclosure of sales revenues, the regulatory
approval of a drug for a pharmaceutical company, or a patent for an important tech34
Table 4: Determinants of EPS variance
Dependent Variable: σ̂0s,q
Variable
Coef.
Std. Err.
Market Capitalization
-.0329∗∗∗
.0117
Volatility (×103 )
.0746∗∗∗
.0089
EPS Report Delay
-.0103∗∗∗
.0010
# of Recommendations
-.0096∗∗∗
.0021
Recommendation Dispersion
.0111
.0372
Last Quarter
.0427
.0275
Time Trend
.0067
.0091
Intercept
.6680∗∗∗
.0554
Nbr of Obs
70,770
∗
p < .1,
a
∗∗
p < .05,
∗∗∗
a
p < .01
clustered at stock level
nological breakthrough. The second source of information is the disclosed forecasts of
analysts.
Table 5 shows the estimates of the parameters, γ, which measure the impacts of
various stock characteristics on the public learning. I find that exogenous information on
the future earnings of companies with highly volatile returns, large market capitalization,
companies which report their EPS late, as well as last quarter earnings exhibits a lower
arrival rate. This result is consistent with the reduced-form evidence presented earlier
showing that returns volatility and market capitalization are negatively associated with
forecast accuracy. Regarding the magnitude of the effects, a one-percent increase in
market capitalization decreases the arrival rate of exogenous information by .7%, and a
one-percent increase in returns volatility decreases the arrival rate by 1.4%. None of the
other potential determinants of the arrival rate of exogenous information appears to have
a significant effect on Γ.
From the estimated parameters γ̂, I derive the estimated value of the public learning,
0
Γ̂ = exp(Zs,q γ). The marginal effect of each passing minute on the precision of the
35
Table 5: Determinants of the public learning
Dependent Variable: Γ
Z
Raw Parameter: γ̂
Marginal Effect
Elasticity
(at mean)
(at mean)
SE
P Value
Market Capitalization (× 107 )
-1.8077
-380.3998
-0.6524
0.8872
0.0416
Volatility (× 103 )
-1.7051
-358.7915
-1.3159
0.4197
0.0000
EPS Report Delay
-0.0604
-12.7122
-1.9855
0.0339
0.0745
# of Recommendations
-0.0134
-2.8184
-0.1057
0.0266
0.6142
0.2500
52.6045
0.2119
0.2979
0.4013
-0.6609
-139.0815
0.2595
0.0109
Time Trend
0.0776
16.3350
0.0761
0.3075
Intercept
8.3137
0.8999
0.0000
Recommendation Variance
Last Fiscal Quarter
0.1358
exogenous information is given by:
f˜0 (t) = Γ
T
(T − t)2
Table A9 reports the summary statistics of Γ̂. At the median value of Γ̂, the precision
of the exogenous public information is estimated to increase by 2.5 from the first to the
second day of the forecasting period, and by 3.6 from the 10th to the 11th day of the
forecasting period. The arrival rate of exogenous information varies considerably across
stocks: from the first to the second day of the forecasting period, the precision of the
exogenous information on stocks in the 10th percentile of the distribution increases by
0.3, while it increases by 9 for stocks in the 90th percentile of the distribution. The
heterogeneity in the public learning translates into a large dispersion of the precision of
the exogenous information at the time of the forecasts: as reported in Table 8, the mean
exogenous public precision is 32, while the interquartile range is 21.
Graph 6 shows how the accuracy of the exogenous information increases over the
forecasting period for stocks at the 25th , 50th , and 75th percentile of the distribution of
Γ̂. Ten days after the beginning of the forecasting period, if investors were to use only
the exogenous information to forecast the future earnings they would forecast with an
36
error that is 4.4% of the mean EPS (.35) for companies at the median of the distribution
of the public learning compared to only 2.7% of the mean EPS for companies in the last
quartile of the distribution.
Figure 6: Heterogeneity in Public Learning
7.3
Initial Ability
The initial ability captures the informativeness of the private signal that the analyst
receives at the very beginning of the forecasting period. Table 6 reports the estimates
of the impacts of analysts’ characteristics on α. Most estimates are noisy and only the
parameter associated to the stock-specific experience appears to be significant. I find
that analysts who have followed a stock for a longer period receive initial signals that are
less accurate.
With the estimated parameters, δ̂, at hand, I estimate the initial ability, α̂, for each
analyst-stock-period observation. Table A9 reports the summary statistics on the initial
ability. I find that analysts start the game with a substantial informational advantage
over the market: the typical analyst initially receives a private signal whose precision is
77% higher than the precision of the public signal.
37
Table 6: Determinants of the initial ability
Dependent Variable: α
W
Raw Parameter: δ̂
Marginal Effect
Elasticity
(at mean)
(at mean)
SE
P Value
Experience
-0.0052
-0.0085
-0.0482
0.0738
0.9436
Stock Experience
-0.0889
-0.1445
-0.3557
0.0426
0.0370
0.0929
0.1509
0.6123
0.0757
0.2202
High Status
-0.1389
-0.2258
0.2940
0.6365
Workload
-0.0397
-0.0645
-0.4352
0.0283
0.1605
Industry Workload
0.0412
0.0670
0.2051
0.0552
0.4551
Intercept
0.4776
0.3998
0.2322
Industry Experience
7.4
Learning Ability
The learning ability captures the efficiency with which the analyst processes public information and converts it into a forecast that is more accurate than the market’s belief
about the future earning. Table 7 reports the estimates of the impacts of analysts’ characteristics on β. As for the determinants of the initial ability, I find that most estimates
are noisy and only the stock-specific experience appears to have a significant and negative
impact on the learning ability.
From η̂, I recover β̂. Table A9 shows the summary statistics on β̂. The average
learning ability is nearly 5, which means that, for the average exogenous public precision,
32, the typical analyst turns the public signal into a forecast whose accuracy is 6% larger
than the accuracy of the information available to the market.
7.5
Informational Value of Financial Analysts
To evaluate the informational value of sell-side analysts, which I define as the amount of
additional information that analysts provide to the market, I estimate the accuracy of
their forecasts relative to the precision of the exogenous information. With the estimates
of the initial ability α̂, the learning ability β̂, and the precision of the exogenous infor38
Table 7: Determinants of the learning ability
Dependent Variable: β
W
Raw Parameter: η̂
Marginal Effect
Elasticity
(at mean)
(at mean)
0.0032
0.0157
0.0291
0.0714
0.9647
-0.0878
-0.4371
-0.3516
0.0462
0.0575
0.0898
0.4467
0.5919
0.0678
0.1857
High Status
-0.2735
-1.3611
0.5970
0.6468
Workload
-0.0360
-0.1793
-0.3948
0.0271
0.1837
Industry Workload
-0.0003
-0.0016
-0.0016
0.0579
0.9957
0.3182
0.0000
Experience
Stock Experience
Industry Experience
Intercept
1.7415
SE
P Value
mation f˜ˆ, I proceed sequentially to recover the precision of the total information made
available to investors. After each released forecast, the precision of the total information
jumps by a quantity equal to the informational content of the forecast. Given the history
of the game, I estimate the precision of the private information disclosed through each
forecast, and I update the precision of the total information accordingly. Before the first
forecast, the only information available to the market is the exogenous information. After
each forecast, the precision of the total public information becomes:
fˆθ̂ (ti,s,q ) = fˆθ̂ (ti,s,q ) + fθ̂i [fˆ(ti,s,q )]
With
fˆθ̂ (ti,s,q ) = fˆ˜θ̂ (ti,s,q ) +
X
fθ̂l (tl )
l | tl <ti,s,q
And
1
1
ti,s,q
fˆ˜θ̂ (ti,s,q ) = + s + γ(Zq,s |γ̂k )
κ σ̂0
Ts,q − ti,s,q
And
fθ̂i [fˆ(ti,s,q )] = α(Wi,s,q ; δ̂) + β(Wi,s,q ; η̂) log[κ fˆ(ti,s,q )]
Table 8 shows the summary statistics for the accuracy of the private information
(fˆi ), the exogenous public information (fˆ˜), the total public information available to the
39
market right before the disclosure of the forecast (fˆ), the total information available to
the market after the disclosure of the forecast (fˆ + fˆi ), the accuracy of the consensus
forecasts, and the absolute forecast error.
The mean of the estimated precision of the total public information at the time of the
forecast is 46.5 compared to 32 for the mean of the exogenous information. This implies
that competition diminishes greatly the market value of the analysts’ private information:
at the time when the typical analyst issues her forecast, about 30% of the information on
earnings available to investors has been produced by competing analysts. The estimated
precision of the private information of the average analyst is 5, implying that the average
informational advantage of the analyst, at the time she issues her forecast, – which
is the precision of her private information relative to the public information – is 10%.
The informativeness of the private signal varies greatly across analysts: analysts who lie
above the 90th percentile of the distribution of the private precision receives a signal that
is more than four times more accurate than analysts who lie below the 10th percentile.
When assessing the contribution of analysts to the accuracy of investors’ expectations
about future earnings, it is worth noting that, when the analyst issues her forecast, she
allows later analysts to use her private signal as an input in their forecasting models. In
other words, the analyst increases the amount of information investors can access both
directly because her private signal becomes immediately available to the market and
indirectly because she produces materials that is later used by her competitors to refine
their forecasts. Because of the informational spillover, the relatively modest informational
advantage of each individual analyst turns into a substantial aggregate contribution. The
average precision of the total information available to the market after the typical analyst
has disclosed her forecast is 51 which is 60% higher than the average precision of the
exogenous information.
7.6
Preemption, Accuracy, and Forecast Timing
In order to measure the distortions caused by preemption, I perform a counterfactual
experiment in which the forecasts’ dates are fixed so as to maximize the relative precision
of each forecast under the constraint that no analyst issues her forecast before the public
40
Table 8: Summary statistics – Precision of: private information, exogenous public, endogenous public information, total information, and consensus forecasts
Variable
fˆi
ˆ
f˜
fˆ
fˆ + fˆi
Consensus
Absolute Forecast Error
fˆi
fˆ+fˆi
(first forecasts)
Mean
Median
Std. Dev.
P10
P25
P75
P90
5.0074
3.6755
5.0032
1.8300
2.4546
5.7999
9.1526
(1.6450)
(2.6404)
(1.3251)
(0.6590)
(0.8811)
(1.9459)
(2.8540)
32.3131
24.6113
35.4409
21.2667
22.2748
29.6842
42.0207
(1.4835)
(0.8943)
(9.0342)
(0.2659)
(0.5383)
(1.2649)
(2.7060)
46.5468
33.7662
44.4677
22.9982
26.2674
49.7088
78.5598
(4.9731)
(2.6404)
(8.7101)
(0.5718)
(1.1018)
(6.5927)
(13.3918)
51.5542
37.9096
47.1948
25.1290
29.0795
55.8348
87.8221
(6.5391)
(3.9731)
(9.0596)
(1.0492)
(1.8690)
(8.7106)
(16.3967)
42.0710
35.8372
29.4517
26.1335
29.5657
45.5063
60.4830
(3.7603)
(3.4490)
(8.0928)
(1.5493)
(2.3607)
(4.9862)
(7.2176)
0.1254
0.1014
0.1010
0.0184
0.0470
0.1793
0.2653
(0.0051)
(0.0048)
(0.0032)
(9.8532e-04)
(0.0023)
(0.0076)
(0.0097)
1.1035
1.0874
0.0656
1.0621
1.0731
1.1087
1.1523
(0.0269)
(0.0232)
(0.0377)
(0.0200)
(0.0211)
(0.0257)
(0.0384)
Note: Bootstrapped standard errors in parentheses
signal reaches her unconstrained optimum. More specifically, I order analysts by their
unconstrained optima, from the analyst with the earliest optimal timing to the analyst
with the latest timing. I assume that each analyst forecasts when the precision of the
public signal reaches her optimal unconstrained level if it is attainable or immediately
after the previous forecast if the public precision following the sequence of previous forecasts exceeds her optimal level. For each analyst, I define the informational loss induced
by preemption as the difference in the relative precision between the forecast issued at
equilibrium and the one issued in the counterfactual benchmark. I also estimate the effect of preemption on forecast delays, by comparing the observed and the counterfactual
forecasts’ dates.
As a first step, I estimate the optimal public precision at which each analyst would
choose to issue her forecast in the absence of competitors. For analyst i who covers stock
41
s in period q with characteristics, Wi,s,q , the estimated unconstrained optimum is derived
from equation 5.3:
α(Wi,s,q ; δ̂)
i,s,q
(Wi,s,q ) = exp 1 −
ŷuc
β(Wi,s,q ; η̂)
!
This optimal public precision corresponds to different unconstrained optimal timing depending on the arrival rate of the exogenous public information on the stock. When
analyst i with characteristics, Wi,s,q , covers stock s with characteristics, Zs,q , her estimated optimal timing is obtained by inverting the fˆ˜ :


i,s,q
i,s,q
fˆ˜−1 (yuc
≥ fˆ˜(0)
) if ŷuc
t̂iuc (Wi,s,q , Zs,q ) =

0
otherwise
As a second step, for each stock, I order analysts by their unconstrained optima from
the analyst with the lowest unconstrained optimum to the analyst with the largest one.
k
Formally, the k th analyst in the sequence issues her forecast at the public precision, ycf
,
such that:
k
ŷcf
=


k
ŷuc
k
if fˆk ≤ ŷuc

fˆk
otherwise
With
fˆ1 = 0
And
fˆk = ŷ k−1 + fˆk−1 (ŷ k−1 ) ∀ k > 1
The counterfactual timing profile is such that, analyst k th forecasts at time:
t̂kcf =


fˆ˜−1 (y k ) if y k ≥ fˆ˜(0)

0
otherwise
Table 9 shows the summary statistics for the counterfactual forecast delays and the
various measures of counterfactual forecasts precision. Preemption is found to reduce
substantially forecast delays: in the counterfactual scenario, the typical analyst issues
her forecast 8 days after the date she chooses in the actual data. The reduction in
average forecast delays is also highly significant (< 1%).
42
I find that preemption generates large and statistically significant informational costs:
the average precision of the counterfactual forecast is nearly 63 which is 24% larger than
the precision of the estimated forecasts. In terms of forecast error, the loss in accuracy
caused by preemption translates into an average absolute forecast error that is 18% larger
than in the absence of preemptive incentives. Similarly, I estimate that the counterfactual
consensus forecast is 26% more accurate than the actual one. Part of this difference
in precision simply reflects the fact that analysts forecast later in the counterfactual
scenario and thereby incorporate more exogenous public information in their forecasts. I
find that the precision of the exogenous public information at the time of the forecasts
is 15% larger in the counterfactual scenario, which means that 42% of the difference
in forecast accuracy is attributable to differences in exogenous information at the time
of the forecasts. It follows that preemption reduces by 45% the amount of endogenous
information that analysts produce. This loss of accuracy stems from sub-optimal timing:
preemption reduces the informational advantage of the typical first forecast issued on
each stock by 1.6%. As shown in Table A10, all effects are statistically significant the 5%
level. The effect on investors welfare is ambiguous. Graph 7 shows that by accelerating
forecasts disclosure, preemption increases the amount of information available to the
market during the beginning of the forecasting period. However, from the 8th day of the
forecasting period on, the precision of the information produced by analysts is lower under
preemption. Table A11 shows that the counterfactual average precision is significantly
lower than the one estimated from the actual data before the end of the second day of
the forecasting period, and become significantly higher after the 8th day.
To illustrate the effects of preemption on accuracy and forecast delay, Graph 8 plots
the precision of the exogenous information and the total information from the actual data
and the counterfactual experiment for the earnings of the company Zillow Inc. for the
first quarter of 2014.
43
Table 9: Summary Statistics on Counterfactual Forecasts
Variable
Mean
ˆ
f˜(tcf )
k )
fˆk (ŷcf
k + fˆk (ŷ k )
ŷcf
cf
Consensuscf
Absolute Forecast Errorcf
Forecast Delaycf
fˆi
fˆ+fˆi
(first forecasts)
Median
Std. Dev.
P10
P25
P75
P90
37.0969
37.2127
1.8464
34.6602
35.9241
38.4941
39.2789
(4.3105e+03)
(3.9282)
(3.4408e+05)
(3.1761)
(3.6853)
(4.0757)
(6.8896)
6.6918
5.1476
5.9054
3.0683
3.8270
7.3893
11.1133
(3.0068)
(2.3543)
(3.8304)
(0.7958)
(1.3980)
(3.9351)
(6.4328)
62.8635
52.8994
31.5254
40.9460
44.6811
69.0329
95.3912
(3.8375)
(2.9586)
(2.7595)
(2.7214)
(2.5988)
(4.4789)
(6.9571)
53.0156
49.9137
11.8436
43.1111
45.6661
56.5462
66.0702
(3.1597)
(2.6301)
(2.5405)
(2.5308)
(2.5305)
(3.2927)
(4.9170)
0.1061
0.0879
0.0828
0.0164
0.0411
0.1519
0.2219
(0.0025)
(0.0020)
(0.0024)
(3.8119e-04)
(9.4978e-04)
(0.0035)
(0.0053)
10.3187
5.6781
12.4172
1.9191
3.0956
11.7682
24.3724
(0.4762)
(0.4445)
(0.7058)
(0.2807)
(0.3350)
(0.6907)
(1.8488)
1.1215
1.1029
0.0775
1.0742
1.0861
1.1265
1.1769
(0.0055)
(0.0038)
(0.0087)
(0.0105)
(0.0049)
(0.0047)
(0.0071)
Note: Bootstrapped standard errors in parentheses
Figure 7: Effect of Preemption on the Information Available to Investors
44
Figure 8: Forecast Timing and Precision of Market’s Beliefs with and without Preemption
for Zillow Inc., 2014, 1st Quarter
45
8
Conclusion
This paper sheds new light on the interplay between competition and timing in the market
for professional forecasts. I model the forecasting behavior of sell-side analysts by using a
timing game in which analysts choose the forecast dates that maximize the revenue that
they can derive from selling their private information to their clients before disclosing
their forecasts publicly. When more than two analysts cover the stock, the game no
longer admits a unique equilibrium. To overcome the issue of multiplicity of equilibria,
I build an identification strategy around a feature of the game that is invariant across
equilibria: unclustered forecasts are issued when the public signal reaches the analysts’
unconstrained optimal precisions. I recover the structural parameters that govern the
arrival rate of exogenous public information and the two-dimensional abilities of the
analysts.
With those parameters at hand, I quantify the informational value of professional
forecasters, in the market for EPS predictions, which I define as the contribution of
financial analysts to the accuracy of investors’ expectations about future earnings. I also
quantify the distortion caused by preemption.
I find that analysts are major contributors to the flow of information available to
investors: they produce 40% of the information on future earnings available during the
fiscal quarter. However there is a countervailing effect of competition. The distortion is
significant and important. Preemption is found to reduce substantially forecast delays
and forecast accuracy: the average forecasts delays is reduced by 8 days while the typical
forecast is 24% less accurate under preemption.
The findings are consistent with other studies of expert reporting behavior showing
that strategic motives can create substantial informational losses. In particular, Camara
and Dupuis (2014) show that reputational concerns lead movie critics to bias their recommendations up to 40% of the time.
By establishing that competition has countervailing effects on information provision,
this work has important policy implications regarding the optimal level of industry concentration. The results also suggest that imposing a fixed forecasting date can increase
the amount of information conveyed by experts.
46
The estimated structural parameters can be used to compute the set of all equilibria
from counterfactual experiments with varying stock coverage in order to estimate the
bounds on the effect of coverage on forecast delay and forecast accuracy. This exercise is
left for future research.
47
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-page
Appendix
●
●
●
●
●
●●
●●
●●●●●
●●●●●● ●
● ●●●●●●●●●●●●
●●●●●●●●●●●●●●
Figure 9: Average Forecast Delay over Coverage
52
●
Table A1: Predicted CDF of Forecast Delays
Delay
# days
CDF
CDF +1 St Dev
at Means for low status analysts
Experience
Stock
High
Stock
Industry
Experience
Status
Workload
Workload
1
.623
.618
.641
.641
.653
.639
5
.797
.793
.813
.813
.823
.811
10
.839
.836
.853
.854
.862
.852
20
.894
.891
.905
.905
.912
.904
30
.924
.922
.933
.933
.939
.932
60
.991
.990
.993
.993
.994
.993
Delay
CDF
# days
CDF +1 St Dev
Market
#
Recommendation
Capitalization
Recommendations
Dispersion
at Means for low status analysts
Coverage
1
.623
.627
.619
.635
.644
5
.797
.801
.794
.808
.815
10
.839
.843
.837
.849
.856
20
.894
.897
.892
.902
.907
30
.924
.926
.922
.931
.935
60
.991
.992
.991
.992
.993
Table A2: Summary Statistics on Forecast Error
Variable
Obs
Mean
Std. Dev.
Min
Max
P25
P50
P75
Forecast Error
304,018
.015
.388
-40.08
68.86
-.02
.02
.07
Centered Absolute Forecast Error
287,389
.114
.368
0
68.836
.02
.048
.113
53
Table A3: Summary Statistics on Brokerage Houses
Size
Variable
# Employed Analysts
Obs
3,493
a
Mean
Std. Dev.
Min
Max
P25
P50
P75
12.277
16.822
1
82
1
5
15
# Covered Companies
3,493
94.164
142.019
1
690
6
32
106
# Covered Industries
3,493
34.067
46.2
1
214
4
14
43
332,028
13.144
37.203
.003
626.55
.841
2.654
9.233
# Employed Analysts
368
54.552
33
82
43
55
64
# Covered Companies
368
449.47
112.137
38
690
364.5
458
525.5
# Covered Industries
368
144.818
35.939
20
214
128
150.5
171.5
167,042
14.59
37.432
.004
626.55
1.157
3.444
11.306
# Employed Analysts
3,125
7.299
7.697
1
32
1
4
11
# Covered Companies
3,125
52.323
66.677
1
332
5
21
73
# Covered Industries
3,125
21.025
24.882
1
131
3
10
30
164,986
11.679
36.912
.003
626.55
.635
1.981
7.205
All
Market Capitalization (in $M)
Big
Market Capitalization (in $M)
Small
Market Capitalization (in $M)
a
# of broker-quarter observations
Table A4: Summary Statistics on Stocks
Size
All
Big
Variable
Obs (stock-quarter)
Mean
Std. Dev.
P25
P50
P75
Coverage
41,795
7.972
6.621
3
6
11
Market Capitalization ($M)
41,794
5.766
21.953
.291
.927
3.151
Volatility (×103 )
41,794
.857
1.382
.273
.535
.991
# of Recommendations
41,795
7.467
7.019
2
5
11
Recommendation Dispersion
34,708
.807
.327
.656
.831
.996
Coverage
6,055
16.987
7.631
12
16
22
Market Capitalization ($M)
6,054
32.228
49.958
9.505
15.277
30.152
Volatility (×103 )
6,054
.302
.268
.136
.228
.374
# of Recommendations
6,055
15.756
7.677
10
14
20
Recommendation Dispersion
6,025
.823
.192
.711
.823
.934
54
Table A5: Summary Statistics on Forecasters
Variable
Obs
Mean
Std. Dev.
Min
Max
P25
P50
P75
Experience
332,169
8.955
6.076
0
30.186
4.255
8.088
12.26
Stock Experience
332,169
4.062
4.081
0
30.518
1
2.753
6.003
Industry Experience
332,169
6.581
5.39
0
29.849
2.249
5.504
9.756
High Status
332,169
.513
.5
0
1
0
1
1
Stock Workload
332,169
11.037
5.083
1
35
8
11
14
Industry Workload
332,169
4.591
2.878
1
22
2
4
6
Table A6: Summary Statistics on Forecast Delays
Variable
Obs
Mean
Std. Dev.
P25
P50
P75
EPS Announcement Delay
392,846
31.252
10.648
24
30
36
Delay before First Forecast by Analyst
332,115
36.512
15.177
26
33
41
Delay following EPS Pre-Announcement (Analyst level)
332,115
4.826
11.275
1
1
2
Delay before First Forecast on Stock
41,754
35.192
13.037
27
33
40
Delay following EPS Pre-Announcement (Stock level)
41,754
.979
4.428
0
0
1
Delay after first EPS Forecast
332,115
4.638
11.247
0
1
2
Table A7: Summary Statistics on Forecast Error
Variable
Obs
Mean
Std. Dev.
Min
Max
P25
P50
P75
Forecast Error
332,115
.0106
.1273
0
9.8235
.0006
.0018
.0046
Consensus Forecast Error (Median)
41,794
.0193
.1777
0
9.3271
.001
.0025
.0065
Consensus Forecast Error (Mean)
41,794
.0197
.1781
0
9.3271
.0011
.0026
.0068
55
.25
Average Forecast Error
.1
.15
.2
5
>1
,1
5
(2
(1
<=
1
,2
]
]
.05
Forecast Delay after EPS pre-announcement(in days)
Distribution of Forecast Order
<Q1
[Q2,Q3)
95%CI
[Q1,Q2)
>Q3
Figure 10: Absolute Forecast Error, Delay, and Order
Table A8: Summary Statistics- Structural Sample
Variable
Obs
Mean
Std. Dev.
Min
Max
P25
P50
P75
Coverage
13,360
6.089
4.102
1
37
3
5
8
Market Capitalization (in $M)
13,360
2.294
7.464
.007
239.791
.292
.74
1.943
Volatility (×103 )
13,360
.844
1.415
.001
64.532
.277
.548
1
# of Recommendations
13,360
5.878
4.714
1
41
3
4
8
Recommendation Dispersion
13,360
.825
.358
0
2.828
.632
.837
1
Experience
3,430
7.146
6.529
0
30.94
1.751
5.667
10.51
Stock Experience
3,430
3.058
3.788
0
28.019
.499
1.748
4.252
Industry Experience
3,430
4.923
5.388
0
29.268
.751
3
7.504
High Status
3,430
.47
.499
0
1
0
0
1
Stock Workload
3,430
7.764
4.988
1
31
4
7
11
Industry Workload
3,430
3.761
2.569
1
18
2
3
5
56
Table A9: Summary Statistics: EPS variance, Arrival Rate of Exogenous Information,
Initial Ability, Learning Ability
Variable
Mean
Median
Std. Dev.
P10
P25
P75
P90
σ̂0
.4339
.0252
3.8377
.0028
.0085
.0710
.2390
(0.2338)
(0.0131)
(1.9060)
(9.9453e-04)
(0.0038)
(0.0425)
(0.1494)
210.4278
138.7571
223.0029
14.3664
52.9579
292.2893
497.9816
(29.3814)
(34.2158)
(83.9467)
(11.4935)
(23.0043)
(39.4110)
(89.9852)
1.6254
1.3890
1.0006
1.0177
1.1930
1.6226
2.3535
(0.5100)
(0.3838)
(0.7491)
(0.3012)
(0.3264)
(0.5157)
(0.8015)
4.9759
4.1610
3.4222
2.8305
3.3681
5.2092
7.5108
(1.1473)
(1.2200)
(1.8766)
(1.0814)
(1.1450)
(1.3065)
(1.9379)
Γ̂
α̂
β̂
Note: Bootstrapped standard errors in parentheses
57
Table A10: Summary Statistics Counterfactual Differences
Variable
ˆ
ˆ
f˜(tcf ) − f˜(t)
k ) − fˆk (ŷ k )
fˆk (ŷcf
k − ŷ k
ŷcf
k + fˆk (ŷ k ) − ŷ k + fˆk (ŷ k )
ŷcf
cf
Consensuscf − Consensus
Absolute Forecast Errorcf − Absolute Forecast Error
Forecast Delaycf − Forecast Delay
k +fˆk (ŷ k )
ŷcf
cf
fˆk (ŷ k )
−
ŷ k +fˆk (ŷ k )
fˆk (ŷ k )
cf
(first forecasts)
Mean
Median
4.7804
11.9963
[3.3117, 1.7519e + 04]
[0.6526, 13.6324]
1.6845
1.4712
[0.7019, 6.3404]
[0.9174, 5.1191]
9.6248
14.0834
[6.0187, 27.1845]
[11.0744, 21.1540]
11.3093
15.7580
[7.7160, 33.5248]
[12.5777, 26.3307]
10.9446
16.0450
[7.8310, 25.4102]
[12.7847, 25.5001]
-0.0190
-0.0120
[−0.0334, −0.0131]
[−0.0235, −0.0074]
7.7140
3.8260
[−8.647, −6.780]
[−4.697, −2.954]
0.0180
0.0147
[0.0037, 0.0857]
[0.0069, 0.0862]
Note: Bootstrapped 95% confidence interval in square brackets
Table A11: Summary Statistics - Precision of Information Available to Investors over
time (Estimated and Counterfactual)
Variable
fˆ + fˆi (average)
i
fˆcf + fˆcf
(average)
i
fˆcf + fˆcf
− (fˆ + fˆi ) (average)
Before 2nd Day
From 3rd Day to 7th Day
From 8th Day to 20th Day
35.3623
79.2891
154.2904
(0.4396)
(1.6106)
(3.6909)
26.9670
72.6806
146.8685
(0.2666)
(1.1736)
(4.0861)
-8.3953
-6.6085
7.4218
[−9.3557, −7.0186]
[−5.2474, 0.1786]
[6.4698, 12.9405]
Note: Bootstrapped standard errors in parentheses and 95% confidence interval in square
brackets
58