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Analyst information acquisition and communication

April 2008

April 2008
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Authors:

University of Pennsylvania

We examine a communication game between an analyst and a decision-maker and investigate how the presence of public information affects the preci-sion of the information the analyst gathers and credibly communicates to the decision-maker. We characterize conditions under which public information causes the analyst to under-invest or over-invest in the information gathered relative to the case where analyst credibility is not an issue. The model also provides circumstances where the presence of public information causes the an-alyst to drop coverage of the firm, suggesting that the introduction of public information can make the decision-maker strictly worse off.

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Analyst Information Acquisition and

Communication∗

Paul E. Fischer

The Pennsylvania State University

Phillip C. Stocken

Dartmouth College

May 28, 2008

Abstract

We examine a communication game between an analyst and a decision-

maker and investigate how the presence of public information aﬀects the preci-

sion of the information the analyst gathers and credibly communicates to the

decision-maker. We characterize conditions under which public information

causes the analyst to under-invest or over-invest in the information gathered

relative to the case where analyst credibility is not an issue. The model also

provides circumstances where the presence of public information causes the an-

alyst to drop coverage of the ﬁrm, suggesting that the introduction of public

information can make the decision-maker strictly worse oﬀ.

∗We thank Tim Baldenius, Ron Dye, Steve Huddart, Nahum Melumad, John Morgan, Jonathan

Rogers, Richard Sansing, Jerry Salamon, Ulf Schiller, Reed Smith, and Ro Verrecchia for helpful

discussion. We also thank workshop participants at the University of Bern, Chicago-Minnesota

Accounting Theory Conference, Columbia University, Dartmouth College, Indiana University, and

University of Michigan.

Please address correspondence to: Phillip Stocken, Tuck School of Business

at Dartmouth, 100 Tuck Hall, Hanover, NH 03755; e-mail: phillip.c.stocken@dartmouth.edu.

Analyst Information Acquisition and Communication

1 Introduction

Decision-makers obtain information from various sources. Some sources have incen-

tives to communicate strategically in a self-serving fashion and face limited regulation

regarding their communication. Other sources have little incentive to communicate

strategically or face fairly stringent regulation regarding their communication. In-

vestors, for instance, can obtain information from sell-side analysts, who are thought

to have incentives to communicate strategically and who face relatively little regula-

tion regarding their communication, and also from a ﬁrm’s audited ﬁnancial state-

ments, where regulation plays a signiﬁcant role in limiting strategic communication

of certain information. This study analyzes how changes in the information disclosed

by a non-strategic source inﬂuences the information gathering and communication

decisions of an information intermediary who is strategic.

The model we employ in this analysis has four stages and two players: an infor-

mation intermediary, which we call an analyst, and a decision-maker. In the ﬁrst

stage, both players observe an imperfect public signal about the state of nature. In

the second stage, the analyst engages in costly information gathering that determines

the precision of a signal about the state of nature that he will privately observe. In

the third stage, the analyst privately observes a signal and costlessly sends a mes-

sage to the decision-maker. In the fourth stage, the decision-maker, given his beliefs

about the state of nature, takes an action that aﬀects both players’ payoﬀs. The

players have divergent preferences regarding the decision-maker’s action. Within the

context of this model, we explore how the precision of the public information that

the players observe in the ﬁrst stage aﬀects the analyst’s information gathering and

communication in the second and third stages.

While the model can be applied to various settings where decision-makers obtain

information from sources that strategically release information and also from other

sources that release information in an impartial manner, we ﬁnd this model useful for

framing the recent evolution in the analyst market. The amount of information that

ﬁrms make available directly to investors has exploded. Following the introduction of

Reg FD in 2000, for instance, ﬁrms can no longer privately reveal information to an-

alysts and hence are more likely to publicly release their forward-looking information

(see Heﬂin, Subramanyam, and Zhang 2003). Further, ﬁrms now routinely hold con-

ference calls following their earnings releases that are open to investors (see Bushee,

Matsumoto, and Miller 2003). In addition, the $1.4 billion settlement between the

large brokerage ﬁrms and the State of New York in 2002 required the investment

ﬁrms to provide information to investors from unbiased sources together with their

own analysis. Following this settlement, there has been a ﬂight of equity analysts

from the research departments at the large investment ﬁrms, and entire industry sec-

tors have lost analyst coverage. As a consequence, several commentators have argued

that these changes are likely to hurt individual investors and reduce stock price eﬃ-

ciency (see Schack 2003). A contribution of this study, therefore, is to illustrate how

alternative sources of information might aﬀect analyst information gathering activi-

ties, the integrity of their communication with investors, and whether investors are

likely to be better oﬀas a consequence of changes in the amount of publicly available

information.

This paper highlights that changes in publicly observed information aﬀects an

analyst’s behavior in two ways. First, when the analyst can credibly communicate

privately observed information, the public information serves as a substitute for the

analyst’s information. As a consequence, improvements in the quality of the public in-

formation reduce the marginal value of the analyst information causing him to gather

less precise information. Second, when the analyst’s credibility is in doubt–because

the analyst’s incentives are misaligned with those of the decision-maker–improving

the quality of the public information makes it more diﬃcult for the analyst to cred-

ibly communicate. Speciﬁcally, an increase in the quality of the other information

reduces the decision-maker’s responsiveness to the analyst’s information, which causes

the analyst to exaggerate his report in an attempt to inﬂuence the decision-maker.

This exaggeration undermines the analyst’s credibility. As a consequence, when the

quality of the public information increases, either the analyst gathers more precise

information to increase the decision-maker’s responsiveness to his information and

thereby facilitate credible communication or he discontinues gathering information

(i.e., leaves the market).

This analysis suggests that competition arising from improvements in the quality

of public information has subtle consequences for analyst behavior. When credibil-

ity issues are minimal, which occurs when information gathering costs are low, an

increase in the precision of public information leads to a marginal reduction in an-

alyst information gathering. Although more precise public information crowds out

some analyst information, this crowding out is not suﬃcient to oﬀset the beneﬁtof

more precise public information. Consequently, the decision-maker is better oﬀ.Al-

ternatively, when credibility issues are more pronounced and information gathering

costs are moderate, more precise public information leads the analyst to improve his

information gathering. The heightened precision of the analyst information coupled

with more precise public information combine to make the decision maker better oﬀ.

Finally, when credibility issues are more pronounced and information gathering costs

are high, an increase in the precision of public information completely crowds out the

analyst information and the analyst leaves the market. Although the decision-maker

obtains more precise public information, the crowding out of the analyst information

can be so severe that it actually reduces the total information the decision-maker

obtains thereby making the decision-maker worse oﬀ.

The primary theoretical antecedent of our paper is Crawford and Sobel (1982).

They consider a communication game between an informed expert and an uninformed

decision-maker. The expert perfectly observes the realization of a payoﬀrelevant

state variable and sends a costless message to the decision-maker who then takes an

action that aﬀects both players. Their cheap-talk model has been extended in various

directions. In work most closely related to our paper, Austen-Smith (1994) considers

a communication game in which the expert chooses whether to perfectly observe the

stateofnatureatsomeﬁxed cost and decides whether to reveal being informed, but

is unable to prove being uninformed. He establishes that there exist circumstances

under which the players cannot communicate when the receiver knows the expert

is informed although they can do so when the receiver is uncertain about whether

the expert is informed. In contrast to Austen-Smith, we consider a model in which

the expert, after observing a public signal, can choose the precision of his privately

observed signal; further, we allow for the possibility that the precision of the expert’s

signal is either publicly observed or privately chosen.

The extant literature also has extended the model in Crawford and Sobel (1982)

by examining the eﬀect of multiple experts on the communication game (e.g., Austen-

Smith 1993; Krishna and Morgan 2001; Wolinsky 2002; Battaglini 2004; Morgan and

Stocken 2008), by introducing multiple decision-makers (e.g., Farrell and Gibbons

1989; Newman and Sansing 1993; Gigler 1994), or by allowing the players to exchange

messages (e.g., Aumann and Hart 2003; Krishna and Morgan 2004). In these studies,

the expert is exogenously endowed with information. We, in contrast, examine a

setting where it is costly for the expert to gather information and consider how the

presence of a non-strategic information source aﬀects the information that the expert

gathers and communicates.

Our paper is also related to the voluntary disclosure literature. Verrecchia (1990)

examines a discretionary disclosure setting in which the quality of information with

which a manager is endowed is exogenously speciﬁed. Analogous to our result that

more public information can thwart credible communication, Verrecchia establishes

that an increase in the precision of the market’s prior beliefs, which corresponds with

an increase in the other information in our model, reduces the probability that the

manager discloses. Penno (1996) considers a mandatory disclosure setting in which a

manager, after observing a public signal, privately chooses the precision of the report

that the ﬁrm will release. He establishes that the precision of the manager’s report is

inversely related to the favorableness of the public information and that the strength

of this relationship diminishes as the public signal becomes less precise. Hence, like

our paper, he links precision of a public signal with the amount of information com-

municated in a subsequent report. Both of these papers, unlike our paper, assume

that the precision of the manager’s information is exogenous. In more recent work,

Pae (1999) explores a manager’s acquisition of costly private information about the

consequence of the manager’s productive eﬀort in the context of a voluntary disclosure

setting. Hughes and Pae (2004) consider a setting in which an entrepreneur gathers

and voluntarily discloses information truthfully about the precision of a signal of an

asset’s value that the entrepreneur is oﬀering for sale. Lastly, Arya and Mittendorf

(2007) explore how public disclosure might aﬀect analyst behavior. They consider a

setting where competing ﬁrms can voluntarily release information to encourage an-

alyst following. Heightened analyst following enriches the information environment

and thereby allows ﬁrms to better coordinate their production choices. A common

feature of these studies, like much of the extant literature examining voluntary disclo-

sure behavior (e.g., Verrecchia 1983; Dye 1985; Einhorn and Ziv 2008), is that private

information, if it is disclosed, must be disclosed truthfully. In the analyst reporting

environment, however, analysts often report in a self-serving fashion and face little

regulation regarding how they report (e.g., Michaely and Womack 1999; Lin and Mc-

Nichols 1998). Indeed, it was precisely this concern that motivated key provisions of

the Sarbanes-Oxley Act and the legal settlement between the large brokerage ﬁrms

and the State of New York in 2002.1We examine a reporting environment in which

the analyst’s disclosure is not constrained by particular disclosure rules and ﬁnd the

desire to communicate credibly fundamentally inﬂuences the analyst’s information

gathering behavior. Hence, a contribution of our paper is to provide insights into

information gathering and communication behavior when reporting credibility is a

key feature of the environment.2

Our paper is also reminiscent of the disclosure literature that considers the credi-

bility of a ﬁrm manager’s communication when investors can gather other information

that allows them to assess the veracity of the manager’s disclosure. For instance, Sans-

ing (1992) and Stocken (2000) examine managers’ earnings forecasting behavior when

investors can use an audited earnings report to assess a forecast’s credibility. In these

papers, the investors are exogenously endowed with the earnings report. Further, the

modeling frameworks and the questions they address diﬀer substantially from ours.

The paper proceeds as follows: Section 2 describes the model and includes a time

line that summarizes the model’s notation. Section 3 characterizes the equilibrium.

Section 4 examines how changes in the precision of public information inﬂuence an an-

alyst’s information gathering and communication. Section 5 considers how changes in

the precision of public information aﬀect the quality of the decision-maker’s informa-

tion. Section 6 relaxes the assumption that the analyst’s precision choice is common

knowledge and discusses how the analyst’s information gathering and communication

changes. Section 7 concludes. All proofs are in the Appendix.

2Model

We consider a communication game in which an analyst can choose to obtain private

information about an unknown state variable and send a report to a decision-maker

who then takes an action. The unknown state variable is represented by the random

variable ˜α, which has support {s, f }where s>f. The common prior beliefs are that

1Some work has studied analyst information gathering. Hayes (1998), for instance, examines an

analyst’s incentives to gather and report information in an environment in which the analyst’s report

inﬂuences an investor’s trading behavior that, in turn, determines the trading commission that the

analyst receives. The analyst always reports truthfully so that issues of strategic disclosure do not

arise.

2In addition, several studies examine how private information acquisition will change in response

to a public information signal within a rational expectations framework (e.g., Verrecchia 1982;

Diamond 1985; Alles and Lundholm 1993).

the successful, s, and failure, f, state realizations are equally likely to occur.3

The game has four stages. In the ﬁrst stage, information represented by the

realization of a random variable ˜xis publicly observed. The support for ˜xis {h, l}.

The probability that ˜x=hconditional on ˜α=sand the probability that ˜x=l

conditional on ˜α=fare both q∈(1/2,1).Thevariableqcaptures the precision

of ˜x, where a higher value for qimplies that ˜xis more informative. Setting q=

1/2is equivalent to supposing that the public information is absent. The public

information may be viewed as the ﬁling of a ﬁrm’s audited ﬁnancial statements or the

release of governmental statistics that are informative about a ﬁrm’s future outlook.

The analyst observes the realization of the public information xbefore choosing the

precision of his private information.

In the second or information gathering stage, the analyst chooses whether to invest

in a costly information generating technology to acquire private non-veriﬁable infor-

mation. The analyst’s private information, if obtained, is represented by the realiza-

tion of a random variable ˜y, which has support {g, b}. Conditional on the realization of

˜α,˜xand ˜yare independent. The probability that ˜y=gconditional on ˜α=sand the

probability that ˜y=bconditional on ˜α=fare both p∈[1/2,1]. The analyst chooses

the precision pand incurs a cost c(p),wherec(p)is a twice diﬀerentiable function that

satisﬁes: (i) c0(p)>0and c00(p)>0for p>1/2; (ii) limp→1/2c0(p)/(p−1/2) →0;

(iii) limp→1c0(p)→∞;and(iv)c00(p)/c0(p)>(1 −3p(1 −p)) /(p(1 −p)(p−1/2))

for all p∈(1/2,1). Condition (i) requires that the analyst’s cost of gathering in-

formation increases in the precision of the information and at an increasing rate.

Conditions (ii) and (iii) are suﬃcient for the analyst to choose an interior level of

precision when he can credibly communicate. Condition (iv) is suﬃcient to insure

the analyst’s optimal precision choice is unique. As an example, the simple power

function c(p)=((p−1/2) /(1 −p))n,wheren>2,satisﬁes these conditions (see

Appendix for details). The analyst choosing not to invest in the information technol-

ogy is equivalent to the case in which the analyst’s private information has precision

p=1/2.

The decision-maker observes the precision of the analyst’s private information, but

not the realization of his private information. This assumption is consistent with the

sell-side equity analyst environment, which is the primary institutional application of

3As in this paper, many cheap-talk models assume the players’ prior beliefs are diﬀuse (e.g.,

Austen-Smith 1993; Krishna and Morgan 2001; and Battaglini 2004).

our model. Analyst stock reports vary in content and often contain detailed analysis

of a company, its key competitors, and its industry. The detail in the analyst’s

stock report, which the investor can readily observe, reﬂects the precision of the

analyst’s information. Investors, however, do not observe the analyst’s procedures for

evaluating and interpreting the information that is gathered. It is this interpretation

and evaluation that provides the analyst with private information y.Intheﬁnal

section of the paper, we suppose the analyst’s choice of precision is unobservable.

In the third or reporting stage, the analyst costlessly sends a report rto the

decision-maker. The analyst need not report truthfully. The analyst’s ability to

communicate the privately observed signal yin his report is potentially thwarted,

however, because the commonly known preferences of the decision-maker regarding

her action choice diﬀer from the commonly known preferences of the analyst. In

particular, the decision-maker chooses an action a∈<given her information Ωdto

maximize

Ud=−E£(˜α−a)2|Ωd¤,(1)

where E[·|·]is the expectation operator. Given this objective function, it is opti-

mal for the decision-maker to choose an action a=E[˜α|Ωd], which is analogous

to investors valuing a ﬁrm at its expected value.4The analyst’s objective function

also depends on the decision-maker’s action; the analyst chooses a report rgiven his

information Ωito maximize

Ui=E£φa −(˜α−a)2−c(p)|Ωi¤,(2)

where φ>0.5When φ=0, the players’ interests are perfectly aligned because,

given the same information, both players would prefer the same action. When φ>

0, however, their interests are misaligned because, for a given information set, the

analyst’s preferred action exceeds the decision-maker’s preferred action. These utility

representations are broadly descriptive of institutional settings where an analyst wants

to induce a higher action than a decision-maker would prefer, but is constrained

from inducing an action that is too high because of, say, (unmodeled) reputation or

litigation concerns associated with misleading the decision-maker (e.g., Dugar and

4The presumption that investors value a ﬁrm at its expected value is standard in the voluntary

disclosure literature (e.g., Verrecchia 1990; Penno 1996; and Einhorn 2007).

5We can also assume φ<0without altering the ﬂavor of the results.

Nathan 1995; Grossman and Helpman 2001; Morgan and Stocken 2003).6

In the fourth stage, the state of nature αis realized and the analyst’s and decision-

maker’s payoﬀs are determined. All aspects of game are common knowledge except

the analyst’s private signal y. The time line of events and the model’s notation is

summarized in Figure 1.

[Figure 1]

We st ud y Perfect Bayesian Equilibria, which require that: the players’ beliefs

satisfy Bayes’ rule whenever possible; and, given beliefs, the decision-maker’s action

amaximizes her expected payoﬀUd=−E[(˜α−a)2|Ωd]and the analyst’s choice

of information precision pmaximizes Ui=E[φa −(˜α−a)2−c(p)|Ωi]and, given

the cost of gathering information is sunk, the analyst’s report rmaximizes Ui=

E[φa −(˜α−a)2|Ωi].

Like most cheap-talk games, there are multiple equilibria. In our model, there

are, at most, two classes of equilibria: one class of equilibria in which the analyst

chooses the same precision p>1/2(i.e., the analyst gathers some information) and

communicates that information to the decision-maker, and one class of equilibria in

which the analyst chooses p=1/2(i.e., the analyst does not gather any information),

which is analogous to a babbling equilibrium in a cheap-talk game without endogenous

information acquisition. There always exists equilibria in which the analyst does

not gather any information. There may or may not exist equilibria in which the

analyst gathers and communicates information. When there exist equilibria in which

information is gathered, we focus on this class because these equilibria ex ante Pareto

dominate any equilibrium in which information is not gathered.7Within the class of

equilibria in which information is gathered, we focus on the truthful communication

equilibrium–the equilibrium in which r=yfor all y. This focus is without loss of

6While the Sarbanes-Oxley Act enacted on July 25, 2002 was drafted to strengthen the inde-

pendence of security analysts (Razaee, 2007) and the legal settlement between the large brokerage

ﬁrms and the State of New York in 2002 has altered the way in which analysts are compensated,

separated research and investment banking activities within investment ﬁrms, and mandated disclo-

sure in stock reports of conﬂicts where they might exist, there still is evidence suggesting analysts

have incentives to curry favor with ﬁrm management. For instance, Mayew (2008) ﬁnds that ﬁrm

management favors those analysts in conference calls who have bullish stock recommendations on

the ﬁrm.

7It is standard in the cheap-talk literature to focus on an ex ante Pareto dominant equilibrium;

see, for instance, Crawford and Sobel (1982).

generality because when there exists an equilibrium with full revelation that involves

the analyst reporting something other than y(e.g., r∈{b, g}and r6=yfor all y), it

is economically equivalent to the truthful communication equilibrium.8

3 Equilibrium

The analyst chooses the precision of his private information after observing the public

information and then decides whether to truthfully reveal his private information. We

use backward induction to characterize the equilibrium and begin with the reporting

stage before considering the information gathering stage.

In the reporting stage, the analyst decides whether to truthfully reveal his private

information after having observed the public signal and his private information. To

assess whether the analyst can communicate yto the decision-maker, note that the

analyst prefers a higher action than the decision-maker given y, and that the decision-

maker would take a higher action if she believes the analyst has observed ˜y=g.It

follows that the analyst is always willing to reveal when ˜y=g, but may want to

mislead the decision-maker when ˜y=bby claiming that ˜y=g. Recalling that the

value of the analyst’s objective is increasing and then decreasing in the decision-

maker’s action implies that the analyst will not try to mislead when ˜y=bif the

action induced from claiming that ˜y=gis much higher than the action preferred by

the analyst when ˜y=b. Hence, the analyst can communicate yif the action he would

induce by misrepresenting his information is suﬃciently high relative to the one he

induces if he truthfully communicates his information.

For either realization of ˜x, the diﬀerence between the actions the decision-maker

might choose when she believes she knows yis

∆(p)≡E[˜α|x, g]−E[˜α|x, b]= q(1 −q)(2p−1) (s−f)

(p(1 −q)+(1−p)q) ((1 −p)(1−q)+pq).(3)

The diﬀerence ∆(p)is an increasing function of p, which implies that the decision-

maker’s action choice is more responsive to the analyst’s information when the an-

alyst’s information is more precise. As discussed above, the analyst can credibly

8To the extent that it is institutionally inappropriate to focus on the properties of the most

informative equilibrium when there exist a multiplicity of equilibria, then the predictive power of

the claims in this paper will be reduced.

communicate yiftheactionheinduceswhenheclaimstohaveobservedrealizationg

is suﬃciently large relative to the action he induces when he claims to have observed

realization b,orformally

∆(p)−φ≥0.

Hence, if pis suﬃciently high, the analyst can credibly communicate y. This obser-

vation is formalized in the next lemma.

Lemma 1 The analyst can communicate yin the presence of the other information

xif and only if the precision of the analyst’s information is suﬃciently high; that

is, there exists a minimum threshold ¯psuch that, for any x, the analyst can credibly

communicate yif and only if p≥¯p.

Having examined the reporting stage, we now step back and consider the infor-

mation gathering stage. In this stage, the analyst chooses the precision of his private

information after having observed the public signal realization x∈{l, h}. To deter-

mine the analyst’s choice, it is useful to ﬁrst examine how the analyst’s objective

function behaves in pwhen we assume the analyst’s information yis publicly ob-

served. Recalling that the decision-maker’s action choice equals the expectation of ˜α,

the analyst’s objective function is

Ey£φE[˜α|x, y]−(˜α−E[˜α|x, y])2−c(p)|x, y¤

=φEy[E[˜α|x, y]] −p(1 −p)(s−f)∆(p)

2p−1−c(p).

The next lemma establishes how the analyst’s objective function behaves in the ana-

lyst’s precision choice p.

Lemma 2 When the analyst’s information yis public, the analyst’s objective function

is strictly quasiconcave and attains a maximum at p∗∈(1/2,1) where p∗is such that

∆2(p∗)/(2p∗−1) −c0(p∗)=0.(4)

Lemma 2 implies the analyst has a single-peaked objective function that is max-

imized at p∗when the analyst’s signal yis public information. The analyst’s signal

y, however, is not publicly observed. Lemma 1 implies that pmust be at least ¯pfor

credible communication to occur when the analyst’s signal is not publicly observed.

It follows from these two lemmas that, when yis not public information, the analyst

chooses p=p∗if p∗≥¯p.Alternatively,ifp∗<¯p, the analyst chooses p=1/2or

p=¯p. The next proposition extends this discussion and characterizes the analyst’s

optimal choice.

Proposition 3 Suppose the analyst privately observes yand both players observe the

other information x.

(i) If φ∆(p∗)/(2p∗−1) ≤c0(p∗), then the analyst chooses a level of precision

p∗∈[¯p, 1) and communicates truthfully in the reporting stage.

(ii) If φ∆(p∗)/(2p∗−1) >c

0(p∗)and c(¯p)≤∆(¯p)q(1 −q)(2¯p−1) (s−f),

then the analyst chooses a level of precision ¯pand communicates truthfully in the

reporting stage.

(iii) If φ∆(p∗)/(2p∗−1) >c

0(p∗)and c(¯p)>∆(¯p)q(1 −q)(2¯p−1) (s−f),

then the analyst chooses to not collect any private information.

Proposition 3 assumes the analyst chooses the precision of his private information

after observing the realization of the public information. Analysts, however, often

choose to gather information in anticipation of a public information event. Because

∆(p)does not depend on whether the public signal realization is either ˜x=hor

l, it follows that the characterization of the equilibrium in Proposition 3 would not

change if we instead assumed that the analyst chose the precision of his information

before observing the public information. Further, there also exists an equilibrium in

which the analyst does not gather any information in cases (i) and (ii) in Proposition

3. As we stated earlier, if there exists an equilibrium in which information gathering

occurs, we assume it is the equilibrium that is played.

4AnalystInformation

While Proposition 3 characterizes the analyst’s information gathering decision, it

oﬀers little insight into the determinants of the information the analyst chooses to

gather and disseminate. To address our primary research question, we examine how

the quality of the other information available to the decision-maker, q,aﬀects the

analyst’s information gathering decision, p. From Proposition 3, we know that the

analyst chooses information quality p∗if credible communication of the resulting

information is possible, speciﬁcally p=p∗≥¯p. Otherwise, the analyst chooses

a higher level of information quality to allow communication, p=¯p>p

∗,orhe

chooses to exit the market if information of higher quality is too costly to obtain,

that is p=1/2. Assessing how the quality of the public information, q,inﬂuences

the analyst’s behavior entails determining how qaﬀects the critical values p∗and ¯p.

The following corollary, which follows directly from Lemmas 1 and 2, characterizes

the relation between qand the critical precision values p∗and ¯p.

Corollary 4 The minimum precision of the analyst’s private information necessary

for the analyst to credibly communicate, ¯p,isincreasing in the precision of public

information q;thatis,∂¯p/∂q > 0. The precision of the analyst’s information chosen

when the analyst’s information is public, p∗,isdecreasing in the precision of the public

information q;thatis,∂p∗/∂q < 0when q6=1/2and ∂p∗/∂q =0when q=1/2.

To develop intuition for the relation between qand ¯p, note that when the precision

of the public information is low, the decision-maker’s action choice is more responsive

to the analyst’s information because the analyst information is relatively precise. As

a consequence of this greater responsiveness, the analyst is less inclined to exaggerate

and report gwhen bis actually observed because, if the report is believed, the decision-

maker takes an action that is undesirably high from the analyst’s perspective. On the

other hand, the analyst is less capable of credibly communicating when the public

information is precise because the decision-maker’s action choice is less responsive to

the analyst’s information. In this case, the analyst is more inclined to exaggerate and

report gwhen bis actually observed because, if the report is believed, the decision-

maker takes a higher action but one that is not so high that the analyst ﬁnds it

undesirable. If there are incentives for such exaggeration, however, the analyst is not

believed and communication does not occur in equilibrium. The relation between

qand p∗is straight forward. As the precision of public information increases, the

marginal beneﬁt of the analyst’s information decreases. Consequently, the level of p

that maximizes the analyst’s expected utility falls.

With Corollary 4 in hand, consider the case when the precision of the public

information is relatively low so that p∗≥¯p. As the precision of the public information

increases, ¯prises and p∗falls. Because the analyst chooses p∗when p∗≥¯p,the

analyst’s choice of pfalls in qbecause p∗falls in q. Eventually the precision of the other

information rises to a point where p∗=¯p.Asqcontinues to rise, communication is no

longer credible if the analyst chooses p∗. Hence, the analyst must choose between the

level of precision necessary for credible communication ¯por drop out of the market by

choosing p=1/2. Initially, the analyst responds by choosing ¯pand over-investing in

the quality of information he gathers to allow credible communication. Given that the

¯pis increasing in q, it follows that the precision of the analyst information increases

in q. Atsomepoint,however,implementing¯pbecomes so costly that the analyst

chooses not to collect any information. In these circumstances, the improvement in

the public information causes the analyst to under-invest in the quality of information

he gathers relative to that which he would gather if he could commit to credibly reveal

his private information. In summary, we have the following observation.

Remark 1 The precision of the information the analyst collects is decreasing in the

precision of the public information, then increasing in the precision of the public

information, and, at some suﬃciently high level of precision of the public information,

the analyst stops collecting private information; that is, there exists a q∗and ¯q>q

∗

such that the equilibrium precision of the analyst’s private information is decreasing in

qover the range (1/2,q

∗],increasinginqover the range (q∗,¯q], and is uninformative

for q>¯q.

Remark 1 provides some insight into the recent evolution of the sell-side analyst

industry. Recent regulatory changes have greatly increased the amount of information

ﬁrms make available directly to investors. For instance, following the introduction of

Reg FD, ﬁrms can no longer privately reveal information to analysts so ﬁrms are more

likely to publicly release their forward-looking information (see Heﬂin, et al., 2003). In

addition, the $1.4 billion settlement between ten large brokerage ﬁrms and the State of

New York requires these ﬁrms to distribute research reports that independent analysts

have prepared along with their own analysis (see Schack 2003). Finally, ﬁrms now

routinely host conference calls following earnings releases that are open to investors

(see Bushee, et al. 2003). These changes have eroded stock analysts’ information

advantage. Remark 1 suggests that, in response to these changes in the information

environment, some intermediaries have reduced the information they collect, others

have increased the quality of their analysis in response to the heightened competition

from other sources, and yet others have discontinued coverage of ﬁrms.

Remark 1 is empirically unsatisfying since it suggests “anything can happen”.

To oﬀer more deﬁnitive guidance as to how intermediaries might alter the quality of

their analysis in response to changes in public information, we consider how some

environmental characteristics might inﬂuence analyst behavior. In particular, we

assess how the extent of the incentive conﬂict, captured by φ,andthedegreeofprior

uncertainty about the ﬁrm’s payoﬀs, as captured by (s−f), would alter the analyst

behavior. Doing so, however, requires that we ﬁrst examine how changes in these

characteristics aﬀect the critical values of precision ¯pand p∗.

Corollary 5 The minimum precision of the analyst’s private information necessary

for the analyst to credibly communicate, ¯p, is increasing in the extent of incentive

misalignment φand decreasing in the diﬀerence between the state payoﬀs(s−f);

that is ∂¯p/∂φ > 0and ∂¯p/∂ (s−f)<0. The precision of the analyst’s information

chosen when the analyst’s information is public, p∗,isunaﬀected by the extent of

incentive misalignment φand is increasing in the diﬀerence between the state payoﬀs

(s−f);thatis∂p∗/∂φ =0and ∂p∗/∂ (s−f)>0.

To develop intuition for how ¯pbehaves, observe that the analyst is more inclined

to truthfully reveal his privately observed signal when the decision-maker’s actions are

highly responsive to his disclosure. The decision-maker is more responsive when the

analyst’s information is relatively more precise or the state payoﬀs are more divergent.

When the extent of incentive misalignment is large, the minimal precision of analyst

information necessary for credible communication must be high. Alternatively, when

the state payoﬀs are far apart and prior uncertainty is large, the decision-maker will

be more responsive to the analyst’s information. Therefore, the minimal precision of

the analyst’s information necessary for credible communication need not be high.

We now turn to how p∗behaves. This value is derived assuming the analyst’s

information is publicly observed. Accordingly, it is clear that the extent of the in-

centive misalignment between the players φshould not inﬂuence the choice of p∗.In

contrast, as the prior variance of the ﬁrm’s payoﬀs, which is proportional to (s−f),

increases, both players prefer more precise information.

Given the intuition underlying Corollary 5, we consider how the extent of incentive

misalignment φinﬂuences the analyst’s response to increases in the precision of other

information. If the extent of incentive misalignment is low, then p∗will exceed the

minimum level of precision necessary for credible communication ¯p. The analyst

therefore will choose p∗. Corollary 4 establishes that an increase in the quality of

public information is associated with a marginal decrease in the analyst’s precision

choice p∗. If the extent of misalignment is moderate, so that the analyst chooses

the minimum level of precision to facilitate credible communication ¯p, Corollary 4

shows that an increase in the quality of the public information is associated with a

marginal increase in the precision of the analyst’s information. Finally, if the extent of

misalignment is high, the analyst responds to an increase in the precision of the public

information by not gathering any addition information or performing any analysis.

Within the sell-side analyst context, these observations suggest that intermediaries

with large incentive conﬂicts, such as those whose employers do a great deal of banking

business (see Lin and McNichols 1998) or those who have substantial equity positions

in the ﬁrm’s stock, may be more incline to drop coverage of that ﬁrm in response to the

increase in public information. In contrast, analysts that face few conﬂicts of interest

will respond more modestly and simply reduce their analysis. Finally, analysts with

more moderate conﬂicts of interest will be more incline to increase their analysis in

response to increases in the availability of public information.

The extent of prior uncertainty also inﬂuences the response of intermediaries to

the increase in public information. Decision-makers might be more uncertain about

aﬁrm’s payoﬀsiftheﬁrm is in an industry that uses an innovative and unproven

technology. Corollaries 4 and 5 suggest that, in response to an increase in public

information, ﬁrms with highly risky payoﬀs will face relatively modest declines in

analyst attention, those with low risk payoﬀs will have analysts drop coverage, and

those with moderately risky payoﬀs will receive greater analyst attention.

In summary, the paper highlights that public information inﬂuences analysts in

two ways. First, improvements in public information make it more diﬃcult for the

analyst to communicate (i.e., ¯pis increasing in q). Second, improvements in public

information reduce the beneﬁt of more precise analyst information because the public

information substitutes for the analyst’s information (i.e., p∗is decreasing in q). When

communication credibility is not an issue (i.e., ¯pis small relative to p∗), the analyst

reduces the quality of his analysis in response to more precise public information. In

contrast, when analyst communication credibility is an issue, the analyst responds

to more precise public information by either gathering more precise information or

alternately dropping coverage of ﬁrms.

Our model, which emphasizes the role of reporting credibility for understanding

the information intermediary’s behavior, contrasts with the discretionary disclosure

models commonly examined in the accounting literature that assume any disclosure

must be truthful, although the manager can choose to withhold information. These

papers oﬀer reasons for why managers might not voluntarily release private informa-

tion. In this paper, we suggest analysts might not disclose non-veriﬁable information

because, in anticipation of being unable to credibly reveal it, they choose to not

gather any information. Further, we ﬁnd the presence of a reporting stage in a model

in which the analyst’s credibility is an important ingredient aﬀects the precision of

information that the analyst gathers in subtle ways. It can cause an analyst to under

or over-invest in information collection relative to the model where any disclosure is

always truthful.

5 Quality of Decision-Maker Information

We considered how the precision of the analyst’s information changes in response

to increases in the precision of the other information. In some cases, we demon-

strate that the analyst reduces the quality of analysis in response to an increase in

precision of public information. An unanswered question in these cases is: What

happens to the precision of the decision-maker’s information? In this section, we

examine how the quality of the decision-maker’s information varies with the precision

of the public information. We deﬁne the quality of information as a function of the

decision-maker’s expected posterior variance after the public signal and analyst re-

port, −Ey[var [˜α|Ωd]]. It can be shown that decision-maker’s objective function and

action choice is such that the quality of the decision-maker’s information is equivalent

to the decision-maker’s expected utility.

Consider the case in which the analyst chooses a level of precision that exceeds

the minimum level of precision necessary to credibly communicate in the reporting

stage prior to an increase in the precision of the other information, that is p∗>¯p.

The decision-maker’s quality of information when the analyst chooses p=p∗is given

−Ey[var [˜α|x, y;p∗]] = −p∗(1 −p∗)q(1 −q)(s−f)2

(p∗(1 −q)+(1−p∗)q) ((1 −p∗)(1−q)+p∗q).

As the precision of the public information qincreases, it follows from our previous

analysis that the precision of the analyst information decreases because the other in-

formation serves as a substitute for the analyst information. Nevertheless, we observe

that an increase in precision of the public information qleads to an increase in the

decision-maker’s information; that is, ∂(−Ey[var [˜α|x, y;p∗]]) /∂q > 0.

Consider the case where the precision of the other information qhas increased to a

point where the analyst optimally chooses the minimum level of precision that allows

credible communication, that is p=¯p. In this case, the decision-maker’s quality of

information is given by

−Ey[var [˜α|x, y;¯p]] = −¯p(1 −¯p)q(1 −q)(s−f)2

(¯p(1 −q)+(1−¯p)q) ((1 −¯p)(1−q)+ ¯pq).

When the truth-telling condition in the reporting stage is binding, the analyst in-

creases the precision of information he collects as the precision of the public in-

formation increases. Here the presence of the public information has a comple-

mentary eﬀect on the analyst’s information gathering activities. The increase in

the precision of the analyst’s information coupled with the increase in the precision

of the public information continues to cause the decision-maker’s information qual-

ity to increase with an increase in the precision of the public information; that is

∂(−Ey[var [˜α|x, y;¯p]]) /∂q > 0.

Finally, consider the case where the precision of the other information becomes

so large that the analyst’s expected utility when ¯pis chosen is less that the analyst’s

expected utility when no information is collected, that is p=1/2. In this case, the

analyst simply decides not to gather any information about the company–the analyst

drops ﬁrm coverage. Since the decision-maker only observes the public information

x, the decision-maker’s quality of information when p=1/2is given by

−Var[˜α|x]=−q(1 −q)(s−f)2.

This latter observation implies that, an increase in qabove some value ¯qcauses the

decision-maker’s information quality to fall discontinuously at ¯q.Thus,theincrease

in public information drives out the analyst’s willingness to collect and communicate

his private information, which makes the decision-maker worse oﬀ. Of course, as the

precision of the public information continues to increase, the quality of the decision-

maker’s information increases and the decision-maker’s information quality attains a

maximum value at q=1. This observation is formalized in the next Corollary.

Corollary 6 As the precision of the public information increases from q=1/2,the

total information the decision-maker obtains initially increases, falls discontinuously

at ¯qwhen the analyst no longer gathers private information, and then increases as q

approaches one.

Corollary 6 suggests that improving the quality of public information can crowd

out the analyst’s ability to credibly communicate his private information. The ex-

pected quality of the decision-maker’s information does not monotonically increase in

the precision of the public information. In the ﬁnancial reporting environment, how-

ever, policy-makers do not choose the precision of the public information. Instead,

they decide whether or not information of a given precision should be gathered and

disclosed. In essence, a policy-maker’s choice is between disclosure and no disclosure.

To assess whether the crowding out phenomenon can make no disclosure the policy-

maker’s preferred choice, we analyze the diﬀerence between the decision-maker’s in-

formation quality in the absence of disclosure, which is equivalent to q=1/2,and

the information quality when other information of precision qis publicly disclosed.

The goal now is to determine whether there are values of the precision of the public

information qfor which the decision-maker is better oﬀin the absence of the public

information.

We show that the introduction of public information can make the decision-

maker worse oﬀwithin the context of an example with a cost function c(p)=

((p−1/2) /(1 −p))nwhere n>2.Sets=2,f=3/20,φ=1/2,andn=3.

On one hand, consider the setting in which public information is absent. The analyst

chooses ¯p=1/2+φ(2 (s−f)) = 47/74 >p

∗; he gathers more precise information

than he would gather if he could commit to truthfully reveal his privately observed

information. Given the analyst chooses a level of precision ¯pand communicates truth-

fully in the reporting game, the decision-maker’s quality of information is given by

−Ey[var [˜α|y;¯p]] = −1

4¡(s−f)2−φ2¢.

On the other hand, consider an environment where the public disclosure of information

is mandatory. It is suﬃciently costly to gather information in this setting that the

analyst prefers to not gather any private information at all; the analyst chooses

p=1/2for all q∈(1/2,1). Although the presence of any public information crowds

out the analyst’s information, the decision-maker beneﬁts from observing the public

information. The decision-maker’s quality of information when p=1/2is given by

−Var[˜α|x]=−q(1 −q)(s−f)2.

When the precision of the public information is such that q∈(1/2,¯p), the beneﬁt

to the decision-maker of observing the public information is not suﬃcient to oﬀset

the analyst’s information that it displaces. The introduction of public information

reduces the total quality of the decision-maker’s information and makes her worse oﬀ.

Alternatively, when the precision of the public information is such that q∈(¯p, 1),

then the public information is suﬃciently precise that its introduction makes the

decision-maker strictly better oﬀ, even though it squashes the analyst’s willingness to

gather private information.

This observation that additional public information may reduce the players welfare

is reminiscent of a result in Christensen’s (1982) study of performance standards in an

agency setting. In that study, Christensen shows that the principal may be worse-oﬀ

when the players observe additional contractual information before the agent takes an

action. Our setting diﬀers from an agency setting because, in our setting, a receiver

cannot commit (i.e., contract) to use a report in a particular way. Consequently, the

character of our equilibrium and the economic forces delivering our results diﬀer from

those in Christensen (1982).

To digress brieﬂy, we have raised the possibility that introducing mandatory disclo-

sures of other information can reduce the total information available to the decision-

maker when the state space is binary. One might be concerned that this result can

arise only when the state space is discrete thereby allowing the analyst either to com-

municate truthfully or not to communicate at all. This possibility result, however,

can also be established when the state space and message space is continuous.

The fact that variations in the precision of the public information can harm the

decision-maker arises not because the state space or message space is discrete, but

because of the discontinuity in the precision with which the analyst can communicate

his private information. A key feature of our model is that the analyst does not

bear a direct cost from issuing any speciﬁc message. The analyst, however, incurs

an indirect cost from inducing the decision-maker to take an action that aﬀects his

expected payoﬀ. When there are no direct reporting costs and the incentives of

the analyst and decision-maker are not perfectly aligned, Crawford and Sobel (1982)

established that the unique equilibrium is characterized by a partition of the state

space and the analyst is only able to credibly reveal the interval containing his signal as

opposed to the signal itself. The lengths of the intervals in a partition vary. Therefore,

the precision with which the analyst can communicate his private information varies

discontinuously with his signal realization.

The following example illustrates the possibility of public information harming

the decision-maker within a game that features a continuous state space and message

space. To simplify the illustration, consider the reporting game when the analyst’s

information gathering activity (that depends on the speciﬁccostfunction)istaken

as given. Thus, the decision-maker’s and analyst’s utility functions are speciﬁed

in (1) and (2), respectively, but with c(p)=0; set φ=1/4. Assume the state

variable, ˜α, is uniformly distributed on the unit interval, and the analyst privately

observes the state variable y=α. The analyst and decision-maker publicly observe

the sum of two independent signals x=P2

i=1 vi, where each signal, vi,isdrawn

from a Bernoulli distribution with an unknown parameter α;thatis,Pr (˜vi=1)=α

for i=1,2. Therefore, the decision-maker’s posterior distribution of ˜αis a beta

distribution with parameters 1+xand 3−x(see DeGroot 1970). Given these beliefs,

when ˜x∈{0,1}, the analyst cannot reveal his information. In contrast, when ˜x=2,

the analyst’s message rcan reveal, at most, whether the state lies in one of three

intervals {[0,0.06] ,(0.06,0.43] ,(0.43,1]}.Whenthesignalxis publicly observable,

the decision-maker’s information quality −E[Var[˜α|x, r]] = −0.04.However,when

the public signal xis unavailable, the analyst’s message can reveal whether the state

lies in one of two intervals {[0,0.25] ,(0.25,1]}, and the decision-maker’s information

quality −E[Var[˜α|r]] = −0.03. Hence, the decision-maker is ex ante better oﬀwhen

the other information is unavailable.9

9When the state is continuously distributed and the other information variable ˜xis such that

it does not change the support of the decision-maker’s beliefs, analytic solutions to the questions

examined in this paper generally cannot be obtained. Characterizing the partitional equilibria to

this game requires ﬁnding solutions to non-linear, second-order diﬀerence equations. These equations

generally do not have analytic solutions. To obtain analytic solutions, we accordingly restrict the

support of the information variables in the model.

6 Unobservable Choice of Precision

In the primary model, the analyst’s choice of precision pis common knowledge. This

assumption is based on the observation that it is often possible to infer an analyst’s

expertise from the depth and clarity of the stock report, even though it is not possible

to infer exactly what the analyst believes. At times, however, the decision-maker

may be unable to determine the analyst’s expertise. As a consequence, in this section

we modify the model and assume the analyst privately chooses the precision of his

information.

As in the analysis of the primary model, it is again useful to initially consider a

setting where the analyst’s signal yis public information. After understanding that

less constrained setting, we consider the eﬀect of the credibility problem faced by

the analyst. In contrast to the analysis in the primary model in which pis public

information, analyzing the setting in which the analyst’s signal yis public information

involves a bit more of a game. In this game where pis not public information, the

decision-maker conjectures the analyst’s choice of pand the analyst conjectures the

decision-maker’s response to the analyst’s report. In the equilibrium to this game,

the choices of both players must maximize their objective functions conditional on

each having conjectures that are consistent with the other player’s equilibrium choices.

Denote the decision-maker’s conjecture regarding the analyst’s choice of pas bp.When

the public information xand analyst information yis realized, the decision-maker’s

action choice must satisfy

axg =bpt

bpt +(1−bp)(1 −t)s+(1 −bp)(1 −t)

bpt +(1−bp)(1 −t)f(5)

and

axb =(1 −bp)t

(1 −bp)t+bp(1 −t)s+bp(1 −t)

(1 −bp)t+bp(1 −t)f,(6)

where t=qwhen ˜x=hand t=1−qwhen ˜x=l. It follows that, in any equilibrium

s≥axg ≥axb ≥f.

Denote the analyst’s conjecture regarding the decision-maker’s response to realiza-

tion (x, y)as ˆaxy. Since in any equilibrium s≥axg ≥axb ≥f, consider the analyst’s

decision choice given xand conjectured actions s≥ˆaxg ≥ˆaxb ≥f.Theanalyst’s

choice of pmust maximize

tp(φbaxg −(baxg −s)2)+(1−t)(1 −p)(φbaxg −(baxg −f)2)

+t(1 −p)(φbaxb −(baxb −s)2)+(1−t)p¡φbaxb −(baxb −f)2¢−c(p).

Given that c(p)is suﬃciently convex, an interior choice of precision pthat satisﬁes the

ﬁrst-order condition maximizes the analyst’s objective function. Hence, the analyst’s

choice of pin an equilibrium with an interior choice of pmust satisfy

(baxg −baxb)(t(2s−baxg −baxb )+(1−t)(baxg +baxb −2f)+φ(2t−1)) −c0(p)=0.(7)

An equilibrium precision choice pand action choice function axy must satisfy (5),

(6), and (7) for each x∈{h, l}after substituting the players’ equilibrium choices for

their conjectured choices. Substituting in pfor ˆpin (5) and (6) and then taking those

actions and substituting them in for baxg and baxb in (7) yields the following condition

that any equilibrium choice for p,namelyp∗

no,mustsatisfy

∆2(p∗

no)/(2p∗

no −1) −c0(p∗

no)+∆(p∗

no)φ(2t−1) = 0.(8)

Proposition 7 When the analyst’s choice of precision is unobservable and the ana-

lyst’s information yis public, there always exists an equilibrium precision choice, p∗

no,

in which the analyst gathers no information, p∗

no =1/2. In addition, if the public

signal is favorable, ˜x=h, there always exists an equilibrium precision choice, p∗

no,

such that p∗

no ∈(1/2,1). Finally, if the public signal is unfavorable, ˜x=l,theremay

exist one or more equilibrium precision choices such that p∗

no ∈(1/2,1).

The ﬁrst point worth noting in Proposition 7 is that there always exists an equilib-

rium in which the analyst does not provide any information. This equilibrium, which

is analogous to the babbling equilibrium that always exists in a standard cheap-talk

game, arises because: (1) the analyst has no incentive to gather information if the

decision-maker does not respond to the resulting signal, and (2) the decision-maker

has no reason to respond to a signal that is believed to be uninformative. Thus, in

contrast to cheap-talk games without endogenous information collection that always

feature a babbling equilibrium in which the analyst misrepresents his private infor-

mation, in this setting in which information collection is endogenous, we ﬁnd that

there is always an equilibrium in which the analyst does not provide the decision-

maker with any information even though the analyst’s signal is public information

and hence cannot be misrepresented. The second point worth noting is that there

always exists one, and perhaps more than one, equilibrium in which the analyst does

gather information for at least one of the two realizations of the public signal. It is

these interior equilibrium choices for pthat are the focus of our remaining analysis.

On comparing the equilibrium condition for p∗

no given in (8) with that for p∗given

in (4), we observe that any interior precision of the analyst’s information depends

on the public information, which determines the value for t.Considerﬁrst the case

when the public information is favorable so ˜x=hand t=q.Inthiscasethere

exists only a signal interior equilibrium choice p∗

no. Furthermore, the observation that

∆(p∗

no)φ(2t−1) >0implies that this choice always exceeds the choice that would

be made if pwere observable, p∗

no >p

∗. The intuition underlying why the precision

choice exceeds the precision choice in the case where pis observable is as follows.

When the favorable public signal is observed, the analyst believes his signal is more

likely to be a good one if he selects a higher level of precision. Because the analyst

prefers a higher action from the decision-maker, it follows that the analyst has an

incentive to choose a higher precision level than he otherwise would choose in order

to increase the probability of getting a higher level of action from the decision-maker.

The cost of precision, however, still provides a disincentive to choosing the maximum

precision level and an interior choice of precision is sustained as an equilibrium.

Consider the case when the public information is unfavorable so ˜x=land t=1−q.

In this case, any equilibrium choice for the precision pis exceed by the choice made

when the the precision choice is observable because ∆(p∗

no)φ(2t−1) <0.Inthiscase

when the unfavorable public signal is observed, the analyst believes his signal is more

likely to be good when the precision level he selects is lower. Given that he prefers

a higher action from the decision-maker, it follows that the analyst has an incentive

to lower the precision level than he otherwise would choose in order to increase the

probability of inducing the higher action. An interior equilibrium can still exist in

face of the incentive to choose a lower precision level, however. For such an interior

equilibrium to exist, the decision maker’s response to the good signal must result in

an action that is too high from the perspective of the analyst who has chosen p=1/2.

Consequently, the analyst chooses a level of precision p∗

no >1/2.10

10These predictions contrast with Penno (1996) who considers a setting where a ﬁrm manager

With an understanding of the game when yis public information established,

we next consider how credibility issues aﬀect equilibrium outcomes by assuming the

analyst privately observes y.Considerﬁrst the case when the favorable public signal is

realized, ˜x=h. In this case there exists one interior value of precision that can be an

equilibrium outcome in the game where credibility is not an issue. When credibility is

also an issue, this value of precision, p∗

no,isstillsustainedasanequilibriumoutcome

ifandonlyifitisweaklygreaterthan¯p. Otherwise, the only equilibrium is one in

which the analyst gathers no information, p=1/2. Next consider the case when the

unfavorable signal is realized, ˜x=l. If there exists an interior equilibrium in this

case, it must again be true that p∗

no exceeds ¯p. Note, however, that the likelihood

that this condition is satisﬁed when ˜x=lis lower because p∗

no must be lower in the

case when ˜x=lthan in the case when ˜x=h. Hence, the analyst is more likely to

not collect any information when the public information is unfavorable.

The observation that the analyst’s precision choice varies with ﬁrm performance

provides an explanation of empirical evidence regarding analyst coverage that Mc-

Nichols and O’Brien (1997) document. They ﬁnd that analysts are more likely to

discontinue coverage on a ﬁrm that is performing poorly. The story they oﬀer as an

explanation for this ﬁnding is that analysts want to avoid jeopardizing their prospects

of winning investment banking business by avoiding issuing a sell recommendation.

Our model provides another explanation for the correlation they observe in the data:

when news is unfavorable, analysts are less likely to be able to credibly communicate

their information and, as a consequence, they do not gather any information–they

discontinue coverage.

7Conclusion

The Sarbanes-Oxley Act of 2002 and the settlement between the large brokerage

ﬁrms and the State of New York in 2002 have led to shrinking of research depart-

ments at investment ﬁrms. The exodus of analysts has left many ﬁrms and, indeed,

observes a public signal about the ﬁrm and then privately chooses the precision of a report that the

ﬁrm will subsequently issue. He ﬁnds that the precision of the report that the manager chooses is

decreasing in the favorableness of the public signal because it lowers the weight investors will place

on the subsequent report, which is likely to be less favorable than the previously observed public

signal. In our model, the public signal and the analyst’s private signal are positively correlated.

Therefore, the analyst chooses to gather more precise information following a favorable public signal

because he is more likely to observe a favorable signal.

entire industry sectors without analyst coverage, raising the ironic possibility that the

new regulations might have made investors that rely on these information intermedi-

aries worse oﬀ(see Schack 2003). Furthermore, recent regulatory changes, including

Reg FD released in 2000, have greatly increased the amount of information available

directly to investors. Against this background, this paper examines analyst informa-

tion gathering and reporting activities in a setting in which the analyst chooses the

precision of information to collect in response to changes in the precision of public

information about a ﬁrm. A key feature of the model that distinguishes it from the

extant reporting literature is that the analyst is not restricted to truthfully report.

Rather, recognizing that analyst credibility is an important feature of the analyst

environment, we assume that the analyst can report in a self-serving fashion.

Using endogenous information collection coupled with reporting credibility as pri-

mary ingredients, this model oﬀers the following insights. First, we consider a set-

ting where the analyst’s precision choice is publicly observed and examine how the

analyst’s information gathering activities vary with the precision of the public in-

formation. When the analyst’s reporting credibility is not an issue, increases in the

precision of the public information cause the analysts to reduce the precision of in-

formation they privately collect and communicate. Nevertheless, because the public

information substitutes for the private information, investors are better oﬀ.Onthe

other hand, when an analyst reporting credibility becomes salient, an increase in the

precision of public information causes the analyst to collect more precise information.

In this case, the public information has a complementary eﬀect on the analyst infor-

mation gathering activities and an investor is again made better oﬀ. However, if the

precision of the public information continues to increase, then a threshold is reached

where an analyst can no longer economically gather suﬃcient information necessary

to credibly communicate with investors. As a consequence, the analyst drops coverage

of the ﬁrm or leaves the market. The analyst’s decision to drop coverage makes the

investors worse oﬀ–which aligns with the concern that the recent regulations might

make investors worse oﬀ.Moreover,weﬁnd, in some circumstances, that investors

would be better oﬀif the public information was never introduced than to have the

public information that drives analysts from the market.

While an analyst stock report might often evidence the precision of the analyst’s

information, at times investors might be uncertain about the precision of the analyst

information. We ﬁnd that the analyst, after observing favorable public information,

gathers more precise information when the precision choice is not publicly observable

than when the analyst’s precision choice is publicly observable, and conversely, the

analyst, after observing unfavorable public information, chooses less precise informa-

tion or is more likely to discontinue coverage when the precision choice is not publicly

observable relative to when the analyst’s precision choice is common knowledge.

Because of the import of the recent changes in the structure of the analyst envi-

ronment, the paper has focused on the information gathering and reporting activities

of analysts. The model, however, is quire general. The insights might be applied to

the voluntary information gathering activities of a ﬁrm manager in the presence of

changes in the mandatory reporting environment, particularly when the manager’s

and investors’ interests are imperfectly aligned and the manager’s voluntary disclosure

is not veriﬁable–such as in the case of management earnings forecasts. The insights

also might be applied to the information gathering and communicating behavior of a

seller of an experience good when the potential buyer has access to another sources of

unbiased information–such as Consumer Reports–that reveals the properties of the

seller’s product. Alternatively, the insights might be applied to the interaction be-

tween a venture capitalist and a ﬁrm that has private information about an innovative

technology for which it is seeking venture ﬁnancing.

8 Appendix

This appendix contains the proofs of the lemmas, propositions, and corollaries.

Proof establishing power cost function is well deﬁned:

Consider the power cost function

c(p)=µp−1/2

1−p¶n

where n>2.The ﬁrst and second derivatives are

c0(p)= n

2(p−1/2)(1 −p)c(p)>0

and

c00(p)= n(n+4p−3)

(2(p−1/2)(1 −p))2c(p)>0if n>1.

The second derivative divided by the ﬁrst derivative is

c00(p)

c0(p)=n+4p−3

2(p−1/2)(1 −p).

Observe that

(1 −3p(1 −p))

(p(1 −p)(p−1/2)) <n+4p−3

2(p−1/2)(1 −p)if and only if 2p2−3p+2

p<n

Since the expression (2p2−3p+2)/p is strictly decreasingly in p, it follows that the

inequality is always satisﬁed if n>2.

ProofofLemma1:

At this stage the analyst’s cost of gathering information is sunk and p,whichis

commonly observed, is ﬁxed. If the analyst communicates his private information

ywhen the other information xis realized, then the decision-maker’s action after

receiving the analyst’s report is a=E[˜α|x, y]. Given the decision-maker’s action,

the analyst reports observing gif and only if

E£φE[˜α|x, g]−(˜α−E[˜α|x, g])2|g, x¤≥E£φE[˜α|x, b]−(˜α−E[˜α|x, b])2|g, x¤.(9)

This truth-telling condition is trivially satisﬁed because the analyst never wants to

dissemble and induce a lower action than the one the decision-maker would take given

the analyst’s information. The analyst reveals observing bif and only if

E£φE[˜α|x, b]−(˜α−E[˜α|x, b])2|b, x¤≥E£φE[˜α|x, g]−(˜α−E[˜α|x, g])2|b, x¤.

(10)

This condition can be shown to be satisﬁed if and only if expression

E[˜α|x, g]−E[˜α|x, b]−φ≥0(11)

is satisﬁed.

It follows from expression (11) that a necessary and suﬃcient condition for the

analyst to reveal ywhen ˜x=lis

E[˜α|l, g]−E[˜α|l, b]−φ

=(2p−1) q(1 −q)(s−f)

(p(1 −q)+(1−p)q) ((1 −p)(1−q)+pq)−φ≥0,(12)

and for the analyst to reveal ywhen ˜x=his

E[˜α|h, g]−E[˜α|h, b]−φ

=(2p−1) q(1 −q)(s−f)

(p(1 −q)+(1−p)q) ((1 −p)(1−q)+pq)−φ≥0.(13)

The incentive compatibility expressions (12) and (13) are identical; hence, without

loss of generality consider (12). When q=1/2, then (12) can be expressed as

(2p−1) (s−f)−φ≥0.Solving for pyields p≥1/2+φ/ (2 (s−f)). On the other

hand, when q∈(1/2,1),Solvingforpin (12) yields two roots:

p1=1

2−2q(1 −q)(s−f)+q4q2(1 −q)2(s−f)2+φ2(2q−1)2

2φ(2q−1)2<1

and

p2=1

2+q4q2(1 −q)2(s−f)2+φ2(2q−1)2−2q(1 −q)(s−f)

2φ(2q−1)2>1

Hence, the truth-telling constraint requires

p≥¯p≡1

2+q4q2(1 −q)2(s−f)2+φ2(2q−1)2−2q(1 −q)(s−f)

2φ(2q−1)2.(14)

ProofofLemma2:

Given the ﬁrst-order condition, the optimal choice of p∗is such that

∂Ui(.)/∂p =(2p−1) q2(1 −q)2(s−f)2

((1 −p)q+(1−q)p)2(qp +(1−q)(1−p))2−c0(p)

=∆2(p∗)

(2p−1) −c0(p∗)=0.

Since Uiis a twice diﬀerentiable function, evaluating ∂2Ui/∂p2yields

∂(∆2(p)/(2p−1) −c0(p))

∂p =2∆(p)∆0(p)

(2p−1) −2∆2(p)

(2p−1)2−c00 (p).

Evaluating the expression ∂2Ui/∂p2at p∗where p∗is such that c0(p∗)=∆2(p∗)/(2p−1)

yields

2c0(p∗)∆0(p)

∆(p)−2c0(p∗)

(2p−1) −c00 (p).

For a unique maximum it must be the case that

c00 (p)

c0(p∗)>µ2∆0(p)

∆(p)−2

(2p−1)¶.

Substituting in for ∆(p)in the right hand side of the inequality gives

µ2∆0(p)

∆(p)−2

(2p−1)¶=2

(2p−1) µ1

p(1 −p)(2q−1)2+q(1 −q)−3¶.

Since the expression is increasing in q,thefollowingisasuﬃcient condition for the

objective function to be strictly quasiconcave

c00 (p)

c0(p∗)>1−3p(1 −p)

p(1 −p)(p−1/2),

which the cost function c(p)is assumed to satisfy.

ProofofProposition3:

For the analyst to credibly communicate his private information yin the reporting

game, it follows from (13) that pmust be such that

q2(1 −q)2(2p−1) (s−f)2

((1 −p)q+(1−q)p)2(qp +(1−q)(1−p))2

−φq (1 −q)(s−f)

((1 −p)q+(1−q)p)(qp +(1−q)(1−p))

≥0.

Further, it follow from (4) that p∗is such that

q2(1 −q)2(2p∗−1) (s−f)2

((1 −p∗)q+(1−q)p∗)2(qp∗+(1−q)(1−p∗))2−c0(p∗)=0.

It follows that p∗≥¯pif and only if

φq (1 −q)(s−f)

((1 −p∗)q+(1−q)p∗)(qp∗+(1−q)(1−p∗)) ≤c0(p∗).

When p∗∈(1/2,¯p), the analyst will only gather information if he can credibly

communicate it in the reporting game. Thus, to determine the precision of informa-

tion the analyst will choose to gather, we compare the analyst’s expected utility from

gathering the minimum precision of information that will allow him to credibly com-

municate in the reporting game, i.e., p=¯p,denotedUi(¯p), with the expected payoﬀ

from not gathering any private information, i.e., p=1/2,denotedUi(1/2).When

p∗∈(1/2,¯p), the analyst prefers ¯pif and only if

Ui(1/2) −Ui(¯p)<0,

or equivalently,

c(¯p)<q2(2 ¯p−1)2(1 −q)2(s−f)2

(¯p(1 −q)+(1−¯p)q)((1−¯p)(1−q)+ ¯pq).(15)

Hence, if p∗∈(1/2,¯p)and if (15) is satisﬁed, then the analyst gathers more

information than he would if his incentives were not misaligned with those of the

decision-maker–i.e., the analyst over-invests in the quality of information he gathers.

Conversely, if p∗∈(1/2,¯p)and if (15) is not satisﬁed, then the analyst gathers

less information than he would if his incentives were not misaligned with those of

the decision-maker–i.e., the analyst under-invests in the quality of information he

gathers.

Proof of Corollary 4:

First consider ∂¯p/∂q.Whenq∈(1/2,1) and ¯pgiven in (14), observe that

∂¯p

∂q =(s−f)q4q2(1 −q)2(s−f)2+φ2(2q−1)2−2q(s−f)2(1 −q)−φ2(2q−1)2

q4q2(1 −q)2(s−f)2+φ2(2q−1)2φ(2q−1)3

∝(s−f)q4q2(1 −q)2(s−f)2+φ2(2q−1)2−2q(s−f)2(1 −q)−φ2(2q−1)2

>0.

To establish the last inequality note that

(s−f)q4q2(1 −q)2(s−f)2+φ2(2q−1)2−2q(s−f)2(1 −q)+φ2(2q−1)2>0,

or equivalently,

(s−f)2¡4q2(1 −q)2(s−f)2+φ2(2q−1)2¢−¡2q(s−f)2(1 −q)+φ2(2q−1)2¢2

=φ2(2q−1)4¡(s−f)2−φ2¢

>0.

To establish that φ2(2q−1)4((s−f)2−φ2)>0, observe that

(2p−1) q(1 −q)

(p(1 −q)+(1−p)q) ((1 −p)(1−q)+pq)<1

for all p. Therefore, for the truth-telling constraint to be satisﬁed,itmustbethecase

that φ/ (s−f)<1; otherwise the truth-telling condition can never be satisﬁed.

Second ∂p∗/∂q. It follows from Lemma 2 that p∗is such that

∂Ui/∂p|p∗=q2(1 −q)2(2p∗−1) (s−f)2

((1 −p∗)q+(1−q)p∗)2(qp∗+(1−q)(1−p∗))2−c0(p∗)=0.

Therefore, the implicit function theorem yields

∂p∗

∂q =2q(1 −q)(2p−1) (s−f)2p(1 −p)(2q−1)

((1 −p)q+(1−q)p)3(qp +(1−q)(1−p))3/∂(∂Ui(.)/∂p|p∗)

∂p∗.

Since Ui(p)is a strictly quasi-concave and twice diﬀerentiable function, it follows that

the denominator is strictly negative. Hence,

∂p∗

∂q ∝(−2q(1−q)(2p−1)(s−f)2p(1−p)(2q−1)

((1−p)q+(1−q)p)3(qp+(1−q)(1−p))3<0when q∈(1/2,1)

0when q=1/2.

Proof of Corollary 5:

The arguments showing ∂¯p/∂φ > 0,∂¯p/∂ (s−f)<0,∂¯p/∂φ =0are straightfor-

ward. Consider ∂p∗/∂ (s−f). Applying the implicit function theorem to Lemma 2

yields

∂p∗

∂(s−f)=−2q2(1 −q)2(2p−1) (s−f)

((1 −p)q+(1−q)p)2(qp +(1−q)(1−p))2/∂(∂Ui(.)/∂p|p∗)

∂p∗.

Since Uiis a strictly quasi-concave and twice diﬀerentiable function, it follows that

the denominator is strictly negative. Hence,

∂p∗

∂(s−f)∝2q2(1 −q)2(2p−1) (s−f)

((1 −p)q+(1−q)p)2(qp +(1−q)(1−p))2>0.

Proof of Corollary 6:

First, we establish that ∂(−Ey[var [˜α|x, y;p∗]]) /∂q > 0. Observe that

∂(−Ey[var [˜α|x, y;p∗]])

∂q =∂(−Ey[var [˜α|x, y;p∗]])

∂q +∂(−Ey[var [˜α|x, y;p∗]])

∂p∗

∂q

∝(p∗)2(1 −p∗)2(2q−1) + q2(1 −q)2(2p−1) ∂p∗

∂q .(16)

Consider ∂p∗/∂q. Applying the implicit function theorem to (4) yields

∂p∗

∂q =−

∂(∂Ui/∂p|p∗)

∂q

∂(∂Ui/∂p|p∗)

∂p∗

=−

−2q(1−q)(2p∗−1)p∗(1−p∗)(2q−1)(s−f)2

((1−p∗)q+(1−q)p)3(qp∗+(1−q)(1−p∗))3

2q2(1−q)2(s−f)2(3p∗(2q−1)2(p−1)+1−3q+3q2)

((1−p∗)q+(1−q)p∗)3(qp∗+(1−q)(1−p∗))3−c00 (p∗)

.(17)

Observe that

∂(∂Ui/∂p|p∗)

∂p∗=2q2(q−1)2(s−f)2¡3p∗(2q−1)2(p∗−1) + 1 −3q+3q2¢

((1 −p∗)q+(1−q)p∗)3(qp∗+(1−q)(1−p∗))3−c00 (p∗)

because Uiis a strictly quasi-concave and twice diﬀerentiable function.

Substituting (17) into (16), factoring, and using the fact that ∂(∂Ui/∂p|p∗)/∂p∗<

0yields

∂(−Ey[var [˜α|x, y;p∗]])

∂q

∝p∗(1 −p∗)c00 (p∗)−2q2(1 −q)2(1 −3p∗(1 −p∗)) (s−f)2

((1 −p∗)q+(1−q)p∗)2(qp∗+(1−q)(1−p∗))2.

On substituting c0(p∗)=∆2(p∗)/(2p∗−1), given in (4), into the assumption that

c00(p)/c0(p)>(1 −3p(1 −p)) /(p(1 −p)(p−1/2)), yields

c00(p∗)>2(s−f)2(1 −q)2q2¡1−3p∗+3(p∗)2¢

(1 −p∗)p∗((1 −p∗)(1−q)+p∗q)2(p∗(1 −q)+(1−p∗)q)2.(18)

Using the relation in (18), it follows that

∂(−Ey[var [˜α|x, y;p∗]])

∂q

∝p∗(1 −p∗)c00 (p∗)−2q2(1 −q)2(1 −3p∗(1 −p∗)) (s−f)2

((1 −p∗)q+(1−q)p∗)2(qp∗+(1−q)(1−p∗))2

∗(1 −p∗)Ã2(s−f)2(1 −q)2q2¡1−3p∗+3(p∗)2¢

(1 −p∗)p∗((1 −p∗)(1−q)+p∗q)2(p∗(1 −q)+(1−p∗)q)2!

−2q2(1 −q)2(1 −3p∗(1 −p∗)) (s−f)2

((1 −p∗)q+(1−q)p∗)2(qp∗+(1−q)(1−p∗))2

=0.

Second, we show the decision-maker’s quality of information falls discontinuously

at ¯q. Observe that when c(¯p)=∆(¯p)q(1 −q)(2¯p−1) (s−f)and q=¯q,then

Ui(1/2) = Ui(¯p),orequivalently,

φE[˜α|x]−q(1 −q)(s−f)2

=φEy[E[˜α|x, y]] −¯p(1 −¯p)q(1 −q)(s−f)2

(¯p(1 −q)+(1−¯p)q)((1−¯p)(1−q)+¯pq)−c(¯p).(19)

The law of iterated expectations, E[˜α|x]=Ey[E[˜α|x, y]] implies (19) may be ex-

pressed as

−Var[˜α|x]≡−q(1 −q)(s−f)2

=−¯p(1 −¯p)q(1 −q)(s−f)2

(¯p(1 −q)+(1−¯p)q) ((1 −¯p)(1−q)+ ¯pq)−c(¯p)

<−¯p(1 −¯p)q(1 −q)(s−f)2

(¯p(1 −q)+(1−¯p)q) ((1 −¯p)(1−q)+ ¯pq)≡−Ey[var [˜α|x, y;¯p]] .

Hence, we observe there exists a q=q+ε>q

∗for ε>0such that

−Var[˜α|x]<−Ey[var [˜α|x, y;¯p]] .

ProofofProposition7:

Because ∆(p=1/2) = 0,it follows from equation (8) that p=1/2is an equi-

librium level of precision for t=qor t=1−q. Consider the case in which t=q.

Rewrite equation (??)asfollows

(1/2)∆(p)2−c0(p)(p−1/2) + ∆(p)φ(2t−1)(p−1/2) = 0.

The ﬁrst derivative with respect to pis

2∆0(p)

∆(p)¡(1/2)∆(p)2+∆(p)φ(2t−1)(p−1/2)¢

−1

(p−1/2) (c0(p)(p−1/2) −∆(p)φ(2t−1)(p−1/2))

−c00(p)(p−1/2) −

∆0(p)

∆(p)∆(p)φ(2t−1)(p−1/2).

Iftheequationissatisﬁed at p, this expression can be rewritten as

2∆0(p)

∆(p)c0(p)(p−1/2) −c00(p)(p−1/2) −(1/2)∆(p)2

(p−1/2)

−

∆0(p)

∆(p)∆(p)φ(2t−1)(p−1/2),

where ∆0(p)

∆(p)=1

2(p−1/2)

1−2p(1 −p)(2t−1)2−2t(1 −t)

p(1 −p)(2t−1)2+t(1 −t).

Hence, the above expression can be written as

1−2p(1 −p)(2t−1)2−2t(1 −t)

p(1 −p)(2t−1)2+t(1 −t)c0(p)−c00(p)(p−1/2) −(1/2)∆(p)2

(p−1/2)

−(1/2)1−2p(1 −p)(2t−1)2−2t(1 −t)

p(1 −p)(2t−1)2+t(1 −t)∆(p)φ(2t−1).

Exploiting the fact that (8) holds in equilibrium allows this expression to be rewritten

µ1

p(1 −p)(2t−1)2+t(1 −t)−3¶c0(p)−c00(p)(p−1/2)

−µ1

2p(1 −p)(2t−1)2+2t(1 −t)−2¶∆(p)φ(2t−1).

Noting that p(1 −p)(2t−1)2+t(1 −t)is decreasing in tand that 2t−1>0because

t=q>1/2implies that the above expression is greater than

µ1−3p(1 −p)

p(1 −p)¶c0(p)−c00(p)(p−1/2),

which is proportional to

(1 −3p(1 −p))c0(p)−p(1 −p)(p−1/2)c00(p).

Hence, there exists only an single equilibrium in which p∈(1/2,1) if

(1 −3p(1 −p)) /(p(1 −p)(p−1/2)) ≤c00(p)/c0(p)

for all p, which is true by assumption.

Finally, consider the case in which t=1−q. In this case, there may or may not

exist an equilibrium in which p∈(1/2,1) and, sometimes there may exist more than

one equilibrium in which p∈(1/2,1). The proof follows from an example in which

there is no equilibrium when p∈(1/2,1),one equilibrium when p∈(1/2,1),and

two equilibria when p∈(1/2,1).Fortheexamples,letc(p)=((p−1/2) /(1 −p))3

and q=.85.Ifφ=2and s−f=2, then there does not exist a p∈(1/2,1) that

satisﬁes the equilibrium condition. If φ=1and s−f=2,thenp=.5227 is the only

p∈(1/2,1) that satisﬁes the equilibrium condition. If φ=110,s−f= 150,then

p=.9072 and p=.5584 both satisfy the equilibrium condition.

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Figure 1: Time line of events

The unknown state α assumes the

values s or f with equal probability.

In stage one, the analyst and

decision-maker observe the public

information x,whichiseither

or

,withprobability

Prh|s

Prl|f









. 

Information gathering stage

In stage two, the analyst chooses the

recision p of his private information

,whichiseither

or

,with

probability

Prg|sPrb|fp

The cost function c(p) reflects the

analyst’s cost of gathering

information with precision p.

Reporting stage

In stage three, the analyst observes

his private information y and sends a

report r, which need not be truthful,

to the decision-maker. The decision-

maker then chooses an action a. The

arameter φ denotes extent to which

the players’ interests are misaligned.

In stage four, the state

of nature α is realized,

and the analyst’s payoff

Ui and the decision-

maker’s payoff Ud are

determined.

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We investigate the information-dissemination role of the business press by examining the coverage of analyst recommendation revisions. Consistent with the press providing wider dissemination of analyst reports, we find evidence that coverage of analyst recommendation revisions significantly increases the initial market reaction to these revisions and decreases the subsequent price drift. Furthermore, we find that news flash coverage, rather than in-depth coverage, of a recommendation revision drives both the initial market reaction results and drift results. Finally, we show that broader press coverage influences the activities of large-trade institutional investors but not high-frequency traders. Overall, our findings suggest a complementary role between analysts and the business press: increased dissemination of recommendation revisions, rather than information creation on the part of the business press, serves to better inform the market about analyst recommendation revision decisions.