Informational Feedback Effect, Adverse Selection, and the Optimal Disclosure Policy

Trading in a secondary stock market not only redistributes wealth among investors but also generates information that guides subsequent investment. We provide a positive theory of disclosure that reflects both functions of a secondary market. By making private information public, disclosure reduces private information acquisition and levels the playing field. However, a leveled playing field has two opposite effects on firm value. On one hand, it ameliorates adverse selection among investors and improves the liquidity of firm shares. On the other hand, it could also impede investment efficiency because less information is produced by the market and used by decision makers. This trade-off determines the optimal disclosure policy. Our theory generates new testable predictions and reconciles disclosure with other parts of securities regulation that encourage private information production.


Introduction
Disclosure has been an important part of corporate policy and the foundation of securities regulation in the United States since its inception in 1930's. One major theoretical support for disclosure to a secondary market is that it levels the playing …eld. By making …rms' otherwise private information public, disclosure discourages traders from private information acquisition. The reduction in private information acquisition attracts liquidity to the secondary market and eventually results in higher …rm value in the primary market. At the heart of this theory is that the private information that guides traders' trading decisions is the root cause of adverse selection and illiquidity in the secondary market.
However, the same private information also guides real decisions when transmitted to relevant decision makers. Through the secondary market trading, traders' private information is impounded into stock price and passed on to the …rm's stakeholders. Capital providers, employees, major customers and suppliers, and the …rm manager may look into stock price when making relevant decisions that a¤ect the …rm value. In other words, the private information produced by traders for their own trading also improves the informational e¢ ciency of stock price, which in turn feeds back to real decisions and resource allocation. We term the e¤ect of private information on real decisions as the informational feedback e¤ect.
In this paper, we study a model of disclosure with the informational feedback e¤ect.
In the model, a …rm sets a disclosure policy at the time of issuing shares in the primary market. The shares are then traded between investors who have liquidity needs and a speculator who could collect information. The …rm's disclosure partially preempts the speculator'information advantage and makes the private information acquisition less pro…table. As a result, the speculator acquires less information, which has two opposite e¤ects on the …rm value. On one hand, the reduction in private information acquisition results in a smaller informational gap between liquidity investors and the speculator. With a more leveled playing …eld, the liquidity investors lose less to the informed speculator and thus are willing to pay more for the shares in the primary market. Thus, disclosure raises …rm value by enhancing liquidity. On the other hand, when the speculator acquires less information, the stock price may become less informative. When the …rm looks to stock price for guidance, the more it has disclosed, the less it gleans news from stock price. As a result, the investment decisions that rely on the information in stock price become less e¢ cient. Thus, disclosure lowers …rm value by weakening the informational feedback from stock price. Hence, the optimal disclosure policy trades o¤ these two e¤ects on …rm value. This trade-o¤ can also be viewed from an incentive provision perspective. When the speculator has a competitive advantage in generating certain information valuable to the …rm, incentives must be provided to the speculator to generate such information. Tolerating more adverse selection in the secondary market enables the speculator to pro…t more from its private information acquisition and thus provides her with stronger incentives to produce the private information.
The explicit consideration of the informational feedback e¤ect enriches the disclosure literature. Our comparative statics results suggest that the …rm value is higher in an environment with a lower cost of private information acquisition if the informational feedback e¤ect is su¢ ciently strong. This is consistent with the institutional feature of the securities market in the United States that encourages private information production and promotes disclosure at the same time. In contrast, if disclosure policy focused mainly on leveling the playing …eld, facilitating private information production and promoting disclosure would be self-contradictory.
Moreover, disclosure is often advocated to both improve liquidity and enhance price discovery. We show that the forces underlying liquidity enhancement and price discovery are actually opposite when private information production is endogenous. Liquidity enhancement results from less private information acquisition while price discovery could be improved by private information production.
Our model also generates new testable prediction on the relation between …rm growth and equilibrium disclosure. In particular, the model predicts that growth …rms are endogenously more opaque than value …rms. Learning from stock price is more important for growth …rms and as a result growth …rms disclose less to attract more private information production.
The critical assumption of our model is that the stock market could produce information that is new to the manager of the …rm and that the incremental information production by the market could be signi…cant enough to in ‡uence the …rm's disclosure policy. To some readers, this assumption is an immediate implication of the e¢ cient market hypothesis that stock price is the most informative source of information. Nonetheless, we provide further motivation for this assumption.
Theoretically, the stock market has competitive advantage in producing some types of information, an idea dated back to Hayek (1945). First, while the manager has a great deal of information about his …rm, the e¢ ciency of the …rm's investment decisions depends also on information about actions of other …rms and factors in the economy-or industry-level, which is dispersed among …rm outsiders and could be aggregated through the trading process. Second, the corporate bureaucracy could be ine¢ cient in collecting some information that exists within the …rm's scope, such as information that is di¢ cult to be standardized, hard to interpret, or incentive incompatible with the information possessors (e.g., Rajan and Zingales (2003)). The pro…t-driven trading in an anonymous stock market could have competitive advantage in eliciting such information. Finally, given the disperse nature of information, the stock market provides a venue for whoever good at information production to supply her talents to the …rm. The traders' pro…t-seeking trading motive saves the …rm extra search cost or incentive cost typically associated with other information generation mechanisms.
Empirically, Rajan and Zingales (2003) survey the evidence that the stock market provides information that a¤ects resource allocation. More direct evidence about the manager using the information in stock price to guide his investment decisions has also started to emerge. Chen, Goldstein, and Jiang (2007) shows that the sensitivity of a …rm's investment decision to its own stock price increases in the level of information asymmetry in the secondary market, suggesting that the private information that creates the adverse selection in the stock market also guides the manager's investment decisions. For the large scale investments, …rms tend to reverse merger and acquisition decisions when confronted by negative market reactions (e.g., Luo (2005)) and those who do not are more likely to become the next targets (e.g., Mitchell and Lehn (1990)). In addition, the development of the prediction markets also lends indirect support to the importance of the informational feedback e¤ect (see Wolfers and Zitzewitz (2004) and section 4.2 of this paper for more discussions).
In addition to the theoretical and empirical support, the informational feedback e¤ect has been contended to be signi…cant enough to a¤ect many other important corporate policies, including insider trading (Fishman and Hagerty (1992), Khanna, Slezak, and Bradley (1994)), public v.s. private …nancing (Subrahmanyam and Titman (1999)), project selection (Dye and Sridhar (2002), Goldstein, Ozdenoren, and Yuan (2010)), securities design and capital structure (Fulghieri and Lukin (2001)), and market-based policy making (Sunder (1989), Bond, Goldstein, and Prescott (2010)). Therefore, the informational feedback e¤ect could be strong enough to a¤ect disclosure policy.
The interactions between public disclosure and private incentive to acquire information have been studied in the literature (e.g., Diamond (1985), Kim and Verrecchia (1994), Demski andFeltham (1994), andMcNichols andTrueman (1994)). However, the informational feedback to the investment decisions subsequent to the trading in our model is new to this literature. Further, our model does not rely on the substitution of disclosure and private information production. We have chosen this as a starting point because the leveled playing …eld is often advocated as one major rationale for disclosure. If disclosure is complimentary to private information production, then more disclosure exacerbates the adverse selection problem and at the same time improves the investment decision. The trade-o¤ are reversed but still exist.
Our paper complements the literature on the real e¤ects of accounting disclosure that emphasizes on the two-way impacts between …rm decisions and capital market pricing (e.g., Kanodia and Lee (1998), Sapra (2002), and Kanodia, Sapra, and Venugopalan (2004), see Kanodia (2007) for a review of the literature). Our paper contributes to this literature by introducing an additional link from the secondary stock market to the …rm's subsequent real decisions: the …rm's real decisions respond to the stock price because it transmits the traders'private information to the decision makers through the faceless, pro…t-driven trading process.
Our paper is also related to a large literature on the monitoring bene…t of the secondary stock market (Diamond and Verrecchia (1982), Holmstrom and Tirole (1993), and Baiman and Verrecchia (1995)). In this literature, the stock price in ‡uences the manager's decisions because the …rm links his compensation to the stock price to exploit the informativeness of the stock price. The monitoring role is absent from our model because we assume away any intra-…rm agency con ‡ict. The major di¤erence between the monitoring role and the informational feedback role of the stock price is that each exploits a di¤erent type of information. The monitoring role relies on the backward-looking information about the past action of the manager, while the informational feedback role takes advantage of the forward-looking information. In fact, information about the future often impedes the monitoring role of the stock price (Paul (1992)).
Section 2 describes the model. Section 3 highlights the basic trade-o¤ of disclosure on liquidity cost and investment e¢ ciency. We then use the trade-o¤ to analyze its implications for securities regulation and the endogenous opaqueness of growth …rms. In Section 4 we discuss two extensions to the baseline model. First, we consider decision makers outside the …rm who glean information from stock prices. Second, we compare the informational feedback e¤ect with other mechanisms of information production such as prediction markets. Section 5 concludes. Detailed proofs are presented in the Appendix.

The Model
We start with a model in which disclosure mitigates adverse selection among traders. We then incorporate the informational feedback role of the secondary market into the model to study its e¤ects on the optimal disclosure policy. Towards this goal, we explicitly model two features of the secondary market. First, some information that is otherwise unknown to the …rm could be produced by the market and transmitted to the …rm through stock price. Second, the …rm uses the information in stock price to guide its real decisions In the baseline model, the …rm learns from stock price and makes investment decisions.
In Section 4.1 we extend the model to show that as long as stock price transmits information to some stakeholders of the …rm whose decisions a¤ect the …rm value, the same trade-o¤ of liquidity provision and investment e¢ ciency for disclosure remains. However, letting the …rm be the decision maker has one advantage of making the model cleaner.
Because the …rm as a decision maker could still utilize the undisclosed information, disclosure a¤ects the information available to the decision maker (the …rm) only through the learning from stock price.
All parties are risk neutral and the risk-free rate of gross return is normalized to be 1.
The timeline of the model consists of four dates, as depicted in Figure 1  At date 1, the …rm owns a stochastic technology that produces cash ‡ow at date 4: The …rm issues equity shares to a continuum of ex ante identical investors (original investors) in the primary market. The total mass of investors is normalized to be 1 and the total number of shares is normalized to be 1 share per capita. In pricing the shares, the original investors at date 1 expect that they will have stochastic liquidity shocks at date 2 that can only be satis…ed by trading in the secondary market. In addition, the …rm sets the disclosure policy at date 1: The disclosure policy commits the …rm to fully disclose its information at date 2 with probability 2 (0; 1) before the secondary market opens.
With probability 1 , nothing is disclosed. thus measures the quality of disclosure.
At date 2; the secondary market for the equity shares opens after the disclosure by the …rm. In addition to the original investors, a speculator who could acquire information at a cost enters the secondary market and the order ‡ow is balanced by a market maker through a Kyle-type setting. The market-maker and the speculator are assumed not to participate in the primary market at date 1. 1 At date 3; the …rm chooses an investment level K based on all information available to the …rm, including the price from the secondary market. At date 4; the cash ‡ow is realized and consumption takes place.
Having completed the timeline, we elaborate on the technology and the information structure. The …rm consists of one asset-in-place (AIP) and one growth opportunity, whose future cash ‡ows are in ‡uenced by a stochastic technology captured by random variable e . Assume e is normally distributed with mean zero and variance 2 , i.e., e N (0; 2 ).
In particular, the terminal cash ‡ow from the AIP is e A = A 0 + e ; where A 0 is the certain component of the cash ‡ow. In contrast, the terminal cash ‡ow from the growth opportunity is where K is the …rm's investment decision made at date 3: Both e A and e G share the same source of uncertainty e . 2 The di¤erence is that the distribution of e G is endogenous to the investment decision K while the distribution of e A is …xed exogenously.
Between date 1 and date 2; the speculator expends resources to acquire a signal e y: e y = e +e " y where e " y is normally distributed with mean zero and variance 2 y , i.e., e " y N (0; 2 y ).
De…ning the quality of signal e y as r 2 2 + 2 y ; the cost of information acquisition is The more resources the speculator spends, the more precise her signal is.
We assume that c > n 2 so that the equilibrium information acquisition is interior, i.e., 2 (0; 1).
The …rm privately learns a signal e z at no cost. e z reveals e perfectly with probability f 2 (0; 1) and is uninformative at all with probability 1 f . Exogenous parameter f measures the quality of the …rm's internally available information. Since the …rm's date-1 choice of disclosure level commits the …rm to disclose its information (z) perfectly with probability ; the actual disclosure at date 2, denoted as e x, has the following property: with probability 1 f where ? denotes the empty set. To avoid discussing various corner solutions, we assume that the …rm incurs a direct cost of disclosure w so that the equilibrium disclosure choice is interior, i.e., 2 (0; 1): Also at date 2, the original investors experience an aggregate liquidity shock, denoted as e n which is assumed to be normally distributed with mean zero and variance 2 n , i.e., e n N (0; 2 n ): 3 Due to the information advantage of the speculator, the original investors who have to trade in the secondary market lose to the speculator on average. Anticipating this trading disadvantage, they demand a higher liquidity discount when pricing the …rm's shares at date 1. This is the channel through which the adverse selection in the secondary market at date 2 is related to the disclosure policy at date 1: The …rm who maximizes the proceeds from the issuance of shares in the primary market has incentives to commit to a disclosure policy at date 1 to mitigate the adverse selection at date 2: The original investors and the speculator trade through a market-maker in a Kyle-type setting. The total order ‡ow thus consists of the information-based order d(x;ỹ) from the speculator and the liquidity-based orderñ from the original investors. The market maker observes the total order ‡ow e n+ e d but cannot distinguish the two components. The market maker then sets a price P to clear the market and break even.
A distinguishing feature of this model with the informational feedback e¤ect is that the cash ‡ow from the growth opportunity at date 4 depends not only directly on~ but also on the investment decision at date 3 which in turn depends on the information about in the price at date 2. As a result, the price of the growth opportunity at date 2 is non-linear in e ; making it not tractable to infer information about e from the price of the growth opportunity. Following the modeling device in Subrahmanyam and Titman (1999) to simplify the analysis, we assume that the AIP is publicly traded but the growth opportunity is not. As discussed on page 1050 of Subrahmanyam and Titman (1999), this assumption has no substantive e¤ect on the main results but allows for closed-form solutions and the explicit characterization of the information content of stock prices. 4 Since the terminal cash ‡ow of the AIP and the growth opportunity are subjected to the same sources of uncertainty (e ); the inference about e made from the price of AIP could market order of e n + e "i where e n represents the market-wide shock and is common to all investors and e "i represents non-systematic, mean-zero iid shocks. The market-wide shock e n is normally distributed with mean zero and variance 2 n : The idiosyncratic shocks across investors sum to zero ( R i2[0;1] e "idi = 0 with probability one). Thus, the total order from investors sums to e n. 4 A more direct but complex solution to this technical issue is use a setting with binary signals and actions (e.g., Goldstein and Guembel (2008), Bond, Goldstein, and Prescott (2010)) in which the price is discrete and the inference could be made even in the presence of the informational feedback e¤ect. be used in the investment decision for the growth opportunity at date 3. 5 As a result, the market maker prices the …rm's AIP at date 2 with his knowledge about the disclosurex and the total order ‡owñ +d; in particular, we have x; e n + d(e x; e y)]: As discussed in Introduction, the informational feedback e¤ect requires that the stock price contain information that is new to the …rm. That is, P is not redundant when the …rm chooses investment K at date 3: This has been operationalized through the information structure summarized by Table 1. In the last row of Table 1, with probability 1 f; the …rm does not learn anything internally about e , but the price P contains information about e that originates ultimately from the speculator's private information acquisition e y.
As a result, stock price is not a redundant source of information to the …rm. In addition, in the …rst row of Table 1, with probability f ; e x completely preempts the speculator's information advantage e y. Thus, from the perspective at date 1 when the disclosure policy is made, the information produced by the speculator is correlated but not a subset of the …rm's information.

Probability
Firm information e z Firm disclosure e x Speculator information e y Price e P f e e e + e " y P (e ) Table 1 Information Structure 5 One interpretation is that the …rm spins o¤ its AIP division to go public and retains control over the growth opportunity privately at date 1. The information in the stock price of the spin-o¤ AIP is useful for the decisions about the growth opportunity given the correlation between the common factors that drive the two businesses.

Preliminary Analysis
In this section, we derive the …rm's objective function when choosing the date-1 disclosure level. At date 2, after the speculator's acquisition of y and the …rm's disclosure x, the speculator submits an order d(x; y) to maximize its expected gross pro…t. If the disclosure reveals perfectly (the …rst row in Table 1), which occurs with probability f , the speculator does not trade and expects zero gross pro…t. Otherwise, we have a standard Kyle model with one informed speculator, one market-maker, and liquidity traders. The following Lemma is obtained by using standard solution techniques for Kyle-model (proof omitted but available upon request).
Lemma 1 If the …rm's disclosure is ine¤ ective at date 2 (the second and third rows in Table 1 Therefore, the speculator's optimal information acquisition is Because of the zero-sum nature of the trading at date 2; the speculator's gross pro…t is equal to the original investors'trading loss. Thus, the date-1 original investors'expected trading loss is Anticipating ( ), the original investors price the AIP at E e [A] ( ) at date 1, making ( ) the liquidity cost to the …rm.
We now turn to the investment decision. At date 3; based on its information set fz; P g; ; P ] and the date-3 expected value of the growth opportunity is K E[~ jz; P ] 1 2g K 2 = g 2 (E[~ jz; P ]) 2 : Our information structure allows us to solve E[~ jz; P ] in closed-form. When the …rm receives the information internally (the …rst and second rows in Table 1), i:e:; z = ; which occurs with probability f; the …rm knows perfectly and ignores P in making the investment decision. When the …rm does not receive any information internally (the last row in Table 1), i:e:; z = ?; the …rm gleans information from P and the posterior belief about~ could be obtained by Bayes rule:~ j(z; P ) N (P (?; y); (1 2 2 ) 2 ). At date 1; the expected value of the growth opportunity is calculated as the expectation taken over all realizations of z and P : 6 6 Explicitly, notice that In summary, at date 1 when the …rm chooses disclosure policy to maximize …rm value, the …rm value could be written as follows: ( ) is the value of AIP, ( ) is the value of the growth opportunity and w 2 2 is the direct cost of disclosure. Accordingly, the optimal disclosure policy is determined by the following …rst order condition: 7

The Basic Trade-o¤
With the preparation above, we examine in detail the …rm's disclosure policy at date 1: Lemma 2 A higher disclosure level by the …rm induces lower information acquisition by the speculator in equilibrium, that is, d ( ) Lemma 2 is straightforward from eqn. 1. The speculator's acquisition of signal y a¤ords her an informational advantage in trading only if the …rm's disclosure x is not informative.
When the …rm's disclosure improves, the costly private information acquisition becomes less pro…table and is pulled back.
This reduction in private information acquisition, resulting from disclosure, has two opposite e¤ects on the …rm value. It levels the playing …eld among traders on one hand but reduces the …rm's investment e¢ ciency on the other. This is the basic trade-o¤ of the disclosure policy at date 1: Proposition 1 By inducing lower private information acquisition, the …rm's disclosure has two countervailing e¤ ects on the …rm value: 1. it reduces the …rm's liquidity cost, that is, d ( ) d < 0; 2. it also reduces the …rm's investment e¢ ciency, that is, d ( ) Proposition 1 is proved by di¤erentiating eqn. 2 and 3 with respect to . Disclosure's …rst e¤ect on the …rm value is positive as more disclosure reduces the liquidity cost. This bene…t of disclosure has been well established in the literature and is often labeled as "leveling the playing …eld". 8 Disclosure reduces not only the chance that the speculator has an informational advantage (i.e., 1 f is lower) but also the magnitude of the informational advantage when it exists (i.e., 2 ( ) 2 2 is lower). As a result, higher disclosure level reduces adverse selection and enhances liquidity in the secondary market, which improves the …rm value at date 1. The speculator's costly information acquisition redistributes wealth from some investors (and eventually from the …rm) to the speculator and generates a negative externality on the …rm, which motivates the preemptive disclosure.
However, the reduction in private information acquisition, which saves the …rm liquidity cost, compromises the …rm's investment decisions, as suggested by Part 2 of Proposition 1. The …rm's investment decisions are more e¢ cient the more the …rm knows about : In the case the …rm does learn from stock price P (the last row in Table 1), the equilibrium informativeness of P , from the …rm's perspective, is measured by the reduction of the …rm's uncertainty about : Thus, price discovery is determined directly by the speculator's information acquisition decision. As disclosure lowers ( ), the stock price becomes less informative to the …rm.
When the …rm looks into stock price for guidance on investment decisions, the more it has disclosed, the more it sees its own information and the less it learns from the stock price.
As a result, higher disclosure level reduces the …rm's price discovery in the secondary market and makes investment decision less e¢ cient.
This e¤ect of disclosure on …rm value, resulting from the informational feedback effect, is new to the disclosure literature. It creates a positive externality of the speculator's private information acquisition to the …rm. Motivated entirely by trading pro…ts, the speculator generates a private signal that is used once for trading at date 2, and then again (with some noise) by the …rm in making the investment decision at date 3. Thus, the informational feedback e¤ect imparts a positive social value to the pro…t-driven speculative information acquisition. Since preemptive disclosure reduces private information acquisition, disclosure has an endogenous cost arising from the foregone investment e¢ciency.
The basic trade-o¤ of the disclosure policy highlights the dual functions of the secondary market. Not only does the secondary market provide liquidity to traders, it also generates information that could improve investment e¢ ciency. Preemptive disclosure could not serve both functions at the same time. A disclosure policy that maximizes …rm value does not narrowly promote a more leveled playing …eld. Put di¤erently, the informational feedback is not provided to the …rm for free. Eventually the …rm pays for the information production service by the speculator in the form of the increased liquidity cost of its shares resulting from reduced disclosure. The more valuable the information provided by the speculator, the more the …rm's disclosure policy is pulled back from fully addressing the liquidity concern.
To see the signi…cance of incorporating the informational feedback e¤ect into the consideration of disclosure policy, we explore two implications of the basic trade-o¤ identi…ed in Proposition 1. First, we use the model to reconcile the institutional feature of the US securities market that encourages …rm disclosure and facilitates private information acquisition at the same time. Second, we use the model to explain why growth …rms could be endogenously opaque.

Private Information Acquisition and Firm Value
Does the …rm bene…t from an increase in parameter c, the speculator's cost of private information acquisition? From the perspective of "leveling-the-playing-…eld" alone, the answer is "Yes" because the adverse selection problem in the secondary market is mitigated by an increase in the private information acquisition. However, when the informational feedback e¤ect is taken into account, the answer changes.
Proposition 2 De…ning V as the date-1 …rm value in equilibrium andĝ Recall that the …rm's investment decision is K (z; P ) = gE[~ jz; P ]: A larger g means that the …rm's growth opportunity is more responsive to information, making the feedback e¤ect more important to the …rm. We label g as the …rm's growth prospect. The …rm value is improved by an increase in c if and only if g is small and thus the informational feedback e¤ect is relatively weak. A higher c induces the speculator to decrease information acquisition, which, by Proposition 1, leads to both a lower liquidity cost and lower investment e¢ ciency. Whether the …rm value increases as a result of a higher c thus depends on the strength of each e¤ect. When the investment opportunity is important and the bene…t of the feedback from stock price is large, the investment e¢ ciency dominates the liquidity cost and the …rm is better o¤ with a lower, rather than a higher, c.
This result is signi…cant for understanding a …rm's disclosure policy in the broad context of securities regulation. Even though the disclosure improves the …rm value by discouraging private information acquisition, the …rm value could increase in an environment that facilitates private information acquisition. This seems paradoxical from the perspective that focuses disclosure narrowly on leveling-the-playing-…eld, but is consistent with the disclosure environment in the United States that promotes disclosure and en-courages private information acquisition at the same time. 9 Alternatively, to the extent that private information production is viewed as a proxy for the health of a stock market and actively pursued as a desirable goal by …rms and regulators alike, the informational feedback e¤ect could be inferred as signi…cant in practice.

Growth and Disclosure Level
The basic trade-o¤ in Proposition 1 points to growth factors that strengthen the informational feedback e¤ect, which in turn creates incentives for …rms to reduce disclosure level in order to preserve the speculator's incentive to acquire information. In our model, growth is represented by Each of the relevant exogenous parameters, g, f , and 2 ; captures one facet of a growth …rm. Their e¤ects on disclosure policy are summarized by the following proposition.
Proposition 3 Ceteris paribus, 1. …rms with higher growth prospect (higher g) disclose less; 2. …rms that are more likely to learn information from the stock price (lower f ) disclose less; and 3. …rms with higher uncertainty (higher 2 ) disclose less if and only if g is su¢ ciently large.
Proposition 3 adds new predictions about the relation between growth and disclosure policy. As growth prospect g increases, information about the pro…tability of the growth 9 The legal literature has established that the tenet of securities regulation in the United States has shifted to the "e¢ ciency enhancement model" since 1970's as part of the triumph of the E¢ cient Market Hypothesis (e.g., Stout (1988), Mahoney (1995)). Under the guidance of this new doctrine institutions and policies have been designed to facilitate the information production in the secondary market. This doctrine has been employed in the public discourse of a wide array of prominent issues, such as insider trading, regulation FD, short sales, program trading, and the regulation of …nancial institutions. opportunity becomes more valuable to a …rm. Thus, the …rm reduces disclosure level to make the information acquisition by the speculator more pro…table, which in turn incentivizes the speculator to acquire more information.
Not only is prospective information more important for growth …rms, but also growth …rms are more likely to have less information generated internally. Thus, growth …rms have a low f: A low f makes the speculator's information more valuable to the …rm, giving the …rm an incentive to lower disclosure level to encourage the speculator's information acquisition. At the same time, a lower f increases liquidity costs by aggravating the adverse selection problem, which provides …rms with incentives to increase disclosure level. As a consequence, disclosure level measured by can be increasing or decreasing in parameter f . However, measured by total disclosure level f , disclosure level is everywhere increasing in f , consistent with the idea that growth …rms are more opaque overall.
Growth …rms face more uncertainty relevant to its future decisions, parameterized by the variance of the uncertainty~ in our model. This parameter a¤ects the value of the information to both the …rm and the speculator. On one hand, as 2 increases, the marginal bene…t of learning by the …rm becomes larger. The …rm reduces disclosure to encourage more information acquisition by the speculator. On the other hand, as 2 increases, the speculator's information acquisition becomes more pro…table because her information gives her a bigger informational advantage. This leads to a higher liquidity cost for the …rm and induces the …rm to improve disclosure level. Since the …rst e¤ect increases in g while the second is independent of g; the …rst e¤ect dominates the second as g is large. Hence, the …rm's disclosure level increases in 2 if and only if g is small. In sum, growth …rms may choose to be more opaque in the hope of learning more information from their own stock prices.

Who Learns?
We have assumed that the …rm is the decision maker who bene…ts from the information in its own stock price. However, the basic idea that preemptive disclosure could reduce …rm value through its suppression of information production incentive is more general.
As long as the information in the stock price in ‡uences decisions, made by the …rm or outsiders, that a¤ect …rm value, the …rm's disclosure policy will balance its e¤ects on liquidity enhancement and decision e¢ ciency.
To illustrate, suppose an outsider takes an action K at date 3 to maximize his own payo¤ e G = e K 1 2g K 2 and the …rm bene…ts from the outsider's decision by an amount H( e G) = h e G where h > 0. The e¤ect of disclosure on liquidity is not a¤ected by this change. So we only look at the e¤ect of disclosure on decision e¢ ciency.
Proposition 4 When an outsider looks to stock price to guide his decisions and the improvement in these decisions indirectly bene…ts the …rm (h > 0), the …rm's disclosure reduces the outsider's decision e¢ ciency (thus the …rm value) if either the …rm's internal information is su¢ ciently limited (f is su¢ ciently small) or the speculative information acquisition is su¢ ciently e¢ cient (c is su¢ ciently small).
To understand Proposition 4, note that action K is improved with the decision maker's better knowledge about e at date 3; just as in the baseline model. The outsider's knowledge about at date 3 is a¤ected by both the …rm's disclosure and the informativeness of stock price. When the disclosure is informative (the …rst row in Table 1), the outsider learns perfectly. When the disclosure is not informative (the second and third rows in Table   1), the outsider's knowledge about comes solely from stock price. The informativeness of the stock price for the outsider is measured by the resolution of uncertainty occasioned by stock price P : The only di¤erence between the knowledge of the …rm and of the outsider about occurs when the …rm has undisclosed information (the second row in Table 1). In this case, the …rm could still use the undisclosed information in making decisions but the outsider can only rely on the stock price. As a result, in addition to its negative e¤ect on decision making as studied in the baseline model, disclosure has an additional, direct e¤ect: it increases the information available to the outside decision maker by directly supplying him with disclosed information. This direct channel changes the e¢ ciency of the decision making from . The net e¤ect of disclosure on the outsider's decision making then depends on the relative importance of the direct and indirect channels.
Proposition 4 shows that when the …rm's internal information is scarce (low f ) or the market information production is more e¢ cient (low c), the information directly provided by increased disclosure is dominated by the reduced learning from stock price and disclosure reduces the e¢ ciency of the outsider's decisions. To the extent that the …rm bene…ts from these decisions, the disclosure policy still trades o¤ its bene…t of saving liquidity cost against the cost of reduced learning from stock price.
Because the direct channel from disclosure to decision e¢ ciency does not alter the basic trade-o¤ for the disclosure policy studied in Proposition 1, we have chosen to let the …rm be the decision maker in the baseline model to make the model cleaner.
Decisions made by outsiders and guided by information in a …rm's stock price could also reduce …rm value, which amounts to h < 0. One example is that competitors and labor unions use information gleaned from the …rm's disclosure and the stock price to the …rm's disadvantage (e.g., the proprietary cost in Verrecchia (1983)). To illustrate we label H( e G) as proprietary cost for the …rm by assuming that h < 0: Corollary 1 When an outsider makes decisions which hurt the …rm (h < 0); the …rm's disclosure reduces, rather than increases, its proprietary cost if either the …rm's internal information is su¢ ciently limited (f is su¢ ciently small) or the speculative information acquisition is su¢ ciently e¢ cient (c is su¢ ciently small).
The intuition is similar to that in Proposition 4. Nonetheless, this extension adds a novel perspective to the literature on the proprietary cost of disclosure. That is, more disclosure could lower proprietary cost, a similar result to Arya and Mittendorf (2005) but with a di¤erent mechanism. Even though disclosure provides information to the competitors, it also reduces the information the competitors could learn from the stock price. The net e¤ect of disclosure on the competitors learning should take into account of both channels.

Who is the Most E¢ cient Information Producer?
We have demonstrated that information production by the secondary market is not free for the …rm in that the …rm eventually pays for the information it learns from the stock price in the form of a higher liquidity cost. We assess the comparative e¢ ciency of this market mechanism of information production. To start we establish a benchmark in which the speculator is absent but the …rm has the same information production technology as the speculator and chooses how much information to produce (before receiving z).
Proposition 5 Compared with the information production in this benchmark case, the information production by the speculator in our baseline model is either too low (when the growth prospect is high) or too high (when the growth prospect is low).
Proposition 5 reveals the suboptimal nature of the information production through the secondary stock market. The e¢ ciency loss originates from the misalignment of the speculator's private incentive with the …rm's. The speculator's pro…t-driven information acquisition has the negative externality on the …rm value through the liquidity cost and the positive externality through the investment decision, but the speculator internalizes neither of them. Since in our model the investment value of information increases with growth prospect but the trading pro…t (or liquidity cost) does not, the speculator's in-centive produces too little information when the net externality is positive and too much when the net externality is negative.
Despite its ine¢ ciency, the advantage of information production through …nancial markets is highlighted in the comparison with its alternatives. One alternative is that the …rm could hire outside consultants or set up internal organizations to produce information. These mechanisms su¤er from the well-known and well-studied agency problems in a contractual relationship. Thus, the market mechanism has competitive advantage for information that is subject to severe agency issues, such as information that is dif-…cult to be quanti…ed, not incentive-compatible for direct revelation by the information owner/producer, and information whose most e¢ cient provider could be not easily iden-ti…ed.
Another alternative is to use prediction markets to produce forward-looking information, a tool that has become increasingly popular (see Wolfers and Zitzewitz (2004) for a survey of prediction markets). Part of the demonstrated success of a prediction market is attributed to its ability to overcome the "comprehensiveness" problem of the stock price (e.g., Bresnahan, Milgrom, and Paul (1992)), a problem abstracted away in our model. 10 However, the number one practical problem for prediction market is that they su¤er lack of market depth and thus incentive for information acquisition (e.g., Wolfers and Zitzewitz (2006)). As illustrated in our model, for markets to produce information, it is indispensable to provide participants with incentive to acquire information. In …nancial market such incentive is provided mainly by trading pro…ts that are a¤ected by market depth and disclosure policy.
1 0 Take as an example that the …rm announces a merger proposal. The market participants'information about the size of synergy of the deal will be re ‡ected in the stock price reaction. The comprehensiveness problem arises from two sources. First, the stock price reaction is also a¤ected by other contemporary factors that are orthogonal to the merger proposal. This issue is absent because in our model the only source of uncertainty is relevant for both pricing and for the investment decision. Second, the stock price also anticipates the probability that the deal could go through, which is partly determined by the market reaction. Thus, a mild reaction could indicate either that the synergy is believed to be moderate or that the market believes that the synergy is so negative that the deal will be abandoned or stopped. A security in prediction markets could be de…ned narrowly over the merger event to mitigate this comprehensiveness issue.
Two lessons from the predictions markets corroborate the importance of our result.
First, the popularity and success of prediction markets attest to the importance of the informational feedback e¤ect. Second, the incentive issue with prediction markets shows that the information production by market relies crucially on private incentives. Thus, leveled playing …eld could hurt …rm value if the informational feedback e¤ect is important for the …rm.

Conclusion
Disclosure has been the foundation of securities regulation in the United State since its inception in 1930's. One major theoretical support for disclosure to a secondary market is that it levels the playing …eld. At the heart of this theory is the notion that private information acquisition is the root cause of adverse selection in the secondary market and disclosure improves …rm value by reducing incentives for private information acquisition.
While widely accepted, this theory of disclosure seems incomplete when disclosure is viewed as an integral part of the broad market infrastructure. More private information production by traders is often viewed as a proxy for the health of a stock market and thus a desirable goal pursued by …rms and regulators alike. The underlying idea is that the private information produced by traders for their trading also guides resource allocation when it is transmitted to relevant decision makers through stock price. As a result, the same private information production that exacerbates adverse selection and illiquidity in the secondary stock market is also the ultimate source of the information market participants look to guide their real decisions. Thus, the disclosure policy that maximizes the …rm value balances the dual e¤ects of disclosure on liquidity enhancement and decision e¢ ciencies.
In other words, the secondary market plays two functions at the same time. On one hand, the secondary market provides liquidity to investors. By providing a venue where investors could take di¤erent positions based on their information and liquidity needs, the secondary stock market provides liquidity to investors and redistributes wealth among investors. On the other hand, through the trading in the secondary market, stock prices aggregate information from every corner of the economy and market participants look to the stock prices for information to improve their decisions. That is, the stock prices both re ‡ect and a¤ ect …rm value.
Private information acquisition has opposite e¤ects on these two functions of the secondary market. It impedes the liquidity provision function but improves the informational feedback function. The leveling-the-playing-…eld theory focuses exclusively on the liquidity provision function of the secondary market. The presence of the informational feedback function creates an endogenous cost for preemptive disclosure. Alternatively, the illiquidity in the secondary market induced by the private information could be viewed as the cost for the secondary market to ful…ll its informational feedback function.
One major bene…t of explicitly considering the informational feedback e¤ect in a theory of disclosure is that it reconciles the joint promotion of disclosure and private information acquisition in securities regulation, which is paradoxical when we focus only on the liquidity provision function of the secondary market. It also explains why growth …rms are more likely to be endogenously opaque.
6 Appendix 6.1 Proof of Proposition 2 For notation, we use subscripts to denote partial derivatives, i:e:; X Y @X @Y and X Y Y @ 2 X @Y 2 ; and write the total derivative as dX dY . We analyze the …rm disclosure choice ( ) at date 1. From eqn. 4, the …rm's decision problem at date 1 is max 2(0;1) The …rst-order condition determines the optimal disclosure policy : Similar to the de…nition of V ; and are de…ned as and being evaluated at = : The second-order condition is V wf = g 2 (1 f ) 4c 2 f 2 2 n 2 4c 2 w: The assumption on w on page 8 ensures that V < 0: Further, the same assumption also ensures that 2 (0; 1) because and V j =1 = g 2 (1 f ) 4c 2 (1 f ) n 2c f n 2c w < 0: De…ne V V ( ): Now we compute comparative statics of V with respect to c. By the envelope theorem, We conclude that d dc V 0 if and only if g ĝ:

Proof of Proposition 3
We now study the determinants of the optimal disclosure policy by the implicit function theorem: di¤erentiating the …rst-order condition (eqn. 8) with respect to relevant parameters.
The impact of growth prospect g on the optimal disclosure policy ; g ; is determined by g + V g = 0: Thus, g < 0 because g = 2 2 (1 f ) < 0 and because V < 0 by the secondorder condition. For the impact of the …rm's own information endowment f on its disclosure quality, we consider the total amount of disclosure by the …rm f ; instead of alone. ( (4c (1 f )g 2 + f g 2 ) > 0

Proof of Proposition 4
When the decision maker of investment K is not the …rm, the only di¤erence in the computation of is that with probability f , not f , the decision maker has perfect information and with probability 1 f , not 1 f , the decision bene…ts from the information in price. So the ex ante value to the outside decision maker, denoted 0 , is 0 = E e z; e P h g 2 (E[ jz; P ]) 2 i = g 2 2 f + (1 f ) ( ( )) 2 2 : The ex ante bene…t to the …rm is