On the Optimality of Public Signals in the Presence of Private Information
[Security regulation relies heavily on the public disclosure of information by firms. Mandated public disclosure has expanded beyond the traditional accounting statements to include information on a firm's segmental performance, competitive environment, R&D expenditures, executive compensation, and pending litigation. Investors, however, also have access to a variety of costly private information. These sources range from analyst forecasts to illegally obtained "inside" information. Many studies have reported the impact of a public signal on traders' welfare absent other private information sources (e.g., Hakansson et al. 1982; Hirshleifer 1971; Marshall 1974; Ng 1975; Ohlson and Buckman 1981), and many others have reported on how private information acquisition will change in response to the public signal (e.g., Gonedes 1980; Gonedes et al. 1976; Hakansson 1977; Lundholm 1991; Verrecchia 1982a). However, little attention has been focused on how welfare will change in response to public information, taking into account both the direct effect of the public signal and its indirect effect due to the change in private information acquisition. In this article, we present three different models designed to elucidate how the disclosure of public information can enhance the welfare of traders in a financial market when some or all traders also have access to costly private information. We begin our investigation by revisiting the work of Diamond (1985). In an economy where traders have the opportunity to acquire private signals about a single asset's payoff, Diamond shows that traders unanimously prefer the release of a public signal sufficiently precise to eliminate all private information acquisition. This is a potentially important result for accounting; positive welfare effects caused by public signals have been difficult to come by (see Verrecchia 1982a). We analyze the underlying cause of Diamond's result and its robustness to changes in the economy. Our first example shows that the result is not robust when the private signals have correlated rather than independent errors. However, our second example shows that Diamond's positive welfare result extends to an economy with multiple assets when the private signals have independent errors, regardless of the degree of correlation between the assets' underlying payoffs. The extension to an economy with multiple correlated assets is one way to assess the welfare properties of "information transfers." Our third example considers an economy where some traders are allowed to acquire private information of varying quality while others are denied access to private information. Some traders clearly have differential access to information about a firm's prospects, possibly because of a unique relationship with the firm (e.g., an employee or supplier), or economies of scale in information acquisition and production (e.g., an analyst). We assess how a public signal can enhance the welfare of traders denied access to the information market, regardless of its effect on the informationally well-endowed traders. We believe that this final application reflects the regulatory concern that brought about the Security and Exchange Acts-that public information should be used to enhance the welfare of uninformed traders. We show, however, that the uninformed traders do not necessarily prefer to use a public signal to eliminate the informed traders' incentives to acquire information; they prefer this solution only when they are in the minority. Paradoxically, uninformed traders prefer to use public signals to enhance their welfare only when they may have insufficient power to do so. This occurs because, when the uninformed traders are in the majority, the loss in risk-sharing opportunities that accompany the public signal outweighs the benefit of informational parity.]