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Discretionary Disclosure of Proprietary Information in a Multi-Segment Firm Anil Arya Ohio State University Hans Frimor University of Aarhus Brian Mittendorf Yale School of Management February 2008 Discretionary Disclosure of Proprietary Information in a Multi-Segment Firm Abstract The seminal "unraveling" result in the disclosure literature posits that discretion inevitably leads to full disclosure, even when such disclosures have competitive consequences. In this paper, we revisit optimal disclosure of proprietary information when firms operate in multiple markets. The analysis demonstrates that the presence of multiple segments reverses the unraveling result in that full disclosure is no longer viable. Instead, the unique equilibrium outcome entails aggregation of segment details. Aggregation arises because any ex post temptation to disaggregate and reveal particularly favorable news in one segment entails revealing unfavorable news in another segment. A desire to balance profits across segments then leads a firm to disclose firmwide information (a temptation which cannot be avoided) but only in the aggregate. This analysis yields implications for (i) industry characteristics that lead firms to aggregate across segments, (ii) value of diversification in multi-segment firms arising from reporting considerations, (iii) synergies among managerial accounting systems across segments, and (iv) welfare consequences of regulations mandating segment disclosures. Keywords: Aggregation; Competition; Disclosure. 1. Introduction Aggregation is a central tenet of accounting practice. The inherent discretion afforded by aggregation means the extent to which a firm chooses to condense information has also been a critical financial reporting consideration. When faced with such discretion, firms may feel pressure to fully disclose key performance indicators, fearing what is conveyed by silence. While such pressures can lead to disclosure, the practice of providing some coarse (aggregate) disclosures has had substantial staying power. This paper considers a model of discretionary disclosure by a multi-segment firm facing competitive threats, and finds that the practice of voluntarily disclosing proprietary information only in the aggregate can arise naturally. To elaborate, we consider a model of a firm and a rival who compete in two distinct segments. While the firm has access to information about its costs in each market, the rival must depend on the firm's public disclosures to glean such information. The key question we consider is what, if any, disclosures does the firm choose to make. If the two firms compete in only one market, the standard "unraveling" of discretionary disclosure obtains (Grossman and Hart 1980; Grossman 1981; Milgrom 1981). That is, despite an ex ante desire to keep information away from the rival, the firm cannot resist the ex post temptation to reveal its competitive position. This temptation arises because if the firm realizes marginally unfavorable news, it realizes silence conveys an even less favorable environment. The net result is that full disclosure is the only equilibrium outcome. Our analysis demonstrates that consideration of multiple segments vastly alters the reporting environment. In fact, with multiple segments, full disclosure cannot even be sustained as an equilibrium. Instead, when the firm and its rival compete in multiple markets, segment aggregation represents the unique equilibrium. In this case, any ex post temptation to provide a disaggregate report so as to convey unusually favorable information in one market inevitably also conveys unusually unfavorable information in the other 2 market. The desire to balance profitability in its markets then leads the firm to use segment aggregation as a means of conveying the overall level of news (an ex post temptation it cannot resist) without unduly harming its profitability in one of its segments. In a sense, with multiple segments, the unraveling result applies but only at an aggregate information level. After establishing the key point that the presence of multiple markets disables full disclosure and brings segment aggregation in its stead, we next examine the robustness of this result and then some of its implications. In terms of robustness, the fact that proprietary considerations alone can justify segment aggregation as a unique equilibrium outcome is shown to persist in circumstances where each firm is privy to private information. In fact, in that case, each firm's strict ex post preference for segment aggregation holds regardless of the other's disclosures. As a result, the nature or sequence of a rival's disclosure will not affect a multi-segment firm's preference for aggregation. Further, while the initial analysis proves aggregation of cost information across segments when firms face price competition, we extend the analysis to demonstrate analogous results when the firm is privy to demand information under quantity competition. In short, whenever the circumstances dictate an ex ante preference for fully withholding information, firms have a strict ex post incentive to provide aggregate reports. Given the robustness of the results, we next consider some potential implications. First, we examine the effects of segment heterogeneity and demonstrate the circumstances under which heterogeneous segments yield aggregation as the unique equilibrium outcome. The results indicate that key determinants of aggregation are similarities in demand and (expected) cost across segments, the level of competition, and inherent uncertainty (risk). These variables provide some testable implications which may help better explain the divide between practice and empirical observation with regard to segment aggregation. Firms' reluctance to provide segment details for proprietary reasons is a long-standing practitioner view. (Prominent examples of this phenomenon are Apple and Dell, two firms who eagerly 3 announce firmwide profits but actively seek to withhold segment details.) Yet, empirical evidence to support such a view has been mixed, perhaps in part because the focus to date has been on a firm's desire to aggregate and not necessarily the firm's wherewithal to actually do so. The results herein indicate that risk, competition, and the similarities among a firm's portfolio of segments may all be critical features in a firm's ability to credibly follow a desired policy of segment aggregation and thus may be confounding factors in empirical analyses. A second implication of the analysis concerns the value of diversification. By including the potential for cross-segment correlation, we demonstrate that statistical dependence across segments does not alter the equilibrium outcome but does affect the value of aggregation (and thereby the value of being a multi-segment firm). Thus, a conglomerate firm may glean diversification benefits despite not having a desire to shield from risk. A third implication concerns a firm's incentives to acquire advanced information about its cost structures. By examining incentives for information acquisition, we demonstrate that a synergy in information gathering exists despite the seemingly independent nature of the segments' competitive environments. In this case synergy arises because gathering of information in multiple markets permits a firm to coarsen its disclosures and, thus, maintain information advantage over its competitor. More specifically, the value of gathering information in only one segment is limited by the fact that the firm knows it will ultimately disclose such information to its rival. In contrast, the incremental value of gathering information in a second segment is enhanced by the fact that such gathering has spillover effects in the first market by affording a viable policy of aggregating segment details and, thereby, withholding some proprietary information. More broadly, the result speaks to an interaction among the value of a firm's internal managerial (cost) accounting systems and its external financial reporting system. 4 A final implication entails an examination of welfare effects of regulations mandating segment disclosures. While much emphasis has been placed on capital market participants' preference for greater transparency, its seems apropos to examine the regulations given firms' underlying reluctance to provide such details. In light of this view, we demonstrate that mandatory segment disclosures can actually be harmful from a welfare perspective in product markets by facilitating tacit price collusion among competing firms. The point of this is not to assail disclosure regulations as universally harmful, but rather to bring attention to the need for a holistic view of such regulations that incorporates not just investors in capital markets but also product markets and their consumers. This paper's analysis is tied to the extensive discretionary disclosure literature and the literature on segment aggregation in particular.1 The viability of segment aggregation under discretionary disclosure demonstrated herein is similar in spirit to other papers that demonstrate partial disclosure as exceptions to the "unraveling" result. Prominent results include Verrecchia (1983), Dye (1985), and Jung and Kwon (1988). In Verrecchia (1983), proprietary costs of disclosure offset the temptation to disclose to capital markets, thereby supporting an equilibrium in which the firm nontrivially exercises discretion. Subsequent studies, including Darrough and Stoughton (1990), Wagenhofer (1990), and Clinch and Verrecchia (1997), have endogenized such proprietary costs. In Dye (1985) and Jung and Kwon (1988), uncertainty about information endowment means that the withholding disclosure does not necessarily convey the worst-case scenario (but perhaps only that the firm did not have information); this feature supports an equilibrium in which firms may conditionally withhold information. This paper presents a different force that gives rise to partial disclosure, one that requires a multiple segment view. In particular, while each segment viewed individually presents a scenario in which a firm would be tempted to fully disclose, coarse (aggregate) 1 For excellent reviews of the expansive literature on disclosure, including studies on discretionary disclosure, see Verrecchia (2001) and Dye (2001). 5 disclosure arises only when the segments are viewed together. Other work that has examined incentives for segment aggregation in the presence of competition include Feltham et al. (1992) and Hayes and Lundholm (1996). In a model where it is assumed that a firm can ex ante commit to its disclosure policy, Feltham et al. (1992) document circumstances under which an incumbent benefits from coarse line of business reporting in the presence of rivals. Interestingly, they note that in the absence of commitment, unraveling is a key stumbling block to implementing such desired disclosure practices and full disclosure is likely to be the end result. In this paper, we demonstrate that not only would a firm like to aggregate information but that it can credibly follow such a strategy despite no upfront commitments. In a similar vein, Hayes and Lundholm (1996) examine a model of a firm facing two audiences, an entrant and a capital market. Their setting demonstrates that the desire to disclose information to capital markets can be tempered by the desire to withhold information from competitors. Further, these competing forces can justify segment aggregation (in addition to full disclosure) as an equilibrium outcome.2 In contrast, the present paper demonstrates that the viability of segment aggregation does not require multiple audiences, only multiple segments subject to competition. In fact, with multiple segments in the forefront, full disclosure is no longer even a viable reporting strategy, leading to segment aggregation being the unique equilibrium outcome. The remainder of this paper proceeds as follows. Section 2 outlines the basic model. Section 3 provides the key results and checks their robustness. Section 4 examines potential implications of the results. Section 5 concludes. 2 The notion that competing demands from two audiences can sustain partial disclosure has also been demonstrated in single market settings (Darrough and Stoughton 1990; Wagenhofer 1990; Feltham and Xie 1992) and in circumstances where ineffective auditing requires competing tensions to add credibility to disclosure (Gigler 1994; Evans and Sridhar 2002). 6 2. Model Two firms (firms 1 and 2) engage in price competition in each of two product markets (markets A and B). Consumer demand in market i for firm j's product is represented by a linear, downward-sloping (inverse) demand function Pj i = α − qj i − γqk i , i = A, B; j, k = 1, 2, j ≠ k; Pj i is product price, and qj i and qk i are the quantities sold by firm j and its rival, respectively, in market i.3 The parameter γ ∈ (0,1) reflects the degree of competitive intensity. As γ approaches 0, the products become independent and, thus, the firms are not rivals; as γ approaches 1, the products become perfect substitutes yielding the most intense competition. Let cj i denote firm j's cost of providing each unit of product in market i. While, on average, each firm's production cost is the same, there is uncertainty associated with firm 1's precise cost. In particular, c1 i = c + δ1 i , δ1 i ∈{−δ ,+δ}, δ > 0, with each cost realization equally likely, and c2 i = c . For now, assume statistical independence between δ1 A and δ1 B . Prior to choosing prices in each market, firm 1 (privately) learns its cost parameters, δ1 A and δ1 B , and thus makes circumstance contingent pricing decisions. Whether firm 2 also can do so depends on firm 1's disclosure. In particular, upon learning δ1 A and δ1 B , firm 1 opts to reveal neither δ1 i value, only one δ1 i value, both δ1 i values, or an aggregate value, δ1 A + δ1 B ; notationally, d ∈D ≡ {(∅,∅),(δ1 A ,∅),(∅,δ1 B ),(δ1 A ,δ1 B ),δ1 A + δ1 B}.4 In this case, the firm's strategy, a mapping from (δ1 A ,δ1 B ) to D, is denoted d(δ1 A ,δ1 B ). Given this setting, we identify equilibrium outcomes using the perfect Bayesian equilibrium solution concept (see, for example, Tirole 1993, pp. 436-438). That is, the strategies are optimal given beliefs, and beliefs are obtained from strategies and observed actions using Bayes' rule (when applicable). The sequence of events is summarized in Figure 1. 3 As is standard, we assume α is sufficiently large that equilibrium prices and quantities, derived from the relevant first-order conditions, are positive throughout the analysis. 4 Clearly, each disclosure option is informationally equivalent to a cost disclosure (since cost in each market is c + δ1 i). 7 Firm 1 privately learns (δ1 A , δ1 B ). Firm 1 decides what, if any, information to disclose, d. Firms 1 and 2 each set prices in markets A and B. Profits for each firm are realized. Figure 1: Timeline of Events. 3. Results 3.1. Viability of Segment Aggregation Under discretionary disclosure, a natural assertion may be that the firm is unable to resist the ex post temptation to disclose information, thereby rendering discretion irrelevant. This view emanates from the seminal "unraveling" result in the voluntary disclosure literature (Grossman 1981; Milgrom 1981). The conjecture of unraveling applies in this setting as well, provided the firms operate in only one market. In the single-market case, firm 1 benefits by disclosing bad news about its costs (δ1 i = δ ) so as to evoke a softened pricing response by its rival. On the other hand, when δ1 i = −δ , firm 1 prefers to be the only party that is aware of the good news, so it can exploit its cost advantage without eliciting a defensive lowering of prices by its competitor. Such one-sided desire for silence is precisely what leads to the familiar unraveling, leaving full disclosure as the unique equilibrium in the single market setup. Roughly stated, with concerns confined to one market, silence by firm 1 speaks volumes (silence implies δ1 i must be −δ ). The result is that the firm cannot credibly withhold information. Further, firm 1 is better off withholding its cost information from an ex ante perspective, thus suffering from its inability to do so ex post. Intuitively, firm profits in duopoly competition are convex (quadratic) in the demand intercept net of marginal cost (α − c1 i), implying there is only a modest gain from disclosing when high cost arises while there is a steep loss from disclosing when a low cost arises. 8 This paper's key insight is that the firms' presence in two product markets can alter the standard unraveling view and permit a firm to credibly adopt a disclosure policy which is not fully revealing. In fact, as confirmed in Proposition 1, the effect of multiple markets is even more stark in that multiple markets actually preclude the possibility of full disclosure. (All proofs are provided in the appendix.) PROPOSITION 1. (i) If the firms compete in only one market, the equilibrium necessarily entails fully revealing disclosure. (ii) If the firms compete in multiple markets, full disclosure cannot be sustained in equilibrium. Part (i) of the proposition follows from the logic presented above that the firm cannot resist the ex post temptation to disclose high cost. Though the result in part (ii) is less obvious, it is rooted in related reasoning. In particular, with multiple markets, the ex post temptation is no longer to fully disclose a high cost; instead, the ex post temptation is to limit cost revelation by providing an aggregate disclosure. Of course, if both segments' costs are high, an aggregate report is tantamount to full disclosure. But, if one segment has a high cost while the other has a low cost, issuing an aggregate report prevents the rival from discerning in which market it should have the more aggressive response. The benefit of keeping the rival guessing through an aggregate report implies the firm can no longer credibly adopt a full disclosure posture, thereby reversing the unraveling result. Why this sort of signal jamming by the firm becomes the pressing ex post temptation warrants a deeper examination. The underlying reasoning behind this result is best seen in the context of outlining why aggregation can be sustained as an equilibrium disclosure policy (the same logic effectively underscores why full disclosure cannot). Intuitively, if firm 1 is tempted to move away from an aggregate disclosure of δ1 A + δ1 B to reveal high cost in one market (say by revealing δ1 A is the higher of the two values), it does 9 so at the cost of revealing low cost in its other market (by revealing δ1 B is the lower of the two values). The temptation to elicit softened competition in market A by disclosure (the basis for the unraveling result) is thus tempered by the aggressive competition that ensues in market B. The balancing of such strategic considerations in the two markets can help sustain aggregate disclosure as an equilibrium. The above intuition is borne out in the following formal analysis. Given the linear inverse demand functions in the model, the demand functions faced by the firms are: q1 i ( p1 i , p2 i ) = α(1− γ ) − p1 i + γp2 i 1− γ 2 and q2 i ( p1 i , p2 i ) = α(1− γ ) − p2 i + γp1 i 1− γ 2 . Given this, consider first the outcome under full disclosure, wherein the firm's disclosure strategy is d(δ1 A,δ1 B) = (δ1 A,δ1 B) for all (δ1 A,δ1 B). With full disclosure, the updated beliefs of firm 2 are trivial since it learns the precise cost of firm 1. Using these beliefs, firm 1 and firm 2 face retail pricing decisions as in (1) and (2): Max p1 i (δ1 A ,δ1 B ;δ1 A ,δ1 B ),i=A,B p1 i (δ1 A,δ1 B;δ1 A,δ1 B)- c − δ1 i [ ] i=A,B ∑ × q1 i p1 i (δ1 A,δ1 B;δ1 A,δ1 B), p2 i (δ1 A,δ1 B;δ1 A,δ1 B) ( ) . (1) Max p2 i (δ1 A ,δ1 B ;δ1 A ,δ1 B ),i=A,B p2 i (δ1 A ,δ1 B ;δ1 A ,δ1 B )- c [ ] i=A,B ∑ × q2 i p1 i (δ1 A ,δ1 B ;δ1 A ,δ1 B ), p2 i (δ1 A ,δ1 B ;δ1 A ,δ1 B ) ( ) . (2) In (1) and (2), p1 i (δ1 A ,δ1 B ;δ1 A ,δ1 B ), denotes firm 1's pricing strategy as a function of (i) its private information and (ii) its disclosure policy (δ1 A ,δ1 B ). Similarly, p2 i (δ1 A ,δ1 B ;δ1 A ,δ1 B ) reflects firm 2's pricing strategy as a function of (i) the disclosure it observes and (ii) the presumed disclosure policy of firm 1. Jointly solving the first-order conditions of (1) and (2) yields: p1 i (δ1 A,δ1 B;δ1 A,δ1 B) = α[2 − γ − γ 2 ] + 2[c + δ1 i ] + γc 4 − γ 2 , and p2 i (δ1 A,δ1 B;δ1 A,δ1 B) = α[2 − γ − γ 2 ] + 2c + γ [c + δ1 i ] 4 − γ 2 , i = A, B. (3) 10 The equilibrium prices reveal that firm j's prices are increasing in its own cost and, to the extent dictated by the degree of competition, by its rival's cost. The latter reflects the fact that prices are strategic complements (Bulow et al. 1985). Substituting prices from (3) into (1) yields the following realized profit for firm 1 under full disclosure: Π1(δ1 A ,δ1 B ;δ1 A ,δ1 B ) = (α − c )(2 − γ − γ 2 ) − δ1 i (2 − γ 2 ) [ ]2 [4 − γ 2 ]2[1− γ 2 ] i=A,B ∑ . (4) In (4), the firm's profit in each market takes a symmetric form, in line with the notion that in each independent market firm profit is increasing in demand and decreasing in (expected) cost. The δ1 i-term reflects firm 1's relative standing in that market: a higher cost (δ1 i = δ ) puts it at a disadvantage to its rival, and this cuts into firm 1's profit. Next consider the outcome if firm 1 adopts the aggregate disclosure strategy, d(δ1 A,δ1 B) = δ1 A + δ1 B for all (δ1 A,δ1 B). In this case, the updated beliefs of firm 2 are again easy to specify: (i) if d = −2δ or 2δ , the aggregate disclosure is fully revealing since these values correspond only to (δ1 A,δ1 B) = (−δ ,−δ ) and (δ1 A,δ1 B) = (δ ,δ ) , respectively, and (ii) if d = 0, from firm 2's perspective it is equally likely that (δ1 A,δ1 B) = (−δ ,δ ) or (δ1 A,δ1 B) = (δ ,−δ ). Thus, firm 1's pricing problem is in (5): Max p1 i (δ1 A ,δ1 B ;δ1 A +δ1 B ),i=A,B p1 i (δ1 A,δ1 B;δ1 A + δ1 B)- c − δ1 i [ ] i=A,B ∑ × q1 i p1 i (δ1 A,δ1 B;δ1 A + δ1 B), p2 i (δ1 A + δ1 B;δ1 A + δ1 B) ( ) . (5) As for firm 2, if d = −2δ or 2δ , firm 2 learns firm 1' cost in each market precisely, and so the equilibrium prices are is as in (3), the full revelation setting. However, if d = 0, firm 2 is uncertain of firm 1's precise cost in each market, and so its pricing problem is: 11 Max p2 i (0;δ1 A +δ1 B ),i=A,B (1 / 2) p2 i (0;δ1 A + δ1 B )- c [ ] i=A,B ∑ × q2 i p1 i (−δ ,δ ;δ1 A + δ1 B ), p2 i (0;δ1 A + δ1 B ) ( ) + (1 / 2) p2 i (0;δ1 A + δ1 B )- c [ ] i=A,B ∑ × q2 i p1 i (δ ,−δ ;δ1 A + δ1 B ), p2 i (0;δ1 A + δ1 B ) ( ) . (6) In (5) and (6), p1 i (δ1 A ,δ1 B ;δ1 A + δ1 B ), denotes firm 1's pricing strategy as a function of its private information and the policy of aggregate disclosure. Similarly, p2 i (d;δ1 A + δ1 B ) reflects firm 2's pricing strategy as a function of the observed disclosure (in (6), d = 0) and the equilibrium conjecture of an aggregate disclosure policy. Jointly solving the first-order conditions of (5) and (6), the equilibrium prices with aggregate disclosure are: p1 i (δ1 A,δ1 B;δ1 A + δ1 B) = α[2 − γ − γ 2 ] + 2[c + δ1 i ] + γc − (1 / 4)γ 2[δ1 i − δ1 j ] 4 − γ 2 , and p2 i (d;δ1 A + δ1 B) = α[2 − γ − γ 2 ] + 2c + γ [c + d / 2] 4 − γ 2 , i , j = A, B; i ≠ j. (7) As before, in equilibrium, firm 2's prices are increasing in both its own cost and its expectation of firm 1's cost. Similarly, firm 1's prices are increasing in its own cost as well as firm 2's cost. The added wrinkle is reflected in the last term of firm 1's pricing expression: the aggregate disclosure policy adds an interlinkage between the otherwise independent markets. This interlinkage reflects that firm 1's price in market A is decreasing in the difference between market A's cost and market B's cost (and vice-versa for the price in market B). This arises because with aggregate disclosure, firm 2 cannot discern which of the two markets has a higher cost and thus takes an average posture in each. This leads firm 1 to lower (raise) its price in the higher (lower) cost market. Substituting prices from (7) into (5) yields the following realized profit for firm 1 under aggregate disclosure: Π1(δ1 A,δ1 B;δ1 A + δ1 B) = Π1(δ1 A,δ1 B;δ1 A,δ1 B) + γ 2[8 − 3γ 2 ][δ1 A − δ1 B]2 8[4 − γ 2 ]2[1− γ 2 ] . (8) 12 The last term on the right-hand-side of (8) is nonnegative for all γ and (δ1 A,δ1 B). Hence, firm 0 prefers aggregate disclosure to full disclosure. Finally, off-equilibrium beliefs (δ1 i = −δ when there is no disclosure in market i) ensure that aggregate disclosure is preferred to all other disclosure strategies as well and, hence, is an equilibrium. As the next proposition confirms, not only is aggregate disclosure an equilibrium, but it also yields the unique equilibrium outcome of the firms' interactions. PROPOSITION 2. For any γ, segment aggregation achieves the unique equilibrium outcome. Stated succinctly, the result in Proposition 2 demonstrates that joint consideration of multiple markets yields a contrast to the typical view of discretionary disclosure. When either segment is viewed individually, the firm would like to commit to a policy of no disclosure (e.g., Darrough 1993). Yet, the ex post pressure to disclose is compelling in each. But, when the firm considers both markets simultaneously, it realizes that issuing an aggregate report is a credible means of achieving its desired non disclosure to a degree. Doing so is credible because it means that a deviation to disclose particularly advantageous news for one market inevitably conveys particularly disadvantageous news in another market. The justification for both the ex ante benefit of non disclosure and the ex post ability of aggregation to sustain a partial disclosure equilibrium lies in the proprietary nature of the information disclosed. As such, the greater the competitive intensity, the greater the benefit of segment aggregation (relative to full disclosure). COROLLARY 1. The benefit of segment aggregation is increasing in γ. Before proceeding to some extensions of the basic setup, we embark on two digressions. First, it is worth noting that the information being disclosed herein is forward looking (i.e., it pertains to production that is yet to occur). In contrast, typical accounting 13 segment reports are historical in nature. However, it is often argued that such historical information is useful to competitors due to correlation with future results. In this vein, we note that the assumption that firm 1 perfectly observes its cost in advance is not critical to the analysis; the critical aspect is that information relevant to future costs in one market can be pooled with information relevant to future costs in another market via aggregation across segments. A second issue worth further discussion is the connection to related literature, in particular the existing work on segment aggregation in the presence of rivals. Feltham et al. (1994) demonstrate the ex ante preference for line of business reporting in various competitive circumstances. Most relevant to the present study, they demonstrate that withholding line of business cost details is optimal for competitive reasons in the presence of incumbent price competition. They stress that the preference for withholding segment information, however, depends on a capacity to fully commit to such a policy, stating that "[i]f such a commitment is not possible, then firms are likely to have ex post incentives to fully disclose their information ... The equilibrium would then unravel to the point at which all multi-segment firms disclose their [line of business] information" (p. 19). As described above, this paper's results demonstrate that such an ex post unraveling is not present in a multi-segment firm and, thus, the desire to aggregate is credible under discretionary disclosure. The distinction between our analysis and that in Hayes and Lundholm (1996) is similar, albeit more subtle. Hayes and Lundholm (1996) demonstrate that when a firm faces two separate report recipients, a capital market (to whom it wishes to disclose) and a potential entrant facing capital constraints (to whom it wishes not to disclose), both full disclosure and aggregate segment reporting can be sustained ex post as equilibria. In effect, competition pushes the firm away from disclosure whereas a capital market pulls the firm toward disclosure; these competing pressures add segment aggregation to the set of possible equilibria. In concluding the paper, Hayes and Lundholm stress that their analysis 14 considers a circumstance wherein the disclosing party makes no payoff-relevant decisions, calling for future research to consider "[a] more general model in which both the firm and rival would make reporting decisions and payoff-relevant decisions" (p. 276). By considering strategic pricing choices subsequent to disclosure, the present paper adds a decision-making aspect to the disclosing party's actions. In doing so, we find that not only is aggregate disclosure sustainable as an equilibrium, but it represents the unique equilibrium outcome. Further, this conclusion is reached even without the offsetting pressures of a capital market. In fact, in our setting, there is only one recipient of the information, a single product rival, and so what is key is that firms eye profits over multiple markets, an assumption which seems particularly natural given the paper's issue of interest (segment aggregation). The next section considers variants of the basic model to check the robustness of the main results. In doing so, it also further expands on the call in Hayes and Lundholm (1996) by considering symmetric disclosure and payoff-relevant choices by the two competing firms. 3.2. Robustness of Segment Aggregation While the preceding analysis demonstrates that a multi-segment firm has unilateral incentives to aggregate cost data across segments for competitive reasons, one may wonder to what extent these conclusions are sensitive to the presumed dispersion of private information and the nature of competition. We next examine these variations. 3.2.1. Symmetric Private Information A natural inquiry that arises from the above analysis is whether aggregate disclosures arise when all parties are privy to private information. In particular, consider the previous setup except that firm 2's cost in market i is also uncertain, c2 i = c + δ2 i , δ2 i ∈{−δ ,+δ}, with each cost realization equally likely (and statistically independent from firm 1's cost). 15 In this symmetric setup, each firm (privately) learns its own cost parameters, on which it can base pricing and disclosure choices. With symmetric disclosure options, we revisit the question of equilibrium disclosure policies. The equilibrium determination is admittedly more tedious in this case, requiring an examination of all possible continuation games given two-sided asymmetric information. Yet, it turns out the basic conclusions (and the intuition) largely follow those of the baseline analysis. Full disclosure is once again precluded from being an equilibrium. And again, aggregation by both firms achieves the unique outcome. The following proposition confirms this claim. PROPOSITION 3. For any γ, segment aggregation by both firms achieves the unique equilibrium outcome. Besides noting that the basic conclusions are insensitive to multi-party private information, the symmetric case also demonstrates a more robust ex post preference for segment aggregation. As the proof of Proposition 3 details, each firm's strict preference to aggregate segments arises regardless of the other firm's disclosure strategy or even its disclosed report. In other words, even if firms' disclosures were made sequentially (i.e., at different points in time), the equilibrium outcome would be unchanged. As another robustness check, we next consider reporting under quantity competition. 3.2.2. Cournot Competition As has been well-documented, the conclusions one can derive about disclosure in oligopoly models depend both on the nature of competition (Bertrand vs. Cournot) and the nature of private information (private-value cost information vs. common-value demand information). The basic analysis herein demonstrates that under Bertrand competition and disclosure of cost information, a firm's ex ante preference for withholding information translates into ex post aggregation of segment information when it operates in multiple markets. If the firm's information were instead about demand, there would be a clear ex ante 16 preference for full disclosure which, of course, implies such disclosures is also sustained ex post. This intuition also undergirds private cost information under Cournot competition. The remaining case to consider is the other circumstance in which a firm has an ex ante preference for withholding information: private information about demand under Cournot competition. In this case, with only one market, an ex ante desire to withhold information again gives way to an ex post desire to reveal unfavorable market demand information. With multiple markets, partial withholding of information again arises as the equilibrium outcome. In particular, say that each firm's costs are known and symmetric, i.e., c j i = c . Demand in market i is represented by a linear, downward-sloping (inverse) demand function Pj i = α + θ i − q j i − γqk i , θ i ∈{−θ,+θ}, θ > 0, with each demand realization equally likely and independent across markets. Analogous to the initial setup, firm 1 (privately) learns market demand parameters after which it can choose what, if any, information to disclose. In this case, the following proposition presents an analog to the basic conclusions in the Bertrand case. PROPOSITION 4. Under Cournot competition, aggregation of segment demand information achieves the unique equilibrium outcome. As the proof of Proposition 4 demonstrates, in the Cournot case, the ex post benefit of aggregation is γ [4 + γ ][θ A − θ B ]2 8[2 + γ ]2 ≥ 0. So, again, the ex ante benefit of aggregation is higher when competition is more intense: when the threat from the rival is pressing, the firm finds it more advantageous to keep the rival unaware of the precise profitability in each market. In short, as might be expected, the incentives for disclosure of proprietary information are sensitive to the nature of competition and type of information. However, there is also a unifying theme. When a firm has a strong ex ante desire to disclose, there 17 remains no reason to deviate from such a policy ex post. However, in circumstances where there is an ex ante desire to withhold information but ex post unraveling to full disclosure (the Bertrand/cost and the Cournot/demand cases), the presence of multiple segments vastly alters the landscape: it not only makes partial withholding possible, it makes it necessary. 4. Implications 4.1. Segment Heterogeneity The analysis thus far has presented a circumstance where a firm with two ex ante homogenous segments opts to employ segment aggregation as a disclosure strategy. The presumption of segment homogeneity is a useful technical simplification but may unduly create the impression that proprietary costs always lead to partial information suppression via aggregation. Since in practice both the nature of segments and the extent of segment aggregation varies across firms and industries, it seems worthwhile to examine the determinants of aggregation in light of heterogeneous segments. To examine the consequences of ex ante segment heterogeneity, consider the baseline model adjusted to reflect differences in demand (intrinsic market size) and supply (production costs). In particular, say the downward-sloping (inverse) demand function for market i is Pj i = α i − q j i − γqk i and the average per unit cost for the firms in market i is c i . Given potential differences in segments (i.e., α A ≠ α B and/or c A ≠ c B), the ex ante desire to withhold information is unchanged. What can differ is the firm's ability to credibly aggregate its information. The next proposition provides the conditions under which segment aggregation arises in heterogeneous markets. PROPOSITION 5. With heterogeneous markets, segment aggregation constitutes an equilibrium disclosure strategy (in which case it achieves the unique equilibrium outcome) if and only if [α A − c A ]− [α B − c B ] ≤ δ[8 − 3γ 2 ] 2 − γ − γ 2 . 18 Besides demonstrating that proprietary costs do not lead all firms to employ segment aggregation, the result in Proposition 5 suggests some testable implications in this regard. Despite the intuitive appeal of the notion that proprietary costs will lead to information suppression, there has been only mixed empirical support of this view.5 One reason offered for this disparity is that empirical efforts have focused on the desire to aggregate not the ability to actually do so. As Berger and Hann (2007) put it, "in studying managers' motives to withhold segment data, one needs to consider not only what managers want to hide, but also what they can hide" (p. 872). The present analysis suggests that critical features in determining the ability to aggregate are the extent the which the markets in question are similar as well as the degree of competition and uncertainty. In particular, Corollary 2 summarizes the relevant comparative statics. COROLLARY 2. Segment aggregation is more likely to arise as an equilibrium (i) the greater the similarities across markets; (ii) the greater the cost variance; and (iii) the greater the competitive intensity. One implication of Corollary 2 is to provide a potential avenue to better parse out the underlying motivations for withholding segment profitability. The results suggest that to identify segment aggregation driven by proprietary costs, one needs to look not only at individual segments but also the portfolio of segments a firm holds and the extent of their similarities. Importantly, these similarities arise in terms of a net intercept (demand net of costs). So, even if a firm has one segment that is much larger than the other (higher α i ), if the smaller segment is more profitable on a per unit basis (lower c i ), the similarity in net terms may help sustain segment aggregation. Parts (ii) and (iii) confirm the notion that the 5 In particular, Harris (1998) and Botosan and Stanford (2005) provide evidence of competitive reasons for segment aggregation, but only in less competitive markets. Subsequently, Berger and Hann (2007) found little support for proprietary explanations for segment aggregation, demonstrating that existing results may instead be driven by agency costs. 19 more the information advantage for firm 1 and more the competitive pressure it faces, the more reason for the firm to aggregate. 4.2. Cross-Segment Correlation While the previous analysis examines effects of inherent ex ante differences across segments, one may also question whether examining overlap is also apropos. In particular, the markets that make up multi-segment firms often have commonalities and such commonalities may arise not just in an ex ante sense but also ex post due to statistical dependence. While the baseline analysis considered statistically independent segments as a means of demonstrating interdependencies due to disclosure most succinctly, similar results can arise if the markets exhibit correlation. In particular, while each cost realization in each market is equally likely, denote the conditional probability of a high (alternatively low) cost in one market given a high (low) cost in the other by [1+ ρ] 2 , i.e., ρ reflects the cross- segment correlation. The next result describes the outcome in the event of segment interdependencies. PROPOSITION 6. (i) For any γ and ρ, segment aggregation achieves the unique equilibrium outcome; and (ii) the benefit of segment aggregation is decreasing in ρ. In short, Proposition 6 (i) confirms that the viability of segment aggregation as an equilibrium outcome is insensitive to the statistical interdependencies in markets. However, this is not to say that interdependencies are unimportant. Proposition 6 (ii) demonstrates that the advantage of aggregation (and, thus, the advantage of having multiple segments in the first place) is tied to cross-segment correlation. In fact, in the setting, consistent with the firm's risk neutral preferences, expected profit in the case of full disclosure is free of ρ. In contrast, under the equilibrium outcome of segment aggregation, the firm's expected profit is 20 decreasing in ρ, reflecting a demand for diversification in spite of risk neutral preferences.6 The demand for diversification arises because the firm can exploit offsetting priorities via aggregation to effectively conceal proprietary information only when the two segments have unequal outlooks. Low correlation implies such eventualities are more likely. 4.3. Synergy in Information Acquisition Another issue to consider pertains to the underlying incentives for a firm to acquire information. Thus far, we have presumed that firm 1 is privy to information relevant to each market. However, in many circumstances, information acquisition (or at least acquisition of precise information) is a result of a concerted effort on the part of management. Effective design of managerial accounting systems ostensibly is aimed at improved decision-making. Yet, the potential interplay between information acquisition and subsequent financial reporting often goes unrecognized (e.g., Hemmer and Labro 2008). Such an interplay between information acquisition and information dissemination is prominent in the current setting. Further, the extent of such interplay depends on whether the firm gathers information in multiple markets. That is, despite the independence of markets, the benefit to information in one market depends on the information available in another. This information synergy comes due to the ensuing ramifications for external reporting of information. If information is gathered in both markets, the firm has a credible means of withholding some information from public view. This, in turn, creates cross- segment synergies in gathering decision-relevant information. 6 Coupled with Corollary 2, this finding may add a subtle consideration to the intense debate over the diversification discount/premium (e.g., Berger and Ofek 1995; Villalonga 2004). That is, when both the ability and desire to aggregate disclosures across segments is considered, cross-segment correlation, similarities in segment characteristics, competition, and inherent uncertainty may all play a role in determining the consequences of diversification. 21 COROLLARY 3. Even when product markets are independent, the value of information exhibits cross-market synergy. That is, the value of gathering cost information in one market is higher if the firm also gathers cost information in another market. The key implication from Corollary 3 is that even if decision making across a firm's segments is not intrinsically interconnected, it does not mean the managerial accounting systems need be disconnected. Instead, understanding the benefits of a managerial accounting innovation in one segment requires a holistic view of managerial accounting in other segments as well as the external financial reporting environment. 4.4. The Effect of Mandatory Segment Disclosures As a final implication, we consider the ramifications of mandatory segment disclosure regulation in light of the paper's results. Presuming such regulations achieve the stated goal of increased transparency, the preceding analysis may shed some insight into the competitive consequences.7 In particular, in this setting a firm gains from the segment aggregation equilibrium that arises under discretionary disclosure because such information suppression yields a competitive advantage. Regulations that require full disclosure of segment details, of course, would yield a different outcome, one that is to the detriment of the informationally- advantaged firm but also to the benefit of its rival. What remains to be seen is the consequences for consumers. As it turns out, consumers actually benefit from segment aggregation, because it undercuts tacit price collusion on the part of the competing firms. With full disclosure, both firms know which market has high cost and which has low cost. As a result, they both cut 7 There is at least anecdotal evidence that some firms have taken efforts to eschew the spirit of such regulations, in which case the issue of regulatory consequences are largely moot. Apple is a prominent example, since it has long refused to report margins on iPod products separate from its computer products. Its finance chief, Peter Oppenheimer, balked at calls for reporting of segment margins, noting that "...our competitors would just love to know what our specific gross margins are ... and we just don't want to help them" (WSJ, 6/24/06, B4). 22 prices in the low cost market but boost prices in the high cost market. Under aggregation, however, one firm is left in the dark and provides average prices for each market. The net result is that in the low cost market, the informed firm still sets low prices, but now the consumers benefit from having only one firm setting excessive prices in the high cost market. By preventing such tacit collusion in high cost (thus, high price) markets, segment aggregation can actually benefit consumers and thereby increase welfare. COROLLARY 4. Mandatory segment disclosure regulations reduce total welfare. There are two notable caveats to the corollary. First, the results do not definitively say the regulations are detrimental. After all, the ramifications for capital markets need also be considered. The point rather is to examine the effects on other parties in light of the reasons firms aggregate in the first place (i.e., if only capital market considerations matter, firms would voluntarily disclose anyway). In this vein, the corollary underscores that a full understanding of the consequences of regulation necessitates weighing the ramification for the range of parties that can be affected. While investors and competing firms have been the focus of much discussion, this result demonstrates that consumers can also be impacted due to induced changes in firm strategy. Second, it is not always the case that consumers are harmed by mandatory segment disclosures. For example, recall that in the case of Cournot competition and demand information, segment aggregation is the unique equilibrium outcome. However, in this case, the opposite conclusion from Corollary 4 holds. In particular, disclosure actually spawns more intense competition in the high demand market (since quantities are strategic substitutes), thereby rendering such regulations beneficial to consumers. That said, a long- term view could again point to consumer losses from regulation: knowing such regulations 23 would undercut a firm's competitive position, the firm may have dampened incentives to gather information or make demand-enhancing investments in the first place.8 5. Conclusion This paper presents a model of segment disclosures when firms encounter competition in multiple segments. The results provide a stark contrast to the typical view that firms subject to discretion cannot help but disclose their private information. The multi- segment view suggests that while firms may be unable to entirely withhold segment information, segment aggregation is a viable means of maintaining competitive advantages. Intuitively, if the firm wishes, ex post, to renege on aggregation and convey particularly helpful information in one market, it does so at the cost of conveying particularly harmful information in another market. By creating offsetting ex post considerations, aggregation is able to survive as a viable strategy despite the fact it suppresses some information. The aggregate disclosure equilibrium identified herein is consistent with firms' behavior in that they are often willing to disclose firmwide performance but are far more reluctant to reveal segment specifics. With this basic tension as a backdrop, we consider potential implications for understanding the role of segment characteristics, induced demand for diversification, incentives for information acquisition, and consequences of regulatory intervention. Of course, the paper also excludes some other considerations in disclosure choice which are likely to be present in practice (e.g., capital market perceptions; attracting talent; conveying expertise). Explicitly incorporating such considerations in disclosure choice may be an avenue worthy of future study. 8 A previous version of the paper provided a more complete analysis of such long-term effects. Details are available from the authors. 24 Appendix Proof of Proposition 1. (i) Consider the case of one market, say market A. Given firm 1's disclosure strategy, d1(⋅), and firm 1's disclosure, d1, denote firm 2's updated beliefs over δ1 A by Pr(δ1 A ). The continuation game thus consists of firm 1 choosing a pricing strategy as a function of its information, p1 A(δ1 A ), as reflected in (A1), and firm 2 choosing a pricing strategy under its updated beliefs, reflected in (A2). Max p1 A (δ1 A ) [p1 A(δ1 A )- c - δ1 A]q1 A( p1 A(δ1 A ), p2 A ), ∀δ1 A. (A1) Max p2 A Pr(δ1 A )[p2 A - c ]q2 A ( p1 A (δ1 A ), p2 A ) δ1 A ∑ . (A2) Jointly solving the first-order conditions of (A1) and (A2) yields: p1 A(δ1 A ) = α[2 − γ − γ 2 ] + 2[c + δ1 A] + γc − γ 2δ1 A[1− Pr(δ1 A )] 4 − γ 2 , and p2 A = α[2 − γ − γ 2 ] + 2c + γ [c + δ Pr(δ ) − δ Pr(−δ )] 4 − γ 2 . (A3) Substituting prices from (A3) into (A1) yields the following profit for firm 1 for any continuation game: Π1(δ1 A ) = (α − c )(2 − γ − γ 2 ) − δ1 A (2 − γ 2 Pr(δ1 A )) [ ]2 [4 − γ 2 ]2[1− γ 2 ] . (A4) From (A4), firm 1's profit from the continuation game when δ1 A = δ is strictly increasing in Pr(δ1 A ). Thus, any proposed equilibrium entailing less than fully revealing disclosure when δ1 A = δ is not an equilibrium, as firm 1 would strictly prefer to fully disclose δ1 A = δ in the continuation game. Given δ1 A = δ results in full revelation, it follows that firm 2 can infer when δ1 A = −δ in any equilibrium. (ii) In the case of two markets, denote firm 2's updated beliefs subsequent to a disclosure by Pr(δ1 A ,δ1 B ). The continuation game thus consists of firm 1 choosing a pricing strategy as a function of its information, p1 i (δ1 A ,δ1 B ), as reflected in (A5), and firm 2 choosing a pricing strategy under its updated beliefs, p2 i , reflected in (A6). Max p1 i (δ1 A ,δ1 B ) [p1 i (δ1 A ,δ1 B )- c - δ1 i ]q1 i ( p1 i (δ1 A ,δ1 B ), p2 i ), ∀(δ1 A , i=A,B ∑ δ1 B ). (A5) 25 Max p2 i Pr(δ1 A ,δ1 B )[p2 i - c ]q2 i ( p1 i (δ1 A ,δ1 B ), p2 i ) (δ1 A ,δ1 B ) ∑ [ ] i=A,B ∑ . (A6) Jointly solving the first-order conditions of (A5) and (A6) yields: p1 A (δ1 A ,δ1 B ) = α[2 − γ − γ 2 ] + 2[c + δ1 A ] + γc − γ 2δ1 A[1− Pr(δ1 A , δ̃1 B )] δ̃1 B ∑ 4 − γ 2 , p1 B (δ1 A ,δ1 B ) = α[2 − γ − γ 2 ] + 2[c + δ1 B ] + γc − γ 2δ1 B[1− Pr(δ̃1 A ,δ1 B )] δ̃1 A ∑ 4 − γ 2 , and p2 i = α[2 − γ − γ 2 ] + 2c + γ [c + δ1 i Pr(δ1 A ,δ1 B )] (δ1 A ,δ1 B ) ∑ 4 − γ 2 . (A7) Substituting prices from (A7) into (A5) yields Π1(δ1 A,δ1 B), firm 1 profit for any continuation game. We now argue that a fully revealing disclosure is not sustainable as an equilibrium. To see this, suppose (δ1 A ,δ1 B ) = (δ ,−δ ). If firm 1 discloses this value, its profit is Π1(δ ,−δ ) with Pr(δ ,−δ ) = 1, which equals 2 (α − c)2 (2 − γ − γ 2 )2 + δ 2 (2 − γ 2 )2 [ ] [4 − γ 2 ]2[1− γ 2 ] . Suppose instead firm 1 submits an aggregate disclosure (δ1 A + δ1 B = 0). For any feasible off-equilibrium beliefs Pr(δ ,−δ ) = p and Pr(−δ ,δ ) = 1− p, firm 1's profit in the continuation game, Π1(δ ,−δ ) , equals 2 (α − c)2 (2 − γ − γ 2 )2 + δ 2 (2 − γ 2 p)2 [ ] [4 − γ 2 ]2[1− γ 2 ] . Comparing profits, a necessary condition for full disclosure to be an equilibrium is p = 1. When (δ1 A ,δ1 B ) = (−δ ,δ ), firm 1 profit under full disclosure is as before; with aggregate disclosure, the only change in the firm 1 profit expression is that "p" is replaced by "1 - p". Thus, another necessary condition for full disclosure to be an equilibrium is p = 0. Obviously, the two identified necessary conditions cannot both hold, and so a fully revealing equilibrium does not exist. Proof of Proposition 2. The proof follows four steps. Step 1. (δ1 A,δ1 B) = (δ ,δ ) is fully revealed in any equilibrium. Some tedious (but straightforward) algebra confirms Π1(δ ,δ ) is maximized when Pr(δ,δ ) = 1. Thus, Π1(δ ,δ ) for Pr(δ,δ ) = 1 (the continuation game under fully revealing disclosure of (δ1 A,δ1 B) = (δ ,δ )) is greater than Π1(δ ,δ ) for any other firm 2 conjectures 26 (the continuation game under any disclosure that does not fully reveal (δ1 A,δ1 B) = (δ ,δ )). As a result, any equilibrium necessarily entails (δ1 A,δ1 B) = (δ ,δ ) being fully revealed. Step 2. (δ1 A ,δ1 B ) = (−δ ,−δ ) is fully revealed in any equilibrium. Suppose (δ1 A ,δ1 B ) = (−δ ,−δ ) is pooled with other realizations of (δ1 A ,δ1 B ) with positive probability. One such possibility entails the pooling of {(−δ ,−δ ),(δ ,−δ ),(−δ ,δ )}. Algebraic comparison confirms Π1(δ ,−δ ) and Π1(−δ ,δ ) are each maximized when Pr(−δ,−δ ) = 0. Since each are maximized at Pr(−δ,−δ ) = 0, the aggregate disclosure which pools {(δ ,−δ ),(−δ ,δ )} is assured to yield a higher profit in the continuation game than pooling {(−δ ,−δ ),(δ ,−δ ),(−δ ,δ )} when (δ1 A ,δ1 B ) = (−δ ,δ ) or (δ1 A ,δ1 B ) = (δ ,−δ ), regardless of the presumed beliefs when aggregate disclosure is chosen. Now consider the pooling possibility of {(−δ ,−δ ),(δ ,−δ )}. Under such pooling, firm 2 in equilibrium infers δ1 B = −δ , and so the problem, in effect, reduces to disclosing only in one market, market A. From Proposition 1(i), in the one market setting, full disclosure is the unique equilibrium. In other words, when (δ1 A ,δ1 B ) = (δ ,−δ ), firm 1 profit in the continuation game is higher if it fully reveals than if it is pools with (−δ ,−δ ). Similar arguments rule out pooling of {(−δ ,−δ ),(−δ ,δ )} in equilibrium. Step 3. (δ1 A ,δ1 B ) = (δ ,−δ ) and (δ1 A ,δ1 B ) = (−δ ,δ ) are always pooled in any equilibrium. Given steps 1 and 2, if (δ1 A ,δ1 B ) = (δ ,−δ ) is not always pooled with (δ1 A ,δ1 B ) = (−δ ,δ ), then the alternative is that it is fully revealed with positive probability. From Proposition 1(ii), revealing (δ1 A ,δ1 B ) = (δ ,−δ ) can be part of an equilibrium only if p = 1 under aggregate disclosure, i.e., (δ1 A ,δ1 B ) = (δ ,−δ ) is revealed with probability 1. In this case, given steps 1 and 2, (δ1 A ,δ1 B ) = (−δ ,δ ) is also fully revealed. But, as already proven in Proposition 1(ii), full disclosure cannot be sustained as an equilibrium. Symmetric arguments shows that (δ1 A ,δ1 B ) = (−δ ,δ ) is also always pooled with (δ1 A ,δ1 B ) = (δ ,−δ ). Step 4. δ1 A + δ1 B is an equilibrium, and yields the unique equilibrium outcome. If aggregate disclosure of δ1 A + δ1 B is an equilibrium, it is clear that it fully reveals (δ1 A,δ1 B) = (δ ,δ ) and (δ1 A ,δ1 B ) = (−δ ,−δ ), and pools (δ1 A ,δ1 B ) = (δ ,−δ ) and (δ1 A ,δ1 B ) = (−δ ,δ ). From steps 1-3, this is the unique equilibrium outcome. So, to complete the proof, we need only show that aggregate disclosure can be sustained as an equilibrium. First, we compare aggregate disclosure with full disclosure. Ifδ1 A = δ1 B , the two disclosure regimes are equivalent. If δ1 A ≠ δ1 B , firm 1 profit under aggregation is Π1(−δ ,δ ) (= Π1(δ ,−δ ) ) with Pr(δ ,−δ ) = Pr(−δ ,δ ) = 1 / 2 , which equals: 27 4[α − c]2[1− γ ]2 + δ 2[2 − γ ]2 2[2 − γ ]2[1− γ 2 ] . (A8) If firm 1 fully discloses, its profit, from Proposition 1(ii), is: 2 (α − c)2 (2 − γ − γ 2 )2 + δ 2 (2 − γ 2 )2 [ ] [4 − γ 2 ]2[1− γ 2 ] . (A9) Subtracting firm 1 profit in (A9) from that in (A8) yields: δ 2γ 2[8 − 3γ 2 ] 2[4 − γ 2 ]2[1− γ 2 ] > 0. (A10) (A10) implies that aggregation is preferred to full disclosure for all (δ1 A ,δ1 B ). Finally, the following off-equilibrium beliefs ensure aggregation is also preferred to any strategy that entails firm 1 withholding in one or both markets: Pr(−δ,−δ ) = 1 for no disclosure, Pr(δ1 A ,−δ ) = 1 for disclosure of only δ1 A , and Pr(−δ ,δ1 B ) = 1 for disclosure of only δ1 B . This completes the proof of the proposition. Proof of Corollary 1. The benefit of aggregation is 0 if δ1 A = δ1 B and, from (A10), is equal to δ 2γ 2[8 − 3γ 2 ] 2[4 − γ 2 ]2[1− γ 2 ] if δ1 A ≠ δ1 B. The probability that δ1 A ≠ δ1 B is 1/2. Hence, the expected benefit of aggregation is: δ 2γ 2[8 − 3γ 2 ] 4[4 − γ 2 ]2[1− γ 2 ] . (A11) The corollary then follows from the fact that the derivative of (A11) with respect to γ equals δ 2γ [32 −16γ 2 − 4γ 4 + 3γ 6 ] 2[4 − γ 2 ]3[1− γ 2 ]2 > 0. Proof of Proposition 3. In this proof, we derive the two key results (i) full disclosure by either firm cannot be sustained as an equilibrium, and (ii) aggregate disclosure by both firms can be sustained as an equilibrium. (The fact that aggregation yields the unique equilibrium outcome follows the same steps as detailed in Proposition 2. In this case, steps 1-3 follow for either firm regardless of the other firm's presumed strategy.) (i) Full disclosure is not an equilibrium. In this case, denote firm j's updated beliefs about firm k's cost subsequent to a disclosure by firm k by Pr j (δ k A ,δ k B ). The continuation game thus consists of each firm choosing a pricing strategy as a function of its information, as reflected in (A12). 28 Max pj i (δ j A ,δ j B ) [ Pr j (δ k A ,δ k B )[p j i (δ j A ,δ j B )- c − δ j i ]q j i ( p1 i (δ1 A ,δ1 B ), p2 i (δ2 A ,δ2 B )) (δk A ,δk B ) ∑ i=A,B ∑ ∀(δ j A ,δ j B ), j,k = 1,2, j ≠ k. (A12) Jointly solving the first-order conditions of (A12) yields: p j A (δ j A ,δ j B ) = α[2 − γ − γ 2 ] + 2[c + δ j A ] + γc 4 − γ 2 − γ 2δ j A[1− Pr k (δ j A , δ̃ j B )] δ̃ j B ∑ 4 − γ 2 + γ [ δ k A Pr j (δ k A ,δ k B )] (δk A ,δk B ) ∑ 4 − γ 2 , and p j B (δ j A ,δ j B ) = α[2 − γ − γ 2 ] + 2[c + δ j B ] + γc 4 − γ 2 − γ 2δ j B[1− Pr k (δ̃ j A ,δ j B )] δ̃ j A ∑ 4 − γ 2 + γ [ δ k B Pr j (δ k A ,δ k B )] (δk A ,δk B ) ∑ 4 − γ 2 , j,k = 1,2; j ≠ k. (A13) Substituting prices from (A13) into (A12) yields Π j (δ j A ,δ j B ), firm j profit for any continuation game. To see that fully revealing disclosure is not an equilibrium for either firm, suppose (δ1 A ,δ1 B ) = (δ ,−δ ). If firm 1 discloses this value, its profit is Π1(δ ,−δ ) with Pr2 (δ ,−δ ) = 1. If instead firm 1 submits an aggregate disclosure (δ1 A + δ1 B = 0), denote the off-equilibrium belief by Pr2 (δ ,−δ ) = p and Pr2 (−δ ,δ ) = 1− p. Taking the difference in profits, firm 1's profit in the continuation game under fully revealing disclosure less that upon disclosing an aggregate signal equals − 2δ 2γ 2 (1− p) 4 − γ 2 (1+ p) − 2γ (Pr1(δ ,−δ ) − Pr1(−δ ,δ )) [ ] [4 − γ 2 ]2[1− γ 2 ] . Thus, a necessary condition for full disclosure to be an equilibrium for firm 1 is p = 1. When (δ1 A ,δ1 B ) = (−δ ,δ ), the same comparison reveals that another necessary condition for full disclosure to be an equilibrium is p = 0. Since the two identified necessary conditions cannot both hold, a fully revealing equilibrium does not exist. By symmetry, the same is true for firm 2. (ii) Aggregation by each firm constitutes an equilibrium. First, we compare aggregate disclosure with full disclosure for firm 1, given any firm 2 disclosure strategy. Ifδ1 A = δ1 B , the two disclosure regimes are equivalent. If δ1 A ≠ δ1 B , firm 1 profit under aggregation is Π1(−δ ,δ ) when (δ1 A ,δ1 B ) = (−δ ,δ ) (= Π1(δ ,−δ ) when (δ1 A ,δ1 B ) = (δ ,−δ )) with Pr2 (δ ,−δ ) = Pr2 (−δ ,δ ) = 1 / 2 . In contrast, upon fully disclosing, firm 1 profit is Π1(−δ ,δ ) with Pr2 (−δ ,δ ) = 1 (= Π1(δ ,−δ ) with 29 Pr2 (δ ,−δ ) = 1). Comparing profits in each case reveals that aggregation yields higher profit by δ 2γ 2[8 − 3γ 2 − 4γ (Pr1(δ ,−δ ) − Pr1(−δ ,δ ))] 2[4 − γ 2 ]2[1− γ 2 ] > 0. (A14) (A14) implies that aggregation is preferred to full disclosure for all (δ1 A ,δ1 B ) and for any firm 2 disclosure. As before, the following off-equilibrium beliefs ensure aggregation is also preferred to any strategy that entails firm 1 withholding in one or both markets: Pr2 (−δ,−δ ) = 1 for no disclosure, Pr2 (δ1 A ,−δ ) = 1 for disclosure of only δ1 A , and Pr2 (−δ ,δ1 B ) = 1 for disclosure of only δ1 B . Thus, for any firm 2 disclosure strategy, firm 1's equilibrium disclosure strategy is achieved by aggregation. By symmetry, the same is true of firm 2. This completes the proof of the proposition. Proof of Proposition 4. In this proof, we again derive the two key results (i) full disclosure by firm 1 cannot be sustained as an equilibrium, and (ii) aggregate disclosure by firm 1 can be sustained as an equilibrium. (The fact that aggregation yields the unique equilibrium outcome follows the steps 1-3 as detailed in Proposition 2 with the only change being that unfavorable news in the Cournot/demand setting corresponds to low demand (−θ ) while it corresponded to high cost ( +δ ) in the Bertrand/cost setting.) (i) Full disclosure is not an equilibrium. Denote firm 2's updated beliefs subsequent to a disclosure by Pr(θ1 A ,θ1 B ). The continuation game here consists of firm 1 choosing its quantity as a function of its information, q1 i (θ1 A ,θ1 B ), as reflected in (A15), and firm 2 choosing its quantity under its updated beliefs, q2 i , reflected in (A16). Max q1 i (θ1 A ,θ1 B ) [α + θ1 i − q1 i (θ1 A ,θ1 B ) − γq2 i - c ]q1 i (θ1 A ,θ1 B ), ∀(θ1 A ,θ1 B i=A,B ∑ ). (A15) Max q2 i Pr(θ1 A ,θ1 B )[α + θ1 i − q2 i − γq1 i (θ1 A ,θ1 B )- c ]q2 i (θ1 A ,θ1 B ) ∑ ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ i=A,B ∑ . (A16) Jointly solving the first-order conditions of (A15) and (A16) yields: q1 A (δ1 A ,δ1 B ) = α + δ1 A − c + γδ1 A[1− Pr(δ1 A , δ̃1 B )] δ̃1 B ∑ 2 + γ , q1 B (δ1 A ,δ1 B ) = α + δ1 B − c + γδ1 B[1− Pr(δ̃1 A ,δ1 B )] δ̃1 A ∑ 2 + γ , and 30 q2 i = α + δ1 i Pr(δ1 A ,δ1 B ) (δ1 A ,δ1 B ) ∑ − c 2 + γ . (A17) Substituting quantities from (A17) into (A15) yields Π̂1(θ1 A ,θ1 B ), firm 1 profit for any continuation game in the Cournot setting. We now argue that a fully revealing disclosure is not sustainable as an equilibrium. To see this, suppose (θ1 A ,θ1 B ) = (−θ,θ ). If firm 1 discloses this value, its profit is Π̂1(−θ,θ ) with Pr(−θ,θ ) = 1, which equals 2 (α − c )2 + θ 2 [ ] [2 + γ ]2 . Suppose instead firm 1 submits an aggregate disclosure (θ1 A + θ1 B = 0). For any feasible off-equilibrium beliefs Pr(−θ,θ ) = p and Pr(θ,−θ ) = 1− p, firm 1's profit in the continuation game, Π̂1(−θ,θ ) , equals 2 (α − c )2 + θ 2 (1+ γ (1− p))2 [ ] [2 + γ ]2 . Comparing profits, a necessary condition for full disclosure to be an equilibrium is p = 1. When (θ1 A ,θ1 B ) = (θ,−θ ), firm 1 profit under full disclosure is as before; with aggregate disclosure, the only change in the firm 1 profit expression is that "1-p" is replaced by "p". Thus, another necessary condition for full disclosure to be an equilibrium is p = 0. Obviously, the two identified necessary conditions cannot both hold, and so a fully revealing equilibrium does not exist. (ii) Aggregation by firm 1 is an equilibrium. First, we compare aggregate disclosure with full disclosure for firm 1. Ifθ1 A = θ1 B , the two disclosure regimes are equivalent. If θ1 A ≠ θ1 B , firm 1 profit under aggregation is Π̂1(θ,−θ ) when (θ1 A ,θ1 B ) = (θ,−θ ) (= Π̂1(−θ,θ ) when (θ1 A ,θ1 B ) = (−θ,θ )) with Pr(θ,−θ ) = Pr(−θ,θ ) = 1 / 2. In contrast, upon fully disclosing, firm 1 profit is Π̂1(θ,−θ ) with Pr(θ,−θ ) = 1 (= Π̂1(−θ,θ ) with Pr(−θ,θ ) = 1). Comparing profits in each case reveals that aggregation yields higher profit by θ 2γ [4 + γ ] 2[2 + γ ]2 > 0. (A18) (A18) implies that firm 1 prefers aggregation to full disclosure for all (θ1 A ,θ1 B ). As before, the following off-equilibrium beliefs ensure aggregation is also preferred to any strategy that entails firm 1 withholding in one or both markets: Pr(θ,θ ) = 1 for no disclosure, Pr(θ1 A ,θ ) = 1 for disclosure of only θ1 A , and Pr(θ,θ1 B ) = 1 for disclosure of only θ1 B . This completes the proof of the proposition. 31 Proof of Proposition 5. In this proof, we demonstrate the conditions under which full disclosure is an equilibrium. (The fact that aggregation yields the unique equilibrium outcome under these conditions follows the same steps as detailed in Proposition 2.) As before, denote firm 2's updated beliefs subsequent to a disclosure by Pr(δ1 A ,δ1 B ). The continuation game thus consists of firm 1 choosing a pricing strategy as a function of its information, p1 i (δ1 A ,δ1 B ), as reflected in (A19), and firm 2 choosing a pricing strategy under its updated beliefs, p2 i , reflected in (A20). Max p1 i (δ1 A ,δ1 B ) [p1 i (δ1 A ,δ1 B )- c i - δ1 i ]q1 i ( p1 i (δ1 A ,δ1 B ), p2 i ), ∀(δ1 A , i=A,B ∑ δ1 B ). (A19) Max p2 i Pr(δ1 A ,δ1 B )[p2 i - c i ]q2 i ( p1 i (δ1 A ,δ1 B ), p2 i ) (δ1 A ,δ1 B ) ∑ [ ] i=A,B ∑ . (A20) Jointly solving the first-order conditions of (A19) and (A20) yields the same prices as in (A7) with the only change being that α and c in p1 i (δ1 A ,δ1 B ) and p2 i are replaced by α i and c i , respectively. Substituting these prices into (A19) yields Π1(δ1 A,δ1 B), firm 1 profit for any continuation game. To determine whether aggregate disclosure is an equilibrium, we compare aggregate disclosure with full disclosure. Ifδ1 A = δ1 B , the two disclosure regimes are equivalent. If (δ1 A ,δ1 B ) = (δ ,−δ ), firm 1 profit under aggregation is Π1(δ ,−δ ) with Pr(δ ,−δ ) = Pr(−δ ,δ ) = 1 / 2 ; under full disclosure, it is Π1(δ ,−δ ) with Pr(δ ,−δ ) = 1. The profit under aggregation less that under full disclosure is: 2δγ 2[(α B − c B − α A + c A )(2 − γ − γ 2 ) + δ (8 − 3γ 2 )] 2[2 − γ ]2[1− γ 2 ] . (A21) Repeating this analysis when (δ1 A ,δ1 B ) = (−δ ,δ ), the difference in profits is: 2δγ 2[(α A − c A − α B + c B )(2 − γ − γ 2 ) + δ (8 − 3γ 2 )] 2[2 − γ ]2[1− γ 2 ] . (A22) Clearly, for aggregation to be an equilibrium, both (A21) and (A22) must be nonnegative. The condition for that to be the case is [α A − c A ]− [α B − c B ] ≤ δ[8 − 3γ 2 ] 2 − γ − γ 2 . (A23) When (A23) is satisfied, the following off-equilibrium beliefs ensure aggregation is also preferred to any strategy that entails firm 1 withholding in one or both markets: Pr(−δ,−δ ) = 1 for no disclosure, Pr(δ1 A ,−δ ) = 1 for disclosure of only δ1 A , and Pr(−δ ,δ1 B ) = 1 for disclosure of only δ1 B . This completes the proof of the proposition. 32 Proof of Corollary 2. (i) The condition in (A24) reflects that as the difference in the net intercepts in the two markets reduces, the easier it is to satisfy the condition for equilibrium. (ii) Cost variance is reflected by E[(c1 i )2 ]− E[c1 i ]2 = δ 2. Thus, as cost variance increases, so does the right-hand side of (A24), making the condition for equilibrium easier to satisfy. (iii) Taking the derivative of the right-hand side of (A24) reveals it is increasing in γ and, thus, as γ increases, the conditions for equilibrium are easier to satisfy. Proof of Proposition 6. (i) The important thing to note here is that under the disclosure strategy of segment aggregation, in the event of a disclosure δ1 A + δ1 B = 0, the rival's posterior belief Pr(δ ,−δ ) = [1 / 2][(1− ρ) 2] [1 / 2][(1− ρ) 2] + [1 / 2][(1− ρ) 2] = 1/ 2 = Pr(−δ ,δ ) . That is, under segment aggregation, the rival's posterior belief is free of the extent of cross-segment correlation. Given this, the fact that aggregation represents an equilibrium disclosure strategy, and that it replicates the unique equilibrium outcome follows precisely the steps in the proofs of Propositions 1 and 2. (ii) As before, the benefit of aggregation is 0 if δ1 A = δ1 B and, from (A10), is equal to δ 2γ 2[8 − 3γ 2 ] 2[4 − γ 2 ]2[1− γ 2 ] if δ1 A ≠ δ1 B. The probability that δ1 A ≠ δ1 B is [1 / 2][(1− ρ) 2] + [1 / 2][(1− ρ) 2] = (1− ρ) 2 . Hence, the expected benefit of aggregation is [1− ρ]δ 2γ 2[8 − 3γ 2 ] 4[4 − γ 2 ]2[1− γ 2 ] , which is decreasing in ρ . Proof of Corollary 3. If firm 1 acquires private cost information in only one market, the unraveling result in Proposition 1(i) applies. Given unraveling, the two markets are independent and thus the benefit of information acquisition arises only in the market in which information is obtained. Denote the profit improvement in market i from information acquisition by ψ i . If instead the firm obtained information in both markets, the benefit of information acquisition presuming it were to result in full disclosure is, by market independence, ψ A + ψ B. In this case, though, segment aggregation yields the unique equilibrium outcome. The benefit of segment aggregation relative to full disclosure is as in (A11). Since (A11) is strictly positive, the benefit of gathering information in both markets strictly exceeds the sum of the benefits of gathering information in either market individually. Proof of Corollary 4. Firm 1's net loss from mandatory disclosure requirements is as in (A11). What remains to show is the effect on firm 2 and consumers. In either case, the only difference 33 arises when δ1 A ≠ δ1 B. In firm 2's case, substituting prices from (A7) into (A6) yields firm 2 profit for any continuation game, Π2 . Taking the average of Π2 when Pr(δ ,−δ ) = 1 and Π2 when Pr(−δ ,δ ) = 1 and comparing that to Π2 with Pr(δ ,−δ ) = Pr(−δ ,δ ) = 1/ 2 yields firm 2's net benefit from mandatory disclosure requirements when δ1 A ≠ δ1 B. Weighting this benefit by the probability of δ1 A ≠ δ1 B reveals firm 2's net benefit from mandatory disclosure requirements: δ 2γ 2 [4 − γ 2 ]2[1− γ 2 ] . (A24) As for consumers, consumer surplus in any continuation game equals: CS = 1 2 [q1 i ( p1 i (δ1 A ,δ1 B ), p2 i )]2 + 2γq1 i ( p1 i (δ1 A ,δ1 B ), p2 i )q2 i ( p1 i (δ1 A ,δ1 B ), p2 i ) [ i=A,B ∑ + [q2 i ( p1 i (δ1 A ,δ1 B ), p2 i )]2 ]. (A25) Taking the average of CS when (δ1 A ,δ1 B ) = (δ ,−δ ), Pr(δ ,−δ ) = 1 and CS when (δ1 A ,δ1 B ) = (δ ,−δ ), Pr(−δ ,δ ) = 1, and comparing that to the average of CS when (δ1 A ,δ1 B ) = (δ ,−δ ), Pr(δ ,−δ ) = Pr(−δ ,δ ) = 1 / 2 and C S when (δ1 A ,δ1 B ) = (δ ,−δ ), Pr(δ ,−δ ) = Pr(−δ ,δ ) = 1 / 2 yields consumers' net loss from mandatory disclosure requirements when δ1 A ≠ δ1 B. Weighting this loss by the probability of δ1 A ≠ δ1 B reveals consumers' net loss from mandatory disclosure requirements: δ 2γ 2[4 + γ 2 ] 8[4 − γ 2 ]2[1− γ 2 ] . (A26) The net welfare loss from mandatory disclosure requirements is thus (A11) less (A24) plus (A26), or: δ 2γ 2[12 − 5γ 2 ] 8[4 − γ 2 ]2[1− γ 2 ] > 0. (A27) The fact that (A27) is positive for all γ confirms the corollary. 34 REFERENCES Berger, P., Hann, R. 2007. Segment profitability and the proprietary and agency costs of disclosure. The Accounting Review 82, 869-906. Berger, P., Ofek, E. 1995. Diversification's effect on firm value. 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