Under What Conditions Does the Manager Withhold Segment Information?

Abstract

This paper considers how a manager decides to disclose or withhold segment information in a capital market setting. In particular, we develop a multi-period model in which a manager in each period decides how to allocate her effort between two businesses. The profit earned in each segment is determined by the manager’s effort and ability as well as each segment’s market profitability and inherent uncertainty. In this setting, in contrast to the expectation of segment disclosure being withheld due to conflicts of interest between managers and shareholders, we identify the conditions under which the manager rationally withholds segment information and achieves higher social welfare. In a setting where the manager is concerned about the current stock price, disclosing more disaggregated information to the stock market does not necessarily lead to more efficient monitoring. The capital market values various segment earnings differently, and in response to this valuation, a rational manager may greatly alter her behavior, leading to inefficient outcomes.

Keywords

segment disclosure career concerns capital market social welfare

Introduction

This paper investigates the consequences of aggregate and segment reporting in a capital market setting. In particular, we identify the conditions under which managers rationally withhold segment information and achieve higher social welfare. These results are contrary to the stylized conception that segment disclosure is withheld as a result of conflicts of interest between managers and shareholders because withholding disaggregated information weakens market monitoring and thus enables managers to pursue their own objectives, which may not necessarily be in the best interests of shareholders (Bens et al., 2011; Berger & Hann, 2007; Hope & Thomas, 2008; Wang et al., 2011).

According to the Statement of Financial Accounting Standards No. 131 (SFAS 131), issued in 1997, disclosures about the segments of an enterprise are intended “to help users of financial statements: (a) better understand the enterprise’s performance, (b) better assess its prospects for future net cash flows, [and] (c) make more informed judgments about the enterprise as a whole” (Financial Accounting Standards Board, 1997). Despite the existence of a mandatory standard, however, there remain ample opportunities to exercise managerial discretion, such as regarding the identification of reportable segments.¹ A number of empirical studies use this segment reporting setting as a way of investigating managers’ motives to engage in discretionary disclosure (Bens et al., 2011; Berger & Hann, 2007; Botosan & Stanford, 2005; Ettredge et al., 2006; Harris, 1998; Hope et al., 2006, 2013; Hope & Thomas, 2008; Wang et al., 2011).

In this literature, one of the most cited hypotheses is that centered on agency costs (Bens et al., 2011; Berger & Hann, 2007; Hope & Thomas, 2008; Wang et al., 2011).² According to this hypothesis, segment disclosure is withheld as a result of conflicts of interest between managers and shareholders. For example, Berger and Hann (2007) argue that managers may exercise their discretion to conceal negative information about certain segments. Wang et al. (2011) posit that managers who take advantage of greater agency costs to engage in empire-building are more reluctant to reveal segment-level differences in growth. This hypothesis is based on the logic that enhanced disclosure mitigates the agency problem through greater outside monitoring.

However, stock market monitoring suffers from some limitations. For example, in a setting in which the manager is concerned about the current stock price, Stein (1989) shows that managers behave myopically to achieve higher stock prices at the expense of shareholders. Moreover, Stein (1989) shows that the more managers are concerned about stock prices, the worse the problem becomes. This finding suggests that disclosing information with a higher level of disaggregation to the stock market does not necessarily lead to more efficient monitoring. In fact, capital markets generally value various segments’ earnings differently (Bodnar et al., 1997, 2003; Chen & Zhang, 2003; Hope et al., 2006, 2008, 2009). In response to this capital market valuation, a rational manager may excessively alter her behavior, leading to inefficient outcomes.

In this paper, we seek to more precisely understand this underlying mechanism. We develop a multi-period model in which a firm manager decides in each period how to allocate her effort between two businesses (i.e., segments of the firm) by considering the firm’s stock price based on public information. The profit earned in each segment is determined by the manager’s effort and ability as well as each segment’s market profitability and inherent uncertainty. We assume that there is uncertainty, but no asymmetric information, about managers ability.

We show that managers rationally withhold segment information and achieve higher social welfare if (a) the segments have similar market profitability or (b) the segment with the more profitable market has a relatively high market uncertainty compared to the other segment. In particular, if the two markets have similar profitability levels, the stock prices under aggregated and segment disclosure cases are nearly identical. However, effort levels differ between the two cases, because under the segment disclosure case, the manager is more sensitive to the market’s reaction. Effort levels in the two segments are thus more volatile than those under the aggregated disclosure case, which is undesirable to minimize the total effort cost. Therefore, if the two segments have similar levels of market profitability, the manager withholds segment earnings information and achieve higher social welfare. Alternatively, if the market uncertainty in the more profitable market is higher under the segment disclosure case, the manager prefers to withhold segment earnings information and thus achieve higher social welfare. This arises because the capital market focuses on the market with greater information precision even if that market is less profitable, and in response, the manager allocates her effort inefficiently under the segment disclosure case.

We focus on equilibria in the stationary case when we examine a manager’s disclosure choice. However, our multi-period model can illustrate the dynamics before a stationary state is reached. In the numerical example, we assume that one market is mature and the other is growing. In other words, although one market is initially more profitable than the other, the less profitable market gradually catches up with the other market in profitability and eventually overtakes it. In this setting, we compare effort level and social welfare over time among the benchmark, aggregated, and segment disclosure cases.

We contribute to the disclosure theory literature by identifying the conditions under which managers withhold segment information and improve social welfare. This means that Blackwell’s theorem (Blackwell, 1953) does not hold in our setting as it states that in a standard single-person decision context, disaggregated information is superior to aggregate information. In our setting, the market price is constrained to be set as the break-even value; the capital market cannot mimic the pricing rule under the disaggregated disclosure case with an equivalent pricing rule under the aggregated disclosure case. This is why disaggregated information is not always superior to aggregate information. Some prior studies show that managers have incentives to withhold segment information, such as Einhorn (2005) and Ebert et al. (2017), but they do not consider the implications from the viewpoint of social welfare.

Our model also relates to other several studies. First, the literature on managerial short-termism emphasizes the inefficiencies that arise when managers are concerned about current stock prices instead of long-term value (Aghion & Stein, 2008; Bolton et al., 2006; Narayanan, 1985; Stein, 1989). The papers most closely related to our model are Holmström, (1982, 1999) Stein (1989), and Aghion and Stein (2008). In a seminal paper, Holmström (1982, 1999) provides a tractable model of career concerns. Stein (1989) extends this setting to one in which the manager is interested in both long-run earnings and the current stock price. We extend Stein (1989)’s work by considering the multi-segment and multi-task context. In addition, Stein (1989) considers how managers inflate short-term earnings at the expense of long-term earnings. This myopic behavior is denoted as real earnings management in the recent accounting literature. We do not consider earnings management but instead focus on the manager’s incentives regarding segment disclosure. Aghion and Stein (2008) also consider a multi-task situation in which the manager devotes effort to either increasing sales growth or improving per-unit profit margins. However, they consider a situation in which signals of both sales growth and profit margins are observed in the capital market, implying that they do not consider aggregate earnings disclosure.³

Second, our paper also relates to aggregation versus disaggregation issues in accounting (Arya et al., 2004; Arya & Mittendorf, 2011; Autrey et al., 2010; Demski & Frimor, 1999). Among these studies, Autrey et al. (2010) and Arya and Mittendorf (2011) are based on the career concerns model. Autrey et al. (2010) consider the interaction between the implicit incentives arising from career concerns and explicit contracts by using aggregated performance measures. The use of aggregated performance measures generally distorts the effort allocation among tasks, but the authors show that in such a setting career incentives combined with disaggregated disclosure can mitigate aggregation costs. A more closely related paper is Arya and Mittendorf (2011), which considers career incentives in the absence of explicit contracts and compares aggregate and disaggregate cases with a focus on the conditions under which aggregation can be beneficial. In contrast to these studies, we focus on the interactions between the manager’s effort allocation and the stock price in the capital market. This enables us to identify direct empirical implications for the disclosure choice of segment earnings information.

The remainder of this paper proceeds as follows. Section 2 describes the basic setting of our model. Section 3 provides a benchmark case as a basis for comparison and then analyzes aggregated and segment disclosure cases. Section 4 compares effort levels and stock prices across these cases and examines the conditions under which the manager chooses to withhold segment earnings information. In Section 5, we provide a numerical example before a stationary state is reached. Section 6 concludes. All proofs appear in the appendix.

The Model

There are two risk-neutral players—a firm manager and a capital market. The firm runs a business composed of two segments that are jointly managed by a manager. The manager allocates her effort level to overseeing the two businesses. We consider an infinite horizon model. First, the manager chooses and follows a policy on disclosing segment earnings information—the manager can disclose either aggregate earnings or those for each segment. We refer to these options as aggregated and segment disclosure cases, respectively. In each period t, the manager is endowed with a certain amount of time and decides how to allocate her time for the effort $e_{it} (i \in {s, m})$ between the two markets s and m; thus, the condition $e_{st} + e_{mt} = 1$ is satisfied for all t.⁴ The manager then discloses aggregate earnings $π_{t}$ under the aggregated disclosure case and segment earnings, $s_{t}$ and $m_{t}$ , under the segment disclosure case.

The firm’s earnings in period t are the sum of earnings in markets s and m, as follows:

π_{t} = s_{t} + m_{t} .

(1)

Both earnings depend on managerial ability as well as the manager’s allocation of effort, that is:

s_{t} = (a_{t} + e_{st}) q_{st} + ε_{st},

(2)

m_{t} = (a_{t} + e_{mt}) q_{mt} + ε_{mt},

(3)

where $a_{t}$ represents the manager’s ability, common to both markets, and $q_{it}$ denotes the profitability of market i ( $i \in {s, m}$ ).⁵ $ε_{it}$ is a random variable capturing shocks in market i; it is normally distributed with mean zero and precision (inverse of variance) $h_{i}$ , which is independent of $ε_{jt} (j \neq i)$ .⁶ $ε_{it}$ is also independently distributed across time. Equations (2) and (3) signify that both the manager’s ability and her effort are positively affected by market profitability: the higher market profitability, the greater is the impact of the manager’s ability and effort.

We assume that the manager’s ability is initially unknown to both the manager herself and the market. There is no information asymmetry between the manager and the market with respect to the manager’s ability in our model. Her ability is inferred at the end of period t based on the firm’s reported earnings. According to Autrey et al. (2010), the manager’s ability can be interpreted as her “gift” for performing that job. In our model, a new manager has no understanding of her own fit for the business segments. Managerial ability in period t depends on that in the previous period and a disturbance term:

a_{t} = a_{t - 1} + u_{t},

(4)

where $u_{t}$ is a random variable that is normally distributed with mean zero and precision $h_{u}$ and is independent of all the other variables. We assume that the initial level of the manager’s ability, $a_{0}$ , is normally distributed with mean $μ_{0}$ and precision $h_{0}$ and is also independent of all the other variables.

The capital market sets the stock price depending on the firm’s disclosure policy for segment earnings. We assume that the capital market cannot directly observe the manager’s effort level. Under the aggregated disclosure case, the manager discloses aggregate earnings, $π_{t}$ , and the capital market observes only these. Under the segment disclosure case, the manager discloses segment earnings, $s_{t}$ and $m_{t}$ , and the capital market observes these earnings. In both cases, the stock price forms accordingly.

The firm immediately pays out all earnings in the form of a dividend, which is assumed to entail no taxes or other dissipative costs. After the dividend payout, the market price of the firm’s stock at the end of period t is thus given by

P_{t} = E [\sum_{j = t + 1}^{\infty} δ^{j - t} π_{j} | Ω_{t}^{M}],

(5)

where $δ = 1 / (1 + r)$ , with r being a discount rate, and $Ω_{t}^{M}$ is the market information set at the end of period t (the time at which the market sets the stock price). $Ω_{t}^{M}$ depends on the firm’s disclosure policy: $Ω_{t}^{AD} = {π_{1}, π_{2}, \dots, π_{t}}$ under the aggregated disclosure case and $Ω_{t}^{SD} = {s_{1}, m_{1}, s_{2}, m_{2}, \dots, s_{t}, m_{t}}$ under the segment disclosure case. We denote stock prices under aggregated and segment disclosure cases as $P_{t}^{AD}$ and $P_{t}^{SD}$ , respectively.

The manager is concerned about not only current-period earnings but also the current stock price. The manager’s stock price preference is modeled simply by adding it to her utility. This term can be interpreted as her preference for the stock price. The manager allocates her effort, $e_{st}$ and $e_{mt}$ , to maximize her expected utility at period t, which is

E U_{t} = E [U_{t} | Ω_{t - 1}] = E [θ_{π} π_{t} + θ_{p} P_{t} - \frac{c_{s}}{2} e_{st}^{2} - \frac{c_{m}}{2} e_{mt}^{2} | Ω_{t - 1}],

(6)

where $U_{t}$ denotes the manager’s utility at period t, $θ_{π}$ and $θ_{p}$ are the incentive weights on current-period earnings and the stock price, respectively, and $Ω_{t - 1}$ is a manager’s information set at period t, which is based on all the information available prior to the release of earnings (the time when the manager decides her effort level). We assume that the manager’s information set is ${e_{s 1}, e_{m 1}, π_{1}, e_{s 2}, e_{m 2}, π_{2}, \dots, e_{s, t - 1}, e_{m, t - 1}, π_{t - 1}}$ under the aggregated disclosure case and ${e_{s 1}, e_{m 1}, s_{1}, m_{1}, e_{s 2}, e_{m 2}, s_{2}, m_{2}, \dots, e_{s, t - 1}, e_{m, t - 1}, s_{t - 1}, m_{t - 1}}$ under the segment disclosure case. This means that the manager can observe only aggregated earnings under the aggregated disclosure case, while she can observe the segment earnings under the segment disclosure case. The reason why we use only one notation for different information sets is that manager’s optimization does not change based on either information set.⁷ The incentive weights satisfy $0 \leq θ_{π} \leq 1$ and $0 \leq θ_{p} \leq 1$ . We assume that the manager’s utility function depends on accounting earnings and the stock price at the end of period t. This utility function corresponds to, for example, Stein (1989) and Ewert and Wagenhofer (2005). The manager’s interest in accounting earnings, for example, results from an explicit accounting-based bonus program, debt covenants, or upcoming tenure decisions. The interest in stock price stems from the manager’s intention to sell shares she owns, an explicit stock-based incentive contract, or a desire to raise new capital. When the manager exerts effort in each segment, this entails convex psychological effort costs, in which $c_{s}$ and $c_{m}$ are the known coefficients of the marginal cost of exerting effort in markets s and m, respectively. This formulation is also similar to Mauch and Schöndube (2019). The convex cost function would be reasonable if engaging in one segment gets more complicated when the manager already takes time for its segment. The manager tends to prioritize working on the easy parts of the tasks to achieve first results and leave the more complex parts for later points in time. Therefore, spending additional time on a segment to which several hours have already been devoted is more costly than spending time on a segment that is still in its nascent stages. For the sake of simplicity, we assume that the manager’s discount rate is equal to that of the market.

The timing of events is as follows. At the outset, the manager commits to a disclosure policy on segment earnings information. In particular, she chooses to disclose either aggregate earnings or each segment’s earnings. In each period t, the manager chooses her effort levels, $e_{st}$ and $e_{mt}$ , to maximize her expected utility. And then, the manager discloses aggregate earnings $π_{t}$ or segment earnings, $s_{t}$ and $m_{t}$ , according to the predetermined disclosure policy. At the end of period t, the stock price, $P_{t}^{AD}$ under the aggregated disclosure case or $P_{t}^{SD}$ under the segment disclosure case, is formed.

Analysis

Benchmark Case

First, we define the benchmark in our model. The natural benchmark is the case in which the manager maximizes social welfare that is defined as the value created by the manager minus the (psychological) cost of providing them. Therefore, the social welfare at period t, $V_{t}$ , as the firm’s dividend net of the effort costs, which is defined as

V_{t} = E [π_{t} - \frac{c_{s}}{2} e_{st}^{2} - \frac{c_{m}}{2} e_{mt}^{2} | Ω_{t - 1}] .

(7)

This benchmark corresponds to the case that the manager receives all dividends ( $θ_{π} = 1$ ) and does not care about the stock price ( $θ_{p} = 0$ ).⁸ This benchmark also corresponds to the case that the manager only cares about dividends and the manager’s ability is public information ex ante. The benchmark effort levels are defined as the solution to maximizing equation (7) subject to $e_{st} + e_{mt} = 1$ for each period t. The maximization problem in period t is expressed as follows:

\begin{matrix} \max_{e_{st}, e_{mt}} (μ_{t} + e_{st}) q_{st} + (μ_{t} + e_{mt}) q_{mt} - \frac{c_{s}}{2} e_{st}^{2} - \frac{c_{m}}{2} e_{mt}^{2}, \\ subject to e_{st} + e_{mt} = 1, \end{matrix}

where $μ_{t} = E [a_{t} | Ω_{t - 1}]$ . Focusing on the interior solutions, we derive the benchmark effort levels in period t, $e_{st}^{BM}$ and $e_{mt}^{BM}$ , as follows:⁹

e_{st}^{BM} = \frac{(q_{st} - q_{mt}) + c_{m}}{c_{s} + c_{m}} and e_{mt}^{BM} = \frac{(q_{mt} - q_{st}) + c_{s}}{c_{s} + c_{m}} .

(8)

Equation (8) states that the effort levels under the benchmark case depend on the difference in market profitability between the two segments and the costs of exerting effort. If the cost parameter in one market increases, the manager decreases her level of effort in that market. The level of effort exerted in one market is related to that in the other market because we assume that the manager faces a trade-off between the efforts in both segments. We also calculate social welfare at period t under the benchmark case. By substituting equation (8) into (7), we derive

V_{t}^{BM} = (q_{st} + q_{mt}) μ_{t} + \frac{{(q_{st} - q_{mt})}^{2}}{2 (c_{s} + c_{m})} + \frac{q_{st} c_{m} + q_{mt} c_{s}}{c_{s} + c_{m}} - \frac{c_{s} c_{m}}{2 (c_{s} + c_{m})} .

(9)

According to equation (9), the first term corresponds to total earnings based on the expected value of the manager’s ability, the second and third terms represent total earnings based on the manager’s effort, and the fourth term is the effort cost. Total earnings based on the manager’s effort can be decomposed into two terms. The second term is related to the difference in market profitability and the third term is not.

Equilibrium Under the Aggregated Disclosure Case

In this section, we examine the aggregated disclosure case, in which the manager only discloses aggregate earnings, $π_{t}$ . Before solving the utility maximization problem of the manager, we explain the belief update of the capital market expectation of the manager’s ability. The capital market updates its expectation of the manager’s ability after observing reported earnings. Under the aggregated disclosure case, the market expects that the manager’s ability at period $t + 1$ , $a_{t + 1}$ , is normally distributed with mean $μ_{t + 1}^{AD}$ and precision $h_{t + 1}^{AD}$ . By using the properties of the normal distribution, the conditional expectation of the manager’s ability at period $t + 1$ can be expressed as follows:

μ_{t + 1}^{AD} \equiv E [a_{t + 1} | Ω_{t}^{AD}] = μ_{t}^{AD} + w_{t} Z_{t} .

(10)

In equation (10), we define the terms $\frac{{(q_{st} + q_{mt})}^{2} \frac{h_{s} h_{m}}{h_{s} + h_{m}}}{h_{t}^{AD} + {(q_{st} + q_{mt})}^{2} \frac{h_{s} h_{m}}{h_{s} + h_{m}}}$ as a weight, $w_{t}$ and $\frac{π_{t} - E [π_{t} | Ω_{t - 1}^{AD}]}{q_{s t} + q_{m t}}$ as a signal, $Z_{t}$ , which represents an adjustment based on the “Earnings Surprise.” $E [π_{t} | Ω_{t - 1}^{AD}]$ is the expected value of reported earnings conditional on the market information set in period $t - 1$ under the aggregated disclosure case, which is equal to $(q_{st} + q_{mt}) μ_{t}^{AD} + q_{st} {\hat{e}}_{st} + q_{mt} {\hat{e}}_{mt}$ , where ${\hat{e}}_{it}$ is the market’s conjecture of the manager’s effort level in market $i \in {s, m}$ . We easily find that $E [Z_{t} | Ω_{t - 1}^{AD}] = 0$ . The conditional expectation of the manager’s ability in period $t + 1$ can be expressed as the sum of the ex-ante expected value of the manager’s ability ( $μ_{t}^{AD}$ ) and the product of the weight and the realized value of the signal ( $Z_{t}$ ). The weight is determined by the ex-ante precision of the manager’s ability ( $h_{t}^{AD}$ ) and the conditional precision of the signal given the ex-ante manager’s ability ( $h_{Zt}$ ). In particular, this conditional precision can be expressed as follows:

h_{Zt} \equiv \frac{1}{Var (Z_{t} | a_{t})} = {(q_{st} + q_{mt})}^{2} \frac{h_{s} h_{m}}{h_{s} + h_{m}} .

In addition, the conditional variance of the manager’s ability at period $t + 1$ , $1 / h_{t + 1}^{AD}$ , can be calculated as follows:

\frac{1}{h_{t + 1}^{AD}} = \frac{1}{h_{t}^{AD} + h_{Zt}} + \frac{1}{h_{u}} .

The interpretation of equation (10) is as follows. The weight $w_{t}$ represents the coefficient that increases the expected value of the manager’s ability in the next period according to the changes in the signal, $Z_{t}$ . In other words, after the capital market observes reported earnings, it adjusts its belief proportional to the weight if they are different from the ex ante expected value of reported earnings. Updating this belief, the difference between the realized and expected values of reported earnings is divided by the sum of market profitability ( $q_{st} + q_{mt}$ ), because the capital market must extract information about the manager’s ability from reported earnings.¹⁰

We next explain the manager’s problem. In each period, the manager chooses $e_{st}$ ( $e_{mt}$ ) to maximize her expected utility, subject to the constraint that $e_{st} + e_{mt} = 1$ . The manager’s problem at period t is as follows:

\begin{matrix} \max_{e_{st}, e_{mt}} E [θ_{π} π_{t} + θ_{p} P_{t}^{AD} - \frac{c_{s}}{2} e_{st}^{2} - \frac{c_{m}}{2} e_{mt}^{2} | Ω_{t - 1}] \\ = E [θ_{π} π_{t} + θ_{p} \sum_{j = t + 1}^{\infty} E [δ^{j - t} π_{j} | Ω_{t}^{AD}] | Ω_{t - 1}] - \frac{c_{s}}{2} e_{st}^{2} - \frac{c_{m}}{2} e_{mt}^{2}, \\ subject to e_{st} + e_{mt} = 1 . \end{matrix}

(11)

Solving this problem yields the equilibrium effort levels and stock price, as summarized in the following proposition.^11,12

Proposition 1

Under the aggregated disclosure case, the equilibrium effort levels and stock price are

e_{st}^{AD} = \frac{(q_{st} - q_{mt}) β_{t}^{AD} + c_{m}}{c_{s} + c_{m}},

(12)

e_{mt}^{AD} = \frac{(q_{mt} - q_{st}) β_{t}^{AD} + c_{s}}{c_{s} + c_{m}},

(13)

P_{t}^{AD} = \sum_{j = t + 1}^{\infty} δ^{j - t} ((q_{sj} + q_{mj}) μ_{t + 1}^{AD} + \frac{{(q_{sj} - q_{mj})}^{2} β_{j}^{AD}}{c_{s} + c_{m}} + \frac{q_{sj} c_{m} + q_{mj} c_{s}}{c_{s} + c_{m}}),

(14)

where $β_{j}^{AD} = θ_{π} + θ_{p} \frac{w_{t}}{q_{st} + q_{mt}} (\sum_{k = j + 1}^{\infty} δ^{k - j} (q_{sk} + q_{mk}))$ , $w_{t} = \frac{h_{Zt}}{h_{t}^{AD} + h_{Zt}}$ , $h_{Zt} = {(q_{st} + q_{mt})}^{2} \frac{h_{s} h_{m}}{h_{s} + h_{m}}$ , and $μ_{t + 1}^{AD} = E [a_{t + 1} | Ω_{t}^{AD}] = μ_{t}^{AD} + w_{t} \frac{π_{t} - E [π_{t} | Ω_{t - 1}^{AD}]}{q_{st} + q_{mt}}$ .

Equations (12)–(14) represent the optimal effort levels in markets s and m and the stock price in period t under the aggregated disclosure case, respectively. In these equations, $β_{t}^{AD}$ is a total effort incentive coefficient for the manager, which can be decomposed into incentives from earnings ( $θ_{π}$ ) and the stock price ( $θ_{p} \frac{w_{t}}{q_{st} + q_{mt}} (\sum_{k = t + 1}^{\infty} δ^{k - t} (q_{sk} + q_{mk}))$ ). $β_{t}^{AD}$ is equal to one under the benchmark case in which the manager maximizes social welfare. Therefore, we can also interpret $β_{t}^{AD}$ as a distortion from the point of view of social welfare maximization. As shown in equations (12) and (13), the effort level exerted in each market depends on the effort costs in both markets, relative market profitability, and total effort incentive. The relationship between effort levels and effort costs are the same as under the benchmark case. Further, under the aggregated disclosure case, if market s (m) is more profitable than market m (s), the rise in total effort incentive increases the optimal level of effort in market s (m). The stock price in period t is expressed in equation (14) as the discounted value of expected future earnings. As in equation (9), the first term in the parenthesis corresponds to total earnings based on the expected value of the manager’s ability, while the second and third terms represent total earnings based on the manager’s effort. The equation implies that if the manager achieves higher than expected earnings, the stock price increases through a rise in the capital market conjecture of the manager’s ability.

Equilibrium Under the Segment Disclosure Case

Next, we examine the case in which the manager discloses both segments’ earnings, $s_{t}$ and $m_{t}$ . As under the aggregated disclosure case, before solving the manager’s problem, we explain the belief update of the capital market expectation of the manager’s ability. The capital market updates its expectation of the manager’s ability after observing reported earnings for each segment. Under the segment disclosure case, the market expects that the manager’s ability at period $t + 1$ , $a_{t + 1}$ , is normally distributed with mean $μ_{t + 1}^{SD}$ and precision $h_{t + 1}^{SD}$ . The expected value of the manager’s ability at period $t + 1$ can be expressed as follows:

μ_{t + 1}^{SD} \equiv E [a_{t + 1} | Ω_{t}^{SD}] = μ_{t}^{SD} + w_{st} Z_{st} + w_{mt} Z_{mt} .

(15)

In equation (15), we define the terms $\frac{q_{i t}^{2} h_{i}}{h_{t}^{SD} + q_{i t}^{2} h_{i} + q_{j t}^{2} h_{j}} i \in {s, m} (i \neq j)$ as a weight, $w_{it}$ and $\frac{i_{t} - E [i_{t} | Ω_{t - 1}^{SD}]}{q_{it}}, i \in {s, m}$ as a signal, $Z_{it}$ , where $E [i_{t} | Ω_{t - 1}^{SD}]$ is the expected value of segment earnings in market $i \in {s, m}$ conditional on the market information set in period $t - 1$ under the segment disclosure case. $E [i_{t} | Ω_{t - 1}^{SD}]$ is equal to $(μ_{t}^{SD} + {\hat{e}}_{it}) q_{it}$ , where ${\hat{e}}_{it}$ is the market’s conjecture of the manager’s effort level in market $i \in {s, m}$ in period t. We easily find that $E [Z_{it} | Ω_{t - 1}^{SD}] = 0$ . The conditional expected value of the manager’s ability in period $t + 1$ can be expressed as the sum of the ex-ante expected value of the manager’s ability ( $μ_{t}^{SD}$ ) and the products of the weight and the realized value of the signal ( $w_{st} Z_{st}$ and $w_{mt} Z_{mt}$ ). The weights are determined by the ex-ante precision of the manager’s ability ( $h_{t}^{SD}$ ) and the conditional precision of the signal ( $h_{Zit}$ ) given the ex-ante manager’s ability ( $a_{t}$ ). This conditional precision is calculated as $h_{Zit} \equiv \frac{1}{Var (Z_{it} | a_{t})}$ . Moreover, the conditional variance of the manager’s ability in period $t + 1$ , $1 / h_{t + 1}^{SD}$ , can be calculated as follows:

\frac{1}{h_{t + 1}^{SD}} = \frac{1}{h_{t}^{SD} + h_{Zst} + h_{Zmt}} + \frac{1}{h_{u}} .

The interpretation of equation (15) is as follows. The weight $w_{it}$ represents the coefficient that increases the expected value of the manager’s ability in the next period according to the changes in adjusted segment earnings in market $i \in {s, m}$ , $(i_{t} - E [i_{t} | Ω_{t}^{SD}]) / q_{it}$ . In other words, after observing segment earnings, the capital market adjusts its belief proportional to the weight if they are different from the ex ante expected value of segment earnings. Updating this belief, the difference between the realized and expected values of segment earnings is divided by market profitability ( $q_{it}$ ), because the capital market must extract information about the manager’s ability from the reported segment earnings in each market.

At period t, the manager chooses $e_{st}$ ( $e_{mt}$ ) to maximize her expected utility subject to $e_{st} + e_{mt} = 1$ . This problem can be expressed as follows:

\begin{matrix} \max_{e_{st}, e_{mt}} E [θ_{π} π_{t} + θ_{p} P_{t}^{SD} - \frac{c_{s}}{2} e_{st}^{2} - \frac{c_{m}}{2} e_{mt}^{2} | Ω_{t - 1}] \\ = E [θ_{π} π_{t} + θ_{p} \sum_{j = t + 1}^{\infty} E [δ^{j - t} π_{j} | Ω_{t}^{SD}] | Ω_{t - 1}] - \frac{c_{s}}{2} e_{st}^{2} - \frac{c_{m}}{2} e_{mt}^{2}, \\ subject to e_{st} + e_{mt} = 1 . \end{matrix}

The equilibrium effort levels and stock price under the segment disclosure case are summarized in the following proposition.¹³

Proposition 2

Under the segment disclosure case, the equilibrium effort levels and stock price are

e_{st}^{SD} = \frac{(q_{st} - q_{mt}) β_{t}^{SD} + c_{m}}{c_{s} + c_{m}},

(16)

e_{mt}^{SD} = \frac{(q_{mt} - q_{st}) β_{t}^{SD} + c_{s}}{c_{s} + c_{m}},

(17)

P_{t}^{SD} = \sum_{j = t + 1}^{\infty} δ^{j - t} ((q_{sj} + q_{mj}) μ_{t + 1}^{SD} + \frac{{(q_{sj} - q_{mj})}^{2} β_{j}^{SD}}{c_{s} + c_{m}} + \frac{q_{sj} c_{m} + q_{mj} c_{s}}{c_{s} + c_{m}}),

(18)

where $β_{j}^{SD} = θ_{π} + θ_{p} \frac{w_{st} - w_{mt}}{q_{st} - q_{mt}} (\sum_{k = j + 1}^{\infty} δ^{k - j} (q_{sk} + q_{mk}))$ , $w_{it} = \frac{h_{Zit}}{h_{t}^{SD} + h_{Zst} + h_{Zmt}}$ , $h_{Zit} = q_{it}^{2} h_{i}$ , and $μ_{t + 1}^{SD} = E [a_{t + 1} | Ω_{t}^{SD}] = μ_{t}^{SD} + w_{st} \frac{s_{t} - E [s_{t} | Ω_{t - 1}^{SD}]}{q_{st}} + w_{mt} \frac{m_{t} - E [m_{t} | Ω_{t - 1}^{SD}]}{q_{mt}}$ .¹⁴

Equations (16)–(18) represent the optimal effort levels in period t in markets s and m and the stock price under the segment disclosure case, respectively. Similar to the aggregated disclosure case, $β_{t}^{SD}$ is the total effort incentive coefficient for the manager, which can be decomposed into incentives from earnings ( $θ_{π}$ ) and the stock price ( $θ_{p} \frac{w_{s t} - w_{m t}}{q_{s t} - q_{m t}} (\sum_{k = t + 1}^{\infty} δ^{k - t} (q_{s k} + q_{m k}))$ ). As shown in equations (16) and (17), the optimal level of effort in each market is the same as that under the aggregated disclosure case except for the total effort incentive coefficient, $β_{t}^{SD}$ . The stock price in period t is expressed in equation (18) as the discounted value of expected future earnings. In equation (18), the first term in the parenthesis corresponds to total earnings based on the expected value of the manager’s ability, while the second and third terms represent total earnings based on the manager’s effort. The equation implies that if the manager achieves higher than expected segment earnings in each market, the stock price increases through a rise in the capital market conjecture of the manager’s ability.

Comparison Between Aggregated and Segment Disclosure Cases

In this section, we compare the equilibrium results for effort levels, stock prices, and the manager’s expected utility between aggregated and segment disclosure cases. We have derived propositions in terms of the equilibrium levels of effort and stock prices in period t. Although it is easy to compare effort levels in period t between aggregated and segment disclosure cases, comparisons of the stock price and expected utility regarding disclosure choice are less clear-cut, since they depend not only on current earnings, but also on all future sequences of market profitability and total effort incentive.

The point, however, is that we specify the conditions that withholding segment earnings dominates disclosing them in a variety of circumstances. To make our comparisons more manageable, we assume that the market profitability is time-invariant, that is, $q_{st} = q_{s}$ and $q_{mt} = q_{m}$ for all t. Furthermore, we assume the stationary state in which the precision of manager’s ability is constant over time. In particular, we derive time-invariant or stationary multipliers in an updating rule—namely, $w_{t}$ under the aggregated disclosure case and $w_{it}$ under the segment disclosure case. The stationarity assumption is commonly found in several previous studies, including the original work of Holmström (1999) and the more recent research of Bar-Isaac & Hörner (2014), Sato (2014), and Acharya and Lambrecht (2015). One of the reason why we focus on the stationary state is that the dynamics system under aggregated and segment disclosure cases converges to it as $t \to \infty$ . Note that when market profitability is time-invariant, the precision of the signal satisfies $h_{Zt} = h_{Z} = (q_{s} + q_{m})^{2} \frac{h_{s} h_{m}}{h_{s} + h_{m}}$ , which is necessary for the stationary state. The effort levels and expected value of stock prices in the stationary case under both cases can be derived as follows:

e_{s}^{d *} = \frac{(q_{s} - q_{m}) β^{d *} + c_{m}}{c_{s} + c_{m}},

(19)

e_{m}^{d *} = \frac{(q_{m} - q_{s}) β^{d *} + c_{s}}{c_{s} + c_{m}},

(20)

P^{d *} = \frac{δ}{1 - δ} ((q_{s} + q_{m}) μ_{0} + \frac{δ {(q_{s} - q_{m})}^{2} β^{d *}}{c_{s} + c_{m}} + \frac{q_{s} c_{m} + q_{m} c_{s}}{c_{s} + c_{m}}),

(21)

where $d \in {AD, SD}$ , $β^{AD *} = θ_{π} + θ_{p} \frac{δ}{1 - δ} w^{*}$ , $w^{*} = \frac{{(q_{s} + q_{m})}^{2} \frac{h_{s} h_{m}}{h_{s} + h_{m}}}{h^{AD *} + {(q_{s} + q_{m})}^{2} \frac{h_{s} h_{m}}{h_{s} + h_{m}}}$ , $β^{SD *} = θ_{π} + θ_{p} \frac{δ}{1 - δ} \frac{w_{s}^{*} - w_{m}^{*}}{q_{s} - q_{m}} (q_{s} + q_{m})$ , $w_{i}^{*} = \frac{q_{i}^{2} h_{i}}{h^{SD *} + q_{s}^{2} h_{s} + q_{m}^{2} h_{m}}, i \in {s, m}$ .

Note that we evaluate stock prices at the beginning of the first period for expositional purposes. In this case, $E [μ_{t}^{AD} | Ω_{0}] = E [μ_{t}^{SD} | Ω_{0}] = μ_{0}$ is satisfied because everyone lacks information at that time and thus uses the expected value at the beginning of the first period.

Comparisons of Effort Levels and Stock Prices

By comparing effort levels between aggregated and segment disclosure cases, as shown in equations (19), we derive the following proposition.

Proposition 3

(a) The effort level exerted in market s under the aggregated disclosure case is larger than that under the segment disclosure case if and only if

\frac{(q_{s}^{2} - q_{m}^{2}) \frac{h_{s} h_{m}}{h_{s} + h_{m}}}{h^{AD *} + {(q_{s} + q_{m})}^{2} \frac{h_{s} h_{m}}{h_{s} + h_{m}}} > \frac{q_{s}^{2} h_{s} - q_{m}^{2} h_{m}}{h^{SD *} + q_{s}^{2} h_{s} + q_{m}^{2} h_{m}} .

(b) When the markets have the same profitability, the effort level exerted in market s (m) is less (greater) under the aggregated disclosure case than under the segment disclosure case if the market uncertainty is lower in market s than in market m. In this case, the effort levels under the aggregated disclosure case correspond to those under the benchmark case.

(c) When market s is more profitable than market m and the conditional precision is lower for market s than for market m ( $q_{s}^{2} h_{s} < q_{m}^{2} h_{m}$ ), more effort is exerted in market s under the aggregated disclosure case than under the segment disclosure case.

The intuition behind Proposition 3 is as follows. Part (a) states that the difference in effort levels between aggregated and segment disclosure cases depends on market profitability, the precision of shocks, and the precision of manager’s ability. Part (b) shows that when both markets have the same profitability, the difference in effort depends only on the difference in the precision of shocks. In this case, the effort level under the aggregated disclosure case corresponds to that under the benchmark case because there is no incentive for the manager to differentiate her effort level across the two markets. In other words, the manager cannot inform the market of her ability by engaging more actively in one market than in the other. On the contrary, under the segment disclosure case, even when the markets have the same profitability, the manager exerts more effort in one market. In this case, the manager tries to inflate her ability by increasing her effort in the market with lower market uncertainties. She does so because the capital market observes more information about her ability from more informative segment earnings. Part (c) states that when the conditional precision is lower in the more profitable market, the manager’s effort level in more profitable market under the aggregated disclosure case is higher than that under the segment disclosure case. This comes from the similar reason in part (b). That is, the manager faces a trade-off between maximizing earnings and informing her ability under the segment disclosure case, which leads to exert a lower effort in more profitable market.

We next investigate the difference in stock prices between aggregated and segment disclosure cases. Taking the difference in the expected stock price between aggregated and segment disclosure cases, we derive the following proposition.

Proposition 4

(a) When the markets have different levels of profitability, the stock price is higher under the aggregated disclosure case than under the segment disclosure case if and only if

\frac{(q_{s} + q_{m}) \frac{h_{s} h_{m}}{h_{s} + h_{m}}}{h^{AD *} + {(q_{s} + q_{m})}^{2} \frac{h_{s} h_{m}}{h_{s} + h_{m}}} > \frac{1}{q_{s} - q_{m}} \frac{q_{s}^{2} h_{s} - q_{m}^{2} h_{m}}{h^{SD *} + q_{s}^{2} h_{s} + q_{m}^{2} h_{m}} .

(b) When the markets have the same profitability, there is no difference in stock prices between aggregated and segment disclosure cases.

(c) When market s is more profitable than market m and the conditional precision is lower for market s than for market m ( $q_{s}^{2} h_{s} < q_{m}^{2} h_{m}$ ), the stock price is greater under the aggregated disclosure case than under the segment disclosure case.

Part (a) of Proposition 4 shows that when the markets have different levels of profitability, the necessary and sufficient condition on the difference in stock prices between aggregated and segment disclosure cases is slightly different from that on the effort levels as shown in part (a) of Proposition 3. This is because the stock price depends on segment earnings, which are determined by both the effort level and market profitability. Thus, the condition depends on the relative market profitability in addition to the effort levels. Part (b) states that when the markets have the same profitability, the stock price is also the same. As shown in part (b) of Proposition 3, effort levels differ between aggregated and segment disclosure cases even for the same market profitability. However, when market profitability is the same, total earnings and stock price are independent of effort allocation. Thus, in this case, there is no difference in stock price between aggregated and segment disclosure cases. Part (c) indicates one sufficient condition that the stock price is greater under the aggregated disclosure case than under the segment disclosure case when market profitability differs. In this case, the manager concentrates on the business which is more profitable and less uncertain under the segment disclosure case. Therefore, the manager may allocate her effort more to the segment with low uncertainty even if that segment is less profitable when the condition specified in Part (c) is satisfied.

The Manager’s Disclosure Choice

Finally, we examine whether the manager chooses a voluntary disclosure of segment earnings by comparing the manager’s utility level at equilibrium. By comparing the manager’s expected utility in the stationary state, we obtain the following proposition.

Proposition 5

(a) When the markets have different levels of profitability, the manager withholds segment earnings if and only if

(2 - w^{*}) w^{*} > (2 - \frac{q_{s} + q_{m}}{q_{s} - q_{m}} (w_{s}^{*} - w_{m}^{*})) \frac{q_{s} + q_{m}}{q_{s} - q_{m}} (w_{s}^{*} - w_{m}^{*}),

where $w^{*} = \frac{{(q_{s} + q_{m})}^{2} \frac{h_{s} h_{m}}{h_{s} + h_{m}}}{h^{AD *} + {(q_{s} + q_{m})}^{2} \frac{h_{s} h_{m}}{h_{s} + h_{m}}}$ and $w_{i}^{*} = \frac{q_{i}^{2} h_{i}}{h^{SD *} + q_{s}^{2} h_{s} + q_{m}^{2} h_{m}}, i \in {s, m}$ .

(b) When the markets have the same profitability, the manager withholds segment earnings.

(c) When market s is more profitable than market m and the conditional precision is lower for market s than for market m ( $q_{s}^{2} h_{s} < q_{m}^{2} h_{m}$ ), the manager withholds segment earnings.

The intuition behind this proposition is as follows. If the manager discloses segment information, the market reacts to each segment’s earnings differently. This motivates the manager to concentrate more on the segment with more profitable and less uncertain, which raises the firm’s stock price. This concentration, however, implies a difference in effort levels across the two segments, which is undesirable for a manager who seeks to set her effort levels equal to the relative costs of exerting effort to minimize the total effort cost. She thus faces a trade-off between stock price maximization and effort cost minimization. By considering this trade-off, the manager withholds segment earnings when the necessary and sufficient condition of part (a) of Proposition 5 is satisfied. This condition indicates that when $w^{*}$ is closer to $1$ than $\frac{q_{s} + q_{m}}{q_{s} - q_{m}} (w_{s}^{*} - w_{m}^{*})$ is, the manager withholds segment earnings. Part (b) shows that if the segments’ markets have the same profitability, stock prices under aggregated and segment disclosure cases are the same. However, as in Proposition 3, the effort level is different in each case because the two segments differ in their precisions of shocks. Under the segment disclosure case, the manager is more sensitive to the market’s reaction; thus, effort levels in the two segments are more volatile than under the aggregated disclosure case. Therefore, if the two segments have the same profitability, the manager withholds segment earnings information. In another case (part (c) of Proposition 5), if the conditional precision is lower in the more profitable market, the manager also withholds segment earnings information. This is because even if the market is less profitable, the capital market might focus on the market with lower uncertainty; in response, the manager allocates her effort inefficiently to both segments.

This result is consistent with real-world businesses. After segment reporting is adopted as a management approach, the number of firms disclosing regional segment information decreases, whereas the number disclosing business segment information increases. According to our results, the characteristics of firms that withhold regional segment earnings are as follows. First, market profitability does not vary widely across the regions in which firms have businesses. In other words, they operate both businesses in similar economic contexts. Second, although market profitability is different in the two regions, the market uncertainty is relatively high in the region with a more profitable market. The second case is generally applicable to firms in developed countries, which expand their businesses overseas into high-profitability markets (e.g., emerging economies). However, the capital market finds it difficult to anticipate the manager’s ability based on foreign earnings because the market uncertainty of segment information in the foreign country is much higher than that in the home country. By considering the market’s reaction, the manager inefficiently allocates her effort level between segments under the segment disclosure case. As a result, the rational manager withholds her regional segment information.

Comparison With the Disclosure Policy for Maximizing Social Welfare

The utility-maximizing disclosure policy for the manager does not always maximize social welfare. We thus investigate the conditions under which a given disclosure policy maximizes social welfare. By comparing social welfare under aggregated and segment disclosure cases, we derive the following proposition.

Proposition 6

(a) When the markets have different levels of profitability, the manager withholds segment earnings, which achieves higher social welfare than would be the case under the segment disclosure case if and only if

\begin{matrix} (2 - w^{*}) w^{*} > (2 - \frac{q_{s} + q_{m}}{q_{s} - q_{m}} (w_{s}^{*} - w_{m}^{*})) \frac{q_{s} + q_{m}}{q_{s} - q_{m}} (w_{s}^{*} - w_{m}^{*}), and \\ (2 - 2 θ_{π} - θ_{p} \frac{δ}{1 - δ} w^{*}) w^{*} > (2 - 2 θ_{π} - θ_{p} \frac{δ}{1 - δ} \frac{q_{s} + q_{m}}{q_{s} - q_{m}} (w_{s}^{*} - w_{m}^{*})) \frac{q_{s} + q_{m}}{q_{s} - q_{m}} (w_{s}^{*} - w_{m}^{*}) . \end{matrix}

(b) When the markets have the same profitability, the manager withholds segment earnings, which achieves higher social welfare than would be the case under the segment disclosure case.

(c) When market s is more profitable than market m and the conditional precision is lower in market s than in market m ( $q_{s}^{2} h_{s} < q_{m}^{2} h_{m}$ ), the manager withholds segment earnings, which achieves higher social welfare than would be the case under the segment disclosure case.

Part (a) in Proposition 6 represents the joint conditions of the manager’s expected utility maximization (Part (a) in Proposition 5) and social welfare maximization. When $w^{*}$ is closer to one and is also closer to $\frac{1 - δ}{δ} \frac{1 - θ_{π}}{θ_{p}}$ than $\frac{q_{s} + q_{m}}{q_{s} - q_{m}} (w_{s}^{*} - w_{m}^{*})$ , the manager withholds segment earnings, which achieves higher social welfare than would be the case under the segment disclosure case, and vice versa. The results noted in Part (b) and (c) in Proposition 6 are consistent with the conditions shaping the manager’s disclosure choice. Therefore, when the markets have the same profitability or when market s is more profitable than market m and the conditional precision is lower for market s than for market m ( $q_{s}^{2} h_{s} < q_{m}^{2} h_{m}$ ), the manager’s choice of withholding segment earnings is also preferable in terms of social welfare.

Although the sufficient conditions for Propositions 5 and 6 (conditions of Part (b) and (c), respectively) are identical, there is a slight difference between the necessary and sufficient conditions. Since social welfare does not include the stock price, the benchmark effort levels purely maximize net earnings (i.e., total earnings minus effort costs). The benchmark effort levels, thus, are not distorted by any consideration of the capital market reaction. On the other hand, when the manager cares about the stock price, the effort levels are distorted compared to those in the benchmark case. Specifically, the effort levels react less to differences in market profitability, because the manager considers the market uncertainty which is an important factor when the manager shows her ability to the capital market.

According to our results, the manager can also withhold segment earnings information when there are no conflicts of interest between managers and shareholders. When the manager withholds segment earnings information, the capital market sets the stock price based on the precision of aggregate earnings information and the covariance between aggregate earnings and the manager’s ability. On the contrary, when the manager discloses segment earnings information, the capital market can more accurately predict her ability based on segment earnings. In this case, the capital market sets a higher price on segment earnings in a high-profit and low-uncertainty (high precision) market. Thus, even if the profitability of one market is high, the capital market might set a lower stock price if the information available for that market is unreliable. By taking this market conjecture into consideration, the manager exerts more effort in the high-profitability, low-uncertainty market under the segment disclosure case; this sometimes distorts her effort levels, making them inefficient. The sufficient conditions we derived here indicate that managers rationally withhold segment information and achieve higher social welfare if both segments have similar market profitability or if the market uncertainty is relatively high in the more profitable market. These results suggest new implications for the manager’s decision to disclose segment earnings. For example, if the firm’s earnings arise from similarly profitable markets or differently profitable markets with poor information available in the highly profitable market, the manager withholds segment earnings.

Our results partly support SFAS 131, which states that separately reporting segment information does not add significantly to an investor’s understanding of an enterprise if the firm’s operating segments are so similar that they can be expected to have essentially the same future prospects.¹⁵ However, the mandatory disclosure of business segment information might harm social welfare if the growth opportunities differ and the market uncertainty is relatively high in the high-growth market.

Numerical Example

In Section 4, we have focused on the stationary state. However, our model is dynamic and can illustrate changes in the relationships among the variables. In this section, we consider numerical examples of the manager’s effort levels and social welfare before a stationary state is reached.

We assume that one market (market m) is mature and the other (market s) is growing. In other words, although market m is initially more profitable than market s, the profitability of market s gradually catches up with market m and overtakes it. Thus, market s becomes attractive to investors over time. In addition, we assume that market uncertainty is lower for market m than for market s. Specifically, each parameter takes the following value: $θ_{π} = 1$ , $θ_{p} = 1$ , $δ = 0.6$ , $h_{s} = 100$ , $h_{m} = 200$ , $h_{u} = 1, 000$ , $c_{s} = 115$ , $c_{m} = 115$ , and $q_{m} = 100$ . Compared with $q_{m}$ , $q_{s}$ is time-variant, takes the value of 80 in period 0, and grows by 2 each period. We also assume that the realized values of the random variables, $ε_{s}, ε_{m}, u$ , are 0 for simplicity. Therefore, market s catches up with market m in period 10. Unlike the model in Section 3, the period is finite with range 0 to 100. In this setting, the manager decides to withhold segment information at the beginning of the first period.

Figure 1 illustrates the effort levels over time. $BM$ , $AD$ , and $SD$ represent the effort levels exerted in market s under the benchmark, aggregated, and segment disclosure cases, respectively. As shown in this figure, the effort level under the aggregated disclosure case is initially closer to that under the benchmark case. From about period 20, however, the effort level under the segment disclosure case is closer to that under the benchmark case. Overall, the effort level under the aggregated disclosure case is closer to that under the benchmark case; the manager thus withholds segment information.

Figure 1.

Effort level in market s over time.

Figure 2 depicts social welfare under all cases. Social welfare, as already defined, is the firm’s dividend net of the effort costs. In Figure 2, $BM$ , $AD$ , and $SD$ represent social welfare under the benchmark, aggregated, and segment disclosure cases, respectively. The figure shows that social welfare under the aggregated disclosure case increases with distance from that under the benchmark value from period 11 to period 33 and then approaches that under the benchmark value. Under the segment disclosure case, social welfare approaches the benchmark level from period 9 to period 33; it then differs from the benchmark value before coinciding with the aggregated disclosure case starting in period 41.

Figure 2.

Social welfare over time.

Concluding Remarks

This paper investigated the consequences of aggregate and segment reporting in a capital market setting. In particular, we identified the conditions under which managers rationally withhold segment information and achieve higher social welfare. This is contrary to the stylized conception that segment-specific information is withheld as a result of conflicts of interest between managers and shareholders. We developed a multi-period model in which a manager decides how to allocate her effort between two businesses by considering the stock price, which is based on public information. Each segment’s profit is determined by the manager’s effort and ability as well as each segment’s market profitability and inherent uncertainty of each segment.

Our main results are that managers rationally withhold segment information and achieve higher social welfare if either (a) the segments have similar market profitability or (b) the market uncertainty is relatively high for the segment in the more profitable market. Our results on disclosure choices of segment earnings information provide more precise conditions, which contribute to the refinement of the agency cost hypothesis documented in empirical research.

As is common with analytical models, our model is limited by several assumptions made to increase tractability. First, we assumed that the manager engages in activities in both markets and faces a trade-off between them. This setting could be easily changed to one in which division managers separately exert effort in each segment; the results could then be compared with those of our model. This extension would enable us to consider the manager’s choice of organizational form. A second constraint of our model is that we do not model the contract between the manager and shareholders endogenously. However, we believe that this paper’s results would continue to hold as long as the manager is concerned to some extent about the firm’s current stock price, a condition generally satisfied in reality.

Footnotes

Appendix

A List of Variables

$π_{t}$	aggregate earnings at time t
$e_{it}$	effort level in segment i at time t
$s_{t}$	segment earnings in market s at time t
$m_{t}$	segment earnings in market m at time t
$q_{it}$	market profitability in market i at time t
$ε_{it}$	random shock on segment earnings in market i at time t
$h_{i}$	precision of shock in market i
$a_{t}$	the manager’s ability at time t
$u_{t}$	noise term of the manager’s ability at time t
$μ_{t}$	expected value of the manager’s ability at time t
$h_{t}$	precision of the manager’s ability at time t
$P_{t}^{d}$	stock price at time t ( $d \in {AD, SD}$ )
$δ$	discount factor
$c_{i}$	effort cost (constant marginal cost exerting an effort) in market i
$θ_{π}$	the manager’s preference for current earnings
$θ_{p}$	the manager’s preference for stock prices
$Z_{t}$	signal about aggregate earnings $π_{t}$ at time t under the aggregated disclosure case
$Z_{it}$	signal about segment earnings in market i at time t under the segment disclosure case
$h_{Z_{t}}$	conditional precision of the signal $Z_{t}$ at time t
$h_{Z_{it}}$	conditional precision of the signal $Z_{it}$ at time t
$κ$	irrelevant terms for the manager’s optimization problem
$β_{t}^{d}$	total effort incentive coefficient for the manager at time t ( $d \in {AD, SD}$ )
$w_{t}$	weight of the signal $Z_{t}$ in an updating rule at time t
$w_{it}$	weight of the signal $Z_{it}$ in an updating rule at time t

Acknowledgements

We would like to thank Bharat Sarath (editor) and the anonymous reviewers. We also thank all the participants at 36th European Accounting Association Annual Congress (Paris), Asian Academic Accounting Association 14th Annual Conference (Penang), 25th Asian-Pacific Conference on International Accounting Issues (Bali), and the 2016 American Accounting Association Annual Meeting (New York).

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for research, authorship, and/or publication for this article: Yutaro Murakami was supported by JSPS KAKENHI Grant Numbers JP21730385, JP23730441, and JP17K04068. Atsushi Shiiba was supported by JSPS KAKENHI Grant Numbers JP24530558, JP15K03769, and JP18H00913.

ORCID iD

Yutaro Murakami

Notes

References

Acharya

V. V.

Lambrecht

B. M.

(2015). A theory of income smoothing when insiders know more than outsiders. Review of Financial Studies, 28(9), 2534–2574.

Aghion

Stein

J. C.

(2008). Growth versus margins: Destabilizing consequences of giving the stock market what it wants. The Journal of Finance, 63(3), 1025–1058.

Arya

Fellingham

J. C.

Schroeder

D. A.

(2004). Aggregation and measurement errors in performance evaluation. Journal of Management Accounting Research, 16(1), 93–105.

Arya

Mittendorf

(2011). The benefits of aggregate performance metrics in the presence of career concerns. Management Science, 57(8), 1424–1437.

Autrey

R. L.

Dikolli

S. S.

Newman

D. P.

(2010). Performance measure aggregation, career incentives, and explicit incentives. Journal of Management Accounting Research, 22(1), 115–131.

Bar-Isaac

Hörner

(2014). Specialized careers. Journal of Economics & Management Strategy, 23(3), 601–627.

Bens

D. A.

Berger

P. G.

Monahan

S. J.

(2011). Discretionary disclosure in financial reporting: An examination comparing internal firm data to externally reported segment data. The Accounting Review, 86(2), 417–449.

Berger

P. G.

Hann

R. N.

(2007). Segment profitability and the proprietary and agency costs of disclosure. The Accounting Review, 82(4), 869–906.

Blackwell

(1953). Equivalent comparisons of experiments. The Annals of Mathematical Statistics, 24, 265–272.

10.

Bodnar

G. M.

Hwang

L.-S.

Weintrop

(2003). The value relevance of foreign income: An Australian, Canadian, and British comparison. Journal of International Financial Management & Accounting, 14(3), 171–193.

11.

Bodnar

G. M.

Tang

Weintrop

(1997). Both sides of corporate diversification: The value impacts of geographic and industrial diversification (National Bureau of Economic Research Working Paper, No. 6224). https://www.nber.org/papers/w6224

12.

Bolton

Scheinkman

Xiong

(2006). Executive compensation and short-termist behaviour in speculative markets. Review of Economic Studies, 73(3), 577–610.

13.

Botosan

C. A.

Stanford

(2005). Managers’ motives to withhold segment disclosures and the effect of SFAS No. 131 on analysts’ information environment. The Accounting Review, 80(3), 751–772.

14.

Chen

P. F.

Zhang

(2003). Heterogeneous investment opportunities in multiple-segment firms and the incremental value relevance of segment accounting data. The Accounting Review, 78(2), 397–428.

15.

Demski

J. S.

Frimor

(1999). Performance measure garbling under renegotiation in multi-period agencies. Journal of Accounting Research, 37(Suppl.), 187–214.

16.

Ebert

Simons

Stecher

J. D.

(2017). Discretionary aggregation. The Accounting Review, 92(1), 73–91.

17.

Einhorn

(2005). The nature of the interaction between mandatory and voluntary disclosures. The Accounting Review, 43(4), 593–621.

18.

Ettredge

M. L.

Kwon

S. Y.

Smith

D. B.

Stone

M. S.

(2006). The effect of SFAS No. 131 on the cross-segment variability of profits reported by multiple segment firms. Review of Accounting Studies, 11(1), 91–117.

19.

Ewert

Wagenhofer

(2005). Economic effects of tightening accounting standards to restrict earnings management. The Accounting Review, 80(4), 1101–1124.

20.

Financial Accounting Standards Board. (1997). Disclosures about segments of an enterprise and related information. statement of financial accounting standards no. 131.

21.

Harris

M. S.

(1998). The association between competition and managers’ business segment reporting decisions. Journal of Accounting Research, 36(1), 111–128.

22.

Herrmann

Thomas

W. B.

(2000). An analysis of segment disclosures under SFAS No. 131 and SFAS No. 14. Accounting Horizons, 14(3), 287–302.

23.

Holmström

(1982). Managerial incentive problems: A dynamic perspective. In Essays in Economics and Management in Honor of Lars Wahlbeck. Helsinki: Swedish School of Economics, 209–230.

24.

Holmström

(1999). Managerial incentive problems: A dynamic perspective. Review of Economic Studies, 66(1), 169–182.

25.

Hope

O.-K.

Kang

Kim

J. W.

(2013). Voluntary disclosure practices by foreign firms cross-listed in the United States. Journal of Contemporary Accounting & Economics, 9(1), 50–66.

26.

Hope

O.-K.

Kang

Thomas

W. B.

Vasvari

(2008). Pricing and mispricing effects of SFAS 131. Journal of Business Finance & Accounting, 35(3-4), 281–306.

27.

Hope

O.-K.

Kang

Thomas

W. B.

Vasvari

(2009). The effects of SFAS 131 geographic segment disclosures by US multinational companies on the valuation of foreign earnings. Journal of International Business Studies, 40(3), 421–443.

28.

Hope

O.-K.

Thomas

W. B.

(2008). Managerial empire building and firm disclosure. Journal of Accounting Research, 46(3), 591–626.

29.

Hope

O.-K.

Thomas

W. B.

Winterbotham

(2006). The impact of nondisclosure of geographic segment earnings on earnings predictability. Journal of Accounting, Auditing & Finance, 21(3), 323–346.

30.

Mauch

Schöndube

R. J.

(2019). Controlling scarce working time in a multi-task incentive problem. European Accounting Review, 28(1), 151–175.

31.

Narayanan

P. M.

(1985). Managerial incentives for short-term results. The Journal of Finance, 40(5), 1469–1484.

32.

Sato

(2014). Opacity in financial markets. Review of Financial Studies, 27(12), 3502–3546.

33.

Stein

J. C.

(1989). Efficient capital markets, inefficient firms: A model of myopic corporate behavior. The Quarterly Journal of Economics, 104(4), 655–669.

34.

Wang

Ettredge

Huang

Sun

(2011). Strategic revelation of differences in segment earnings growth. Journal of Accounting and Public Policy, 30(4), 383–392.