compatibility:the lemon owner must not have the incentive to offer the same warranty as the owner of a good car.The second condition is individual rationality,which ensures that the seller of a good quality car is in fact better off in the separating equilibrium than in the pooling equilibrium.In the used car market,a warranty is a credible signal of quality because a sufficiently large warranty is too expensive to be attractive to sellers of lemons,because they are more likely to have to pay the warranty. In this type of asymmetric information model the informed agent moves first,and the separating equilibrium is more commonly known as a signaling equilibrium.The term separating equilibrium is generally used in models in which the uninformed agent moves first by offering a menu of incentive compatible choices (contracts)from which the informed self-select,revealing their private information through their choice.As an example,compare the analysis of a signaling equilibrium in Akerlof or Spence(1973)with that of the separating equilibrium in Rothschild and Stiglitz (1976). 3. Leverage signaling with investment fixed 3.1.The Ross model In the Ross(1977)model,we see the intuition of Akerlof(1970)as it applies to capital structure.Ross illustrates that managers with an informational advantage have an incentive to signal their private information through their choice of debt level.Firms with lower expected cash flows find it more costly to incur higher levels of debt(because bankruptcy is more likely) than do firms with higher expected cash flows.Just as sellers of lemons find a large warranty too costly,managers of firms with low expected cash flows find a relatively high level of debt too costly because it imposes a high probability of bankruptcy.Thus,high-valued firms can signal this information to the market by issuing a sufficiently high amount of debt. 5
5 compatibility: the lemon owner must not have the incentive to offer the same warranty as the owner of a good car. The second condition is individual rationality, which ensures that the seller of a good quality car is in fact better off in the separating equilibrium than in the pooling equilibrium. In the used car market, a warranty is a credible signal of quality because a sufficiently large warranty is too expensive to be attractive to sellers of lemons, because they are more likely to have to pay the warranty. In this type of asymmetric information model the informed agent moves first, and the separating equilibrium is more commonly known as a signaling equilibrium. The term separating equilibrium is generally used in models in which the uninformed agent moves first by offering a menu of incentive compatible choices (contracts) from which the informed self-select, revealing their private information through their choice. As an example, compare the analysis of a signaling equilibrium in Akerlof or Spence (1973) with that of the separating equilibrium in Rothschild and Stiglitz (1976). 3. Leverage signaling with investment fixed 3.1. The Ross model In the Ross (1977) model, we see the intuition of Akerlof (1970) as it applies to capital structure. Ross illustrates that managers with an informational advantage have an incentive to signal their private information through their choice of debt level. Firms with lower expected cash flows find it more costly to incur higher levels of debt (because bankruptcy is more likely) than do firms with higher expected cash flows. Just as sellers of lemons find a large warranty too costly, managers of firms with low expected cash flows find a relatively high level of debt too costly because it imposes a high probability of bankruptcy. Thus, high-valued firms can signal this information to the market by issuing a sufficiently high amount of debt
To see how the Ross signaling model works,assume there are two firms,good (G)and bad(B).During the next period,firms realize a cash flow where the density function f'x) is uniform on the interval 0,x,t=G,B.The cash flow distributions are ordered by first- order stochastic dominance(xx).The market knows the distributions of cash flows,but cannot distinguish firm G from firm B because the firms are identical in all other respects.By pooling firms,the market undervalues the good firm and overvalues the bad firm,so the good firm would like to convey its quality to the market.Conversely,the bad firm would prefer to hide amidst the uncertainty. One key difference between the Ross signaling model and Akerlof's is the objective function.In the example of the used car market,the sellers'objective is to maximize their profits.The objective function that Ross uses is the manager's wage.Ross assumes this wage has two components.One is a function of firm value,and the other is a bankruptcy penalty.This penalty is a cost the manager incurs(separate from any bankruptcy costs the firm may incur)if the firm goes bankrupt.The manager's objective is to choose the firm's level of debt,D,to maximize his wage. Suppose that managers have the following wage contract: 0 W'=av(D')-Lf(x)dx (1) The first term is a positive scalar times the current market value of the firm,V(D'),which is a function of the face value of debt,D',that the firm t issues.This term reflects the fact that the market uses the firm's debt level as a signal of firm value,which is the same as used car buyers using the seller's warranty as a signal of car quality.The second term is the bankruptcy penalty, L,times the likelihood of bankruptcy,FD').The incentive compatibility condition requires 6
6 To see how the Ross signaling model works, assume there are two firms, good (G) and bad (B). During the next period, firms realize a cash flow x ~ , where the density function f ( x ) t is uniform on the interval [ ,x ] t 0 , t = G,B . The cash flow distributions are ordered by firstorder stochastic dominance ( x x ) G B > . The market knows the distributions of cash flows, but cannot distinguish firm G from firm B because the firms are identical in all other respects. By pooling firms, the market undervalues the good firm and overvalues the bad firm, so the good firm would like to convey its quality to the market. Conversely, the bad firm would prefer to hide amidst the uncertainty. One key difference between the Ross signaling model and Akerlofís is the objective function. In the example of the used car market, the sellersí objective is to maximize their profits. The objective function that Ross uses is the managerís wage. Ross assumes this wage has two components. One is a function of firm value, and the other is a bankruptcy penalty. This penalty is a cost the manager incurs (separate from any bankruptcy costs the firm may incur) if the firm goes bankrupt. The managerís objective is to choose the firmís level of debt, D, to maximize his wage. Suppose that managers have the following wage contract: ∫ = − t D t t t W V ( D ) L f ( x )dx 0 α 0 . (1) The first term is a positive scalar times the current market value of the firm, V ( D ) t 0 , which is a function of the face value of debt, t D , that the firm t issues. This term reflects the fact that the market uses the firmís debt level as a signal of firm value, which is the same as used car buyers using the sellerís warranty as a signal of car quality. The second term is the bankruptcy penalty, L, times the likelihood of bankruptcy, F ( D ) t t . The incentive compatibility condition requires
ovo(D)-L(x)d s avo(D)-LJ(x)dx. (2) The left-hand side of this condition is manager B's wage if he chooses D,the debt level chosen by manager G.The right-hand side is his wage if he chooses not to mimic.Because debt is personally costly to managers,in a separating equilibrium D=D'will be the lowest debt level sufficient to satisfy incentive compatibility.Also,D=0 because any debt level above this,but strictly less than D',imposes a cost on the B manager while still revealing his firm's type to the market.Finally,in a separating equilibrium,the market correctly identifies and thus correctly values,the firms.We can rearrange the incentive compatibility condition and make some substitutions to interpret the requirement for D': D f(x)k≥，(D)-y。10] (3) LFB(D)≥ (4) The last condition tells us that if D'is set so that firm B manager's expected bankruptcy penalty from financing with D'outweighs the gain in wage from being perceived as firm G,then incentive compatibility results. 3.2.Other leverage signaling models Another fundamental signaling model is that of Leland and Pyle (1977),in which insider ownership provides the signal of firm quality.Under certain conditions,managers of high-quality firms signal their type by retaining a high proportion of ownership,and therefore finance with higher levels of debt than managers of low-quality firms.Financing with debt allows a manager to retain a larger ownership stake in the firm,but the larger equity stake is costly to a risk-averse manager.The fact that a larger equity stake is less costly to a manager of a high-quality firm 7
7 ∫ ∫ − ≤ − G B D B B D G B V ( D ) L f ( x )dx V ( D ) L f ( x )dx 0 0 0 α 0 α . (2) The left-hand side of this condition is manager Bís wage if he chooses G D , the debt level chosen by manager G. The right-hand side is his wage if he chooses not to mimic. Because debt is personally costly to managers, in a separating equilibrium G * D = D will be the lowest debt level sufficient to satisfy incentive compatibility. Also, = 0 B D because any debt level above this, but strictly less than * D , imposes a cost on the B manager while still revealing his firmís type to the market. Finally, in a separating equilibrium, the market correctly identifies and thus correctly values, the firms. We can rearrange the incentive compatibility condition and make some substitutions to interpret the requirement for * D : L f ( x )dx [V ( D ) V ( )] * D B * 0 0 0 0 ≥ − ∫ α (3) − ≥ 2 B * G B x x LF ( D ) α (4) The last condition tells us that if * D is set so that firm B managerís expected bankruptcy penalty from financing with * D outweighs the gain in wage from being perceived as firm G, then incentive compatibility results. 3.2. Other leverage signaling models Another fundamental signaling model is that of Leland and Pyle (1977), in which insider ownership provides the signal of firm quality. Under certain conditions, managers of high-quality firms signal their type by retaining a high proportion of ownership, and therefore finance with higher levels of debt than managers of low-quality firms. Financing with debt allows a manager to retain a larger ownership stake in the firm, but the larger equity stake is costly to a risk-averse manager. The fact that a larger equity stake is less costly to a manager of a high-quality firm
drives the incentive compatibility of the signal.As in Ross(1977),the Leland and Pyle model predicts a positive correlation between firm quality and leverage Heinkel (1982)devises a model of debt signaling in which the information asymmetry is about both the mean and the variance of returns.The assumed(positive)relations between mean and variance drives a signaling equilibrium in which higher-value firms signal their quality with higher debt levels.The Heinkel assumption,that more-valuable firms are also more risky,is consistent with the Ross result that more-valuable firms have a higher likelihood of default.This key assumption allows for a costless signaling equilibrium in which riskier,more-valuable firms have higher levels of debt financing.This positive correlation between firm value and leverage is the same result found by Ross,but Heinkel does not assume that managers face a bankruptcy penalty.Instead,managers own the firm and they make capital structure decisions to maximize the value of their claim.In a pooling equilibrium,high-value,high-risk firms(low-quality firms in Heinkel's model)find their equity undervalued and their debt overvalued,but low-value,low- risk firms(high-quality firms)have the opposite misvaluations.Thus,the high-value firms are attracted to the debt market and the low-value firms are attracted to the equity market.In this model,the incentive compatibility that is necessary for separation must run both ways.A low- value firm will not find it to desirable to mimic a high-value firm because that would require issuing more undervalued debt and less overvalued equity.Similarly,a high-value firm would not mimic a low-value firm because that would require issuing more undervalued equity and less overvalued debt.The signaling is costless because the manager/owner's utility is derived entirely IThis assumption is not necessary for the separating equilibrium in Heinkel,but it is necessary for a costless separating equilibrium.If firm value and credit risk were negatively correlated,as in Ross,a separating equilibrium may exist provided both the incentive compatibility and individual rationality conditions are met. 8
8 drives the incentive compatibility of the signal. As in Ross (1977), the Leland and Pyle model predicts a positive correlation between firm quality and leverage. Heinkel (1982) devises a model of debt signaling in which the information asymmetry is about both the mean and the variance of returns. The assumed (positive) relations between mean and variance drives a signaling equilibrium in which higher-value firms signal their quality with higher debt levels. The Heinkel assumption, that more-valuable firms are also more risky, is consistent with the Ross result that more-valuable firms have a higher likelihood of default. This key assumption allows for a costless signaling equilibrium in which riskier, more-valuable firms have higher levels of debt financing.1 This positive correlation between firm value and leverage is the same result found by Ross, but Heinkel does not assume that managers face a bankruptcy penalty. Instead, managers own the firm and they make capital structure decisions to maximize the value of their claim. In a pooling equilibrium, high-value, high-risk firms (low-quality firms in Heinkelís model) find their equity undervalued and their debt overvalued, but low-value, lowrisk firms (high-quality firms) have the opposite misvaluations. Thus, the high-value firms are attracted to the debt market and the low-value firms are attracted to the equity market. In this model, the incentive compatibility that is necessary for separation must run both ways. A lowvalue firm will not find it to desirable to mimic a high-value firm because that would require issuing more undervalued debt and less overvalued equity. Similarly, a high-value firm would not mimic a low-value firm because that would require issuing more undervalued equity and less overvalued debt. The signaling is costless because the manager/ownerís utility is derived entirely 1 This assumption is not necessary for the separating equilibrium in Heinkel, but it is necessary for a costless separating equilibrium. If firm value and credit risk were negatively correlated, as in Ross, a separating equilibrium may exist provided both the incentive compatibility and individual rationality conditions are met
from the firm's equity value and debt is assumed to carry no financial distress or bankruptcy costs. The information asymmetry in the Blazenko(1987),John (1987),and Ravid and Sarig (1991)models concerns only the mean return.Blazenko shows that if managers are risk averse in wealth(which is a stake in the firm's equity),then managers of high-value firms signal their type by issuing debt.Managers of low-value firms prefer to avoid the additional risk imposed on the equity claim when debt exists,and so their firms issue equity.In the pure signaling analysis of the John model,the firm pre-commits to implementing investment policies that are more risky than optimal.Ravid and Sarig build a full-information valuation model for the firm that they base on cash flows,corporate taxes,bankruptcy costs,and limited liability.In this framework,Ravid and Sarig obtain a separating equilibrium in which debt and dividends serve as signals of firm quality.These three signaling models also find a positive correlation between financial leverage and firm quality. The Brick,Frierman,and Kim(1998)model is unique,in that the information asymmetry is only about variance of returns.In this model,the authors assume risk-neutral investors.but the firm's full information value is related to return variance through limited liability and corporate taxes,all else equal.The result is a model in which,when information is symmetric,the firm's variance determines its optimal financial leverage.When information about the variance is asymmetric,a lower level of leverage signals a lower variance of firm returns,all else equal.In the signaling equilibrium,a higher-value firm has a lower debt level.This result,in which firm variance,taxes and bankruptcy costs drive differences in firm value,contrasts with the signaling models reviewed above,where differences in firm value are driven by differences in expected cash flows and where more debt signals higher quality.Although the Brick,Frierman,and Kim 9
9 from the firmís equity value and debt is assumed to carry no financial distress or bankruptcy costs. The information asymmetry in the Blazenko (1987), John (1987), and Ravid and Sarig (1991) models concerns only the mean return. Blazenko shows that if managers are risk averse in wealth (which is a stake in the firmís equity), then managers of high-value firms signal their type by issuing debt. Managers of low-value firms prefer to avoid the additional risk imposed on the equity claim when debt exists, and so their firms issue equity. In the pure signaling analysis of the John model, the firm pre-commits to implementing investment policies that are more risky than optimal. Ravid and Sarig build a full-information valuation model for the firm that they base on cash flows, corporate taxes, bankruptcy costs, and limited liability. In this framework, Ravid and Sarig obtain a separating equilibrium in which debt and dividends serve as signals of firm quality. These three signaling models also find a positive correlation between financial leverage and firm quality. The Brick, Frierman, and Kim (1998) model is unique, in that the information asymmetry is only about variance of returns. In this model, the authors assume risk-neutral investors, but the firm's full information value is related to return variance through limited liability and corporate taxes, all else equal. The result is a model in which, when information is symmetric, the firmís variance determines its optimal financial leverage. When information about the variance is asymmetric, a lower level of leverage signals a lower variance of firm returns, all else equal. In the signaling equilibrium, a higher-value firm has a lower debt level. This result, in which firm variance, taxes and bankruptcy costs drive differences in firm value, contrasts with the signaling models reviewed above, where differences in firm value are driven by differences in expected cash flows and where more debt signals higher quality. Although the Brick, Frierman, and Kim