a theory of socialistic internal capital markets

ARTICLE IN PRESS

Journal of Financial Economics 80 (2006) 485–509

0304-405X/$

doi:10.1016/j

$We than

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A theory of socialistic internal capital markets$

Antonio E. Bernardoa,�, Jiang Luob, James J.D. Wangc

aUCLA Anderson School of Management, 110 Westwood Plaza, Box 951481, Los Angeles, CA 90095, USAbDepartment of Finance, HKUST, Clear Water Bay, Hong Kong

cDepartment of Economics and Finance, City University of Hong Kong, Kowloon, Hong Kong

Received 9 May 2005; received in revised form 19 July 2005; accepted 28 July 2005

Available online 6 January 2006

Abstract

We develop a model of a two-division firm in which the ‘‘strong’’ division has, on average, higher

quality investment opportunities than the ‘‘weak’’ division. We show that, in the presence of agency

and information problems, optimal effort incentives are less powerful and thus managerial effort is

lower in the strong division. This leads the firm to bias its project selection policy against the strong

division. The selection bias is more severe when there is a larger spread in the average quality of

investment opportunities between the two divisions.

r 2005 Elsevier B.V. All rights reserved.

JEL classification: D82; G31

Keywords: Internal capital markets; Capital budgeting; Investment policy

- see front matter r 2005 Elsevier B.V. All rights reserved.

.jfineco.2005.07.002

k Francesca Cornelli, Sudipto Dasgupta, Denis Gromb, Lixin Huang, and seminar participants at

ge, Carnegie Mellon, HKUST, Tsinghua University, University of Hong Kong, and the 2005 China

Conference in Finance in Kunming, China, for helpful comments. We are particularly grateful to

us referee whose numerous insightful comments and guidance greatly improved the paper. Luo

s financial support from the Wei Lun Fellowship. Luo and Wang acknowledge the support of a

t from the Research Grants Council of the Hong Kong Special Administrative Region, China [CityU

ll errors are ours.

nding author. Tel.: +1310 825 2198.

dress: [email protected] (A.E. Bernardo).

www.elsevier.com/locate/jfec

ARTICLE IN PRESSA.E. Bernardo et al. / Journal of Financial Economics 80 (2006) 485–509486

1. Introduction

A vast majority of corporate investment is financed with internal funds.1 Sinceinvestment decisions made using internal funds are not subject to the same scrutiny fromthe external capital markets as those funded with new equity or debt issues, it is importantto examine how effectively internal capital markets allocate funds to their best use.Although this research question is difficult to tackle directly, the availability of data oninvestments by major business lines (segments) of U.S. public companies allowsresearchers to compare investment decisions in conglomerate firms against investmentdecisions in focused firms. The related empirical literature typically shows that investmentin one division of a conglomerate firm is sensitive to the cash flows of unrelated divisionsand that conglomerate firms invest less in divisions from industries with good investmentopportunities and more in divisions from industries with poor investment opportunitiescompared to their focused counterparts (see, e.g., Lamont, 1997; Scharfstein, 1998; Shinand Stulz, 1998; Rajan et al., 2000; Gertner et al., 2002).2 Moreover, the empiricalliterature finds that this socialistic behavior is more severe when there is more diversity inthe quality of investment opportunities across divisions in the firm (Rajan et al., 2000;Lamont and Polk, 2002; Billett and Mauer, 2003).3

These empirical observations are difficult to reconcile with agency models at the level ofthe CEO. For example, if the CEO has empire-building preferences, such models wouldpredict overinvestment in all divisions instead of a reallocation of funds from strong toweak divisions. Accordingly, two recent models go a level deeper into a firm’s hierarchyand focus on the role of rent-seeking activity by division managers. First, Scharfstein andStein (2000) develop a model in which managers divert their time away from productiveeffort to enhance their outside options and increase their bargaining power whennegotiating total compensation. The authors argue that such behavior is more problematicwith respect to managers of weak divisions because the opportunity cost of beingunproductive is relatively low for them. One way to mitigate this problem is to offer themanager a cash payment to refrain from such behavior. However, Scharfstein and Steinsuggest that if there is another layer of agency between the CEO and shareholders, theCEO may prefer to distort investment in favor of the weak division rather than increasecash payments to the manager because the latter comes from discretionary funds (whichthe CEO can control and potentially divert to himself) rather than investment funds (whichare assumed to be under the control of shareholders). One problem with this explanation is

1The use of internal funds as a percentage of total investment for nonfinancial corporations in the U.S. ranged

from 72% to 108% annually between the years 1990 and 2000 (Brealey and Myers, 2003). The same percentage

exceeds two-thirds in Germany, Japan, and the U.K. (Corbett and Jenkinson, 1997).2The typical empirical strategy is to use the median Tobin’s q of (traded) stand-alone firms in an industry to

measure the quality of investment opportunities in a (non-traded) division of a conglomerate firm. Chevalier

(2000), Whited (2001), Bernardo and Chowdhry (2002), Campa and Kedia (2002), and Gomes and Livdan (2004)

argue against this empirical strategy because the decision to diversify (i.e., form a conglomerate) is endogenous

and may be determined in part by the quality of the division’s investment opportunities, and thus the median q of

stand-alone firms may not be an accurate measure of the investment opportunities of a conglomerate division. A

notable exception to the finding of socialistic cross-subsidization is that of Maksimovic and Phillips (2002) who

use plant-level data from manufacturing firms and find that these firms reallocate resources in favor of strong

plants when they experience a positive demand shock.3Khanna and Tice (2001) show that firms with operations in multiple divisions of the same broad industry do

not engage in inefficient cross-subsidization.

ARTICLE IN PRESSA.E. Bernardo et al. / Journal of Financial Economics 80 (2006) 485–509 487

that it seems implausible that CEOs would prefer to misallocate potentially hundreds ofmillions of investment dollars in order to maintain discretion over a relatively small cashpayment to the division manager. Second, Rajan et al. (2000) develop a model in whichdivision managers have autonomy to choose between an efficient investment and a‘‘defensive’’ investment that protects their division’s surplus from being appropriated byother managers. Thus, while the efficient investment maximizes firm value, a manager mayprefer the defensive investment particularly when the surplus created is far greater thanthat in other divisions. The firm can mitigate this inefficiency by tilting the capital budgetin favor of the division with lower-quality investments.

A key feature of both these models is that the firm cannot write managerial incentivecontracts based on the project cash flows. If even crude contracts could be written, therent-seeking behavior in these models would likely be mitigated at a much lower cost thanby tilting the capital budget. In this paper, we develop a model in which a firm invests toomuch (little) in weak (strong) divisions relative to first-best even when it can writemanagerial compensation contracts based on division cash flows. Our firm consists of twodivisions, such that each has a single investment project. The two projects have the sameinitial cost and the firm has enough capital to fund only one of them. Each division is runby a manager with private information about the project’s quality who can enhance projectcash flows by exerting unverifiable and noncontractible effort. The firm selects whichproject to fund based on analyses (or ‘‘reports’’) provided by the division managers. Weshow that the firm increases the likelihood that a project is selected and compensates the(winning) manager with more performance pay and less salary when she reports a higherquality project. This mechanism induces truthful reporting because the greaterperformance pay obtained from reporting a higher project quality is sufficient tocompensate the manager of a high quality project but insufficient to compensate themanager of a low quality project for the reduction in salary.

Our main result is that the firm does not necessarily choose the highest quality project.Instead, the firm optimally biases project choice in favor of the weak division: specifically,the strong division’s project is chosen only when its reported (and, in equilibrium, true)quality exceeds the weaker division’s project quality by a positive premium. The key tounderstanding this result is that, for any fixed project quality, the cost of providingincentive pay while maintaining truthful reporting is increasing in the proportion ofprojects of higher quality. This makes the cost of providing effort incentives higher whenthe division’s investment opportunities have higher average quality, which in turn results inlower incentive pay and lower managerial effort in the strong division.4 Thus, since cashflows depend on both project quality and managerial effort, the strong division’s projectmust be of sufficiently higher quality to offset the lower level of managerial effort.

The spread in managerial effort widens when the spread in average investment qualitywidens. We therefore also predict that the bias in favor of the weak division is more severewhen the spread between the ex ante quality of investments in the two divisions is greater.This is consistent with the empirical evidence that socialistic cross-subsidization is morepronounced when there is a greater spread in the industry Tobin’s-q across divisions(Rajan et al., 2000; Lamont and Polk, 2002). The bias in favor of the weak division alsoincreases when the firm is less effective at monitoring the managers’ actions. This is

4The costs of incentive provision are also higher when the division’s investment opportunities have higher

variance. We examine this possibility in Section 4.


consistent with the empirical evidence that cross-subsidization is more pronounced whenfirms have ineffective boards of directors (Palia, 1999) and when the CEO has poorlyaligned incentives (Scharfstein, 1998). We also show that when the two divisions share thesame average project quality but they differ in terms of the uncertainty about projectquality, the firm biases project selection against the division with more uncertainty. Thus,we argue that idiosyncratic risk may be relevant for project evaluation not because itaffects the appropriate discount rate—all our agents are risk neutral—but instead becauseit affects equilibrium incentives for managerial effort. Finally, a division manager’scompensation depends on the attributes of the other divisions in the firm; for example,expected compensation and performance pay is greater for division managers in low-growth businesses when the other divisions in the firm are in high-growth businesses.5

Beyond the theoretical and empirical literature on internal capital markets that wedescribe above, our paper is also related to the literature that examines mechanisms forsolving agency and information problems in the capital budgeting process. Harris andRaviv (1996, 1998) focus on the role of monitoring; Holmstrom and Ricart i Costa (1986)and Ozbas (2005) focus on the role of reputation; and Berkovitch and Israel (2004),Bernardo et al. (2001, 2004), and Garcia (2002) focus on the role of managerialcompensation. Our model is most closely related to Bernardo et al. (2001), which examinesoptimal investment and managerial compensation in a single-division firm in the presenceof asymmetric information and moral hazard, and Bernardo et al. (2004), which extendsthis analysis to the case of a multidivision firm with technological and informationalspillovers across divisions. Laffont and Tirole (1986, 1993) examine the related problem ofregulating a monopoly with unobserved efficiency (asymmetric information) andnoncontractible effort to lower costs (moral hazard). However, in the above models,there is no heterogeneity across agents; in this paper, in contrast, we are concerned aboutthe degree to which firms bias the investment selection process and design compensation tomitigate agency and information problems when there is heterogeneity in the quality ofinvestment opportunities across divisions.Our paper is also related to work by Myerson (1981) and McAfee and McMillan (1989)

that shows in an optimal auction with heterogeneous bidders, the seller rationally biasesagainst bidders with higher average valuations to get them to bid more aggressively. Inthese models, the auction is not ex post efficient, i.e., the winner is not necessarily thebidder with the highest valuation. These and other auction models have asymmetricinformation but no moral hazard. In our model, the presence of moral hazard leads tointeresting implications about managerial compensation contracts. In particular, thedesign of managerial compensation contracts forms an integral part of the investmentprocess, with the result that the firm’s investment selection policy is ex post efficient, i.e.,given the equilibrium managerial efforts, the firm chooses the investment that maximizesexpected cash flows net of compensation costs. Our model also differs substantially from

5Goel et al. (2004) offers an explanation of socialistic internal capital markets due to CEO career concerns. In

their model, the CEO wishes to maximize her perceived ability and thus finds it optimal to allocate more

intangible (unobservable) resources to divisions with cash flows that are more informative about her ability.

Anticipating this bias, the firm’s owners also find it optimal to allocate more physical (observable) capital to these

divisions. The model’s cross-sectional predictions about socialistic cross-subsidization follow mainly from cross-

division differences in the informativeness about CEO ability whereas our model’s predictions follow mainly from

cross-division differences in the investment opportunity set.


the auction literature because we can derive numerous implications for the composition ofmanagerial compensation contracts.

The remainder of the paper is organized as follows. Section 2 presents our model.Section 3 derives the first-best allocation and the optimal second-best mechanism in thecase in which the two divisions’ distributions of project quality have the same variance butdifferent means. We derive implications for project selection bias, hurdle project qualities,and division manager compensation. Section 4 considers the case in which the twodivisions’ distributions of project quality have the same mean but different variances.Section 5 concludes and provides direction for future research.

2. The model

We consider a model of a firm with two divisions, which are indexed by i ¼ 1; 2. Eachdivision has a single investment opportunity and is run by a manager with privateinformation, denoted ti, about its quality.

6 The two projects have the same initial cost andthe firm is assumed to have capital sufficient to fund only one of them.7 If her project isfunded, the successful division manager can increase her project’s future expected cashflows by taking privately costly, unverifiable, and noncontractible actions, denoted ei.These actions may include firing other top managers, shutting down an inefficient plant,etc. In keeping with the moral hazard literature, we refer to these actions as managerial‘‘effort.’’ We use the following functional form for the cash flows of investment project i:

Vi ¼ dti þ yei þ �i,

where d40 measures the importance of unknown (to the firm) project quality, y40measures the importance of the division manager’s effort, and �i are independent noiseterms with mean zero.8 For simplicity, we assume no discounting. While we assume eachmanager knows the precise quality, ti, of her own project, the firm only knows that ti isdrawn from a normal distribution with mean Zi and variance s2i , i.e., ti�NðZi;s

2i Þ. The

firm’s prior belief is that division 2 has better investment opportunities, on average, thandivision 1, i.e., Z24Z1. We normalize Z1 ¼ 0 and let Z2 ¼ Z40 for notational convenience.We refer to division 2 as the strong division and division 1 as the weak division. For nowwe assume that the variance of project quality is equal in the two divisions and normalizes21 ¼ s22 ¼ 1. We consider the case of equal means but different variances in Section 4.

We assume both managers are risk neutral and that their expected utility is given by

Ui ¼ E�i wi � 0:5ge2i ,

where wi is her compensation, E�i wi is the expected compensation (expectation over �i), andg parameterizes the manager’s effort cost. Each manager has an outside option that yields

6In our model, the scope of the firm is given exogenously. We do not specifically model either the potential

benefits of integration, e.g., the possibility that the CEO may be better informed about the firm’s investment

opportunities than the external capital market (e.g., Alchian, 1969; Williamson, 1975; Stein, 1997) or the potential

costs of integration, e.g., the diversion of managerial talent.7We relax this assumption in Section 3.4.8The �i represent measurement error, which makes it impossible for the board to infer an exact relation between

ti and ei by observing the cash flows Vi . However, since everyone is risk neutral in our model, the mean zero noise

term and its distribution have no effect on our results.


reservation utility U ¼ 0. We assume that a manager receives compensation wi if herproject is funded and receives her reservation utility, U ¼ 0, if her project is not funded.9

In the capital budgeting process, the firm chooses which project to fund based onanalyses or ‘‘reports,’’ denoted ti, that are provided by the division managers.10 Forexample, these reports might include a detailed analysis of the project’s discounted cashflows. The firm’s problem is to design a project selection and managerial compensationpolicy to mitigate these agency and information problems and maximize the expectedpayoff to its risk-neutral shareholders. Specifically, the firm designs an optimal mechanismthat consists of (i) a selection policy, fpiðtÞg, which is the probability that project i getsfunded as a function of both reports t � ft1; t2g, and (ii) a compensation schedulefwiðt;V iÞg, which is the compensation to manager i (if her project is selected) as a functionof both reports and the project’s cash flows. Importantly, we assume that the manager’sprivate information is not directly observable or verifiable by the firm ex post. Thus,contracts cannot be written on ti directly. Moreover, since the effort choice is unobservableand unverifiable by the firm, contracts cannot be written on ei directly. We allow selectionpolicy to be probabilistic in order to admit the largest set of feasible mechanisms; however,we shall show below that the equilibrium selection policy becomes deterministic once bothmanagers announce their type, i.e., the firm chooses the candidate with the highest ‘‘score’’(not necessarily the highest quality) with probability one and rejects the other.The sequence of moves in the game is as follows:

Date 1.

9Althou

is globally10We as

selection b

two-type v

presence o

because it11In our

allows us

rules and

not speak

The firm offers the mechanism fwiðt;ViÞ; piðt Þg.
Date 2. Each manager reports on the quality of her project, ti. Date 3. The firm selects project i according to the selection probabilities fpiðt Þg. Date 4. Successful manager i chooses the effort level ei. Date 5. The cash flows, V i, are realized and distributed to shareholders less the
compensation wiðt;V iÞ paid to manager i.

We make the standard assumption in these types of models that the firm can commit tothe mechanism offered at date 1. Absent a commitment device, it might be optimal for thefirm to choose a different project at date 3 from the one specified by the selection policyoffered at date 1. However, if the managers believed the firm would act in this manner,they would not report truthfully in the first place. Although we do not model thisexplicitly, the firm’s commitment to the mechanism offered at date 1 may be optimal if itrecognizes that it will likely play this game repeatedly with the division managers in thefuture.11

gh this seems to restrict us to a narrow class of mechanisms, one can show that the mechanism we derive

optimal.

sume the managers cannot collude when submitting their reports. The robustness of our project

ias result to collusion is extremely difficult to examine in our continuous-type model. We have solved a

ersion of our model which suggests that there exists an equilibrium with project selection bias in the

f collusion, but it cannot be proved conclusively. We therefore leave this discussion out of the paper

requires a considerable amount of setup yet provides few clear insights.

model, the firm can commit to an ex post inefficient investment policy. The assumption of commitment

to apply the Revelation Principle to find the optimal mechanism. This mechanism specifies investment

compensation that motivate the managers to reveal their information truthfully. Thus, our model does

directly to the issue of who should make investment decisions. Dessein (2002), Harris and Raviv (2005),


3. Optimal mechanism

To provide a benchmark, we begin by demonstrating the following result for the sociallyefficient (first-best) solution, assuming no moral hazard or information problems. Thissolution maximizes the expected total surplus (expectation over �i’s).

Proposition 1. The first-best project selection policy and managerial effort are given by

pfbi ðtÞ ¼

1 if ti4max tj ;�0:5y2

dg

� �;

0 otherwise;

8><>:

efbi ¼yg.

The proof is in the Appendix. Since each manager’s effort has the same marginalproductivity ðyÞ and cost ðgÞ parameters, the firm would request the same level of effort nomatter which project is financed. Therefore, in the first-best solution, the ranking of eachproject is determined solely by the ranking of its quality, ti. The firm should write acomplete contract that specifies the effort choice in Proposition 1 for the manager of thehigher quality project and this manager should receive a fixed wage that satisfies thedivision manager’s participation constraint.

We now solve for the firm’s optimal mechanism assuming the firm does not know eitherproject quality ti or effort ei. By the Revelation Principle, without loss of generality, we canrestrict our attention to direct revelation mechanisms in which the managers report theirproject qualities truthfully. Thus, the firm’s mechanism design problem can be stated as

maxwiðt;ViÞ;piðtÞ;eiðtÞ

EP �Xi¼1;2

Z 1�1

Z 1�1

piðtÞE�i ½V i � wiðt;ViÞ�dFðt1ÞdFðt2 � ZÞ

such that, 8i

(IC1)

(footnot

Marino

the opti

eiðtÞ 2 arg maxei

E�i wiðt;V iðti; ei; �iÞÞ � 0:5ge2i ,^

R1 ^ ^ 2
(IC2) ti 2 arg maxti
Uiðti; tiÞ � �1piðti; tjÞ½E�i wiðti; tj ;Viðti; ei; �iÞÞ � 0:5gei �dFðtj � ZjÞ,

U ðt ; t ÞX0,
(IR) i i i
(NN)
eiðtÞ; piðtÞX0,and p1ðtÞ þ p2ðtÞp1,
where Fð�Þ denotes the cumulative distribution function (c.d.f.) of the standard normaldistribution, and Uiðti; tiÞ is the expected utility of the manager who reports ti, has truetype ti, and assumes that the other manager is reporting her true type. The first incentivecompatibility constraint (IC1) requires that the successful division manager chooses effortto optimize her expected utility. The second incentive compatibility constraint (IC2)requires that, for every project type, each manager finds it optimal to report truthfullygiven that the other manager also reports truthfully. The constraint (IR) is the standardinterim individual rationality constraint, which requires that each manager’s expectedequilibrium payoff is at least as large as her outside reservation utility, U ¼ 0. The

e continued)

and Matsusaka (2005), and Boot et al. (2005) provide alternative models without commitment to study

mal delegation of investment decisions.


nonnegativity constraint (NN) requires that effort allocations be nonnegative and that theselection policy be well defined.Let fð�Þ denote the probability distribution function (p.d.f.) of the standard normal

distribution and mð�Þ � ð1� Fð�ÞÞ=fð�Þ denote the inverse of its hazard rate.12 We define the‘‘score’’ function as

Hðti; ZiÞ � dti þ 0:5g max 0;yg�

dymðti � ZiÞ

� �� 2.

The following proposition specifies the optimal mechanism and demonstrates that the firmchooses the project with the highest score, Hðti; ZiÞ, which is not necessarily the projectwith the highest quality.

Proposition 2. The optimal mechanism can be implemented in dominant strategies by the

following project selection policy and linear compensation contract:

piðtÞ ¼1 if Hðti; ZiÞ4maxð0;Hðtj ; ZjÞÞ;

0 otherwise;

(

wiðt;V iÞ ¼ aiðtÞ þ biðtÞVi,

where

biðtÞ ¼ max 0; 1�dg

y2mðti � ZiÞ

� �,

aiðtÞ ¼

Z ti

�1

dpiðs; tjÞbiðs; tjÞds� biðtÞ dti þ 0:5y2

gbiðtÞ

� �.

If project i is selected, manager i will provide effort

eiðtÞ ¼ybiðtÞ

g¼ max 0;

yg�

dymðti � ZiÞ

� �.

The proof is in the Appendix.The optimal mechanism can be implemented by a project selection policy, piðtÞ, and a

linear compensation contract consisting of a salary component, aiðtÞ, and a profit-sharingcomponent, biðtÞ. It can be shown that the selection policy and the profit-sharing rule aremonotone increasing and the salary is monotone decreasing in the manager’s (truthful)report of her own project’s quality, ti. The compensation contract induces truthfulreporting by requiring the manager to ‘‘buy’’ more shares in the project (i.e., higher profitsharing) with cash (i.e., lower salary) when she reports a higher quality. In other words, theincrease in profit sharing from reporting a higher project quality compensates the managerof a high quality project but does not sufficiently compensate the manager of a low qualityproject for the reduction in salary.The optimal mechanism is implementable in dominant strategies, thus it is robust to

each manager’s beliefs about the other manager’s actions. Moreover, the optimalcompensation contract is not affected by the noise term, �i. The reason is that thecompensation contract trades off the benefit of providing effort incentives against the costof eliciting truthful reporting. In our model, the additive noise term does not affect the

12Below we shall use two important properties of the standard normal distribution: m0o0 and m0040.


firm’s ability to infer ti and ei separately (e.g., even if the noise term �i � 0 the firm can onlyinfer dti þ yei by observing Vi) or the cost of providing effort incentives because bothmanagers are risk neutral.13

3.1. Project selection bias

The optimal mechanism in Proposition 2 reveals that the firm selects the project with thehighest score, which is given by Hðti; ZiÞ, and not necessarily the project with the highestquality. The following result demonstrates that the optimal selection policy biases againstthe strong division.

Corollary 1. The firm chooses to finance project 2 only if its quality is (sufficiently) higher

than the quality of project 1, i.e., given t1, p2 ¼ 1 only if t24t1 þ t, where tX0 and for high

t1, t40.

The proof is in the Appendix. The reason the selection policy biases against the strongdivision is that for fixed project quality, t1 ¼ t2 ¼ t, the optimal profit-sharing rule is lowerin the strong division, i.e., b2ðt Þpb1ðt Þ, implying that managerial effort is lower inthe strong division; consequently, since project cash flows are additive in quality and effort,the strong division’s project must be of (sufficiently) higher quality to compensate for thelower effort.

To see why profit sharing and thus effort incentives are more powerful in theweak division than in the strong division, consider the incentive compatibility constraintfor the manager of division i of type t 04t. Since the manager’s compensation is linearin project cash flows, wiðt;V iÞ ¼ aiðt Þ þ biðt ÞV i, where t is the reported quality, themanager’s equilibrium effort is given by eiðt Þ ¼ ybiðt Þ=g. Incentive compatibility requiresthat the manager of type t 0 does not wish to report that she is type t, i.e.,Uiðt

0; t 0ÞXUiðt0; t Þ, or

aiðt0Þ þ biðt

0Þ dt 0 þ

y2biðt0Þ

g

� �� 0:5

y2b2i ðt0Þ

gXaiðt Þ þ biðt Þ dt 0þ

y2biðt Þ

g

� �� 0:5

y2b2i ðt Þ

g,

which implies

Uiðt0; t 0ÞXUiðt; t Þ þ biðt Þdðt

0� t Þ.

The term biðt Þdðt0� t Þ represents the extra utility, or information rents, that must be

paid to a manager of type t 0 to get her to report her type truthfully. The information rent isintuitive. By reporting the lower type t, the manager of type t 0 would get the same contractðaiðt Þ; biðt ÞÞ and exert the same effort as a manager of type t but would receive higherexpected compensation of biðt Þdðt

0� t Þ because the project’s expected cash flows would be

greater by the amount dðt 0 � t Þ. Thus, to induce truth telling, the expected compensationof a type-t 0 manager must exceed the expected compensation of a type-t manager by atleast the amount biðt Þdðt

0� t Þ.

13In contrast, noise terms do affect the cost of providing incentives, and thus the optimal contract, when

managers are risk averse. We include the noise term because it shows that our results hold more generally and it is

natural to assume that cash flows are subject to measurement errors and other random shocks. A more technical

proof of the robustness of the linear contract to additive noise is given in Laffont and Tirole (1993, pp. 72–73).


The important thing to notice is that the information rents that must be paid to amanager of type t 0 is increasing in the effort incentives given to a manager of type t, biðt Þ.In fact, providing effort incentives to the type-t manager increases the expectedcompensation (i.e., information rents) that must be paid to all higher type managers.14

This makes the cost of providing effort incentives particularly high when the distributionof project quality has a higher mean because there are more possible higher types, i.e., thefirm must commit to higher expected compensation to a larger proportion of projects.Since the mean project type is higher in the strong division, this implies that the marginalcost of providing effort incentives is greater in the strong division. The marginal benefit ofproviding effort incentives, however, is independent of the division or the project quality,thus it follows that b1ðt ÞXb2ðt Þ.

15

In what follows, fix project quality t large enough so that biðt Þ40 for both divisionsi ¼ 1; 2. The more powerful effort incentives in the weak division, b1ðt ÞXb2ðt Þ, has twoeffects on the firm’s profits. First, the manager of the weak division provides more effort,which increases expected project cash flows. Using the fact that eiðt Þ ¼ ybiðt Þ=g, theexpected cash flow in the weak division is greater by the amount

E½V 1ðt Þ � V 2ðt Þ� ¼ d½mðt� ZÞ � mðt Þ�40

since m0o0 and Z40. Thus, the ‘‘output effect’’ in and of itself leads to a bias in favor ofthe weak division. Second, the manager of the weak division must receive highercompensation for working harder. The ‘‘compensation effect’’ has two components. Thefirst component is the extra compensation for the higher disutility of effort,

0:5g½e21ðt Þ � e22ðt Þ� ¼ d½mðt� ZÞ � mðt Þ� �0:5d2g

y2½m2ðt� ZÞ � m2ðt Þ�40.

The second component is the extra information rents that accrue to the manager of theweak division. In the Appendix, we show that the information rents that accrue to a type-tmanager are equal to IRiðt Þ ¼ dbiðt Þmðt� ZiÞ, and thus

IR1ðt Þ � IR2ðt Þ ¼ �d½mðt� ZÞ � mðt Þ� þd2g

y2½m2ðt� ZÞ � m2ðt Þ�.

Combining the two components we see that the compensation effect, in and of itself,lowers firm profits by ð0:5d2g=y2Þ½m2ðt� ZÞ � m2ðt Þ� and leads to a bias against the weakdivision.The net effect of the increase in cash flows (the output effect) and the increase in

compensation (the compensation effect) is to increase the firm’s profit net of compensationcosts by the amount

d½mðt� ZÞ � mðt Þ� �0:5d2g

y2½m2ðt� ZÞ � m2ðt Þ�40. (1)

Thus, the strong division’s project must be of (sufficiently) higher quality to compensatefor the lower managerial effort. Let t denote the smallest quality premium required to

14This is what makes it costly for the firm to provide profit-sharing incentives even though all agents are risk

neutral. In a pure moral hazard model with a risk-neutral firm and risk-averse manager, the cost of providing

profit sharing is the inefficient risk-bearing by the manager.15Another implication is that biðtÞ is increasing in t since, within a division, there are fewer higher types as t

increases. In fact, it is easy to show that biðtÞ increases and tends toward one as t!1. Thus, first-best effort is

achieved only in the limit.


select the strong division’s project, i.e., Hðtþ t; ZÞ ¼ Hðt; 0Þ. If t is sufficiently large so thatbiðt Þ40 for i ¼ 1; 2, then t solves

dt ¼ d½mðtþ t� ZÞ � mðt Þ� �0:5d2g

y2½m2ðtþ t� ZÞ � m2ðt Þ�. (2)

Comparing Eqs. (1) and (2), it is clear that the equilibrium selection policy chooses thestrong division’s project if and only if its quality is sufficiently high to offset the lower cashflows to the firm from lower managerial effort.16 Thus, the firm selects the project thatmaximizes the payoff to shareholders net of compensation costs, which is not necessarilythe highest quality project.

The next result, which describes the conditions under which the project selectionbias is large or small, follows immediately from the expression in Eq. (2) for the qualitypremium, t.

Corollary 2. The quality premium, t, increases in Z (the difference in average project quality

between the two divisions) and y (importance of effort), and decreases in d (importance of

unknown project quality) and g (effort aversion).

The proof is in the Appendix. We establish earlier that the cost of providing effortincentives is greater in the strong division and thus b2ðt Þpb1ðt Þ. The reason is that the costof providing profit sharing to a manager who reports project quality t is the higherexpected compensation (information rents) the firm must offer the manager when projectquality exceeds t. This commitment is especially costly when there is a higher probabilitythat project quality exceeds t, i.e., the distribution of project types has a higher mean. Asthe spread between the average project quality in the strong division and the weak divisionwidens (higher Z) the divergence in effort incentives also widens, thus the quality premiumfor project 2 must increase to compensate for the greater spread in managerial effort. Thus,our model predicts that the bias in favor of the weak division is stronger when thedifference between the average quality of projects in the two divisions is greater. Thisprediction is also made by Scharfstein and Stein (2000) and Rajan et al. (2000) and isconsistent with the empirical evidence that socialistic cross-subsidization is morepronounced when there is a greater spread in the industry Tobin’s-q across divisions(Rajan et al., 2000; Lamont and Polk, 2002).

Further empirical implications follow from reasonable interpretations of the other keyparameters in our model; namely, d, y, and g. The parameter d represents the relevance ofthe division manager’s private information for the project cash flows; thus, we expect d tobe greater, for example, when the firm is early in its lifecycle or is in a high-growthindustry. The parameter y represents the importance of unverifiable managerial effort;thus, we expect y to be greater, for example, when the division manager’s tasks requiremore firm-specific human capital. Finally, the parameter g represents effort cost; however,an alternative and more empirically useful interpretation of 1=g (more generally, theinverse of the second derivative of the cost function 1=C00ðeiÞ) is the responsiveness ofunverifiable actions to an increase in incentives (Milgrom and Roberts, 1992). Under thisinterpretation, g is lower when the division managers have more discretion, which is morelikely to be the case if, for example, the firm’s board of directors is ineffective. Similarly,

16In our derivation, we assume t sufficiently large so that biðtÞ40 for both divisions i ¼ 1; 2. The equilibrium

selection policy in Proposition 2 also accounts for the possibility that biðtÞ ¼ 0.


while there is no conflict between the CEO and shareholders in our model, g is lower whenthe CEO has poorly aligned incentives because he will not be motivated to providemonitoring effort and division managers will have more discretion. Thus, we predict thatinternal capital markets are more socialistic (i.e., biased more in favor of weak divisions)when (i) the firm is relatively mature, (ii) the division managers require more firm-specifichuman capital, (iii) the board is less effective at monitoring managers, and (iv) the CEOhas poorly aligned incentives. The last two predictions are also made by Scharfstein andStein (2000) and are consistent with the empirical evidence that cross-subsidization is morepronounced when firms have ineffective boards of directors (Palia, 1999) and when theCEO has low-powered incentives (Scharfstein, 1998).

3.1.1. Comparison to single-division firms

Our model suggests that the firm invests too much (little) in the weak (strong) divisionrelative to first-best. The empirical literature, however, compares investment in divisions ofconglomerate (multidivision) firms to investment in focused (single-division) firms. Toaddress this literature we would need to specify more fully the costs and benefits of formingconglomerates, describe the nature of capital constraints in focused and conglomeratefirms, and model explicitly why it is that our firm has chosen to bring together the twodivisions. A full analysis of these issues is beyond the scope of this paper. However, belowwe present a plausible scenario in which our results apply when comparing investmentpolicies of conglomerate and focused firms.Consider the case in which the two divisions in our firm are split up into two focused

firms and each of these firms has information and agency problems of the type describedin our model. It is straightforward to show that for focused firm i the internal project isfunded if Hðti; ZiÞ40. This is identical to our selection criterion except there is no internalcompetition for funds. Now assume the total amount of capital available from the externalcapital market is limited (as in our firm) so that only one of the two firms obtains funding.Furthermore, assume that the external capital market does not have an effective screeningmechanism for learning the information ti from managers, i.e., the firm is more efficient atscreening project types than the external capital market. This is a plausible assumptionbecause screening requires commitment on the part of the mechanism designer, i.e., ourmultidivision firm commits to an ex post inefficient investment policy to elicit truthfulinformation. A firm has a stronger incentive to build a reputation for honoring itscommitments than the external capital market because it will have to deal with itsmanagers repeatedly in the capital budgeting process. It is well known that in a dynamicsetting without commitment, agents of different types have a tendency to ‘‘pool’’(Fudenberg and Tirole, 1991, p. 301). In the presence of pooling, the external capitalmarket funds the firm that gives the highest expected payoff according to its ex antedistribution—in this case the strong firm. Thus, the internal capital market invests more(less) in the weak (strong) division compared to its focused counterparts.

3.2. Hurdle quality

In the first-best solution, the firm funds a project only when ti4tfb ¼ �0:5y2=ðdgÞ. Thehurdle quality level, tfb, takes into consideration the contribution of first-best managerialeffort; it is therefore negative. In the second-best solution, the firm funds a project only


when ti4tsbi , where tsbi solves Hðtsbi ; ZiÞ ¼ 0. Comparing these investment policies yields thefollowing result.

Corollary 3. The firm has a higher hurdle quality in the second-best than in the first-best, i.e.,tsbi 4tfb, and the firm has a higher hurdle quality for the strong division than for the weak

division, i.e., tsb2 Xtsb1 , where the inequality holds strictly for some parameter values.

The proof is in the Appendix. In the second-best mechanism, effort incentives areweaker than in the first-best (i.e., biðtÞp1), thus the equilibrium level of managerial effort islower. The total project cash flows depend additively on project quality and managerialeffort, thus the hurdle project quality must be higher in the second-best to compensate forthe lower effort. Moreover, since effort is lower in the strong division for any given projectquality, the firm optimally imposes a higher hurdle quality on the strong division than inthe weak division.

3.3. Managerial compensation

The optimal mechanism can be implemented with a linear managerial compensationcontract, thus performance pay is measured by the slope of the contract, biðtÞ. Conditionalon having her project selected, the manager of the weak division 1 receives expectedperformance pay b1 and expected total compensation w1 given by

b1 ¼ Eft1;t2g½b1ðtÞjHðt1; 0Þ4maxð0;Hðt2; ZÞÞ�,

w1 ¼ Eft1;t2g½a1ðtÞ þ b1ðtÞE�1V 1jHðt1; 0Þ4maxð0;Hðt2; ZÞÞ�.

We now show the following result.

Corollary 4. Conditional on having her project selected, the manager of the weak division

receives higher-powered incentives and greater total compensation, on average, when the

other division in the firm has better investment opportunities, i.e., b1 and w1 increase in Z.

The proof is in the Appendix. The intuition for this follows from two features of theoptimal mechanism. First, performance pay for manager i is increasing in ti because, as weargue earlier, the marginal cost of providing effort incentives is lower when there are fewerpossible higher types. Second, the hurdle quality required for the weak division’s project tobe selected will be, on average, higher when the strong division has better investmentopportunities. One empirical implication of this result is as follows. Consider a set ofmultidivision firms, each of which has a division operating in a mature industry with fewgood growth opportunities. We predict that the performance pay and total compensationfor these division managers will be higher in the subset of firms that also operate in otherindustries with many good growth opportunities.

3.4. Unlimited capital

If the firm has sufficient capital to fund both projects, the only change to thefirm’s optimization problem is to remove the requirement p1 þ p2p1 in the (NN)constraint. It can be shown that the new optimal profit-sharing rule, biðtÞ, is identicalto the earlier case in which the firm is constrained to fund only one project. The reasonfor this result is that competition for capital only affects the lower bound of project


types that get funded; the cost of incentive provision, however, is the increasedinformation rents that must be given to all higher types within a division which isunaffected by the lower bound.17 The new salary for manager i, aiðtÞ, althoughdifferent than in the earlier case (reflecting a new optimal selection policy), is stilldecreasing in the manager’s type. Again, the firm gets the division managers to revealtheir type by requiring them to buy shares (higher performance pay) in the project withcash (lower salary).Since the optimal profit-sharing rule, biðtÞ, is unchanged from the capital constrained

case, the level of managerial effort is also unchanged. It is easy to show that the newoptimal selection policy is to fund project i if and only if Hðti; ZiÞ40. The new selectionpolicy does not depend on the quality of the other project since the two projects do nothave to compete for limited resources. Following the arguments we make earlier, thispolicy is equivalent to the firm selecting a project if and only if its expected cash flows netof compensation costs exceed zero. In other words, the firm selects all positive net presentvalue (NPV) projects taking into consideration the second-best level of managerial effort.Second-best effort, however, is lower than first-best effort (since biðtÞp1) so the firm rejectssome projects that would be accepted in the absence of agency and information problems,i.e., the second-best hurdle quality is greater than the first-best hurdle quality. Moreover,b2ðtÞpb1ðtÞ implies that second-best effort is lower in the strong division so the firm rejectseven more projects in the strong division that would be accepted in the absence of agencyand information problems.

3.5. N divisions

In our optimal mechanism, the firm selects the project with the highest score (given byHðti; ZiÞ) and compensates the winning manager with greater performance pay, biðtÞ, whenthe project quality is higher. These results extend to the case of N42 divisions. Tounderstand the effect of having N divisions, we note two important features of our optimalmechanism. First, since performance pay to manager i is increasing in the project quality,ti, the spread between first-best and second-best effort vanishes as the true project qualityapproaches its upper bound. Second, for fixed quality ti, performance pay does not dependon the quality of the other project tj. Thus, extending our model to N divisions does notchange the form of the compensation contract but it does increase the expected quality ofthe winning project. Consequently, in an N-division firm, average performance payconditional on the project’s selection will be higher and expected agency and informationcosts will be lower. The argument that, as N becomes larger, N-division firms are betterable to mitigate agency and information problems within the firm suggests an interestingbenefit to forming conglomerates. However, this argument takes as fixed the degree ofinformation asymmetry between division managers and the firm, whereas in reality,information asymmetries between informed division managers and centralized decisionmakers are likely to be greater in multidivision firms, especially if the divisions are inunrelated lines of business. A fuller examination of the costs and benefits of formingconglomerates is beyond the scope of this paper.

17See Laffont and Tirole (1993, Chapter 7) for a similar result in a model of competition for procurement

contracts.


4. Same mean quality but different variances

We now consider the case in which the firm’s prior belief is that the two projects havesimilar average quality, normalized to 0, but different variances, i.e., t1�Nð0; s21Þ andt2�Nð0; s22Þ, where s2 ¼ s4s1 ¼ 1. In what follows, we make the following assumption:

(A1)
yg�
dsymð0Þo0.

Assumption (A1) requires that the quality of project 2 be significantly uncertain (high s) sothe two projects are sufficiently different. Our results still hold (for high project qualities)when this assumption is violated.

It is straightforward to show that the first-best solution is the same as in Proposition 1;in the absence of asymmetric information and moral hazard, the firm always selects thehigher-quality project. Following the derivation in Proposition 2, we can solve for theoptimal second-best mechanism. First, define the score function:

Rðti; siÞ � dti þ 0:5g max 0;yg�

dsi

ym

ti

si

� �� 2.

Proposition 3. The optimal mechanism can be implemented in dominant strategies by the

following selection policy and linear compensation scheme:

piðtÞ ¼1 if Rðti;siÞ4maxð0;Rðtj ; sjÞÞ;

0 otherwise;

(

wiðt;ViÞ ¼ aiðtÞ þ biðtÞV i,

where

biðtÞ ¼ max 0; 1�dgsi

y2m

ti

si

� �� ,

aiðtÞ ¼

Z ti

�1


gbiðtÞ

� �.

If project i is selected, manager i will provide effort

eiðtÞ ¼ybiðtÞ

g¼ max 0;

yg�

dsi

ym

ti

si

� �� .

The proof is omitted since it parallels that of Proposition 2. We now demonstrate theexistence of a selection bias in favor of the division with lower variance in project quality.

Corollary 5. The firm chooses to finance project 2 only if its quality is (sufficiently) higher

than the quality of project 1, i.e., given t1, p2 ¼ 1 only if t24t1 þ r, where rX0 and for high

t1, r40.

The proof is in the Appendix. The intuition is similar to the case of different means. Inthis case, for a fixed (positive) project quality, t, there are more possible higher types indivision 2 because its distribution of project types has a higher variance. Consequently, it iscostlier for the firm to provide effort incentives to the manager of division 2, i.e.,


b2ðtÞpb1ðtÞ, and division 2’s project must offer a quality premium to compensate for thelower level of managerial effort. The comparative statics results for the relative strength ofthe selection bias are very similar to the case of different means.

Corollary 6. Given that project 1 has quality t1, the quality premium that project 2 has to

offer, r, increases in s (the variance difference between the two divisions) and y (importance

of effort), and decreases in d (importance of unknown project quality) and g (effort aversion).

The proof is omitted since it parallels that of Corollary 2. Recall, in the first-bestsolution, the firm funds a project only when ti4tfb ¼ �0:5y2=ðdgÞ. The hurdle quality level,tfb, takes into consideration the contribution of managerial effort; therefore, it is negative.In the second-best solution, the firm funds a project only when ti4tsbi , where tsbi solvesRðtsbi ;siÞ ¼ 0. Comparing these investment policies yields the following result.

Corollary 7. The firm has a higher hurdle quality in the second-best than in the first-best,tsbi 4tfb, and the firm has a higher hurdle quality for the division with more uncertainty,tsb2 Xtsb1 , where the inequality holds strictly for some parameter values.

The proof is in the Appendix. The firm requires a higher hurdle quality for projects fromthe division with more uncertainty about its investment opportunities. Since thisuncertainty is idiosyncratic, this result implies that firms are bias against makinginvestments with greater idiosyncratic risk. In standard applications of the discounted cashflow (DCF) methodology without agency or information problems, idiosyncratic risk doesnot affect project evaluation because such risks vanish in a well-diversified portfolio. In thepresence of agency and information problems, however, it is costlier for the firm to provideeffort incentives when it is more uncertain about the project’s true quality. The firmcompensates for this by biasing its investment policy against projects with greateridiosyncratic risk. This is one potential explanation for the survey evidence that firms use amuch higher hurdle rate of return than that justified by standard asset pricing models(Poterba and Summers, 1995).

5. Conclusions

In this paper, we develop a model of a two-division firm in which the optimal effortincentives to division managers with private information about project quality are lesspowerful in the division with higher quality investment opportunities. This leads the firmto bias its project selection policy against the strong division to offset the lower level ofmanagerial effort. The selection bias is more severe when there is a larger spread in averageproject quality between the two divisions. One important advantage of our model overcompeting theoretical models of socialistic internal capital markets based on managerialrent-seeking behavior (Scharfstein and Stein, 2000; Rajan et al., 2000) is that we derive ourresults under the plausible assumption that firms can write managerial compensationcontracts based on division cash flows. While our model makes several similar predictionsto the above competing theories, we make numerous novel testable predictions about theseverity of the bias in internal capital markets, the effect of idiosyncratic risk on projectevaluation, and the form of managerial compensation.In our model, firm scope is given exogenously but in reality it is determined by

considering the various costs and benefits of integration. For example, the benefits ofintegration include the slackening of financial constraints (e.g., Billett and Mauer, 2003)


and the possibility that the CEO may be better informed about the firm’s investmentopportunities than the external capital market (e.g., Stein, 1997), while the costs ofintegration include the diversion of managerial talent, higher influence costs within theorganization, and weaker incentives to improve the firm’s investment opportunity set (e.g.,Brusco and Panunzi, 2005). In future research, we hope to endogenize firm scope to obtaina fuller understanding of observed differences in investment policy across conglomerateand focused firms.

Appendix

Proof of Proposition 1. The expected total surplus (expectation over �i) is

maxpiðtÞ;eiðtÞ

EP �Xi¼1;2

piðtÞ½E�i V i � 0:5geiðtÞ2� ¼

Xi¼1;2

piðtÞ½dti þ yeiðtÞ � 0:5geiðtÞ2�

such that piðtÞX0 and p1ðtÞ þ p2ðtÞp1.The first order condition (FOC) for eiðtÞ is: efbi ðtÞ ¼ y=g. The second order condition

(SOC) holds obviously. Substituting efbi ðtÞ into the above yields

EP ¼Xi¼1;2

piðtÞðdti þ 0:5y2=gÞ.

Therefore, pfbi ðtÞ ¼ 1 if ti4maxðtj ;�0:5ðy

2=dgÞÞ; otherwise, pfbi ðtÞ ¼ 0. &

Proof of Proposition 2. Denote the firm’s optimization problem as P. Our proofstrategy for finding the optimal Bayesian–Nash mechanism follows the two-stepapproach of Laffont and Tirole (1986). In step 1, we consider a program (denoted R)that relaxes some constraints in P. With relaxed constraints, the firm should get atleast as much expected payoff in R as in P. In step 2, we consider a program(denoted L) that uses compensation contracts that are linear in cash flows. Since Lrestricts us to a narrower class of mechanisms, the firm can get at most the sameexpected payoff in L as in P. Finally, we demonstrate that the firm’s expected payoffs fromR and L are the same. Consequently, the optimal solution for L must be the optimalsolution for P.

Step 1: Consider a relaxed program, denoted R, in which the firm can verify dti þ yei. Inthis hypothetical case, assuming that the other manager will report her true type, themanager of the funded project who reports ti must choose ei such thatdti þ yei ¼ dti þ yeiðti; tjÞ. Otherwise, the firm would be sure that the manager hadeither lied about her true type or did not exert the required effort, and could punishher (arbitrarily) severely. Consequently, if the manager of a true type ti reports ti,she must choose ei ¼ eiðti; tjÞ þ dðti � tiÞ=y, resulting in the cash flow V iðti; tj ; �iÞ

¼ dti þ yeiðti; tjÞ þ �i. Compared with P, the (IC1) constraint for effort is completelyrelaxed in R.

In program R, if the manager of a true type ti reports ti, her expected payoff is

Uiðti; tiÞ ¼

Z 1�1

piðti; tjÞ E�i wiðti; tj ;Viðti; ; tj ; �iÞÞ � 0:5g eiðti; tjÞ þdðti � tiÞ

y

� �2" #

�dFðtj � ZjÞ.


By the Envelope Theorem,

dUiðti; tiÞ

dti

¼qUiðti; tiÞ

qti

��ti¼ti

þqUiðti; tiÞ

qti

��ti¼ti

¼qUiðti; tiÞ

qti

��ti¼ti

¼

Z 1�1

dgpiðti; tjÞeiðti; tjÞ

ydFðtj � ZjÞ.

Integrating yields

UiðtiÞ ¼ Uið�1Þ þ

Z ti

�1

Z 1�1

dgpiðs; tjÞeiðs; tjÞ

ydFðtj � ZjÞds,

and imposing Uið�1Þ ¼ 0 from the (IR) condition and taking the expectation yields

EUi ¼

Z 1�1

Z ti

�1

Z 1�1


ydFðtj � ZjÞdsdFðti � ZiÞ

¼ �

Z 1�1

Z ti

�1

Z 1�1


ydFðtj � ZjÞdsdð1� Fðti � ZiÞÞ

¼ � ð1� Fðti � ZiÞÞ

Z ti

�1

Z 1�1


ydFðtj � ZjÞds

� �1�1

þ

Z 1�1

ð1� Fðti � ZiÞÞ

Z 1�1

dgpiðti; tjÞeiðti; tjÞ

ydFðtj � ZjÞdti

¼

Z 1�1

1� Fðti � ZiÞ

fðti � ZiÞ

Z 1�1

dgpiðtÞeiðtÞ

ydFðtj � ZjÞdFðti � ZiÞ

¼

Z 1�1

Z 1�1

dgpiðtÞeiðtÞ

ymðti � ZiÞdFðtj � ZjÞdFðti � ZiÞ.

Substituting the expression EðpiwiÞ ¼ EUi þ 0:5gEðpie2i Þ into the firm’s expected payoff

yields

EPR ¼Xi¼1;2

Z 1�1

Z 1�1

E�i ½piðtÞVi � 0:5gpiðtÞeiðtÞ2�Ui�dFðt1ÞdFðt2 � ZÞ

¼Xi¼1;2

Z 1�1

Z 1�1

piðtÞ dti þ yeiðtÞ � 0:5geiðtÞ2�

dgeiðtÞ

ymðti � ZiÞ

� �

�dFðt1ÞdFðt2 � ZÞ. ð3Þ

Since program R provides the firm more flexibility to discipline its managers, it shouldyield the firm at least the same expected payoff as P does, i.e., EPR

XEPP.Step 2: Now consider a program, denoted L, in which the firm is constrained to use

linear compensation contracts: wiðt;V iÞ ¼ aiðtÞ þ biðtÞV i. Under this contract andassuming the other manager reports her true type, the manager of type ti can get thefollowing expected payoff by reporting ti and choosing effort ei:

Uiðti; tiÞ ¼

Z 1�1

piðti; tjÞ½aiðti; tjÞ þ biðti; tjÞðdti þ yeiÞ � 0:5ge2i �dFðtj � ZjÞ. (4)

Ignoring the (NN) constraint for the moment, the FOC for ei is ei ¼ ybiðti; tjÞ=g. Again, theSOC holds obviously.


By the Envelope Theorem,

dUiðti; tiÞ

dti

¼qUiðti; tiÞ

qti

��ti¼ti

þqUiðti; tiÞ

qti

��ti¼ti

¼qUiðti; tiÞ

qti

��ti¼ti

¼

Z 1�1

dpiðti; tjÞbiðti; tjÞdFðtj � ZjÞ.

Integrating yields

UiðtiÞ ¼ Uið�1Þ þ

Z ti

�1

Z 1�1

dpiðs; tjÞbiðs; tjÞdFðtj � ZjÞds, (5)

and imposing Uið�1Þ ¼ 0 from the (IR) condition and taking the expectation yields

EUi ¼

Z 1�1

Z 1�1

dpiðtÞbiðtÞmðti � ZiÞdFðtj � ZjÞdFðti � ZiÞ

¼

Z 1�1

Z 1�1

dgpiðtÞeiðtÞ

ymðti � ZiÞdFðtj � ZjÞdFðti � ZiÞ,

where the first equality obtains by integrating by parts, and the last equality obtains bysubstituting in the FOC for ei.

Substituting the expression EðpiwiÞ ¼ EUi þ 0:5gEðpie2i Þ into the firm’s expected payoff

yields

EPL ¼Xi¼1;2

Z 1�1

Z 1�1

E�i½piðtÞV i � 0:5gpiðtÞeiðtÞ

2�Ui�dFðt1ÞdFðt2 � ZÞ

¼Xi¼1;2

Z 1�1

Z 1�1

piðtÞ dti þ yeiðtÞ � 0:5geiðtÞ2�

dgeiðtÞ

ymðti � ZiÞ

� �

�dFðt1ÞdFðt2 � ZÞ. ð6Þ

Since program L allows only a subset of the mechanisms available in P, it mustbe that EPLpEPP. However, comparing Eqs. (3) and (6) shows that EPL ¼ EPR

XEPP.Therefore, EPL ¼ EPP, so the optimal linear contract cannot be further improvedupon.

Optimal Bayesian– Nash mechanism:Now we solve the optimal mechanism with linearcontracts. The point-wise FOC for ei is

eiðtÞ ¼ max 0;yg�

dymðti � ZiÞ

� �.

The SOC holds obviously.Substituting the expression for ei into the expected payoff yields

EP ¼Xi¼1;2

Z 1�1

Z 1�1

piðtÞ dti þ 0:5g max 0;yg�

dymðti � ZiÞ

� �� 2" #dFðt1ÞdFðt2 � ZÞ.

Define a function

Hðy;xÞ � dyþ 0:5g max 0;yg�

dymðy� xÞ

� �� 2.


The firm therefore chooses

piðtÞ ¼1 if Hðti; ZiÞ4maxð0;Hðtj ; ZjÞÞ;

0 otherwise:

�

To derive other parts of the optimal mechanism, it is immediate that

biðtÞ ¼geiðtÞ

y¼ max 0; 1�

dg

y2mðti � ZiÞ

� �,

and it follows from Eqs. (4) and (5) that

UiðtiÞ ¼

Z ti

�1

Etj½dpiðs; tjÞbiðs; tjÞ�ds

¼ Etj½piðtÞðaiðtÞ þ biðtÞðdti þ yeiðtÞÞ � 0:5geiðtÞ

2Þ�,

thus

Etj½piðtÞaiðtÞ� ¼

Z ti

�1

Etj½dpiðs; tjÞbiðs; tjÞ�ds� Etj

½piðtÞðbiðtÞðdti þ yeiðtÞÞ � 0:5geiðtÞ2Þ�.

The Bayesian–Nash implementation of the firm’s mechanism design problem only requiresthat the salary satisfy the above expectation expression.We immediately obtain some monotonic properties of the mechanism. Note that m0o0,

and thus qHðti; ZiÞ=qti40; therefore, piðtÞ is nondecreasing in ti. Also, from m0o0, biðtÞ andeiðtÞ are nondecreasing in ti. By standard arguments (Mirrlees, 1971), the (IC2) constraintis satisfied.So far we have studied the Bayesian–Nash implementation of the firm’s mechanism

design problem. Since the optimal mechanism, in particular piðtÞ and biðtÞ, is monotonic inboth t1 and t2, by the results of Mookherjee and Reichelstein (1992), it can also beimplemented in dominant strategies. We now consider a specific form of salary and showthat the resulting mechanism can be implemented in dominant strategies.

Implementation in dominant strategies: Our proof strategy is as follows. First,we consider a specific form of aiðti; tjÞ. Note that in the Bayesian–Nash mechanismabove we only need to specify the expected salary (integrating over the tj) assumingthe other manager reports the truth, i.e., tj ¼ tj. Second, we express the manager’sutility as a function of her true ti, her reported ti, and the other manager’s reported tj.Unlike the Bayesian–Nash mechanism, we allow the other manager to misreport her tj.Finally, we show that, given every realization of tj, which may or may not be the true tj,reporting the truth ti ¼ ti maximizes the manager’s utility and therefore is her dominantstrategy.Consider the following specification of ai:

aiðtÞ ¼

Z ti

�1

dpiðs; tjÞbiðs; tjÞds� ðbiðtÞðdti þ yeiðtÞÞ � 0:5geiðtÞ2Þ

¼

Z ti

�1


gbiðtÞ

� �,

where the last equality obtains by substituting into the expression of the effort levelei ¼ ybi=g. Plugging the compensation into the payoff of the manager who observes ti and


reports ti, assuming the other manager observes tj and reports tj, yields

Uðti; tijtjÞ ¼ piðti; tjÞ

Z ti

�1

dpiðs; tjÞbiðs; tjÞdsþ dbiðti; tjÞðti � tiÞ

" #.

Note that this payoff is independent of the true tj. We just need to show that the manager i

finds reporting ti ¼ ti to be the dominant strategy.Given manager i’s belief about the other manager’s reported tj, consider two cases:

�
Suppose piðti; tjÞ ¼ 1. The manager must report ti such that piðti; tjÞ ¼ 1; otherwise,piðti; tjÞ ¼ 0 leads to Uðti; tijtjÞ ¼ 0, which is obviously inferior to telling the truth. Thus,
Uðti; tijtjÞ ¼

Z ti

�1

dpiðs; tjÞbiðs; tjÞdsþ dbiðti; tjÞðti � tiÞ.

Taking derivatives yields

qUðti; tijtjÞ

qti

¼ dpiðti; tjÞbiðti; tjÞ � dbiðti; tjÞ þ dðti � tiÞqbiðti; tjÞ

qti

¼ dðti � tiÞqbiðti; tjÞ

qti

,

which, because biðtÞ is nondecreasing in ti, is nonnegative (nonpositive) for tioti (ti4ti).The manager will report the true quality, i.e., ti ¼ ti.
� Suppose piðti; tjÞ ¼ 0. If the manager reports ti such that piðti; tjÞ ¼ 1, then
Uðti; tijtjÞ ¼

Z ti

ti

dpiðs; tjÞbiðs; tjÞdsþ dbiðti; tjÞðti � tiÞ

pZ ti

ti

dbiðti; tjÞdsþ dbiðti; tjÞðti � tiÞ

¼ 0.

Here we use the facts that piðtÞ ¼ 0; 1, piðtÞ is nondecreasing in ti, and biðtÞ isnondecreasing in ti. If the manager reports ti (particularly ti ¼ ti) such that piðti; tjÞ ¼ 0,she gets Uðti; tijtjÞ ¼ 0. Thus, she will report the true quality, i.e., ti ¼ ti.

To summarize, manager i will report the true ti for every belief of the other manager’sreported tj . Therefore, the mechanism is implementable in dominant strategies.

Finally, to examine the monotonicity of aiðtÞ, note that when piðtÞ ¼ 1, i.e.,Hðti; ZiÞ4maxð0;Hðtj ; ZjÞÞ, we have

qaiðtÞ

qti

¼ dpiðtÞbiðtÞ � dbiðtÞ �qbiðtÞ

qti

dti þ 0:5y2

gbiðtÞ

� �� biðtÞ0:5

y2

gqbiðtÞ

qti

¼ �qbiðtÞ

qti

dti þ 0:5y2

gbiðtÞ

� �� biðtÞ0:5

y2

gqbiðtÞ

qti


p�qbiðtÞ

qti

dti þ 0:5y2

gbiðtÞ

� �p0

since biðtÞ is nondecreasing in ti and

dti þ 0:5y2

gbiðtÞ ¼ dti þ 0:5g

yg

eiðtÞXdti þ 0:5geiðtÞ2¼ Hðti; ZiÞX0.

Therefore, aiðtÞ is nonincreasing in ti. &

Proof of Corollary 1. Note that the firm funds project 2 only when Hðt2; ZÞ4Hðt1; 0Þ.Define t such that Hðt1 þ t; ZÞ ¼ Hðt1; 0Þ, i.e.,

dtþ 0:5g max 0;yg�

dymðt1 þ t� ZÞ

� �� 2¼ 0:5g max 0;

yg�

dymðt1Þ

� �� 2. (7)

Since m0o0, Hðt1 þ t; ZÞ increases from �1 to1 as t increases from �1 to1; therefore,given t1, t is uniquely determined. In addition, Hðt2; ZÞ4Hðt1; 0Þ ¼ Hðt1 þ t; ZÞ only whent24t1 þ t, thus we just need to show that tX0 with strict inequality for high t1.Note that (i) t! 0 as Z! 0, and (ii) the implicit derivative of t with respect to Z is

qtqZ¼ �

ðdg=yÞm0ðt1 þ t� ZÞmax 0; ðy=gÞ � ðd=yÞmðt1 þ t� ZÞ� �

d� ðdg=yÞm0ðt1 þ t� ZÞmax 0; ðy=gÞ � ðd=yÞmðt1 þ t� ZÞ� �X0,

where the inequality holds strictly for high t1 implying y=g� d=ymðt1 þ t� ZÞ40;therefore, tX0 with strict inequality for high t1. &

Proof of Corollary 2. The monotonicity of t in Z is immediate from the proof of Corollary 1.To save space, here we just prove the monotonicity of t in d. The monotonicities of t in yand g can be derived similarly.There are three cases to consider. First, if ðy=gÞ � ðd=yÞmðt1Þp0, Eq. (7) implies t ¼ 0

and it holds trivially that ðqt=qdÞp0. Second, if ðy=gÞ � ðd=yÞmðt1Þ40 butðy=gÞ � ðd=yÞmðt1 þ t� ZÞp0, Eq. (7) becomes

dt ¼ 0:5gyg�

dymðt1Þ

� �2¼ 0:5

y2

g� dmðt1Þ þ 0:5

gd2

y2mðt1Þ

2.

Implicitly differentiating yields

qtqd¼ �

g

2d2yg

� �2

�dymðt1Þ

� �2" #

o0.

Finally, if ðy=gÞ � ðd=yÞmðt1Þ40 and ðy=gÞ � ðd=yÞmðt1 þ t� ZÞ40, Eq. (7) becomes

dtþ 0:5gyg�

dymðt1 þ t� ZÞ

� �2¼ 0:5g

yg�

dymðt1Þ

� �2.


Since t40 from the proof of Corollary 1, it follows that mðt1 þ t� ZÞ4mðt1Þ. Taking theimplicit derivative of t w.r.t. d yields

qtqd¼ �

ðgd=2y2Þ½mðt1 þ t� ZÞ2 � mðt1Þ2�

d� ðdg=yÞ ðy=gÞ � ðd=yÞmðt1 þ t� ZÞ

m0ðt1 þ t� ZÞo0.

To summarize, t decreases in d. &

Proof of Corollary 3. Note that

Hðtfb; ZiÞodtfb þ 0:5y2=g ¼ 0 ¼ Hðtsbi ; ZiÞ,

which implies tfbotsbi since qHðy;xÞ=qy40.Now compare the hurdle rates for the two divisions. Since qHðy;xÞ=qxp0, it follows

that

Hðtsb1 ; ZÞpHðtsb1 ; 0Þ ¼ 0 ¼ Hðtsb2 ; ZÞ,

which implies tsb1 ptsb2 since qHðy;xÞ=qy40. The inequality holds strictly for certainparameter values. &

Proof of Corollary 4. Since Hðt2; ZÞ ¼ Hðt2 � Z; 0Þ þ dZ, we can write

b1 ¼ Eft1;t2�Zg max 0; 1�dg

y2mðt1Þ

� ��Hðt1; 0Þ4maxð0;Hðt2 � Z; 0Þ þ dZÞ� �

¼ Ex Et1 max 0; 1�dg

y2mðt1Þ

� ��Hðt1; 0Þ4maxð0;Hðx; 0Þ þ dZÞ� ��

,

with x � t2 � Z�Nð0; 1Þ and x ? t1. Note that maxð0; 1� ðdg=y2Þmðt1ÞÞ and Hðt1; 0Þincrease in t1 and are independent of Z. Thus, Et1 ½maxð0; 1� ðdg=y2Þmðt1ÞÞjHðt1; 0Þ4maxð0;Hðx; 0Þ þ dZÞ� increases in Z since it puts more weight on high t1. It follows that b1

increases in Z.Now consider the total compensation. It is straightforward to show that

w1 ¼ Eft1;t2g 0:5gmax 0;yg

� �2

�dymðt1Þ

� �2" #" ��Hðt1; 0Þ4maxð0;Hðt2; ZÞÞ

#.

Following the same approach we used to show that b1 increases in Z, it is simple to showthat w1 increases in Z. &

Proof of Corollary 5. Note that the firm funds project 2 only when Rðt2;sÞ4Rðt1; 1Þ.Define r such that Rðt1 þ r;sÞ ¼ Rðt1; 1Þ, i.e.,

drþ 0:5g max 0;yg�

dsym

t1 þ rs

� �� 2¼ 0:5g max 0;

yg�

dymðt1Þ

� �� 2. (8)

Since m0o0, Rðt1 þ r; ZÞ increases from �1 to1 as r increases from �1 to1; therefore,given t1, r is uniquely determined. In addition, Rðt2;sÞ4Rðt1; 1Þ ¼ Rðt1 þ r;sÞ only whent24t1 þ r; thus, we just need to show rX0 with strict inequality for high t1.

Before we proceed, we show that if ðy=gÞ � ðds=yÞmðy=sÞ40 then y40. Suppose not.Since m0o0, it follows that ðy=gÞ � ðds=yÞmð0ÞXðy=gÞ � ðds=yÞmðy=sÞ40, which contradictsAssumption (A1).


Taking the implicit derivative of r w.r.t. s yields

qrqs¼ðdg=yÞ m ðt1 þ rÞ=s

� �� ððt1 þ rÞ=sÞm0 ðt1 þ rÞ=s

� �� max 0; ðy=gÞ � ðds=yÞm ðt1 þ rÞ=s

� �� d� ðdg=yÞm0 ðt1 þ rÞ=s

� �max 0; ðy=gÞ � ðds=yÞm ðt1 þ rÞ=s

� �� .

The denominator is positive since m0o0. The nominator is zero when ðy=gÞ � ðds=yÞmððt1þrÞ=sÞp0, and positive when y=g� ðds=yÞmððt1 þ rÞ=sÞ40 implying t1 þ r40. Therefore,qr=qsX0 with strict inequality for high t1. This result, combined with the fact r! 0 ass! 1, therefore implies that rX0 with strict inequality for high t1. &

Proof of Corollary 7. Note that

Rðtfb; siÞodtfb þ 0:5y2=g ¼ 0 ¼ Rðtsbi ;siÞ,

which implies tfbotsbi since qRðy;xÞ=qy40.Now compare the hurdle rates for the two division. Under Assumption (A1), Rð0; sÞ ¼

0 ¼ Rðtsb2 ;sÞ and thus tsb2 ¼ 0. Since Rð0; 1ÞX0 ¼ Rðtsb1 ; 1Þ, then tsb1 p0 fromqRðy;xÞ=qy40. Therefore, tsb1 p0 ¼ tsb2 with strict inequality for certain parametervalues. &

References

Alchian, A.A., 1969. Corporate management and property rights. In: Manne, H. (Ed.), Economic Policy and the

Regulation of Corporate Securities. American Enterprise Institute, Washington DC, pp. 337–360.

Berkovitch, E., Israel, R., 2004. Why the NPV criterion does not maximize NPV. Review of Financial Studies 17,

239–255.

Bernardo, A.E., Chowdhry, B., 2002. Resources, real options, and corporate strategy. Journal of Financial

Economics 63, 211–234.

Bernardo, A.E., Cai, H., Luo, J., 2001. Capital budgeting and compensation with asymmetric information and

moral hazard. Journal of Financial Economics 61, 311–344.

Bernardo, A.E., Cai, H., Luo, J., 2004. Capital budgeting in multi-division firms: information, agency, and

incentives. Review of Financial Studies 17, 739–767.

Billett, M.T., Mauer, D.C., 2003. Cross-subsidies, external financing constraints, and the contribution of the

internal capital market to firm value. Review of Financial Studies 16, 1167–1201.

Boot, A.W.A., Milbourn, T.T., Thakor, A.V., 2005. Sunflower management and capital budgeting. Journal of

Business 78, 501–527.

Brealey, R.A., Myers, S.C., 2003. Principles of Corporate Finance, 7th ed. McGraw-Hill Irwin, New York.

Brusco, S., Panunzi, F., 2005. Reallocation of corporate resources and managerial incentives in internal capital

markets. European Economic Review 49, 659–681.

Campa, J.M., Kedia, S., 2002. Explaining the diversification discount. Journal of Finance 57, 1731–1762.

Chevalier, J., 2000. What do we know about cross-subsidization? Evidence from the investment policies of

merging firms. Unpublished working paper, Yale University.

Corbett, J., Jenkinson, T., 1997. How is investment financed? A study of Germany, Japan, the United Kingdom,

and the United States. The Manchester School 65 (Suppl.), 69–93.

Dessein, W., 2002. Authority and communication in organizations. Review of Economic Studies 69, 811–838.

Fudenberg, D., Tirole, J., 1991. Game Theory. MIT Press, Cambridge, MA.

Garcia, D., 2002. Optimal contracts with privately informed agents and active principals. Unpublished working

paper, Dartmouth College.

Gertner, R., Powers, E., Scharfstein, D.S., 2002. Learning about internal capital markets from corporate spin-

offs. Journal of Finance 57, 2479–2506.

Goel, A.M., Nanda, V., Narayanan, M.P., 2004. Career concerns and resource allocation in conglomerates.

Review of Financial Studies 17, 99–128.


Gomes, J., Livdan, D., 2004. Optimal diversification: reconciling theory and evidence. Journal of Finance 59,

507–536.

Harris, M., Raviv, A., 1996. The capital budgeting process: incentives and information. Journal of Finance 51,

1139–1174.

Harris, M., Raviv, A., 1998. Capital budgeting and delegation. Journal of Financial Economics 50, 259–289.

Harris, M., Raviv, A., 2005. Allocation of decision-making authority. Review of Finance 9, 353–383.

Holmstrom, B., Ricart Costa, J., 1986. Managerial incentives and capital management. Quarterly Journal of

Economics 101, 835–860.

Khanna, N., Tice, S., 2001. The bright side of internal capital markets. Journal of Finance 56, 1489–1526.

Laffont, J.-J., Tirole, J., 1986. Using cost observation to regulate firms. Journal of Political Economy 94, 614–641.

Laffont, J.-J., Tirole, J., 1993. A Theory of Incentives in Procurement and Regulation. MIT Press, Cambridge,

MA.

Lamont, O., 1997. Cash flow and investment: evidence from internal capital markets. Journal of Finance 52,

83–109.

Lamont, O., Polk, C., 2002. Does diversification destroy value? Evidence from industry shocks. Journal of

Financial Economics 63, 51–77.

Maksimovic, V., Phillips, G.M., 2002. Do conglomerate firms allocate resources inefficiently across industries?

Theory and evidence. Journal of Finance 57, 721–767.

Marino, A.M., Matsusaka, J.G., 2005. Decision processes, agency problems, and information: an economic

analysis of capital budgeting procedures. Review of Financial Studies 18, 301–325.

McAfee, R.P., McMillan, J., 1989. Government procurement and international trade. Journal of International


Milgrom, P., Roberts, J., 1992. Economics, Organizations and Management. Prentice-Hall, Englewood Cliffs.

Mirrlees, J.A., 1971. An exploration in the theory of optimum income taxation. Review of Economic Studies 38,

135–208.

Mookherjee, D., Reichelstein, S., 1992. Dominant strategy implementation of Bayesian incentive compatible

allocation rules. Journal of Economic Theory 56, 378–399.

Myerson, R.B., 1981. Optimal auction design. Mathematics of Operations Research 6, 58–73.

Ozbas, O., 2005. Integration, organizational processes, and allocation of resources. Journal of Financial


Palia, D., 1999. Corporate governance and the diversification discount: evidence from panel data. Unpublished

working paper, Rutgers University.

Poterba, J., Summers, L., 1995. A CEO survey of U.S. companies’ time horizons and hurdle rates. Sloan

Management Review 37, 43–53.

Rajan, R., Servaes, H., Zingales, L., 2000. The cost of diversity: the diversification discount and inefficient

investment. Journal of Finance 55, 35–80.

Scharfstein, D.S., 1998. The dark side of internal capital markets II: evidence from diversified conglomerates.

Unpublished working paper, Harvard University.

Scharfstein, D.S., Stein, J.C., 2000. The dark side of internal capital markets: divisional rent-seeking and

inefficient investment. Journal of Finance 55, 2537–2564.

Shin, H., Stulz, R., 1998. Are internal capital markets efficient? Quarterly Journal of Economics 113, 531–552.

Stein, J.C., 1997. Internal capital markets and the competition for corporate resources. Journal of Finance 52,

111–133.

Whited, T., 2001. Is it inefficient investment that causes the diversification discount? Journal of Finance 56,

1667–1692.

Williamson, O.E., 1975. Markets and Hierarchies: Analysis and Antitrust Implications. Collier Macmillan,

New York.

a theory of socialistic internal capital markets

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