Research " A dissertation submitted in partial satisfaction of the requirements fog the degree Doctor of Philosophy in Economics " ppt

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UNIVERSITY OF CALIFORNIA

Los Angeles

Human Capital, Incomplete Information, and Capital Structure: Theory and Evidence

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UMI Number: 3121231

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For

My parents: Qi Yang and Fenggin Chong &

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Table of Contents 1 Introduction 2 Literature Review 2.1 Tax-based Theories 2.2 Pecking-Order Theory 2.3 Non-tax Theories

2.4 A Recent Empirical Challenge

The Formal Model

3.1 Settings and Assumptions

3.2 Optimal Contract under Incomplete Information

3.3 Equilibrium Contract under Incomplete Information

3.4 Further Analysis of the Equilibrium Contract 3.4.1 A Second Best Policy

3 4.2 Implications for Financing Policy and Capital Structure Further Discussion

4.1 Debt v.s Equity

4.2 The Separation of Ownership with Control

5 Empirical Test

5.1 The Empirical Model

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ACKNOWLEDGMENTS

I am greatly indebted to Professor Harold Demsetz, the chair of my

dissertation committee, and I thank Professors Daniel Ackerberg, Hongbin Cai, Ekaterini Kyriazidou, Fred Weston, Jean-Laurent Rosenthal, and all the

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VITA August, 2, 1972 Born, Jilin Province, China 1995 B.A., Economics Peking University, Beijing, China 1998 M.A., Economics Peking University, Beijing, China 1998-99 University Fellowship,

University of California, Los Angeles

Los Angeles, California

1999-00 Teaching Assistant,

Department of Economics

2001 M.A., Economics,

2001 Ph.D Candidate in Economics,

University of California, Los Angeles Los Angeles, California

Presentation

Yang, G (uly, 2003) Human Capital, Incomplete Information, and Capital Structure: Theory and Evidence Paper presented at the

annual meeting of Western Economic Association International

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ABSTRACT OF THE DISSERTATION

Human Capital, Incomplete Information, and

Capital Structure: Theory and Evidence

by

Guohua Yang

Doctor of Philosophy in Economics

University of California, Los Angeles, 2003

Professor Harold Demsetz, Chair

A puzzling issue in the field of capital structure is that the observed debt- equity ratios of many firms are much lower than finance theory would predict

In this paper, we explain this phenomenon in terms of specificity of human

capital and contracting incompleteness In a costly information world, a

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demonstrate that under these conditions the pattern of observed debt-equity

ratios is consistent with the need to resolve the "two-sided" holdup problem

embedded in dealings between management and equity owners The seeming

inefficiency of financing practices results from a second-best policy for

protecting the interests of investors when information is incomplete We Apply our theory to explain the capital structure choice by human capital intensive

firms We find strong supporting evidence that there is a negative relationship

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1 Introduction

Modigliani and Miller (1958) demonstrate that the capital structure of a firm is irrelevant in determining the market value of the firm if capital markets are perfect

and taxes are neutral between debt and equity This striking conclusion, however,

is surely not consistent with the financing practices in the real world, and many

theories have been developed to explain why capital structure matters to a firm’s

stakeholders These theories have greatly improved our understanding of the deter- minants of capital structure, yet there are still some important empirical findings

that existing theories cannot explain satisfactorily For example, the debt-equity ratios of many firms, especially those that are profitable, are significantly lower than

the efficient level suggested by capital structure theory if debt is treated preferen- tially by the tax authorities

In the U.S and many other countries, interest payments to creditors are shielded from corporate income tax while dividends paid to shareholders are not There- fore, in these countries, it would seem that a firm can increase its market value

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theory predicts Moreover, firm profitability is significantly negatively correlated

with the debt-equity ratio across firms and time periods(e.g., Titman and Wessels (1988), Rajan and Zingales (1995), and Graham (2000)) High-profit firms have more taxable income to shield, a lower probability of bankruptcy and lower borrow- ing costs than low-profit firms According to the trade-off theory high-profit firms should have higher debt-equity ratios than low-profit firms Myers(1984) called the

disparity between trade-off theory predictions and actual data a capital structure puzzle Existing explanations of this puzzle have theoretical shortcomings and lack convincing empirical support !

In this paper, I propose a new explanation for this seeming paradox by taking

into account the specificity of human capital and the potential for opportunistic behavior The theory is based on two basic assumptions The first is that it is costly for the owner of a firm to replace managers and key employees who possess special skills and knowledge with regard to the tasks they conduct The second is that information is imperfect, and therefore economic agents planning to cooperate cannot write a complete contract that takes all the future contingencies into

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by investors and the human capital provided by firm managers and employees who

here are identified as insiders As they gain work experience, insiders may develop special skills that are valuable to the firm Such skills give them bargaining power

that allows them to exact more compensations from the firm’s owners because it is

too costly to have written a wage contract that fully anticipates this In an imperfect information world, it is impossible to write a complete contract that would prespecify

every future contingency and thus prevent investors from being held up by insiders’

Realizing this, investors have reduced incentives to invest, even if the investment

projects proposed by insiders are profitable This is because the insiders cannot make a credible commitment to pay investors all the investment returns specified

by the original contract (for a detailed analysis, see Hart and Moore(1994))

This holdup problem can be solved by an under-and-over compensation contract, under which investors underpay insiders in the initial phase of their employment and overpay them in the final phase Under-and-over payments are calculated according

to the equilibrium wage rate in the labor market This compensation arrangement, however, creates an opportunity for investors to hold up insiders If unpredicted new

profitable investment opportunities emerge before insiders have received the entire overpayment portion of their compensation, investors can threaten to liquidate the

firm and transfer the revenue to new investment opportunities, thus denying insiders

*For further analysis of this “holdup” problem, see Noe and Rebello (1996), Hart and

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the overpayment they are due This is feasible between present insiders do not obviously have a type of human capital that guarantees superior performance in the new opportunities

When information is incomplete, it is impossible to arrive at a complete contract that would eliminate investors’ opportunistic behavior In the absence of such

protection, insiders have an incentive to acquire influence over the reinvestment of their firm’s residual earnings, thus to forestall investors’ opportunistic behavior.’ By investing in projects targeted at their own unique skills, insiders can increase the

liquidation costs born by investors To assure the fundings for these special projects,

insiders are inclined to retain earnings higher than the level efficient to investors, which leads to a debt-equity ratio lower than the level optimal to investors The difference between an insider-efficient earning payout ratio and an investor-efficient payout ratio is determined by trading off the agency cost of investing in insider- specific assets with the cost of replacing the insiders with special human capital

Given that the profitability of.a firm is an indicator of the quality of its human cap-

ital, insiders at profitable firms can retain a higher level of earnings than those at less profitable firms Thus, other things being equal, profitable firms will generally

have a lower debt to equity ratio than less profitable firms

In an incomplete information world, it is a second-best policy for investors to

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adopt an under-and-over compensation mechanism and thus allow for a certain de-

gree of agency costs associated with insider-specific investment Investors endow

insiders with managerial power, including the right of deciding the allocation of

residual earnings, because insiders possess special human capital The separation of

ownership and control allows both investors and insiders to obtain the best possi- ble return from their investments in physical and human capital respectively The

possibility of being held up by insiders makes it necessary for investors to adopt

an under-and-over compensation arrangement Such an arrangement will result in agency cost when insiders leverage their power of determining the allocation of resid-

ual earnings to secure their future overpayment If insiders could not protect their

investment return, they would lack incentive to make firm-specific investments in

human capital Observed debt-equity ratios of firms may not be optimal if judged solely from the perspective of investors, but they are efficient if the necessity for pro-

tecting insiders is taken into account of Maintaining such ratios can help preserve the incentive for insiders to invest in firm-specific human capital Assuming the firm has a relatively effective governance mechanism, the benefits investors obtain from the under-and-over compensation arrangement will be greater than the agency costs associated with it

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managers pursuing their interests at the expense of investors My analysis shows

that investors also have an incentive to engage in opportunistic behavior if they

have to overpay managers to compensate them for their previous contributions To prevent investors’ opportunistic behavior, insiders have a motivation not to invest

in the projects that can enhance insiders’ bargaining power but may not be in the best interest of investors.’ Shleifer and Vishny(1989) suggests that managers can become entrenched in a firm by making manager-specific investments that make it costly for investors to replace them My theory extends their ideas to incomplete

and asymmetric information situations

My theory adopts similar frameworks as financial contracting literature developed during the last ten years or so (e.g., Aghion and Bolton (1992), Dewatripont

and Tirole (1994), Hart (1995), Hart and Moore (1998), etc.) This literature re-

gards firms’ financial structures as mechanisms that help to ameliorate problems of incomplete contracts between investors and entrepreneurs The literature em- phasizes that there are always certain circumstances which are uncontractible when entrepreneurs seek financing from investors In these circumstances agents may behave opportunistically at the cost of their partners’ benefits A firm’s financial

4Myers (2000) holds a similar idea and suggests that going public can help preserve incentives for insiders to make firm-specific investment in human capital The reason is that the ownership of a firm will become diffused after the firm goes public, and this can increase the intervention costs for the equity holders of the firm to replace the insiders What Myers(2000) suggests is that imsiders can take advantage of the collective action problem facing investors to protect their

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structure, however, can allocate residual control rights in a way that limits the ten- dency of its agents to behave inefficiently ex post A theoretical shortcoming of

this literature is the identification of control with ownership (for recent survey, see

Zingales (2000)) My analysis separates these two entities Although insiders do not

own residual earnings, they can take advantage of their control power of residual

earnings to limit the opportunistic behavior of equity holders

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2 Literature Review

The modern corporate finance theory starts from Franco Modigliani and Merton Miller’s classical work in 1958 In this later so-called Modigliani and Miller(MM)

theorem, these two scholars demonstrate that the market value of a firm is unaffected

by how the firm is financed if there are no taxes, incentive or information problems

in capital market Since then academic research has focused on whether the intro-

duction of market imperfections into the Modigliani and Miller (MM) framework makes financing decisions relevant

2.1 Tax-based Theories

The first important factor to be considered is the tax benefits of debt Modiliani and Miller (1963) modify their irrelevancy theory by introducing the effect of corporate tax In the U.S and many other countries dividends are not tax deductible but interest payments are This implies that if investors choose to finance projects with debt they can save all the taxes which they need to pay if instead investors finance projects with equity Therefore if judged solely from the taxes point of view, a firm’s overall value can be increased if the firm increases the debt to equity ratio in its

capital structure The proposition of Modiliani and Miller(1963) actually implies

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The implication of Modiliani and Miller(1963), however, is too extreme and is definitely not the case in the real world Researchers believe that offsetting costs must exist to discourage 100% debt financing In Modiliani and Miller(1963) firm bankruptcy is assumed to be cost free Researchers believe that this assumption is

unrealistic and therefore the first cost proposed in the literature is the cost of bank-

ruptcy, or more generally, costs of financial distress (Kraus and Lizenberger(1973),

and Scott(1976)) According to these researchers the optimal debt level is achieved

through balancing the tax benefits of debt against the bankruptcy costs associated with debt usage This is the basic of classic trade-off theory in capital structure Until late 1970’s this is the dominant theory in capital structure

On the other hand, empirical evidence show that the bankruptcy cost alone can not explain corporate financing practice in the real world Warner (1977) shows that direct costs of bankruptcy for large railroads average no more than 5.3% ex post Weiss(1990) found that direct bankruptcy costs average about 3.1% of the total value of debt and equity for large firms For small firms, these costs may be fairly large, perhaps 20-25 percent of a firm’s value (Ang, Chua, and McConnell(1982)

and Altman(1984)) More recently, Andrade and Kaplan(1998) show that the ex

post costs of financial distress brought about by financing choice amount to 20% of firm value for a group of industrial firms Miller(1977) points out that firms choose

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the costs mentioned above need to be multiplied by the conditional probability of distress to measure ex ante costs The ex ante costs of financial distress, however,

appears to be too small to balance the apparently large tax benefits of debt Miller

explained this point with a comparison of Horse to Rabbit: if the tax benefit of debt financing is as big as a horse, the ex ante bankruptcy cost is then only as big as a rabbit, and they can not cancel out each other

Miller (1977) proposes the difference in personal taxes on debt interest and equity incomes(dividend and capital gain) to offset the tax benefits of debt He shows that

although there is a tax advantage of debt financing at the firm level, investors in person need to pay more taxes on their interest incomes than on equity incomes, and

under certain conditions, these two effects will cancel each other out This implies there does not exist an optimal balance between debt and equity financing for an individual firm Miller’s new point implies that overall taxes can not change the

original conclusion in Modiliani and Miller (1958)

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corporate tax benefits of debt When the personal tax penalty of debt is combined

with significant leverage-related costs, such as bankruptcy costs, loss of non-debt tax

shields, agency costs of debt, it is sufficient to offset the corporate tax advantage of debt at the margin and leads to interior optimal debt-equity ratios

The analysis of trade-off theory shows that taxes play an important role in determining the debt-equity mix of U.S corporations Firms that are generating substantial taxable earnings before interest and taxes(EBIT) should use a substantial amount of debt financing to take advantage of the tax benefit of debt On the

other hand, firms with substantial amount of other tax shields, such as depreciation

deductions and R&D expenses, are likely to have lower EBIT relative to their values and would thus choose lower debt-equity ratios

In reality, however, we do not observe a positive cross-sectional relation between

EBIT and debt ratios Indeed, those firms that generate the largest amount of tax-

able earnings tend to have the lowest debt ratios( ex., Titman and Wessels(1988))

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offset the apparent tax benefits

2.2 Pecking-Order Theory

Myers(1984) and Myers and Majluf (1984) suggest a approach different from trade- off theory to explain the obvious difference between corporate financing practice and academic theories Their explanation starts from Gordon Donaldson’s findings in 1961 Donaldson(1961) observes that firms prefer internal funds to external funds(e.g., through issuing debt or outside equity) to finance their investment projects If external funds are needed, firms issue the safest security first That is, they start with bank loans and corporate debt, then possibly hybrid securities such as convertible bonds, then perhaps equity as a last resort Donaldson called this the pecking order of financial choices Myers and Majluf(1984) give a theoretical explanation for this by the information asymmetry that exists between corporate insiders and outside investors

Myers and Majluf(1984) claims that financing through external markets, includ-

ing both equity and debt financing, is more expensive than internal financing They

do not assume that the transaction costs of outside financing is precludingly high

Empirical evidence shows that the transaction costs cannot make up the huge tax benefits of debt financing Their approach relies on information asymmetry to jus-

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have better information than the market about the project in need of financing, and that firm managers act on behalf of existing shareholders Because the market believes that firm managers will turn to the capital market for financing only when it is beneficial to the existing shareholders, the market will undervalue any risky securities issued by the firms Realizing this, firm managers will choose to finance

their investment projects, first with internal funds, then with riskless debt, followed

by risky debt and lastly with equity, because the uncertainty of the project has more influence on the value of equity than on debt This pecking order theory of financing argues that it may be efficient for profitable firms to retain great amount of earnings for future financial slack Hart (2001), however, points out that the adverse selection problem in this case is essentially a managerial incentive problem and that it can be actually resolved by paying managers based on the firm’s total

market value Hart argues that it is puzzling to use capital structure instead of

an incentive scheme to solve a moral hazard problem Empirical findings are also controversial in supporting pecking order theory (e.g., see Fama and French (2002))

2.3 Non-tax Theories

In addition to trade-off and pecking order theories, in existing literature there are also various nontax capital structure theories based on agency costs, asymmetric

information, product/input market interactions, and corporate control considera-

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a representative work of these theories and it is based on agency conflicts between managers and shareholders It argues that firm managers suffer more loss than

shareholders if the firm goes bankrupt, because managers gain private benefits from

operating the firm To prevent losing power during financial distress, managers may

prefer a debt level lower than is optimal from the perspective of shareholders

This agency theory, however, can not explain why equity holders are so passive in deciding firms’ capital structure If an inefficient capital structure is solely due to manager entrenchment, equity holders can just specify a bottom line for earning

payout and debt-equity ratios in the corporate chapter However we rarely see

investors do so Another shortcoming of this agency theory is that it is almost impossible to quantify private benefits Therefore it can never be known if these benefits are great enough to trade off the reward managers can obtain if they choose debt levels optimal to firms’ market value This agency theory is also inconsistent with fact in as much as it is profitable firms that seem to have great short fall of debt in their capital structures The theory cannot explain why managers in profitable firms are more likely to fail to optimize firm value than their counterparts in less

profitable firms Moreover, empirical research does not find significant evidence to support the agency problem argument, since debt usage and management ownership

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Most of other non-tax driven theories predict a positive relation between prof-

itability and firm’s debt usage and None of these theories can explain why we per- sistently observe that profitable firms tend to have much lower debt to equity ratios

than less profitable firms

2.4 A Recent Empirical Challenge

Although the opinion is unanimous in academia that there is a tax advantage debt at firm level, there is a great divergence among researchers as to its size Significant

progress has been made recently in empirical research.(e.g., Graham(1996)and Gra-

ham(2000)) dealing with this issue Through an innovative method Graham(2000) measures the magnitude of tax benefits It finds that the tax benefits of debt forgone by the U.S firms are indeed in huge amount The average tax benefits forgone by the U.S firms are around 10% of the market value of these firms and debt conservatism

is persistent

Graham(2000) also tests the explanation power of various existing theories and finds that none of them can explain satisfactorily the current corporate financing practices He shows that large, liquid, profitable firms with low expected distress

costs, such as Boeing, Coca-Cola, Compaq, Eastman Kodak, Exxon, GE, Hewlett-

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Motors, IBM, Lockheed Martin, Pepsi, etc tend to use debt conservatively Some of these firms may experience a brief unprofitable periods, but once they return to

a very profitable state, their leverage declines to (or below) its predifficulty level These findings show that trade-off theories alone can not explain why firms choose their capital structures as what we observed in practice

Further investigation in Graham(2000) finds that, in general, firms using debt conservatively pay dividends, have positive owners’ equity Graham(2000) does not find significant evidence of management entrenchment These findings contradict

directly pecking-order theory and agency-conflict based theories

Graham and Harvey(2001) conducts a comprehensive survey of 392 firms that describes the current practice of corporate finance Their results show that firms care most about financial flexibility (the question in the survey is: we restrict debt so we

have enough internal funds available to pursue new projects when they come along)

and credit rating (as assigned by rating agencies) when they make debt policies The

tax advantage of interest deductibility is ranked 4th, moderately important The

factor ranking 3rd is the volatility of firm earnings and cash flows The transactions costs and fees for issuing debt is ranked 5th Only 21.35% of the firms believe the

potential cost of bankruptcy or financial distress is an important or very important

factor when they choose the appropriate amount of debt for their firms

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to explain corporate ñnancing practice

3 The Formal Model

3.1 Setting and Assumptions

I consider a model with four time periods and three agents: an investor, and two

entrepreneurs To simplify my analysis I assume that interest rate is zero All the agents are risk-neutral, expected-value maximizers The investor owns only physical capital, and the entrepreneurs possess only human capital The investor initially chooses and only chooses to cooperate with one of the entrepreneurs who

becomes the incumbent Subsequently, the investor has the choice to stay with the

incumbent or switch to the other entrepreneur who I call the rival

At time 0 the investor and the incumbent negotiate a financing contract for an

investment project The earnings generated by the project are verifiable This makes

equity financing feasible to the project.? The investor and the incumbent agree on an

equity contract, which endows the ownership of the project to the investor, and the control rights of the project to the incumbent.® The investor will pay the incumbent

5Some economists argue that outside equity financing can still be feasible even if the cash flow

generated by a firm cannot be verified (Fluck (1998), Myers (2000)) In their models, however,

the payment paths of outside equity are more like that of debt than that of equity, and equity investors can receive their returns on their investment only at a break-even level

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a market wage and receive all the residual earnings created by the project as her investment return The cost needed to set up the project at time 0 is K K is provided by the investor since the incumbent has no personal wealth and the only

production asset he can provide to the market is his human capital I assume that

both the investor and the incumbent can withdraw their capital from the project.’1 also assume that information is symmetric, that is, all the information is publicly known to all the agents

The incumbent’s human capital, indexed by i, can be either high quality or low

quality, that is, i ¢ {£,H} I assume that neither the investor nor the entrepreneurs

know the value of i until the end of the project The prior information about i is

that prob(i = L| t = 0) = prob(i = H| t = 0) = 4 At time 1, earnings of Yyare

realized The distribution function of Yj, | f (1), conditional on i, satisfies the

following conditions: E(Y;| i= L) = ay, E(Y%| 1 = H) = Tụy, and 7¡ € 7 The agents’ beliefs about i will be updated at later time periods by applying Bayes rule

however, may not be feasible due to asset substitution problem (Miller (1977)) and managerial

opportunism We will discuss this point further in part four Also in that part we will discuss why the investor delegates the control rights to the incumbent

7The Investor and the incumbent can restrict each other from withdrawing their capital in the

contract In an uncertain world, however, neither the investor nor the incumbent can know for

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Figure 1

t=0 t=1 t=2 t=3

Project is set Earnings of Y; Valueof Earnings of Y3 up at cost K are realized risrevealed are realized

h ——ỒgÐ

An additional project be set up at either time 1 or 2

The investor can hire the rival to replace the incumbent at either time 1 or time 2° The rival’s human capital, indexed by r, can also either be low quality or high

quality, that’s, r € {L, H}, and f(Yi| r) is the same as f (Yi|2) At time 0 and 1 it

is publicly known that prob(r = L) = prob(r = H) = 4 At time 2, the value of r will be revealed to all the agents

At time 3, final earnings of Y3 are realized The distribution function of Y3, f

(¥3),depends on the value of ¢ (or r), E(Y3| i = L) = my, E(Y3| i = H) = Tan,

E(¥3| r= L) = a1, and E(¥3| r = H) = Trụ

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Assumption 1 13, > Trt, T3n = Tran aNd Trp > Ti

Ta > Wry and 13, > Try imply that the incumbent can develop special skills from

his work experience at time 1 and the value of the project will depend partially on

such skills This makes it costly to replace the incumbent after the project is set up rh = 3;.means that it is beneficial to replace an incompetent entrepreneur, even if he has developed special skills in previous time periods

An additional project can be set up along with the existing project either at time 1 or at time 2 The cost to set up the project is J The expected value added by the additional project at time 3 is Am; ifi = L, and Am, if i= H Note 0 < Am, < L < Ath

Assumption 2 E(¥3| r= L,I)—E(¥3| r = L) = 0, and E(Y3| r = H, T1) — E(| r= HH) =0

I assume that the additional project can help entrench the incumbent in the firm,

that is, after J is invested in the existing project, it will be more costly to replace

the incumbent

The capital J can also be invested in a separate project proposed by the rival,

and I assume that the corresponding profit functions are B(/ | r = L) = Am and

BU |r = H) = Am

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I assume that the labor market is efficient The market wage rate for the entrepreneurs is w, if i(or r) = L, and wy, if ior r) = H, where w; < wy The market wage rate that the entrepreneurs can earn will change according to the market belief

about the quality of their human capital Both entrepreneurs can earn w; at time 1, and at time 3 the incumbent will be paid wz w,and wz are defined below.!° Since

the value of r is revealed at time 2, the replacement manager will earn either w; or

+u„ at time 3

Definition1 w= sew +5 *Wh, and w3 = wx prob( i = L| Y;)+wnxprob(i = H

| Yi)

Assumption3 E(Y, + Yq|t = 0) -—2* wy —- X = 0, and (1w + Tạp) —2* Wn > K I assume that the expected NPV of the project at time 0 is zero, and the project is expected to earn profit if and only if ¢ = H

of the firm into the assets that are specific to their human capital Insiders may also invest in the

projects that need a long time period to realize the returns These activities may not be value-

maximizing, but they can increase the cost for investors to liquidate the firm and therefore can help entrench insiders in the firm Shleifer and Vishy (1989) show that managers bind shareholders to themselves by using shareholders’ money to make manager-specific investments Here we take a similar approach In our model, however, we do not prespecify such investment projects as value-decreasing ones We will elaborate on this point later

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Lemma 1 (T4 + Tại) — 2 * ws < K

This can be easily derived from assumption 3, and it shows that it is inefficient

to build up the project if 2 = L

Assumption 4 1,1 = wy, and Trp, > Wr Lemma 2 Trai > wy, and 73n > Wh

This lemma can be easily derived based on assumptions 1 and 4 In combination

with assumption 4 it means that it is profitable to replace the incumbent with the rival if and only if i = Ù and at the same time r = H

Assumption 5 5 * Amy + SAN¡ = Jf,

I assume that the expected NPV of the additional project is also zero at time 0

In my model, once the capital K and / are invested, they can not be used for

consumption ‘This implies that once the investment projects are set up, the investor

only has one choice: whether to continue cooperating with the incumbent or turn to the rival

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In this model 73; — w; to represent the value of the special human capital developed by the high quality entrepreneur

To further specify the properties of the additional project | make the following

assumptions

Assumption 7 5 (Tin +7) — wy > Ï Assumption 8 I > 5 (rn — wh)

Assumption? implies that if the project is set up at time 0 can earn an above normal return then the income earned at time 1 will be able to cover the construction cost of the additional project Assumption8 defines the lower bound of the scale of the additional project According to assumption 2 this is also the lower bound of the agency cost when the incumbent entrenches himself in the role of controlling the

project

3.2 Optimal Contract under Incomplete Information

First let us clarify an important condition for the incumbent manager to continue the project

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Proof :

E(¥3|¥1) = mai+ prob( ¿ = | Y1) + Tay x prob( = H | Y;)

from lemma 2 we know 7s¡ > 1, and 73, > wa By applying the definition of

w3, we can easily obtain the result

Q.E.D

Therefore, if r = L, it the investor will let him continue the project regardless of his performance at time 1, since the investor has no better options The special

skills developed by the incumbent can at least make up part of the investor’s investment returns The theorem below states the optimal contract under the incomplete information condition

Theorem 1 After the project is set up at time 0, the investor has the right to

decide when to replace the incumbent entrepreneur and when to set up the additional project The compensation for the incumbent is w, at time 1, and is w3 at time 3

if the investor continues hiring the incumbent

Proof: See Appendiz1

According to this contract, the project will be set up at time 0 The investor will receive max{Y; — w,,0} at time 1 At time 2, ifr = L, the incumbent will

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additional capital will be invested into the existing project otherwise the investor will refuse to finance the additional project In this situation the investor will receive max{Y3 — w3,0} If r = H, the incumbent will be replaced if and only if

E(¥3|¥1) — w3 < tn — wa Uf the rival controls the project the investor will receive max{Y3 ~ wp, 0} at time 3 The additional project will be set up with the rival

no matter who controls the existing project [ define the optimal contract as the first-best policy

This optimal contract, however, is not an equilibrium result Note when r = L, E(W3|Y1) — w3 > a1 — wy In this case the incumbent can hold up the investor and

extract the rent E'(Y3/Y,) — ws from the investor Even when r = H, if E(¥Y3|Yi) —

Wg > Tpp—Wa, the incumbent can still hold up the investor The intuition supporting

this argument is that after working for the project for a certain time period, the incumbent entrepreneur may have developed special skills that partially determines

the prospects of the project The incumbent can take advantage of his special skills to hold up the investor, e.g., the incumbent can threaten to withdraw his human

capital from the project and extract a rent from the investor

Noe and Rebello (1996) acknowledge this holdup problem and argue that the incumbent can capture a share of the rents generated by his special skills if he

cannot be forced to work for the firm Hart and Moore(1994) show that some

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suboptimal time due to this holdup problem My analysis has a similar result (Note the project has a zero NPV at time 0) If the investor realizes that the entrepreneur

has opportunities to capture a return more than w3 at time 3 (E(ws|t = 0) = wy), she will have no incentive to invest at time 0 since she will suffer loss due to the

holdup potential This is because £(Y, + Y3|t = 0)-2*w, — K =0

3.3 Equilibrium Contract under Incomplete Information

If the investor is not completely passive, however, the equilibrium result will be

different from what Noe and Rebello (1996) and Hart and Moore(1994) demonstrate

I suggest that the investor can underpay the incumbent in the initial stage of the

employment contract and overpay him at the ending stage of the contract Such a compensation arrangement can prevent the incumbent’s opportunistic behavior and

in equilibrium the incumbent only earns a market equilibrium return on his human

capital

Formally, realizing the possibility of being held up by the incumbent, the investor agrees to pay the incumbent only wp; = (1 — a) * uw, (0 < a < 1) at time 1, and commits to pay him wy,3 = œ #10 + ws at time 3 The incumbent can only earn w3 at time 3 from the labor market if he withdraws his human capital from the

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incumbent will be paid market equlibrium wage rate 0 + ws Assumption 9 a = (m3 — w)/w1

Assumptiơn10 Š(Trn — 1y) > (tại — 0ì) > (rn — wa)

Assumption11 An, — An; > 3s — Uy)

Assumption9 implies that the incumbent entrepreneur will lose w3, — w, if he is replaced by the rival entrepreneur Note that ws; — w; measures the value of firm-specific human capital Assumption 10 gives the boundaries of the value of

firm-specific human capital Assumption 11 gives the lower bound of the value of the additional project

This compensation arrangement, however, has a time-inconsistency problem The investor’s commitment at time 0 is not creditable because she has the right to withdraw her assets from the project at any time If at time 2 E(Y3|Yi) - (ws + a * wi) < Tn — Wp, the investor will always choose to liquidate the project

instead of fulfilling her commitment This is an instance of the holdup problem: the

entrepreneur can accept the under-and-over compensation arrangement and have his human capital specific to the project, but his incentive is reduced by the risk

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To motivate the incumbent entrepreneur to participate in the project, there must be a mechanism to ensure that the investor will fulfill his commitment Shleifer and Vishny(1989) suggest that managers can entrench themselves in a firm by making

manager-specific investments that makes it costly for investors to replace them

Similarly, I assume that in the contract made at time 0 the investor allows the incumbent manager to set up the additional project at time 1 if and only if prob(i =

this power can secure the entrepreneur’s stake in the project and preserve both contracting parties’ incentive to participate in the project The following theorem

states the equilibrium contract under the incomplete information condition

Theorem 2 At time 0 the investor agrees to pay the entrepreneur (1 — 30)10 at time 1 and commits to pay him (aw; + w3) at time 3 The investor has the power to replace the entrepreneur at any of the subsequent times If at time 1 prob(i = H | ¥1) > prob(i = H|t = 0) = §, the incumbent will be given the power to set up the additional project at time 1

Proof: See Appendix 2

Under the equilibrium contract, if Y; > su +71,), the incumbent will set up

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if r = H at time 2, the incumbent will be replaced by the rival and the additional project will be set up with the rival If, however, r = L, the incumbent will continue operating the project but the additional project will not be set up

3.4 Further Analysis of the Equilibrium Contract

3.4.1 A Second Best Policy

In this part I demonstrate that the equilibrium contract is a second best policy for the investor

The other approach to protect the incumbent entrepreneur from being held up by

the investor is a compensation arrangement Instead of authorizing the incumbent

entrepreneur the power to set up the additional project at timel, the investor will pay the incumbent more than (aw + w3) at time 3 so that the entrepreneur’s expected

income at time 3 is still (aw, + ws) even if there is a possibility that the incumbent may be replaced I claim that such a compensation arrangement will bring less

profits to the investor than the equilibrium contract I proposed in theorem 2 Claim 1 A compensation contract necessary to protect the incumbent entrepreneur’ stake in the project is an inefficient choice

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