Lecture 7: Managerial Incentives and Market Competitionccfour/EO7.pdf · Lecture 7: Managerial...

Lecture 7: Managerial Incentives and MarketCompetition

Cheng Chen

School of Economics and Finance

The University of Hong Kong

(Cheng Chen (HKU)) Econ 6006 1 / 18

Introduction

Motivation

Managerial Incentives and Moral Hazard.

How does aggregate economic environment a�ects managerialincentives?

I This is fundamentally related to e�ciency of �rm.

How does it behave empirically?

References:I Klaus Schmidt: �Managerial Incentives and Product Market

Competition� Review of Economic Studies

I Michael Raith: �Competition, Risk and Managerial Incentives�American Economic Review

I Vicent Cunat and Maria Guadalupe: �Globalization and the Provisionof Incentives inside the Firm: the E�ect of Foreign Competition�Journal of Labor Economics


Introduction

Motivation










Introduction

Motivation










Introduction

Motivation










Theory Partial Equilibrium Analysis

Previous Research

Hart (1983): A common shock is transmitted through market price.

More competitive market → relative performance is more precise →higher-powered incentive contracts.

Scharfstein (1988): Hart's result crucially hinges on assumption that

manager is in�nitely risk averse, and that income above a subsistence

level has no value for manager.



Schmidt (1997)

Two e�ects due to intensi�ed competition:1 Threat-of-liquidation e�ect: Competition ↑ → Prob. of liquidation ↑→ High incentive power

2 Value-of-a-cost-reduction-e�ect: Ambiguous.

In total, e�ect of intensi�ed competition on managerial incentives is

ambiguous.



Schmidt (1997)

Two e�ects due to intensi�ed competition:1 Threat-of-liquidation e�ect: Competition ↑ → Prob. of liquidation ↑→ High incentive power

2 Value-of-a-cost-reduction-e�ect: Ambiguous.

In total, e�ect of intensi�ed competition on managerial incentives is

ambiguous.



Premises

Agents are all neutral.

Cost realization: c ∈ {cL, cH}.Prob. for cL: p. Cost of raising Prob. is G (p).

Ex post pro�t for �rm: π = π(c , φ, ε), where ε is random error and φis degree of competition.

Assumption 1: Standard assumptions on π(c , φ, ε).



Premises

Agents are all neutral.

Cost realization: c ∈ {cL, cH}.Prob. for cL: p. Cost of raising Prob. is G (p).

Ex post pro�t for �rm: π = π(c , φ, ε), where ε is random error and φis degree of competition.

Assumption 1: Standard assumptions on π(c , φ, ε).



Payo�s

Principal's payo�:

UP = max{0,π(c , φ, ε)} − w ,

Agent's payo�: Um = w − G (p) if no liquidation and

Um = w − G (p)− Lm if liquidation happens.

Ex ante pro�t:

Πj (φ) =∫

εmax{0,π(c j , φ, ε)}dF (ε) j ∈ {L,H}.

If c = cL: Prob. of liquidation is zero. If c = cH : Prob. of liquidationis l(φ) and l

′(φ) > 0.



Payo�s


UP = max{0,π(c , φ, ε)} − w ,



Ex ante pro�t:

Πj (φ) =∫



′(φ) > 0.



Payo�s


UP = max{0,π(c , φ, ε)} − w ,



Ex ante pro�t:

Πj (φ) =∫



′(φ) > 0.



Objective Function

Principal's optimization problem at date 0 is

maxp,wL,wH

p[ΠL − wL] + (1− p)[ΠH − wH ]

s.t.

p ∈ arg maxp′∈[0,1]

p′wL + (1− p

′)wH − G (p

′)− (1− p

′)l(φ)Lm (IC )

pwL + (1− p)wH − G (p)− (1− p)l(φ)Lm ≥ Um (PC )

w j ≥ 0 j ∈ {L,H} (WC )

Assumption 2: Assure global concavity.



Objective Function

Principal's optimization problem at date 0 is

maxp,wL,wH

p[ΠL − wL] + (1− p)[ΠH − wH ]

s.t.

p ∈ arg maxp′∈[0,1]

p′wL + (1− p

′)wH − G (p

′)− (1− p

′)l(φ)Lm (IC )

pwL + (1− p)wH − G (p)− (1− p)l(φ)Lm ≥ Um (PC )

w j ≥ 0 j ∈ {L,H} (WC )

Assumption 2: Assure global concavity.



Objective Function (Cont.)

FOC: G′(p) = wL − wH + l(φ)Lm.

FB: G′(pFB) = ΠL −ΠH + l(φ)Lm.

Note that we can achieve FB, if there is no WC .

Assumption 3: manager's cost to work for �rm and to choose pFB is

smaller than expected increase in pro�ts:

Um + G (pFB) + (1− pFB)l(φ)Lm < pFB(ΠL −ΠH)

Under Assumption 3, there is no way to fully incentivize agent without

giving him rent.



Objective Function (Cont.)

FOC: G′(p) = wL − wH + l(φ)Lm.

FB: G′(pFB) = ΠL −ΠH + l(φ)Lm.

Note that we can achieve FB, if there is no WC .

Assumption 3: manager's cost to work for �rm and to choose pFB is

smaller than expected increase in pro�ts:

Um + G (pFB) + (1− pFB)l(φ)Lm < pFB(ΠL −ΠH)

Under Assumption 3, there is no way to fully incentivize agent without

giving him rent.



Solution

Optimal SB e�ort level pSB = max{p∗, p}:

If PC does not bind : G′(p∗) + p∗G

′′(p∗) = ΠL −ΠH + l(φ)Lm

If PC binds : pG′(p)− G (p) = l(φ)Lm + Um

and

wH = 0; wL = G′(pSB)− l(φ)Lm.

Rent for agent:

Um − Um = pwL − G (p)− (1− p)l(φ)Lm − Um

Term p∗G′′(p∗) = d(Um−Um)

dp captures rent accruing to agent (SB).



Solution

Optimal SB e�ort level pSB = max{p∗, p}:

If PC does not bind : G′(p∗) + p∗G

′′(p∗) = ΠL −ΠH + l(φ)Lm

If PC binds : pG′(p)− G (p) = l(φ)Lm + Um

and

wH = 0; wL = G′(pSB)− l(φ)Lm.

Rent for agent:

Um − Um = pwL − G (p)− (1− p)l(φ)Lm − Um

Term p∗G′′(p∗) = d(Um−Um)

dp captures rent accruing to agent (SB).



E�ect of Increased Bankruptcy Cost

Suppose Lm increases

If PC is not binding.I Principal must bene�t (revealed preference argument).I E�ect on agent's payo� is ambiguous.

If PC is binding.I No e�ect on agent's payo�.I E�ect on principal's payo� is ambiguous.



E�ect of Increased Bankruptcy Cost

Suppose Lm increases

If PC is not binding.I Principal must bene�t (revealed preference argument).I E�ect on agent's payo� is ambiguous.

If PC is binding.I No e�ect on agent's payo�.I E�ect on principal's payo� is ambiguous.



Market Competition and Incentive power

Suppose φ increases.

If PC is not binding:

dp∗

dφ=

[∂ΠL(φ)/∂φ− ∂ΠH(φ)/∂φ] + (dl(φ)/dφ)Lm

2G ′′(p∗) + p∗G ′′′(p∗)

If PC is binding:dp

dφ=

(dl(φ)/dφ)Lm

pG ′′(p)

Threat-of-liquidation e�ect ((dl(φ)/dφ)Lm) exists in both cases and

is positive

It becomes cheaper for principal to incentivize agent.

Value-of-a-cost-reduction-e�ect appears only when PC does not bind,

since p is independent of ΠH and ΠL.

And direction of its e�ect is ambiguous.






dp∗

dφ=


2G ′′(p∗) + p∗G ′′′(p∗)

If PC is binding:dp

dφ=

(dl(φ)/dφ)Lm

pG ′′(p)


is positive










dp∗

dφ=


2G ′′(p∗) + p∗G ′′′(p∗)

If PC is binding:dp

dφ=

(dl(φ)/dφ)Lm

pG ′′(p)


is positive










dp∗

dφ=


2G ′′(p∗) + p∗G ′′′(p∗)

If PC is binding:dp

dφ=

(dl(φ)/dφ)Lm

pG ′′(p)


is positive






Theory Managerial Incentives in Industry Equilibrium

Raith (1997)

Endogenize �rm structure (number of �rms in equilibrium) and discuss

how market size and reduction in transport costs a�ect managerial

incentives.

Also discusses how managerial incentives are related to volatility of

�rm performance.

Di�erent from Schmidt (1997):I No role for bankruptcy.I Agent is risk averse.I Only value-of-a-cost-reduction-e�ect exists.



Raith (1997)

Endogenize �rm structure (number of �rms in equilibrium) and discuss

how market size and reduction in transport costs a�ect managerial

incentives.

Also discusses how managerial incentives are related to volatility of

�rm performance.

Di�erent from Schmidt (1997):I No role for bankruptcy.I Agent is risk averse.I Only value-of-a-cost-reduction-e�ect exists.



Setup

A Salop (1979) circle model with optimal incentive contract.

Firms are homogeneous, and cost realization is

ci = c − e i − ui ,

where ui ∼ N(0, σ2).

Free entry with �xed entry cost: F .

Managerial contract:

wi = si + bi (c − ci ),

bi measure the incentive power.

Two questions: Is linear contract optimal? What happens if

managerial compensation is based on pro�t or sales (more realistic?)?



Setup



ci = c − e i − ui ,




wi = si + bi (c − ci ),






Setup



ci = c − e i − ui ,




wi = si + bi (c − ci ),






Setup (Cont.)

Agent's utility: −e−r [wi−ke2i /2]. Reservation utility: zero.

Agent's objective function

maxei

si + biei −1

2rb2i σ2 − k

2e2i .

Consumer's utility (the circle model):

Vi (x) = y + a− pi − t(x − zi )2.

Three exogenous parameters: Transport cost t, market size m, and

cost of entry F .

Firms post prices after observing realized cost.

Assumption 1: existence of hinterland → σ can't be too big.

Assumption 2: existence of hinterland → incentive power can't be too

strong → marginal cost of exerting e�ort (k) can't be too small.



Setup (Cont.)



maxei

si + biei −1

2rb2i σ2 − k

2e2i .


Vi (x) = y + a− pi − t(x − zi )2.


cost of entry F .







Setup (Cont.)



maxei

si + biei −1

2rb2i σ2 − k

2e2i .


Vi (x) = y + a− pi − t(x − zi )2.


cost of entry F .







Optimal Incentive Contract

Proposition 3: optimal incentive power is

b =m

n(1+ krσ2).

Let us �x n (number of �rms in equilibrium)I m ↑ → b ↑ (market size e�ect).

I t and F do not a�ect b directly. Why?I Business-stealing-e�ect and business-stolen-e�ect (or scale e�ect)

perfect o�sets each each other..

However, key is to endogenizing n.



Optimal Incentive Contract

Proposition 3: optimal incentive power is

b =m

n(1+ krσ2).

Let us �x n (number of �rms in equilibrium)I m ↑ → b ↑ (market size e�ect).I t and F do not a�ect b directly. Why?I Business-stealing-e�ect and business-stolen-e�ect (or scale e�ect)

perfect o�sets each each other..

However, key is to endogenizing n.



Incentive Power and Market competition

Proposition 4: The equilibrium number of �rms (n∗) increases withtransport costs t (decreases with product substitutability), increases,

but less than proportionally, with market size m, and decreases with

the cost of entry.

Intuitions...

Proposition 5: With endogenous market structure, piece rates are

higher in markets with more substitutable products and in larger

markets, but lower in markets with lower entry costs.

Key is change in equilibrium number of �rms (n∗).

After all, only value-of-a-cost-reduction-e�ect plays a roll.

Existence of �X� ine�ciency.






the cost of entry.

Intuitions...












the cost of entry.

Intuitions...












the cost of entry.

Intuitions...









Incentive Power and Volatility

Proposition 7: With endogenous market structure, the variance of

�rms' gross and net pro�ts is higher in markets with more

substitutable products and in larger markets, but lower in markets with

lower entry costs.

Corollary: Piece rates are positively correlated with the variance of

�rms' pro�ts across markets that di�er in product substitutability,

market size, or entry costs.

Insight: Incentive Power and Volatility (or riskiness) are just correlated

(no causal relationship).







lower entry costs.












lower entry costs.








Managerial E�ort, Firm Heterogeneity and InternationalTrade

Does �rm heterogeneity matter?

Does agency problem (family �rms v.s. non-family �rms) matter for

change in managerial e�ort choice?

How do managerial incentives a�ect aggregate productivity and

welfare?

Paper one: Import Competition and Agency Problems in Family Firms.

Paper two: Agency Problem, Trade Liberalization, and Aggregate

Productivity.








welfare?



Productivity.








welfare?



Productivity.








welfare?



Productivity.


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