Recent Developments in Contract Theory Scott Masten University of Michigan May 20, 2009 ESNIE 2009.

Recent Developments in Contract Theory

Scott Masten

University of Michigan

May 20, 2009

ESNIE 2009

Issue 1: Why contract?

Contracting is used to make promises legally enforceable and thereby protect reliance or relationship-specific investments.

Issue 2: Contract design

Emphasis on substantive price: – Align substantive incentives (≈ incentive compatibility)

– Divide expected surpluses (≈ participation constraint)

– Allocate risk

Conventional analysis

1. Contracts with no commitment

Detailed, long-term agreements with

• little or no relationship-specific investment

• broad discretion to terminate the agreement on little or no notice (and often make termination the exclusive remedy in the event of dissatisfaction with the other party’s performance)

Examples: franchise contracts, equipment leases, distribution and advertising agreements, software licenses

2. Pricing with no apparent incentive effects

• Stock options and profit sharing compensation for employees who cannot significantly affect outcomes

• Executive compensation that does not filter out market-wide risks.

• Fixed quantity contracts with elaborate price adjustment provisions

Anomalies

What’s missing?

Treatment of ex post adjustment

In conventional (agency) theory, ex post adjustment (renegotiation) is either prohibitively costly or costless.

Illustration: Efficient breach

Definitions: v = value to the buyer of seller's performances = value of seller's next best alternative to performance

(i.e., to trading with buyer). pk = contract priceπ = economic profit (surplus; private gain)

Illustration: Efficient Breach

Profits:For buyer: πB = v − pk

For seller: πS = pk − s

Efficiency:

Exchange is efficient if there are gains from trade:

v − s > 0 or v > s

Incentives

Transactors only want to exchange if π is positive:

For buyer: πB = v − pk > 0.

For seller: πS = pk − s > 0 .


With no enforcement, buyer would perform only when v > pk

=> inefficient breach

vpks

efficient performance

buyer performance (no contract)inefficient breach

No enforcement


With specific performance contract, buyer would perform too often (i.e, for all v)

vpks


buyer performance (specific performance)

inefficient performance

Specific performance contract


Expectation (or stipulated) damages:

Set δB = pk − s

=> Buyer performs if v – pk > – δB

or v > pk – δB = pk – (pk − s) = s

vpks

buyer performance (expectation damages)

Expectation damages contract

efficient breach

δB


That’s fine, as far as it goes, but note:

1. It does not matter whether a court or the contract sets damages.2. It does not matter what price is set as long as the ex ante

distribution constraint is satisfied; ex post distribution is irrelevant.3. It does not matter when the price is paid: ex ante, ex post.

4. In fact, unless renegotiation is costly, it does not matter what the contract says or whether a contract is written at all: Any inefficiency implies gains from negotiation.

vpks


buyer non-performance (no contract)

efficient nonperformance

buyer performance (specific performance)

Buyer loses but either (i) damages assure performance or (ii) renegotiation results in efficient performance.

The role of price

time

st

vtv0

s0

pk

If either courts or renegotiation is costless, price doesn’t matter.

Pricing costs

1. It is costly (but not infinitely so) to settle on price.

• Costly bargaining/negotiation• Costs of evaluating whether price is satisfactory or “appropriate” may involve

nontrivial time and attention

2. It is costly (but not prohibitively so) to enforce prices. Even after price has been agreed on, transactors may attempt to evade

performance or force a renegotiation if dissatisfied with terms of trade.

Contrive cancellation by • exploiting ambiguous terms• suing for trivial deviations or making false claims of dissatisfaction• withholding relevant information• interfering with or failing to cooperate with other party’s performance• inducing breach

“Post-agreement jockeying”• foot dragging• working to rule• perfunctory performance

“No contract in the world will cause an unwilling partner to perform.”

Michael Levine via Bob Gibbons (2005).

The role of price

Costs of arriving at and enforcing price implies third function of price:

• “Equilibrating hazards” (Williamson) • Keeping transactions within the “self-enforcing range” (Klein)• Avoiding “post-agreement jockeying” (Goldberg)• Maintaining “smooth trading relationship” to avoid “aggrievement

costs” (Hart) • Satisfying the “ex post participation constraint” (Oyer)

Common feature is that price now matters even if substantive incentives don’t. Want to set price to avoid having to re-set price.

Model:

Risk neutral buyer and seller

Discrete performance (no substantive incentive issues)

v = the uncertain value (net revenue) of the transaction to the buyer (gross of payments to the seller)

s = the uncertain cost of performing the transaction to the seller

v, s distributed F(v,s)

pk = “agreed-on” (contract) price

(Re)negotiated price: p' = γ v + (1 – γ )s, where γ ε [0, 1]

=> F(v,s) → G(p′)

(Re)negotiation costs: n = nB + nS

Indefinitely repeated performance

“Equilibrating hazards”

p'

pk

nB nS

buyer rejection seller rejection

For single transaction, given an agreed-on price = pk

Seller reneges if p′ – pk > nS

Buyer reneges if pk – p′ > nB


p'

nB+WB


nS+WS

pk

With repeated transactions and reputational capital, Wi

Seller reneges if p′ – pk > nS + WS

Buyer reneges if pk – p′ > nB + WB


Maximum negotiation costs:

∑(nB+nS)/(1+r)t over t ε [0, ∞)

= (nB+nS)/r

Transactors objectives:

Maximize joint surplus ↔ minimize (re)negotiation costs (because only source of inefficiency is negotiation costs)


' *min ( ) ( ) ,

k

S Bppn n dG p

* { : ( ) ( )}.k B B k S Sp p n W p p n W

where

p'

nB+WB


nS+WS

pk

Choosing pk to minimize probability of rejection =>

( ) ( ).k B B k S Bg p n W g p n W

“hazard equilibration”


Pricing matters

With costly pricing, price now matters: Transactors would want to adjust price over time so that transaction stays within the self-enforcing range.

time

st

vtv0

s0

pk0

pt

p'- pk0

g(p'- X)

g(p'- )

nS+WS-(nB+WB)-(nB+WB*) (nS+WS*)

Expected negotiation costs can be reduced if can relate the contract price to something correlated with p′: pk = αX

Price adjustment

Savings = difference between shaded and hashed areas

Tying pk to X reduces

variance of (p′– pk)

p'pknS+WS-(nB+WB)

-(nB+WB*) (nS+WS*)

Implication: The value of accurate price adjustment increases with the variance of p′ = γ v + (1 – γ )s

Price adjustment

Applications and evidence

shippers receivers

Organization of Freight Transportation

Also: loading/unloading, maintenance, ….

carriers

drivers

vehicles

Relations between Carriers and Truck Drivers Stylized facts:

• Little or no relationship-specific investments • Yet long-haul truckers operate mainly under long-term

contracts (“permanent leases”) or vertical integration (employee drivers).

• Permanent leases require drivers to carry a particular carrier’s hauls exclusively for some (possibly indefinite) period (> 30 days) but are flexible: carrier or driver can terminate on short notice, and driver can reject hauls.

• Haul pricing specified in advance: either “by mile” or “percent of freight bill”


Relations between Carriers and Truck Drivers Anomalies:

1. Vertical integration and long-term contracts can’t be explained by relationship-specific investments (in most cases).

2. Pricing can’t be explained by incentives: Mileage is standardized (“bureau miles” not actual) and freight bill is known before haul accepted.


Relations between Carriers and Truck Drivers


Why contract? Intertemporal bundling

Hauls are heterogeneous vary by

size, weight, distance, time, origin and destination, route, backhaul potential;

need for special handling (fragile or perishable items) or equipment (oversized or liquid cargos);

time sensitivity, flexibility and cooperativeness of shippers and receivers.

Haggling between driver and dispatcher over price for each haul is socially unproductive: Ultimately, all hauls will get carried; only question is at what price.

Agreeing to perform a series of hauls at a price that reflects expected cost of hauls avoids need to price hauls individually.

Analogous to bundling transactions to reduce excessive search/sorting costs diamonds (Barzel, 1982; Kenney and Klein, 1983), movies (Kenney and Klein, 1983), and tuna (Gallick, 1996)



Driver and carrier can further reduce haul rejection (and need to

re-price) by relating price to haul costs.

Tradeoff: Accuracy versus manipulation• “by mile” pricing can’t be manipulated but neglects many

other (non-mileage) cost determinants• “percent revenue” pricing can incorporate more cost

determinants but can be misreported or otherwise manipulated by carrier

Therefore, expect greater use of percent revenue for hauls with

greater variance in non-mileage costs.



DataSurvey of drivers conducted under the University of Michigan Trucking Industry Program (UMTIP)

Data from 798 over-the-road truck drivers collected at 22 different truck stops, approximately 45 minutes each (~ 220 questions)

Topics include • compensation; • driving and non-driving work hours and hours of rest; • work duties; • specific inquiries about the characteristics of the last load carried by

the driver



Haul Pricing



Haul attributes

Table 3. Kolmogorov-Smirnov Non-Driving Time Equality of Distribution Tests

Parameters significant at the 0.05 percent level in bold.

0 720 1440 2160 2880 3600

by mile

percent revenue

Distributions of non-driving time (minutes)

by mile

(n=411)

pct. rev.

(n=162)

mean 280 505

s.d. 485 1,050

equality of s.d. rejected at .001 level

Drivers paid as a percent of revenue (freight bill) carried loads with higher variance in non-driving times.

Haul heterogeneity by trailer type

Dry vans: Carry a wide range of products and use standard loading docks and equipment

dry-van drivers tend to face fewer delays waiting for dispatch and require less time loading and unloading.

Flatbeds: Carry loads that are often “over-dimensional and short-haul, tend to be high value, and sometimes require slower speeds, alternate routes and even escorts" (Heine, 1999); often require tarping, tie-downs.

Tankers: “Reefers”:

Table 3. Kolmogorov-Smirnov Non-Driving Time Equality of Distribution Tests

Parameters significant at the 0.05 percent level in bold.

0 720 1440 2160 2880 3600

dry vans

non-vans

Distributions of non-driving time (minutes)

dry van

(n=366)

non-van

(n=265)

mean 279 448

s.d. 558 843

equality of s.d. rejected at the .001 level

Drivers of non-vans had higher variance of in non-driving times than did drivers of dry vans.

Redetermination versus Renegotiation

0.27

0.02

0.730.98

0%

20%

40%

60%

80%

100%

1 20

Contract Duration (in years)

Prop

ortio

n Redetermination

Renegotiation

Price Adjustment in Natural Gas Contracts (Crocker and Masten, 1993)


Renegotiation, which is more accurate but also more costly than redetermination (e.g., price escalators), is more common in longer term contracts, where uncertainty would be greater.


0.43

1

0.56

0%

20%

40%

60%

80%

100%

0 100

Take-or-pay Percent

Pro

port

ion

Redetermination

Renegotiation

Price Adjustment in Natural Gas Contracts


Renegotiation is more common in fixed-quantity contracts than in variable-quantity contracts.


0.68

1

0.32

0%

20%

40%

60%

80%

100%

Pro

po

rtio

n

Redetermination

Renegotiation

take%=0

duration=1

take%=100

duration=20



Renegotiation is most common in long-term, fixed-quantity contracts.

Frequency of price adjustment: OILVAR=.311

00.10.20.30.40.50.60.7

> 5 3-5 2 1 <1Adjustment frequency (in years)

Pro

ba

bilit

y

Redetermination

Renegotiation

Prices are adjusted more frequently with (low cost) redetermination than with (high cost) renegotiation.



Frequency of price adjustment: OILVAR=.610

00.10.20.30.40.50.60.7

> 5 3-5 2 1 <1Adjustment frequency (in years)

Pro

ba

bili

ty

Redetermination

Renegotiation

Greater energy market volatility implies more frequent adjustment




Other applications and evidence• Oyer (2004) and Oyer and Shafer (2005): Awarding of stock options to

low-level employees represents low-cost way of adjusting compensation to reflect market conditions.

• Other studies showing that adjustment costs are important– Fordes and Lederman (AER forthcoming) – Ownership of regional airlines

consistent with economizing on adjustment costs.

All of these findings are consistent with the view that ex post

adjustment/negotiation costs are important determinants of contract

form and of the efficiency of contracting.

Contracts as Constitutions

Why contract? (reprise)

• Like constitutions, contracts establish the process by which transactors adjust the terms of trade over time. – Can specify substantive rights and/or procedures for adapting.

• Important goal becomes avoiding court ordering. – If courts effectively and inexpensively fill contract gaps, the best

contract would be one that specified only a vague intention to transact and would let courts “fill the gaps with the terms the parties would have wanted.”

– The only reason to incur time and expense including more specific performance obligations in contracts is to reduce the cost or inaccuracy of judicial gap filling; substitute “private ordering” for “court ordering.”

• Like judges interpreting a constitution, judges in commercial

settings may enforce contracts actively or passively.

Recent Developments in Contract Theory Scott Masten University of Michigan May 20, 2009 ESNIE 2009.

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