Recent Developments in Contract Theory

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

2. Conventional analysis • 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

3. Anomalies • 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

4. 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 performance • s = value of seller's next best alternative to performance • (i.e., to trading with buyer). • pk = contract price • π = economic profit (surplus; private gain)

5. 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 .

6. v s pk Illustration: Efficient Breach No enforcement inefficient breach buyer performance (no contract) efficient performance With no enforcement, buyer would perform only when v > pk => inefficient breach

7. v s pk Illustration: Efficient Breach Specific performance contract buyer performance (specific performance) inefficient performance efficient performance With specific performance contract, buyer would perform too often (i.e, for all v)

8. v s pk Illustration: Efficient Breach Expectation damages contract efficient breach buyer performance (expectation damages) δB Expectation (or stipulated) damages: Set δB = pk− s => Buyer performs if v – pk>–δB or v > pk – δB = pk – (pk − s) = s

9. v s pk Illustration: Efficient Breach buyer performance (specific performance) buyer non-performance (no contract) efficient nonperformance efficient performance • That’s fine, as far as it goes, but note: • It does not matter whether a court or the contract sets damages. • It does not matter what price is set as long as the ex ante distribution constraint is satisfied; ex post distribution is irrelevant. • It does not matter when the price is paid: ex ante, ex post. • 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.

10. The role of price If either courts or renegotiation is costless, price doesn’t matter. vt v0 pk st s0 time Buyer loses but either (i) damages assure performance or (ii) renegotiation results in efficient performance.

11. 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).

12. 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.

13. “Equilibrating hazards” • 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

14. nB nS p' pk buyer rejection seller rejection “Equilibrating hazards” For single transaction, given an agreed-on price = pk Seller reneges if p′ – pk > nS Buyer reneges if pk – p′ > nB

15. “Equilibrating hazards” With repeated transactions and reputational capital, Wi Seller reneges if p′ – pk > nS + WS Buyer reneges ifpk – p′ > nB + WB nB+WB nS+WS p' pk buyer rejection seller rejection

16. “Equilibrating hazards” • 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) where

17. pk nB+WB nS+WS p' buyer rejection seller rejection “Equilibrating hazards” Choosing pk to minimize probability of rejection => “hazard equilibration”

18. vt v0 pt pk0 st s0 time 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.

19. g(p'- aX) g(p'- m) 0 nS+WS p'- pk -(nB+WB) (nS+WS*) -(nB+WB*) Price adjustment Expected negotiation costs can be reduced if can relate the contract price to something correlated withp′: pk = αX Tyingpkto Xreduces variance of(p′– pk) Savings = difference between shaded and hashed areas

20. pk nS+WS p' -(nB+WB) (nS+WS*) -(nB+WB*) Price adjustment Implication: The value of accurate price adjustment increases with the variance ofp′ =γ v + (1 – γ )s

21. Applications and evidence Organization of Freight Transportation drivers shippers receivers carriers vehicles Also: loading/unloading, maintenance, ….

22. Relations between Carriers and Truck Drivers Applications and evidence • 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”

23. Relations between Carriers and Truck Drivers Applications and evidence • Anomalies: • Vertical integration and long-term contracts can’t be explained by relationship-specific investments (in most cases). • Pricing can’t be explained by incentives: Mileage is standardized (“bureau miles” not actual) and freight bill is known before haul accepted.

24. Relations between Carriers and Truck Drivers Applications and evidence 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.

25. Applications and evidence Relations between Carriers and Truck Drivers 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)

26. Applications and evidence Relations between Carriers and Truck Drivers 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.

27. Applications and evidence Relations between Carriers and Truck Drivers • Data • Survey 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

28. Applications and evidence Relations between Carriers and Truck Drivers Haul Pricing

29. Haul attributes

30. Table 3. Kolmogorov-Smirnov Non-Driving Time Equality of Distribution Tests Parameters significant at the 0.05 percent level in bold.

31. Drivers paid as a percent of revenue (freight bill) carried loads with higher variance in non-driving times. by mile percent revenue Distributions of non-driving time (minutes)

32. 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”:

33. Table 3. Kolmogorov-Smirnov Non-Driving Time Equality of Distribution Tests Parameters significant at the 0.05 percent level in bold.

34. Drivers of non-vans had higher variance of in non-driving times than did drivers of dry vans. dry vans non-vans Distributions of non-driving time (minutes)

36. Price Adjustment in Natural Gas Contracts (Crocker and Masten, 1993) Applications and evidence 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.

37. Price Adjustment in Natural Gas Contracts Applications and evidence Renegotiation is more common in fixed-quantity contracts than in variable-quantity contracts.

38. Price Adjustment in Natural Gas Contracts Applications and evidence Renegotiation is most common in long-term, fixed-quantity contracts. take%=0 duration=1 take%=100 duration=20

39. Applications and evidence Price Adjustment in Natural Gas Contracts Prices are adjusted more frequently with (low cost) redetermination than with (high cost) renegotiation.

40. Applications and evidence Price Adjustment in Natural Gas Contracts Greater energy market volatility implies more frequent adjustment

41. Applications and evidence • 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.

42. 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.