Efficiency vs. Flexibility in Public-Private Partnerships Thomas W. Ross and Jing Yan Sauder School of Business Univer

1. Efficiency vs. Flexibility in Public-Private PartnershipsThomas W. Ross and Jing YanSauder School of BusinessUniversity of British ColumbiaOctober 2013

2. Economists have noticed PPPs Previously studied issues by theorists: • Efficiency of bundling tasks • Effect of non-contractible elements (e.g. quality) • Private vs. public financing • Transaction costs in PPP procurement Efficiency vs. Flexibility in PPPs UNIVERSITY OF BRITISH COLUMBIA 2

3. Recognized potential advantages of PPPs • Greater productive efficiency through use of the high-powered incentives available in the private sector. • Greater efficiency through the exploitation of economies of scale or access to key skills using the private sector. • Benefits from bundling tasks to recognize complementarities of some tasks • Greater innovation and dynamic efficiency from private sector. Efficiency vs. Flexibility in PPPs UNIVERSITY OF BRITISH COLUMBIA 3

4. Challenges for PPPs • High transaction costs with such long (sometimes > 50 years) contracts. • May be very difficult to assure all key aspects of service delivery via contract – i.e. some important elements may not be contractible (e.g. quality) • Some loss of flexibility for government – decision-making authority allocated to private partner and adapting to changing circumstances done in bilateral (i.e. non-competitive) environment This paper is about challenge 3 Efficiency vs. Flexibility in PPPs UNIVERSITY OF BRITISH COLUMBIA 4

5. This Paper • Explores in a simple, but formal way, the trade-off between efficiency and flexibility that exists in PPP contracts. • Closest paper is by Bajari and Tadelis (2001) • The flexibility challenges in PPP arrangements are well recognized in the literature and by practitioners: • National Audit Office (2008) • OECD (2008) • PwC (2005) • Yescombe (2007) Efficiency vs. Flexibility in PPPs

6. Key Idea • Strong incentives lead private sector to greater productive efficiency • As long as competition is intense, these savings are transferred to the government (and taxpayers) through lower bids • However, if contract needs to be renegotiated, this is not done in a competitive environment – it is two-party bargaining under which some of the benefits are likely to flow to the private parties Result: An important trade-off – PPPs bring productive efficiency but, when they need to be renegotiated, they can be costly for taxpayers Efficiency vs. Flexibility in PPPs

7. Model Overview: Some Basics • The government (G): the principal, wishes to procure certain public services over an extended period of time • The “firm” (F): the agent, bids to deliver these services -- • could be a public sector agency/department, or a private sector firm • F is taxed on its profits at a rate t • Contract changes will be negotiated via Nash bargaining with weights λ for G and (1-λ) for F Efficiency vs. Flexibility in PPPs

8. Two Special Cases We can use two special cases of this model to explore the differences between PPPs and traditional public procurement (PUB) PPP: 0 < λ < 1 (both parties with bargaining weight) 0 ≤ t < 1 (not all F’s profits taxed away) PUB: λ = 1 (all bargaining power to G) t → 1 (all profits collected by G) Efficiency vs. Flexibility in PPPs

9. Basic set-up: Costs . • The cost function of the project: • K: the innate cost of the project • e: cost reducing effort (non-verifiable) • δ > 0: e’s marginal productivity (private information of F) • monetary costs of this effort Efficiency vs. Flexibility in PPPs

10. Basic set-up: Benefits . • Benefit of Project (not contractible): Right project b0 > 0 Wrong project b1< b0 • With probability μ an unexpected change in demand happens – current project becomes the wrong project. • If changes are needed they are negotiated via Nash bargaining • After the contracts are settled, F picks its level of effort, costs are incurred, contracts honoured and payoffs received. . Efficiency vs. Flexibility in PPPs

11. Objective Functions • Firm: makes decisions to maximize its after-tax profits subject to honouring its contracts. • Government: two possibilities – differences depend on treatment of transfers • social welfare or total social surplus (TSS) TSS = benefits minus real economic costs (not transfers) 2) “value for money” (services of the quality desired are provided at lowest cost to the ultimate payers) (VFM) VFM = benefits – costs to government (net of tax receipts) Or in expected value terms: E (VFM) =(1-μ) [benefits - costs]no changes + μ[benefits - costs]changes Efficiency vs. Flexibility in PPPs

12. Timing . • Government puts project out for bids. • Firms bid, it is awarded to the firm offering to provide it at the lowest fixed fee, . • Nature may move to change demand – if no change, proceed to 5. • If demand changes, is renegotiated (to ) via (weighted) Nash bargaining and the design is changed, both parties incur switching costs . • F chooses level of effort, . • Benefits are realized and the government honours its contract. Efficiency vs. Flexibility in PPPs

13. Solving: working backwards starting with effort choice . • Government taxes supplier’s profit at rate t, so F maximizes: • Maximizing this w.r.t. e yields: Efficiency vs. Flexibility in PPPs

14. Renegotiation: Nash Bargaining . A method of allocating the surplus to be created by a renegotiated agreement. Splits the new surplus between the two parties. Key factors in this division: 1. Parties’ threat points (what if there is no agreement) 2. Bargaining weights Efficiency vs. Flexibility in PPPs

15. Axioms of Nash 2-Party Bargaining . Bargaining solution should satisfy: • Individual rationality (no one accepts less than he/she can get by disagreement) • Invariant to linear transformations (units don’t matter) • Pareto Optimality (cannot make everyone better off) • Independence of Irrelevant Alternatives (when you compare two outcomes it does not matter what other alternatives are available) • Symmetry (both parties treated the same by process) Efficiency vs. Flexibility in PPPs

16. Typical form of solution . Notation: S1, S2 = amounts going to party 1, party 2 respectively D1, D2 = disagreement payoffs for party 1, party 2 respectively Basic solution will be S1, S2 that, subject to being viable, maximizes (where NP = “Nash Product”) NP = (S1 - D1) • (S2 - D2) or with bargaining weights added: NP = (S1 - D1)λ• (S2 - D2)1-λ Efficiency vs. Flexibility in PPPs

17. Solving: renegotiation . • G threat-point: • F threat-point: Efficiency vs. Flexibility in PPPs

18. Nash Product . NP = Efficiency vs. Flexibility in PPPs

19. Renegotiated Price . • Maximizing this with respect to yields: Efficiency vs. Flexibility in PPPs

20. Initial Price . • Important Assumptions: Competitive Bidding with Limited Liability • Substituting for e* = (1-t) Efficiency vs. Flexibility in PPPs

21. So now we have solved the model . • We know: • The initial price (α0); • If there is renegotiation what the new prices will be (α1); • That the right project will always be implemented; and • The effort that the firm will exert (e*) and therefore what the real costs of providing the service will be. Efficiency vs. Flexibility in PPPs

22. Objective is to maximize expected VFM: . E(VFM) = (1-μ)[b0 – α0] + μ[b0 – α1] • = b0 – [(1-μ)α0 + μα1] • Where α0 and α1 will depend on the procurement method used. Efficiency vs. Flexibility in PPPs

23. Putting it together: expected VFM here . Efficiency vs. Flexibility in PPPs

24. Result 1: General Case . Expected VFM will be greater: • the lower is the cost of the project (K); • the greater is the gross benefit ( and ); • the greater is the cost reducing effect of effort (; • the smaller is the probability design will need to change; • the smaller is the switching cost (); and • the lower the tax rate (). Assuming net benefit of renegotiation ( ) is always positive – (i.e. renegotiation is efficient and always occurs when there are changes in demand) -- VFM is higher when the government is in a stronger bargaining position (i.e. when λ is greater). Efficiency vs. Flexibility in PPPs

25. Special cases: PPP . PPP: t= 0 and 0 ≤ λ≤ 1 , , Efficiency vs. Flexibility in PPPs

26. Special cases: PUB . PUB: t →1 and λ = 1 Efficiency vs. Flexibility in PPPs

27. Comparing PPP and PUB . Result 2: Under the VFM standard, PPP will dominate PUB when: PPP is more likely to dominate procurement under PUB: • the greater is the cost reducing effect of effort (; • the smaller the probability project design will need to change • the greater is the switching cost (); and, • the smaller the difference between values . Assuming that the net benefit of renegotiation () is always positive, then the VFM of a PPP is relatively higher when government is in a stronger bargaining position ( Efficiency vs. Flexibility in PPPs

28. Illustrating the flexibility-efficiency trade-off: . Efficiency vs. Flexibility in PPPs

29. Extension 1: TSS Standard Need to add shadow cost of taxation: if government pays Z to firm it costs government (1+γ)Z Efficiency vs. Flexibility in PPPs

30. Comparing PPP/PUB under TSS Result 3: Under the TSS standard, a PPP will dominate PUB when: As before, a PPP approach is more likely to dominate PUB • the greater is the cost reducing effect of effort , • the smaller is the probability the project design will need to change , • the larger is the switching cost , and, • the smaller is the difference between the project values and • the greater is the deadweight loss of government finance (γ). Assuming that the net benefit of renegotiation [] is always positive, so renegotiation always occurs when there are changes in demand, the TSS of a PPP is higher when government is in a stronger bargaining position. Efficiency vs. Flexibility in PPPs

31. Differences between VFM & TSS Result 4: When the public and private partners have different bargaining weights the following cases become possible: • When the government has the greater bargaining weight (i.e. λ > ½) it is possible for a PPP to maximize VFM while PUB maximizes TSS; • When the government has the lesser bargaining weight (i.e. λ< ½) it is possible for a PPP to maximize TSS while PUB maximizes VFM; and; • When the government and firm have equal bargaining weight (i.e. λ = ½), comparisons under are the same as those under TSS. Efficiency vs. Flexibility in PPPs

32. Extension 2: Toll Contract Could a toll contract change renegotiation incentives? • In many PPP arrangements, private parties are paid according to the use of the services. e.g. road and bridge projects funded by tolls • With a toll contract, private partner has stronger incentive to change project if it means meeting more demand Efficiency vs. Flexibility in PPPs

33. Toll Contract Our extension: under PPPs contract, the fraction of the benefit that F gets (via usage fees) is • incentive compatibility constraint: • participation constraint: Efficiency vs. Flexibility in PPPs

34. Toll Contract: Changes in Demand • G's threat point: G has stronger bargaining position compared with baseline. • F’s threat point: assume F can walk away. So F's threat point still generates zero profits (in this case via exit). Nash Bargaining result: Efficiency vs. Flexibility in PPPs

35. Toll Contract: Comparisons with Availability Contract Compare the toll contract and the availability contract Efficiency vs. Flexibility in PPPs

36. Toll Contracts: Results Result 5: When the objective of the government is to maximize VFM, the toll contract dominates the availability contract. Advantage of toll contract is greater: • The more likely change is needed (μ); • The greater is cost K; • The lower is the productivity of effort (δ); and • The greater the percentage difference between good and bad projects [(b0-b1)/b0] . So PPPs more likely to dominate PUB if tolls can be used! Efficiency vs. Flexibility in PPPs

37. Summary: The PPP Trade-off Efficiency vs. Flexibility PPPs more likely to dominate PUB when: (i) effort more important (i.e. δ larger) (ii) probability of change ( µ) lower (iii) switching cost (s) higher (iv) difference betweenright and wrong projects (b0-b1) smaller (v) governments have greater bargaining power (vi) toll contracts (not availability contracts) used And choice can depend on government’s objective. Efficiency vs. Flexibility in PPPs

38. Future work: possibilities • How do parties try to reduce these costs? • Contracts contingent on signals • Arbitration rights in renegotiation • Better incentives in public sector • Risk aversion • Other functional forms • e.g. what if effort affects demand, not just costs? Efficiency vs. Flexibility in PPPs

39. Thank you tom.ross@sauder.ubc.ca Efficiency vs. Flexibility in PPPs