Efficiency vs. Flexibility in Public-Private Partnerships

Thomas W. Ross and Jing YanSauder School of Business

University of British Columbia

October 2013

Efficiency vs. Flexibility in PPPs 2UNIVERSITY OF BRITISH COLUMBIA 2

Economists have noticed PPPs

Previously studied issues by theorists:

1. Efficiency of bundling tasks

2. Effect of non-contractible elements (e.g. quality)

3. Private vs. public financing

4. Transaction costs in PPP procurement

Efficiency vs. Flexibility in PPPs 3UNIVERSITY OF BRITISH COLUMBIA 3

Recognized potential advantages of PPPs

1. Greater productive efficiency through use of the high-powered incentives available in the private sector.

2. Greater efficiency through the exploitation of economies of scale or access to key skills using the private sector.

3. Benefits from bundling tasks to recognize complementarities of some tasks

4. Greater innovation and dynamic efficiency from private sector.

Efficiency vs. Flexibility in PPPs 4UNIVERSITY OF BRITISH COLUMBIA 4

Challenges for PPPs

1. High transaction costs with such long (sometimes > 50 years) contracts.

2. 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)

3. 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

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 5

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 6

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

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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 8

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 9

.

eKC

2)(

2ee

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 10

.

Objective Functions

– Firm: makes decisions to maximize its after-tax profits subject to honouring its contracts.

– Government: two possibilities – differences depend on treatment of

transfers1) 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 11

Timing

1. Government puts project out for bids.2. Firms bid, it is awarded to the firm offering to provide it at

the lowest fixed fee, .3. Nature may move to change demand – if no change,

proceed to 5.4. If demand changes, is renegotiated (to ) via (weighted)

Nash bargaining and the design is changed, both parties incur switching costs .

5. F chooses level of effort, .6. Benefits are realized and the government honours its

contract.

Efficiency vs. Flexibility in PPPs 12

.

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 13

.

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 14

.

Axioms of Nash 2-Party Bargaining

Bargaining solution should satisfy:

1. Individual rationality (no one accepts less than he/she can get by disagreement)

2. Invariant to linear transformations (units don’t matter)3. Pareto Optimality (cannot make everyone better off)4. Independence of Irrelevant Alternatives (when you compare

two outcomes it does not matter what other alternatives are available)

5. Symmetry (both parties treated the same by process)

Efficiency vs. Flexibility in PPPs 15

.

Typical form of solutionNotation:S1, S2 = amounts going to party 1, party 2 respectivelyD1, 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 16

.

Solving: renegotiation

G threat-point:

F threat-point:

Efficiency vs. Flexibility in PPPs 17

.

Nash Product

NP =

Efficiency vs. Flexibility in PPPs 18

.

Renegotiated Price

• Maximizing this with respect to yields:

Efficiency vs. Flexibility in PPPs 19

.

Initial Price• Important Assumptions:

Competitive Bidding with Limited Liability

• Substituting for e* = (1-t)

Efficiency vs. Flexibility in PPPs 20

.

So now we have solved the model

Efficiency vs. Flexibility in PPPs 21

.

We know:

(i) The initial price (α0);(ii) If there is renegotiation what the new

prices will be (α1);(iii) That the right project will always be

implemented; and(iv) The effort that the firm will exert (e*) and

therefore what the real costs of providing the service will be.

Objective is to maximize expected VFM:

Efficiency vs. Flexibility in PPPs 22

.

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.

Putting it together: expected VFM here

Efficiency vs. Flexibility in PPPs 23

.

Result 1: General CaseExpected VFM will be greater:

(i) the lower is the cost of the project (K); (ii) the greater is the gross benefit ( and ); (iii) the greater is the cost reducing effect of effort (; (iv) the smaller is the probability design will need to change; (v) the smaller is the switching cost (); and(vi) 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 24

.

Special cases: PPP

PPP: t = 0 and 0 ≤ λ ≤ 1 , ,

Efficiency vs. Flexibility in PPPs 25

.

Special cases: PUB

PUB: t →1 and λ = 1

Efficiency vs. Flexibility in PPPs 26

.

Comparing PPP and PUB

Result 2: Under the VFM standard, PPP will dominate PUB when:

PPP is more likely to dominate procurement under PUB: (i) the greater is the cost reducing effect of effort (; (ii) the smaller the probability project design will need to change (iii) the greater is the switching cost (); and, (iv) 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 27

.

Illustrating the flexibility-efficiency trade-off:

 

   

Efficiency vs. Flexibility in PPPs 28

.

μ

𝛿

0

PUB

PPP

1

൫2ሺ1− 𝜆ሻሺ𝑏0 − 𝑏1 − 2sሻ൯12

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 29

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(i) the greater is the cost reducing effect of effort , (ii) the smaller is the probability the project design will need to change , (iii)the larger is the switching cost , and, (iv) the smaller is the difference between the project values and (v) 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 30

Differences between VFM & TSS

Result 4: When the public and private partners have different bargaining weights the following cases become possible:

(i) 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;

(ii) 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;

(iii) 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 31

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 32

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 33

0

2eδe)(Kb τMaxπ Max

2

00 PPPe

022

)(2

00

2

00 eKbeeKb

)2

(1 2

00

Kb

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 34

10 )1( b

Toll Contract: Comparisons with Availability Contract

Compare the toll contract and the availability contract  

Efficiency vs. Flexibility in PPPs 35

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:

(i) The more likely change is needed (μ);(ii) The greater is cost K;(iii) The lower is the productivity of effort (δ); and (iv) 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 36

Summary: The PPP Trade-offEfficiency 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 between right 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 37

Future work: possibilities

1. How do parties try to reduce these costs?• Contracts contingent on signals• Arbitration rights in renegotiation• Better incentives in public sector

2. Risk aversion

3. Other functional forms• e.g. what if effort affects demand, not just

costs?Efficiency vs. Flexibility in PPPs 38

Thank you

tom.ross@sauder.ubc.ca

Efficiency vs. Flexibility in PPPs 39