The Simple Microeconomics of Public-Private Partnerships

3.1. Pure Agency Considerations: Bundling Dominates

Unbundling. Under traditional procurement, G first approaches a builder (B) and then a separate operator (O). The operator receives a cost-reimbursement rule , while the builder gets only a fixed payment .21 With such payment unrelated to his own effort, the builder does not exert any effort:

(4)

The operator maximizes the certainty equivalent of its expected payoff, taking as given the zero effort exerted by the builder. The corresponding incentive constraint writes as

(5)

An increase in the incentive power β, the share of the profit risk borne by the operator, boosts its cost-reducing effort. However, as more operational risk is transferred to the operator, the risk premium also increases which is at the core of a standard moral hazard trade-off between incentives and insurance.

Since G has all the bargaining power, it sets the fixed payments to the builder and the operator α so as to extract all their surplus. The principal's payoff then coincides with the expected value of the project net of the risk premium, that is,

Maximizing the above expression with respect to while taking into account the incentive constraints 4 and 5 that hold under unbundling yields the following expressions of the second-best operating effort and the share of the risk borne by the operator:

(6)

Because providing incentives requires the agent to bear more risk which is socially costly, the second-best effort is lower than its first-best level so as to reduce the corresponding risk premium. More risk ( larger) also tilts the trade-off between insurance and incentives toward low powered incentives.22 G's expected payoff is then

(7)

Bundling. The building and the operational phases are now both in the same hands. The consortium () chooses the effort levels so as to maximize the sum of its profit at both the building and operational stages and thus internalizes the impact of the design stage on the operational costs. The corresponding effort levels thus solve

Taking into account the additional nonnegativity constraint we obtain the following incentive constraints:

(8)

Observe that, in the case of a negative externality (), those effort levels just replicate those found under unbundling. Instead, with a positive externality (), the first-stage effort is positive because now the firm at least partially takes into account the impact of this first stage on costs.

As before, the fixed fee α is adjusted by G so that to extract all surplus from the consortium. Now, G's maximization problem consists in maximizing subject to the incentive constraints in 8.

Of course, efforts remain unchanged with respect to the unbundling scenario in the case of a negative externality:

Instead, effort levels are higher under bundling in the case of a positive externality:

Using these values of efforts, the expression for the expected welfare can be written as

We can thus immediately conclude:

PROPOSITION 1.Bundling is strictly desirable in the presence of positive externality and there is an indifference between organizational forms otherwise.

When the consortium never performs any quality-enhancing effort because it is not rewarded for doing so. This replicates the case of unbundling. With a negative externality, investment a is already at a minimum under unbundling (the builder having no incentives to invest), and the internalization of the negative externality under bundling cannot depress these incentives further. Investment a remains at a minimum under both organizational forms which yield the same expected benefits to the principal.

When , a consortium anticipates how a high-quality infrastructure also reduces costs. Bundling then induces the consortium to internalize the positive externality generated by its quality-enhancing effort a on the fraction of costs that it bears at the operational stage. This unambiguously raises welfare as it reduces the underinvestment problem during the building stage, raising quality-enhancing effort.24 Quality-enhancing effort however remains suboptimal: the consortium only internalizes the effect of a on the fraction of costs that it bears (this effect is measured by and thus not the total effect on costs (measured by ), and also it does not internalize the effect on social benefits (measured by ).

Moving from traditional procurement to PPP changes cost-reimbursement rules. Bundling shifts more risk to the operator ( and increases incentives to invest in asset quality. This is intuitive: Transferring more operational risk (through higher values of β) induces the operator to exert higher cost-reducing effort but it brings the cost of a higher risk premium. Under bundling, the transfer of operational risk brings the additional benefit of also inducing quality-enhancing effort. This justifies transferring more operational risk. Thus, bundling and fixed-price contracts go hand in hand under PPP whereas unbundling and cost-plus contracts are more likely under traditional procurement. This is in lines with existing evidence that PPPs are characterized by more risk transfer and thus greater risk premium than traditional procurement.

Other scenarios. The benefits of bundling in the presence of a positive externality carry over to the other contractual scenarios mentioned in Section 2.. When users pay for the service and the contractor is residual claimant for the revenues (as in the case of contractible profits or of contractible revenues), the consortium's incentives to enhance quality are still stronger than those of the builder under unbundling. For example, in the case where there is no moral hazard on costs and B in expression 1 denotes the revenues from the service, the expected revenues from the service are

where the approximation holds for small enough. In this case, it is immediate that the builder obtains no benefit from raising operational revenues under unbundling and thus . At the same time, the operator chooses

(9)

In that scenario, G's problem is to maximize with respect to its expected payoff

(10)

subject to the incentive constraint 9. This gives the following expressions of the incentive power and the second-best effort under unbundling:

Under bundling instead the consortium maximizes

(11)

G's problem is thus to maximize

(12)

subject to the incentive constraints 11. This yields the following expressions of the incentive power and the second-best effort under bundling:

It is immediate to show that welfare is higher under bundling since and 25

Intuitively, the consortium anticipates that increasing a raises revenues B. The greater the share β of revenues kept by the consortium, the greater the incentives to increase a. Since the builder under unbundling gets no revenues, incentives are there absent. As with verifiable costs, bundling boosts effort at the building stage. This unambiguously raises welfare and the stronger the effect of infrastructure quality on revenues (higher b) the greater the benefits of bundling. Furthermore, since higher risk transfer (higher β) raises both e and a, bundling again comes with more risk transfer: . Finally, comparative statics on characterizes the optimal allocation of demand risk under a PPP. The optimal payment mechanism trades off incentives and insurance: transferring demand risk to the contractor gives it incentives to boost demand (a increases) and raises consumer surplus (B increases) but it costs the government a higher risk premium (). Thus, the more demand levels are affected by the contractor's action (higher b), the lower the demand risk (lower ) or the risk aversion of the contractor (r), the more demand risk should be borne by the contractor.

In PPP projects such as prisons, users do not pay, and government policies determine most of demand changes. Since the contractor's effort has little impact on demand levels (b small), not transferring demand risk to the contractor () is indeed optimal. With financially free-standing projects, such as leisure centres, the contractor recoups its initial investment through charges to final users. Here, revenue risk lies entirely with the contractor () since the contractor's effort has large impact on demand levels (b high). Transport projects instead typically fall in the intermediate case, where there is some revenue sharing between the contractor and the public authority.26

3.2. More Complete Contracting

As a robustness check of our previous findings, we now envision the consequences of allowing more complete contracts. This may be by making the builder's payment depend on costs under unbundling or on a quality index for the infrastructure. We focus on the case of positive externality under the contractible-cost scenario.

3.2.1. Costs incentives

Suppose that the builder's payment is now linked to the realized level of operating costs with a contract of the form . If the builder is risk-averse (assuming the same degree of risk aversion as the operator) such payment comes with an extra risk premium worth to induce the builder's participation. This premium quickly increases when the positive externality is small enough, i.e., when the noisy observable does not track so easily the builder's effort. The builder then maximizes

While nothing changes under bundling, under unbundling such a scheme now gives to the builder some incentives to exert effort a. His incentive constraint is indeed given by

The quality-enhancing effort is then easily obtained by trading off the efficiency gain of more effort against the risk premium and one finds

(13)

This effort level is second order in δ for small externalities. Contracting on costs is thus of little help if the builder's effort does not significantly affect those costs.

Other scenarios. The insights from this robustness check carry over when profit-sharing or revenue-sharing rules can be used. When profits or revenues are verifiable, G can reward the builder when higher profits or revenues are observed. With this induces higher quality-enhancing effort under unbundling. However, with a positive externality bundling still strictly dominates unbundling, since the incentive scheme at the operating stage (the profit sharing or revenue-sharing rule) helps to incentivize both efforts at building and operating stages.

3.2.2. Quality incentives

Let us now suppose that a noisy index q for the quality of the infrastructure (which is also an imperfectly aligned proxy for the social benefit) is available:

where is a random variable which is assumed to be normally distributed with (for simplicity) variance and zero mean. For simplicity, we keep the same variance of noise on this quality index and on the operating costs. This assumption is particularly relevant when q stems for an earlier realization of operating costs in a context where the investment consists of complementary and renewed assets. The builder's incentive scheme is now of the form .

Unbundling. The builder's incentive constraint is now

(14)

while that of the operator remains unchanged as 5. Although the ability to contract on a quality index improves the builder's incentives and raises the quality of the infrastructure, it does not change the operator's incentives.

Bundling. The consortium's incentive constraint can be written as

(15)

By making the firm's payment depend on the quality index, the cost reimbursement rule is made more powerful and welfare increases.

PROPOSITION 2.Bundling strictly dominates unbundling when complete contracts on both operating costs and a quality index are feasible and the externality is positive.

Even if using a quality index eases agency problems under unbundling, bundling remains preferable whenever this index remains imperfect as the nature of the agency problem remains unchanged.

Robustness check. It can be shown that when the quality index is on the service quality rather than infrastructure quality, the main insights of this section continue to hold. Since a service quality index is positively affected by a, via the effect that a has on social benefits B, a payment system that rewards the builder for higher service quality eases the agency problem under unbundling. Bundling however remains preferable whenever the firm is risk-averse.

3.3. Residual Value and Ownership

Proposition 1 told us that bundling always weakly dominates unbundling. We now show that, when instead the builder has some incentives to invest under unbundling and the externality is negative, unbundling may become the preferred mode of provision.27

To tackle the issue of ownership, we now identify PPP as an organizational form where there is bundling of the design and operation phases but also private ownership of the assets over the whole length of the contract. Traditional contracting corresponds instead to the case where G buys an asset built by the private sector and delegates operations to a second firm.

When contracts allocate rights and duties and there are no unforeseen contingencies, ownership matters only to the extent that assets have some residual value at the end of the contract. Ownership entitles the owner with the market value of these assets. This residual value provides incentives to invest in asset quality. Of course, that residual value will depend on assets specificity. In the case of generic facilities (such as, leisure centers, office accommodation, general IT systems, and land use), there is demand from users other than the government, so that the public and private residual value do not differ significantly. This is of course different for specific facilities, such as hospitals, prisons, and schools.

Let thus sa () denote the value of the assets at the end of the contract when these assets are used by the government for public service provision. Let also with denote their value for private use. Consistent with the incomplete contracts literature, the residual value of these assets cannot be specified ex ante in a contract although it is ex post observable and can be bargained upon at that date.28 The parameter π captures the degree of asset specificity, with π being higher the less specific is the facility.29 Since public ownership is always optimal at the end of the contract.30

As a benchmark, note that the first-best level of a now solves

Public Ownership. Suppose that assets are publicly owned throughout the contract. Since a is not contractible and there is no sale of the facility once the contract expires, the builder cannot be incentivized. Whether bundling or unbundling is chosen, efforts and welfare with public ownership remain the same as before. Public ownership has no impact on incentives. Whether bundling strictly dominates depends only on the sign of the externality as in Section 3.1..

Private Ownership. Suppose assets are privately owned. At the end of the contract, efficiency requires to transfer ownership to G. Ex post, the price at which ownership is transferred results from Nash bargaining (assuming equal bargaining powers):

The private owner's net benefit boosts his incentives to enhance assets quality if he is a builder.31 The owner's incentives to invest are also greater with less specific assets. Indeed, asset specificity reduces the status quo payoff if ownership is not transferred to the public sector. This exacerbates the hold-up problem that occurs through ex post bargaining and dampens the private owner's incentives.

Private ownership and unbundling: The builder's incentive constraint when he is also the owner can be written as

(16)

On the other hand, the operator's effort and optimal incentive scheme remain the same as in Section 3.1.:

(17)

Private ownership and bundling: Ownership has still some value with bundling. The consortium's expected payoff is maximized for effort levels that solve32

(18)

Comparing public and private ownerships, we immediately obtain:

Comparing now PPPs and traditional procurement, we get:

PROPOSITION 4.PPPs, i.e., private ownership and bundling, strictly dominates traditional contracting, i.e., private ownership and unbundling, with a positive externality:

Efforts are greater under bundling with a positive externality:

Compared to public ownership, under private ownership bundling implements strictly lower efforts than unbundling if the externality is negative. Ownership gives to the builder some incentives to invest in asset quality. These incentives are depressed if the builder internalizes the negative externality that quality exerts on costs.

3.4. Related Literature

Our baseline model has merged two strands of the literature on PPPs which have both emphasized the multitask nature of the procurement problem when building and managing assets matter. Using the property rights approach, Hart (2003) provided a model where the sole source of incentives is ownership. A builder can perform two kinds of investment (productive and unproductive) which may both reduce costs, although only the productive investment raises also benefits. Under traditional procurement, the builder cannot internalize the impact of his effort neither on benefits nor on costs. He implements too little of the productive investment but the right amount of the unproductive one. Under PPP, the builder somewhat internalizes the impact of his productive investment whereas he also exerts too much of the unproductive one. Francesconi and Muthoo (2011) and King and Pitchford (2001) considered the case of impure public goods and showed that shared authority can be optimal when the parties' investments are comparable. Bennett and Iossa (2006) studied the desirability of bundling project phases and of giving ownership to the investor. Innovations are noncontractible ex ante but verifiable ex post. Ownership gives control right to the owner to decide whether to implement quality enhancing or cost-reducing innovations proposed by the investor. The hold-up problem is less severe under PPP, compared with traditional procurement, when there is a positive externality between the building and managing stages, and vice versa when the externality is negative. Public ownership acts as a commitment for the government to renegotiate and share with the investor the surplus from implementing the innovation. Private ownership is nevertheless optimal for generic facilities with high residual value. Chen and Chiu (2010) extend Bennett and Iossa (2006) to the case of interdependent tasks and show that complementarity between tasks favors unbundling.

In a complete contracting framework, Martimort and Pouyet (2006) built a model where both the quality of the infrastructure and operating costs are contractible. Incentives and welfare are higher under a PPP when there is a positive externality between building and managing assets compared to traditional procurement.33 Ownership aligns incentives but, to a large extent, the important issue is not who owns the asset but instead whether tasks are bundled or not. That insight is developed in various extensions of their basic model allowing for risk-sharing as a motive for forming consortia, or for political economy. In the same spirit, Iossa and Martimort (2011) built an agency model where operating costs are noncontractible but both the quality of the infrastructure and the demand for the service are contractible. They focus on how bundling affects incentives to raise demand, and the optimal allocation of demand risk. Our baseline model borrows a lot from these principal-agent models: a common theme is that PPP comes with higher powered incentives.

Taking also a complete-contract approach, Benz, Grout, and Halonen (2001) showed that the government should buy services (as in PFI) rather than facilities (as in traditional procurement) if the building and service delivery costs are low.34 Hoppe and Schmitz (2013) focused instead on the incentives to gather information about future costs to adapt the service provision to changing circumstances. They showed that whether bundling or unbundling is better for information gathering depends on the costs of efforts in innovation and in information gathering, and on the degree to which effort is contractible. Finally, Iossa and Martimort (2012a) considered a dynamic multitask moral hazard environment where the mapping between effort and performance is ex ante uncertain but information may come along during operations. In that context, compounding of asymmetric information ex post plus moral hazard and renegotiation may generate diseconomies of scope in agency costs which, for high operational risk, can make unbundling optimal also with positive externalities.

3.5. Implications

Our results suggest that PPPs deliver efficiency gains when a whole-life cost approach to the project yields significant cost savings and when risk is effectively transferred to the private operator. Transferring design, construction, and operating risks to the contractor provides incentives for keeping project costs down and efficiently providing the service. A report commissioned by the Treasury Taskforce estimated saving on a sample of PFI projects equal to 17%, compared to traditional procurement.35 Significant cost savings were realized in the prison sector. The National Audit Office (NAO 2003a) reported that innovative designs helped to reduce the level of staffing needed to ensure security and this resulted in an overall cost reduction by approximately 30%. Conclusive evidence is however still to be found. Blanc-Brude, Goldsmith, and Välilä (2009) studied a sample of road projects financed by the EIB between 1990 and 2005 in all EU-15 countries plus Norway. They found that ex ante construction costs (i.e., costs before construction actually starts) are some 20% higher for PPP roads than for traditionally procured roads.36

Our results also suggest that, when a higher asset quality increases social benefit but has a negative impact on whole-life cost, the scope for PPP might be limited. Evidence of negative externalities is more difficult to find. However, a report by the Audit Commission (see PPP Focus, Education 2, 2004) noted that the quality of many early PFI school buildings was disappointing. School quality has a direct positive impact on pupil behavior and educational achievement. Local education authorities now anticipate this problem and include more detailed output specifications in the contract. As a result the quality of school buildings has improved.

Our results also shed some light on the current approach to facility ownership. Under PPP, ownership during the contract length goes to the consortium, but ownership once the contract expires varies depending on the circumstances. Assets tend to revert to the public sector either when they have no obvious alternative use or when they are required to continue the service after contract ends (for example, schools, prisons, and hospitals). For generic facilities with an alternative use outside the public sector and no clear long-term public sector needs, ownership is retained by the private sector.

We have focused on the benefits of bundling that may come from inducing the contractor to take a long-term approach to the project. However, bundling also brings other benefits. First, PPPs are characterized by a longer procurement process and by higher costs of bidding than traditional procurement. Albeit with differences between sectors, it has been estimated that PPP tendering periods last an average of 34 months (NAO 2007) and that procurement costs can reach 5%–10% of the capital cost of a project (Yescombe 2007). These transaction costs are also to a large extent independent of the size of a project, which suffices to make PPP unsuitable for low capital value projects.37

Second, bundling of different phases of the project increases project complexity and limits participation of small construction companies that do not have the necessary financial resources to sustain the costs and risks of bidding for PPP contracts. Albeit with differences across sectors, in the United Kingdom, there is an average of four bidders per PPP contract. This is problematic, as collusion among bidders is certainly more likely if the number of participants is small.38

In our basic model, we have only focused on “build” and “operate.” In practice, the realization of a project comprises a wider variety of tasks. Services in the operational stage for example include “soft” facility-management services (e.g., cleaning, catering, security) and “hard” facility-management services (e.g., routine and/or life-cycle maintenance of buildings and equipment). The arguments set up in Section 3. apply to hard services where asset quality matters and externalities are significant but less so to soft services where asset quality plays a limited role and externalities are relatively small. Whether to include soft services in PPPs should then follow other considerations. On the one hand, their inclusion creates a single point of responsibility within the private sector in charge of service provision and allows to internalize the externalities. On the other hand, unbundling helps to employ short-term contracts for soft services and thus to benefit from more competitive pressure. Separate tendering for soft services also favors the participation of small firms. There are no uniform experiences across countries regarding service unbundling and the HM Treasury (2006) currently advises against their inclusion.

4.1. The Benefits of Outside Finance

So far we have focused on the effects of bundling building and operation in a single contract with a single agent. PPPs however are often also characterized by the private sector financing a substantial part, or all of, the project (the “F” in the DBFO model). The firm then recoups its initial investment through charges to final users or from government availability payments, that is, government contributions for making the service (e.g., prison services) available. In this section, we briefly study the rationale for private finance in PPPs.

The relationship between investment and their financing is particularly critical for privately financed infrastructure. On the one hand, an often heard benefit of PPPs is that they might bring in the expertise of outside financiers in evaluating risks. In this respect, bundling the task of looking for outside finance (be it through outside equity or debt) and operating assets could improve on the more traditional mode of procurement where the cost of investment is paid through taxation and investment is not backed up by such level of expertise within the public sphere. On the other hand, private finance adds an additional layer of contracting, the one between the consortium and the financier, and this could have perverse effects on incentives.

To analyze the effect of private finance, we consider the case of contractible profits and focus on the benefit of bundling operation and financing, assuming away any incentive problem on a. We let so that, there are no benefit of building a better infrastructure. All the benefits of having private finance, if any, are thus due to the reduced agency costs that it might bring. For simplicity we also let , , so that the profit function is given by

(19)

To model the transaction costs that might still arise when the operator looks for outside finance, we assume now that financiers have expertise to get access to some informative signal y on the contractor's effort:

(20)

where ς is a random variable normally distributed with variance and zero mean. Such informative signal may be quite useful to provide cheaper incentives.

We investigate in turn the case of public finance where the investment is financed by taxation and the case of outside private finance. We assume throughout that financiers operate in a perfectly competitive financial market.

Public finance. The government itself provides funds to cover an investment I. It does not observe the informative signal y and implements only the second-best effort .

Outside finance. The operator has now full control over his access to the financial market on top of control over operations. To fix ideas, suppose that only profits are verifiable, so that the firm operates under a linear scheme and therefore keeps a gross payoff of . The operator and its financiers agree on how to share the remaining risk induced by such a contract.

Let ω denote the fraction of the gross payoff that is kept by the operator. Because outside financiers can condition the firm's repayment on the extra signal y, a linear repayment scheme that share risk between the operator and its financiers is given by

The term () is a bonus in case the signal on the firm's effort is positive and a punishment otherwise. Since financiers are competitive, the fixed payment E is the price of equity they hold in the project net of the investment cost I.

The operator's incentive constraint is now written as

(21)

This incentive constraint highlights two important features. First, only a fraction of the incentive power of the government's scheme ends up being useful to foster operational effort because of subsequent risk-sharing between the firm and financiers. Second, financiers can improve incentives by conditioning the firm's repayment on the informative signal they get on its effort.

Going backwards, let us turn now to the design of the overall repayment scheme given the transfer scheme with the government. Because financiers are competitive, this repayment maximizes the certainty equivalent of the operator's payoff taking into account the moral hazard incentive constraint 21:

(22)

The optimal repayment scheme designed by financiers is straightforward. The share of risk left to the operator is independent of the government's scheme. The firm gets positive bonus in case y is good news on the firm's effort:

This corresponds to a risk premium borne by the operator which is worth

Finally, the effort level implemented by the operator when one compounds the impact of government's and the financiers' contracts can be written as

(23)

This is the incentive constraint of the coalition made of the operator and its financiers.

Notice that this effort level converges toward β when goes to zero. When financiers have a very informative signal on the firm's effort, there is no further dilution of incentives within their coalitional agreement: Effort is efficiently set within the firm/financiers coalition. Instead, when converges toward infinity, the effort level converges toward , which captures the fact that part of the incentives given by G are dissipated through further risk-sharing with financiers.

Comparing with public finance, private finance unambiguously raises incentives and comes closer to the first-best.

Relying on outside finance brings two contrasting effects. On the one hand, it adds a new layer of contracting, which may exacerbate moral hazard by introducing further risk-sharing. On the other hand, the financial contract is made under a better information structure, which improves incentives. This trade-off is resolved in favor of outside finance because financiers are competitive, so that everything happens as if the government itself was enjoying the financiers' expertise to provide funds at a cheaper cost.

4.2. Related Literature

Engel, Fisher, and Galetovic (2006) were the first to study the rationale for private finance in PPPs. They showed that private finance cannot save on distortionary taxation. Any additional $1 invested by the contractor saves society some distortionary taxes but the concessionaire must be compensated for the additional investment through a longer contract term. This costs society future distortionary taxes equal to the initial tax saving. De Bettignies and Ross (2009) also discussed the benefit of private finance in PPPs. In their model, information is symmetric but private finance may lead to the efficient termination of bad projects, while public developers may sustain such projects for political reasons. On a related line, Auriol and Picard (2009, 2013) showed that the cost of public funds may actually justify outsourcing activities through PPPs in more incomplete contracting environments. The model of this section bears some similarities with Iossa and Martimort (2012a). In that paper, like here, the financier has better information than the government, though the information refers to operational risk rather than operational effort.

4.3. Implications

Our analysis has shown that outside finance improves risk allocation if it helps alleviate moral hazard. In practice, the use of private finance has been made also because it has allowed the public sector to finance the construction of infrastructure “off the balance sheet” and to accelerate delivery of projects.39 The accounting treatment of PPPs stream of payments can vary and it can often make the government budget look healthier than it is, thereby undervaluing the cost of PPP-financed infrastructure. This not only biases decisions in favor of PPPs as opposed to more traditional procurement arrangements but it can make PPPs a means to unduly transfer costs from current to future generations.40 There is no economic justification for PPPs being promoted for allowing investment off the balance sheet. To ensure homogeneity across member states and limit accounting tricks made to comply with the rules of the Stability and Growth Pact, Eurostat made a decision (news release 18/2004) on the accounting of PPPs which clarified and made the process of accounting true PPPs more transparent. However, the temptation to adopt PPPs as a tool to window dress budget deficits has not been fully removed.41

5.1. The Trade-Off between Investment and Maintenance

To analyze the trade-off between investment and maintenance, we consider a twice-repeated and slightly modified version of our basic model with contractible costs. To focus on the operator's incentives to invest, we assume that the firm gets a basic stock of infrastructure to run off public service at date . Improving this stock requires some extra investment which costs today but it lowers operating costs at date by an amount a. Another strategy would be to avoid incurring any initial investment and then cutting operating costs with more maintenance.

There is no discounting. Operating costs in each period are, respectively, given by

where the shocks are normally distributed with zero mean and variance σ², and is the maintenance effort undertaken at date i.42

Investing increases accounting costs in the short run but, because of a positive externality between design and operation, reduces the long-run cost of the service.43 Implicit in our formulation is the fact that the cost of investment is noncontractible, e.g., because it is (at least partly) aggregated with other costs, noticeably the first-period operating costs, in the firm's book.44

Consistently with Section 3., we assume that the stock of new investment has a social value with . In practice, this simply means that there is a difference between the social and the private returns on investment. Assuming that investment is verifiable, its first-best level is whereas would be privately optimal.

Noncontractible investment. Suppose that the investment a is noncontractible and must be induced by designing adequate incentives. Denote by the cost-reimbursement rule used at date i.45 The firm's gross profit is thus . Let us first consider the case where G can commit himself to such a two-period contract .

Still assuming a quadratic disutility of maintenance effort in each period, the firm chooses its whole array of actions to maximize the certainty equivalent of its intertemporal payoff:

This leads to the following incentive constraints:

(24)

An interesting benchmark is obtained when G offers the stationary contract with slope , i.e., the contract that would be optimal without any concern on the renewal of the infrastructure. This contract induces a stationary effort and an investment level, , which is privately optimal but not socially so when . There is too little investment in renewing infrastructure with such stationary contract. Raising investment requires modifying the intertemporal pattern of incentives.

PROPOSITION 6.Assuming full commitment, the optimal long-term contract entails higher powered incentives toward the end of the contract than at the beginning and an inefficient level of investment:

To boost incentives to undertake a nonverifiable investment, G must let bear less of the costs and enjoy most of the benefits associated to that investment. This is best achieved by offering cost-plus contracts in the earlier periods and fixed-price contracts toward the end of the relationship.46 Still, this is not enough to align the private incentives to invest with the socially optimal ones and underinvestment follows.

Remark 2.History-dependent contracts. Let us suppose now that G can commit to two-period history dependent contract where and The benefit of considering this larger class of incentive schemes is well-known since Rogerson (1985), pushing part of the rewards (and punishments) for a good first-period cost toward the second period improves the first-period trade-off between insurance and incentives. To then check the robustness of our earlier results, observe first that, given the history-dependent contract above, the agent chooses his effort array so that

(25)

For a given β₁ the risk borne by the agent over the two periods is better spread when half of those incentives are pushed to the second period, i.e., when . Everything happens as if the first-period variance on costs was lowered by one half. This implies high-powered incentives to reduce costs in the first period and an unambiguously increase in welfare. But, it has a detrimental impact on investment which becomes less attractive than improved maintenance.

Other scenarios. In the case of verifiable profits or of verifiable revenues, the optimal long-term contract also calls for low-powered incentives in the earlier periods of the contract and high-powered incentives toward the end of the relationship. By offering greater profit or revenue shares to the firm toward the end of the contract than at the beginning, G makes bear less of the costs and enjoy most of the benefits associated to its noncontractible investment.47

5.2. Cost Overruns

As we already stressed, long-term contracting takes place under significant uncertainty on the realizations of future costs and demand. In infrastructure projects, and maybe due to competitive pressures in awarding projects, contractors are often overly optimistic in estimating future costs.48 Following costs overruns, long-term contracting may be subject to renegotiation. Firms may obtain a tariff increase or an increase in the number of cost components passed through tariffs, a reduction in their payment to the public sector and delays and reduction in investments.

To model cost overruns in a nutshell, we will simplify the modeling of Section 5.1., neglect the investment issue or the building stage of contracting and instead focus only on the hazard coming from uncertainty on costs. To model this uncertainty, we assume that, although it may not be known ex ante at the time of contracting, the base cost level θ₀ is later on privately observed by the firm. Asymmetric information allows us to consider the firm's strategic incentives to exaggerate costs and pretend that costs overruns occur. More formally, we assume now that costs can be written as

(26)

where the base cost level θ₀ is random and may be either high, with probability or low, with probability ν (denote ).

An incentive mechanism must now not only induce the firm to choose a high level of effort but also to reveal private information once it knows whether costs are high or low. From the revelation principle, there is no loss of generality in restricting the analysis to direct revelation mechanisms which consist of a pair of contracts stipulating a fixed fee and a share of the cost borne by the firm as a function of its report on its innate base cost level. Since, for any slope of the incentive scheme , the firm always choose an effort level given by , we define the certainty equivalent of the firm's expected utility when knowing θ₀ as

(27)

Taking the profile of rents and slopes of the incentive schemes as the true primitives of our problem allows to write the truthtelling constraint for an efficient firm as49

(28)

The contract consisting in offering a rent/effort profile given by and that would be offered had θ₀ been contractible can no longer be implemented under asymmetric information because an efficient firm would strategically inflate its costs. Cost overruns arise for such badly designed contracts.

To avoid cost overruns, the truthtelling constraint 28 must be binding at the optimum. This imposes some extra risk on the firm and an extra risk premium that society bears to induce the firm's participation. Reducing this risk premium requires to distort downward below its complete information value, which is obtained by giving to an inefficient firm a low-powered cost-plus contract.

PROPOSITION 7.With ex post asymmetric information, strategic cost overruns are a concern. The optimal menu of incentive contracts that prevents cost overruns is such that the less efficient firm produces under low powered incentives whereas the firm receives incomplete insurance against the realizations of innate cost:

Remark 4.Cost overruns, renegotiation and the soft budget constraint. The optimal contract found above is not renegotiation-proof once θ₀ is known. Indeed, to induce revelation information, this contract requires that an inefficient firm runs a loss. This creates incentives for the least efficient firm to stop the ongoing project if its innate costs are high. Anticipating this outcome, G may not refrain from instilling more subsidy to ensure that even the worst firms breaks even; another instance of the soft budget constraint fallacy. Such renegotiation is akin to assuming that the firm is protected by a pair of interim participation constraints ensuring it indeed always breaks even:

(29)

Such constraints harden the trade-off between incentive and participation. It can be easily seen that only the firm with type obtains now a positive expected payoff and the corresponding distortion needed to induce truthtelling are exacerbated leading to a large effort distortion.

5.3. Related Literature

Laffont and Tirole (1993, chapter 8) proposed an adverse selection model with repeated auctions of incentive contracts which shares many features of our model, most noticeably the shift toward higher powered incentives over time. An incumbent invests in period 1 but, because of contract renewal, may lose the benefits of its investment if it is not granted the new contract for date 2. They particularly focused on the necessary bias toward the incumbent as an incentive tool to secure investment. Our pure moral hazard model can be viewed as providing a simplified version of the same insight. Dewatripont and Legros (2005) argued that ex ante competition between potential consortia may limit the extent of cost overruns and that introducing a third-party (typically outside shareholders or creditors) in a PPP contract may improve monitoring which limits cost overruns as well.50

5.4. Implications

Empirical evidence on effort allocation in long-term projects shows that effort rises over time. Projects within firms often run beyond deadlines and most resources are increased toward the final stages as in Marshall and Meckling (1962) and Mansfield, Schnee, and Wagner (1995). Actual costs often significantly exceed cost estimates used to decide whether public projects should be built. PPPs are not immune to cost overruns, though no clear evidence exists as to whether cost overruns under PPPs are more or less likely than under traditional procurement. In the United Kingdom, with traditionally procured contracts in 73% of central government's construction projects, the price to the public sector had exceeded the contractors' tender price and the project ran over budget; actual costs were between 2% and 14% above estimates. The equivalent figure with PFI was 22% although that was due to the private companies bearing the cost increase rather than the cost increase not occurring (NAO 2003b). Examples of cost overruns under PPP also include the disastrous case of Metronet, the private tube contractor for London Underground, whose cost overruns led it to bankruptcy.

While risk allocation in PPPs generally forces the contractor to bear a significant part of the construction and operational risks, the actual risk allocation may differ from what was originally planned. Governments are providers of last resort and contractors are aware that public authorities cannot afford prolonged service disruption. The re-tendering of a PPP contact is a long and costly process. Also, as the case of London Underground points out, a market for secondary contracts may not always exist. In fact very few PPP contracts have been prematurely terminated. The Channel Tunnel Raillink is one example of the government bailing out the PPP contractor. More generally, empirical evidence supports that risk allocation in practice often departs from what is laid out in theory (see, e.g., Lobina and Hall 2003). As stressed by The World Bank, “whether PPPs perform better than full provision by state-owned enterprises depends in particular on whether performance risk is effectively shifted from taxpayers to the private shareholders of the company that enters into a concession-type arrangement.” 51

6.1. Under-Investment and Opportunistic Governments

The nonstationary path of incentives described in Proposition 6 is highly dependent of G's ability to commit to increase subsidies in the second period to reward 's initial investment. Assume now that such commitment power is absent and that renegotiation takes place at date with G still having all bargaining power at that stage and extracting all surplus that could withdraw from renegotiation.

At date 2, 's investment a⁰ is sunk and the second-period cost reimbursement rule is renegotiated to reach the optimal trade-off between maintenance effort and risk that would arise in a static context, i.e., conditionally on the investment level a⁰.52 This yields the standard expressions for the second period maintenance effort and the slope of the renegotiated incentive scheme:

Under limited commitment, G can still adjust the second-period fixed-fee to extract all surplus of the firm given his expectation over the investment level a⁰ at this date and, of course, expectations are correct in equilibrium.

Anticipating the slope of date 2 incentive scheme, and knowing also the slope of the first-period incentive scheme, chooses his investment so that

(30)

With an opportunistic government, welfare is obviously lower than with full commitment. The second-period contract also entails lower powered incentives because, at date 2, G does not take into account the impact of the second-period contract the first-period investment. Since , 30 implies that enjoys less of the benefits of its investment. To maintain incentives, must be even more reimbursed for its first-period costs than under full commitment. This tilts first-period incentives even further toward cost-plus contracts.

PROPOSITION 8.With an opportunistic government, investment is lower and cost-reimbursement rules are even more tilted toward cost-plus contracts than under full commitment:

Regulatory risk. Assume now that renegotiation takes place at date 2 only with probability p. This parameter is a measure of institutional quality, with higher values of p meaning weaker enforcement. For instance, the government may change between dates 1 and 2 with some probability due to elections or renegotiation takes place due to exogenous events. In some cases, PPP contract clauses indeed seek to insure the private operator against aggregate risks, but episodes have occurred where governments have reneged on these clauses when a severe macroeconomic crisis occurred. The assumption of limited commitment also fits quite well the case of developing countries with weak enforcement power.

At date 2, 's investment a⁰ is sunk and with probability p the second period cost reimbursement rule is renegotiated to implement the conditionally optimal maintenance effort through an incentive scheme having slope . This leads to the following expression of 's incentive constraint:

(31)

The effort levels in this model with political risk are intermediary between the full commitment and the case of an opportunistic government viewed above. An increase in regulatory risk (i.e., p greater) thus lowers incentives for investment and induces more low powered incentives.

Other scenarios. In the case of contractible profits or of contractible revenues, where infrastructure-improving investment in the first period enhances second period's quality and service demand, similar insights are obtained. With an opportunistic government, investment is lower and incentives are even less high-powered in both periods than under full commitment.53

6.2. Related Literature

In a pure adverse selection framework, Aubert and Laffont (2002) analyzed the mechanism through which a government can affect future contracting by distorting regulatory requirements to take into account possible political changes and renegotiation. Assuming that the current contract binds all future governments, imperfect commitment implies that the amount information revealed in the first period is strategically determined to affect the beliefs of the future governments.

Several political motives have been proposed to explain why governments may want to renegotiate PPP contracts. A government may increase its chances to be re-elected by expanding spending or by promoting investment in public works that create jobs and boost economic activity (Guasch 2004, Engel et al. 2006).

6.3. Implications

Institutional quality plays a critical role in the provision of public services by the private sector. Hammami, Ruhashyankiko, and Yehoue (2006) indeed found that private participation (in the form of PPP, privatization, or traditional procurement) is more prevalent in countries with less corruption and with an effective rule of law. For PPP contracts, the benefit of whole-life management cannot be realized in the absence of strong governance and minimal risk of unilateral changes of contract terms by the government.

Governments' failure to honor the terms of concession contracts is a pervasive phenomenon. In LAC countries, it is common for a new administration to decide not to honor tariff increases stated in the concession contract granted by previous administrations. Examples include the Limeira water concession in Brazil which was denied a tariff adjustment allowed by a contract signed by a previous administration. There are also cases where legislation was passed to nullify contractual clauses. The Buenos Aires water concession indexed local-currency denominated tariffs to the U.S. dollar to protect the contractor against currency risk. However, after a devaluation of the local currency, the U.S. Congress passed an economic emergency law that nullified these guarantees (Lobina and Hall 2003). Using a sample of 307 water and transport projects in five Latin American countries between 1989 and 2000, Guasch, Laffont, and Straub (2006) found that 79% of the total government-led renegotiations occurred after the first election that took place during the life of the project. In many cases the central or local government during a re-election campaign decided in a unilateral fashion to cut tariffs or not to honor agreed tariff increases to secure popular support.

Political risk has also played a crucial role in Central and Eastern Europe. As reported by Brench et al. (2005), a major obstacle to the PPP policy in Hungary was the frequent change in political attitudes toward PPPs and user tolls. Since 1990, each change in government resulted in a different attitude and a different institutional framework for PPPs.

The impact of regulatory risk in PPPs is significant as it discourages potential investors and raises the cost of capital and the risk premium (higher tariffs, or smaller transfer price) paid for a PPP contracts. Guasch and Spiller (1999) estimate that the cost of regulatory risk ranges from 2% to 6% age points to be added to the cost of capital depending on country and sector. An increase of 5% age points in the cost of capital to account for the regulatory risk leads to a reduction of the offered transfer fee or sale price of about 35% or equivalently it requires a compensatory increase in tariffs of about 20%. Regulatory risk also discourages investors. In the 16 billion London Underground project of 2002–03 a high level of political controversy made lenders nervous, with the result that 85% of the debt had to be guaranteed by the public sector at a fairly late stage in the procurement process.

Renegotiation by the government of concession contracts in LAC countries is also widespread. Considering a compiled data set of more than 1000 concessions granted during 1985–2000, Guasch (2004) showed that 30% of the concessions were renegotiated and in 26% of the cases the government initiated the renegotiation. Using a data set of nearly 1000 concessions awarded from 1989 to 2000 in telecommunications, energy, transport, and water, Guasch, Laffont, and Straub (2008) showed that the probability of firm-led renegotiation is positively related to the characteristics of the concession contract among other things. Firm-led renegotiation on average tend to favor contractors. Guasch, Laffont, and Straub (2007) showed that the role of an experienced and independent regulator (or in general the quality of bureaucracy) is especially important in contexts characterized by weak governance and high likelihood of political expropriation. In LAC countries, regulatory agencies were rarely given training and instruments adequate to their mandate and even lacked political support from the government.

To improve governance, a number of countries have created dedicated PPP units—centers of expertise—to manage the contract with the private contractor.54 Different approaches have been taken with regard to the governance of these units as some of them have been set up within the public sector (e.g., Central PPP Policy Unit in the Department of Finance 1 in Ireland or the Unita' Tecnica della Finanza di Progetto in Italy), others outside (partnership UK in the United Kingdom which is a joint venture between the public and private sector with a majority stake held by the private sector).