In a contract, the risk allocation between the contractual parties should accomplish two sets of goals: to provide incentives for the parties to undertake efficient actions when these actions cannot be directly contracted upon (because they are not immediately observable) and to provide insurance to a risk averse party against the risks of the project. In a PPP contract, in particular, the goals of risk allocation should be:
(i) to provide incentives to reduce the long-term cost of a project;
(ii) to provide incentives to complete the project in time and within budget;
(iii) to provide incentives to improve the quality of services and revenues yield; and
(iv) to insure the risk averse public and private partners against risk. Risk insurance for the public partner helps to improve its profile of expenditure on the project by converting variable operation and capital costs into predictable unitary payments. Risk insurance for the private partner helps to reduce the cost of capital.
In order to accomplish the above goals in the most effective way, two principles should guide the allocation of risk between the public and private partners:41
(P1) given partners with similar risk-aversion, the risk should be allocated to the party that is responsible or has relatively more control over the risk factor, and
(P2) given partners with similar responsibility or control over the risk factor, the risk should be allocated to the party that is more able to bear it, i.e. the less risk-averse party.
The intuition and the implications of the above principles can be understood by way of an example. Consider a PPP where the private-sector party is in charge of constructing a facility for the provision of a public service. Suppose that there are two construction practices that can be followed, practice G (good) and practice B (bad), and that the type of construction practice adopted by the private-sector party is not observable by the public-sector party.
Suppose that if practice G is chosen, then with probability 10% problems arise during construction that lead to an increase in the cost of the project by $10.000. If instead practice B is chosen, then the corresponding probability is 50%. That is, we are in a situation where the efficiency of the construction practice affects the likelihood of cost overruns. Suppose also that practice G has a non-contractible cost for the private-sector party of $7.000 whilst practice B has a non-contractible cost of $6.000. Non-contractibility implies that this cost is borne by the private-sector party who then has incentives to take it into account when choosing between practice G and B.
Finally, consider the possibility that the private-sector party and the public-sector party are risk averse. A risk averse party faces a cost for bearing risk (we call it 'risk premium') which generally increases with: (i) the degree of risk aversion of the party, (ii) the likelihood that adverse events will occur, and (iii) the amount of risk borne, in the example given by the expected cost overruns. Denote by rpr and rpu the parameters, with values between 0 and 1, that capture the degree of risk aversion of the private-sector party and of the public-sector party, respectively. Denote by x the fraction of risk borne by the private-sector party as provided by the contract; 1-x is the fraction of risk borne by the public-sector party.
For the sake of simplicity, we can use the following expressions as a simplified measure of the cost of bearing risk for the private-sector party in our example:
rpr ∙ x ∙ 10% ∙ $10.000 | when practice G is used, |
rpr ∙ x ∙ 50% ∙ $10.000 | when practice B is used. |
Whilst the cost of bearing risk for the public-sector party is:
rpu ∙ (1-x) ∙ 10% ∙ $10.000 | for practice G, |
rpu ∙ (1-x) ∙ 50% ∙ $10.000 | for practice B. |
Consider now the expected total cost of any given practice. This is given by the sum of the expected cost overruns, the non-contractible cost for the private-sector party, and the risk premium for each of the party that bears the risk.
For practice G the expected total cost is given by:
CG = [10% ∙ $10.000] + $7.000 + [rpr ∙ x ∙ 10% ∙ $10.000 + rpu ∙ (1-x) ∙ 10% ∙ $10.000]
= $8.000 + $1.000 ∙ [rpu + x ∙ (rpr - rpu)].
Whilst the expected total cost of practice B is:
CB = [50% ∙ $10.000] + $6.000 + [rpr ∙ x ∙ 50% ∙ $10.000 + rpu ∙ (1-x) ∙ 50% ∙ $10.000]
= $11.000 + $5.000 ∙ [rpu + x ∙ (rpr - rpu)].
It then follows that practice G always minimizes the cost of the project since CG is always lower than CB. Therefore, the efficient practice is practice G.
The issue is then whether the private-sector party has incentives to select practice B, given that its choice of practice cannot be contracted upon. As we show below, a problem may arise because the private-sector party only takes into account its own cost and not the total cost of the project, and because of the presence of some non-contractible costs.
In particular, consider the rational choice for the private-sector party. If the private-sector party chooses practice G, it will face the cost:
[x ∙ 10% ∙ $10.000] + $7.000 + rpr ∙ x ∙ 10% ∙ $10.000 = $7.000 + x ∙ $1.000 ∙ (1 + rpr).
Whilst if it chooses practice B, it will face the cost:
[x ∙ 50% ∙ $10.000] + $6.000 + rpr ∙ x ∙ 50% ∙ $10.000 = $6.000 + x ∙ $5.000 ∙ (1 + rpr).
By comparing the above two formulas, it is immediate that unless the private-sector party bears sufficient risk (i.e. x is sufficiently high), it will choose practice B instead of the efficient practice G. In fact, consider the case where the public-sector party bears all the construction risk and therefore pays for all cost overruns, i.e. x=0. In this case, the private-sector party will not have incentives to choose practice G since practice B will cost it less ($6.000 instead of $7.000).
If instead the private-sector party bears a sufficient amount of risk, it will choose the efficient practice G. In particular, for any x at least equal to 25%, the private-sector party will have incentives to choose practice G independently of its level of risk aversion rpr. This is because for any x at least equal to 25%, the cost of practice G for the private-sector party is never greater than the cost of practice B:
$7.000 + 25% ∙ $1.000 ∙ (1 + rpr) ≤ $6.000 + 25% ∙ $5.000 ∙ (1 + rpr).
The above example shows the rationale behind principle (P1), which leads to the following criterion: when the private-sector has relatively more control over a risk factor, then transferring the risk to the private-sector party (i.e. setting x sufficiently high) helps to provide incentives for efficient actions (i.e. choice of practice G rather than B).
Note that for x between 0 and 25% the inequality above is satisfied only for sufficiently high rpr. In other words, the more risk averse is the private party, the smaller is the risk it must bear to have correct incentives to perform.
Note also that the non-contractibility of the action undertaken by the private-sector party to control the risk factor (in our example given by the type of construction practice) is critical for principle (P1) to be relevant. Should the action undertaken by the private-sector party be perfectly observable by the public-sector party, it would suffice for efficiency that the public-sector party specified in the contract which particular action it wishes the private sector to undertake (in our example, to choose construction practice G).
The above example also explains principle (P2). Consider again the total cost of practice G, as given above by:
CG = $8.000 + $1.000 ∙ [rpu + x ∙ (rpr - rpu)].
We see immediately that transferring risk to the private partner increases the total cost of the project whenever the private-sector party is more risk averse than the public-sector party. Formally, whenever rpr>rpu, the greater the risk transfer x, the greater the total cost CG. More importantly, the total cost of practice G is minimized by letting the party with the lower degree of risk aversion bear most of the risk. That is, by choosing x that minimizes the term [rpu + x ∙ (rpr - rpu)].
The aim to minimize the total cost of the project, isolating risk averse parties from risk, explains principle (P2) and yields the following criteria that abstract from the effects of risk allocation on incentives (i.e., they hold assuming that project G is selected). First, when the public-sector party is more risk averse than the private-sector party (rpu>rpr), then the total cost of the project is minimized by letting the private-sector party bear all the risk; this can be achieved by setting x=1. Second, when instead the public-sector party is less risk averse than the private-sector party (rpu<rpr), then (in the absence of incentive problems) the total cost of the project is minimized by letting the public-sector party bear all the risk; this can be achieved by setting x=0.
When we put together both the issue of incentives and that of risk premiums minimization, it is then clear that risk is optimally allocated if the following holds:
i. When the public-sector party is more risk averse than the private-sector party (rpu>rpr), then risk transfer to the private-sector party helps both to ensure incentives over non-contractible actions and to minimize the total cost of the project. The optimal risk allocation then calls for the private-sector party to bear all the risk: x=1.
ii. When the public-sector party is less risk averse than the private-sector party (rpu<rpr), then risk transfer to the private-sector party generates a trade-off: it helps to ensure incentives but it may lead to an excessive risk premium. Typically, however, the incentives consideration prevails and the efficient risk allocation has the private-sector party bearing a substantial amount of risk, the more the less risk averse it is.
Case Study: TransMilenio Bus Rapid Transit System in Bogota (Colombia) (Part I) The TransMilenio (TM) Bus Rapid Transit System was developed in 2000 to upgrade and operate the Bogotá bus transport system by a partnership between the public sector and a number of private companies. Before the TM project, the bus transport service was provided by a few bus companies that owned the government-issued routes and rented them to private bus owners and by small private bus operators serving fixed routes. Since the operators' revenue depended on the number of passengers, there were often 'price wars' to attract passengers (Colombians referred to this phenomenon as 'war of the cents' because only minimal price reductions were feasible in bus fares). Outcomes from such a system were far from efficient: long delays, oversupply of seat capacity, and low quality of service. The TM project planned to rationalize bus routes by building exclusive bus lanes in critical areas of Bogotá and using a system of feeder routes to complement the main lanes. A modern infrastructure was planned involving a network of enclosed bus stops, pedestrian bridges, terminals, and transfer stations. The overall bus route system was to be built over 15 years and would include 22 exclusive corridors covering around 400 km with a capacity to transport 5 million people daily. Contracts and partners A publicly owned company, TransMilenio SA, was set up to manage the project. The company developed the planning and contract drafting stages. It also conducted the tendering to select private partners that would build infrastructure and operate the main routes, the feeder routes, the ticketing system, and the payments system. After launching the TM project, TransMilenio SA was responsible for administering the new bus transport system. The TM contracts entitled TransMilenio SA to undertake monitoring and verification activities in order to ensure quality performance and customer service. In this regard, a system of fines was implemented to penalize the private partners failing to comply with their contractual obligations, responsibilities and investment requirements A remarkable feature of the TM project was that the public sector established a partnership with several private partners simultaneously: not only the building and operation stages were developed by different private companies, but also different activities within the operation stage were assigned to different private companies Long-term concession contracts were used to set out the TM project coordinating the activities of the many partners involved, ensuring bankability, an adequate balance of risks and rewards, and minimum scope for conflict of interests. In a sort of service unbundling, the private partners in charge of the operation activities were responsible for the provision of a specific service and had to meet certain investment requirements, e.g. transport companies operated the buses, a company was in charge of collecting fares, another company managed the distribution of collected revenue among the bus operators, etc. Financing In the TM project, there was a clear distinction between activities to be financed by the public-sector party and those to be financed by the private partners. Public funding was required to invest in the transport infrastructure. The cost of the main construction works was estimated in USD 240 million for the period 1998-2002, and USD 480 million for 2002-2005. Most of the infrastructure cost was to be borne by the national and local governments. The contribution of the national government was around two-thirds of the infrastructure cost, partly financed with a loan granted by the World Bank. The Bogotá government was able to financially support the TM project thanks to its strong fiscal position and the autonomy granted to local authorities to fund the provision of public services. The city of Bogotá committed half of the revenues from a gasoline sales surcharge for financing the project. On the other hand, the private partners provided financing for buses and ticket machines. Their invested funds were to be recouped by charging fares to final users, with no subsidies nor guarantees offered by the public sector to the private-sector parties. Activities and risk allocation As was mentioned above, the TM project was a partnership between the public sector and many private partners that required complex contractual arrangements to coordinate the building and operation activities. To build the infrastructure, the public-sector party contracted with private constructors selected on a competitive basis. Being responsible for financing the investment in infrastructure, the public-sector party retained the financial risk of the project. As the works were to be undertaken in different urban districts while the bus transport services were being provided, a coordination committee was formed to monitor the building and facilitate the bus transport service provision. To conduct the operation activities, the public-sector party contracted with different partners and unbundled the operation of buses, the collection of revenues, and the distribution of revenues among the bus operators. The existing bus companies awarded concessions through competitive bidding to operate the bus routes. The award criterion was based in a system of points in which bidders received points according to their experience, bus quality, and emission levels. Thus, TM encouraged the bus operators to provide an efficient, modern, and non-polluting vehicle fleet. The bus operators had to invest in new buses, so financial risk was transferred to them. Two different private companies were selected by competitive bidding to collect fares and to distribute revenues among the bus operators. One company had responsibility for investing in ticket machines and managing the ticketing system. The other company, a financial service provider, had responsibility for managing the trust fund where fare revenues were deposited and the payments system to distribute the revenues. Sources: see TransMilenio (Part II) |
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41 See Martimort and Sand-Zantiman (2006) for a discussion of how risk allocation can also help to address situations where the public-sector party is more informed than the private sector party about the quality of the assets.