governs the assignment of exogenous demand risk to the PPP.<sup>16</sup> It is somewhat surprising that, as we will see, some contractual forms can create demand risk---that is, the sum of the risks borne by the government and the PPP exceeds the risk of the project.

To understand PPP risk, it is useful to use a framework developed in Engel, Fischer and Galetovic (2010). Assume that the consumer surplus generated by an infrastructure project at time _t_ , CS , and user fee revenues, , are random variables determined by the state of demand, _v_ , that is, by one possible trajectory of future demand realizations. Denote the upfront investment tt tt by _I_ and, for simplicity, assume that operating and maintenance costs are zero. The PPP firm is RR selected in a competitive auction that dissipates rents. We assume, for simplicity, that there is neither construction nor availability risk.

The upper half of Table 3 depicts the distribution of the present value of cash flows and surpluses in a demand state _v,_ for alternative funding sources and types of contracts. Rows distinguish between the funding sources (user fees versus taxes), columns between governance structures (traditional public provision versus PPPs). Two alternative PPP contractual forms are considered under PPPs, for each funding source, either fiscal payments or user fees.

Consider first PPPs funded by user fees. Under a PVR contract, firms bid on the present value of revenue that they will receive over the term of the project, and the concession ends when that present value is collected. Thus, the term of the PPP is variable---the PPP lasts longer for lowdemand realizations. Under a fixed term concession, by contrast, the PPP collects user fees for a fixed number of years and revenues can be higher or lower depending on demand realizations.

**Table 3. Risk allocation, source of revenues, and contractual form (based on Engel et al (2014)).**

|||_Contractualform_<br>_PP_<br>|_P_<br>|
|---|---|---|---|
||_Traditional provision_|_PVR contract_|_Fixed-term contract_|
|_Funding source_|_(1)_<br><br> <br>|_(2)_<br><br> <br>|_(3)_<br><br> <br>|
|_User fees_|<br><br><br>|<br><br><br>|<br><br><br> <br>|
|Users|CS0<br>∞(v) −R0<br>∞(v)<br><br> <br>|CS0<br>∞(v) −R0<br>∞(v)<br><br> <br>|CS0<br>∞(v) −R0<br>∞(v)<br><br> <br><br><br>|
|Taxpayers|<br><br>R0<br>∞(v) −I<br>|<br><br>R0<br>∞(v) −I<br>|<br><br>R0<br>∞(v) −R0<br>T(v)<br><br>|
|Firms|<br><br><br> <br>I−I|<br><br><br> <br>I−I|<br><br><br> <br><br>R0<br>T(v) −I|
|_Taxes_|<br><br><br><br>|<br><br>_Availability payment_<br><br><br>|<br><br><br> <br>_Fixed-term_<br>_shadow toll_<br><br><br><br>|
|Users|CS0<br>∞(v)<br><br>|CS0<br>∞(v)<br><br>|CS0<br>∞(v)<br><br><br><br>|
|Taxpayers|−I<br>|−I<br>|−R0<br>T(v)<br><br>|
|Firms<br>_Notation._ _v_= state of dem<br>present discounted value o|I−I<br>and; CS = consumer surplus; R = us<br>f_X_between times s and t, as of ti|I−I<br>er fee or shadow toll revenue;<br>me 0;_T_= length of fixed-term|R0<br>T(v)−I<br> _I_= upfront investment;_Xs_<sup>_t_</sup>=<br>contract.|

_Notation. v_ = state of demand; CS = consumer surplus; R = user fee or shadow toll revenue; _I_ = upfront investment; _Xs_<sup>_t_</sup> = present discounted value of _X_ between times s and t, as of time 0; _T_ = length of fixed-term contract. _Assumptions._ The table depicts cash flows and social surplus for a given demand state _v_ (corresponding to present discounted value of user fee revenue in the state) for alternative sources of funds and contractual arrangements. Rows distinguish between sources of funds (user fees and taxes); columns between procurement forms (public provision and PPPs). Demand for the infrastructure is uncertain, so consumer surplus, CS, and user fee revenues, R, are random variables of the demand state, _v_ . The upfront investment, _I_ , is the same in all demand states, and operating and maintenance costs are zero. Firms are selected in competitive auctions that dissipate all rents.

> 16 When we consider the possibility of renegotiations, the contractual risk assignment may be altered ex post.

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