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Risk Sharing in Public-Private Partnerships

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Abstract

Public-private partnerships (PPPs) have been widely used to finance many projects. Despite the growing importance of PPPs, a serious attempt has not been made to come up with a unified theory which can understand the different incentive mechanisms, risks, and heterogeneity embedded in a PPP structure which can often lead to their failure. Using a global games framework, this paper achieves to do exactly that by elaborating upon the role of coordination and uncertainty in these projects. With heterogeneous information, the incidence of failure can be uniquely identified by characterizing and defining the equilibrium. Comparative static results point to how policymakers can improve the probability of success in these partnerships. The incentive mechanisms also highlight how a PPP structure can do better than other forms of investment organization.

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Data Availability

Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

Code Availability

No code was used to conduct the study.

Notes

  1. The investment by the World Bank in support of PPPs across the globe has also increased significantly in both absolute terms and in relative terms, from $ 0.9 to $ 2.9 billion and from 4% in 2002 to 7% in 2012 [38].

  2. Levin and Tadelis [31], Iossa and Martimort [11] and Renneboog and Sarmento [32]

  3. [38].

  4. This database has data on 6400 infrastructure projects in 139 low- and middle-income countries.

  5. This is an aspect that I model explicitly later.

  6. Yuan et al. [33] study a novel Z-number-based real option model to study PPPs.

  7. We can assume there is a monetary equivalent to this utility gain, which is the total investment required to complete the project.

  8. A standard assumption in papers trying to study public good provision [34, 35].

  9. Simply think of all citizens privately, equating marginal utility and marginal cost, where the cost can be either through votes or through taxes.

  10. Think of this as a hydro-project which generates electricity. The fact that it generates electricity for the citizens is a utility gain; however, the electricity is sold at a certain price which depends on several factors besides demand and is therefore uncertain.

  11. We assume away the existence of debt repudiation mechanisms—openly or through inflation, as highlighted by Calvo [36]

  12. This can be thought of as the funds it is ready to collect and still leave enough to win votes and the election.

  13. The source of the fund for \(\alpha\) is not considered in the model. The only assumption is that this source does not affect the economy in any other way. We can think of the utilization of taxes to generate funds for the project. It can also be sourced from printing money.

  14. Alternatively, one can think about each i as a shareholder or investor in a firm when a group of firms are acting as the private creditors.

  15. The assumption of no time discounting can be made without loss of generality as I have assumed that the private investors are risk-neutral and have a negligible share as compared to the total investment in the project.

  16. \(\alpha + \beta\) being equal to at least one guarantees the completion of the project. If it is greater than one, it just means that the project still has enough funds to allow it to be completed.

  17. We assume that the project generates high revenue stream even when gains equal disruption. All results go through if equality leads to low revenue.

  18. First highlighted by Carlsson and Van Damme [15]

  19. This is proved when we identify the conditions for the uniqueness of the equilibrium.

  20. This lemma was first used by Vives [37] for supermodular games. The use of this proof here is possible because the structure of our model is similar to the one used by Morris and Shin [17], which is a simplification of the supermodular games where iterated deletion of dominated strategies yields unique equilibrium.

  21. Here, I have that the single private investor undertaking the entire project has a private noisy signal about \(\theta\).

  22. Although the total investment is higher when the project is being completed by a single individual, using assumptions on risk-neutrality, we can make comparisons on the marginal investment.

  23. The next aim would be to calibrate the model and run a counterfactual analysis. That is out of the scope of the paper. It would also allow for more formal sensitivity tests which were addressed in the comparative static exercises.

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Contributions

RM wrote and analyzed the model for the study. RM has read and approved the final manuscript.

Corresponding author

Correspondence to Ronit Mukherji.

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Appendix

Appendix

1.1 Model Variables

S.No.

Variable

Definition

1

g

Government

2

i

Private Investor

3

\(\alpha\)

Government’s share of the total finance in the project

4

\(\beta\)

Private Creditor’s share of the total finance in the project

5

m

Mass of private investors

6

a

Investment by a single investor

7

R

Revenue generated from the project

8

\(R^{*}\)

Maximum revenue possible from the project

9

\(R_{*}\)

Lowest revenue possible from the project

10

\(\theta\)

Underlying state of the economy

11

p

Share of investors who withdraw from the project

12

A

Total wealth of private investors

13

y

Mean of \(\theta\)

14

\(\delta\)

Precision of \(\theta\)

15

\(x_{i}\)

Signal of \(\theta\)

16

\(\gamma\)

Precision of preivate noisy signal

17

\(\epsilon _{i}\)

Mean of posterior Beliefs

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Mukherji, R. Risk Sharing in Public-Private Partnerships. Oper. Res. Forum 4, 72 (2023). https://doi.org/10.1007/s43069-023-00254-z

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