Corruption versus efficiency in water allocation under uncertainty: is there a trade-off?

ABSTRACT

In the absence of a cooperative solution to the problem of rights over shared water, water allocation through third-party intervention is most commonly used. This paper considers water allocation within a federal set-up with the requisite legal institutions to enforce third-party adjudication and tries to capture the politically charged motivations that often guide such allocations. It compares two mechanisms generally used by central planners to allocate water between up- and downstream regions, namely fixed and proportional allocation rules. By considering a corrupt central planner, this paper models the underlying political manoeuvring that drives the assignment of water rights. It is found that the politically pliable central planner’s choice of allocation rule depends on the expected state of nature. Interestingly, the corrupt central planner’s equilibrium choice of allocation rule turns out to be efficient, unless the problem of severe water scarcity is expected to occur.

KEYWORDS:

• domestic water conflict
• allocation rule
• corruption
• efficiency
• third-party adjudication

JEL:

• D73
• D74
• P14
• Q34

ACKNOWLEDGEMENTS

We gratefully acknowledge the helpful comments from an associate editor and three anonymous referees. This paper is partially based on a chapter of Pati’s MPhil thesis undertaken at the Indira Gandhi Institute of Development Research (IGIDR). We thank seminar participants at the IGIDR. The usual disclaimer applies.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the authors.

Notes

1. In the case of transboundary water flows, third-party interventions may not be very effective due to lack of enforceability and it may also lead to inefficiency by jeopardizing the possibilities of cooperation (Ansink & Weikard, 2009).

2. It is observed that parties involved in disputes over water rights do not comply with the water-sharing agreements in some cases, despite the agreement being legally binding. Bennett and Howe (1998) examine factors behind non-compliance in interstate river compacts. Ambec et al. (2013) explore conditions for water-sharing agreements to be sustainable to reduced flows. Richards and Singh (2002) argue that non-compliance might stem from a perverse combination of political affiliations that is not compatible with the states’ incentives, and centre–state politics plays crucial role in this regard. This paper, however, sidesteps the issue of compliance for simplicity.

3. For example, it could refer to the electoral votes cast in the respective regions in favour of the political party at the centre. It could also denote the increasingly fierce contestation between different policy objectives such as economic rationalism and environmentalism and the impact of the central planner’s preference for one over the other on its choice of water-allocation rule. In Australia’s Darling–Murray Basin, for example, water reforms were heavily contested on account of conflicting policy positions between pro-irrigation and environmental interests (Alexandra, 2018).

4. The central planner’s bias may be his private information and different regions may have different beliefs about it. In case each region has the same belief regarding the form of the bias function $\lambda \left(C_D,C_U\right)$, the qualitative results of this paper go through. Alternatively, suppose that: $\tilde{Z}={\theta }_U\left(C_U,C_D\right)B_U\left(W_U\right)+{\theta }_D\left(C_U,C_D\right)B_D\left(W_D\right),$where ${\theta }_U\left(C_U,C_D\right)$ and ${\theta }_D\left(C_U,C_D\right)$ are the weights give to benefits of up- and downstream regions, respectively. Further, $\begin{array}{rl}& {\theta }_U\left(C_U,C_D\right)+{\theta }_D\left(C_U,C_D\right)=1,{\theta }_i\left(C_i,C_j\right)\\ & ={\displaystyle \frac{1}{2}\mathrm{\forall }{C}_i=C_j\in \left[0,1\right],}\end{array}$ $\begin{array}{r}\genfrac{}{}{0ex}{}{{\theta }_i\left(C_i,C_j\right)\in \left[0,1\right];{\displaystyle \frac{\mathrm{\partial }{\theta }_i}{\mathrm{\partial }{C}_i}>0\mathrm{a}\mathrm{n}\mathrm{d}}}{{\displaystyle \frac{\mathrm{\partial }{\theta }_i}{\mathrm{\partial }{C}_j}<0,\mathrm{\forall }i,j\in \left\{U,D\right\}\mathrm{a}\mathrm{n}\mathrm{d}i\ne j.}}\end{array}$

Clearly, ${\theta }_U\left(C_U,C_D\right)$ and ${\theta }_D\left(C_U,C_D\right)$ can be interpreted as contest success functions of up- and downstream regions, respectively (Skaperdas, 1992, 1996; Baik, 1998; Ansink & Weikard, 2009). Now, for any given $C_U$ and $C_D$: $\begin{array}{r}E\left(\tilde{Z}\right)={\theta }_U\left(C_U,C_D\right)E\left(B_U\left(W_U\right)\right)+{\theta }_D\left(C_U,C_D\right)E\left(B_D\left(W_D\right)\right)\\ ={\theta }_U\left(C_U,C_D\right)\left[E\left(B_U\left(W_U\right)\right)+{\displaystyle \frac{{\theta }_D\left(C_U,C_D\right)}{{\theta }_U\left(C_U,C_D\right)}E\left(B_D\left(W_D\right)\right)}\right]\end{array}$and, thus, maximization of $E\left(\tilde{Z}\right)$ with respect to $W_0\left(\mathrm{o}\mathrm{r}\text{β}\right)$ is equivalent to the maximization of $E\left(Z\right)$ with respect to $W_0\left(\mathrm{o}\mathrm{r}\text{β}\right)$ where: $Z=E\left(B_U\left(W_U\right)\right)+{\displaystyle \frac{{\theta }_D\left(C_U,C_D\right)}{{\theta }_U\left(C_U,C_D\right)}E\left(B_D\left(W_D\right)\right),{\displaystyle \frac{{\theta }_D\left(C_U,C_D\right)}{{\theta }_U\left(C_U,C_D\right)}=\lambda .}}$Note that $\lambda =1+C_D-C_U$ (the functional form considered in this analysis) is supported by contest success functions: ${\theta }_U={\displaystyle \frac{1+C_D-C_U}{2+C_D-C_U}\mathrm{a}\mathrm{n}\mathrm{d}{\theta }_D={\displaystyle \frac{1}{2+C_D-C_U}.}}$

(It is easy to check that: ${\theta }_D\left(C,C\right)={\theta }_U\left(C,C\right)={\displaystyle \frac{1}{2};\mathrm{\forall }C\in \left[0,1\right],}$ $\genfrac{}{}{0ex}{}{{\displaystyle \frac{\mathrm{\partial }{\theta }_D}{\mathrm{\partial }{C}_D}={\displaystyle \frac{\mathrm{\partial }{\theta }_U}{\mathrm{\partial }{C}_U}>0,{\displaystyle \frac{\mathrm{\partial }{\theta }_D}{\mathrm{\partial }{C}_U}={\displaystyle \frac{\mathrm{\partial }{\theta }_U}{\mathrm{\partial }{C}_D}<0\mathrm{a}\mathrm{n}\mathrm{d}}}}}}{{\theta }_D\left(C_U,C_D\right)+{\theta }_U\left(C_U,C_D\right)=1.)}$

5. If $\overline{W}<{\displaystyle \frac{2a}{b}}$, we have: ${\displaystyle \frac{\mathrm{\partial }{W}_0}{\mathrm{\partial }\lambda }>0,\frac{\mathrm{\partial }(\overline{W}-W_0)}{\mathrm{\partial }\lambda }<0,}$${\displaystyle \frac{\mathrm{\partial }E{\left(B_D\right)}_F}{\mathrm{\partial }{W}_0}>0\mathrm{a}\mathrm{n}\mathrm{d}}$ ${\displaystyle \frac{\mathrm{\partial }E{\left(B_U\right)}_F}{\mathrm{\partial }(\overline{W}-W_0)}>0,}$

since: $\overline{W}<{\displaystyle \frac{2a}{b}\Rightarrow W_0<{\displaystyle \frac{a}{b}}}$and (5a) holds. Otherwise, if: $\overline{W}>{\displaystyle \frac{2a}{b}}$we have: ${\displaystyle \frac{\mathrm{\partial }{W}_0}{\mathrm{\partial }\lambda }<0,{\displaystyle \frac{\mathrm{\partial }(\overline{W}-W_0)}{\mathrm{\partial }\lambda }>0,{\displaystyle \frac{\mathrm{\partial }E{\left(B_D\right)}_F}{\mathrm{\partial }{W}_0}<0\mathrm{a}\mathrm{n}\mathrm{d}}}}$${\displaystyle \frac{\mathrm{\partial }E{\left(B_U\right)}_F}{\mathrm{\partial }(\overline{W}-W_0)}.<0.}$

6. It can be checked that either both: ${\displaystyle \frac{\mathrm{\partial }E{\left(B_D\right)}_P}{\mathrm{\partial }\text{β}}\mathrm{a}\mathrm{n}\mathrm{d}{\displaystyle \frac{\mathrm{\partial }\text{β}\left(\lambda \right)}{\mathrm{\partial }\lambda }}}$are positive, or both are negative. On the other hand, ${\displaystyle \frac{\mathrm{\partial }E{\left(B_U\right)}_P}{\mathrm{\partial }\left(1-\text{β}\right)}\mathrm{a}\mathrm{n}\mathrm{d}{\displaystyle \frac{\mathrm{\partial }\left(1-\text{β}\right)}{\mathrm{\partial }\lambda }.}}$cannot be of the same sign.

7. ${\displaystyle \frac{\mathrm{\partial }{W}_0\left(\lambda \right)}{\mathrm{\partial }\lambda }=-{\displaystyle \frac{\mathrm{\partial }(\overline{W}-W_0(\lambda \left)\right)}{\mathrm{\partial }\lambda }={\displaystyle \frac{b\overline{W}-2a}{{\left(1+\lambda \right)}^2}>(<)0\mathrm{i}\mathrm{f}\overline{W}>(<){\displaystyle \frac{2a}{b}.}}}}$