The corruptible inspector

How does the possibility of corrupting an inspector affect the quality of the product a procurer is able to obtain from his supplier? In his BSE Working Paper (No. 798) “Procurement design with corruption,” Roberto Burguet identifies optimal rules for a procurer when he incorporates the possibility that a supplier can bribe the inspector to misrepresent quality.

Bribery is a tricky thing

While the concept of corruption seems easy to define, modeling it in an economic context so as to find remedies is much more difficult. Burguet considers a basic set up with a corruptible inspector to whom the procurer (the principal, as he is generally referred to in this type of problems) has delegated the responsibility of monitoring the contracted quality of his supplier’s product. The procurer has an interest in designing a contracting system that would prevent the corruption of his inspector by the contractor (with a bribe), so that quality is indeed as contracted.

The more general case of a corruptible agent as an intermediary between the procurer and the supplier in a procurement auction is difficult to assess. This is because the agent’s ability to manipulate depends on the very rules he has to bend: for the procurer the problem is not well defined from the outset since he has to understand how the agent can manipulate these rules in all possible designs. Burguet thus looks at the more specific instance of the agent as an inspector in charge of reporting delivered quality, and investigates optimal contracts under the shadow of bribery.

When bribes are fixed

Burguet first analyzes the simple case when the inspector is willing to take a fixed bribe to certify whatever quality the supplier claims upon delivery. The supplier may be of one of many possible types, differing in terms of how costly it is for him to deliver high quality goods. The procurer does not know the type of his supplier, only this distribution of types. This is the traditional “adverse selection” problem encountered by procurers.

Bribery complicates this problem. Burguet shows that it curtails the level and range of qualities that the procurer will be able to obtain from the supplier. This will eliminate corruption at a (quality) cost that the procurer is willing to pay. The procurer gives up attempting to obtain quality from low efficiency suppliers. But more surprisingly, Burguet also finds that even for high efficiency types of supplier the procurer will have to lower the quality he expects. Indeed, a contract is, in the end, a schedule of prices paid for quality. Higher prices need to be offered for a higher quality good expected, implicitly from a higher efficiency supplier. But the higher this quality and price, the stronger the incentive a low efficiency supplier has to bribe the inspector so as to claim that he is delivering such high quality. So overall a fixed bribe will end up reducing the quality the procurer can demand from both the most efficient and the least efficient suppliers.

Burguet also studies an alternative case, where the supplier only learns the amount of the bribe he will have to pay the inspector after contracting with the procurer. Totally preventing bribery is too expensive under these conditions. No matter how efficient the supplier is, he will prefer to bribe if the bribe needed happens to be sufficiently small. The procurer will have to live with bribery in such event, but will optimally reduce its occurrence by reducing the quality expected from all types of supplier.

What about when the bribe depends on the amount of manipulation?

Finally, Burguet looks at the case of a variable bribe that the contractor would need to pay the inspector. The variability appears simply because the size of the inspector’s manipulation will determine his required bribe to certify the supplier’s product. The results depend on the shape of the bribe function – whether it is concave or convex. The shape may be better understood as a consequence of general honesty of individuals in a society: concave here would indicate that what is expensive is to induce the inspector into an illegal activity like taking bribes, but increasing degrees of manipulation then come at relatively lower additional costs. Meanwhile convexity of the bribe indicates that petty corruption is in some ways accepted but increasing the amount of manipulation is more expensive because it somehow may cross the line of credibility.

When the shape of the bribe as a function of manipulation is sufficiently concave, Burguet finds that the procurer will impose quality floors for low efficiency types and ceilings for the high types. Within this range bribes will not be paid. So, again, quality is distorted downwards. This result is a generalization of the fixed and known bribe case, which is in fact the extreme result of this bribe-manipulation scenario. However, when the bribe function is convex the procurer will find it too expensive to eliminate bribes altogether, and will have to accept some level of manipulation and bribes. In this instance, which is a generalization of the alternative fixed bribe case discussed above, the procurer will have to accept lower quality from every type of supplier to reduce the amount of manipulation – but as before even within this range of qualities bribes will still result with some probability. Burguet then shows how to implement these procurement rules for both these types of bribery-manipulation scenarios as menus of contracts.

Expanding the research

Burguet’s research can be expanded since only a specific instance is considered. Burguet highlights that while only one contractor is considered and that they undertake the procurer’s project with certainty, introducing both competition for the project and the possibility of not contracting would not alter the results. However the pressing issue is how introducing some bargaining power in the hands of the supplier vis-a-vis the supplier may affect the results in this model. Future research should introduce bargaining models in combination with the mechanism design problem to enrich our understanding of these results.