Truth-telling and the Role of Limited Liability in Costly State Verification Loan Contracts

Recent literature has considered the form of loan contract between two or more risk neutral parties where the revelation principle is inappropriate due to the lack of commitment to an auditing policy by the lender. The privately informed debtor has a stochastic return; once he knows the state realisation, auditing and cheating are determined as Nash equilibria. The literature assumes that this leads to randomised cheating and auditing. In this paper we verify that the contract may involve this randomisation; but that it may also involve truthtelling with random auditing and one or more investors in line with Persons (1996); or a single state independent repayment with no auditing. We define conditions on the state observation cost and the distribution of returns which determine which of these three forms of contract is optimal. We find that under unlimited liability when the loan size is fixed the two investor truthtelling contract dominates all the other forms; and that this is also true when the loan size is optimally chosen. On the other hand under limited liability if the cost of observation is large relative to the lowest state revenue, the random auditing contract or a constrained two investor truthtelling contract may be optimal. The limited liability condition in the constrained truthtelling contracts forces the level of finance to be higher than under unlimited liability.