The Loan Contract with Costly State Verification and Subjective Beliefs

We generalize the characterization of the loan contract due to Gale and Hellwig (1985) to the case of risk aversion of the borrower and diverse subjective beliefs about the outcome of the investment. We continue to assume costly state verification (Townsend, 1979) i.e. that the lender must incur costs in order to observe the outcome of the project. Contract terms now reflect returns on capital as well as risk sharing and trade on the differences in probabilities. Because there are no financial markets where agents could purchase insurance for state contingencies, private contracting replaces markets for contingent claims. This also means that verification states are not necessarily interpreted as "default" states. We characterize the optimal contract showing that (i) the contractual payoff in verification states varies by states in accord with risk aversion and probability belief of the two parties, and (ii) the verification region may consist of several intervals. We provide conditions and examples to show that when the borrower is more optimistic than the bank, there may be fewer verification regions.