Optimal Income Taxation and Hidden Borrowing and Lending: The First-Order Approach in Two Periods

We provide sufficient conditions for the validity of the first-order approach for two period dynamic moral hazard problems, where the agent can save and borrow secretly. We show that in addition to the concavity requirements for the standard moral hazard problem, non-increasing absolute risk aversion (NIARA) utility functions and Frisch elasticity of leisure less than one imply that the agent's problem is jointly concave in effort and asset decisions when facing the optimal contract. We also characterize the optimal contract in detail. One of the key observations is that the possibility of hidden asset accumulation makes the supporting tax-transfer system more regressive (or the optimal compensation scheme more convex) under a general class of preferences (HARA).