Banking with Inside Money: An Efficiency Analysis

This paper demonstrates that the canonical efficiency result of Diamond and Dybvig (1983) — that banks using maturity transformation can decentralize the first-best risk-sharing allocation — breaks down when banking is conducted with inside money rather than real contracts. The paper constructs a minimal modification of the Diamond-Dybvig (DD) model in which output requires combining labor (supplied by workers) and technology (owned by entrepreneurs), so that bank deposits arise as inside money created ex nihilo when loans are extended, and shows three results: (1) non-contingent nominal demand deposits cannot reproduce the first-best allocation, because the constraint that nominal deposits earn the same real return as the productive technology prevents banks from providing state-contingent real payoffs; (2) state-contingent deposit rate contracts, which are proposed as an efficiency fix in the DD tradition, also fail to reach the first best — Proposition 2 establishes that contingent deposit rates produce a consumption allocation inconsistent with efficiency (specifically, aggregate consumption at each date cannot satisfy the efficiency ratio required by equation 8), and the allocation under contingent contracts is no better in welfare terms than the non-contingent baseline; (3) allowing entrepreneurs to liquidate loans before maturity (Proposition 3) likewise leaves the equilibrium inefficient, because competition equalizes deposit and lending rates in a way that prevents supply of goods from matching the efficient schedule across periods. The paper then characterizes when central bank intervention can improve welfare and shows that outside money is not demanded in the baseline economy, limiting the central bank’s leverage, and that the lender-of-last-resort function can prevent bank runs even when efficiency is unachievable.

David Rivero | Macro Paper Warehouse

Banking with Inside Money: An Efficiency Analysis