Central Bank Digital Currency, Tax Evasion, and Monetary Policy With Heterogeneous Agents

We investigate the effects of central bank digital currency (CBDC) issuance in an economy where individuals can evade taxes by using cash. Our tractable model features agent heterogeneity with unobservable idiosyncratic shocks and voluntary exchange, where CBDC and cash compete as payment methods. CBDC's transparency enables governments to collect a labor tax that proves non‐distortionary in our quasi‐linear environment. Agents with higher marginal utility voluntarily pay fixed fees to access interest‐bearing CBDC when their debt constraints bind, thereby enabling the implementation of optimal policy with strictly positive inflation and nominal interest rates. We demonstrate how CBDC enables redistribution between agent types that is not possible in cash‐only economies. We conjecture that an optimal CBDC policy involves higher nominal interest rates and lower inflation compared to cash regimes. By reducing tax evasion incentives, the introduction of CBDC can increase both output and aggregate welfare.