CBDC, cash, and financial intermediary in HANK

The introduction of interest-bearing Central Bank Digital Currency (CBDC) presents central banks with an additional instrument for implementing monetary policy. This article develops a Heterogeneous Agents New Keynesian model, incorporating financial frictions, to investigate the transmission mechanism and wealth distribution effects of digital currency interest rate from two distinct perspectives: (i) the interaction between the central bank and financial intermediaries and (ii) the substitution dynamics between cash and digital currency. By comparing models that include and exclude financial intermediaries, our research uncovers that in a society where CBDC is fully implemented, the reverse actions of financial intermediaries can hinder the efficacy of the central bank’s monetary policy and result in elevated costs associated with policy formulation. Additionally, the leverage effect of financial intermediaries exacerbates wealth inequality and contributes to the expansion of investment, thereby promoting an increase in economic output. Comparing societies where CBDC entirely replaces cash with those where CBDC coexists alongside cash, this paper demonstrates that the presence of cash mitigates significant economic fluctuations triggered by CBDC, while the complete elimination of cash amplifies wealth inequality. Consequently, it is crucial for the central bank to account for the behavior of financial intermediaries when adjusting digital currency interest rate and explore the development of an appropriate interest rate mechanism tailored to digital currency. Simultaneously, maintaining cash circulation for a specific period can act as an economic stabilizer.