Page 101 - Azerbaijan State University of Economics

Nazim Hajiyev, Daniyar Aliyev: A DSGE Framework For Sovereign Digital Currency
Adoption in Small Open Economies: Macro-Financial Channels, Bank Intermediation, and
Policy Trade-Offs

Banks face balance sheet constraint:

= ( + ), (4)

where are other funding sources (e.g., wholesale). The parameter θ captures

maturity transformation capacities; lower θ limits lending per unit of deposits.

Banks also face regulatory capital constraint; they choose taking into account

expected loan returns and default risk.

Firms and Prices
A continuum of monopolistically competitive firms produces differentiated goods.
Prices are set under Calvo stickiness: each firm can reoptimize with probability 1 −
, which yields the standard New-Keynesian Phillips curve after aggregation. The

goods market clears

= + + + ; (5)

Investment and capital accumulation follow standard laws of motion. These
assumptions supply the Phillips-curve and output-gap ingredients used in Section 4
(equations (A14)–(A15) in the appendix).

SDC design, monetary policy and central-bank balance sheet
This subsection consolidates the SDC design choices and the monetary-policy /
central-bank balance-sheet representation used in the model and in the numerical
exercises. We state these design choices explicitly so the reader can reproduce the
comparative statics and numerical experiments.

SDC design choices (model implementation)
In the baseline model the sovereign digital currency (SDC) is implemented as a retail,
account-based central-bank liability with the following properties (these design

choices are directly mapped to policy levers in the numerical experiments):

1. Nature and claims: SDC is a nominal, account-based liability of the central bank,
held by households and redeemable at par. It is modeled as a convenience-bearing
outside asset that imperfectly substitutes for bank deposits.

2. Remuneration: The central bank can set a nominal remuneration rate on SDC

holdings. The baseline calibration uses = 1% with experiments varying .
Remuneration is an explicit policy instrument in welfare experiments.

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