Page 103 - 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

In the reduced-form arithmetic used in Section 5 the instantaneous effect of a deposit
reallocation on loans is

= (1 − ) , (8)

so that with baseline = 0.80 and = 0.60 a 10% deposit reallocation into SDC
reduces loans by 0.8 × (1 − 0.6) × 0.10 = 3.2%.

Operational remarks and robustness
The above modeling choices are intentionally modular: tiering, cross-border

parameter psi, recycling γ, and define the policy space. The intuition and

comparative statics map directly to empirical policy levers central banks are
considering in practice (see e.g. BIS and central-bank working papers).

External sector
Small open economy: uncovered interest parity (UIP) with risk premium:

∗
1 + = (1 + ) ( +1 ) + , (9)

∗
where is world interest rate, is nominal exchange rate, and is a country-

specific premium that depends on capital flows and SDC attractiveness (since SDC
can be used cross-border if not geographically restricted).
EQUILIBRIUM AND STEADY STATE CHARACTERIZATION

Define competitive equilibrium given policy paths { , , } as

allocations and prices solving households’, banks’, firms’ problems and market
clearing.

Money substitution and deposit demand
Linearizing the liquidity demand equations gives:

− = + ( − ) + , (10)

2
1

where and are log SDC and deposit holdings, and collects convenience and

structural shocks; > 0 implies higher SDC remuneration increases SDC holdings.
1
This relation is central: it captures substitution that triggers bank funding adjustments.

Bank loan supply response
Log-linearizing bank first order conditions and balance sheet constraints yields:
= ( + ) − ( − ), (11)

where is log loans, reflects sensitivity to lending rate and credit risk; importantly,

103