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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

Steady-state mapping.
For intuition and quick arithmetic checks we use the reduced-form mapping from
deposit reallocation into loans:

= (1 − ) . (13)

Interpretation: when a fraction of deposits Δd moves from banks into SDC, only the
non-recycled share (1−γ) reduces bank funding; θ maps funding to loans. Use this
relation to sanity-check solver output.

Illustrative numeric example used in the text: for a 10% reallocation away from
deposits (Δd = −0.10), θ = 0.80 and γ = 0.60 imply
= 0.80 × (1 − 0.60) × (−0.10) = −0.032, i.e., loans fall ≈ 3.2%. (14)

Robustness sweep
Keep the same = −0.10 and = 0.80 while varying γ. Results reported in the
paper use the following compact sweep and the accompanying figure:

γ = 0.00 → Δℓ ≈ −8.0% (15)
γ = 0.20 → Δℓ ≈ −6.4% (16)
γ = 0.60 → Δℓ ≈ −3.2% (baseline) (17)
γ = 0.80 → Δℓ ≈ −1.6% (18)

Note: alternative experiments in the appendix vary θ ∈ {0.6, 0.7} and ∈ {3, 10}.

Figure 1: Loan change (%) for a 10% deposit reallocation vs. recycling share γ (baseline θ
= 0.80).
Source: Compiled by the authors

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