Page 115 - 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

∞

∑ [ ((1 + ) ‾) − ( ‾)] ≈ ,
0
=0

leading to the linear approximation ≈ . Simulate impulse responses under
(1− ) ‾ −1

alternative ( , ) and map into .

Appendix C — Compact extensions and implementation guidance
C.1 Endogenous bank risk-taking

Introduce bank choice over loan risk with expected default rising in loan-to-capital

ratio. Loan supply gains a risk-taking term:

= ( + ) − ( − ‾ ) + ⋅ , (C1)

where captures endogenous risk-taking; > 0 parametrizes sensitivity.

C.2 Heterogeneous agents
Two household types ∈ { , } with type-specific convenience parameters lead to:

− = ( − ) + . (C2)

2

1

Aggregate substitution depends on population weights and heterogeneity of .
1
C.3 Cross-border SDC use and coordination
If SDC has cross-border usability parameter ∈ [0,1], UIP premium in the main

text becomes a function of foreign demand for the SDC and capital-flow induced
exchange-rate pressures. Coordination is required if is large.
C.4 Operational and institutional constraints
Central-bank balance-sheet constraint (flow form):
= − − ℎ , (C3)

and recycling capacity may be constrained by fiscal/backstop limits.

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