## Annex 2: Sensitivity Analysis ## Source details **Canonical URL:** [Annex 2: Sensitivity Analysis](https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026129-source-pdf.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2026/english/wpiea2026129-source-pdf.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2026/english/wpiea2026129-source-pdf.pdf.json) --- ### Background and context - Timeline and market context: - June 2019: Facebook released a white paper proposing Libra. - August 7, 2023: PayPal launched PYUSD (USD-denominated stablecoin issued by a licensed financial institution in collaboration with a public blockchain platform (Paxos)). - USDT (Tether) identified as the pioneering USD stablecoin and is now the largest stablecoin globally. - Variety of digital money forms: CBDCs, tokenized deposits, private/platform stablecoins, crypto assets (Bitcoin, Ethereum). - Stablecoin taxonomy and collateral structures: - Fiat-backed, crypto-backed, commodity-backed, and algorithmic stablecoins. - Stablecoins designed to be backed/pegged to assets and aim for stability. ### Literature and empirical perspectives (enumerated findings) - Stablecoins aim to maintain a stable value relative to a reference asset (Eichengreen, 2019). - Scaling and peg maintenance challenges, especially during financial stress (bank-run analogies). - Catalini and Massari (2021): lower volatility, faster transactions, lower costs, greater accessibility versus traditional crypto assets. - Lyons and Viswanath-Natraj (2020): USDT can stabilize Bitcoin prices. - Historical governance challenges: maintaining trust, managing reserves, monetary governance (Frost et al., 2020). - Uhlig (2022): theory and quantification for algorithmic stablecoin collapse (Terra’s UST). - Ma et al. (2025): Tether limits redemption to a concentrated group (around six agents per month), centralization introduces run risk. - Gross and Senner (2026): systemically large fiat-backed stablecoins can amplify financial stress via redemption-driven fire sales; capital and liquidity buffers are most effective mitigants; redemption gates and shorter asset duration provide additional mitigation. - Iyer (2022): transmission from crypto asset markets (Bitcoin and USDT) to traditional equity markets is strengthening. - Calls for global coordination in crypto regulation (IMF, FSB, SSBs referenced). ### Macroeconomic and monetary policy implications (enumerated findings) - IMF (Finance and Development magazine, 2025): demand for U.S. Treasuries could increase due to rising dollar-backed stablecoins; risks to banking sectors and fiscal accounts noted. - Private stablecoins challenge fiat currency and central bank autonomy, especially in countries with monetary instability or high inflation. - Benigno et al. (2022): “Crypto-Enforced Monetary Policy Synchronization (CEMPS)” — a global cryptocurrency tightens constraints on monetary policy autonomy. - Rivalry between private stablecoins and CBDCs (Choi and Kim, 2024); CBDCs affect banking structure (Chiu et al., 2023). - Azzimonti and Quadrini (2025): dollar-backed stablecoins may increase demand for U.S. Treasuries, potentially lowering U.S. interest rates and raising U.S. foreign borrowing in the long run. - Reuter (2025), Cardozo et al. (2024): cross-border movement estimation and channel reviews. ### Model innovation and scope - First comprehensive DSGE model of fiat-backed stablecoins integrating a micro-founded monetary search framework into a New Keynesian DSGE with sticky prices. - Three distinguishing attributes modeled: - Pseudonymity: public blockchain pseudonymous wallet addresses. - Digitization: lower issuance and transaction costs relative to fiat money. - Fiat-backing: pegged to fiat currency with possibility of de-pegging subject to a penalty. - Model builds on Aruoba and Schorfheide (2011) and Lagos and Wright (2005). - Closed-economy focus; international stablecoin flows and non-fiat collateral types are discussed conceptually but not modeled in depth. ### Calibration and key parameter values (exact figures preserved) - Stablecoin penetration benchmark: χt MS t / YN = 0.18 (benchmark predicted GDP share in next 10-15 years). - Discount factor β = 0.99 (one model period = one quarter) to match nominal annual interest rate 4%. - CRRA coefficient γ = 1; scale factor B = 2.28; preference parameter κ = 0.0001. - Disutility parameter A = 71.249 to match h/Y = 0.03. - Stablecoin transaction cost parameter ψ = 0.32. - Backing ratio target ν = 1 (regulation); scale parameter φ = 1 to match steady state GDP share of stablecoins. - Share of buyer/seller in VE σ = 0.2 (implies about 40% household participation in stablecoin transactions). - Buyers’ bargaining power θ = 0.95. - Production parameters: α = 0.33; δ = 0.014; κi = 4; ε = 8; ζ = 0.83; ι = 0.72. - Policy parameters: φπ = 1.5; φy = 0.125; ρr = 0.61; fiscal parameter g = 1.22 to match G/Y = 0.21. - Shock persistence: ρg = 0.840; ρz^s = 0.970; ρz^P = 0.830. - Shock standard deviations: σr = 0.360; σg = 1.010; σz^s = 1.800; σz^P = 1.040. ### Quantitative findings — impulse responses and variance decomposition - Responses to a positive one-standard-deviation productivity (TFP) shock: - RE and overall GDP increase; consumption and investment rise; inflation declines; demand for both stablecoins and fiat money rises. - Productivity increase reduces stablecoin transaction cost, causing an initial fall then subsequent rise in stablecoin price. - Responses to a one-standard-deviation monetary policy shock (unexpected policy rate increase): - Nominal interest rates rise sharply; investment and real GDP decline; consumption falls; inflation declines; stablecoin price and real balances decline. - Responses to a one-standard-deviation fiscal policy shock (increase in government spending): - GDP rises; private investment and consumption partially displaced; inflation declines; holdings of both stablecoins and fiat money decline. - Responses to a one-standard-deviation stablecoin preference shock: - Agents shift real fiat money balances toward stablecoins; stablecoin price rises; RE consumption and investment decline; VE expansion offsets RE contraction, total output increases. - Variance decomposition (shares in percent; model with VE = 18% of GDP): - Total Y (Y total): ε_z 28.69; ε_r 18.55; ε_g 51.52; ε_z^s 1.24. - Y (RE): ε_z 27.14; ε_r 15.92; ε_g 56.78; ε_z^s 0.15. - Consumption: ε_z 32.76; ε_r 34.32; ε_g 32.24; ε_z^s 0.68. - Investment: ε_z 50.78; ε_r 10.67; ε_g 37.49; ε_z^s 1.06. - Capital: ε_z 51.44; ε_r 6.73; ε_g 38.52; ε_z^s 3.31. - Inflation: ε_z 92.53; ε_r 5.00; ε_g 0.54; ε_z^s 1.93. - m_S balance: ε_z 9.14; ε_r 14.81; ε_g 5.99; ε_z^s 70.06. - m_F balance: ε_z 27.37; ε_r 29.15; ε_g 41.93; ε_z^s 1.54. - m_S price: ε_z 0.47; ε_r 5.72; ε_g 0.16; ε_z^s 93.65. - Interpretation of variance decomposition: - Fiscal shock is largest contributor to real output and consumption volatilities. - TFP shock primarily drives investment, capital, and explains about 93% of inflation volatility. - Monetary shock significant for consumption volatility. - Stablecoin preference shock dominates variance in stablecoin balances and stablecoin price. ### Stablecoins, macro stability, and prudential regulation — σ experiments (exact values) - Varying σ (share of consumers using stablecoins in VE) with all four shocks active; benchmark σ = 0.2; alternatives σ = 0.1, 0.3, 0.4. Selected standard deviations from Table 3: - Y (total): σ = 0.1 → 1.7553; σ = 0.2 → 1.7614; σ = 0.3 → 1.7727; σ = 0.4 → 1.7910. - Y (RE): σ = 0.1 → 1.7405; σ = 0.2 → 1.7664; σ = 0.3 → 1.7956; σ = 0.4 → 1.8284. - Consumption: σ = 0.1 → 1.1917; σ = 0.2 → 1.2003; σ = 0.3 → 1.2122; σ = 0.4 → 1.2276. - Investment: σ = 0.1 → 2.9866; σ = 0.2 → 3.0161; σ = 0.3 → 3.0578; σ = 0.4 → 3.1116. - m_S balance: σ = 0.1 → 4.9521; σ = 0.2 → 4.2813; σ = 0.3 → 4.0397; σ = 0.4 → 3.8894. - m_S price: σ = 0.1 → 4.0028; σ = 0.2 → 3.7217; σ = 0.3 → 3.6732; σ = 0.4 → 3.6536. - Findings: - Increasing σ raises volatility of macro variables (Y, Y_RE, consumption, investment, capital, inflation) while reducing volatility of stablecoin balances and stablecoin price. - Example magnitude: moving σ from 0.2 to 0.4 raises aggregate real output standard deviation from 1.7614 to 1.7910 (an increase of 1.7 percent as reported). - Real interest rate effects (Table 4): - Fiat real interest rate standard deviation: σ = 0.1 → 0.4634; σ = 0.2 → 0.4651; σ = 0.3 → 0.4677; σ = 0.4 → 0.4711. - Stablecoin interest rate standard deviation: σ = 0.1 → 4.2981; σ = 0.2 → 2.1542; σ = 0.3 → 1.4399; σ = 0.4 → 1.0829. - Mechanism: - r^VE_t (implicit real net interest rate of stablecoins) is inversely related to σ; larger σ reduces variance of r^VE_t and thus reduces volatility of stablecoin balances and prices. - However, increasing σ undermines monetary policy traction because stablecoins operate outside the Taylor-rule framework, increasing R_t/π_{t+1} volatility and propagating instability to the real economy. ### Prudential regulation experiments — backing ratio ν (exact values) - Vary ν with all four shocks active; ν alternatives: 0.8, 1, 1.2. Selected standard deviations from Table 5: - Y (total): ν = 0.8 → 1.7843; ν = 1 → 1.7614; ν = 1.2 → 1.7431. - Y (RE): ν = 0.8 → 1.7874; ν = 1 → 1.7664; ν = 1.2 → 1.7469. - m_S balance: ν = 0.8 → 4.8234; ν = 1 → 4.2813; ν = 1.2 → 3.4549. - m_S price: ν = 0.8 → 3.0921; ν = 1 → 3.7217; ν = 1.2 → 4.7814. - Findings and policy implications: - Increasing ν from 1 to 1.2 reduces standard deviations of most macro variables (aggregate real output falls from 1.7614 to 1.7431). - ν functions as a stabilizer: higher ν can offset macro instability induced by larger σ. - Prudential regulation targeting backing ratio ν can restore monetary anchoring and reduce likelihood of runs and macro instability. - Analogous to liquidity requirements in fiat systems (e.g., liquidity coverage ratio). ### Sensitivity analysis across adoption scenarios (exact scenarios and select quantitative results) - Adoption scenarios for χt MS t / YN: - Benchmark: 0.18. - Aggressive: 0.30. - Status quo: 0.02. - Robust qualitative results across scenarios: - Increasing σ amplifies macroeconomic volatility for non-monetary variables and fiat money balances, while dampening volatility of stablecoin balances and prices. - Higher ν mitigates excess fluctuations; magnitudes larger when χt MS t / YN is larger. - Notable quantitative illustration: - Under aggressive adoption (χM S/YN = 0.30), increasing σ from 0.2 to 0.4 raises volatility of total real output by 5.9 percent (reported in text). - Selected excerpts for aggressive adoption (χM S/YN = 0.30, Table 6): - Y (total): σ = 0.1 → 1.7810; σ = 0.2 → 1.8016; σ = 0.3 → 1.8412; σ = 0.4 → 1.9073. - m_S price: σ = 0.1 → 4.0556; σ = 0.2 → 3.7597; σ = 0.3 → 3.7056; σ = 0.4 → 3.6848. - Status quo scenario (χM S/YN = 0.02) findings: - Effects of higher σ on non-monetary macro variables are negligible at current penetration. - Selected excerpts (Table 8): σ = 0.02 → Y (total) 1.7243; σ = 0.2 → 1.7256; σ = 0.4 → 1.7260. - Stablecoin balance volatility can be very high at low penetration (e.g., mS balance 10.5336 when σ = 0.02), but overall macro effects remain small. ### Robustness to alternative bargaining solutions - Alternative bargaining: Kalai solution (equation (13)) tested. - Robustness results: - Qualitative patterns persist under Kalai: increases in σ raise volatility in macro variables (except stablecoin balances and prices). - Magnitudes generally larger under Kalai versus Nash bargaining, implying bargaining solution choice can amplify macroeconomic implications. - Selected Kalai excerpts (Table 10): - Y (total): σ = 0.1 → 1.7422; σ = 0.2 → 1.7680; σ = 0.3 → 1.7970; σ = 0.4 → 1.8296. - m_S price: σ = 0.1 → 3.8132; σ = 0.2 → 3.7476; σ = 0.3 → 3.7317; σ = 0.4 → 3.7186. ### Policy conclusions and recommendations (concise) - Stablecoin adoption can amplify macroeconomic volatility when adoption reaches macro-critical scale (higher χ and higher σ). - Prudential regulation targeting backing ratio ν is an effective stabilizer: - Raising ν (stricter backing requirements analogous to liquidity requirements) reduces volatility of real output, investment, and inflation in calibrated experiments. - Regulators can use ν to restore monetary anchoring and reduce run risk. - At current penetration (χt MS t / YN = 0.02), macro impacts are limited; prudential regulation has smaller stabilizing benefits and in some cases may increase volatility of specific stablecoin variables. - Monetary policy effectiveness can be weakened by stablecoins under money search frictions; central banks face reduced traction when stablecoin usage rises outside policy frameworks. - Recommendation: subject stablecoins to regulatory oversight with prudential tools (backing ratio, capital and liquidity buffers, redemption gates, shorter asset duration) to mitigate destabilizing effects and support monetary stability. *Source: Annex 2: Sensitivity Analysis — wpiea2026129-source-pdf (Working Paper No. WP/2026/129).* ### 1. Introduction ........................................................................................................ ### wpiea2026129-source-pdf - 1. Introduction ........................................................................................................ ### Table of contents — major sections and subsections - 1. Introduction ............................................................................................................................................ 3 - 2. Model ...................................................................................................................................................... 6 - 2.1 Households ......................................................................................................................................................... 7 - 2.2 Firms ................................................................................................................................................... 14 - 3. Model parameterization and calibration .............................................................................................. 17 - 3.1 Parameter parameterization ............................................................................................................... 17 - 3.2 Calibration ........................................................................................................................................... 18 - 3.3 Solution method ................................................................................................................................. 19 - 4. Dynamic Analysis .................................................................................................................................. 19 - 4.1 Impulse responses of various shocks .................................................................................................. 19 - 4.2 Stablecoins, macro stability, and prudential regulation ..................................................................... 24 - 4.3 Sensitivity Analysis .............................................................................................................................. 26 - 5. Conclusions ........................................................................................................................................... 28 - References ................................................................................................................................................ 28 - Annex 1: General Equilibrium Conditions ................................................................................................. 31 *Source: https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026129-source-pdf.pdf* ### Annex 2: Sensitivity Analysis .......................................................................................... ### Annex 2: Sensitivity Analysis ### Introduction and background - In the digital era, the global financial landscape and the nature of money have rapidly evolved. - June 2019: Facebook released a white paper proposing a simple and borderless stablecoin named Libra. - August 7, 2023: PayPal launched a native stablecoin, PYUSD — the first time a USD-denominated stablecoin was issued by a licensed financial institution in collaboration with a public blockchain platform (Paxos). - USDT (Tether) is identified as the pioneering USD stablecoin and is now the largest stablecoin globally. - Various digital forms of money have emerged, including CBDCs, tokenized deposits, private/platform stablecoins, and crypto assets (for example, Bitcoin and Ethereum). - Stablecoins are distinguished by being designed to be backed/pegged to assets and aim for stability; underlying collateral structures include fiat-backed, crypto-backed, commodity-backed, and algorithmic. ### Key perspectives from literature (enumerated findings) - Stablecoins aim to maintain a stable value relative to a reference asset (Eichengreen, 2019). - Stablecoins may face challenges scaling and maintaining pegs, especially during financial stress (bank-run analogies). - Catalini and Massari (2021): stablecoins can offer lower volatility, faster transactions, lower costs, and greater accessibility versus traditional crypto assets. - Lyons and Viswanath-Natraj (2020): USDT can stabilize Bitcoin prices; theoretical and empirical investigations exist. - Historical precedents (Frost et al., 2020) show longstanding governance challenges: maintaining trust, managing reserves, and monetary governance. - Uhlig (2022): provides theory and quantification for algorithmic stablecoin collapse (Terra’s UST). - Ma et al. (2025): Tether limits redemption to a concentrated group of agents (around six agents per month) — centralization of arbitrage and backing by imperfectly liquid USD assets introduce run risk. - Gross and Senner (2026): systemically large fiat-backed stablecoins can amplify financial stress via redemption-driven fire sales that spill over into sovereign bond markets; capital and liquidity buffers are most effective mitigants, with redemption gates and shorter asset duration providing additional mitigation. - Iyer (2022): transmission from crypto asset markets (particularly Bitcoin and USDT) to traditional equity markets is strengthening; spillovers to financial markets are rising. - Calls for global coordination in crypto regulation to mitigate systemic risks (IMF, FSB, SSBs referenced). ### Macroeconomic and monetary policy implications - IMF (Finance and Development magazine, 2025): demand for U.S. Treasuries could increase due to rising dollar-backed stablecoins; potential risks to banking sectors and fiscal accounts noted. - Private stablecoins vs. fiat currency: currency competition can exert pressure on central banks, particularly in countries with monetary instability or high inflation. - Benigno et al. (2022): “Crypto-Enforced Monetary Policy Synchronization (CEMPS)” — presence of a global cryptocurrency tightens constraints on monetary policy autonomy; classic Impossible Trinity becomes less reconcilable in a two-country economy with a global cryptocurrency. - Rivalry between privately issued stablecoins and CBDCs (Choi and Kim, 2024); CBDCs also present competitive and structural effects on banking (Chiu et al., 2023). - Cross-border movement and international implications: Reuter (2025) offers methodology to estimate geographic distribution of international stablecoin flows; Cardozo et al. (2024) review channels; Azzimonti and Quadrini (2025) model reserve demand effect where dollar-backed stablecoins may increase demand for U.S. Treasuries, potentially lowering U.S. interest rates and raising U.S. foreign borrowing in the long run. ### Policy and regulatory developments - 2019: G20 countries agreed no stablecoin should proceed until associated risks/challenges are adequately addressed. - International institutions (IMF, FSB, SSBs) have issued comprehensive recommendations and standards guided by “same activity, same risk, same regulation.” - GENIUS Act (Guiding and Establishing National Innovation for U.S. Stablecoins) signed into law in July 2025 — first major federal U.S. framework for stablecoins; USDT and USDC represent around 90% of the stablecoin market capitalization. - Hong Kong’s Stablecoins Ordinance enacted on August 1, 2025 — fiat-referenced stablecoin issuers required to obtain licenses from the HKMA. - Adrian et al. (2025): stablecoins pegged to the USD represent 97% of total issuance worldwide. - These legislative developments are expected to encourage further stablecoin issuance in the long run. ### Risks and stabilization tools - Stablecoins expose financial systems to regulatory uncertainty, consumer protection issues, and financial instability. - Centralization of redemptions and backing by imperfectly liquid USD assets increase run risk and systemic spillovers. - Effective policy tools identified: - Capital and liquidity buffers (Gross and Senner, 2026). - Redemption gates and shorter asset duration as additional mitigants. - Prudential regulation of backing ratios between stablecoins and fiat assets as “stabilizers” to limit amplification of macroeconomic volatility. ### Model innovation and contributions of the paper - First comprehensive DSGE model of stablecoins focused on fiat-backed stablecoins, incorporating a micro-founded monetary search framework into a New Keynesian DSGE model. - Model features three distinguishing attributes of fiat-backed stablecoins: - Pseudonymity: transactions recorded on public blockchains using pseudonymous wallet addresses. - Digitization: lower issuance and transaction costs compared to fiat money. - Fiat-backing: pegged to fiat currency with possibility of de-pegging subject to a penalty. - Model builds on Aruoba and Schorfheide (2011) who integrated a monetary search model (Lagos and Wright, 2005) into NK-DSGE with sticky prices. - The model endogenously justifies demand for stablecoins via a monetary search framework and explicitly models coexistence and currency competition between fiat money and stablecoins. ### Calibration, quantitative findings, and policy implications - Model calibrated to represent the US economy with forward-looking dynamics; stablecoin-related parameters informed by data and projections from major U.S. fiat-backed stablecoins. - Key quantitative findings: - A higher stablecoin penetration rate amplifies volatilities of all major macroeconomic variables. - Stablecoins may not contribute to macroeconomic stability; they can increase business-cycle volatility as a by-product of their design. - Significant currency switching effect between fiat money and stablecoins indicates currency competition in the payment system. - Policy implications: - Results lend support to regulatory frameworks targeting stablecoins. - Well-designed prudential regulations—particularly those governing the backing ratio between stablecoins and fiat assets—can mitigate additional macroeconomic volatility associated with stablecoin adoption and act as effective stabilizers. - Monetary transmission can be weakened by stablecoins in environments with money search frictions, making monetary policy effectiveness contingent on payment frictions and monetary dominance rather than solely on expectations management. ### Model scope and limitations - Paper focuses on a closed-economy DSGE framework; the international dimension of stablecoin flows (item (4) in background) remains outside scope and would require an open-economy extension. - The analysis centers on fiat-backed stablecoins; other collateral types (crypto-backed, commodity-backed, algorithmic) are discussed conceptually but not modeled in depth here. _Annex 2: Sensitivity Analysis — source PDF content (excerpts)._ ### 2.1 Households ### 2.1 Households ### Model environment and timing - Continuum of infinitely lived households with unit measure; ex ante identical prior to transactions. - Two segmented markets: - Decentralized virtual economy (VE) — anonymous bilateral matching; only stablecoins (M_S_t) are usable. - Centralized real economy (RE) — standard NK DSGE; only fiat money (M_F_t) is usable. - Dual-currency structure: M_S_t used solely in VE; M_F_t used solely in RE. - Period timing: - At beginning of each period households carry M_S_t and M_F_t into period t and are hit by an exogenous idiosyncratic type shock dividing them into sellers, buyers, and non-participants with probabilities σ, σ, and 1−2σ respectively. - First sub-period: buyers and sellers transact in VE using stablecoins M_S_t to trade consumer goods q_t, generating utility u(q_t) − c(q_t,...). - Second sub-period: all households enter centralized RE carrying (M_S_t, M_F_t) and use fiat money for RE consumption c_t, labor supply h_t, and asset holding, with utility U(c_t) − A h_t. - Stablecoin nominal balance in VE is χ_t M_S_t; χ_t is the nominal price of stablecoins. ### Household behavior in RE - Value function in RE (backward induction): - V_RE_t(M_S_t, M_F_t, k_t, i_{t−1}, B_t, S_t) = max_{M_S_{t+1},M_F_{t+1},k_{t+1},i_t,B_{t+1}} { U(c_t) − A h_t + β E_t [ V_VE_{t+1}(...) ] } . (equation (1)) - State variables and parameters: - c_t: RE consumption; k_t: beginning-of-period real capital; i_{t−1}: previous period real capital investment; B_t: nominal government bonds; Π_t: profits; T_t: lump-sum tax/transfer; A > 0; 0 < β < 1. - RE constraints: - Budget: P_t c_t + P_t i_t + B_{t+1} + χ_t M_S_{t+1} + M_F_{t+1} = P_t W_t h_t + P_t R^k_t k_t + R_{t−1} B_t + χ_t M_S_t + M_F_t + Π_t − T_t. (equation (2)) - Capital law of motion: k_{t+1} = (1 − δ) k_t + [1 − Φ(i_t / i_{t−1})] i_t. (equation (3)) - Cash-in-advance (CIA) constraint: c_t + i_t = M_F_t / P_t. (equation (4)) - Lagrange multipliers: λ_t (constraint (2)), Ψ_t (constraint (3)), φ_t (constraint (4)); λ_t is marginal utility of income, φ_t is marginal utility of liquidity services from fiat money. ### Household behavior in VE - Ex ante VE value function (probability-weighted across types): - V_VE_t(...) = σ V_VE,seller_t(...) + σ V_VE,buyer_t(...) + (1 − 2σ) V_RE_t(...). (equation (5)) - Buyer and seller value functions: - V_VE,buyer_t(...) = z^S_t u(q^b_t) + V_RE_t(M_S_t − d^b_t, ...). (equation (6)) - V_VE,seller_t(...) = − c(q^s_t, k_t, z^P_t) + V_RE_t(M_S_t + d^s_t, ...). (equation (7)) - q^b_t, d^b_t (buyer consumption and stablecoin spending); q^s_t, d^s_t (seller production and stablecoin receipts). - z^S_t: buyer preference for stablecoins (demand shock for stablecoins). - Seller cost c(.) depends on q_t, capital k_t, and aggregate productivity z^P_t — IT capital and infrastructure reduce cost of stablecoin transactions. - Aggregated VE value function: - V_VE_t(...) = V_RE_t(...) + σ [ z^S_t u(q^b_t) − λ_t χ_t d^b_t ] + σ [ λ_t χ_t d^s_t − c(q^s_t, k_t, z^P_t) ]. (equation (8)) - In equilibrium (LW (2005) property inherited): d^b_t = d^s_t ≡ d_t = M_S_t. (equation (10)) ### Bilateral negotiation in VE - Bilateral constrained Nash bargaining problem (buyers’ surplus and sellers’ surplus; bargaining power θ for buyers): - max_{q_t, d^b_t, d^s_t} [ z^S_t u(q_t) − A χ_t d^b_t W_t / P_t ]^θ [ A χ_t d^s_t W_t / P_t − c(q_t, k_t, z^P_t) ]^{1−θ}. (equation (9)) - First-Order Condition (FOC), with q^s_t = q^b_t = q_t: - A W_t / P_t χ_t M_S_t = g(q_t, k_t, z^S_t, z^P_t). (equation (11)) - g(·) specification: - g(q_t,k_t,z^S_t,z^P_t) = [ θ z^S_t u′(q_t) c(q_t,k_t,z^P_t) + (1−θ) c_q(q_t,k_t,z^P_t) z^S_t u(q_t) ] / [ θ z^S_t u′(q_t) + (1−θ) c_q(q_t,k_t,z^P_t) ]. (equation (12)) - Special bargaining solutions: - Kalai solution reduces g(·) to a weighted mean: g(q^*_t) = θ c(q^*_t) + (1−θ) z^S_t u(q^*_t). (equation (13)) - Rubinstein (θ = 1) yields g(q_t) = c(q_t). ### Optimal conditions (first-order systems) - Define μ_t = Ψ_t U′(c_t) and π_{t+1} = P_{t+1}/P_t. - System of non-linear optimality conditions: - W_t = A u′(c_t) − φ_t. (equation (14)) - 1 = β E_t [ (u′(c_{t+1}) − φ_{t+1})/(u′(c_t) − φ_t) * R_t / π_{t+1} ]. (equation (15)) - 1 = μ_t [ 1 − Φ(i_t / i_{t−1}) + (i_t / i_{t−1}) Φ′(i_t / i_{t−1}) ] + β E_t [ μ_t (u′(c_{t+1})/u′(c_t)) (i_{t+1}/i_t)^2 Φ′(i_{t+1}/i_t) ]. (equation (16)) - μ_t = β E_t [ (u′(c_{t+1})/u′(c_t)) (R^k_{t+1} + (1−δ) μ_{t+1}) − φ_{t+1} R^k_{t+1}/u′(c_t) − σ Γ(q_t,k_t,z^S_t,z^P_t)/u′(c_t) ]. (equation (17)) - 1 = β E_t [ (u′(c_{t+1}) − φ_{t+1})/(u′(c_t) − φ_t) * 1/π_{t+1} * ( σ u′(q_{t+1}) z^S_{t+1} / g_q(q_{t+1},...) + 1 − σ ) ]. (equation (18)) - m^s_t ≡ M^s_t / P_{t−1} = g(q_t,k_t,z^S_t,z^P_t) π_t W_t / (A χ_t). (equation (19)) - λ_t − φ_t = β λ_{t+1} / π_{t+1}. (equation (20)) - Combining (18) and (19) yields stablecoin demand: - M^s_{t+1} = β E_t [ g(q_{t+1},k_{t+1},z^S_{t+1},z^P_{t+1}) / χ_{t+1} (u′(c_t) − φ_t) * ( σ z^S_{t+1} u′(q_{t+1}) / g_q(q_{t+1},...) + 1 − σ ) ]. (equation (21)) - Qualitative features of stablecoin demand (from equation (21)): 1. Demand decreases with their own price χ_{t+1}, ceteris paribus. 2. Demand increases with marginal benefit of holding stablecoins g(·). 3. Demand increases with the share of bilateral traders σ. 4. Demand increases with buyer preference z^S. ### Supply of stablecoins - Private issuers profit from spread (χ_t − R_t) and face a regulatory penalty to keep backing ratio M_S_t/(M_F_t + B_t) close to target peg ν. - Issuer maximization (tractable form): - max_{M_S_t} (χ_t − R_t) M^s_t − φ [ (M_S_t / (M_F_t + B_t) − ν)^2 ] (M_F_t + B_t)^2. (equation (22)) - First-order condition (supply rule): - χ_t − R_t = φ ( M_S_t / (M_F_t + B_t) − ν ). (equation (23)) - Economic intuition: - Positive (χ_t − R_t) incentivizes minting more stablecoins; negative spread incentivizes reducing supply. - Regulatory cost (quadratic penalty) denominated in fiat increases with deviation from ν. - Note: In the representative-agent equilibrium B_t = 0, so the model is isomorphic to stablecoins backed only by fiat currency M_F_t. ### Real interest rate of stablecoins and pricing - Euler equation for stablecoins (rearranged pricing equation): - β E_t [ λ_{t+1} / λ_t * ( (1 − σ) + σ z^S_{t+1} u′(q_{t+1}) / g_q(q_{t+1},...) ) ] = 1. (equation (25)) - Rearranged condition linking marginal utilities and returns: - z^S_t u′(q_t) / g_q_t = 1 + (R_t / π_{t+1} − 1) / σ. (equation (26)) - Define implicit real net interest rate of stablecoins r^VE_t: - r^VE_t ≡ R_t / π_{t+1} − 1 / σ. (equation (27)) - Key implications: - Maximum σ is 0.5 (since 1 − 2σ ≥ 0), implying implicit real interest rate on stablecoins r^VE_t is at least twice the real interest rate on fiat money. - r^VE_t is inversely related to σ: as σ decreases (stablecoin transactions more restricted), r^VE_t increases. - Volatility in σ (e.g., from riskier DeFi protocols) amplifies volatility in r^VE_t. - Special boundary case: if z^S_t u′(q_t) = g_q(q_t,k_t,z^P_t), then equality in (26) implies R_t / π_{t+1} = 1 and zero real interest rate on stablecoins. *Source: IMF working paper chapter 2.1 (Households) from the provided PDF content.* ### 2.2 Firms ### 2.2 Firms ### Final product producer - Final product aggregates intermediate inputs Yt according to equation (28): - Yt = [∫0 1 Yt(i)^(ε−1)/ε di]^(ε/(ε−1)). - ε > 1 is the elasticity of substitution among intermediate inputs. - The final good firm takes intermediate input prices Pt(i) as given and maximizes profits, leading to the standard demand for intermediate good i (demand FOC omitted in source for space). ### Intermediate input producers - Producers indexed by i operate in monopolistic competition and use constant returns to scale production (equation (29)): - Yt(i) = zPt kt(i)^α ht(i)^(1−α), - where zPt is total factor productivity (TFP). - Calvo (1983) price rigidity: - At any period t, probability of not resetting price = 1 − ζ; probability of resetting = ζ. - If reset, optimal price denoted P∗t(i). - Price update when not resetting uses AS (2011) adjustment factor (equation (30)): - πadjt+s|t = ∏s l=1 πι t+l−1 π1−ι ∗∗, with πadjt|t = 1. - ι is the weight on last period’s inflation; π∗∗ is the fixed inflation rate. - Profit maximization for a price-resetting firm (equation (31)): - maxP∗t(i) Σ∞ s=0 ζ^s β^s Ξt+s|t [P∗t+s|t πadjt+s|t − Pt+s MCt+s] Yt+s(i), - where the stochastic discount factor used by the price-reset firm is (equation (32)): - Ξt+s|t = u′(xt+s) / u′(xt) πt+s. - First-order conditions linking optimal reset price P∗t and marginal cost MCt (equations (33)-(35)): - X1,t = (P∗t / Pt)^−ε Yt Pt MCt / P∗t + ζβ(πι t π1−ι ∗∗)^−ε Et[(P∗t / P∗t+1)^−ε−1 Λt,t+1 X1,t+1]. - X2,t = (P∗t / Pt)^−ε Yt + ζβ(πι t π1−ι ∗∗)^(ε−1) Et[(P∗t / P∗t+1)^−ε Λt,t+1 X2,t+1]. - P∗t = ε/(ε−1) X1,t / X2,t. - Aggregate price dynamics (equation (36)) link inflation πt to reset prices and past inflation: - πt = [(1− ζ)(πt P∗t)^(1−ε) + ζ(πι t−1 π1−ι ∗∗)^(1−ε)]^(1/(1−ε)). - Equations (33)-(36) lead to the standard New Keynesian Phillips Curve (NKPC) (NKPC omitted in source for space). ### General equilibrium and aggregations - Consolidated government budget in RE (equation (37)): - Pt Gt + Rt−1 Bt + MFt = Tt + Bt+1 + MFt+1. - Combining government budget into household constraint yields (equation (38)): - Pt ct + Pt it + Pt Gt + χt MS t+1 = Pt Wt ht + Pt Rk t kt + χt MS t + Πt. - With stablecoins market clearing MS t+1 = MS t, simplify to (equation (39)): - Pt ct + Pt it + Pt Gt = Pt Wt ht + Pt Rk t kt + Πt. - Aggregate resource constraint (equation (40)), after substituting profits Πt: - ct + it + Gt = Yt. - Aggregated production (equation (41)): - ∫0 1 Yt(i) di = zPt ∫0 1 kt(i)^α ht(i)^(1−α) di = zPt kt^α ht^(1−α). - Price dispersion Dt for intermediate producers (equation (42)): - Dt = ∫0 1 (Pt(i)/Pt)^−ε di. - Price dispersion law of motion (equation (43)): - Dt = ζ [ (πt−1 / πt)^ι (π∗∗ / πt)^(1−ι) ]^−ε Dt−1 + (1− ζ)(P∗t)^−ε. - Relationship between final real output and aggregated factors (equation (44)): - Yt Dt = zPt kt^α ht^(1−α). - Valuation of output in VE and inclusion in aggregate: - Real output in VE = σ qt; nominal output in VE = σχt MS t (text). - Price level in VE (equation (45)): PVEt = χt MS t qt. - Nominal total output (equation (46)): YNt = Pt Yt + σχt MS t. - Real total output using RE final good as numeraire (equation (47)): - Yt = Yt + σ χt ms t / πt. ### Monetary and fiscal policies - Taylor rule for monetary policy (equation (48)): - Rt / R = [(Rt−1 / R)]^ρr [(πGDPt / π)]^φπ [(Yt / Y)]^φy ^(1−ρr) exp(σr εrt), - εrt is the (short-run) monetary policy shock; σr is its standard deviation; 0 < ρr < 1 is interest rate smoothing. - Policy parameters: φπ > 0, φy > 0. - Fiscal policy via government expenditure (equation (49)): - Gt = [1 − 1/gt] Yt, - gt measures gross growth rate of government spending share in GDP and is exogenous. ### Exogenous aggregate shocks - Four aggregate shocks: - TFP shock zP (affects both RE and VE). - Preference for stablecoins shock zS (digital money demand shock). - Monetary policy shock εrt (embedded in equation (48)). - Fiscal policy shock to gt (equation (49)). - AR(1) processes for shocks (equations (50)-(52)): - ln(zPt / zP) = ρzP ln(zPt−1 / zP) + σzP εzP t. - ln(zSt / zS) = ρzS ln(zSt−1 / zS) + σzS εzS t. - ln(gt / g) = ρg ln(gt−1 / g) + σg εg t. - Notation: - σX measures the standard deviation of shock X. - ρX denotes persistence of shock X. - εX is the innovation of shock X. - All shocks stacked into a vector follow a multivariate standard normal distribution. ### Model parameterization and calibration - Utility functions (equations (53)-(54)): - u(xt) = B x_t^(1−γ) / (1− γ). - u(qt) = ln(qt + κ) − ln κ. - Seller transaction cost (equation (55)): - c(qt, kt, zPt) = 1 / (zPt)^(1/(1−ψ)) qt^(1/(1−ψ)) kt^(−ψ/(1−ψ)). - Capital adjustment cost (equation (56)): - Φ(it / it−1) = κi / 2 (it / it−1 − 1)^2. - Calibration targets and parameter values: - Stablecoin penetration benchmark χt MS t / YN = 0.18 (benchmark predicted GDP share of stablecoin market cap in next 10-15 years). - Discount factor β = 0.99 (one model period = one quarter) to match nominal annual interest rate 4%. - CRRA coefficient γ = 1 (RE utility reduces to log). - Scale factor B = 2.28 to match steady state consumption-GDP ratio 0.64 (average 1972-2023, World Bank). - Preference parameter κ = 0.0001 (follows AS (2011)). - Disutility parameter A = 71.249 to match h/Y = 0.03 (AS (2011)). - Stablecoin parameters: - ψ = 0.32 for transaction cost function (equation (55)). - Backing ratio ν = 1 for regulation (equation (22) referenced). - Scale parameter φ = 1 to match steady state GDP share of stablecoins. - Share of buyer/seller in VE σ = 0.2 (implies about 40% of households participate in stablecoin transactions and 60% do not). - Bilateral bargaining buyer bargaining power θ = 0.95 (following AS (2011) Bayesian estimate). - Production side: - α = 0.33 (capital share in Cobb-Douglas, equation (29)). - Quarterly depreciation δ = 0.014 (AS (2011)). - Capital adjustment cost scale κi = 4 (Rannenberg (2016)). - Elasticity of substitution ε = 8 (final good production, equation (28)). - Sticky price parameter ζ = 0.83 (AS (2011)). - Price adjustment factor ι = 0.72 (AS (2011) Bayesian estimate). - Policy parameters: - φπ = 1.5, φy = 0.125 (Taylor rule, equation (48)). - ρr = 0.61 (interest rate smoothing, AS (2011) Bayesian estimate). - Fiscal parameter g = 1.22 to match long-run average G/Y = 0.21 (1972-2023 US data). - Shock processes: - All σX and ρX taken from Bayesian estimates in AS (2011). - Calibration notes from the source: - The target χt MS t / YN = 0.18 is chosen as a benchmark projection for next 10-15 years. - Under ψ = 0.32, steady-state transaction cost of stablecoins is around 0.36, about 64% lower than fiat money normalized to 1 (no direct real-world data provided). - The σ = 0.2 choice implies a 40% household participation rate in 2021–projected growth scenario. ### Solution method - The model is summarized as 40 simultaneous non-linear equations with 40 unknowns (detailed system in Appendix A of the source). - Steady state: - Closed-form solutions derived for all unknowns except q t, χ t, k t; those three solved numerically. - Dynamics: - Dynare code written to simulate the model using steady state as the starting point. - Simulations produce impulse responses to shocks and variance decompositions; results are presented in the next section of the source. *Source: wpiea2026129-source-pdf - 2.2 Firms* ### 4.1 Impulse responses of various shocks ### 4.1 Impulse responses of various shocks ### 4.1.1 Responses to productivity shock - Setup: - Figure 2 shows IRFs to a one-standard-deviation positive productivity (TFP) shock; y-axis = percentage deviation from steady state. - Nine panels: real total output (Y), real RE output (Y_RE), real RE consumption (c), real investment (i), real capital (k), RE inflation (π), real balances of stablecoins (M_S) and fiat money (M_F), stablecoin price (χ). - Key dynamic effects: - Positive TFP shock (supply-side) leads to: - Increase in GDP in the RE sector and overall economy. - Rises in consumption and investment. - Hump-shaped IRFs due to capital adjustment cost. - Decline in inflation. - Demand for both stablecoins (VE sector) and fiat money (RE sector) rises. - Productivity increase z_P reduces stablecoin transaction cost (via equation (55)), causing: - Initial fall in stablecoin price. - Subsequent rise in stablecoin price due to higher demand for stablecoin holding. - Relevant calibrated parameters (excerpt from Table 1): - Preference: Discount factor β = 0.990; Scale factor B = 2.280; Preference parameter κ = 0.0001; Weight on labor disutility A = 71.249; Stablecoin trans. cost ψ = 0.320; Buyers’ barg. power θ = 0.950; Share of buyer/seller σ = 0.200. - Production: Capital income share α = 0.330; Depreciation rate δ = 0.014; Investment adjustment cost κ^i = 4. - Price setting: Elasticity substitution ε = 8; Sticky price parameter ζ = 0.830; Price adjustment parameter ι = 0.720. - Policy: Taylor rule φ_π = 1.500; φ_y = 0.125; Interest rate smoothing ρ_r = 0.610; Reg. intensity param. ν = 1; Reg. scale parameter φ_1 target to χ_M_S/Y_N ratio = 0.18; Gross gr. rate, gov. exp. share g = 1.22. - Shock persistence: ρ_g = 0.840; ρ_z^s = 0.970; ρ_z^P = 0.830. - Shock standard deviations: σ_r = 0.360; σ_g = 1.010; σ_z^s = 1.800; σ_z^P = 1.040. ### 4.1.2 Responses to monetary policy shock - Setup: - Figure 3 shows IRFs to a one-standard-deviation positive monetary policy shock. - Key dynamic effects: - Unexpected increase in policy interest rate: - Nominal interest rates rise sharply. - Pronounced decline in investment in RE. - Sharp drop in real GDP and consumption. - Deflationary response (inflation declines). - Aggregate demand tightening dampens output in VE sector: - Decrease in stablecoin price. - Reduction in real balances of stablecoins. ### 4.1.3 Responses to fiscal policy shock - Setup: - Figure 4 shows IRFs to a one-standard-deviation positive government expenditure shock. - Key dynamic effects: - Increase in government spending (expansionary fiscal policy) leads to: - Rise in GDP. - “Crowding out” effect: private investment and consumption partially displaced. - Inflation declines in response to weakening private consumption demand. - Agents reduce holdings of both stablecoins and fiat money reflecting contraction in private-sector demand for liquidity. ### 4.1.4 Responses to stablecoin preference shock - Setup: - Figure 5 shows IRFs to a one-standard-deviation positive shock to stablecoin preference. - Key dynamic effects: - Demand-side shock increases agents’ preference for stablecoins: - Real fiat money balances shift toward stablecoin holdings (currency competition effect). - Price of stablecoins rises. - Transactions shift from RE to VE: - RE consumption and investment decline. - RE inflation falls. - Expansion in VE offsets RE contraction, yielding an overall increase in total output. ### 4.1.5 Variance decomposition - Objective: - Quantify contribution of four exogenous shocks to volatility of key macro variables (Table 2). - Assumption: virtual economy accounts for 18% of GDP (long-run perspective on stablecoin adoption). - Main findings (from Table 2: variance shares in percent): - Total Y (Y total): ε_z 28.69; ε_r 18.55; ε_g 51.52; ε_z^s 1.24. - Y (RE): ε_z 27.14; ε_r 15.92; ε_g 56.78; ε_z^s 0.15. - Consumption: ε_z 32.76; ε_r 34.32; ε_g 32.24; ε_z^s 0.68. - Investment: ε_z 50.78; ε_r 10.67; ε_g 37.49; ε_z^s 1.06. - Capital: ε_z 51.44; ε_r 6.73; ε_g 38.52; ε_z^s 3.31. - Inflation: ε_z 92.53; ε_r 5.00; ε_g 0.54; ε_z^s 1.93. - m_S balance: ε_z 9.14; ε_r 14.81; ε_g 5.99; ε_z^s 70.06. - m_F balance: ε_z 27.37; ε_r 29.15; ε_g 41.93; ε_z^s 1.54. - m_S price: ε_z 0.47; ε_r 5.72; ε_g 0.16; ε_z^s 93.65. - Interpretation: - (1) Fiscal policy shock largest for volatilities in real output and consumption; about 42% of variation in fiat money real balance attributed to fiscal shock. - (2) TFP shock primarily drives investment and capital fluctuation; explains about 93% of inflation volatility. - (3) Monetary policy shock important for consumption volatility but less so for real output and investment than fiscal shock. - (4) Preference shock dominates variation in real balance of stablecoins and almost entirely explains stablecoin price volatility. - Implication: modeling stablecoin price shock separately is unnecessary if model succinctness is pursued—preference shock suffices to capture stablecoin price volatility. ### 4.2 Stablecoins, macro stability, and prudential regulation #### 4.2.1 Stablecoins and macroeconomic stability - Experiment: - Vary parameter σ (proportion of consumers using stablecoins in VE) and report standard deviations of key macro variables with all four shocks active (Table 3). - Benchmark σ = 0.2; alternatives σ = 0.1, 0.3, 0.4. - Note: each change in σ is followed by re-calibration to match moments in Table 1. - Standard deviations (Table 3): - σ = 0.1 | σ = 0.2 | σ = 0.3 | σ = 0.4 - Y (total): 1.7553 | 1.7614 | 1.7727 | 1.7910 - Y (RE): 1.7405 | 1.7664 | 1.7956 | 1.8284 - Consumption: 1.1917 | 1.2003 | 1.2122 | 1.2276 - Investment: 2.9866 | 3.0161 | 3.0578 | 3.1116 - Capital: 0.6682 | 0.6798 | 0.6983 | 0.7238 - Inflation: 0.2828 | 0.2844 | 0.2875 | 0.2924 - m_S balance: 4.9521 | 4.2813 | 4.0397 | 3.8894 - m_F balance: 1.3193 | 1.3355 | 1.3592 | 1.3906 - m_S price: 4.0028 | 3.7217 | 3.6732 | 3.6536 - Findings: - As σ increases from 0.2 to 0.3 and 0.4, volatility of all macro variables rises except for stablecoin balance and stablecoin price which decline. - When σ = 0.4 (share of consumers transacting with stablecoins from 40% to 80%), standard deviation of aggregate real output rises by 1.7% (from 1.7614 to 1.7910). Real economy output increases by 3.5% (from 1.7664 to 1.8284). - Stablecoin real balances and price exhibit reduced volatility with higher σ. - Mechanism and intuition: - Equations (26)-(27): real net interest rate of stablecoins r_VE_t is inversely related to σ. - Under certain conditions, variance of r_VE_t equals variance of fiat real net interest rate (R_t/π_{t+1} − 1) scaled by 1/σ^2. - Increasing σ reduces variance of r_VE_t, lowering volatility of stablecoin balance and price. - Because σ < 0.5 in calibrated model, variance of r_VE_t remains greater than variance of fiat real interest rate. - Real interest rate fluctuations (Table 4): - σ = 0.1 | σ = 0.2 | σ = 0.3 | σ = 0.4 - real interest rate (fiat): 0.4634 | 0.4651 | 0.4677 | 0.4711 - Stablecoin interest rate: 4.2981 | 2.1542 | 1.4399 | 1.0829 - Additional channel: - As σ rises, volatility of fiat real interest rate R_t/π_{t+1} also rises, undermining central bank control because stablecoins operate outside the Taylor-rule framework. - Reduced traction of monetary policy increases R_t volatility, propagating instability through the real economy. #### 4.2.2 Stablecoins and prudential regulation - Policy instrument: - ν governs the ratio of stablecoins to reserve assets; regulators can adjust ν to influence monetary anchoring and macro stability. - Higher ν = regulatory preference for greater stablecoin volume backed by given fiat reserves (more accommodative); lower ν = tighter supervision. - Loss function (equation (22)) is quadratic; optimal ratio M_S_t/(M_F_t + B_t) aligns with ν. - Experiment: - Table 5 reports standard deviations of key macro variables for ν = 0.8, ν = 1, ν = 1.2 with all four shocks activated. - For comparability, monetary policy shock is introduced as negative so all four shocks are expansionary in this exercise. - Standard deviations (Table 5): - ν = 0.8 | ν = 1 | ν = 1.2 - Y (total): 1.7843 | 1.7614 | 1.7431 - Y (RE): 1.7874 | 1.7664 | 1.7469 - Consumption (RE): 1.2018 | 1.2003 | 1.2005 - Investment: 3.0242 | 3.0161 | 3.0145 - Capital: 0.6890 | 0.6798 | 0.6750 - Inflation: 0.2880 | 0.2844 | 0.2819 - m_S balance: 4.8234 | 4.2813 | 3.4549 - m_F balance: 1.3433 | 1.3355 | 1.3321 - m_S price: 3.0921 | 3.7217 | 4.7814 - Findings and policy implications: - Increasing ν from 1 to 1.2 reduces standard deviations of all macro variables except consumption (unchanged) and stablecoin price (which increases). - Aggregate real output standard deviation falls by 1.0% when ν increases from 1 to 1.2 (from 1.7614 to 1.7431). - ν functions as a stabilizer: higher ν can offset macro instability induced by higher σ. - Prudential regulation targeting backing ratio ν can restore monetary anchoring and improve macro stability. - Adjusting ν is analogous to liquidity requirements in fiat systems (e.g., liquidity coverage ratio) and can reduce likelihood of self-fulfilling runs and macro instability. - Core policy recommendation: - Stablecoins should be subject to regulatory oversight. A well-designed prudential framework targeting the backing ratio parameter ν can mitigate destabilizing effects of stablecoin adoption and help central banks reassert influence over monetary conditions. *Source: wpiea2026129-source-pdf - 4.1 Impulse responses of various shocks (IMF working paper chapter).* ### 4.3 Sensitivity Analysis ### 4.3 Sensitivity Analysis ### Different adoption scenarios - Calibration targets for χt Ms t/YN considered: - Benchmark: χt Ms t/YN = 0.18 (forward-looking long-run scenario). - Aggressive: χt Ms t/YN = 0.30 (possible exploding adoption in next 10-15 years). - Status quo: χt Ms t/YN = 0.02 (current penetration). - Core qualitative results robust across scenarios: - An increase in σ amplifies macroeconomic volatility across non-monetary variables and fiat money balances, while dampening the volatility of stablecoin balances and prices. - A higher backing ratio ν acts as a stabilizing mechanism, mitigating excess fluctuations introduced by stablecoins; magnitudes are larger when χt Ms t/YN is larger. - Notable quantitative illustration (reported in text): - When σ increases from 0.2 to 0.4 under aggressive adoption, the volatility of total real output increases by 5.9 percent. - Key table excerpts for χM S/YN = 0.30 (Table 6) — volatilities by σ: - σ = 0.1: Y (total) 1.7810; Y (RE) 1.7539; Consumption 1.1863; Investment 2.9690; Capital 0.6671; Inflation 0.2852; mS balance 4.8902; mF balance 1.3139; mS price 4.0556. - σ = 0.2: Y (total) 1.8016; Y (RE) 1.8013; Consumption 1.2043; Investment 3.0331; Capital 0.6969; Inflation 0.2906; mS balance 4.1887; mF balance 1.3508; mS price 3.7597. - σ = 0.3: Y (total) 1.8412; Y (RE) 1.8594; Consumption 1.2328; Investment 3.1339; Capital 0.7472; Inflation 0.3012; mS balance 3.8954; mF balance 1.4110; mS price 3.7056. - σ = 0.4: Y (total) 1.9073; Y (RE) 1.9319; Consumption 1.2746; Investment 3.2781; Capital 0.8200; Inflation 0.3182; mS balance 3.6768; mF balance 1.4997; mS price 3.6848. - Key table excerpts for χM S/YN = 0.30 (Table 7) — volatilities by ν: - ν = 0.8: Y (total) 1.8428; Y (RE) 1.8328; Consumption (RE) 1.2110; Investment 3.0602; Capital 0.7195; Inflation 0.2980; mS balance 4.6085; mF balance 1.3720; mS price 3.2832. - ν = 1: Y (total) 1.8016; Y (RE) 1.8013; Consumption (RE) 1.2043; Investment 3.0331; Capital 0.6969; Inflation 0.2906; mS balance 4.1887; mF balance 1.3508; mS price 3.7597. - ν = 1.2: Y (total) 1.7686; Y (RE) 1.7726; Consumption (RE) 1.2012; Investment 3.0183; Capital 0.6820; Inflation 0.2853; mS balance 3.5908; mF balance 1.3379; mS price 4.4732. - Status quo scenario (χM S/YN = 0.02) findings: - Effects of higher σ on non-monetary macro variables are negligible at current penetration. - Reducing σ to 0.02 (proximate to current usage) yields very small changes in volatilities of non-stablecoin variables, implying current stablecoin penetration is not macro-critical. - Key table excerpts for χM S/YN = 0.02 (Table 8) — volatilities by σ: - σ = 0.02: Y (total) 1.7243; Y (RE) 1.7217; Consumption 1.1999; Investment 3.0153; Capital 0.6738; Inflation 0.2805; mS balance 10.5336; mF balance 1.3297; mS price 7.5864. - σ = 0.2: Y (total) 1.7256; Y (RE) 1.7265; Consumption 1.2011; Investment 3.0180; Capital 0.6743; Inflation 0.2805; mS balance 4.7730; mF balance 1.3314; mS price 4.1276. - σ = 0.4: Y (total) 1.7260; Y (RE) 1.7320; Consumption 1.2031; Investment 3.0235; Capital 0.6756; Inflation 0.2804; mS balance 4.4432; mF balance 1.3343; mS price 4.1640. - Key table excerpts for χM S/YN = 0.02 (Table 9) — volatilities by ν: - ν = 0.8: Y (total) 1.7277; Y (RE) 1.7218; Consumption 1.1984; Investment 3.0101; Capital 0.6726; Inflation 0.2807; mS balance 13.3477; mF balance 1.3275; mS price 4.5187. - ν = 1.0: Y (total) 1.7243; Y (RE) 1.7217; Consumption 1.1999; Investment 3.0153; Capital 0.6738; Inflation 0.2805; mS balance 10.5336; mF balance 1.3297; mS price 7.5864. - ν = 1.2: Y (total) 1.7210; Y (RE) 1.7216; Consumption 1.2014; Investment 3.0206; Capital 0.6750; Inflation 0.2802; mS balance 3.5714; mF balance 1.3320; mS price 22.3285. - Policy implication highlighted: - When stablecoins become macro-critical (larger χ), the amplified quantitative effects may require more significant prudential regulatory intervention. ### Alternative bargaining solution - Benchmark bargaining: Nash bargaining solution (equation (9); Section 2.1.3). - Alternative considered: Kalai bargaining solution (corresponding FOC in equation (13)); model re-solved and quantitative exercises replicated. - Robustness results: - Qualitative patterns persist under the Kalai solution: increases in σ raise volatility in all macro variables except stablecoin balances and prices (whose volatilities decline with increased usage). - Magnitudes of effects are generally more pronounced under the Kalai solution versus Nash, implying the bargaining solution choice can amplify macroeconomic implications of stablecoin adoption. - Key table excerpts for Kalai solution (Table 10) — volatilities by σ: - σ = 0.1: Y (total) 1.7422; Y (RE) 1.7398; Consumption 1.1989; Investment 3.0105; Capital 0.6736; Inflation 0.2818; mS balance 4.4450; mF balance 1.3298; mS price 3.8132. - σ = 0.2: Y (total) 1.7680; Y (RE) 1.7461; Consumption 1.2077; Investment 3.0399; Capital 0.6850; Inflation 0.2835; mS balance 4.1137; mF balance 1.3465; mS price 3.7476. - σ = 0.3: Y (total) 1.7970; Y (RE) 1.7582; Consumption 1.2199; Investment 3.0807; Capital 0.7030; Inflation 0.2869; mS balance 3.9640; mF balance 1.3705; mS price 3.7317. - σ = 0.4: Y (total) 1.8296; Y (RE) 1.7778; Consumption 1.2354; Investment 3.1332; Capital 0.7277; Inflation 0.2921; mS balance 3.8530; mF balance 1.4023; mS price 3.7186. - Key table excerpts for Kalai solution (Table 11) — volatilities by ν: - ν = 0.8: Y (total) 1.7896; Y (RE) 1.7622; Consumption (RE) 1.2125; Investment 3.0577; Capital 0.6960; Inflation 0.2868; mS balance 4.6389; mF balance 1.3589; mS price 3.0998. - ν = 1.0: Y (total) 1.7680; Y (RE) 1.7461; Consumption (RE) 1.2077; Investment 3.0399; Capital 0.6850; Inflation 0.2835; mS balance 4.1137; mF balance 1.3465; mS price 3.7476. - ν = 1.2: Y (total) 1.7479; Y (RE) 1.7344; Consumption (RE) 1.2047; Investment 3.0282; Capital 0.6781; Inflation 0.2814; mS balance 3.3035; mF balance 1.3383; mS price 4.8342. ### Summary of sensitivity conclusions - Qualitative conclusions are robust to alternative calibration of χt Ms t/YN (0.30 aggressive; 0.02 status quo) and to alternative bargaining solutions (Kalai vs Nash). - When stablecoins reach macro-critical scale (larger χ), quantitative effects on macro volatility intensify, strengthening the case for prudential regulation (adjusting backing ratio ν analogous to liquidity requirements). - At current penetration (χt Ms t/YN = 0.02 and low σ), stablecoins’ impact on macro-stability is limited and prudential regulation has smaller stabilizing benefits; some variables may even become more volatile when ν increases slightly. *Source: 4.3 Sensitivity Analysis, Working Paper No. WP/2026/129.* --- _Source: https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026129-source-pdf.pdf_