## 1. Introduction ## Source details **Canonical URL:** [1. Introduction](https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021292-print-pdf.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2021/english/wpiea2021292-print-pdf.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2021/english/wpiea2021292-print-pdf.pdf.json) --- ### Background and motivation - Many emerging market economy (EME) central banks with inflation targeting (IT) frameworks continue to rely on foreign exchange interventions (FXI) and some also use capital flow management tools (CFMs), particularly during episodes of volatile capital flows. - Policymakers in EMEs frequently list volatile capital flows as a predominant concern, often absent from advanced economy (AE) communications. - Aim: quantify monetary tradeoffs facing EMEs and analyze how the use of FXI and CFMs can affect those tradeoffs. ### The unpleasant monetary dilemma - Two main elements: - Adverse external capital flow shocks that depreciate the exchange rate cannot be met with monetary policy easing in EMEs because of inflationary and financial stability concerns (can induce procyclical tightening). - "Sudden stops"—financial crises associated with large current account reversals and deep recessions—are a key consideration and occur more frequently/severely in EMEs than in most AEs. ### Model contributions and key features - Main contribution: analyze and quantify underlying tradeoffs in a structural framework that jointly features financial, nominal, and real frictions relevant for EMEs. - Financial intermediation frictions: - Friction 1 (Gabaix–Maggiori-style): limited risk-bearing capacity in FX market → inefficient UIP risk premium fluctuations captured by parameter Γ. - Friction 2 (sudden stop): occasionally binding external debt limit with Lagrange multiplier Θt that can trigger sharp credit-spread increases and contractions. - Nominal and real rigidities: price and wage stickiness, Kimball aggregator for intermediate goods, partial adaptive expectations allowing weaker inflation anchoring. ### Inflation expectations, pass-through, and asymmetries - Model allows medium-term inflation expectations to be destabilized by exchange rate changes via indexation; high exchange rate pass-through to import prices. - Calibrated to representative small open EME and AE for comparison. - Consistent with empirical evidence: - Exchange rate changes have larger and more persistent effects on inflation in EMEs than in AEs; depreciations may be contractionary for output in EMEs. - Pass-through is asymmetric: depreciations have larger effects than appreciations. - Higher sensitivity largely attributable to less well-anchored inflation expectations in many EMEs. ### Policy relevance - Combination of financial frictions and weakly anchored inflation expectations creates an important role for FXI or CFMs to help avoid procyclical monetary tightening during capital outflow pressures. - Framework used to quantify tradeoffs and assess relative importance of market imperfections for EME policy. --- ### Core mechanisms and the retail-rate UIP identity - Kimball aggregator generates strategic complementarities and asymmetric inflation responses (addresses “missing deflation puzzle”). - Retail-rate-based UIP identity (exact form preserved): - (1−τF,t)Ib,t = Et{I∗t εt+1/εt} + ΓIt BF,t/(Y PD,t) + |(1−τF,t)Θt. - Isolates standard UIP, Γ-driven Gabaix–Maggiori wedge, and “sudden stop” wedge active when borrowing constraint binds. ### Policy instruments analyzed - Conventional monetary policy: Taylor-type rule - It = I + ψπ(ΠD,t − ΠD) + ψx(Yt/Ypot t − 1) - FXI: sterilized reserve operations BM,t with carry cost TM,t = (I∗t−1 εt εt−1 − It−1) BM,t−1. - FX sales limit depreciation, reduce need for tighter domestic rates, can mitigate sudden stops but may postpone balance-sheet adjustment and increase future vulnerability. - CFMs: tax on capital inflows τF,t. - Precautionary CFMs that lean against external debt buildup can reduce probability/severity of crises; effective even when FX markets are deep. - International policy at the ELB: - FXI by a bloc at the ELB can provide stimulus but may create negative output spillovers for other constrained economies; effect depends on foreign policy space. --- ### Calibration and quantitative findings ### Selected calibration highlights (exact entries preserved) - Sudden stop frequency target: constrained regime occurs for about 3 percent of time in stochastic simulations (EME baseline). - Unhedged FX exposure: median EME unhedged FX exposure ≈ 16 percent of GDP. - FX market shallowness Γ: - Γ = 0.02 (AE) - Γ = 0.06 (EME) - Calibrated so a foreign currency purchase worth 10 percent of GDP generates roughly 15 percent exchange rate depreciation in EMEs. - Home ownership shares: - ωF = 0.75 - ωP = 0.75 - ωB = 1 (baseline) - Debt limit parameter: - m∞1.36 (Debt limit parameter) - Steady-state debt-to-annual-GDP chosen 12 percentage points below constraint → ≈3 percent constrained frequency. - Steady State Calibration (selected exact entries): - Real Interest Rate (annual) 4(1/β−1) : 0.01 | 0.015 | 0.019 (Foreign | AE | EME) - Inflation (annual) 4(π−1) : 0.02 | 0.02 | 0.04 - FX Reserves (to annual GDP) BM/4Y : -0 | 0.2 | 0.2 - Nominal rigidities (selected exact entries): - ι : 0.23 | 0.23 | 0.75 (Price indexation, Foreign | AE | EME) - ιw : 0.5 | 0.5 | 0.75 (Wage indexation) - ιe : -0 | 0 | 0.25 (Weight on exchange rate in wage indexation) - κ0 : 0.007 | 0.007 | 0.014 (Phillips curve slope (domestic production)) ### Empirical fit - Model IRFs lie within 90% confidence intervals for AE and EME comparisons. - Reproduces: - Contractionary depreciations in EMEs with larger inflation responses compared to AEs. - Asymmetric responses through Kimball aggregator: larger reactions to depreciations than appreciations. --- ### Policy experiments and mechanisms ### Monetary policy tradeoffs (portfolio risk appetite shocks) - Frictions amplify vulnerability: shallow FX markets (Γ large), external borrowing constraints, nominal rigidities, FX mismatches. - AE vs EME responses to capital outflow shock (AR(1) persistence 0.95; scaled to ≈10 percent real exchange rate depreciation in AEs): - AE: depreciation stimulates net exports → output expansion; well-anchored inflation expectations allow monetary policy to "look through" transient inflation. - EME: depreciation raises inflation persistently; central bank tightens → output contracts while inflation rises (stagflation-like). - Using policy rate to lean against depreciation is unattractive: stabilizing exchange rate increases pass-through of portfolio shocks to domestic interest rate → large activity fluctuations. ### Flight-to-safety and sudden-stop scenario - Scenario: adverse global risk tolerance shock + sharp global output fall; shocks AR(1) root 0.95 (demand shocks root 0.80). - Vulnerable EME (high net foreign liabilities + shallow FX market) vs less vulnerable EME: - Vulnerable EME: much larger UIP premium rise and depreciation, larger balance-sheet losses, sharp rise in net foreign liabilities, risk of hitting borrowing limit → sudden stop with sharp credit-spread increases and contraction. - Monetary policy during sudden stop: - Large policy rate hikes yield modest output improvements and can raise UIP premium further. - Monetary policy relatively less powerful; alternative tools (FXI, CFMs) may be superior. ### One-off FXI vs CFM intuition (persistent interventions, AR(1) coeff 0.9) - FXI sales: - Reduce depreciation; permit more accommodative monetary policy; mitigate stagflation; can avoid sudden stop if strong enough. - Medium-run tradeoff: stronger exchange rate and domestic demand → less trade balance improvement → slower NFA accumulation → higher future vulnerability. - CFMs (inflow tax): - Limit depreciation; prevent sudden stop. - Associated with slower accumulation of net foreign assets and negative income effects for intervening country (NFA law of motion implies decreasing τF,t to support exchange rate reduces domestic income). - Elevated UIP premium persists longer under CFMs → weaker exchange rate and higher inflation over medium run → depresses consumption and improves trade balance. - Quantity CFMs with lump-sum rebate yield outcomes similar to FXI. - Main distinction: income implications for intervening country—CFMs generally have more negative income effects than FXI unless CFMs are quantity-like. ### Policy feedback rules (exact forms preserved) - FXI feedback rule (Equation (25)): - ˜BM,t = ψm,1 ˜BP,t − ψm,2 Θt - Parameter restrictions: 0 ≤ ψm,1 ≤ 1, ψm,2 ≥ 0 - CFM feedback rule (Equation (26)): - τF,t = max(0, −ψf ˜Bt), where ψf ≥ 0 - Asymmetric: leans against overborrowing; non-negativity prevents subsidizing inflows. --- ### Simulation design and ergodic results ### Simulation setup - Shocks: intertemporal preferences, productivity, wage markups, exogenous portfolio flow variation following independent AR(1) processes: s_t = (1−ρ_s) s + ρ_s s_{t−1} + e_{s,t}, e_{s,t} ∼ i.i.d. (0, σ^2_s). - Most shock roots set to 0.95 except demand shocks 0.80. - Solution method: Levenberg-Marquardt mixed complementarity problem (LMMCP) solver in Dynare; preserves nonlinearities. - Long-sample simulation: 10,000 observations with FXI and CFMs off to establish baseline ergodic distributions. ### Baseline ergodic properties (no FXI/CFM) - Severe financial stress probability and borrowing spreads low when foreign debt moderate; rise sharply as net foreign liabilities approach sudden-stop territory. - Exchange rate mainly driven by risk appetite shocks. - Output distribution: heavy left tail due to sudden stops. - CPI inflation: leptokurtic with heavier right tail due to Kimball aggregator; positive skew driven by depreciations. ### Ergodic implications of FXI and CFM rules — selected exact outcomes (Table 5, occasionally binding debt limit columns) - Policy variants evaluated include: Standard MP Rule; FXI UIP Rule (ψm,1 = 0.5); CFM Rule (ψf = 0.01); FXI Spread Rule (ψm,2 = 1); Combined FXI UIP & CFM. - Selected exact outcomes (occasionally binding debt limit columns; preserved as printed): - Sudden Stop Probability: Standard MP Rule 0.00; FXI UIP Rule 0.73; CFM Rule 0.00; FXI UIP & CFM Rules 0.73; FXI Spread Rule 0.00 - Financial Stress Probability: Standard MP Rule 0.00; FXI UIP Rule 1.52; CFM Rule 0.00; FXI UIP & CFM Rules 1.52; FXI Spread Rule 0.00 - Borrowing Spread (mean): 0.00 under FXI UIP; 0.05 under CFM Rule; 0.09 under Standard MP Rule - Output (mean): -0.16 under FXI UIP; -0.23 under CFM Rule; -0.17 under Standard MP Rule - Output (std): 1.92 under FXI UIP; 2.00 under CFM Rule; 1.92 under combined - Output (skewness): -0.13 FXI UIP; -0.41 CFM Rule; -0.13 combined - CPI Inflation (std): 1.33 FXI UIP; 1.83 CFM Rule; 1.32 combined - CPI Inflation (skewness): 0.13 FXI UIP; 0.21 CFM Rule; 0.13 combined - Real Exchange Rate (std): 4.23 FXI UIP; 7.27 CFM Rule; 4.14 combined - Welfare Gain Relative to Standard MP Rule (permanent consumption equivalent, percent): 0.27 FXI UIP Rule; 0.16 CFM Rule; 0.34 FXI UIP & CFM Rules; −0.01 FXI Spread Rule - Loss Decrease Relative to Standard MP Rule (percent): 35.67 FXI UIP Rule; 6.59 CFM Rule; 36.25 FXI UIP & CFM Rules; −0.92 FXI Spread Rule ### Interpretation of main ergodic results - FXI UIP Premium Rule (ψm,1 = 0.5): - Welfare-improving: reduces exchange rate and inflation volatility, trade balance volatility. - Eliminates sudden stops in simulated setup; lowers financial stress probability. - Generates larger welfare gains than completely eliminating the debt limit. - CFM Rule (ψf = 0.01): - Precautionary leaning against net foreign liability accumulation; reduces sudden-stop frequency; stabilizes activity. - Generates welfare gains partly via tax revenue and decreased average foreign debt. - Slower accumulation of net foreign assets implies intertemporal tradeoff. - Combined FXI and CFM: - Complementary near debt limit: CFMs facilitate gradual decumulation of net foreign liabilities; FXI protects against abrupt outflows. - Yields largest welfare gains in many calibrations. - FXI Spread Rule (ψm,2 = 1) that intervenes only in reaction to spreads when debt limit binds: - Attenuates spread spikes but prevents needed external adjustment (stronger exchange rate) → undermines competitiveness, slows NFA accumulation. - In ergodic sense increases vulnerability: reduces average output, amplifies volatility and negative skewness → welfare and loss criteria show detrimental effects (Welfare Gain −0.01; Loss Decrease −0.92). - Robustness notes: - FXI spread-responsive rule might be welfare-positive under different structural assumptions (e.g., high foreign ownership of domestic banks (1−ωB)). - Proper identification of portfolio component of UIP premium (BP,t) is critical; imperfect identification increases role for CFMs. --- ### FXI at the ELB and multilateral spillovers ### Liquidity trap scenarios - AE liquidity trap (ELB binding): - Baseline shocks: negative home and foreign preference shocks (AR(1) root 0.95) + positive risk appetite shock (flight to safety, root 0.90) → appreciation pressure; policy rate pinned at zero. - FX purchases (sterilized), persistent AR(1) root 0.95; magnitude: 20% of annual trend GDP in first quarter. - Deep recession baseline: inflation falls below zero; output falls about 8 percent; policy rate at zero. - With FXI purchases: - Induced depreciation raises net exports and output. - ELB stops binding earlier → real interest rates decline → domestic demand crowds in. - CPI inflation closer to target; FXI stabilizes inflation and output in AE liquidity trap. - EMEs at ELB: - Under EME calibration (more responsive inflation expectations), same-sized intervention yields larger stimulative effects on domestic absorption and output via stronger second-round inflation effects. - FXI and CFMs may alleviate ELB tradeoffs if indebtedness safely below debt limit. ### Multilateral considerations - When home economy is large (size = half world): - If foreign economy also in liquidity trap: - FXI can have sizable beggar-thy-neighbor effects; may be globally contractionary short run. - If foreign economy unconstrained and can provide stimulus: - Output spillovers small; world economy benefits from FX purchases in constrained economy. - Policy space of foreign economies matters for global spillovers of FXI. --- ### Robustness, extensions, and data ### Robustness to optimized monetary rules (Appendix D) - Alternative monetary rule including exchange rate term considered: - I_t = I + ψ_π (Π^D,t − Π^D) + ψ_x (Y_t / Y^pot_t − 1) + ψ_q (Q_t−1) - Findings: - Aggressive monetary policy (ψ_π = 5) can improve welfare/loss measures but may elevate frequency of financial stress. - Main conclusions on FXI and CFMs hold: preemptive deployment yields sizable gains; reactive-only use during sudden stops is suboptimal. - Selected exact outcomes (Table A.4, selected entries): - Sudden Stop Probability: Baseline model 1.39; Aggressive MP 1.30; FXI UIP Prem. Rule 0.00; CFM Rule 0.64; FXI Spread Rule 1.38 - Welfare Gain Relative to Standard MP Rule: Baseline 0.00; Aggressive MP 0.09; FXI UIP Prem. Rule 0.32; CFM Rule 0.23; FXI Spread Rule 0.09 ### Data and moment matching - Country sample for empirical moments: - AEs: Australia, Canada, Czechia, Germany, Iceland, Israel, Japan, Korea, New Zealand, Norway, Sweden, Switzerland, United Kingdom. - EMEs: Argentina, Brazil, Chile, China, Colombia, Hungary, India, Indonesia, Malaysia, Mexico, Peru, Philippines, Poland, South Africa, Thailand, Turkey. - Primary data sources: Haver Analytics, WEO database, JPMorgan Real Broad Effective Exchange Rate Index. - Coverage: most countries 2000Q1-2019Q4. - Moment matching results show the model reproduces key volatilities, autocorrelations, and cross-correlations reasonably well (selected exact comparisons in Appendix C). ### Extensions noted - Behavioral portfolio investors (Appendix A): allowing endogenous portfolio response (b > 0) effectively deepens FX market (modifies Γ-driven term via Γ/(1 + b Γ I_t)). - Suggested future work: Bayesian estimation across countries, incorporate macroprudential policy, housing sector, bank capital, quantify longer-term costs of FXI/CFMs. --- ### Conclusions and policy implications (preserved framing) - FXIs and CFMs can complement conventional monetary policy in vulnerable EMEs, especially when: - Inflation expectations are less well-anchored, - Significant foreign currency mismatches exist, - High debt levels and shallow FX markets prevail. - Key tradeoffs: - FXIs and CFMs reduce probability of sudden stops and stabilize inflation/output but may slow accumulation of net foreign assets and raise future vulnerability. - Reactive-only interventions can be welfare-detrimental by postponing necessary balance-sheet adjustment. - Uncertainty about shock persistence and the unobserved debt limit necessitates caution—risk of reserve losses if shocks are more persistent than anticipated. - Policy recommendations (preserved emphasis): - Use rules that respond preemptively as well as during stress (leaning against buildups when investor risk appetite is high). - Precautionary CFMs that curb inflows as external debt rises can yield welfare improvements, particularly when reserves are limited and debt is near the constraint. - International coordination is important because FXI by constrained blocs at the ELB can generate negative spillovers for other vulnerable countries. *Source: wpiea2021292-print-pdf — A Quantitative Microfounded Model for the Integrated Policy Framework (IMF Working Paper No. WP/21/292).* ### 1. Introduction1 ### 1. Introduction ### Background and motivation - Many emerging market economy (EME) central banks with inflation targeting (IT) frameworks continue to rely on foreign exchange interventions (FXI) and some also use capital flow management tools (CFMs), particularly during episodes of volatile capital flows. - Policy makers in EMEs frequently list volatile capital flows as a predominant concern, a concern often absent from advanced economy (AE) communications. - Aim: quantify monetary tradeoffs facing EMEs and analyze how the use of FXI and CFMs can affect those tradeoffs. ### The unpleasant monetary dilemma (two main elements) - The dilemma comprises two main elements. - First: unlike in their AE counterparts, inflationary and financial stability concerns mean that an adverse external capital flow shock that depreciates the exchange rate cannot be met with monetary policy easing, which would otherwise cushion the effects of external tightening on domestic demand. - Footnote 1 (as in source): "This is, arguably, why monetary policy responses to adverse capital flow shocks were procyclical, i.e., associated with a tightening, in about half of the emerging market sample in Vegh and Vuletin (2013). By contrast, in small open advanced economies domestic factors appeared to dominate, translating into countercyclical responses." - Second: "Sudden stops" are a key consideration. - Footnote 2 (as in source): "These are typically defined as financial crises associated with large current account reversals and deep recessions." - EMEs face higher frequency and severity of such episodes relative to most AEs, making mitigation an important policy objective. ### Model contributions and key features - Main contribution: analyze and quantify underlying tradeoffs in a structural framework that is rich enough to capture empirically relevant frictions yet parsimonious enough to isolate key transmission channels. - The model jointly features financial, nominal, and real frictions important for emerging markets (e.g., pass-through of exchange rate shocks to inflation and economic activity), overcoming limitations of more stylized models that do not incorporate these frictions together. - Two key frictions in financial intermediation (analogous to Basu et al., 2020): - Friction 1: Based on Gabaix and Maggiori (2015), captures limited risk-bearing capacity of agents trading in the FX market and gives rise to inefficient fluctuations in the uncovered interest rate parity (UIP) risk premium. - Friction 2: In the spirit of the “sudden stop” literature (Arellano and Mendoza, 2002; Chari et al., 2005; Mendoza, 2010; Bianchi, 2011; Chang, 2019), an occasionally binding external debt limit that can trigger sharp increases in credit spreads, current account reversals and deep contractions in economic activity. - The model also incorporates nominal and real rigidities commonly used in central bank policy models, including price and wage stickiness. ### Inflation expectations, pass-through, and asymmetries - The model allows for medium-term inflation expectations to be destabilized by exchange rate changes via indexation mechanisms and high pass-through of exchange rate changes to import prices. - Calibrated to a “representative” small open emerging market economy and a “representative” small open advanced economy for comparison. - Model is consistent with empirical evidence that: - Exchange rate changes tend to have larger and more persistent effects on inflation in EMEs than in AEs, so that depreciations may even be contractionary for output in EMEs. - Exchange rate pass-through to inflation in EMEs is asymmetric, with depreciations having larger effects than appreciations. - Higher sensitivity of inflation to exchange rate movements in many EMEs appears largely attributable to less well-anchored inflation expectations. ### Policy relevance and implications - The combination of financial frictions and weakly anchored inflation expectations can create an important role for using FXI or CFMs, including to help avoid procyclical monetary tightening in the face of capital outflow pressures. - The framework aims to inform policy by quantifying tradeoffs and assessing relative importance of underlying market imperfections relevant to EME policymakers. *Source: wpiea2021292-print-pdf - 1. Introduction1* ### Chapter 3 in the IMF World Economic Outlook (2018), Kamber et al. (2020) and Bems et al. (2021). ### Chapter 3 in the IMF World Economic Outlook (2018), Kamber et al. (2020) and Bems et al. (2021) ### Purpose and headline conclusions - The paper develops a two-country, microfounded New Keynesian model with richer nominal and real frictions to study the role of foreign exchange interventions (FXI), capital flow management (CFM) tools, and international policy coordination in economies subject to external capital flow shocks. - Key conclusion: Simple FXI and CFM rules can deliver sizeable welfare gains by smoothing UIP (uncovered interest parity) fluctuations and reducing the frequency/severity of “sudden stops,” but these tools involve important intertemporal tradeoffs and can be welfare-detrimental if used only reactively during stress episodes. - The welfare benefits of strengthening monetary autonomy are largest when there are: substantial balance sheet FX mismatches, low FX market liquidity, and weakly anchored inflation expectations. - FXI by a large bloc of countries at the effective lower bound (ELB) can create negative output spillovers for other constrained economies but is fairly innocuous when the foreign economy has ample policy space. ### Core mechanisms and frictions captured - Nonlinear Kimball aggregator for intermediate goods introduces strategic complementarities in price setting and generates asymmetric inflation responses (helps explain the “missing deflation puzzle”). - Key frictions: - FX market moral hazard faced by financiers → generates a Gabaix–Maggiori-style UIP premium sensitive to bond holdings and FX market shallowness Γ. - Occasionally binding external borrowing constraint in banks → generates a “sudden stop” wedge via the Lagrange multiplier Θt on borrowing constraint. - Incomplete financial markets and partial foreign ownership of financial intermediaries → determine FX mismatches and who bears exchange rate risk (parameters ωF, ωP, ωB). - Nominal rigidities and partially adaptive expectations (some agents form expectations adaptively) → weaker inflation anchoring in many EMEs and larger second-round inflation effects of exchange rate depreciation. - Retail-rate-based UIP identity (exact form preserved): - (1−τF,t)Ib,t = Et{I∗t εt+1/εt} + ΓIt BF,t/(Y PD,t) + |(1−τF,t)Θt. - This expression isolates: the standard UIP component, the Γ-driven Gabaix–Maggiori wedge, and the “sudden stop” wedge active when the borrowing constraint binds. ### Policy instruments analyzed and tradeoffs - Conventional monetary policy: simple Taylor-type rule - It = I + ψπ(ΠD,t − ΠD) + ψx(Yt/Ypot t − 1) - Foreign exchange interventions (FXI): sterilized FX reserve operations B M,t with carry cost TM,t = (I∗t−1 εt εt−1 − It−1) B M,t−1. - FX sales can limit depreciation and reduce the need for tighter domestic policy rates, potentially avoiding or mitigating sudden stops. - But FX interventions can forestall balance-sheet adjustment and increase future vulnerability; reactive-only rules can reduce welfare in stochastic environments. - Capital flow management (CFM): represented by tax on capital inflows τF,t. - Precautionary CFMs that lean against external debt buildup can reduce the probability and severity of crises, especially when an economy is near its debt limit but lacks sufficient reserves. - CFMs can be effective even when FX markets are deep, while FXIs’ efficacy depends on FX market shallowness Γ. - International policy (IPF) at the ELB: - FXI by a bloc at the ELB can provide stimulus; multilateral considerations matter because constrained foreign economies may suffer spillovers. ### Quantitative findings and calibration highlights - Model solved nonlinearly; evaluation includes impulse responses and stochastic simulations to assess distributions and tail events (e.g., sudden stops). - Sudden stop frequency target: the baseline EME calibration sets parameters so the constrained regime occurs for about 3 percent of time in stochastic simulations. - Unhedged FX exposure: the calibration implies a median EME unhedged FX exposure of around 16 percent of GDP. - FX market shallowness Γ calibrated so that for EMEs a purchase of foreign currency worth 10 percent of GDP generates roughly 15 percent exchange rate depreciation; reported calibration values: - Γ = 0.02 (AE) - Γ = 0.06 (EME) - Home ownership shares set at: - ωF = 0.75 (home ownership of financiers) - ωP = 0.75 (home ownership of portfolio investors) - ωB = 1 (home ownership of banks) in baseline - Debt limit parameter and sudden-stop calibration: - m∞1.36 (Debt limit parameter) - Chosen so steady-state debt-to-annual-GDP is 12 percentage points below the constraint for EMEs, yielding ≈3 percent constrained frequency. ### Model structure (agents, markets, and price-setting) - Agents and roles: - Households: utility from consumption, leisure, real money balances; some form expectations adaptively; face budget constraint with bonds BG,t and claims Bt; set wages under Calvo-style staggered contracts with indexation. - Financiers: intermediate cross-border borrowing and FX trading, face diversion/moral hazard; incentive compatibility yields UIP premium term ΓIt BF,t/(Y PD,t); subject to capital flows tax τF,t (CFM). - Banks: transfer funds between financiers and households; face occasionally binding borrowing constraint −Bt PD,t ≤ m Et Yt+1; produce retail-rate spread Ib,t = It + Θt when constraint is active. - Portfolio investors: take positions BP,t in home-currency bonds; exogenous swings capture investor risk appetite shocks. - Pricing and production: - Kimball aggregator for intermediate goods introduces parameter ψ and generates state-dependent demand elasticities and quasi-kinked demand curves. - Calvo-style price and wage setting with indexation parameters ι (prices), ιw (wages), and ιe (weight on exchange rate in wage indexation). - Local currency pricing (LCP) for exports; distinct export price stickiness. - Potential economy: all firms can reset prices and wages each period, no price dispersion; potential output and marginal cost specified (Ypot t formula and MCpot t/Ppot D,t = Υ/(1 + θp)). ### Calibration tables (selected exact entries preserved) - Table 1. Steady State Calibration (columns: Foreign | AE | EME) - Real Interest Rate (annual) 4(1/β−1) : 0.01 | 0.015 | 0.019 - Inflation (annual) 4(π−1) : 0.02 | 0.02 | 0.04 - Government Consumption (share of GDP) G/Y : 0.15 | 0.14 | 0.14 - Import Content (public) ωG : -0.1 | 0.1 - Import Content (private) ωC : -0.3 | 0.3 - Net Foreign Assets (to annual GDP) B/4Y : -0 | -0.22 - FX Reserves (to annual GDP) BM/4Y : -0 | 0.2 | 0.2 - Table 2. Calibration of Nominal Rigidities (columns: Foreign | AE | EME) - ι : 0.23 | 0.23 | 0.75 (Price indexation) - ιw : 0.5 | 0.5 | 0.75 (Wage indexation) - ιe : -0 | 0 | 0.25 (Weight on exchange rate in wage indexation) - κ0 : 0.007 | 0.007 | 0.014 (Phillips curve slope (domestic production)) - κw : 0.007 | 0.007 | 0.011 (Phillips curve slope (wages)) - κm : -0.012 | 0.006 (Phillips curve slope (exports)) - κ∗m : -0.012 | 0.06 (Phillips curve slope (imports)) - Table 3. Calibration of Financial Intermediation Block - m∞1.36 (Debt limit parameter) - Γ : 0.02 (AE) | 0.06 (EME) (Gabaix-Maggiori friction) - ωF : 0.75 (Home ownership of financiers) - ωP : 0.75 (Home ownership of portfolio investors) - ωB : 1 (Home ownership of banks) - Table 4. Calibration of Other Parameters (selected) - α : 0.3 (Coefficient on capital in the production function) - χ : 1 (Inverse of Frisch elasticity of labor supply) - χ0 : 1 (Relative weight on labor disutility (home)) - ψπ : 1.5 (Coeff. on domestic inflation in Taylor rule) ### Empirical fit and illustrative results - The model, when solved nonlinearly and calibrated separately for AEs and EMEs, reproduces key empirical differences in the transmission of exchange rate shocks: - Contractionary depreciations in EMEs (output falls) and a much larger inflation response in EMEs than in AEs. - The Kimball aggregator generates asymmetric responses: larger reactions of prices and output to a depreciation than to an appreciation of the same absolute size. - Figure-based comparison (model IRFs vs data) reported in the chapter shows model IRFs comfortably within 90% confidence intervals estimated for AEs and EMEs. ### Policy implications and recommendations (preserved framing) - FXI and CFMs can be useful complements to conventional monetary policy in vulnerable EMEs: - Use rules that respond not only in crises but also preemptively (lean against overheating when investor risk appetite is high) to avoid perverse intertemporal effects. - Precautionary CFMs that impose restrictions on capital inflows as external debt rises can yield considerable welfare improvements, particularly when reserves are limited and the economy is near its debt limit. - Beware of reactive-only interventions: - FX interventions that solely respond to episodes of financial stress can be detrimental ex ante in a stochastic environment by postponing necessary balance-sheet adjustment and increasing future crisis risk. - Multilateral considerations: - FXI by a large bloc at the ELB can act as stimulus but may generate negative spillovers to other constrained countries; coordination and attention to foreign policy space are important. *Italicized source: Chapter 3 in the IMF World Economic Outlook (2018), Kamber et al. (2020) and Bems et al. (2021); source PDF filename: wpiea2021292-print-pdf - Chapter 3 in the IMF World Economic Outlook (2018), Kamber et al. (2020) and Bems et al. (2021).* ### 0.0625 Coeff. on output gap in Taylor rule ### wpiea2021292-print-pdf - 0.0625 Coeff. on output gap in Taylor rule ### Model parametrization and stochastic shocks - Key calibrated parameters and steady-state terms: - σ1 Intertemporal elasticity of substitution - τC 0.15 Consumption tax rate - τN 0.15 Labor income tax rate - θp 0.2 Steady state net markup in product markets - θw 0.5 Steady state net markup in labor market - Υ1.2 Steady state price cost-push term - ΥW 1.5 Steady state wage cost-push term - ψy =.0625 Coeff. on output gap in Taylor rule - Monopolistic distortions offset by subsidies so that Υ = 1 + θp and ΥW = 1 + θw, ensuring efficiency absent taxation and zero intermediary positions. - Exogenous shock vector s_t = {ς_t, ς*_t, G_t, G*_t, Z_t, Z*_t, ΥW,t, Υ*W,t, Υ_t, Υ*_t, BP,t, BM,t, τF,t} follows independent AR(1) processes: - s_t = (1−ρ_s) s + ρ_s s_{t−1} + e_{s,t}, e_{s,t} ∼ i.i.d. (0, σ^2_s) (Equation (24)) - Persistence and standard deviation (ρ_s, σ_s) discussed where used; most shock roots set to 0.95 except demand shocks root 0.80 in some exercises. - Occasionally binding constraints: external borrowing limit in home economy; effective lower bound (ELB) on nominal interest rate in home and foreign economies. - Solution method: Levenberg-Marquardt mixed complementarity problem (LMMCP) solver in Dynare; preserves non-linearities under certainty equivalence. ### Monetary policy tradeoffs: transmission of portfolio (risk appetite) shocks - Frictions amplifying vulnerability to swings in financial investors’ risk appetite (BP,t): - Shallow FX markets (Γ large), external borrowing constraints, nominal rigidities, FX mismatches. - When FX markets are deep (Γ low), economy better insulated from portfolio flow shocks. - AE vs EME transmission of an exogenous capital outflow shock (AR(1) persistence 0.95; scaled so real exchange rate depreciates by about 10 percent in AEs): - Advanced Economies (AE): - Exchange rate depreciation stimulates net exports → expansion in economic activity. - Higher output + higher import prices → inflation rise, but with well-anchored inflation expectations monetary policy can “look through” the transient rise and focus on output. - Shock resembles a standard aggregate demand shock. - Emerging Market Economies (EME): - Less well-anchored inflation expectations; exchange rate depreciation has large and persistent effects on inflation. - Central bank tightens, crowding out domestic demand; export-price stickiness in foreign currency moderates foreign demand boost. - Result: output contracts while inflation rises in parallel (stagflation-like outcome). - Disparate AE/EME responses mainly due to differences in nominal rigidities parametrization (higher intrinsic persistence in price and wage setting; stronger exchange rate pass-through in EMEs). - FX mismatches (negative net foreign asset position) do not amplify contractionary nature of depreciation while debt constraint is slack; if debt limit binds, output contracts more. ### Policy experiments: baseline monetary policy vs tighter responses - Baseline EME central bank follows standard Taylor rule. - Tighter monetary policy (more vigorous responses to domestic and imported inflation): - Limits size and persistence of inflation increases. - Generates markedly sharper output contraction. - Using policy rate to lean against exchange rate depreciation (for given Γ) is unattractive: - UIP condition implies stabilizing nominal exchange rate increases pass-through of portfolio shocks to domestic interest rate → potentially huge activity fluctuations. ### Flight-to-safety scenario and sudden stops - Scenario: adverse external shock to global risk tolerance + sharp fall in global output (captures aspects of COVID onset); driven by negative, persistent shocks to productivity and intertemporal preferences domestically and abroad. - All shocks follow AR(1) with root 0.95, except demand shocks root 0.80. - Vulnerable EME (high net foreign liabilities + shallow FX market) vs less vulnerable EME (low net foreign liabilities + ample FX liquidity): - Identical shocks produce much larger UIP risk premium rise and larger exchange rate depreciation in vulnerable EME. - Greater depreciation boosts net exports but exacerbates FX-mismatch balance sheet losses → sharp increase in net foreign liabilities → risk of hitting external borrowing limit → sudden stop with sharp credit-spread increases, contraction in economic activity, current account reversal. - Monetary policy in sudden stop: - To stimulate activity, one may need to tighten policy (limit depreciation) to mitigate balance sheet effects. - Large policy rate hikes yield only modest output improvements and can push UIP premium up further. - Monetary policy is less powerful during sudden stops and may be inferior to alternative tools. ### Foreign exchange interventions (FXI) and capital flow measures (CFM): mechanisms and one-off interventions - Intuition from one-off persistent interventions calibrated to produce same real exchange rate reaction on impact (autoregressive coefficient 0.9): - FXI sales: - Reduce depreciation; allow more accommodative monetary policy due to less inflation pressure. - Mitigate stagflation: reduce inflation, boost output, expand domestic demand; if strong enough to avoid sudden stop, gains large. - Medium-run tradeoff: stronger exchange rate and domestic demand → less trade balance improvement → slower accumulation of net foreign assets → intertemporal tradeoff (prevent recession today vs higher future vulnerability). - CFMs (tax on capital inflows): - Also limit depreciation; can prevent sudden stop. - Associated with much slower accumulation of net foreign assets and negative income effects for intervening country (NFA law of motion implies decreasing τF,t to support exchange rate reduces domestic income). - Elevated UIP risk premium persists longer under CFMs → weaker exchange rate and higher inflation over medium run → depresses consumption and improves trade balance. - If CFMs implemented as quantity restrictions with lump-sum rebate to payers (no cross-country wealth transfers), outcomes resemble FXI. - Main distinction: different income implications for intervening country (CFMs generally more negative income effects than FXI unless CFMs are quantity-like). ### Policy rules for FXI and CFMs - FXI feedback rule (Equation (25)): - ˜BM,t = ψm,1 ˜BP,t − ψm,2 Θt - Parameter restrictions: 0 ≤ ψm,1 ≤ 1, ψm,2 ≥ 0 - Motives: - ψm,1 > 0: intervene in response to portfolio capital flows to offset UIP premium movements. - ψm,2 > 0: sell FX reserves in response to sudden stops (Θt) to compress positive spreads and appreciate currency, lowering foreign-debt value per unit of domestic production. - CFM feedback rule (Equation (26)): - τF,t = max(0, −ψf ˜Bt), where ψf ≥ 0 - Targets overborrowing by leaning against buildup of net foreign liabilities; asymmetric (does not tax accumulation of net foreign assets above steady state); non-negativity prevents subsidizing inflows. ### Simulation setup and stochastic calibration - Shocks considered: intertemporal preferences, productivity, wage markups, exogenous portfolio flow variation. - Simulated method of moments used to calibrate shock properties for US (output, inflation, short-term rates) and representative EME (plus effective real exchange rate). Two-step procedure: calibrate foreign country shocks treating as closed, then calibrate domestic shocks conditional on foreign. - Long-sample simulation: 10,000 observations with FXI and CFMs switched off to establish baseline ergodic distributions. ### Baseline ergodic properties (no FXI/CFM) - Severe financial stress probability and borrowing spreads low when foreign debt moderate/low; rise sharply as net foreign liabilities expand and approach sudden-stop territory. - Exchange rate mainly driven by risk appetite shocks, not NFA position. - Financial crises occur mainly when UIP premium elevated (capital outflows + depreciation). - Distributions: - Output: heavy left tail due to sudden stops. - Trade balance: left-tail asymmetry (debt limit curbs deficits → strong surpluses during sudden stops). - CPI inflation: leptokurtic with heavier right tail due to Kimball aggregator; positive skew partly driven by exchange rate depreciations and marginal cost behavior. ### Ergodic implications of FXI and CFM policy rules — simulation results (summary of Table 5) - Rule calibration and variability: - Most aggressive FXI rule responding to portfolio flows → standard deviation of FX reserves (relative to annual GDP) ≈ 5 percent; steady state reserves = 20 percent. - Capital flow tax rate standard deviation ≈ 0.5 percent (annualized) when CFM rule alone; about half that when used with FXI. - Evaluation metrics: probability of sudden stop, financial stress probability, mean borrowing spread, output mean/std/skewness, CPI inflation std/skewness, real exchange rate std, welfare gain (permanent consumption equivalent, percent), and loss decrease (quadratic loss on output gap and inflation). - Key policy variants considered in Table 5: - No debt limit vs Occasionally binding debt limit - Standard MP Rule (baseline) - FXI UIP Premium Rule (ψm,1 = 0.5) - CFM Rule (ψf = 0.01) - FXI Spread Rule (ψm,2 = 1) - Combined FXI UIP & CFM Rules - Selected exact outcomes from Table 5 (occasionally binding debt limit columns): - Sudden Stop Probability: Standard MP Rule 0.00; FXI UIP Rule 0.73; CFM Rule 0.00; FXI UIP & CFM Rules 0.73; FXI Spread Rule 0.00; (note: table layout indicates values across columns—preserve exactly as printed) - Financial Stress Probability: Standard MP Rule 0.00; FXI UIP Rule 1.52; CFM Rule 0.00; FXI UIP & CFM Rules 1.52; FXI Spread Rule 0.00 - Borrowing Spread (mean): 0.00 under FXI UIP; 0.05 under CFM Rule; 0.09 under Standard MP Rule - Output (mean): -0.16 under FXI UIP; -0.23 under CFM Rule; -0.17 under Standard MP Rule; -0.26 under some specifications - Output (std): 1.92 under FXI UIP; 2.00 under CFM Rule; 1.92 under combined; 2.12 in other columns - Output (skewness): -0.13 FXI UIP; -0.41 CFM Rule; -0.13 combined; -0.85 in another variant - CPI Inflation (std): 1.33 FXI UIP; 1.83 CFM Rule; 1.32 combined; 1.91 other - CPI Inflation (skewness): 0.13 FXI UIP; 0.21 CFM Rule; 0.13 combined; 0.11 other - Real Exchange Rate (std): 4.23 FXI UIP; 7.27 CFM Rule; 4.14 combined; 7.51 other - Welfare Gain Relative to Standard MP Rule (permanent consumption equivalent, percent): 0.27 for FXI UIP Rule; 0.16 for CFM Rule; 0.34 for FXI UIP & CFM Rules; −0.01 for FXI Spread Rule - Loss Decrease Relative to Standard MP Rule (percent): 35.67 FXI UIP Rule; 6.59 CFM Rule; 36.25 FXI UIP & CFM Rules; −0.92 FXI Spread Rule - Interpretation of main results: - FXI UIP Premium Rule (ψm,1 = 0.5) is welfare-improving: - Reduces exchange rate volatility, inflation volatility, and trade balance volatility. - Completely eliminates sudden stops in the simulated setup; lowers probability of financial stress. - Generates larger welfare gains than completely eliminating the debt limit. - CFM Rule (ψf = 0.01) used precautionarily to lean against net foreign liability accumulation: - Reduces frequency of sudden stops and stabilizes activity. - Generates welfare gains, partly via tax revenue collected when net foreign liabilities rise above steady state, and by decreasing average foreign debt (compressing UIP premium). - Slower accumulation of net foreign assets increases intertemporal tradeoff. - Combining FXI and CFM rules yields largest gains: - Complementary when economy close to debt limit: CFMs facilitate gradual decumulation of net foreign liabilities; FXI protects against abrupt outflows. - FXI Spread Rule (ψm,2 = 1) that intervenes only in reaction to spreads when debt limit binds: - Attenuates spread spikes but prevents needed external adjustment (stronger exchange rate) → undermines competitiveness and slows NFA accumulation. - In ergodic sense increases vulnerability: reduces average output and amplifies volatility and negative skewness → welfare and loss criteria show detrimental effects (Welfare Gain −0.01; Loss Decrease −0.92). - Robustness and caveats: - Welfare of spread-responsive FXI could be positive under different structural assumptions (e.g., high share of foreign ownership of domestic banks (1−ωB)). - Precise identification of portfolio component of UIP premium (BP,t) is critical to FXI rule performance; imperfect identification increases role for CFMs. - FXI rules responding directly to exchange rate can still yield welfare gains if portfolio flows dominate exchange rate fluctuations. ### FXI in liquidity trap and multilateral spillovers - Liquidity trap scenario (AE calibration; ELB binding): - Baseline shocks: negative home and foreign preference shocks (AR(1) root 0.95) + positive risk appetite shock (flight to safety, root 0.90) → appreciation pressure; policy rate pinned at zero. - FX purchases (sterilized), persistent AR(1) root 0.95; magnitude: 20% of annual trend GDP in first quarter. - Deep recession baseline: inflation falls below zero; output falls about 8 percent; policy rate at zero. - With FXI purchases: - Induced depreciation raises net exports and output. - ELB stops binding earlier → real interest rates decline → crowds in domestic demand. - Weaker exchange rate keeps CPI inflation closer to target. - FXI helps stabilize both inflation and output in AE liquidity trap. - Emerging Markets at ELB: - Under EME calibration (with more responsive inflation expectations), same-sized intervention yields larger stimulative effects on domestic absorption and output gap via stronger second-round inflation effects. - FXI and CFMs may alleviate ELB tradeoffs if indebtedness safely below debt limit. - Multilateral effects when home economy is large (size = half world): - Two cases: foreign economy in liquidity trap vs unconstrained. - If foreign economy also in liquidity trap: - FXI can have sizable beggar-thy-neighbor effects; may be globally contractionary in short run. - If foreign economy unconstrained and can provide monetary stimulus: - Output spillovers small; world economy benefits from FX purchases in constrained economy. - Implication: foreign policy space matters for global spillovers of FXI. ### Conclusions and policy implications - Augmenting conventional monetary policy with FXIs and CFMs can improve monetary policy tradeoffs and mitigate downside risks, especially in economies with: - Less well-anchored inflation expectations, - Significant foreign currency mismatches, - High debt levels and shallow FX markets. - Key tradeoffs and limitations: - FXIs and CFMs can reduce probability of sudden stops and stabilize inflation/output but may slow accumulation of net foreign assets and raise future vulnerability. - Decisions must consider uncertainty about shocks and distance to unobserved debt limit — risk of reserve losses if shocks more persistent than anticipated. - Long-term costs: potential impediments to financial market development and encouragement of foreign-currency debt accumulation. - Suggested extensions and caveats for future work: - Bayesian estimation across countries to understand empirical transmission heterogeneity. - Incorporation of macroprudential policy, housing sector, and bank capital. - Need to quantify longer-term costs and integrate them into structural analyses. *Italic: Source — wpiea2021292-print-pdf (IMF working paper content as provided).* ### References ### References and Appendices (Content Unit: wpiea2021292-print-pdf - References) ### References (bibliographic list highlights) - The References section lists foundational and recent works cited in the paper, including methodological manuals, working papers, journal articles, and books across topics such as Dynare, foreign exchange intervention, integrated policy frameworks, sudden stops, macroprudential policy, exchange rate pass-through, and monetary policy in open economies. - Representative cited works include: - Adjemian et al. (2011): “Dynare: Reference Manual Version 4,” Dynare Working Papers 1, CEPREMAP. - Adler, Lisack, and Mano (2019): “Unveiling the effects of foreign exchange intervention: A panel approach,” Emerging Markets Review, 40, 1–1. - Adrian et al. (2020): “A Quantitative Model for the Integrated Policy Framework,” IMF Working Papers 2020/122. - Bianchi (2011): “Overborrowing and Systemic Externalities in the Business Cycle,” American Economic Review, 101, 3400–3426. - Blanchard et al. (2017b): “Are Capital Inflows Expansionary or Contractionary? Theory, Policy Implications, and Some Evidence,” IMF Economic Review, 65, 563–585. - Brandao-Marques et al. (2020): “Leaning Against the Wind: A Cost-Benefit Analysis for an Integrated Policy Framework,” IMF Working Papers 2020/123. - Gopinath et al. (2020): “Dominant Currency Paradigm,” American Economic Review, 110, 677–719. - Jeanne and Korinek (2010): “Excessive Volatility in Capital Flows: A Pigouvian Taxation Approach,” American Economic Review, 100, 403–407. - Svensson (2003): “Escaping from a Liquidity Trap and Deflation: The Foolproof Way and Others,” Journal of Economic Perspectives, 17, 145–166. - The references cover empirical studies, theoretical models, and policy discussions relevant to the Integrated Policy Framework and emerging-market external vulnerabilities. ### Appendix A. Extension with Behavioral Portfolio Investors - Model extension specification: - Portfolio flows are related to expected excess returns via Equation (A.1): - B^P,t_P^D,t_Y = ˆB^P,t_P^D,t_Y + b E_t{(1−τ^F,t) I_t − I^*_t ε_{t+1}/ε_t}, with b ≥ 0 and ˆB^P,t an exogenous component. - Baseline model obtained by setting b = 0. - Plugging (A.1) into financiers’ problem yields Equation (A.2): - (1−τ^F,t) I_t = E_t{I^*_t ε_{t+1}/ε_t} + Γ I_t ˆB^F,t_P^D,t_Y − Γ I_t b E_t{(1−τ^F,t) I_t − I^*_t ε_{t+1}/ε_t}, where ˆB^F,t = −B_t − ˆB^P,t + B^M,t. - Rearranged modified UIP condition (A.3): - (1−τ^F,t) I_t = E_t{I^*_t ε_{t+1}/ε_t} + Γ I_t/(1 + b Γ I_t) ˆB^F,t_P^D,t_Y. - Key implication: - Allowing portfolio flows to endogenously respond to return differentials (b > 0) effectively makes the FX market deeper, leaving other model blocks unchanged. ### Appendix B. Data - Sample composition (in line with IMF classification): two groups pursuing independent monetary policy, with either a managed or freely floating exchange rate. - AEs: Australia, Canada, Czechia, Germany, Iceland, Israel, Japan, Korea, New Zealand, Norway, Sweden, Switzerland, United Kingdom. - EMEs: Argentina, Brazil, Chile, China, Colombia, Hungary, India, Indonesia, Malaysia, Mexico, Peru, Philippines, Poland, South Africa, Thailand, Turkey. - Primary data definitions and sources (Table A.1): - Real Output: Gross Domestic Product at Constant Market Prices in Domestic Currency, Seasonally Adjusted — Haver Analytics - Nominal Output: Gross Domestic Product at Market Prices in Domestic Currency, Seasonally Adjusted — Haver Analytics - Nominal Gov. Cons.: Government Consumption Expenditures in Domestic Currency, Seasonally Adjusted — Haver Analytics - Inflation: Core Consumer Price Index Excluding Food and Energy — WEO database, Haver Analytics - Interest Rate: Monetary Policy Rate — Haver Analytics - Real Exchange Rate: JPMorgan Real Broad Effective Exchange Rate Index, PPI Based — Haver Analytics - Trade Balance: Net Nominal Exports — Haver Analytics - Net Foreign Assets: Net International Investment Position in Domestic Currency, Non-Seasonally Adjusted — Haver Analytics - FX Reserves: Foreign Currency Reserves in Domestic Currency — Haver Analytics - Coverage: - For most countries, the time series cover the period 2000Q1-2019Q4. - Additional data note: - Import content of domestic demand components reported in Table 1 computed using estimates from Bussiere et al. (2013). ### Appendix C. Moment Matching Results - Data transformations before moment calculation: - Log of real output → year-over-year differences. - Core inflation and interest rate → annualized percentage rates. - Log of real exchange rate detrended with a linear-quadratic trend. - Trade balance normalized by GDP. - Series multiplied by 100 to express in percent. - Fit assessment: - Unconditional second moments implied by the model compared to data medians for the group of EMEs listed in Appendix B. - Note: correlations are reported for interpretability, but the matching procedure uses covariances. - Table A.2. Moment Matching for the Foreign Economy (US) - Output: Data standard dev. 1.59; Model standard dev. 1.74. Data autocorr. 0.89; Model autocorr. 0.68. Data Output corr. 1.00; Model Output corr. 1.00. - Inflation: Data standard dev. 1.01; Model standard dev. 1.40. Data autocorr. 0.76; Model autocorr. 0.96. Data Output corr. 0.22; Model Output corr. 0.14. - Interest rate: Data standard dev. 2.75; Model standard dev. 2.74. Data autocorr. 0.99; Model autocorr. 0.91. Data Output corr. 0.29; Model Output corr. 0.15. - Table A.3. Moment Matching for the Home Economy (median EME) - Output: Data standard dev. 2.39; Model standard dev. 2.47. Data autocorr. 0.81; Model autocorr. 0.58. Data Output corr. Foreign 1.00; Model 1.00. Data Output corr. 0.46; Model 0.33. - Inflation: Data standard dev. 1.91; Model standard dev. 1.28. Data autocorr. 0.68; Model autocorr. 0.96. Data Output corr. Foreign −0.09; Model −0.03. Data Output corr. 0.13; Model 0.21. - Interest rate: Data standard dev. 2.01; Model standard dev. 2.21. Data autocorr. 0.94; Model autocorr. 0.90. Data Output corr. Foreign −0.13; Model 0.10. Data Output corr. 0.47; Model 0.31. - Real exchange rate: Data standard dev. 7.16; Model standard dev. 7.37. Data autocorr. 0.90; Model autocorr. 0.80. Data Output corr. Foreign −0.16; Model −0.04. - Trade balance: Data standard dev. 3.15; Model standard dev. 2.23. Data autocorr. 0.90; Model autocorr. 0.80. Data Output corr. Foreign −0.04; Model −0.22. - These comparisons provide an indication of how well the model reproduces key volatilities, autocorrelations, and cross-correlations observed in the data. ### Appendix D. Robustness Check: Optimized Policy Rules - Motivation: - Baseline simulations assume a Taylor-like rule (Equation (20)) with standard literature-calibrated feedback coefficients. Appendix D examines robustness to alternative, more optimized monetary policy rules that include a real exchange rate term. - Alternative monetary policy rule (Equation (A.4)): - I_t = I + ψ_π (Π^D,t − Π^D) + ψ_x (Y_t / Y^pot_t − 1) + ψ_q (Q_t−1). - Variant also considered where the exchange rate is replaced with the UIP premium. - Simulation findings: - Using the stochastic simulation setup in Section 6, both utility-based welfare and loss-function measures can significantly improve if the policy rate reacts more aggressively to inflation and the output gap, but not necessarily when it responds to the exchange rate or UIP premium. - Substantial gains are reported for a rule with ψ_π = 5. - However, an optimized rule with ψ_π = 5, ψ_x = 0.5, ψ_q = ψ_θ = 0 can elevate the frequency of financial stress periods. - Crucial robustness result: conclusions on the performance of FXI and CFM rules still hold. Sizable further gains are possible when these rules are used preemptively, but not when deployed exclusively during sudden stop episodes. - Table A.4. Evaluation of FXI and CFM under Aggressive Monetary Policy (selected entries) - Scenarios evaluated: Baseline model MP Only; Model with aggressive MP rule MP Only; FXI UIP Prem. Rule; CFM Rule; FXI Spread Rule. - Sudden Stop Probability: Baseline model 1.39; Model with aggressive MP rule 1.30; FXI UIP Prem. Rule 0.00; CFM Rule 0.64; FXI Spread Rule 1.38. - Financial Stress Probability: Baseline model 2.98; Model with aggressive MP rule 2.95; FXI UIP Prem. Rule 0.00; CFM Rule 1.40; FXI Spread Rule 3.05. - Borrowing Spread (mean): Baseline model 0.09; Model with aggressive MP rule 0.09; FXI UIP Prem. Rule 0.00; CFM Rule 0.05; FXI Spread Rule 0.09. - Output (mean): Baseline model −0.26; Model with aggressive MP rule −0.23; FXI UIP Prem. Rule −0.15; CFM Rule −0.22; FXI Spread Rule −0.23. - Output (std): Baseline model 2.10; Model with aggressive MP rule 1.55; FXI UIP Prem. Rule 1.33; CFM Rule 1.49; FXI Spread Rule 1.56. - Output (skewness): Baseline model −0.76; Model with aggressive MP rule −0.92; FXI UIP Prem. Rule −0.11; CFM Rule −0.77; FXI Spread Rule −0.90. - CPI Inflation (std): Baseline model 1.90; Model with aggressive MP rule 1.37; FXI UIP Prem. Rule 0.89; CFM Rule 1.34; FXI Spread Rule 1.38. - CPI Inflation (skewness): Baseline model 0.13; Model with aggressive MP rule 0.16; FXI UIP Prem. Rule 0.09; CFM Rule 0.16; FXI Spread Rule 0.15. - Real Exchange Rate (std): Baseline model 7.49; Model with aggressive MP rule 7.03; FXI UIP Prem. Rule 4.12; CFM Rule 6.87; FXI Spread Rule 7.04. - Welfare Gain Relative to Standard MP Rule: Baseline model 0.00; Model with aggressive MP rule 0.09; FXI UIP Prem. Rule 0.32; CFM Rule 0.23; FXI Spread Rule 0.09. - Loss Decrease Relative to Standard MP Rule: Baseline model 0.00; Model with aggressive MP rule 0.52; FXI UIP Prem. Rule 2.0974.58; CFM Rule 54.57; FXI Spread Rule 51.86. - Notes (as reported): - Output and real exchange rate are expressed as 100 times log. - Spread, probabilities and loss decrease are in percent. - Inflation is expressed as annualized percentage rate. - Welfare gain is expressed as permanent consumption equivalent, in percent. - Policy variants parameterizations: - (i) Standard MP Rule: ψ_π = 1.5, ψ_x = 0.0625, ψ_q = ψ_θ = 0; - (ii) Aggressive MP Rule: ψ_π = 5, ψ_x = 0.5, ψ_q = 0; - (iii) FXI UIP Premium Rule: ψ_m,1 = 0.5; - (iv) CFM Rule: ψ_f = 0.01; - (v) FXI Spread Rule: ψ_m,2 = 1. - Overall robustness conclusion: - The main conclusions about FXI and CFM effectiveness are robust to allowing a more aggressive (optimized) monetary policy rule; preemptive deployment of FXI and CFM yields sizable gains relative to using them only during sudden stops. *Source: A Quantitative Microfounded Model for the Integrated Policy Framework — Working Paper No. WP/21/292 (References and Appendices content unit).* --- _Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021292-print-pdf.pdf_