## wpiea2020097-print-pdf ## Source details **Canonical URL:** [wpiea2020097-print-pdf](https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020097-print-pdf.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2020/english/wpiea2020097-print-pdf.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2020/english/wpiea2020097-print-pdf.pdf.json) --- ### Introduction - Motivation and central questions: - Over the last two decades central banks in emerging economies have increasingly operated within an inflation targeting framework and relied on multiple instruments to achieve policy mandates. - Two central policy questions addressed: - Are multiple instruments typically used by central banks complements or substitutes to the monetary policy rate? - What is the optimal policy mix for addressing fluctuations in capital flows and the associated macroeconomic volatility? - Objective: - Characterize the optimal FX reserves and reserve requirements policies, relying on a conventional loss function. ### Model framework and policy instruments - Model overview: - Small open-economy DSGE model with financial frictions. - Financial frictions via a Bernanke et al. (1999) financial accelerator and partial liability dollarization (fraction  domestic, 1 foreign). - Central bank instruments: - Monetary policy rate. - Foreign Exchange Intervention (FXI). - Reserve requirements (rr_t). - Shocks analyzed: - External shock: increase in the foreign interest rate R̃_t. - Domestic shock: increase in entrepreneurs' idiosyncratic risk ε!;t (modeled as in Christiano et al. (2014)). ### Entrepreneurs and the financial accelerator - Loan currency composition and constraints: - Domestic debt and foreign debt split: B_e;t =   B_e;t; E_t B' _e;t = (1)  B_e;t; 1 is degree of dollarization. - Entrepreneur budget constraint: N_t + B_e;t + E_t B' _e;t = Q_t K_{t+1} (equation (6)). - Idiosyncratic risk and returns: - log(!_{t+1}) ~ Normal(mean m_{!;t}, sd _{!;t}); m_{!;t} = _{!;t}^2/2 ensures E[!_{t+1}] = 1. - Ex-post return: !_{t+1} R_{K;t+1} = !_{t+1} Z_{t+1} + (1) Q_{t+1}/Q_t (equation (7)). - Monitoring, default, and zero-profit intermediation: - Intermediaries verify realization at cost proportional to investment income:  !_{t+1} R_{K;t+1} Q_t K_{t+1},  ∈ (0,1). - Default cutoff !_{t+1} determined by equation (9). - Zero-profit condition for intermediaries accounts for reserve requirement rr_t and monitoring losses (equation (11)). - Credit spread and leverage: - Effective credit spread sp_{t+1} defined by equation (12) and increasing in leverage Q_t K_{t+1} / N_t: sp_{t+1} = _t( Q_t K_{t+1} / N_t ); '_t(·) > 0 (equation (13)). - Net worth dynamics and entry/exit: - Survival rate e, entrants with initial wealth w_e. - N_t = e _t(!_t) R_{K;t} Q_{t-1} K_t + w_e (equation (14)). - Reserve requirements and opportunity costs: - Reserves earn no interest; reserve requirement rule responds to credit spread: - rr_t rr = [ rr_{t-1} rr ] _{rr} (sp_{t-1})^{_{rr}}. ### Aggregation, equilibrium conditions, and endogenous risk premium - Aggregation and market clearing: - Aggregates: D_t = ∫_0^1 D_t(j), D̃_t = ∫_0^1 D̃_t(j), B_t = ∫_0^1 B_t(j), B̃_t = ∫_0^1 B̃_t(j) (equation (21)). - Reserve implication: D_t (1 − rr_t) = B_e;t and D̃_t (1 − rr_t) = B̃_e;t (equation (22)). - Labor and capital aggregation: l_t (equation (23)), K_t (equation (24)). - Final home good equilibrium: Y_H;t = C_H;t + C_e;H;t + I_H;t + C̃_H;t + µ [ ∫_0^{µ!_{t+1}} f_t(!) d! ] (R K_{t+1} / Q_t K_{t+1}) (equation (25)). - Balance of payments / net foreign assets: - E_t (F̃_t − B̃_t) = R̃_{t−1} E_t F̃_{t−1} − ρ_t E_t B̃_{t−1} + X_t − M_t (equation (28)). - Endogenous risk premium ρ_t: - ρ_t = ρ(B̃_t, B_t / E_t) determines asset substitution between domestic and foreign bonds. - Elasticities calibrated: %1 = 0.01, %2 = 0.035. ### Calibration (quarterly) — key parameter values and steady-state targets - Discount factor: β = 0.9975 (steady state risk-free rate of 1 percent). - Preferences: σ_C = 1.00; σ_L = 2.00. - Consumption/investment import shares and elasticities: - C_import_share = 0.30; σ_C_import_domestic = 0.5. - I_import_share = 0.30; σ_I_import_domestic = 0.5. - Share of imported goods matches average import-GDP ratio of 27 percent (WEO 2000-2018). - Financial accelerator and entrepreneurs: - Credit spread in SS = 1.035 (annual terms). - Default premium in SS = 0.03 (annual terms). - Capital-Networth ratio = 2.00; survival rate e = 0.975. - Liability dollarization and reserve requirement: θ = 0.50; rr = 0.06. - Capital and steady-state ratios: - Capital share α = 0.5; I/Y = 0.20; (X − M)/Y = 0.01; steady-state FX reserves F̃ = 0.25 of output. - Nominal rigidities and monetary policy: - Calvo parameters: ϑ_L = ϑ_H = ϑ_F = 0.75. - Indexation = 0.0. - Substitution elasticities: ϵ_L = 6.0; ϵ_H = 11.0; ϵ_F = 11.0. - Taylor rule coefficients: ϕ_i = 0.70; ϕ_π = 1.5; ϕ_y = 0.5/4 = 0.125. - Persistence: ρ_R̃ = 0.95; ρ_{ε!} = 0.95. - Risk-premium elasticities: %1 = 0.01; %2 = 0.035. ### Shock experiments, optimized rules, and parameter results - Objective: minimize loss L = var(y_t) + var(π_t) subject to a specific shock. - Two shocks: (i) foreign interest rate R̃_t; (ii) entrepreneurs' risk ε!;t. - Three instrument scenarios per shock: - Only monetary policy rate (baseline). - Monetary policy + optimized reserve requirement rule (foreign reserves constant). - Monetary policy + optimized reserve requirement + optimized FXI rule (both instruments optimized). - Selected optimized rule parameters (reported): - For R̃_t shocks: - Only RR rule: ζ_rr = 0.81, ξ_rr = −6.00. - Both rules: ζ_fx = 0.99, ξ_fx = −6.36, ζ_rr = 0.91, ξ_rr = −0.29. - For ε!;t shocks: - Only RR rule: ζ_rr = 0.00, ξ_rr = −0.89. - Both rules: ζ_fx = 0.00, ξ_fx = −23.11, ζ_rr = 0.00, ξ_rr = −0.89. - Note on restrictions: - For only RR rule need ξ_rr ≥ −6 for unique RE equilibrium. - Only FXI rule coefficients (reported): ζ_fx = 0.99, ξ_fx = 12.52 for foreign interest rate shocks; ζ_fx = 0.00, ξ_fx = −39.30 for risk shocks. ### Quantitative responses and policy insights — foreign interest rate shock (1 percent) - Baseline (only policy rate): - Exchange rate: nominal and real depreciation. - Trade balance: improvement. - Inflation: upward pressure via import prices. - Output and investment: decline; credit spread widens. - Policy dilemma: inflation rises while GDP and investment fall → policy rate increases. - Adding only optimized reserve requirement: - Partial attenuation of output and inflation effects. - Reserve requirement loosening stimulates output and inflation in same direction — limited when facing high inflation and low output. - Partial stabilization in medium term. - Adding both optimized FXI and reserve requirement: - Large stabilization gains: sell FX reserves to contain exchange rate pressure + moderate reduction in rr to stabilize output. - Contraction in GDP and investment greatly attenuated. - Depreciation less intense → inflation tamed → smaller rise in policy rate. - Credit spread increase moderated. - Aggregate capital outflows partially contained; trade balance increases less than baseline. - FXI used more intensely relative to rr in this shock. - Predicted small loss in FX reserves (about 2 percent of GDP) for the calibrated shock; larger shocks could deplete reserves (non-negativity constraints noted). ### Quantitative responses and policy insights — risk shock (8 percent ε!;t) - Baseline (only policy rate): - Higher default probability → higher credit spread → investment and aggregate demand fall → GDP falls. - Trade balance improves and exchange rate depreciates. - Short-run inflation falls then rises after a few quarters. - Policy rate initially declines then increases. - Adding only optimized reserve requirement: - Substantial macroeconomic stabilization achieved. - rr used intensively; FX reserve sales moderate. - Combination largely stabilizes investment, output, and inflation → smaller trade balance adjustment and net capital outflows. - Smaller reduction in policy rate required and gradual normalization later. - Adding both optimized FXI and reserve requirement: - Minor additional gains over rr alone. - Policy principle: - Optimal policy mix depends on shock origin: FXI leads for foreign interest rate shocks; rr leads for domestic risk shocks. - Reserve requirements and FXI are complementary to the policy rate and help stabilize activity, inflation, and financial conditions. ### Extensions: differentiated reserve requirements and capital flow tax - Differentiated rr (foreign and domestic currency): - Modify equations (11) and (12) to include rr^d_t and rr'_t. - Reserve requirement rules specified as autoregressive rules responsive to sp. - Optimized coefficients (Table 4 reported rows): - R^*_t row: 0.00 -1.95 0.63 -1.35 0.99 -0.19 - ψ_!;t row: 0.00 -4.20 0.00 -0.37 0.00 -1.51 - Macroeconomic impacts: output stabilization with differentiated rr is quantitatively indistinguishable from uniform rr baseline. - For foreign interest rate shocks: differentiated rr allows tolerating slightly larger exchange rate depreciation to boost short-run output without additional foreign-currency balance-sheet effects. - FXI remains the leading response to foreign interest rate shocks; rr used more intensively for risk shocks. - Capital flow tax (ζ_{kf;t}): - Effective foreign interest rate becomes R'_t-1 (1 + ζ_{kf;t-1})^{-1}. - Capital flow tax rule (exact functional form preserved) links ζ_{kf;t} to RER dynamics. - Optimized coefficients (Table 6 reported rows): - R^*_t row: 0.99 -0.23 0.91 -0.29 - ψ_!;t row: 0.00 -0.84 0.00 -0.89 - Capital flow tax reacts by reduction when RER depreciates after a rise in R̃_t or ε!;t. - Equivalence: allocation from FXI policies and capital flow tax implementation are exactly the same in the model. ### Summary of macroeconomic gains across regimes (Table 7 — exact values) - For shocks in R^'_t: - No additional instruments: Var(π) 7.26 Var(y) 110.94 Loss 118.20 - Rule for RR only: Var(π) 3.10 Var(y) 24.90 Loss 27.99 - Rule for FXI only: Var(π) 0.72 Var(y) 15.38 Loss 16.10 - Rules for RR and FXI: Var(π) 0.29 Var(y) 4.19 Loss 4.48 - Expanded rules for RR and FXI: Var(π) 0.09 Var(y) 1.17 Loss 1.26 - Rules for diff. RR and FXI: Var(π) 0.26 Var(y) 1.88 Loss 2.15 - Rules for RR and cap. flow tax: Var(π) 0.29 Var(y) 4.19 Loss 4.48 - For shocks in ψ_!;t: - No additional instruments: Var(π) 2.73 Var(y) 61.91 Loss 64.64 - Rule for RR only: Var(π) 0.07 Var(y) 1.04 Loss 1.11 - Rule for FXI only: Var(π) 2.44 Var(y) 27.81 Loss 30.25 - Rules for RR and FXI: Var(π) 0.07 Var(y) 0.99 Loss 1.06 - Expanded rules for RR and FXI: Var(π) 0.05 Var(y) 0.29 Loss 0.34 - Rules for diff. RR and FXI: Var(π) 0.06 Var(y) 0.88 Loss 0.94 - Rules for RR and cap. flow tax: Var(π) 0.07 Var(y) 0.99 Loss 1.06 - Key takeaways from loss comparisons: - Simple policy rules for FXI and rr that target one variable deliver substantial stabilization gains relative to relying only on monetary policy. - Expanding rule targets or differentiating rr yields marginal additional gains beyond baseline optimized FXI and rr rules. - Combining rr with FXI or with a capital flow tax delivers essentially identical macroeconomic stabilization. - rr is more effective against risk shocks; FXI or capital flow tax are more effective against foreign interest rate shocks. *Source: wpiea2020097-print-pdf — IMF working paper content as provided.* ### 1. Introduction ....................................................................................................... ### 1. Introduction ### Motivation and central questions - Over the last two decades central banks in emerging economies have increasingly operated within an inflation targeting framework and relied on multiple instruments to achieve policy mandates. - Two central policy questions addressed: - Are multiple instruments typically used by central banks complements or substitutes to the monetary policy rate? - What is the optimal policy mix for addressing fluctuations in capital flows and the associated macroeconomic volatility? ### Model framework (overview) - A small open-economy DSGE model with financial frictions is developed to provide quantitative answers to the above questions. - Financial frictions are incorporated through: - A financial accelerator mechanism proposed by Bernanke et al. (1999). - Liability dollarization: a fraction of corporate debt is denominated in foreign currency (following Gertler et al. (2007) and Cespedes et al. (2004)). - The central bank in the model uses three policy instruments: - The monetary policy rate. - Foreign Exchange Intervention (FXI). - Reserve requirements. - Shocks analyzed: - An external shock: increase in the foreign interest rate. - A domestic shock: increase in the risk of the idiosyncratic productivity of entrepreneurs (risk shock modeled as in Christiano et al. (2014)). - Objective: characterize the optimal FX reserves and reserve requirements policies, relying on a conventional loss function. ### Transmission, trade-offs, and role of instruments - Capital outflows generate trade-offs between output and inflation stabilization: - Exchange rate depreciation raises inflation and increases the cost of servicing foreign-currency debt, lowering investment. - Monetary tightening can stabilize the exchange rate but also lowers asset prices, weakening firm balance sheets and reducing investment and demand (Cespedes et al., 2004). - Complementary roles of additional tools: - FX intervention can stabilize the exchange rate and reduce the cost of servicing foreign-currency debt, improving firm balance sheets. - Expansionary macroprudential measures (e.g., reduction in reserve requirements) can lower the cost of credit, stimulate investment and foreign borrowing, and reduce FX pressures. - The model produces allocation of instruments that directly target exchange rate volatility and disruptions in financial markets, allowing the policy rate to focus on price stability. ### Main results (key findings) - Two key results: - For both types of shocks, FXI and reserve requirements are complementary tools to the monetary policy rate; they help stabilize economic activity, inflation, and financial conditions. - The intensity of deployment of each instrument depends on the shock source (extending Poole (1970)): - For a foreign interest rate shock: FXI plays the leading role, followed by modest adjustments in reserve requirements and the policy rate. - For domestic risk shocks: reserve requirements lead the response, accompanied by modest FXI interventions and policy rate adjustments. - These results provide a rationale for a multi-tool policy framework in environments with financial frictions common in emerging economies. - The findings synthesize Mundell (1968) ("policies should be paired with the objectives on which they have the most influence") and Poole (1970) (optimal intensity depends on disturbance source). ### Relationship to literature and scope - Builds on literature analyzing optimal policies under financial frictions: - Monetary policy and liability dollarization: Cespedes et al. (2004), Gertler et al. (2007). - Interaction of monetary and macroprudential policy: Carrillo et al. (2018), Leduc and Natal (2016), Medina and Roldós (2018), Aoki et al. (2018). - Interaction between FXI and monetary policy: Ghosh et al. (2016), Benes et al. (2015), Canzoneri and Cumby (2014), Liu and Spiegel (2015). - Focuses on business-cycle implications of capital flows (as in Blanchard et al. (2017)): - Short-run capital outflows can contract output and raise inflation, posing challenges to central bank mandates. - The analysis complements literature on long-run effects (e.g., Lucas (1990)) and on pecuniary externalities and capital controls (e.g., Bianchi (2011); Jeanne and Korinek (2010)), by addressing short-run management of capital flows via a loss-function approach (Woodford, 2003). ### Paper organization (brief) - Section 2: model specification — small open economy with financial frictions. - Section 3: calibration strategy. - Section 4: simulations and optimal choice of policy instruments for managing capital flows. - Section 5: concluding remarks. *Source: wpiea2020097-print-pdf — 1. Introduction* ### 2.4 Entrepreneurs ### 2.4 Entrepreneurs ### Financial accelerator and loan currency composition - The external finance premium follows Bernanke et al. (1999) and depends positively on entrepreneursí leverage. - Debt contracts are partially dollarized: a fraction  of the loan is denominated in domestic currency and 1 is denominated in foreign currency. Hence: - B_e;t =   B_e;t - E_t B' _e;t = (1)  B_e;t - 1 is the degree of dollarization of loans. - Entrepreneur budget/financing constraint (period t): - N_t + B_e;t + E_t B' _e;t = Q_t K_{t+1} (equation (6)) - Adjustment cost of investment satisfies: S(1) = 1, S'(1) = 0, S''(1) = _S < 0 (see Altig et al. (2005)). ### Production, idiosyncratic risk, and returns - Each entrepreneur faces idiosyncratic risk !_{t+1} affecting effective capital: !_{t+1} K_{t+1}. - Distributional assumptions for !_{t+1}: - log(!_{t+1}) is normal with mean m_{!;t} and standard deviation _{!;t}. - Imposing m_{!;t} = _{!;t}^2/2 ensures E[!_{t+1}] = 1 and stdev = _{!;t}. - _{!;t} follows AR(1) with autoregressive coefficient _{}! and innovations "_{;t} ~ N(0, _{}!). - Ex-post return to entrepreneur in t+1: - !_{t+1} R_{K;t+1} = !_{t+1} Z_{t+1} + (1) Q_{t+1}/Q_t (equation (7)) ### Asymmetric information, monitoring costs, and default cutoff - Only entrepreneurs observe !_{t+1}; intermediaries can verify realization at cost proportional to investment income:  !_{t+1} R_{K;t+1} Q_t K_{t+1}, with  ∈ (0,1). - Debt instruments: - Domestic debt gross interest R_{L;t+1} - Foreign debt gross interest R'_{L;t+1} - Effective interest rate for the loan: -  R_{L;t+1} =  R_{L;t+1} + (1) E_{t+1} E_t R'_{L;t+1} (equation (8)) - Default: entrepreneurs default if !_{t+1} < !_{t+1}, where the cutoff satisfies: - !_{t+1} R_{K;t+1} Q_t K_{t+1} =  R_{L;t}  B_{e;t} =  R_{L;t+1} (Q_t K_{t+1} N_t) (equation (9)) - Upon default, intermediary recovers fraction 1 of revenue (monitoring losses ). ### Net expected benefits to entrepreneurs and zero-profit for intermediaries - Net expected benefits for entrepreneurs: - ∫_{!_{t+1}}^1 ! R_{K;t+1} Q_t K_{t+1} f_t(!) d!  R_{L;t}  B_{e;t} ∫_{!_{t+1}}^1 f_t(!) d! - Simplifies to: _t(!_{t+1}) R_{K;t+1} Q_t K_{t+1} (equation (10)) - Functions f(·) and (·) reflect variation over time of entrepreneurs' risk _{!;t}. - Zero-profit condition for competitive financial intermediaries (accounting for reserve requirement rr_t and monitoring losses): - [  R_t + (1) E_{t+1} E_t R' _t ] (Q_t K_{t+1} N_t)/(1rr_t) =  R_{L;t}  B_{e;t} ∫_{!_{t+1}}^1 f_t(!) d! + (1) R_{K;t+1} Q_t K_{t+1} ∫_0^{!_{t+1}} f_t(!) d! - Rearranged form: - _t(!_{t+1}) R_{K;t+1} Q_t K_{t+1} (equation (11)) - Subindexing in f(·) and (·) denotes dependence on _{!;t}. ### Credit spread, leverage, and the financial accelerator - Definition of effective credit spread sp_{t+1} (external finance premium): - sp_{t+1} = R_{K;t+1}/(1rr_t) / [  R_t + (1) E_{t+1} E_t R' _t ] = _t(!_{t+1}) (equation (12)) - Here _t(·) = (_t(·) _t(·) 0_t(·) _t(·))^{-1}. - With log-normal !_{t+1}, credit spread sp_{t+1} is increasing in entrepreneurs' leverage Q_t K_{t+1} / N_t: - sp_{t+1} = _t( Q_t K_{t+1} / N_t ); '_t(·) > 0 (equation (13)) - Dependence on _{!;t}: _t(·) = (·; _{!;t}). ### Entrepreneurs' net worth dynamics and entry/exit - Survival and entry: - A fraction e of entrepreneurs survives each period; 1e exit and consume all wealth. - New entrants enter with initial real net wealth w_e. - Evolution of net worth: - N_t = e _t(!_t) R_{K;t} Q_{t-1} K_t + w_e (equation (14)) - Consumption of exiting entrepreneurs: - C_{e;t} = (1e) _t(!_t) R_{K;t} Q_{t-1} K_t / P_{C;t} (equation (15)) ### Financial intermediaries, reserve requirements, and opportunity costs - Intermediaries face a time-varying reserve requirement rr_t (macroprudential regulation following Leduc and Natal (2018)); reserves earn no interest. - Opportunity cost of intermediaries to lend funds (for a given rr_t): - Domestic currency: R_t = (1rr_t) - Foreign currency: R' _t = (1rr_t) - Uniform reserve rate assumed across currencies (note: section 5 relaxes to differentiated reserve requirements). - The reserve requirement rule responds to credit spread: - rr_t rr = [ rr_{t-1} rr ] _{rr} (sp_{t-1})^{_{rr}} - rr is the steady state reserve requirement; _{rr} controls reaction degree to sp_{t-1}; _{rr} determines persistence. *Source: wpiea2020097-print-pdf - 2.4 Entrepreneurs (https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020097-print-pdf.pdf)* ### 2.7 Aggregation and equilibrium conditions ### 2.7 Aggregation and equilibrium conditions ### Market clearing and aggregation conditions - Aggregate holdings (integrals over j in [0,1]): - D_t = ∫_0^1 D_t(j) - D̃_t = ∫_0^1 D̃_t(j) - B_t = ∫_0^1 B_t(j) - B̃_t = ∫_0^1 B̃_t(j) (equation (21)) - Reserve requirement implication for financial intermediaries (equilibrium): - D_t (1 − rr_t) = B_e;t and D̃_t (1 − rr_t) = B̃_e;t (equation (22)) - Labor and capital market aggregation: - l_t = [ ∫_0^1 l_t(j)^(L−1) dj ]^(1/(L−1)) = ∫_0^1 l_t(z_H) dz_H (equation (23)) - K_t = ∫_0^1 K_t(z_H) dz_H (equation (24)) - Final home good equilibrium: - Y_H;t = C_H;t + C_e;H;t + I_H;t + C̃_H;t + µ [ ∫_0^{µ!_{t+1}} f_t(!) d! ] (R K_{t+1} / Q_t K_{t+1}) (equation (25)) - Exports of final domestic goods specification: - C̃_H;t = θ̃ [ (P_H;t / E_t P̃_t)^(−η̃) ] C̃_t (equation (26)) - θ̃ is the share of domestic goods in foreign agents' consumption basket; η̃ is the price elasticity. ### Foreign goods market and balance of payments - Foreign goods market equilibrium: - Y_F;t = C_F;t + C_e;F;t + I_F;t = [ ∫_0^1 Y_F;t(z_F)^(F−1) dz_F ]^(1/(F−1)) (equation (27)) - Balance of payments / net foreign assets dynamics (combined household, entrepreneur, government budgets): - E_t (F̃_t − B̃_t) = R̃_{t−1} E_t F̃_{t−1} − ρ_t E_t B̃_{t−1} + X_t − M_t (equation (28)) - Exports and imports: - X_t = P_H;t C̃_H;t - M_t = E_t P̃_F;t ∫_0^1 Y_F;t(z_F) dz_F ### Endogenous risk premium and asset substitution - Endogenous risk premium ρ_t governs degree of asset substitution between domestic and foreign bonds and thus the transmission of FX intervention (FXI). - In perfect asset substitution (ρ_t = 1) accumulation of FX reserves financed by increased supply of domestic bonds is fully offset by households borrowing abroad. - Specification: ρ_t = ρ(B̃_t, B_t / E_t) - Elasticities defining imperfect asset substitution: - ∂ρ/∂B̃_t · (B̃_t / ρ(·)) = %1 - ∂ρ/∂(B_t / E_t) · ((B_t / E_t) / ρ(·)) = %2 - Calibrated values: %1 = 0.01, %2 = 0.035 ### Calibration (quarterly frequency) — key parameter values and steady-state targets - Discount factor: - β = 0.9975 (steady state risk-free rate of 1 percent) - Preferences: - σ_C = 1.00 (intertemporal substitution elasticity) - σ_L = 2.00 (inverse of the labor supply elasticity; Frisch elasticity = 1/2) - Consumption and investment baskets: - C_import_share = 0.30 - σ_C_import_domestic = 0.5 (substitution elasticity between domestic and imported goods in consumption) - I_import_share = 0.30 - σ_I_import_domestic = 0.5 - Share of imported goods matches average import-GDP ratio of 27 percent (WEO 2000-2018) - Financial accelerator and entrepreneurs: - Credit spread in SS = 1.035 (annual terms) - Default premium in SS = 0.03 (annual terms) - Capital-Networth ratio of entrepreneurs = 2.00 - Survival rate of entrepreneurs e = 0.975 - Liability dollarization and reserve requirement: - Degree of liability dollarization θ = 0.50 - Reserve requirement in steady state rr = 0.06 - Capital and steady-state ratios: - Capital share α = 0.5 - Investment-output ratio I/Y = 0.20 - Net export-output ratio (X − M)/Y = 0.01 (steady state target) - Export size parameter θ̃ chosen to yield net exports = 1 percent - Steady-state FX reserves share: F̃ = 0.25 of output - Nominal rigidities and monetary policy: - Calvo parameters: ϑ_L = ϑ_H = ϑ_F = 0.75 (average duration of optimized wages and prices = 4 quarters) - Indexation to past inflation in wages and prices: 0.0 - Substitution elasticities across varieties: - ϵ_L = 6.0 - ϵ_H = 11.0 (H varieties) - ϵ_F = 11.0 (F varieties) - Taylor rule coefficients: - ϕ_i = 0.70 (smoothing) - ϕ_π = 1.5 (reaction to inflation) - ϕ_y = 0.5/4 = 0.125 (reaction to output) - Persistence: - ρ_R̃ = 0.95 (foreign interest rate shocks) - ρ_{ε!} = 0.95 (risk shocks) - Parameters for risk-premium elasticities: - %1 = 0.01 - %2 = 0.035 ### Optimized rules and shock experiments — setup - Objective: minimize loss L = var(y_t) + var(π_t) subject to a specific shock. - Two shocks analyzed: - (i) foreign interest rate R̃_t - (ii) entrepreneurs' risk ε!;t - Three instrument scenarios per shock: - Only monetary policy rate (baseline) - Monetary policy + optimized reserve requirement rule (foreign reserves constant) - Monetary policy + optimized reserve requirement + optimized FXI rule (both instruments optimized) - Optimized rule parameters (Table 2): (Only RR rule | Both rules) - For R̃_t shocks: - ζ_rr = 0.81, ξ_rr = −6.00 | ζ_fx = 0.99, ξ_fx = −6.36, ζ_rr = 0.91, ξ_rr = −0.29 - For ε!;t shocks: - ζ_rr = 0.00, ξ_rr = −0.89 | ζ_fx = 0.00, ξ_fx = −23.11, ζ_rr = 0.00, ξ_rr = −0.89 - Note on restrictions: - For only RR rule need to restrict ξ_rr ≥ −6 to guarantee unique RE equilibrium. - For only FXI rule operating the coefficients obtained: ζ_fx = 0.99, ξ_fx = 12.52 for foreign interest rate shocks and ζ_fx = 0.00, ξ_fx = −39.30 for risk shocks. ### Quantitative results and policy insights - Responses to a 1 percent increase in foreign interest rate R̃_t: - Baseline (only policy rate): - Exchange rate: nominal and real depreciation - Trade balance: improvement (capital outflows manifest as improved trade balance) - Inflation: upward pressure via import prices - Output and investment: decline (financial accelerator and partial dollarization widen credit spread) - Policy dilemma: inflation rises while GDP and investment fall → policy rate increases to stabilize inflation - Adding only optimized reserve requirement: - Partial attenuation of effects on output and inflation - Reserve requirement loosening stimulates output and inflation in same direction — limited power when facing high inflation and low output - Partial stabilization in medium term - Adding both optimized FXI and reserve requirement: - Large stabilization gains: selling FX reserves to contain exchange rate pressure + moderate reduction in reserve requirement to stabilize output - Contraction in GDP and investment greatly attenuated - Depreciation less intense → inflation tamed → smaller rise in policy rate - Credit spread increase moderated - Aggregate capital outflows partially contained; trade balance increases less than baseline - FXI is used more intensely relative to reserve requirement in this shock - For a foreign interest rate shock, the model predicts a small loss in FX reserves (about 2 percent of GDP) for the calibrated shock; larger shocks could deplete reserves (note regarding non-negativity constraints) - Responses to an 8 percent risk shock (ε!;t): - Baseline (only policy rate): - Higher entrepreneur default probability → higher credit spread → investment and aggregate demand fall → GDP falls - Trade balance improves (demand contraction) and exchange rate depreciates - Short-run inflation falls (demand effect dominates), but rises after a few quarters - Policy rate initially declines then increases - Adding only optimized reserve requirement: - Substantial macroeconomic stabilization achieved (contrast with foreign interest rate shock) - Reserve requirement is used more intensively; FX reserve sales are moderate - Combination largely stabilizes investment, output, and inflation → smaller trade balance adjustment and net capital outflows - Smaller reduction in policy rate required and gradual normalization later on - Adding both optimized FXI and reserve requirement: - Some minor additional gains over reserve requirement alone - Policy principles emerging: - Reserve requirements and FXI are critical for dealing with capital outflows; they can largely stabilize output and inflation. - Optimal policy mix depends on shock origin: - Foreign financial condition shocks (foreign interest rate): FXI plays leading role. - Domestic risk shocks (entrepreneur risk): reserve requirement response is key. - Policymakers should not rely on the same instruments irrespective of the shock origin. ### Model extensions and robustness checks - Three extensions evaluated: - Expanded rules: allow FXI and reserve requirements to react simultaneously to real exchange rate (RER) and financial spread (sp). - Expanded rule functional forms include persistence and responses to RER and sp. - Table 3 optimized parameters for expanded rules: - For R̃_t: ζ_fx = 0.98, ξ_fx = −0.01, φ_fx = −5.89, ζ_rr = 0.99, ξ_rr = −0.07, φ_rr = 0.00 - For ε!;t: ζ_fx = 0.00, ξ_fx = −51.82, φ_fx = −3.46, ζ_rr = 0.00, ξ_rr = −0.69, φ_rr = 0.00 - Impulse responses under expanded rules are similar to single-target rules; most stabilization gains are obtained by conditioning reserve requirement and FXI on one target variable (Mundell principle). - Differentiated reserve requirement ratios for foreign and domestic currency borrowing (considered, details not restated here). - Capital flow tax scenario (central bank can manage outflows via a capital flow tax; considered, details not restated here). *Source: IMF working paper chapter section 2.7 (aggregation and equilibrium conditions), calibration and policy experiment results as presented in the source PDF.* ### 5.2 Reserve requirement di§erentiated in foreign and domes- ### 5.2 Reserve requirement differentiated in foreign and domestic currency ### Model extension and key equations - The model economy is partially dollarized; the central bank can deploy differentiated reserve requirements for domestic and foreign currency borrowing. - Equations (11) and (12) are modified to incorporate differentiated reserve requirements: - R_t [1 - rr^d_t] + (1 - ε) E_{t+1}/E_t R'_t [1 - rr'_t] = - τ_t (μ!_{t+1}) R^K_{t+1} Q_t K_{t+1} sp_{t+1} = R^K_{t+1} - ε R_t [1 - rr^d_t] + (1 - ε) E_{t+1}/E_t R'_t [1 - rr'_t] = ζ_t (μ!_{t+1}) - rr^d_t and rr'_t are the reserve requirements for deposits in domestic and foreign currency, respectively. - The FXI rule specification remains the same as equation (19) (in the source). - Reserve requirement rules for each currency are specified as autoregressive rules with responsiveness to the price of sovereign paper (sp): - rr^d_t: rr^d_t = [ rr^d_{t-1} ]^{ζ_rr^d} (sp_{t-1})^{ζ_rr^d} - rr'_t: rr'_t = [ rr'_{t-1} ]^{ζ_rr'} ( - sp'_{t-1} )^{ζ_rr'} - (Exact functional notation preserved from source.) ### Optimized rules and parameters (Table 4) - Table 4 reports the optimized coefficients for differentiated reserve requirements and FXI. - Optimized coefficients (as reported): - R^*_t row: 0.00 -1.95 0.63 -1.35 0.99 -0.19 - ψ_!;t row: 0.00 -4.20 0.00 -0.37 0.00 -1.51 - The optimized coefficients indicate differences between domestic and foreign currency reserve requirements according to the type of shock simulated. ### Macroeconomic impacts and comparisons - Figure 6 (referenced in source) shows output stabilization achieved by relying on differentiated reserve requirements is quantitatively indistinguishable from the baseline case of a uniform reserve requirement. - For a foreign interest rate shock: - Differentiated reserve requirements allow the central bank to tolerate a slightly larger exchange rate depreciation, which helps boost output in the short run. - This additional exchange rate depreciation is allowed without triggering additional balance sheet effects in foreign currency borrowing. - In this extension, FXI takes the leading role in responding to foreign interest rate shocks while reserve requirements are used more intensively in the case of risk shocks. ### Capital flow tax (Section 5.3) — rule specification and equivalence - A capital flow tax affects the effective cost of borrowing for households by modifying the household budget constraint: the effective foreign interest rate becomes R'_t-1 (1 + ζ_{kf;t-1})^{-1}, where ζ_{kf;t-1} is the capital flow tax on foreign debt issued in period t-1. - Reserve requirement rule follows equation (21) (in the source). The capital flow tax rule is specified as: - [1 + ζ_{kf;t}] / [1 + ̄ζ_{kf}] = [1 + ζ_{kf;t-1}] / [1 + ̄ζ_{kf}]^{ζ_kf} ( RER_t / RER_{t-1} )^{ζ_kf} - (Exact functional notation preserved from source.) - Optimized coefficients for capital flow tax and reserve requirement (Table 6): - R^*_t row: 0.99 -0.23 0.91 -0.29 - ψ_!;t row: 0.00 -0.84 0.00 -0.89 - Table 6 highlights the optimal response features a reduction in the capital flow tax when the real exchange rate depreciates in response to a rise in the foreign interest rate or in domestic risk. - The exact reaction of the capital flow tax to the real exchange rate depends on the type of shock, resembling results obtained when using FXI. - Figure 7 (referenced in source) shows that the allocation derived from implementing FXI policies and the ones obtained from the capital flow tax are exactly the same, consistent with the equivalence result in the literature. ### Summary of macroeconomic gains across regimes (Table 7) - Table 7: Macroeconomic variances and loss function in each regime and shock (values reported exactly). - For shocks in R^'_t: - No additional instruments: Var(π) 7.26 Var(y) 110.94 Loss 118.20 - Rule for RR only: Var(π) 3.10 Var(y) 24.90 Loss 27.99 - Rule for FXI only: Var(π) 0.72 Var(y) 15.38 Loss 16.10 - Rules for RR and FXI: Var(π) 0.29 Var(y) 4.19 Loss 4.48 - Expanded rules for RR and FXI: Var(π) 0.09 Var(y) 1.17 Loss 1.26 - Rules for diff. RR and FXI: Var(π) 0.26 Var(y) 1.88 Loss 2.15 - Rules for RR and cap. flow tax: Var(π) 0.29 Var(y) 4.19 Loss 4.48 - For shocks in ψ_!;t: - No additional instruments: Var(π) 2.73 Var(y) 61.91 Loss 64.64 - Rule for RR only: Var(π) 0.07 Var(y) 1.04 Loss 1.11 - Rule for FXI only: Var(π) 2.44 Var(y) 27.81 Loss 30.25 - Rules for RR and FXI: Var(π) 0.07 Var(y) 0.99 Loss 1.06 - Expanded rules for RR and FXI: Var(π) 0.05 Var(y) 0.29 Loss 0.34 - Rules for diff. RR and FXI: Var(π) 0.06 Var(y) 0.88 Loss 0.94 - Rules for RR and cap. flow tax: Var(π) 0.07 Var(y) 0.99 Loss 1.06 - Key takeaways from the loss-function comparisons: - Simple policy rules for FXI and reserve requirements featuring one target achieve substantial improvement in macroeconomic stabilization relative to the case where only monetary policy operates. - Expanding rule targets or introducing differentiated reserve requirements can reduce the loss function, but additional gains are marginal relative to the baseline optimized rules for FXI and reserve requirement. - Relying only on reserve requirement or FXI as an additional instrument also provides benefits; simultaneous use of FXI and reserve requirement tends to provide the largest gains. - Combining reserve requirement with FXI or capital flow tax delivers exactly the same macroeconomic stabilization. - Reserve requirements are more effective against risk shocks than for foreign interest rate shocks, whereas FXI or capital flow tax are more effective to deal with foreign interest rate shocks. *Source: wpiea2020097-print-pdf (5.2 Reserve requirement differentiated in foreign and domestic currency and related sections).* --- _Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020097-print-pdf.pdf_