## IMF Working Paper wp17237 — 1. Introduction; Macroeconomic policies; Transmission; Calibration; Results; Welfare; Conclusions ## Source details **Canonical URL:** [IMF Working Paper wp17237 — 1. Introduction; Macroeconomic policies; Transmission; Calibration; Results; Welfare; Conclusions](https://www.imf.org/-/media/files/publications/wp/2017/wp17237.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2017/wp17237.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2017/wp17237.pdf.json) --- ### Overview and motivation - Over the last two decades central banks in both advanced and emerging economies resorted to unconventional policies that led to a steep expansion of their balance sheets. - Emerging market central banks amassed large foreign asset stocks via Foreign Exchange (FX) interventions since the mid-1990s. - Advanced-economy central banks expanded balance sheets via Quantitative Easing (QE) after the global financial crisis when interest rates reached the zero lower bound (ZLB). - Historical co-movements: - 1997-2007: sustained FX reserves accumulation coincided with increases in current account balances in emerging market economies. - 2007-2015: current account deficits in advanced economies narrowed while QE was deployed. - Key policy questions: - What are the effects of unconventional policies on the exchange rate and the current account? - Are these effects desirable globally? - How large are welfare gains from international policy cooperation? - Does the ZLB affect optimal implementation of unconventional policies? ### Modeling approach and experiment - Two-country DSGE model with asymmetric unconventional policy tools: - Home: FX intervention. - Foreign: QE. - Features: local currency pricing (LCP), incomplete asset markets, portfolio-balance effects from imperfect substitution between short-term and long-term bonds and between domestic and foreign bonds. - Numerical experiment: - Simulate a crisis: foreign country experiences a negative demand (preference) shock causing GDP decline of 1 percent. - Compare exchange rate dynamics and macro outcomes under: - Self-oriented (Nash) equilibrium. - Cooperative equilibrium. - Environments considered: - Normal times (positive nominal interest rates). - At the ZLB. ### Main qualitative findings - Normal times: - Cooperative equilibrium: moderate use of unconventional instruments; real exchange rate acts as shock absorber. - Nash equilibrium: active deployment of unconventional policies by both countries; limited real exchange rate adjustment. - At the ZLB: - Negative demand shock produces much larger output contraction since short-term policy rate cannot adjust. - Cooperative equilibrium: more aggressive unconventional policies and larger real exchange rate depreciation in the foreign country that accelerates recovery. - Nash equilibrium: limited exchange rate adjustment similar to normal times. - Welfare: welfare gains from international cooperation are quantitatively small. ### Contributions - Characterize cooperative and non-cooperative global outcomes with asymmetric unconventional policies (QE and FXI) at the ZLB. - Show exchange rate dynamics depend crucially on international policy cooperation: cooperative policies can produce large exchange rate adjustments that speed recovery without necessarily being “beggar-thy-neighbor.” ### Paper organization (as structured in source) - Section 2: model description. - Section 3: calibration. - Section 4: normal times results. - Section 5: ZLB results. - Section 6: welfare analysis. - Section 7: conclusions. ### Policy rules and government budget (model equations preserved) - Taylor-type short-term interest rate rule: - R_t / ̄R = [(P_t / P_{t−1})^{γ_π} (GDP_t / ̄GDP)^{γ_y}] (equation (20)) - ̄R and ̄GDP are steady state interest rate and GDP. - FX intervention rule: - F_t / ̄F = [(P_t / P_{t−1})^{θ_π} (GDP_t / ̄GDP)^{θ_y}] (equation (21)) - F_t = stock of FX reserves in foreign currency; ̄F = steady-state reserves. - QE (government control of real supply of long-term bonds): - (P_{L,t} B_{L,t}) / P_t = (̄P_L ̄B_L) [(P_t / P_{t−1})^{φ_π} (GDP_t / ̄GDP)^{φ_y}] (equation (22)) - Government budget constraint: - B_t + P_{L,t} B_{L,t} − S_t F_t = R_{t−1} B_{t−1} + (1 + κ P_{L,t}) B_{L,t−1} − S_t R^*_ {t−1} F_{t−1} + P_t G_t − T_t (equation (23)) - G_t = government consumption; T_t = total lump-sum taxes net of transfers (including seigniorage and profits from FX intervention and QE). - Fiscal reaction function for sustainable public debt: - T_t / P_t − G_t = Ψ( (P_{L,t−1} B_{L,t−1}) / P_{t−1} )^{φ_T} (equation (24)) - φ_T > 0 and Ψ > 0. ### Aggregation and equilibrium conditions (selected identities) - Final goods market-clearing: - Y_t = ω_u C_{u,t} + (1−ω_u) C_{r,t} + G_t + I_t (equation (25)) - GDP definition: - GDP_t ≡ ∫_0^1 Y_t(h) dh (equation (28)) - Domestic bond aggregation: - B_t = ω_u B_{u,t}, B_{L,t} = ω_u B_{u,L,t} + (1−ω_u) B_{r,L,t} (equation (31)) - Balance of payments identity (aggregated foreign short-term and long-term bonds D_t and D_{L,t}): - ( S_t D_t + S_t P^*_{L,t} D_{L,t} + S_t F_t ) = ( S_t P_{H^*,t} Y_{H^*,t} − P_{F,t} Y_{F,t} + S_t R^*_{t−1} Θ_t D_{t−1} + S_t P^*_{L,t} R^*_{L,t} Θ_{L,t} D_{L,t−1} + S_t R^*_{t−1} F_t ) (equation (32)) - Endogenous risk premiums and transaction costs: - Θ_t = Θ(D_t, D_{L,t}), Θ_{L,t} = Θ_L(D_t, D_{L,t}) (equation (33)) - (1 + η_t) = Θ^η( P_{L,t} B_{L,t}, S_t P^*_{L,t} B^*_{L,t} ) (equation (34)) - Parameters Θ_1, Θ_2, Θ_{L,1}, Θ_{L,2}, Θ^η_1, Θ^η_2 jointly control QE and FX intervention effects. ### Transmission mechanism of unconventional policies - General: FXI and QE operate via portfolio-balance effects due to imperfect asset substitutability; Wallace neutrality does not hold. - FX intervention (FXI): - Central bank purchases short-term foreign bonds and sells short-term domestic bonds. - Endogenous risk premium Θ_t makes borrowing cost increase with foreign debt, preventing full household offset. - Real effects: increase in Net Foreign Asset position; nominal exchange rate depreciation; higher inflation; improved current account; higher output. - Quantitative Easing (QE): - Central bank purchases domestic long-term bonds, reducing supply to private sector and interacting with government budget constraint (equation (23)). - Financial friction: transaction costs (1 + η_t) depend positively on private holdings of long-term bonds; QE lowers transaction costs. - Real effects: lower transaction costs and term premium; expansion in consumption, investment, output, and inflation; nominal exchange rate depreciation via widening long-term interest rate differentials. ### Calibration — key parameter values and targets (selected) - Frequency: quarterly. - Discount factors: - β_u = 0.995 - β_r = 0.993 - Steady state real interest rates targeted: short-term 2% per annum; long-term 2.75% per annum. - Long-term bond duration parameter κ set to match duration of 30 quarters. - Asset market segmentation: ω_u = 0.50. - Elasticities and structural parameters: - σ_w = 6, ε_p = 11. - Steady-state government expenditures over GDP = 0.25. - Home bias: α_Y = α^*_Y = 0.7. - Elasticity substitution home-foreign goods: η_Y = η^*_Y = 0.9. - Capital depreciation δ = 0.025 per quarter. - Investment adjustment cost μ_S = 2.5. - Capital share α = 0.36. - Calvo price-setting: θ_H = θ^*_F = 0.75. - Wage rigidity: θ_w = θ^*_w = 0.75. - Frisch elasticity: 1/φ = 1. - Taylor rule coefficients: γ_π = 1.5 and γ_y = 0.5. - Fiscal rule parameter: φ_T = 1.5. - Persistency of preference shock χ_t: AR(1) coefficient 0.95. - Calibrated elasticities for risk premiums and transaction costs: - Θ_1 = 0.035 - Θ_2 = 0.035 - Θ_{L,1} = 0.040 - Θ_{L,2} = 0.060 - Θ^η_1 = 0.011 - Θ^η_2 = 0.005 - Θ^*_η,1 = 0.011 - Θ^*_η,2 = 0.005 - QE calibration targets and empirical anchors: - A 1 percent of GDP long-term bond purchase ⇒ reduction of 15 basis points in domestic term premium. - International spillover: 1 percent of GDP QE reduces foreign term premium by 9 basis points. - A 1 percent of GDP QE depreciates the exchange rate by 0.4 percent. - Empirical anchor: during QE1 long-term US rates declined by 90-100 basis points and exchange rate depreciated 3.5 to 8 percent (contextual empirical references in source). - FX intervention calibration targets: - A 1 percent of GDP accumulation of FX reserves ⇒ exchange rate depreciation of 2 percent. - Improves current account around 0.4 percent of GDP. ### Unconventional policies in normal times — spillovers (persistent shock 0.9) - Foreign QE (1 percent of GDP): - Foreign direct effects: - Term premium falls; QE boosts aggregate demand. - Short-term nominal interest rate increases via Taylor response. - Capital outflows from term-premium compression → real exchange rate depreciation → modest current account improvement. - Home effects: - Expenditure shifting raises home GDP initially. - Expenditure switching (capital inflows to home) ⇒ exchange rate appreciation → lowers home output, inflation, and short-term nominal interest rate. - Under calibration used: expenditure shifting dominates initially; expenditure switching lowers home output after two quarters. - Home FX intervention (1 percent of GDP): - Domestic effects: real exchange rate depreciation; higher output, current account, and nominal interest rate. - International spillovers: chiefly expenditure switching → negative effects on foreign economy (appreciation, declines in foreign current account, output, and short-term nominal interest rate). ### Cooperative vs. Nash equilibria in normal times (negative foreign demand shock: foreign GDP −1 percent) - Baseline (no unconventional policies): - Foreign: reduction in short-term interest rate, small real exchange rate depreciation, modest current account improvement; negative spillovers to home (declines in output, interest rates, current account, small appreciation). - Cooperative equilibrium (global welfare maximization): - Foreign QE ≈ 1 percent of GDP (expansion). - Home FX reserves decline by 2 percent of GDP (sale). - Foreign outcomes: real exchange rate depreciation of 4 percent; current account increase of 0.6 percent of GDP; smaller output decline and more stable nominal interest rates. - Home outcome: larger output decline (global-optimal sharing of recession costs). - Nash equilibrium (each country maximizes own welfare): - Foreign QE = 5 percent of GDP. - Home accumulates FX reserves by 3 percent of GDP. - Outcomes: current account stabilized; small appreciation in foreign country; home largely insulated; foreign slower recovery due to limited exchange rate adjustment. - Key qualitative contrast: - Cooperative equilibrium achieves larger external adjustment (exchange rate depreciation) in the shock-hit foreign country supporting faster recovery. - Nash equilibrium features competitive use of unconventional policies that limit exchange rate adjustment and worsen recession in affected country. ### Unconventional policies at the ZLB — spillovers (summary) - QE of 1 percent of GDP at the ZLB in foreign country: - Impact on foreign output on impact: 0.3 percent (noted as "two times larger than in the normal times scenario"). - Mechanism: nominal interest rate pinned at zero; aggregate demand expansion raises inflation → decline in real rates → additional output boost. - Decline in real rate induces real exchange rate depreciation and current account improvement in foreign country. - Home country when foreign conducts QE at ZLB: - Short-term home output expands from higher world demand; after four quarters exchange rate appreciation reduces output. - Increased home activity raises real interest rate, appreciates real exchange rate, and lowers current account. - FX intervention by home of 1 percent of GDP when foreign at ZLB: - Induces capital flows into foreign → foreign real exchange rate appreciates; foreign output and inflation decline. - Foreign nominal interest rate stuck at ZLB: decline in inflation raises foreign real interest rate → additional contraction in foreign output. - Foreign current account "does not change significantly" (appreciation effect offset by import compression). - Home output declines relative to normal times as foreign demand declines at the ZLB; lower home interest rates trigger a larger depreciation. - Net: FX intervention at the ZLB lowers output in both foreign (via higher real interest rates) and home (via negative spillovers). - Negative demand shock at ZLB: - Foreign output contraction exacerbated since real rate is higher relative to normal times; induces real exchange rate appreciation and decline in current account. - Spillovers to home are magnified: home experiences real exchange rate depreciation and a small current account improvement. ### Cooperative and Nash equilibria at the ZLB - Cooperative equilibrium at ZLB: - Foreign recession deeper; cooperative policy requires larger real exchange depreciation and external adjustment. - Supported by larger expansionary QE in foreign relative to normal times and larger sale of FX reserves by home. - Nash equilibrium at ZLB: - Competitive use of unconventional policies yields limited real exchange rate adjustment and lower foreign output growth. - Both countries engage in competitive devaluations; external adjustment limited. - Summary: "Under the ZLB international policy spillovers are magnified." Qualitatively similar to normal times: cooperative equilibrium → significant external adjustment in foreign economy; Nash equilibrium → limited external adjustment. ### Welfare gains from international policy cooperation (numerical results from Table 2; normalized) - Normal times (A). Welfare losses associated with the negative demand shock (normalized to 1 in scenario with no unconventional policies; world economy welfare loss under that scenario is 0.02 percent of steady state consumption): - 1. Baseline Scenario: Home Country -0.25 | Foreign Country -1.75 | World -1.00 - 2. Nash Equilibrium: Home Country -0.18 | Foreign Country -1.35 | World -0.74 - 3. Cooperative Equilibrium: Home Country -0.27 | Foreign Country -1.09 | World -0.68 - 4. Gains from Cooperation (3-2): Home Country -0.09 | Foreign Country 0.26 | World 0.07 - At the ZLB (B): - 1. Baseline Scenario at ZLB: Home Country -0.58 | Foreign Country -4.85 | World -2.70 - 2. Nash Equilibrium: Home Country -0.02 | Foreign Country -0.45 | World -0.20 - 3. Cooperative Equilibrium: Home Country -0.03 | Foreign Country -0.21 | World -0.16 - 4. Gains from Cooperation (3-2): Home Country -0.01 | Foreign Country 0.24 | World 0.04 - Interpretation: - Nash (self-oriented) unconventional policies yield welfare gains close to cooperative equilibrium (consistent with Obstfeld and Rogoff (2002)). - Welfare gains from international cooperation remain quantitatively small even at the ZLB. ### Conclusions and suggested research avenues - Cooperative equilibrium: moderate unconventional instrument use and real exchange rate depreciation as shock absorber. - Nash equilibrium: more intensive unconventional policy use with largely stabilized real exchange rate. - At the ZLB: intensity of unconventional policies and exchange rate adjustment are magnified. - Welfare gains from international policy cooperation are small. - Suggested further research: - Consider high exchange rate pass-through or foreign currency liabilities in corporate sector (could increase costs of exchange rate movements and lead to more aggressive cooperative policies). - Investigate role of business cycle synchronization: greater synchronization may reduce differences between cooperative and self-oriented policies, lowering scope for exchange rate adjustment. *Source: wp17237 (IMF Working Paper).* ### 1. Introduction ....................................................................................................... ### 1. Introduction ### Overview and motivation - Over the last two decades, central banks in both advanced and emerging economies resorted to unconventional policies with the objective of stabilizing their business cycles, leading to a steep expansion of their balance sheets. - Since the mid-1990s central banks in emerging market economies amassed a large stock of foreign assets as a result of Foreign Exchange (FX) interventions. - In advanced economies, central banks expanded their balance sheets by conducting Quantitative Easing (QE) in response to the global financial crisis, once interest rates reached the zero lower bound (ZLB). - The expansion of central banks’ balance sheets through unconventional policies coincided with notable adjustments in current accounts and real exchange rates: - During the period of sustained FX reserves accumulation (1997-2007), emerging market economies experienced an increase in their current account balances. - In the aftermath of the global financial crisis (2007-2015), the current account deficits in advanced economies narrowed while central banks were deploying QE measures. - Key policy questions posed: - What are the effects of unconventional policies on the exchange rate and the current account? - Are these desirable from a global standpoint? - How big are the welfare gains from international policy cooperation? - Does the ZLB affect the optimal implementation of unconventional policies? ### Modeling approach and experiment - Model framework: - A two-country DSGE model extending Christiano et al. (2005), Smets and Wouters (2007), and Chen et al. (2012) to a two-country setting with asymmetric unconventional policy tools. - Home country relies on FX intervention; foreign country deploys QE. - Features: local currency pricing (LCP), incomplete asset markets, portfolio-balance effects from imperfect substitution between short-term and long-term bonds and between domestic and foreign bonds. - Numerical experiment: - Simulate a crisis scenario in which the foreign country experiences a negative demand shock resulting in a decline of GDP by 1 percentage point. - Analyze exchange rate dynamics and macroeconomic outcomes under self-oriented (Nash) and cooperative equilibria in: - Normal times (positive nominal interest rates). - At the ZLB. ### Main findings (normal times vs. ZLB) - Normal times (positive nominal interest rates): - Cooperative equilibrium entails a moderate use of unconventional policy instruments. - The real exchange rate plays its traditional role of shock absorber. - Nash equilibrium: both countries engage actively in unconventional policies, leading to a limited adjustment of the real exchange rate. - At the ZLB: - A negative demand shock generates a much larger output contraction as the short-term policy rate is unable to adjust to domestic economic conditions. - Cooperative equilibrium entails a more aggressive use of unconventional policies and a larger real exchange rate depreciation in the foreign country that accelerates the recovery. - Nash equilibrium at the ZLB features limited exchange rate adjustment, similar to the normal times scenario. - Welfare implications: - The welfare gains from international policy cooperation are found to be quantitatively small (consistent with Obstfeld and Rogoff (2002)). ### Contributions to the literature - Two main contributions: 1. Characterize cooperative and non-cooperative global outcomes with asymmetric unconventional policies (QE and FX intervention) at the ZLB. 2. Demonstrate that exchange rate dynamics depend crucially on the degree of international policy cooperation: - Cooperative unconventional policies can produce large exchange rate adjustments that speed recovery in the shock-affected country. - Large exchange rate movements do not necessarily imply “beggar-thy-neighbor” policies; they can reflect desirable external adjustment that improves global welfare. ### Paper organization - Section 2: Description of the two-country model. - Section 3: Calibration strategy. - Section 4: Results of optimal unconventional policies in normal times. - Section 5: Results at the ZLB. - Section 6: Welfare analysis. - Section 7: Conclusions and discussion of key findings. *Source: wp17237 - 1. Introduction (IMF Working Paper).* ### 2.6 Macroeconomic policies ### 2.6 Macroeconomic policies ### Policy rules and government budget - Short-term interest rate follows a Taylor-type rule: - R_t / ̄R = [(P_t / P_{t−1})^{γ_π} (GDP_t / ̄GDP)^{γ_y}] (equation (20)) - ̄R and ̄GDP are the steady state interest rate and GDP. - FX intervention rule: - F_t / ̄F = [(P_t / P_{t−1})^{θ_π} (GDP_t / ̄GDP)^{θ_y}] (equation (21)) - F_t is the stock of FX reserves denominated in the foreign currency; ̄F is steady-state reserves. - Government control of real supply of long-term bonds (QE rule): - (P_{L,t} B_{L,t}) / P_t = (̄P_L ̄B_L) [(P_t / P_{t−1})^{φ_π} (GDP_t / ̄GDP)^{φ_y}] (equation (22)) - ̄P_L ̄B_L is steady state real market value of long-term bonds. - Government budget constraint: - B_t + P_{L,t} B_{L,t} − S_t F_t = R_{t−1} B_{t−1} + (1 + κ P_{L,t}) B_{L,t−1} − S_t R^*_ {t−1} F_{t−1} + P_t G_t − T_t (equation (23)) - G_t is government consumption; T_t are total lump-sum taxes net of transfers (including seigniorage and profits from FX intervention and QE). - Interpretation: market value of government debt net of FX reserves equals total deficit (servicing cost of maturing bonds minus income from FX reserves plus government spending net of taxes). - Fiscal reaction function to ensure sustainable public debt: - T_t / P_t − G_t = Ψ( (P_{L,t−1} B_{L,t−1}) / P_{t−1} )^{φ_T} (equation (24)) - φ_T > 0 and Ψ > 0. ### 2.7 Aggregation and equilibrium conditions - Final goods market-clearing: - Y_t = ω_u C_{u,t} + (1−ω_u) C_{r,t} + G_t + I_t (equation (25)) - Intermediate goods market-clearing (home and foreign varieties): - Y_t(h) = Y_{H,t}(h) + Y_{H^*,t}(h) (equation (26)) - Y_t(f) = Y_{F,t}(f) + Y_{F^*,t}(f) (equation (27)) - GDP definition: - GDP_t ≡ ∫_0^1 Y_t(h) dh (equation (28)) - Labor and capital market clearing: - L_t = ∫_0^1 L_t(h) dh (equation (29)) - K_t = ∫_0^1 K_t(h) dh (equation (30)) - Domestic short-term and long-term bond equilibrium: - B_t = ω_u B_{u,t}, B_{L,t} = ω_u B_{u,L,t} + (1−ω_u) B_{r,L,t} (equation (31)) - Balance of payments identity (aggregated foreign short-term and long-term bonds D_t and D_{L,t}): - ( S_t D_t + S_t P^*_{L,t} D_{L,t} + S_t F_t ) = ( S_t P_{H^*,t} Y_{H^*,t} − P_{F,t} Y_{F,t} + S_t R^*_{t−1} Θ_t D_{t−1} + S_t P^*_{L,t} R^*_{L,t} Θ_{L,t} D_{L,t−1} + S_t R^*_{t−1} F_t ) (equation (32)) - Endogenous risk premiums (imperfect substitutability): - Θ_t = Θ(D_t, D_{L,t}), Θ_{L,t} = Θ_L(D_t, D_{L,t}) (equation (33)) - Partial derivatives denoted Θ_1, Θ_2, Θ_{L,1}, Θ_{L,2}. - Transaction costs (depend on long-term bond stocks home and abroad): - (1 + η_t) = Θ^η( P_{L,t} B_{L,t}, S_t P^*_{L,t} B^*_{L,t} ) (equation (34)) - Elasticities of transaction costs: Θ^η_1 and Θ^η_2. - Parameters Θ_1, Θ_2, Θ_{L,1}, Θ_{L,2}, Θ^η_1, and Θ^η_2 jointly control QE and FX intervention effects domestically and internationally. ### 2.8 Transmission Mechanism of Unconventional Policies ### Overview - Both FX intervention and QE operate through portfolio balance effects arising from imperfect asset substitutability. - Wallace neutrality benchmark: in frictionless markets, open market operations are neutral (households offset central bank asset swaps), implying no real effects. - With imperfect substitutability, central bank asset purchases alter private sector portfolios and produce real effects. ### 2.8.1 Foreign Exchange Intervention (FXI) - Mechanism: - Central bank purchases short-term foreign bonds and sells short-term domestic bonds. - Endogenous risk premium in foreign debt (Θ_t) implies cost of borrowing increases with foreign debt size, preventing full household offset of central bank transactions. - Real effects: - Increase in Net Foreign Asset position. - Nominal exchange rate depreciation. - Higher inflation. - Improved current account. - Higher output. ### 2.8.2 Quantitative Easing (QE) - Mechanism: - Central bank purchases domestic long-term bonds, reducing supply available to private sector (interacts with government budget constraint, equation (23)). - Financial friction: transaction costs (1 + η_t) depend positively on private holdings of long-term bonds; expansionary QE lowers those transaction costs. - Real effects: - Lower transaction costs and term premium. - Expansion in consumption, investment, output, and inflation. - Via interest rate parity, QE leads to nominal exchange rate depreciation through widening long-term interest rate differentials. ### 3 Calibration — key parameter values and targets - Frequency: quarterly; standard literature values used. - Discount factors: - β_u = 0.995 for unrestricted households. - β_r = 0.993 for restricted households. - Targets: steady state short-term and long-term real interest rates equal to 2% and 2.75% per annum, respectively. - Long-term bond duration parameter κ set to match duration of 30 quarters (consistent with 10-year US Treasury secondary market). - Asset market segmentation: ω_u = 0.50 (half of households unrestricted). - Elasticities and structural parameters: - σ_w = 6, ε_p = 11. - Steady-state government expenditures over GDP = 0.25. - Home bias: α_Y = α^*_Y = 0.7. - Elasticity substitution home-foreign goods: η_Y = η^*_Y = 0.9. - Capital depreciation δ = 0.025 per quarter (implies annual depreciation of capital equal to 10 percent). - Investment adjustment cost μ_S = 2.5. - Capital share α = 0.36. - Calvo price-setting: θ_H = θ^*_F = 0.75 (average price duration of 4 quarters). - Wage rigidity: θ_w = θ^*_w = 0.75 (average wage duration of 4 quarters). - Frisch elasticity: 1/φ = 1. - Taylor rule coefficients: γ_π = 1.5 and γ_y = 0.5 (consistent with Taylor (1993)). - Fiscal rule parameter: φ_T = 1.5 (as in Chen et al. (2012)). - Persistency of preference shock χ_t: AR(1) with coefficient 0.95. - Calibrated elasticities for risk premiums and transaction costs: - Θ_1 = 0.035 - Θ_2 = 0.035 - Θ_{L,1} = 0.040 - Θ_{L,2} = 0.060 - Θ^η_1 = 0.011 - Θ^η_2 = 0.005 - Θ^*_η,1 = 0.011 - Θ^*_η,2 = 0.005 - QE calibration targets: - A 1 percent of GDP long-term bond purchase implies a reduction of 15 basis points in domestic term premium. - International spillover: 1 percent of GDP QE reduces foreign term premium by 9 basis points. - A 1 percent of GDP QE depreciates the exchange rate by 0.4 percent. - Empirical anchor: during QE1 long-term US rates declined by 90-100 basis points and exchange rate depreciated 3.5 to 8 percent (contextual empirical references in source). - FX intervention calibration targets: - A 1 percent of GDP accumulation of FX reserves depreciates the exchange rate by 2 percent. - Improves current account around 0.4 percent of GDP. - Empirical context: comparable studies find increases in FX reserves of 1 percent of GDP increase current account about 0.5 percent. ### 4 Unconventional Policies in Normal Times ### 4.1 Spillovers from Unconventional Policies (exogenous process, persistency 0.9) - QE in foreign country: purchase of 1 percent of GDP of domestic long-term bonds (foreign QE). - Direct effects in foreign country: - Term premium falls; QE boosts aggregate demand. - Short-term nominal interest rate increases (Taylor rule response to higher output and inflation). - Capital outflows induced by term-premium compression → real exchange rate depreciation → modest current account improvement. - Effects in home country: - Two opposing forces: - Expenditure shifting (global demand increases) → home GDP expands initially. - Expenditure switching (capital flows into home → exchange rate appreciation) → lowers home output, inflation, and nominal short-term interest rate. - For parametrization used: expenditure shifting initially dominates; expenditure switching leads to lower home output after two quarters. - FX intervention in home country: accumulation of FX reserves equal to 1 percent of GDP. - Domestic effects: - Real exchange rate depreciation. - Higher output, current account, and nominal interest rate. - International spillovers: - Operates mainly via expenditure switching → negative effects on foreign economy: foreign appreciation, decline in foreign current account, output, and nominal short-term interest rate. ### 4.2 Cooperative and Nash equilibria (policy rules optimized per equilibrium) - Negative foreign demand shock scenario: foreign GDP declines by 1 percent due to a negative preference shock χ_t. - Baseline (no unconventional policies): foreign country sees reduction in short-term interest rate, small real exchange rate depreciation, modest current account improvement; negative spillovers to home country (declines in domestic output, interest rates, current account, and small appreciation). - Cooperative equilibrium (global welfare maximization): - Foreign QE expands by about 1 percent of GDP. - Home country FX reserves decline by 2 percent of GDP. - Outcomes in foreign country: - Real exchange rate depreciation of 4 percent. - Current account increase of 0.6 percent of GDP. - Smaller output decline and more stable nominal interest rates. - Home country experiences larger output decline (global-optimal sharing of recession costs). - Nash equilibrium (each country maximizes own welfare taking other’s reaction as given): - Foreign QE of 5 percent of GDP. - Home country accumulates FX reserves by 3 percent of GDP. - Outcomes: - Current account stabilized; small appreciation in foreign country. - Home country largely insulated from external shock. - Foreign country experiences slower recovery; limited exchange rate adjustment aggravates recession there. - Key distinction: - Cooperative equilibrium: larger external adjustment (exchange rate depreciation) in shock-hit country supports faster recovery. - Nash equilibrium: competitive use of unconventional policies limits exchange rate adjustment and worsens recession in affected country. ### 5 Unconventional Policies at the ZLB - The source introduces that the next section analyzes unconventional policies when the foreign country reaches the ZLB. - Structure: - First sub-section: transmission mechanism and spillovers assuming exogenous processes. - Second sub-section: characterization of cooperative and Nash equilibria of unconventional policies at the ZLB. *Source: wp17237 - 2.6 Macroeconomic policies (pdf chapter).* ### 5.1 Spillovers from Unconventional Policies at the ZLB ### 5.1 Spillovers from Unconventional Policies at the ZLB ### QE at the ZLB: foreign country shock and cross-border spillovers - A QE stimulus of 1 percent of GDP in the foreign country at the ZLB: - Effect on foreign output on impact: 0.3 percent (red line). - This effect is "two times larger than in the normal times scenario." - Mechanism: nominal interest rate pinned at zero while aggregate demand expands → inflation rises → decline in real rates → additional boost to output. - The decline in real interest rate induces a real exchange rate depreciation and an improvement in the current account balance in the foreign country. - Home country response when foreign country conducts QE at the ZLB: - Short-term output expansion from increased world demand, but after four quarters exchange rate appreciation reduces output. - Increased activity in the home country induces a higher real interest rate, a real exchange rate appreciation, and a decline in the current account balance. ### Foreign exchange intervention (FXI) when foreign country is at the ZLB - Home country accumulates FX reserves by 1 percent of GDP: - Induces capital flows into the foreign country; foreign real exchange rate appreciates; foreign output and inflation decline. - Because the foreign nominal interest rate cannot go below the ZLB, the decline in inflation raises the foreign real interest rate → induces additional contraction in foreign output. - Foreign current account balance response: "does not change significantly" because the negative effect from appreciation is offset by import compression. - Home country effects: - Output in the home country declines relative to the normal times scenario as foreign demand declines at the ZLB. - Lower interest rates in the home country trigger a larger depreciation. - Net: FX intervention at the ZLB leads to lower output in both the foreign country (via higher real interest rates) and the home country (via negative spillovers). ### Negative demand shock when foreign country is at the ZLB - Impact on foreign output is exacerbated at the ZLB: - With nominal interest rate fixed at zero, the real rate is higher relative to normal times, inducing real exchange rate appreciation and a decline in the current account balance. - Spillovers to the home country are magnified relative to normal times: - As the real interest rate increases in the foreign country, the home country experiences a real exchange rate depreciation and a small improvement of the current account balance. ### 5.2 Cooperative and Nash Equilibria at the ZLB ### Equilibrium dynamics when foreign country hits the ZLB - Cooperative equilibrium: - Foreign recession is deeper at the ZLB, therefore cooperative equilibrium requires a larger real exchange depreciation and external adjustment to stabilize foreign output. - Supported by a larger expansionary QE policy in the foreign country relative to normal times and a larger sale of FX reserves in the home country. - Nash equilibrium: - Both countries compete in the use of unconventional policies, resulting in limited real exchange rate adjustment and lower output growth in the foreign country. - Both countries engage in competitive devaluations; external adjustment is limited. - Summary statement: - "Under the ZLB international policy spillovers are magnified." Qualitatively similar results to normal times: cooperative equilibrium → significant external adjustment in foreign economy; Nash equilibrium → limited external adjustment. ### 6 Welfare Gains from International Policy Cooperation ### Key welfare findings (Table 2) - Normal times (A) — welfare losses associated with the negative demand shock are sizable and greater for the foreign country (shock origin). - Nash equilibrium (self-oriented unconventional policies) reduces welfare losses relative to no unconventional policies as countries partially stabilize their economies. - Cooperative equilibrium entails a trade-off: foreign country better off (exchange rate depreciation cushions shock), home country worse off than in Nash; world welfare higher in cooperative equilibrium as costs are shared. - Welfare gains from cooperation are "quantitatively small." - At the ZLB in the foreign country (B) — welfare costs of a negative demand shock become significantly larger for both home and foreign countries. - In the Nash equilibrium, both economies are "highly effective" in stabilizing their economies with unconventional policies; welfare losses reduced significantly. - Expansionary unconventional policies at the ZLB increase inflation and reduce the real interest rate, providing additional demand boost. - As in normal times, welfare gains from cooperation remain quantitatively small. - Quantitative values from Table 2 (normalized to 1 in the scenario of a negative demand shock and no unconventional policies; world economy welfare loss under that scenario is 0.02 percent of steady state consumption): - A. Unconventional Policies in Normal Times - 1. Baseline Scenario: Home Country -0.25 | Foreign Country -1.75 | World -1.00 - 2. Nash Equilibrium: Home Country -0.18 | Foreign Country -1.35 | World -0.74 - 3. Cooperative Equilibrium: Home Country -0.27 | Foreign Country -1.09 | World -0.68 - 4. Gains from Cooperation (3-2): Home Country -0.09 | Foreign Country 0.26 | World 0.07 - B. Unconventional Policies at the ZLB - 1. Baseline Scenario at ZLB: Home Country -0.58 | Foreign Country -4.85 | World -2.70 - 2. Nash Equilibrium: Home Country -0.02 | Foreign Country -0.45 | World -0.20 - 3. Cooperative Equilibrium: Home Country -0.03 | Foreign Country -0.21 | World -0.16 - 4. Gains from Cooperation (3-2): Home Country -0.01 | Foreign Country 0.24 | World 0.04 ### Interpretation - Unconventional policies implemented in a self-oriented (Nash) fashion yield welfare gains close to those obtained under the cooperative equilibrium (consistent with Obstfeld and Rogoff (2002)). - Welfare gains from international cooperation remain small even at the ZLB. ### 7 Conclusions - Cooperative equilibrium features moderate use of unconventional instruments and real exchange rate depreciation as shock absorber. - Nash equilibrium features more intensive deployment of unconventional policies and a largely stabilized real exchange rate. - At the ZLB, intensity of unconventional policies and exchange rate adjustment are magnified. - Welfare gains from international policy cooperation are small. - Suggested avenues for future research noted in the text: - Consider high exchange rate pass-through or foreign currency liabilities in the corporate sector (could increase costs of exchange rate movements and lead to more aggressive unconventional policies in cooperative equilibrium). - Investigate the role of business cycle synchronization: as cycles become more synchronized, optimal unconventional policies under cooperative and self-oriented regimes could converge, reducing scope for exchange rate adjustment. *Source: IMF Working Paper — section "5.1 Spillovers from Unconventional Policies at the ZLB" (wp17237).* --- _Source: https://www.imf.org/-/media/files/publications/wp/2017/wp17237.pdf_