## wpiea2024038-print-pdf - 2.1 Normative Advice ## Source details **Canonical URL:** [wpiea2024038-print-pdf - 2.1 Normative Advice](https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024038-print-pdf.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2024/english/wpiea2024038-print-pdf.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2024/english/wpiea2024038-print-pdf.pdf.json) --- ### Normative role of the IPF diagram - Mundell-Fleming is positive; IS curve uses reduced-form behavioral consumption and Keynesian cross; it typically assumes restoring pre-shock home output and trade balance is desirable but does not justify that objective. - IPF fills the normative gap by: - Incorporating optimization (maximization of welfare subject to a resource constraint). - Focusing on policymaker’s perspective and economy-wide welfare. - Basing intervention rationale on externalities not internalized by the private sector (aggregate demand externality from price stickiness; pecuniary externalities in housing). - Showing how each policy tool affects welfare along different dimensions and leaving trade-offs for judgment. - IPF preserves insight that the exchange rate plays a key role in the open economy while replacing IS-LM money-market diagram with an intertemporal, optimization-based presentation. ### Policy tools and additions relative to Mundell-Fleming - Monetary policy tool: policy rate (reaction function determines macro stability) rather than fixed money supply; LM curve upward-sloping interpretation abandoned. - Additional tools incorporated: - Sterilized FX intervention - Capital controls (capital inflow taxes/subsidies) - Domestic macroprudential measures (taxes on domestic debt transactions) - Fiscal policy: excluded from first two model-building steps, included in third step; empirical motivation is that EMDEs frequently use the non-monetary tools to manage capital flows; fiscal policy matters mainly after large shocks. ### Financial frictions added by IPF - IPF introduces frictions tied to currency denomination of debts: - Imperfect capital mobility / limited arbitrage in FX market → premium spikes. - Occasionally-binding external borrowing constraints → sudden stops. - Occasionally-binding domestic borrowing constraints → domestic credit crunches. - Borrowing constraints bind only after large shocks. - IPF links use of tools to impacts on the economy’s intertemporal budget constraint (omitted in Mundell-Fleming). --- ### IPF without financial frictions (first-step summary) - Only friction: price stickiness; no financial frictions. - Yields a visual intertemporal New Keynesian framework where monetary policy stabilizes home output gap under floating regime or implements a peg under fixed regime. - Diagram converts equations into curves and explains shifts in textual bullets. --- ### Model overview, structure, and tools ### Microfoundations and assumptions (first-step specification) - Based on Basu et al. (2023) with financial frictions turned off. - Households optimize across goods; price stickiness and dominant currency assumptions: - Imports and exports of produced tradable goods have sticky prices set in dollars. - Domestically-sold part of home-produced tradable goods: sticky local currency prices. - Nontradable housing services: flexible local currency rents. - Exports of commodity endowments: flexible dollar prices. - Under assumptions: depreciation raises relative price of imports to home goods → expenditure switching from imports to home goods; exports unchanged (dollar price/quantities fixed). - Financial intermediation chain: global financiers → domestic banks → domestic private sector (no frictions in this channel for first step). - Tools available: - FX intervention (circumvent intermediaries) - Capital controls (taxes on capital inflows at border, φ_1) - Domestic macroprudential measures (taxes on household domestic borrowing, θ_HH1) - Monetary policy sets policy rate determining exchange rate - Three periods: 0, 1, 2; shocks in period 1 only; tools usable ex ante (period 0) or ex post (1 and 2); ex post illustrated. --- ### Construction of the IPF diagram — Panels and key relations ### Panel A. Imports — intertemporal current-account theory (no frictions) - Supply of external financing (no frictions): - I_1 = (1 + i^*_1). (1a) - Supply horizontal at gross dollar interest rate (1 + i^*_1); absent frictions, FX intervention and non-fundamental shocks do not affect (1a); no premium spikes; no external borrowing constraint. - Demand for imports (policymaker’s Euler and external budget): - C_F1 = C_F2 β I_1 (1 − 1/α_H A_1 ˜Y_H1 1 − 1/α_H A_2 ˜Y_H2 ). (2a) - C_F2 = X_2 + (X_1 − C_F1 − Z_1(B_1(+),1−λ E_1(+))) I_1. (2b) - Demand curve downward-sloping: lower I_1 → consume more in period 1. - Repayment term Z_1 depends on inherited debt B_1, currency composition λ, and E_1 via term 1−λ E_1. - Policy tools affecting demand: - Capital inflow tax φ_1 and household macroprudential tax θ_HH1 alter effective interest faced by households. - Optimal setting for rational long-lived households: - (1−φ_1) / (1 + θ_HH1) = (1 − 1/α_H A_1 ˜Y_H1 1 − 1/α_H A_2 ˜Y_H2 ). (2d) - Take-aways: - Demand curve shifts right if export income increases, repayment on inherited debt decreases, or home output gap temporarily lower in period 1. - Intersection of supply and demand determines desired C_F1 and I_1. - FX intervention ineffective on Panel A in no-frictions case; capital controls and macroprudential measures affect external position. ### Panel B. Housing — land price and domestic credit - Relation (no frictions): - ̂q1 = (1−φ1) CF2 / I1. (3) - Land price equals discounted dollar value of period-2 rents CF2 divided by domestic financing rate I1/(1−φ1). - Key implications: - Higher I1 lowers dollar land price ̂q1. - Capital inflow tax φ1 increases domestic financing rate and can cut transmission from I1 to domestic financing rate for all agents; household-specific macroprudential tax does not affect housing-sector financing cost. - In absence of frictions, ex post land-price volatility does not create housing-sector distortions; no case for ex post policy to support land prices; ex ante macroprudential measures targeted at housing to support ex post land prices have no welfare benefit in this frictionless step. ### Panel C. Home goods — expenditure-switching and exchange rate - Demand for home goods anchored by imports and productivity; home output gap ˜Y_Ht defined as excess demand for home goods normalized by α_H and A_t. - Exchange rate E_1 interacts with home output gap through expenditure-switching; monetary policy sets E_1 (floating) to stabilize ˜Y_H1 = 0 or peg fixes E_1. ### Panel D. Policy rate — modified UIP (no frictions) - Policy rate related to external financing and expected exchange rates; in first-step UIP modifications are simpler and policy rate stabilizes home output gap or implements peg. --- ### Financial frictions incorporated (amended relations, section 5.2) ### Panel A. Imports — amended supply and demand with frictions - Amended supply and constraint: - I_1 = (1 + i^*_1) + (1−λ) Γ (C_F1 − X_1 + Z_1 + FXI_1 − S_1). (1a*) - B_2 = C_F1 − X_1 + Z_1(B_1(+),1−λ E_1(+)) ≤ B_2^{binding}(κ_H(+),E_1(−)). (1b*) - Amended demand and premium: - C_F1 = C_F2 / [β[I_1 + (1−λ) Γ (B_2 + FXI_1)] (1 − 1/α_H A_1 ˜Y_H1 1 − 1/α_H A_2 ˜Y_H2 )]. (2a*) - C_F2 = X_2 + (X_1 − C_F1 − Z_1) I_1 − FXI_1 (1−λ) Γ (B_2 + FXI_1 − S_1). (2b*) - μ_1 = [I_1 + λ Γ (B_2 + FXI_1 − S_1)] / I_1. (2c*) - Optimal taxes (constraint not binding): - (1−φ_1) / (1 + θ_HH1) = [I_1 μ_1] / [I_1 + (1−λ) Γ (B_2 + FXI_1)] × (1 − 1/α_H A_1 ˜Y_H1 1 − 1/α_H A_2 ˜Y_H2 ). (2d*) - Key parameters and mechanisms: - λ: fraction of external debt in dollars. - Γ: FX market shallowness; Γ = 0 if deep. - S_1: fixed amount of debt held by noise traders (S_1 > 0 eases premium). - FXI_1: sterilized FX intervention (dollar assets accumulation). - B_2^{binding} depends on κ_H and E_1. - Supply curve shape: - Horizontal up to kink if Γ = 0 or λ = 1. - Upward-sloping up to kink if Γ > 0 and λ < 1; kink vertical when external borrowing constraint binds. - Kink shifts left (tightens) if κ_H declines or depreciation reduces collateral; movement depends on λ. ### Panel B. Housing — amended land price and gray zone - Amended land price: - ̂q_1 = (1−φ_1) μ_1 ∆ C_F2 / I_1. (3*) - ∆ ≥ 1: spread ratio of domestic borrowing rate to domestic policy rate. - Domestic borrowing constraint binding point: - ̂q^{binding}_1 = ̂q^{binding}_1(κ_q(−), B^{housing}_1(+), C_F1(−)). (4*) - Gray zone: region ̂q_1 < ̂q^{binding}_1 where domestic borrowing constraint binds → domestic credit crunch and welfare loss. - Curve shifts: - Right if C_F2 increases. - Left if φ_1 increased, μ_1 rises (shallower FX market), or ∆ increases. ### Panel C. Home goods — amended demand with external constraint - Demand relation: - ˜Y_H1 = C_F1 E_1^{−α_H} A_1. (5a*) - Boundary: ˜Y_H1 = 0 if floating regime and no binding external constraint; E_1 = E if fixed regime. (5b*) - External-debt impact when constraint binds: - E_1^{binding} = E_1^{binding}(κ_H(+), B_1(−), X_1 − C_F1(+)). (6a*) - ˜Y_H1 = −T + (1−λ) B_1 L if floating regime and binding external constraint. (6b*) - Depreciation always tightens external borrowing constraint to some degree; effect on welfare and desired E_1 depends on λ. ### Panel D. Policy rate — modified UIP with frictions - Modified UIP: - (1 + i_1) = I_1 μ_1 (1−φ_1) E_2 / E_1. (7*) - Take-aways: - Modified UIP downward-sloping; shifts right if expected exchange rate increases, foreign interest rate increases, capital inflow tax increased, or FX market shallow with more external debt/FX accumulation/S_1 < 0. ### Complete IPF system (all financial frictions) - System of key equations (preserved exactly): - (1a*) I_1 = (1 + i_1^*) + (1−λ) Γ (C_F1 − X_1 + Z_1 + FXI_1 − S_1) - (1b*) B_2 = C_F1 − X_1 + Z_1(B_1(+),1−λ E_1(+)) ≤ B_2^{binding}(κ_H(+),E_1(−)) - (2a*) C_F1 = C_F2 β[I_1 + (1−λ) Γ (B_2 + FXI_1)] (1 − 1/α_H A_1 ˜Y_H1 1 − 1/α_H A_2 ˜Y_H2) - (2b*) C_F2 = X_2 + (X_1 − C_F1 − Z_1) I_1 − FXI_1 (1−λ) Γ (B_2 + FXI_1 − S_1) - (2c*) μ_1 = [I_1 + λ Γ (B_2 + FXI_1 − S_1)] / I_1 - (2d*) (1−φ_1) / (1 + θ_HH1) = I_1 μ_1 / [I_1 + (1−λ) Γ (B_2 + FXI_1)] (1 − 1/α_H A_1 ˜Y_H1 1 − 1/α_H A_2 ˜Y_H2) - (3*) ̂q_1 = (1−φ_1) μ_1 ∆ C_F2 / I_1 - (4*) ̂q^{binding}_1 = ̂q^{binding}_1(κ_q(−), B^{housing}_1(+), C_F1(−)) - (5a*) ˜Y_H1 = C_F1 E_1^{−α_H} A_1 - (5b*) {˜Y_H1 = 0 if floating regime and no binding external constraint; E_1 = E if fixed regime} - (5c*) ˜Y_H2 = C_F2 E_2^{−α_H} A_2, {˜Y_H2 = 0 if floating regime; E_2 = E if fixed regime} - (6a*) E_1^{binding} = E_1^{binding}(κ_H(+), B_1(−), X_1 − C_F1(+)) - (6b*) ˜Y_H1 = −T + (1−λ) B_1 L if floating regime and binding external constraint - (7*) (1 + i_1) = I_1 μ_1 (1−φ_1) E_2 / E_1 - Solution instruction: solve algebraic system (1a*), (2a*)-(2d*), (3*), (5a*)-(5c*), (7*); if solution implies binding constraints, nonlinear relations (1b*), (4*), (6a*)-(6b*) become relevant. ### Shock classification and policy guidance (conceptual) - Four shocks considered: commodity price shock (real fundamental), dollar interest rate shock (financial fundamental), premium spike (non-fundamental outflow shock), sudden stop (may combine non-fundamental and fundamental elements). - Normative guidance: - If shock is fundamental, facilitate adjustment unless frictions cause destabilizing transition distortions. - If shock is non-fundamental and appropriate tools exist, it may be optimal to resist the shock and stabilize macro variables. - Financial frictions can cause non-fundamental shocks to have destabilizing effects and change optimal policy mixes. --- ### Selected shock analyses and policy implications ### 6.1 Commodity Price Shock (permanent adverse, floating regime, shallow FX markets) - Setup: X1 = X2 = X with X decreasing; floating regime; (1−λ) Γ > 0; B1 = Z1 = 0; ˜YH1 = ˜YH2 = 0 and β I1 = 1 in baseline. - Panel A outcomes (no FX intervention): - Upward-sloping supply shifts up/left by decrease in X (1a*); demand shifts left. - CF1 decreases by same amount as decrease in X; I1 unchanged. - φ1 = θHH1 = 0; μ1 = 1. - Panel B: - Land price curve shifts left because CF2 decreases; ̂q1 decreases at unchanged I1; economy moves closer to gray zone but does not enter it. - Panel C: - Demand rotates anticlockwise; E1 depreciates to set ˜YH1 = 0; E2 depreciates equally. - Panel D: - Modified UIP shifts right because E2 increases; i1 unchanged. - Remark: allowing exchange rate depreciation and keeping policy rate unchanged achieves adjustment; resisting adjustment via sterilized FX intervention is costly — it can break consumption smoothing and generate carry losses that reduce future import consumption. ### 4.2 U.S. Monetary Tightening (excerpt; comparison floating vs fixed) - Shock: increase in dollar interest rate i^*_1, from (1 + i^*_1) = 1/β to (1 + i^*_1) > 1/β. - Floating regime: - Panel A: supply shifts up; CF1 decreases and I1 increases; with ˜YHt = 0 set φ1 = θHH1 = 0. - Panel B: ̂q1 decreases; land price curve shifts right because CF2 increases, but ̂q1 still falls. - Panel C: E1 depreciates to set ˜YH1 = 0; E1 = αH A1 CF1, E2 = αH A2 CF2. - Panel D: modified UIP shifts right; i1 unchanged because E1 depreciates enough. - Policy implication: keep policy rate unchanged and allow depreciation; imports reduced, trade balance improved, external debt reduced in period 1. - Fixed regime: - Exchange rate cannot depreciate; ˜YHt ≠ 0 possible; demand shifts right because ˜YH1 is temporarily low; ex post capital inflow subsidy φ1 < 0 may be desirable if θHH1 unavailable. - CF1 decreases by less than in floating regime; I1 increases by same amount. - i1 increases but by less than increase in i^*_1. - Policy implication: lack of exchange rate flexibility creates role for ex post capital controls (e.g., φ1 < 0) to prevent large negative ˜YH1; fiscal policy may be useful if shock persists. ### 6.2 U.S. Monetary Tightening (with shallow FX markets and optional FX accumulation) - Shallow FX markets (1−λ) Γ > 0 dampen adjustment: CF1 decreases and I1 increases by less than without frictions; μ1 < 1. - Adding sterilized FX accumulation (FXI1 > 0) can replicate no-frictions outcome by restoring B2 + FXI1 = 0 and eliminating premium (μ1 = 1), allowing larger reduction in imports and external debt in period 1 while keeping policy rate at pre-shock value. ### 6.3 Non-fundamental Outflow Shock (S1 < 0, premium spike) - Setup: S1 < 0, floating regime, (1−λ) Γ > 0, external/domestic constraints initially not binding but domestic constraint close to binding. - Remark: policy rate and exchange rate flexibility alone cannot prevent destabilization. - Panel A: supply shifts up/left by |S1|; C_F1 falls, I1 rises; μ1 > 1; demand shifts left when φ1 and θHH1 unavailable → welfare loss. - Panel B: land price ̂q1 decreases and economy can enter gray zone; ex ante macroprudential measures on housing can improve welfare by reducing B_housing1. - Panel C: E1 depreciates; ˜YH1 = 0 if floating; E2 appreciates. - Panel D: i1 unchanged (E1 depreciates sufficiently). - Remark: ex post FX intervention (FX sales, FXI1 < 0) can cushion economy: - FX sales mitigate fall in CF1 and rise in I1, generate carry profits shifting demand right, mitigate movement into gray zone. - Adding ex post capital inflow subsidy φ1 < 0 further stabilizes imports and can fully relax domestic borrowing constraint ex post; with both tools available, no strict ex ante macroprudential measures on housing may be needed. - Key policy judgment: distinguishing fundamental vs non-fundamental nature of outflow shock is critical; ex post tools (FX intervention + capital controls) are effective for non-fundamental shocks and can reduce need for ex ante regulation. ### Sudden Stop Shock (κ_H decline) - Floating regime (Figure 24): - Kink moves left until demand intersects vertical part; C_F1 and I1 decrease; C_F2 increases; μ1 decreases. - Domestic borrowing constraint can bind ex post (gray zone entered); ex ante macroprudential measures on housing and ex ante capital controls (to reduce B_1) can improve welfare. - Exchange rate may depreciate but home output gap stays negative when in gray zone; depreciation can amplify tightening if λ near 1. - Policy implication: financial stability concerns can rationalize ex ante capital controls; ex post tools limited once constraint binds. - Fixed regime: - No exchange-rate amplification; C_F1 and I1 still decline but home output gap more negative; ex ante debt regulations remain useful. - Sensitivity to λ: - If λ low (more local-currency external debt), amplification smaller; less need for ex ante controls. --- ### Fiscal policy in the IPF (sections 7–8) ### Fiscal tools and amended panels (section 7.2) - Fiscal spending categories explicitly modeled: - G_Ft: government purchase of imports. - G_Ht: government purchase of home goods. - G_Rt and T_GR: government purchase/transfers for housing services. - Amended Panel A supply and demand: - (1a’) I_1 = (1 + i^*_1) + (1−λ) Γ (C_F1 + G_F1 − X_1 + Z_1 + FXI_1 − S_1) - (1b’) B_2 = C_F1 + G_F1 − X_1 + Z_1(B_1(+),1−λ E_1(+)) ≤ B_2^{binding}(κ_H(+),E_1(−)) - Demand: - (2a’) C_F1 = C_F2 β[I_1 + (1−λ) Γ (B_2 + FXI_1)] (1 − 1/α_H A_1+ν_1 ˜Y_H1 1 − 1/α_H A_1+ν_2 ˜Y_H2 ) - (2b’) C_F2 = X_2 − G_F2 + (X_1 − C_F1 − G_F1 − Z_1) I_1 − FXI_1 (1−λ) Γ (B_2 + FXI_1 − S_1) - Premium: (2c’) μ_1 = [I_1 + λΓ (B_2 + FXI_1 − S_1)] / I_1 - Optimal taxes (2d’) analogous to (2d*) with fiscal terms. - Panel B land price augmented: - (3’) ̂q_1 = (1−φ_1) μ_1 ∆ C_F2 + G_R2 / I_1 - Binding domestic constraint: - (4’) ̂q^{binding}_1 = ̂q^{binding}_1(κ_q(−), B^{housing}_1(+), C_F1 + G_R1(−), T_GR(−)) - Government promises to increase G_R2 support land prices today; G_R1 and T_GR in period 1 relax domestic borrowing constraint ex post. - Panel C home demand with fiscal terms: - (5a’) ˜Y_H1 = C_F1 / E_1 ( C_F1 / E_1 + G_H1 + Y_XH )^{ν−α_H} A_1+ν_1 - (5c’) ˜Y_H2 = E_2 C_F2 / (E_2 C_F2 + G_H2 + Y_XH )^{ν−α_H} A_1+ν_2 - E^binding_1 now depends on X_1 − C_F1 − G_F1. (6a’) - Panel D UIP with fiscal impact: - (7’) (1 + i_1) = I_1 μ_1 (1−φ_1) E_2 / E_1 - An increase in G_F1 raises total external debt and shifts modified UIP right if FX markets shallow. ### Fiscal policy applications (section 8.1 example) - Fixed peg, permanent commodity price decline, financial frictions none: - Baseline GF1 = GF2 = GF > 0; GHt = GRt = 0; CF1 = CF2 = X − GF in absence of shock. - Policy mix: decrease GF and increase GHt until ˜YHt = 0. - Results: - Panel A: CF1 increases by same amount as decrease in GF; I1 unchanged; μ1 = 1; φ1 = θHH1 = 0. - Panel B: ̂q1 increases (land price curve shifts right) as CF2 increases. - Panel C: home demand rotates clockwise; ˜YH1 = 0 achieved with E1 = E and specific GH formula: - GH1 = GH2 = GH = ( (αH A1+ν E(X−GF))^(1/ν) ) − E(X−GF) − YXH. (expression preserved) - Panel D: i1 unchanged. - Policy insight: under peg, decreasing government import spending GF and increasing home spending GH can stabilize output and external accounts; policymakers must weigh stabilization benefits against fiscal costs outside diagram. ### Comparative policy insights (section 8.5) - IPF distinguishes fiscal tool composition effects: - Spending on home goods tends to raise home output (may prompt policy-rate responses if labor constraints bind). - Spending on imports tends to depreciate exchange rate and reduce households’ imports when financed by lump-sum taxes. - Housing support raises asset prices without altering tradable output or exchange rate. - Interaction with capital controls and FX intervention: - Under peg, if fiscal policy flexible and can set gaps to zero, capital controls may be unnecessary. - If fiscal policy unavailable or slow, ex post capital flow tools and FX intervention may be appropriate, especially for non-fundamental outflow shocks. - For sudden stops, combine ex post fiscal responses with ex ante capital-flow regulation to address FX mismatches. --- ### Policy-design take-aways and normative guidance (summary bullets) - Distinguish fundamental vs non-fundamental shocks; policy prescription changes: - Fundamental shocks: typically facilitate adjustment unless frictions make transition distortive. - Non-fundamental shocks: if appropriate ex post tools exist (FX intervention, capital controls), resisting the shock to stabilize macro variables may be optimal. - Exchange rate regime matters: - Floating: exchange rate flexibility plus policy-rate decisions can stabilize home output; sterilized FX intervention may be used selectively to amplify or dampen adjustment. - Fixed: lack of exchange rate flexibility can create role for ex post capital-flow measures or fiscal adjustments. - Financial frictions and debt composition critical: - FX-market shallowness (Γ>0) and higher local-currency fraction (1−λ) interact to determine premium amplification and how depreciation affects borrowing constraints. - High λ (dollar-denominated external debt) makes depreciation tighten external constraint more (kink shifts left more). - Housing sector policies: - Ex ante macroprudential measures on housing reduce B^{housing}_1 and can shift gray zone left — welfare improving when domestic borrowing constraint likely to bind. - Ex post subsidies to constrained housing sector unlikely to be effective if borrowing constraint already binding. - Tool interactions: - Sterilized FX intervention can generate carry profits or losses depending on shock type (carry loss resisting fundamental commodity shock; carry profit resisting non-fundamental outflow). - Capital inflow taxes/subsidies and household macroprudential measures can substitute or complement each other per optimality conditions (2d* / 2d’). - Fiscal policy: - Decomposing government spending into imports, home goods, and housing support refines policy choices; composition matters for exchange rate, output, and asset-price effects. - Under a peg, fiscal reallocation (reduce G_F, increase G_H) can stabilize output and external accounts after commodity shock, subject to fiscal costs. *Italic source: wpiea2024038-print-pdf (IMF Working Paper WP/2024/038; excerpts provided).* ### 2.1 Normative Advice ### wpiea2024038-print-pdf - 2.1 Normative Advice ### Normative role of the IPF diagram - The Mundell-Fleming approach is positive in nature; its IS curve relies on a reduced-form behavioral (i.e., unoptimized) equation for consumption and uses the Keynesian cross diagram to describe how changes in demand affect output. - The framework typically assumes restoring pre-shock levels of home output and trade balance is desirable, but the framework itself does not justify that objective. - Policymakers may need to resist some shocks and facilitate adjustment to others; desirable levels of home output, trade balance, and asset prices can be altered by shocks. - The IPF diagram fills the normative gap by: - Incorporating optimization (maximization of welfare subject to a resource constraint). - Focusing on the policymaker’s perspective and economy-wide welfare. - Basing intervention rationale on externalities not internalized by the private sector. - Showing how each policy tool affects welfare along different dimensions and leaving trade-offs for judgment. - The IPF approach replaces the IS-LM Keynesian cross while preserving the insight that the exchange rate plays a key role in the open economy. ### Policy tools (comparison to Mundell-Fleming) - Mundell-Fleming’s LM curve is upward-sloping because money supply is fixed; modern practice uses interest rate control instead. - The IPF diagram assumes the monetary policy rate is the relevant monetary tool; the reaction function of this policy rate to macro variables determines macro stability. - The IPF diagram replaces the IS-LM money market diagram and incorporates additional tools absent from the typical Mundell-Fleming approach: - Sterilized FX intervention - Capital controls - Domestic macroprudential measures - Fiscal policy is excluded from the first two steps of model-building in the IPF diagram and included only in the third step. - Empirical motivation: these tools are frequently used by EMDEs to manage capital flows; fiscal policy is used less for this purpose but matters after large shocks. ### Financial frictions (limitations of Mundell-Fleming and IPF additions) - Mundell-Fleming lacks frictions to explain premium spikes, sudden stops, and domestic credit crunches; many versions feature perfect capital mobility. - IPF adds financial frictions tied to currency denomination of debts: - Imperfect capital mobility modeled as limited arbitrage in the FX market → premium spikes. - Occasionally-binding external borrowing constraints → sudden stops. - Occasionally-binding domestic borrowing constraints → domestic credit crunches. - These borrowing constraints become relevant only after large shocks. - The IPF diagram connects use of tools to impacts on the economy’s intertemporal budget constraint, which the Mundell-Fleming approach omits. ### Looking forward (overview) - The IPF diagram discards some Mundell-Fleming elements, preserves others, and adds new elements—setting the scene for an updated approach. ### The IPF diagram without financial frictions (section summary) - First-step IPF: only friction is price stickiness; no financial frictions. - Result: a visual intertemporal New Keynesian framework with monetary policy set to stabilize the home output gap (floating regime) or implement a peg (fixed regime). - The diagram illustrates welfare impacts of policy decisions and whether policymakers should stabilize macro variables or facilitate adjustment. - Equations are converted into curves with textual bullets explaining curve shifts, allowing both graphical and algebraic analysis. ### Model overview (specifications and assumptions) - Based on Basu et al. (2023) with financial frictions turned off. - Micro-foundations for expenditure-switching from optimizing households consuming several goods; price stickiness creates a role for exchange rate flexibility. - Assumptions extending the “dominant currency paradigm”: - Imports and exports of produced tradable goods have sticky prices set in dollars. - The domestically-sold part of home-produced tradable goods has sticky local currency prices. - Nontradable housing services have flexible local currency rents. - Exports of commodity endowments have flexible dollar prices. - Under these assumptions: an exchange rate depreciation raises the relative price of imports to home goods, inducing expenditure switching from imports to home goods; exports do not change because their dollar price and quantities are fixed in the dominant currency paradigm. - Price stickiness generates an aggregate demand externality: households do not internalize how individual consumption affects aggregate demand; the policymaker does and can use tools to address the externality. - Financial intermediation (figure structure): global financiers → domestic banks → domestic private sector; no frictions assumed in this channel for this step. - Tools available in the model: - FX intervention (circumvent intermediaries) - Capital controls (taxes on capital inflows at the border) - Domestic macroprudential measures (taxes on domestic debt transactions) - Monetary policy sets the policy rate determining the exchange rate - Three periods assumed: 0, 1, and 2; shocks strike in period 1 and no further uncertainty thereafter. - Policy tools can be used ex ante (period 0) or ex post (periods 1 and 2); ex post values are illustrated and ex ante policies are unnecessary in this version. ### Construction of the diagram (four interlinked panels; Panel A detailed) - The IPF diagram has four interlinked panels; each panel’s curves are numbered and described. - Panel A. Imports — “Intertemporal theory of the current account” - Presents optimal consumption of imports C_F1 in period 1 from the policymaker’s perspective (welfare-maximizing). - Import consumption worsens the trade balance and increases external debt. - The optimal level depends on I_1, the dollar value of the gross interest rate on external financing between periods 1 and 2. - I_1 averages and converts into dollars the rates on the economy’s dollar and local currency external debts. - I_1 is generally different from the monetary policy rate (policy rate is local currency and applies only to local currency debt). - Key relations on Panel A: 1. Supply of external financing: - I_1 = (1 + i^*_1). (1a) - Interpretation: horizontal supply curve at gross dollar interest rate (1 + i^*_1) because, absent financial frictions, global financiers charge zero expected premium on local currency debt relative to dollar debt. With no remaining uncertainty after period 1, realized premium is also zero. I_1 equals (1 + i^*_1) irrespective of currency denomination of external debt. - Consequences: non-fundamental capital flow shocks and FX intervention do not show up in equation (1a); country does not experience premium spikes on local currency debt; FX intervention is ineffective; no external borrowing constraint can bind to cause a sudden stop. - Take-away: “The supply curve is horizontal at the gross dollar interest rate. It is unaffected by non-fundamental capital flow shocks and FX intervention, and there is no external borrowing constraint.” 2. Demand for imports: - C_F1 = C_F2 β I_1 (1− 1/α_H A_1 ~Y_H1 1− 1/α_H A_2 ~Y_H2 ) (2a) - C_F2 = X_2 + ( X_1 − C_F1 − Z_1 ( B_1 (+) , 1−λ E_1 (+) ) ) I_1 . (2b) - Explanation: Equations (2a)-(2b) are the Euler condition and external budget constraint for the policymaker’s welfare optimization problem. The Euler condition explains smoothing of consumption over time; the external budget constraint bounds the net present value of consumption. - The demand curve is downward-sloping (Euler condition): lower I_1 → consume more in period 1 and save less. - Demand curve shifts if normalized home output gaps ~Y_H1 and ~Y_H2 are not balanced over time; these gaps are determined in Panel C. - Definitions: in period t the gap ~Y_Ht is excess demand for home goods (actual output minus efficient level), normalized by α_H and productivity A_t. - The policymaker can shift demand for home goods between periods by shifting import consumption between periods. - External budget constraint determinants: - Export incomes X_1 and X_2 (home-produced tradable goods fixed in dollars; commodity export income depends on flexible dollar commodity prices). - Z_1: dollar value of interest repayments on inherited debt B_1. If B_1 = 0 then Z_1 = 0. - Repayment Z_1 depends on currency denomination of inherited debt and exchange rate via term 1−λ E_1. λ is fraction of external debt in dollars; (1−λ) fraction in local currency. E_1 is local currency per dollar, determined in Panel C. - If λ = 1 (all inherited debt in dollars) then 1−λ E_1 = 0 and exchange rate has no effect on Z_1. If λ < 1, a depreciation in period 1 reduces Z_1 and shifts the demand curve right. - Policy tools affecting demand curve: - Capital inflow tax φ_1 (tax on banks’ external borrowing). - Domestic macroprudential tax θ_HH1 (tax on households’ domestic borrowing). - Both tools have identical effect on the demand curve: a subsidy via either reduces the interest rate faced by households and increases consumption in period 1 (shift right); a tax shifts the demand curve left. - Constraint on tools can reduce welfare if optimal subsidy is unavailable or set too low. - Optimal setting for rational, long-lived household case: - (1−φ_1) / (1 + θ_HH1) = (1− 1/α_H A_1 ~Y_H1 1− 1/α_H A_2 ~Y_H2 ). (2d) - Interpretation: capital inflow tax and/or domestic macroprudential tax needed to correct aggregate demand externality; if neither available, the demand curve is replaced by households’ Euler condition β I_1 C_F1 = C_F2 (backed out from (2a) and (2d)). - Panel A take-aways: - The demand curve is downward-sloping. - The demand curve shifts to the right if export income increases. - The demand curve shifts to the right if repayment on inherited debt decreases. - The demand curve shifts to the right if the home output gap is temporarily lower in period 1. - Intersection of supply and demand on Panel A determines desired C_F1 and I_1. - FX intervention is ineffective on Panel A; capital controls and domestic macroprudential measures affect the external position; spillovers from Panel C (home output gaps and E_1) shift the demand curve. ### Panel B introduction (housing / credit transmission) - Panel B. Housing — “Global financial cycle in credit” - Shows how external financing rate I_1 from Panel A spills into domestic credit markets, with variables in dollar values. - Vertical axis: gross external financing rate I_1 (same as Panel A). - Horizontal axis: q̂_1, the dollar value of the land price in period 1 (housing sector proxy for domestic credit markets). - One key relation is plotted on the panel (details continue beyond provided excerpt). *Source: wpiea2024038-print-pdf - 2.1 Normative Advice (IMF).* ### 3. Land price: ### 3. Land price: ### Land price determination - Equation (3): ̂q1 = (1−φ1) CF2 / I1 . - Land is purchased by the housing sector to produce nontradable housing services in the next period. The land price in period 1 equals the value of housing rents in period 2, discounted by the domestic financing rate between periods 1 and 2. - Dollar value of rents in period 2 is captured by CF2 (consumption of imports in period 2). Rents are flexibly set and reflect household demand for housing services; this demand moves together with demand for imports in period 2 because both are determined by overall household resources in that period. - The domestic financing rate (dollar value) equals the external financing rate I1 adjusted by the capital inflow tax φ1, i.e., I1/(1−φ1) appears in the denominator of equation (3) so I1 is in the denominator and (1−φ1) is in the numerator. - Higher external financing rate I1 lowers the dollar value of the land price. I1 applies to external debt (partly dollars, partly local currency); integration between domestic and external financial markets allows I1 to affect the dollar value of the domestic financing rate, which in turn determines the dollar value of the land price: the higher the rate, the lower the land price. - The capital inflow tax φ1 can cut the transmission from the external financing rate to the domestic financing rate and land price by increasing the domestic financing rate for all domestic agents including the housing sector. By contrast, a household macroprudential tax raises borrowing rates only for households and not for the housing sector, so it does not affect the land price via the housing sector’s financing cost. - In the absence of financial frictions, there are no distortions in the housing sector: irrespective of volatility in domestic land prices, housing sector firms can purchase all the land they need to produce the desired quantity of nontradable housing services in each period. ### Key take-aways (from the above discussion) - The land price curve is downward-sloping. - The land price curve shifts to the right if period-2 imports increase. - The land price curve shifts to the right if the capital inflow tax is decreased. ### Policy implications and welfare assessment - Panel B addresses whether policies should mitigate spillovers from external financing conditions onto domestic asset prices. - In the absence of financial frictions, ex post volatility in land prices does not cause housing sector distortions or hurt overall welfare; therefore, there is no case for ex post policy action to support land prices. - There is no case for ex ante macroprudential measures targeted at the housing sector purely to support ex post land prices; even if ex ante measures reduce inherited housing sector debt and thereby support ex post land prices, there is no welfare benefit from supporting those prices. *Source: wpiea2024038-print-pdf - 3. Land price:* ### 4.2 U.S. Monetary Tightening ### 4.2 U.S. Monetary Tightening ### Floating exchange rate regime: immediate effects and adjustment - Shock considered: increase in the dollar interest rate i∗1, from (1 +i∗1) = 1/β to (1 +i∗1) > 1/β. - Initial conditions: starting point of the economy is the same as in section 4.1. Findings (Figure 10, Panels A–D): - Panel A (Imports) - The supply curve shifts up because i∗1 increases. Equation (1a) is affected. - The demand curve is unchanged. - For a floating regime, panel C produces ̃YHt = 0. - Equations (2a)-(2b) imply: - CF1 = X(1+I1)/(1+β)I1 - CF2 = Xβ(1+I1)/(1+β) - CF1 decreases and I1 increases. - Since home output gaps are closed, there is no need for an ex post capital inflow tax or household macroprudential tax. Since ̃YHt = 0, we can set φ1 = θHH1 = 0 in equation (2d). - Panel B (Housing) - The increase in I1 causes a decrease in ̂q1 for a given land price curve. - The land price curve shifts to the right because CF2 increases; however, ̂q1 still decreases relative to its pre-shock value. - Equation (3) indicates the post-shock land price follows ̂q1 = Xβ(1+I1)/(1+β)I1. - Panel C (Home Goods / Exchange rate) - The demand curve rotates anticlockwise because CF1 decreases; the decrease in CF1 enters equation (5a). - E1 depreciates to set ̃YH1 = 0. - Equations (5a)-(5c) establish: - E1 = αH A1 CF1 - E2 = αH A2 CF2 - Panel D (Policy Rate) - The modified UIP condition shifts to the right because the increase in i∗1 dominates the decrease in E2. Equation (7) incorporates φ1 = 0 and (1 +i∗1)E2 = αH A2 X/(1+β)I1 β(1+I1) . - i1 is unchanged. - Substituting equations (5a)-(5c) into (7) establishes that E1 depreciates by enough such that no change in i1 is needed. Policy implication (floating regime): - Standard policy tools can achieve macroeconomic adjustment by keeping the policy rate unchanged and allowing the exchange rate to depreciate. - Outcome: imports are reduced, the trade balance is improved, external debt is reduced in period 1, and home consumption is stabilized. ### Fixed exchange rate regime: role for ex post capital controls Findings (Figure 11, Panels A–D): - Panel A (Imports) - The supply curve shifts up because i∗1 increases. Equation (1a) is affected. - For I1 = (1 +i∗1) > 1/β, the demand curve shifts to the right because ̃YH1 is temporarily low. - For a fixed regime, panel C allows ̃YHt ≠ 0. Given the shock I1 = (1 +i∗1) > 1/β, equations (2a)-(2b) and (5a)-(5c) imply: - CF1 < X < CF2 - ̃YH1 < ̃YH2 - The shift can be implemented using an ex post capital inflow subsidy, φ1 < 0. - Substituting ̃YH1 < ̃YH2 into equation (2d) indicates φ1 < 0 is desirable if θHH1 is not available. - CF1 decreases by less than in the floating regime, while I1 increases by the same amount. - CF1 is higher and CF2 is lower than in the floating regime. Relevant expressions: - CF1 = X(1 − 1/αH A1 ̃YH1 / 1 − 1/αH A2 ̃YH2) / (1 − 1/αH A1 ̃YH1 / 1 − 1/αH A2 ̃YH2 + β(1 +I1)/I1) - CF2 = X β(1 +I1) / (1 − 1/αH A1 ̃YH1 / 1 − 1/αH A2 ̃YH2 + β) - where (1 − 1/αH A1 ̃YH1 / 1 − 1/αH A2 ̃YH2) = 1 in the floating regime and > 1 in the fixed regime. - Panel B (Housing) - The increase in I1 causes a decrease in ̂q1 for a given land price curve. - For I1 = (1 +i∗1) > 1/β, the land price curve shifts to the right by more than in the floating regime if φ1 < 0; however, ̂q1 still decreases relative to its pre-shock value. - Equation (3) indicates both the subsidy and the increase in CF2 push the curve to the right. - Panel C (Home Goods / Output gap) - The demand curve rotates anticlockwise because CF1 decreases, but the subsidy mitigates the decrease in CF1. - ̃YH1 decreases because E1 = E, but the subsidy mitigates the decrease in ̃YH1. From equation (5c), the subsidy also mitigates the increase in ̃YH2. - Panel D (Policy Rate) - The modified UIP condition shifts to the right because i∗1 increases, but any subsidy mitigates the rightward shift. Equation (7) incorporates φ1 < 0 and the increase in i∗1. - i1 increases by less than the increase in i∗1. Policy implication (fixed regime): - Macroeconomic adjustment remains desirable and imports should still be reduced after a U.S. monetary tightening. - Lack of exchange rate flexibility creates a case for ex post use of capital controls (e.g., a capital inflow subsidy φ1 < 0) to prevent period-1 home output gap from getting too negative. - Mitigating the decline in import consumption also mitigates the worsening of the home output gap. - If the shock persists long enough, fiscal policy may also be useful (addressed in section 8.2). ### Comparison with the IS-LM diagram and normative differences - The IPF diagram differs from IS-LM in two key ways: - It offers normative advice on whether policymakers should stabilize macroeconomic variables or facilitate their adjustment to shocks. - It incorporates additional policy tools (although sterilized FX intervention remains ineffective). - For the shocks considered: - Commodity price shock: IPF finds no change to desirable levels of home output and trade balance, and no need to stabilize asset prices—outcome similar to IS-LM but mechanism differs (monetary policy rule stabilizes home output in IPF, rather than fixed money supply). - U.S. monetary tightening: IPF finds no change to desirable level of home output and no need to stabilize asset prices, but external debt should be reduced. Imports should be reduced to improve the trade balance while home output is stabilized. - This causes divergence with IS-LM: IS-LM outcome features immediate depreciation and boost in home output reined in by policy rate increase, reverting trade balance and external debt to pre-shock values. IPF emphasizes immediate deleveraging of external debt, reduction in imports, and a persistent exchange rate depreciation with no policy rate increase. - For fixed exchange rate regimes, IPF allows that a capital inflow tax/subsidy may be available when fiscal policy is not. Specifically: - Capital inflow tax may not be useful after a commodity price shock. - A capital inflow subsidy may be useful after a U.S. monetary tightening if fiscal policy is absent, though it does not fully stabilize the home output gap. *Source: 4.2 U.S. Monetary Tightening (excerpt provided).* ### 5.2 Construction of the Diagram ### 5.2 Construction of the Diagram ### Panel A. Imports — Intertemporal theory of the current account - Amended relations incorporate financial frictions from shallow FX markets and an external borrowing constraint; these change optimal imports C_F1 and the gross external financing rate I_1 between periods 1 and 2. - Key relations (as amended): - 1*. Supply of external financing: - I_1 = (1 + i^*_1) + (1−λ) Γ (C_F1 − X_1 + Z_1 + FXI_1 − S_1)(1a*) - B_2 = C_F1 − X_1 + Z_1 (B_1(+), 1−λ E_1(+)) ≤ B^binding_2 = B^binding_2(κ_H(+), E_1(−)).(1b*) - 2*. Demand for imports (policymaker Euler and budget): - C_F1 = C_F2 / [β[I_1 + (1−λ) Γ (B_2 + FXI_1)] (1 − 1/α_H A_1 ̃Y_H1 1−1/α_H A_2 ̃Y_H2 )] (2a*) - C_F2 = X_2 + (X_1 − C_F1 − Z_1) I_1 − FXI_1 (1−λ) Γ (B_2 + FXI_1 − S_1).(2b*) - Premium adjustment factor: - μ_1 = [I_1 + λΓ (B_2 + FXI_1 − S_1)] / I_1.(2c*) - Optimal taxes (rational long-lived households, constraint not binding): - (1−φ_1) / (1 + θ_HH1) = [I_1 μ_1] / [I_1 + (1−λ) Γ (B_2 + FXI_1)] × (1 − 1/α_H A_1 ̃Y_H1 1−1/α_H A_2 ̃Y_H2 ).(2d*) - Economic mechanisms and parameter meanings: - λ: fraction of external debt in dollars; (1−λ) is fraction in local currency. - Γ: measure of FX market shallowness; Γ = 0 if market deep, Γ > 0 if shallow. - S_1: fixed amount of debt held by noise traders; S_1 > 0 eases premium, S_1 < 0 raises premium. - FXI_1 > 0: sterilized FX intervention where policymaker accumulates dollar assets; affects supply curve position. - Z_1: dollar value of interest payments depends on currency denomination of inherited debt and exchange rate movements. - B^binding_2: maximum amount global financiers willing to lend; depends on κ_H (external pledgability) and E_1 (exchange rate). - Supply curve implications: - If FX market deep and/or all external debt in dollars, supply is horizontal up to a kink (unaffected by S_1 and FXI_1). - If FX market shallow and some external debt in local currency, supply is upward-sloping up to a kink; this upward segment shifts up after a non-fundamental outflow shock S_1 < 0 and shifts down if policymaker decumulates FX reserves (FXI_1 decreases). - Kink represents external borrowing constraint where supply becomes vertical; kink position not affected by FXI_1 or S_1 because constraint applies to total external debt. - Borrowing-constraint dynamics: - Kink moves left (tightens) if κ_H declines (loss of foreign trust) or if exchange rate depreciation E_1 increases reduces dollar value of collateral. - The extent kink moves left after a depreciation depends on FX mismatch (λ): if λ = 1 (all debt in dollars), depreciation only reduces B^binding_2 and moves kink substantially left; if λ < 1, depreciation also reduces Z_1 and thus tightens constraint less. - Demand curve dynamics and policy tools: - Demand curve is downward-sloping and shifts with: - Right if export income increases. - Right if repayment on inherited debt decreases. - Right if home output gap ̃Y_Ht is temporarily lower in period 1. - Left if FX market shallow and local-currency premium increases. - Right if FX intervention earns a profit; left if it generates a loss. - Policymaker can guide household demand using capital inflow tax φ_1 and household macroprudential tax θ_HH1; if external borrowing constraint binds, these taxes become welfare-irrelevant (set φ_1 = θ_HH1 = 0 for simplicity). - Premium externality and spillovers: - Upward-sloping supply and kink both shift when E_1 changes. - Non-fundamental capital flow shocks S_1 cause premium and import variation but intersection remains left of kink if FX market shallow and some local-currency debt exists. - Sudden stop (κ_H decline) can move kink left of prior intersection, forcing imports down; subsequent depreciation can further move kink left and amplify contraction — effect depends on λ. ### Panel B. Housing — Global financial cycle in credit - Amended panel plots I_1 (external financing rate) against ̂q_1 (dollar value of land price in period 1), incorporating shallow FX markets, external borrowing constraint, and domestic borrowing constraint. - Key relations: - 3*. Land price: - ̂q_1 = (1−φ_1) μ_1 ∆ C_F2 / I_1.(3*) - μ_1: premium adjustment factor from panel A (equation (2c*)). - ∆ ≥ 1: interest rate spread representing ratio of domestic borrowing interest rate to the domestic policy rate (friction from external borrowing constraint). - 4*. Point at which domestic borrowing constraint binds: - ̂q^binding_1 = ̂q^binding_1(κ_q(−), B^housing_1(+), C_F1(−)).(4*) - Economic interpretation: - Land price depends inversely on the domestic financing rate: domestic financing rate = I_1 μ_1 ∆ / (1−φ_1). - Shallow FX markets (μ_1 > 1) raise the dollar-equivalent domestic financing cost and shift land price curve left. - External borrowing constraint can force domestic banks to charge borrowing rates above policy rate (∆ > 1), shifting land price curve left. - If external constraint binds, C_F1 falls and C_F2 rises (via (2b*)), which raises period-1 land rents through higher period-2 demand; however assumed effect of increased ∆ dominates, so land price decreases in a sudden stop. - Gray zone and domestic borrowing constraint: - For ̂q_1 < ̂q^binding_1, domestic borrowing constraint binds, causing a domestic credit crunch and welfare decline (gray zone in figure). - Determinants moving gray zone left (less likely for constraint to bind): - Higher pledgability parameter κ_q of land. - Lower inherited housing sector debt B^housing_1. - Lower C_F1 shifts ̂q^binding_1 via its negative effect in (4*), making constraint more likely to bind when imports contract. - Take-aways for land price curve shifts: - Curve is downward-sloping. - Shifts right if period-2 imports increase (C_F2 increases). - Shifts left if capital inflow tax φ_1 is increased. - Shifts left if FX market shallow and local-currency premium increases (μ_1 rises). - Shifts left if domestic borrowing rate increases above domestic policy rate (∆ increases). *Source: wpiea2024038-print-pdf — 5.2 Construction of the Diagram* ### 1. Lower inherited debt means that there are lower debt rollover needs between periods 1 and 2, so ### wpiea2024038-print-pdf - 1. Lower inherited debt means that there are lower debt rollover needs between periods 1 and 2, so ### Housing sector, gray zone, and policy tools - Lower inherited debt implies lower debt rollover needs between periods 1 and 2, so there is less debt subject to any domestic borrowing constraint. - Because of the dependence of the gray zone on B_housing_1, ex ante macroprudential measures on the housing sector can be welfare-improving. - Mechanism: the economy features a pecuniary production externality — individual housing sector firms do not internalize the impact of their borrowing decisions on sector-wide debt and the severity of the domestic borrowing constraint. As a result, they may borrow too much in period 0 and end up with too much debt at the start of period 1. - Policy implication: by setting an appropriate ex ante tax or quantity regulation on housing sector debt, the policymaker can induce the housing sector to borrow less in period 0, reducing B_housing_1 and thereby pushing the gray zone to the left. - Higher imports C_F1 push the gray zone to the left because higher C_F1 is associated with higher resources for consumption in period 1, a higher value of housing rents that can be used to pay down inherited debt, and reduced rollover needs between periods 1 and 2. Take-aways (housing/domestic constraint): - The gray zone (representing a binding domestic borrowing constraint) shifts to the left if the domestic pledgability of assets is higher. - The gray zone shifts to the left if the policymaker sets an ex ante tax or quantity regulation on housing sector debt. - The gray zone shifts to the left if period-1 imports increase. - Amended assessment with financial frictions (panel B): shallow FX markets and the external borrowing constraint amplify transmission of the external financing rate to domestic asset prices, but this amplification is not by itself a rationale for policy tools to support asset prices. There is a case for policy tools only if shocks risk causing the domestic borrowing constraint to become binding ex post. - An ex post capital inflow subsidy can boost the land price in period 1, preventing entry into the gray zone. - Ex ante macroprudential measures on the housing sector can reduce overborrowing in period 0 and mitigate ex post salience of the domestic borrowing constraint by shifting the gray zone to the left. - Optimal mix between ex ante and ex post tools depends on their relative distortive effects in practice. - Note: ex post macroprudential subsidies targeted at the constrained housing sector are unlikely to be effective in supporting land price because constrained firms cannot succeed in borrowing more when their borrowing constraint is already binding. ### Panel C. Home Goods — demand, external constraint, and expenditure-switching - The amended Panel C plots the exchange rate E_1 against the home output gap ̃Y_H1 in period 1. - The impact of adding the financial friction of the external borrowing constraint depends on whether the constraint is binding in panel A and on the exchange rate regime. If binding, it shifts the position of the home goods demand curve. In a fixed exchange rate regime, the constraint has no further effect on panel C. In a floating regime, an extra line appears on panel C if the constraint is binding. Key relation (Demand for home goods): - (5a*) ̃Y_H1 = C_F1 E_1^{−α_H} A_1 - (5b*) where { ̃Y_H1 = 0 if floating regime and no binding external constraint; E_1 = E if fixed regime. } Exposition and mechanisms: - The demand curve is upward-sloping and anchored on imports C_F1 and productivity level A_1. - If the external borrowing constraint is binding in panel A, C_F1 decreases and the demand curve rotates anticlockwise around its intersection with the horizontal axis. - Two cases where demand curve alone determines panel C: - Fixed exchange rate: E_1 = E and the country goes to intersection of demand curve and peg line. - Floating exchange rate and external constraint not binding: policymaker uses exchange rate flexibility to set ̃Y_H1 = 0. Conditions ensuring external constraint never binds for floating regime: - The kink in the supply curve in panel A moves left when E_1 depreciates. If the kink always remains to the right of the intersection of supply and demand in panel A regardless of shock, the external constraint never binds. This configuration is true if pledgability parameter κ_H is high, inherited external debt B_1 is low, and/or the trade balance (X_1 − C_F1) is high. Take-aways (home goods demand): - The demand curve is upward-sloping and intersects the vertical axis at the point where the home output gap is zero. - The demand curve rotates clockwise if imports increase. - The demand curve shifts to the left if productivity increases. - For a fixed exchange rate regime, the home output gap depends on the level at which the exchange rate is fixed. External debt impact when floating regime and constraint sometimes binds: - (6a*) E_1^{binding} = E_1^{binding}(κ_H (+), B_1 (−), X_1 − C_F1 (+)) - (6b*) ̃Y_H1 = −T + (1−λ) B_1 L if floating regime and binding external constraint. Interpretation of (6a*)-(6b*): - A depreciation makes the external borrowing constraint more likely to bind because it shifts the kink in the supply curve in panel A to the left. For exchange rates higher than E_1^{binding}, the constraint becomes binding (gray zone on panel C). - E_1^{binding} is higher if the pledgability parameter κ_H is higher, inherited external debt B_1 is lower, and the trade balance (X_1 − C_F1) is higher. - Equation (6b*) captures the external debt impact from the depreciation: - Right-hand side uses constants T (“tightening”) and L (“loosening”). - Term −T captures how depreciation tightens the constraint because of a decline in B_2^{binding}; it is the only term if all external debt is in dollars (λ = 1). - Term (1−λ) B_1 L captures how depreciation may loosen the constraint because of a decline in the dollar value of repayments Z_1; it is relevant if some external debt is in local currency (λ < 1). - Since depreciation always tightens the external borrowing constraint to some degree under the assumptions, the RHS of (6b*) is negative; the equation appears on panel C as a vertical line to the left of the vertical axis. - If λ = 1 (all external debt in dollars), the vertical line is substantially to the left and the desired E_1 is substantially lower than the value that sets ̃Y_H1 = 0, so ̃Y_H1 is substantially negative. - If λ < 1 (some debt in local currency), the vertical line shifts right; desired E_1 is closer to the value that sets ̃Y_H1 = 0 and ̃Y_H1 is less negative. Policy implications and external debt composition: - Because gray zone depends on inherited external debt B_1, ex ante capital controls at the border or ex ante macroprudential measures on household borrowing can be welfare-improving. - Rationale: pecuniary aggregate demand externality — domestic agents do not internalize how their borrowing affects economy-wide external debt and aggregate demand, which affect the chosen exchange rate and severity of the external borrowing constraint. Agents may overborrow in period 0; ex ante taxes or quantity regulations can reduce B_1 and push up the gray zone. - The case for such regulation diminishes if a large portion of external debt is in local currency: higher (1−λ) reduces distortions to E_1 and ̃Y_H1 generated by the external constraint. Take-aways (external constraint and home goods): - The gray zone (representing a binding external borrowing constraint) shifts up if the external pledgability of assets is higher. - The gray zone shifts up if the policymaker sets an ex ante tax or quantity regulation on external debt. - The gray zone shifts up if the trade balance increases. - The external debt impact line appears on the panel as a vertical line to the left of the vertical axis once the exchange rate increases into the gray zone. - The external debt impact line shifts to the right if some of the external debt is in local currency. Period-2 relation: - (5c*) ̃Y_H2 = C_F2 E_2^{−α_H} A_2, where { ̃Y_H2 = 0 if floating regime; E_2 = E if fixed regime. } - The amended panel C augments expenditure-switching theory with the external borrowing constraint; interaction between panels A and C can generate amplification and a larger sudden stop when more external debt is in dollars. ### Panel D. Policy Rate — modified UIP and implications - The amended Panel D plots the period-1 monetary policy rate i_1 against the exchange rate E_1. Key relation (Modified UIP condition): - (7*) (1 + i_1) = I_1 μ_1 (1−φ_1) E_2 / E_1. Interpretation: - Addition of the friction of shallow FX markets changes the UIP condition because global financiers can no longer perfectly arbitrage between local currency and dollar assets; returns on domestic local currency assets can diverge from returns on foreign dollar assets. - New terms: - I_1: the external financing rate — the after-tax return required on external debt by optimizing global financiers. The policy rate must be increased if there is an increase in external debt, if policymaker accumulates FX assets FXI_1 > 0, or if there is a non-fundamental capital outflow shock S_1 < 0. - μ_1: the premium adjustment factor needed to translate the dollar value of the premium on external debt into the dollar value of the premium on domestic debt. Take-aways (modified UIP and policy rate): - The modified UIP condition is downward-sloping. - The modified UIP condition shifts to the right if the expected exchange rate increases. - The modified UIP condition shifts to the right if the foreign interest rate increases. - The modified UIP condition shifts to the right if the capital inflow tax is increased. - The modified UIP condition shifts to the right if the FX market is shallow and there is an increase in external debt, FX accumulation, or a non-fundamental capital outflow shock. - The monetary policy rate i_1 is set in an environment with multiple frictions and tools, incorporating policy decisions from panels A, B, and C. Beyond the IS-LM view, the policy rate must account for FX market shallowness and policy tools such as sterilized FX intervention and capital controls. ### Complete IPF diagram and system of equations (all financial frictions) - The complete IPF diagram integrates panels A–D and depends on country-specific configuration of lines and relevant tools/frictions. - Associated system of equations: - (1a*) I_1 = (1 + i_1^*) + (1−λ) Γ (C_F1 − X_1 + Z_1 + FXI_1 − S_1) - (1b*) B_2 = C_F1 − X_1 + Z_1 ( B_1 (+), 1−λ E_1 (+) ) ≤ B_2^{binding} ( κ_H (+), E_1 (−) ) - (2a*) C_F1 = C_F2 β[I_1 + (1−λ) Γ (B_2 + FXI_1)] ( 1 − 1/α_H A_1 ̃Y_H1 1 − 1/α_H A_2 ̃Y_H2 ) - (2b*) C_F2 = X_2 + (X_1 − C_F1 − Z_1) I_1 − FXI_1 (1−λ) Γ (B_2 + FXI_1 − S_1) - (2c*) μ_1 = [I_1 + λ Γ (B_2 + FXI_1 − S_1)] / I_1 - (2d*) (1−φ_1) / (1 + θ_HH1) = I_1 μ_1 / [ I_1 + (1−λ) Γ (B_2 + FXI_1) ( 1 − 1/α_H A_1 ̃Y_H1 1 − 1/α_H A_2 ̃Y_H2 ) ] - (3*) ̂q_1 = (1−φ_1) μ_1 ∆C_F2 / I_1 - (4*) ̂q_1^{binding} = ̂q_1^{binding} ( κ_q (−), B_housing_1 (+), C_F1 (−) ) - (5a*) ̃Y_H1 = C_F1 E_1^{−α_H} A_1 - (5b*) where { ̃Y_H1 = 0 if floating regime and no binding external constraint; E_1 = E if fixed regime } - (5c*) ̃Y_H2 = C_F2 E_2^{−α_H} A_2, where { ̃Y_H2 = 0 if floating regime; E_2 = E if fixed regime } - (6a*) E_1^{binding} = E_1^{binding}(κ_H (+), B_1 (−), X_1 − C_F1 (+)) - (6b*) ̃Y_H1 = −T + (1−λ) B_1 L if floating regime and binding external constraint - (7*) (1 + i_1) = I_1 μ_1 (1−φ_1) E_2 / E_1 - Readers are advised: solve the algebraic system given by (1a*), (2a*)-(2d*), (3*), (5a*)-(5c*), and (7*). If the solution indicates binding borrowing constraints, then nonlinear dynamics in (1b*), (4*), and/or (6a*)-(6b*) become relevant. ### Policy mixes with financial frictions — shock classification and policy guidance - The IPF diagram with financial frictions allows consideration of four shocks and policy mixes. Key conceptual distinction: - Fundamental shock: changes optimal level of macroeconomic variables even in the absence of financial frictions. - Non-fundamental shock: does not change optimal levels absent frictions, but does change actual levels in presence of frictions. - Implications: - Financial frictions can generate destabilizing impact from non-fundamental shocks and modify impact of fundamental shocks. - Whether to accommodate or resist a shock depends on whether it is fundamental or non-fundamental: - If fundamental, policymaker should facilitate economy’s adjustment to the shock unless financial frictions cause destabilizing transition distortions. - If non-fundamental and policymaker has the necessary tools to address the relevant frictions, it may be optimal to resist the shock and stabilize macroeconomic variables. - Classification of the four shocks from figure 1: - Commodity price shock: a real fundamental shock. - Dollar interest rate shock: a financial fundamental shock. - Premium spike: focus on a spike caused by a non-fundamental capital outflow shock. - Sudden stop shock: an additional financial shock that may combine non-fundamental and fundamental elements; relevance and severity may vary across countries and may be idiosyncratic or part of the global financial cycle. *Source: wpiea2024038-print-pdf - content unit as provided* ### 6.1 Commodity Price Shock ### 6.1 Commodity Price Shock ### Setup and assumptions - Consider a permanent adverse commodity price shock: X1 = X2 = X and there is a decrease in X. - Country characteristics: - Floating exchange rate regime. - Shallow FX markets interacting with the local currency fraction of external debt: (1−λ) Γ > 0. - External and domestic borrowing constraints are not binding (unless noted). - Baseline assumptions for the counterfactual (absence of shock): - No inherited debt: B1 = Z1 = 0. - ˜YH1 = ˜YH2 = 0 and βI1 = 1. - Without shock and without sterilized FX intervention, consumption smoothing holds: CF1 = CF2 = X. - Equation (2d*) holds (see text). ### Panel A — Imports (standard policy response, no FX intervention) - Supply and demand shifts: - Upward-sloping part of the supply curve shifts up and to the left because X decreases. The leftward shift equals the decrease in X (equation (1a*)). The kink moves further left due to the increase in E1 from panel C (equation (1b*)), but the kink does not affect the panel outcome. - Demand curve shifts to the left because X decreases. - For a floating regime with ˜YHt = 0 and FXI1 = 0, equations (2a*)-(2b*) yield: - CF1 = X - CF1 = X (1 + I1) / [(1 + β) I1 + β(1−λ) Γ (CF1 − X)] (expression given in text) - At I1 = 1/β, CF1 = CF2 = X remains a solution, so the leftward shift equals the decrease in X. - Outcomes: - CF1 decreases by the same amount as the decrease in X, and I1 is unchanged. - No ex post capital inflow tax or household macroprudential tax is needed: ˜YHt = 0 and B2 = FXI1 = 0 imply μ1 = 1 and permit φ1 = θHH1 = 0. ### Panel B — Housing (standard policy response) - Land price effects: - Land price curve shifts to the left because CF2 decreases (the decrease in CF2 from panel A enters equation (3*), while φ1 = 0 and μ1 = Δ = 1). - q̂1 decreases at unchanged I1. - Economy moves closer to the gray zone but is assumed not to enter it. - Simultaneously, equation (4*) implies the decrease in CF1 from panel A causes an increase in q̂binding1. ### Panel C — Home goods and exchange rate (standard policy response) - Demand curve rotates anticlockwise because CF1 decreases (decrease in CF1 enters equation (5a*)). - E1 depreciates to set ˜YH1 = 0 (equations (5a*)-(5b*)). From (5c*), E2 depreciates by the same amount. - No gray zone: equation (6a*) indicates arbitrarily high Ebinding1 because external borrowing constraint cannot become binding if panel A produces B2 = 0. ### Panel D — Policy rate (standard policy response) - Modified UIP condition shifts to the right because E2 increases (equation (7*) incorporates φ1 = 0, I1 unchanged, μ1 = 1, and E2 increases). - i1 is unchanged (E1 and E2 depreciate by the same amount in equation (7*)). ### Overall inference (Remark 5) - Macroeconomic adjustment is achievable using standard policy tools: keep policy rate unchanged and allow exchange rate depreciation. - Imports can be reduced so that the trade balance and external debt in period 1 remain zero, while home consumption is stabilized. ### Cost of resisting adjustment using sterilized FX intervention (Remark 6) - Adding sterilized FX intervention (FXI1 < 0; selling FX reserves) can produce the following (Figure 18 scenarios): - Panel A (with FXI1 < 0): - Upward-sloping part of the supply curve shifts down and to the right; the rightward shift equals |FXI1| (equation (1a*)). Kink moves right due to decrease in E1 from panel C (equation (1b*)). - This shift increases CF1 and decreases I1. Because demand is downward-sloping, CF1 increases by less than |FXI1|, so CF1 + FXI1 decreases. Unlike the no-intervention case where B2 = 0, FX intervention generates B2 > 0 and B2 + FXI1 < 0. - Equation (2c*) implies μ1 < 1. - FX intervention generates carry losses and decreases CF2: carry profits term −FXI1 (1−λ) Γ (B2 + FXI1) in equation (2b*) is negative. These carry losses and interest payments on B2 cause CF2 to decrease. - Demand curve effect is ambiguous because the reduction in premium externality (denominator) shifts demand right, while carry loss shifts it left. - Panel B: - Change in land price q̂1 is ambiguous: decrease in I1 tends to increase q̂1, while changes in CF2 and μ1 may shift land price curve. - Gray zone shifts left because CF1 increases; equation (4*) implies increased CF1 leads to decrease in q̂binding1. - Welfare is unaffected here because domestic borrowing constraint is not binding; welfare could improve if that constraint were binding initially. - Panel C: - Exchange rate appreciates to set ˜YH1 = 0 (equations (5a*)-(5b*)); from (5c*), E2 depreciates. - Gray zone appears but remains very high: Ebinding1 decreases because CF1 increases and B2 > 0. - Panel D: - Change in policy rate i1 is ambiguous: in equation (7*) modified UIP may shift left as I1 decreases and μ1 < 1, but increase in E2 and decrease in E1 complicate sign. A country plotted where policy rate does not change. - Key take-away: Resisting the fundamental shock via sterilized FX intervention breaks consumption smoothing, can generate carry losses, hurts future import consumption, and postpones (but does not avoid) exchange rate depreciation. The diagram does not automatically recommend additional tools (sterilized FX intervention, capital controls, domestic macroprudential measures) just because frictions exist; the interaction of the shock and frictions determines their usefulness. - Boundary notes: - With shallow FX markets but non-binding borrowing constraints, the shock moves the country closer to the zone where the domestic borrowing constraint binds; setting B1 > 0 can also move the country closer to the external borrowing-constraint-binding zone. In cases where constraints bind, FX intervention may possibly improve welfare by mitigating constraints. --- ### 6.2 U.S. Monetary Tightening ### Setup and assumptions - Consider increase in dollar interest rate i∗1 in a floating exchange rate country with shallow FX markets ( (1−λ) Γ > 0 ), external and domestic borrowing constraints not binding. - Starting point same as in section 6.1. ### Remark 7 — Standard tools (monetary policy and exchange rate flexibility) achieve partial adjustment - Shallow FX market friction dampens adjustment to the dollar interest rate shock. - Figure 19 (standard tools only) — Panel summaries: - Panel A: - Period-1 imports decrease and external financing rate increases, but both by less than in case without financial frictions. - Supply curve: upward-sloping part shifts up because i∗1 increases (equation (1a*)). Kink moves left due to increase in E1 from panel C (equation (1b*)), but kink does not affect outcome. - Demand curve unchanged. - CF1 decreases and I1 increases, but both by less than in figure 10. - For a floating regime with ˜YHt = 0, small-shock derivatives from equations (2a*)-(2b*): - dCF1/di∗1 = − βX / [ (1 + β) (1 + i∗1) + 2β(1−λ) Γ X ] < 0 - dCF2/di∗1 = − (1 + i∗1) dCF1/di∗1 > 0 - Signs same as in figure 10 but magnitudes smaller if (1−λ) Γ > 0. - Equation (2c*) implies μ1 < 1. - If any tax needed, household macroprudential tax used instead of capital inflow tax; from equation (2d*) impact on φ1 ambiguous but assume φ1 = 0 (either RHS of (2d*) is 1 or θHH1 is used). - Panel B: - Change in land price ambiguous. - Increase in I1 causes decrease in q̂1 for a given land price curve. - Land price curve shifts right because CF2 increases and μ1 decreases; overall q̂1 ambiguous. Example plotted where q̂1 decreases. - Economy moves closer to gray zone but does not enter it. Decrease in CF1 from panel A causes increase in q̂binding1 (equation (4*)). - Panel C: - Exchange rate depreciates and home output gap is zero. - Demand curve rotates anticlockwise because CF1 decreases (equation (5a*)). - E1 depreciates to set ˜YH1 = 0 (equations (5a*)-(5b*)); from (5c*), E2 appreciates. - No gray zone: Ebinding1 arbitrarily high because external borrowing constraint cannot bind if panel A produces B2 < 0. - Panel D: - Change in policy rate i1 ambiguous: modified UIP (equation (7*)) may shift right as I1 increases, although decrease in μ1 and E2 may offset. Increase in E1 decreases i1. Example plotted where policy rate does not change. ### Remark 8 — Adding FX intervention (FX accumulation) can increase adjustment - Figure 20 illustrates adding sterilized FX accumulation (FXI1 > 0) to the policy mix to reinforce the shock and replicate the outcome of section 4.2 (no financial frictions). - Key mechanics and outcomes when FXI1 > 0: - Panel A: - Upward-sloping part of supply curve shifts up (left) because FXI1 > 0; leftward shift equals |FXI1| (equation (1a*)). Kink moves left due to further increase in E1 from panel C. - FX intervention shifts demand curve left via FXI1 entering equations (2a*)-(2b*). - CF1 decreases and I1 increases by more because FXI1 > 0. Before shock economy had B2 + FXI1 = 0. In figure 19 decrease in CF1 caused B2 + FXI1 < 0; any leftward shift from FX accumulation reduces CF1 by less than the shift so CF1 + FXI1 increases. To replicate figure 10, intervention used until B2 + FXI1 = 0 is restored. Carry profits from this intervention are zero because the premium is eliminated; combining with ˜YHt = 0 yields same outcome as figure 10. Equation (2c*) implies μ1 = 1. - No need for ex post capital inflow tax or household macroprudential tax: since B2 + FXI1 = 0 and μ1 = 1, equation (2d*) becomes identical to equation (2d). - Panel B: - Land price decreases relative to pre-shock value. With μ1 = Δ = 1 from panel A, equation (3*) becomes identical to equation (3). - Economy assumed not to enter gray zone. Decrease in CF1 causes increase in q̂binding1 (equation (4*)). - Panel C: - Exchange rate depreciation is reinforced by FX accumulation; home output gap remains zero. - Demand curve rotates further anticlockwise because CF1 decreases further (equation (5a*)). - E1 depreciates more to set ˜YH1 = 0 (equations (5a*)-(5c*) identical to (5a)-(5c)). - No gray zone: Ebinding1 arbitrarily high because external borrowing constraint cannot bind if panel A produces B2 < 0. - Panel D: - Policy rate returns to pre-shock value. With μ1 = 1 and I1 = (1 + i∗1) from panel A, equation (7*) becomes identical to equation (7). - Combined insight: - Shallow FX markets dampen the effect of the dollar interest rate shock: external financing rate increases but less than without frictions, because the premium reduction associated with reduced external debt partly offsets the shock. - Magnitudes of import changes are smaller if only policy rate and exchange rate flexibility are used. - If policymaker desires more adjustment, sterilized FX accumulation (FXI1 > 0) can ensure larger reduction in imports and external debt in period 1. - Boundary notes: - FX market shallow and borrowing constraints not binding initially, but shock moves country closer to domestic borrowing-constraint-binding zone; if that constraint binds, selling FX rather than accumulating it may become useful. - If B1 > 0, the shock may move country closer to or further from the external borrowing-constraint-binding zone. *Source: wpiea2024038-print-pdf - 6.1 Commodity Price Shock* ### 6.3 Non-fundamental Outƒow Shock ### 6.3 Non-fundamental Outflow Shock ### Setup and key assumptions - Shock: local currency premium spike caused by an outflow shock from local currency debt unrelated to domestic macroeconomic fundamentals, i.e., S1<0. - Regime: floating exchange rate. - Market friction: shallow FX markets interacting with the local currency fraction of external debt, i.e., (1−λ) Γ>0. - Constraints: external and domestic borrowing constraints are not binding to begin with, but the latter constraint is close to being binding. - Starting point: same as in section 6.1. ### Remark 9: Standard policy tools cannot prevent macroeconomic destabilization - Figure 21 (IPF diagram): dotted lines = pre-shock positions; solid lines = post-shock positions when policymaker uses only the policy rate and exchange rate flexibility. Result: macroeconomic destabilization. Panel A — imports and external financing - Period-1 imports decrease and the external financing rate increases. - Supply curve: - Upward-sloping part shifts up and to the left because S1<0. - Equation (1a*) indicates the leftward shift equals |S1|. - Equation (1b*) indicates the kink moves left because of the increase in E1 from panel C; kink does not affect panel outcome. - Demand and quantities: - Shift decreases C_F1 and increases I1. - If equation (2a*) held, demand would not shift. The decrease in C_F1 would be smaller than supply leftward shift, so B2 = C_F1 − X <0 while B2 − S1 >0. - Equations (2a*)-(2b*) would establish that C_F2 increases. - Side-effect when capital inflow tax and household macroprudential tax unavailable: - Demand curve also shifts left. - Under floating regime, panel C produces ̃Y_Ht = 0. - Equation (2d*) implies a subsidy, i.e., φ1<0 and/or θ_HH1<0, would be needed to implement (2a*): (1−φ1)(1 +θ_HH1) = [I1 + λΓ (B2 − S1)] / [I1 + (1−λ) Γ B2] > 1. - Since those tools are not available, demand curve shifts further left and welfare is reduced. - The curve becomes β[I1 + λΓ (B2 − S1)] C_F1 = C_F2, and the shock causes B2 − S1 > 0. - Equation (2c*) indicates μ1 > 1: higher external premium has amplified pass-through to domestic financing rate and no tool to dampen it. - Net: shift amplifies decrease in C_F1; I1 remains above pre-shock value; C_F2 increases. Panel B — housing and binding domestic borrowing constraint - Increase in I1 causes a decrease in ̂q1 for a given land price curve. - Shift in land price curve ambiguous; ̂q1 still decreases relative to pre-shock. - Equation (3*) indicates increase in C_F2 from panel A tends to shift curve right, but μ1 > 1 tends to shift left. Authors plot a country where land price curve shifts slightly right. - Ex post, economy enters the gray zone. - Alongside decrease in ̂q1, equation (4*) indicates decrease in C_F1 from panel A causes increase in ̂q_binding1. - Policy implication: - Ex ante macroprudential measures on housing can improve welfare by decreasing B_housing1, which reduces ̂q_binding1 (equation (4*)) and shifts gray zone left. Panel C — exchange rate and home output - Exchange rate depreciates and home output gap is zero. - Demand curve rotates anticlockwise because C_F1 decreases (entering equation (5a*)). - E1 depreciates to set ̃Y_H1 = 0 (equations (5a*)-(5b*)). From (5c*), E2 appreciates. - No gray zone: equation (6a*) indicates arbitrarily high E_binding1 because external borrowing constraint cannot become binding if panel A yields B2 < 0. Panel D — policy rate - Modified UIP condition shifts right because S1<0. - Equation (7*) incorporates increase in I1 and μ1>1 from panel A, partially mitigated by decrease in E2 from panel C. - i1 is unchanged. - Combining (5a*)-(5c*) with (7*) and households’ Euler condition shows E1 depreciates enough that no change in i1 is needed. ### Remark 10: Ex post FX intervention and/or capital controls can improve stabilization - Consider sterilized FX intervention (FX sales, FXI1<0) and then add capital inflow tax/subsidy. - FX sales can cushion the economy. Figure 22 illustrates intervention; dotted = no intervention; solid = partial offset of shock. Assume intervention offsets some but not all of shock. Panel A with FX intervention — imports and external financing - FX intervention mitigates decrease in period-1 imports and increase in external financing rate. - Supply curve: - Intervention reduces upward and leftward shift of upward-sloping part. - Equation (1a*): relative to Figure 21 panel A, supply curve shifts right by |FXI1|. - Equation (1b*): kink moves less left because increase in E1 is mitigated. - Demand and quantities: - Change mitigates decrease in C_F1 and increase in I1. - Without demand shift, C_F1 would increase by less than intervention, so C_F1 + FXI1 would still decrease. Correspondingly, B2 + FXI1 − S1 decreases. - Authors assume limited intervention stopping while B2 < 0, B2 + FXI1 < 0, and B2 + FXI1 − S1 > 0. Intervention mitigates increase in C_F2. - Beneficial side-effect: generates a carry profit and shifts demand curve right. - Demand follows β[I1 + λΓ (B2 + FXI1 − S1)] C_F1 = C_F2 and equation (2b*). - Decrease in B2 + FXI1 − S1 and positive carry profits term −FXI1 (1−λ) Γ (B2 + FXI1 − S1) shift demand right relative to Figure 21. - Equation (2c*) indicates μ1 > 1. - Remaining limitation: absent capital inflow tax and household macroprudential tax, demand curve remains left of where it should be. - If available, equation (2d*) still suggests subsidy is appropriate: (1−φ1)(1 +θ_HH1) = [I1 + λΓ (B2 + FXI1 − S1)] / [I1 + (1−λ) Γ (B2 + FXI1)] > 1. Panel B with FX intervention — housing - Domestic borrowing constraint less severe ex post; case for ex ante macroprudential regulation weaker. - FX intervention mitigates increase in I1 and decrease in ̂q1 for a given land price curve. - Shift in land price curve ambiguous; overall decrease in ̂q1 mitigated. - Equation (3*) indicates smaller changes in C_F2 and μ1 < 1 push land price curve in opposite directions; authors plot land price curve shifting further right. - FX intervention mitigates rightward shift in gray zone (equation (4*)); ̂q_binding1 increases by less if C_F1 decreases less. - Ex post domestic borrowing constraint is less severe; authors plot economy remains in gray zone. - Implication: availability of ex post FX intervention reduces need for strict ex ante macroprudential measures on housing. Panel C with FX intervention — exchange rate and home output - Exchange rate depreciation mitigated by FX sales; home output gap remains zero. - Demand curve rotates anticlockwise by less because C_F1 decreases less (entering equation (5a*)). - E1 depreciates by less to set ̃Y_H1 = 0 (equations (5a*)-(5b*)). From (5c*), E2 appreciates by less. - No gray zone: equation (6a*) continues to indicate arbitrarily high E_binding1 because B2 < 0 from panel A. Panel D with FX intervention — policy rate - Modified UIP remains right of pre-shock position (equation (7*)); incorporates increase in I1 and μ1>1, partially mitigated by decrease in E2 from panel C. - i1 unchanged; combining (5a*)-(5c*) with (7*) and Euler condition shows E1 depreciates so no change in i1 needed. Adding ex post capital inflow subsidy (φ1<0) - Further stabilizes economy. Figure 23 illustrates FX sales + capital inflow subsidy; authors choose mix such that imports are smoothed over time, i.e., C_F1 = C_F2 (Basu et al. 2023 prove optimality in related work). Panel A with FX intervention + capital subsidy — imports stabilized over time - Upward-sloping part of supply curve unchanged relative to Figure 22 (equation (1a*) unaffected). - Equation (1b*): kink moves a little right relative to pre-shock because E1 decreases a little relative to panel C pre-shock. - Demand curve shifts right if ex post capital inflow subsidy φ1<0 imposed. - Equation (2d*) establishes subsidy is optimal; use of this tool enables policymaker to satisfy equations (2a*)-(2b*). - C_F1 can be stabilized a little higher than pre-shock because of carry profits; subsidy causes I1 to increase further. - Using subsidy + FX intervention to set C_F1 − X + FXI1 = S1/2, authors achieve: C_F1 = C_F2 = X + (1−λ) Γ (S1)^2 / 4 [1 + (1 + i∗1)], where second term is small boost to imports from carry profits of FX intervention. - Correspondingly, B2 = C_F1 − X > 0 but small. Equation (2c*) indicates μ1 > 1. Panel B with both tools — housing - Domestic borrowing constraint can be fully relaxed ex post; no case for ex ante macroprudential regulation on housing. - Further increase in I1 causes further decrease in ̂q1 for a given land price curve. - Ex post capital inflow subsidy can shift land price curve sufficiently right so that ̂q1 ends up higher than pre-shock. - Substituting φ1 from panel A into equation (3*) gives ̂q1 = C_F2 (1 + i∗1): domestic financing rate can be fully insulated from increase in I1 and μ1 > 1; C_F2 is higher than pre-shock. - Ex post, economy no longer in gray zone. Equation (4*) indicates ̂q_binding1 decreases relative to pre-shock because C_F1 increases relative to pre-shock in panel A. - Conclusion: when ex post FX intervention and capital controls are available to handle premium spikes, there is no need for restrictive ex ante macroprudential measures on housing if domestic borrowing constraint not binding ex post. Panel C with both tools — home output and exchange rate - Home output gap at zero without need for exchange rate depreciation. - Demand curve rotates clockwise a little relative to pre-shock because C_F1 increases a little (entering equation (5a*)). - E1 appreciates a little relative to pre-shock to set ̃Y_H1 = 0 (equations (5a*)-(5b*)); from (5c*), E2 appreciates by same amount. - Gray zone appears but remains very high. Equation (6a*) indicates E_binding1 decreases because C_F1 increases and B2 > 0 from panel A. Panel D with both tools — policy rate - Modified UIP shifts a little left relative to pre-shock because E2 appreciates a little. - In equation (7*), panel A indicates changes in φ1, I1, μ1 offset each other; panel C indicates E2 appreciates. - i1 unchanged; in equation (7*), E1 and E2 appreciate by the same amount. Overall conclusions and policy implications - Country can improve macroeconomic stabilization by using FX intervention, capital controls/subsidies, or both. - Benefits of these tools: - Stabilize imports and home output. - Cut transmission of global financing conditions to domestic borrowing constraints. - Reduce need to alter monetary policy or to depreciate exchange rate. - If more ex post stabilization tools available, ex ante macroprudential regulations on housing can be less restrictive. - Important judgment: distinguishing whether an outflow shock is fundamental or non-fundamental is critical in practice. - Shallow FX market friction dampened effect of fundamental dollar interest rate shock in section 6.2 but amplifies effect of non-fundamental outflow shock. - Using FX sales to resist non-fundamental outflow shock generates a carry profit and helps stabilize imports (contrast with carry loss when resisting a fundamental commodity price shock in section 6.1). *Source: wpiea2024038-print-pdf - 6.3 Non-fundamental Outflow Shock* ### 1. Solving equations (2a*)-(2b*), we can show that these assumptions mean that in the absence of ### wpiea2024038-print-pdf - 1. Solving equations (2a*)-(2b*), we can show that these assumptions mean that in the absence of ### Sudden Stop Shock — Floating Exchange Rate Regime (Figure 24) - Baseline implication: In the absence of the shock and sterilized FX intervention, consumption can be smoothed between periods 1 and 2: - C_F1 = C_F2 = X − Z_1 I_1 / (1 + I_1). - Panel A — Period-1 imports and the external financing rate decrease: - The decrease in κ_H moves the kink of the supply curve left until the demand curve intersects the vertical part of the supply curve; thereafter the position of the kink determines C_F1. - C_F1 and I_1 both decrease while C_F2 increases. - I_1 is determined by the supply curve (1a*). C_F1 is determined by the values of B_binding_2 and Z_1 in equation (1b*). C_F2 is determined by equation (2b*). - Equation (2c*) indicates that μ_1 decreases. - When the external borrowing constraint binds, capital inflow and household macroprudential taxes become irrelevant to welfare; set φ_1 = θ_HH1 = 0. - An amplification mechanism: further leftward movement in the kink, slight downward shift in upward-sloping part, and substantial decrease in C_F1. - The decrease in C_F1 causes an exchange rate depreciation (panel C), further decreasing B_binding_2 and Z_1 in equations (1a*)-(1b*). Since λ is near 1, impact on Z_1 is small, and the kink moves substantially left. - Panel B — Housing (domestic borrowing constraint binds ex post): - The decrease in I_1 causes an increase in ˆq_1 for a given land price curve. - Shift in land price curve ambiguous; assume ∆>1 is so large that the curve shifts substantially left and ˆq_1 decreases relative to pre-shock value. - In equation (3*), increase in C_F2 and decrease in μ_1 shift the curve right, but binding external borrowing constraint causes ∆>1 which shifts the curve left; assume latter dominates. - Ex post, economy enters the gray zone; alongside decrease in ˆq_1, equation (4*) implies decrease in C_F1 from panel A causes an increase in ˆq_binding_1. - Ex ante macroprudential measures on housing can improve welfare by decreasing B_housing_1, which decreases ˆq_binding_1 in equation (4*) and shifts the gray zone left. - Panel C — Home goods (exchange rate depreciates but home output gap stays negative): - Demand curve rotates anticlockwise because C_F1 decreases; decrease in C_F1 from panel A enters equation (5a*). - Assume E_1 depreciates but ˜Y_H1 < 0 because economy enters gray zone. Since λ is near 1, equation (6b*) appears as a vertical line substantially left of vertical axis. - Decrease in C_F1 from panel A causes E_binding_1 to increase in equation (6a*) but not enough to escape gray zone. - Amplification mechanism causes further depreciation of E_1, which feeds back to further decrease in C_F1 and further anticlockwise rotation of demand curve in panel C. Equation (5c*) indicates E_2 appreciates. - Policy implication: Ex ante restrictions on capital inflows can improve welfare by decreasing B_1, increasing E_binding_1 in equation (6a*), and shifting up the gray zone; if C_F1 decreases less in panel A, demand curve rotates less in panel C (via equation (5a*)). - Panel D — Policy rate: - Modified UIP shifts left. Equation (7*) incorporates φ_1 = 0, decreases in I_1 and μ_1 from panel A, and decrease in E_2 from panel C. - i_1 decreases further because of increase in E_1, but there is some “interest rate defense”: to prevent external borrowing constraint tightening too much, i_1 is not loosened all the way to set ˜Y_H1 = 0. - Remark 11 (implication): Financial stability concerns may rationalize ex ante capital controls. ### Sensitivity to currency composition of external debt (Remark 12) - If most external debt is in local currency (λ is low) — contrast with λ near 1 case: - Panel A: - Amplification mechanism is smaller; kink may move less left. - Impact effect still decreases C_F1 via external borrowing constraint (1b*); assume associated exchange rate depreciation in panel C still occurs. - Lower λ implies any given depreciation causes larger decrease in Z_1 in equation (1b*); final decrease in C_F1 may be mitigated. - Decreases in C_F1 and I_1 and increase in C_F2 may be mitigated (determined by (1a*)-(1b*) and (2b*)). - Panel B: - Domestic borrowing constraint may be less severe ex post; case for ex ante macroprudential housing regulation weaker. - Shift in land price curve and decrease in ˆq_1 may be mitigated; looser external borrowing constraint may decrease term ∆ in equation (3*). - Ex post, ˆq_binding_1 increases by less if C_F1 decreases by less in panel A (equation (4*)). - Panel C: - Exchange rate depreciation may be mitigated and home output gap less negative; ex ante capital controls may be less useful. - Demand curve rotates anticlockwise by less because C_F1 decreases by less (equation (5a*)). - E_1 still depreciates relative to pre-shock but ensures ˜Y_H1 is close to zero. Since λ is low, equation (6b*) appears as a vertical line just a little left of vertical axis. Equation (5c*) indicates E_2 still appreciates. - Ex ante restrictions on capital inflows may be less welfare-improving because external borrowing constraint no longer severe ex post. - Panel D: - Less “interest rate defense”; i_1 can be set closer to value that achieves ˜Y_H1 = 0. ### Sudden Stop Shock — Fixed Exchange Rate Regime (Figure 25) and policy implications (Remark 13) - In fixed rate case (E_1 = E), interlinkage between panels A and C via exchange rate amplification no longer exists. - Panel A: - Decrease in κ_H still moves kink left and decreases C_F1 and I_1 and increases C_F2 (via (1a*)-(1b*) and (2b*)). - No amplification through exchange rate depreciation; kink does not move further left; decrease in C_F1 has no effect on E_1 in panel C. - Panel B: - Domestic borrowing constraint may be less severe ex post; case for ex ante macroprudential housing regulation decreased. - Shift in land price curve and decrease in ˆq_1 may be mitigated; looser external borrowing constraint decreases ∆ in equation (3*). - Ex post, ˆq_binding_1 increases by less if C_F1 decreases by less (equation (4*)). - Panel C: - Negative home output gap remains, so ex ante capital controls may still be useful. - Demand curve rotates anticlockwise by less because C_F1 decreases by less (equation (5a*)). - ˜Y_H1 is more negative than in floating regime (equations (5a*)-(5b*)). If immediate impact would tend to depreciate E_1 in figure 24, inability to depreciate (fixed E_1) makes ˜Y_H1 even more negative. Equation (5c*) indicates ˜Y_H2 > 0. - Ex ante restrictions on capital inflows can improve welfare by decreasing B_1 and thereby making external borrowing constraint less severe or non-binding ex post via equation (1b*). If C_F1 decreases less in panel A, demand curve rotates less in panel C so ˜Y_H1 is less negative. - Panel D: - Policy rate decreases relative to pre-shock value. - Modified UIP shifts left because external debt decreases. Equation (7*) incorporates φ_1 = 0 and decreases in I_1 and μ_1 from panel A, and unchanged E_2 from panel C. - i_1 decreases at fixed exchange rate E_1 = E. - Overall policy conclusion: - There is a case for ex ante debt regulations in countries with large unhedged FX mismatches on external debt. - Once a sudden stop occurs, ex post tools become constrained: capital inflow taxes become ineffective, policy rate is not loosened fully to stabilize home output gap. - Therefore, ex ante capital inflow regulations to reduce external FX debt and ex ante domestic macroprudential measures to reduce housing domestic debt are warranted. - The higher the local currency fraction of external debt, the less salient the external and domestic borrowing constraints after the same shock, and weaker the case for ex ante capital controls or macroprudential measures. ### Differences from the IS-LM Diagram (section 6.5) - Adding financial frictions makes the amended IPF diagram diverge further from the IS-LM model; it analyzes a wider range of shocks and policy mixes. - Over-arching observation: desirability of any policy mix depends on each country’s precise combination of financial frictions and available policy tools. Standard tools may help adjust after fundamental shocks; additional tools may be especially useful to resist non-fundamental shocks. - Commodity price shock: - Single friction of shallow FX markets does not alter outcomes relative to IS-LM because post-policy outcome features no change in trade balance and external debt. - If external debt unchanged, external premium need not change, so final outcomes similar. - U.S. monetary tightening shock: - IPF recommends external debt reduction; IS-LM (with stabilized home output) implies external debt does not change. - Introducing shallow FX markets: external debt reduction reduces external premium; external financing rate faced by domestic households and banks increases by less than dollar interest rate does. - Up-shot: standard tools alone achieve less adjustment; sterilized FX intervention can be added to help increase adjustment. - Adding external and domestic borrowing constraints widens divergence further: - In IPF, shocks can cause one or both constraints to bind; IS-LM does not incorporate these frictions or the mix of ex ante and ex post tools to address them. - Non-fundamental outflow shock: - IS-LM-BP with imperfect capital mobility: immediate depreciation, improved trade balance, boost in home output. - IPF: immediate deleveraging of external debt reduces imports and home output; exchange rate depreciation then needed to stabilize home output. - Policy divergence: IS-LM recommends similar policies for U.S. tightening and non-fundamental outflow shocks; IPF can recommend different policies because non-fundamental shock can be insulated via sterilized FX intervention and capital controls to remove need for macroeconomic adjustments. - Sudden stop shock: - IPF can generate contractionary depreciation (if much external debt is in foreign currency): depreciation tightens external constraint, reduces imports and home output — exchange rate flexibility may not cushion sudden stop. - Ex post exchange flexibility may be welfare-improving only if supported by ex ante capital inflow tax and/or ex ante macroprudential regulation on external debt. - Flexibility of IPF: - Combination of financial frictions allows more tailoring than IS-LM. Example: U.S. tightening may aggravate balance-sheet problems in domestic banks, increasing spread term in panel B without economy-wide sudden stop in panel A. ### The IPF Diagram With Fiscal Policy — introduction (section 7) and model overview (7.1) - Scope: Introduce fiscal policy into IPF diagram; add fiscal tools to framework described in section 5.1 and financial intermediation structure in figure 2. - Normative stance: Advice on fiscal policy is partial — explore how fiscal policy changes alter prior normative trade-offs; do not consider all costs and benefits of fiscal policy adjustments. - Practical note: Fiscal policy may be difficult to adjust due to political obstacles; may be an option in some countries and after some shocks. - Fiscal tools of interest (three categories of government spending): - Purchase of imports, G_Ft. - Purchase of home goods, G_Ht. - Purchase of housing services, G_Rt, and/or period-1 transfers to housing sector, T_GR. - Modeling assumptions: - All spending financed via lump-sum taxes on households (excludes distortive tax impacts). - Amended IPF diagram will show each category of spending has different impact on macro variables and alters normative trade-offs from previous sections. - If distortive tax tools are available, model advice for them ties to previous results: e.g., distortive tax adjustments should support previously-recommended capital inflow taxes and macroprudential measures (if loosening macroprudential measures on households is required to boost imports, reducing consumption tax could also help). - Additional modeling detail: - The IPF approach here is based on Basu et al. (2024); technical details and approximations connecting diagram to system of equations are in appendix A.2. - Basu et al. (2024) derive optimal fiscal policy assuming spending on welfare-improving public goods; such an assumption implies fiscal adjustments may generate substantial welfare costs beyond scope of diagram. *Italic source: wpiea2024038-print-pdf (excerpt as provided)* ### 7.2 Construction of the Diagram ### 7.2 Construction of the Diagram ### Panel A. Imports — Intertemporal theory of the current account - Key modifications: every relation on panel A adds government spending on imports G_F1 alongside households’ imports C_F1; total external debt at end of period 1 is B_2 = C_F1 + G_F1 − X_1 + Z_1 (with inherited total external debt B_1 and period-1 interest repayments Z_1). - Supply of external financing (amended): - (1a’) I_1 = (1 + i^*_1) + (1−λ) Γ (C_F1 + G_F1 − X_1 + Z_1 + FXI_1 − S_1) - (1b’) B_2 = C_F1 + G_F1 − X_1 + Z_1 ( B_1 (+) , 1−λ E_1 (+) ) ≤ B^binding_2 ( κ_H (+) , E_1 (−) ) - Interpretation: fiscal policy does not affect the horizontal part of the supply curve when no financial frictions; if (1−λ) Γ > 0 (shallow FX market and some local-currency debt), G_F1 increases push the upward-sloping part of the supply curve up. - Kink behavior: inherited debt B_1 increases with ex ante G_F1 so kink moves left if ex ante G_F1 increases; to loosen constraint when binding, period-1 G_F1 must decrease. - Demand for imports (amended): - (2a’) C_F1 = C_F2 β[I_1 + (1−λ) Γ (B_2 + FXI_1)] ( 1 − 1/α_H A_1+ν_1 ˜Y_H1 1 − 1/α_H A_1+ν_2 ˜Y_H2 ) - (2b’) C_F2 = X_2 − G_F2 + (X_1 − C_F1 − G_F1 − Z_1) I_1 − FXI_1 (1−λ) Γ (B_2 + FXI_1 − S_1) - Premium adjustment: (2c’) μ_1 = [I_1 + λΓ (B_2 + FXI_1 − S_1)] / I_1 - Optimal tax/macroprudential setting when households are rational and long-lived and borrowing constraint not binding: - (2d’) (1−φ_1) (1 + θ_HH1) = [I_1 μ_1] / [I_1 + (1−λ) Γ (B_2 + FXI_1)] ( 1 − 1/α_H A_1+ν_1 ˜Y_H1 1 − 1/α_H A_1+ν_2 ˜Y_H2 ) - If neither tax is available and constraint not binding: β[I_1 + λΓ (B_2 + FXI_1 − S_1)] C_F1 = C_F2. - Take-aways (exact list preserved): - The supply curve is horizontal up to a kink if the FX market is deep and/or all external debt is in dollars. This horizontal part of the curve is unaffected by non-fundamental capital flow shocks, FX intervention, and fiscal policy. - The supply curve is upward-sloping up to a kink if the FX market is shallow and some of the external debt is in local currency. This upward-sloping part of the curve shifts up after a non-fundamental outflow shock, shifts down if the policymaker decumulates FX reserves, and shifts up if government spending on imports increases. - The supply curve has a kink at the external borrowing constraint, when it becomes vertical. - The kink moves to the left if there is a decline in investors’ trust in domestic creditworthiness. - The dependence of the kink on the exchange rate depends on the economy’s FX mismatch. The higher the fraction of external debt in dollars, the more that the kink moves to the left after a depreciation. - The kink moves to the left if the ex ante and/or ex post government spending on imports increases. - The demand curve is downward-sloping. - The demand curve shifts to the right if export income increases. - The demand curve shifts to the right if the repayment on inherited debt decreases. - The demand curve shifts to the right if the home output gap is temporarily lower in period 1. - The demand curve shifts to the left if the FX market is shallow and the local currency premium increases. - The demand curve shifts to the right if FX intervention earns a profit, but shifts to the left if FX intervention generates a loss. - The demand curve shifts to the left if government spending on imports increases. - Policy experiments (three): 1. If {G_F1, G_F2} held unchanged, {C_F1, C_F2} unchanged even if lump-sum taxes/transfers change → Ricardian equivalence holds in this form (transfers financed by issuing equal debt leave {C_F1, C_F2} unchanged; if constraint binds, transfer does not affect economy because constraint depends on total external debt). 2. Permanent increase in {G_F1, G_F2} → permanent decrease in {C_F1, C_F2}; demand curve shifts left; if FX market shallow, supply shifts up and kink moves left when constraint binding. 3. Fiscal front-loading (increase G_F1, decrease G_F2, with unchanged NPV G_F1 + G_F2 / I_1), assume no external borrowing constraint and ˜Y_Ht = 0: - If (1−λ) Γ = 0 (deep FX market/all external debt in dollars): no effect on {C_F1, C_F2}. - If (1−λ) Γ > 0: supply curve shifts up and left; premium externality may shift demand left; intersection shifts left → C_F1 decreases. Postponing G_F from period 1 to 2 can increase C_F1. ### Panel B. Housing — Global financial cycle in credit - Visual: plots I_1 against ˆq_1 (dollar value of land price in period 1). - Government support for housing: - Can alter the land price curve position (regardless of frictions). - Can alter the gray zone representing the domestic borrowing constraint; fiscal policy can determine whether this constraint binds. - Government spending on imports and home goods do not directly shift panel B curves, but outcomes from panel A may spill over. - Land price relation (amended): - (3’) ˆq_1 = (1−φ_1) μ_1 Δ C_F2 + G_R2 / I_1 - New term G_R2 = dollar value of government spending on housing services in period 2 increases dollar housing rents in period 2, raising ˆq_1 in period 1; credible announced future support can support land price today. - Binding domestic constraint: - (4’) ˆq^binding_1 = ˆq^binding_1 ( κ_q (−) , B^housing_1 (+) , C_F1 + G_R1 (−) , T_GR (−) ) - New terms relative to section 5.2: G_R1 (dollar value of government spending on housing services in period 1) and T_GR (dollar lump-sum transfers to housing sector in period 1). Both relax the domestic borrowing constraint and shift gray zone left. - Ex ante macroprudential measures reduce B^housing_1 but do not provide ex post help; ex post lump-sum transfers provide help but may be infeasible in required magnitudes and may create moral hazard raising B^housing_1. - Take-aways (exact list preserved): - The land price curve is downward-sloping. - The land price curve shifts to the right if period-2 imports increase. - The land price curve shifts to the left if the capital inflow tax is increased. - The land price curve shifts to the left if the FX market is shallow and the local currency premium increases. - The land price curve shifts to the left if the domestic borrowing rate increases above the domestic policy rate. - The land price curve shifts to the right if the government promises to increase its spending on housing services in period 2. - The gray zone (representing a binding domestic borrowing constraint) shifts to the left if the domestic pledgability of assets is higher. - The gray zone shifts to the left if the policymaker sets an ex ante tax or quantity regulation on housing sector debt. - The gray zone shifts to the left if period-1 imports increase. - The gray zone shifts to the left if government spending on housing services and/or lump sum transfers to the housing sector increase in period 1. ### Panel C. Home Goods — Aggregate demand stabilization via the exchange rate - Visual: plots E_1 against ˜Y_H1 (home output gap in period 1); government spending on home goods G_H1 can change shape and position of demand curve under labor-supply-related conditions (parameter ν governs marginal disutility of labor). - Demand for home goods (amended): - (5a’) ˜Y_H1 = C_F1 / E_1 ( C_F1 / E_1 + G_H1 + Y_XH )^{ν−α_H} A_1+ν_1 - (5b’) { ˜Y_H1 = 0 if floating regime and no binding external constraint ; E_1 = E if fixed regime. } - Interpretation: if ν = 0 (no labor supply constraints), G_H1 has no effect on panel C (previous assumption used in sections 3.2 and 5.2). If ν > 0 (marginal disutility of labor increasing in output), an increase in G_H1 rotates home demand curve clockwise, implying an exchange rate appreciation to keep ˜Y_H1 = 0 under a floating regime. - Debt-limit impact from depreciation (external borrowing constraint): - (6a’) E^binding_1 = E^binding_1 ( κ_H (+) , B_1 (−) , X_1 − C_F1 − G_F1 (+) ) - (6b’) ˜Y_H1 = −T + (1−λ) B_1 L if floating regime and binding external constraint. - Inclusion of G_F1 in (6a’) makes trade balance term (X_1 − C_F1 − G_F1) consistent with panel A; reduction in G_F1 reduces B_2 and loosens constraint → E^binding_1 increases. - Period-2 home gap: - (5c’) ˜Y_H2 = E_2 C_F2 / (E_2 C_F2 + G_H2 + Y_XH)^{ν−α_H} A_1+ν_2 ; { ˜Y_H2 = 0 if floating regime ; E_2 = E if fixed regime. } - Take-aways (exact list preserved): - The demand curve is upward-sloping and intersects the vertical axis at the point where the home output gap is zero. - The demand curve rotates clockwise if imports increase. - The demand curve shifts to the left if productivity increases. - The demand curve rotates clockwise if government spending on home goods increases and the economy faces labor supply constraints. - For a fixed exchange rate regime, the home output gap depends on the level at which the exchange rate is fixed. - Interaction examples: - Floating regime: optimal monetary policy sets E_1 so ˜Y_H1 = 0. Increase in G_F1 reduces C_F1 in panel A → home demand curve rotates anticlockwise → exchange rate depreciation. Increase in G_H1 with ν > 0 → home demand rotates clockwise → exchange rate appreciation. - Fixed regime: increase in G_F1 moves intersection with E = fixed line left (˜Y_H1 below zero); increase in G_H1 moves intersection right (˜Y_H1 up); after negative gap shock, increase in G_H1 can push gap back toward zero. - Application: For sudden stop shocks, when ν > 0 an increase in G_H1 can rotate demand clockwise and produce a lower E_1, thereby loosening the external borrowing constraint in panel A. ### Panel D. Policy Rate — Monetary policy decision - Modified UIP condition (amended): - (7’) (1 + i_1) = I_1 μ_1 (1−φ_1) E_2 / E_1 - If FX market shallow, an increase in G_F1 increases total external debt, which raises I_1 and μ_1, shifting the modified UIP to the right. - Take-aways (exact list preserved): - The modified UIP condition is downward-sloping. - The modified UIP condition shifts to the right if the expected exchange rate increases. - The modified UIP condition shifts to the right if the foreign interest rate increases. - The modified UIP condition shifts to the right if the capital inflow tax is increased. - The modified UIP condition shifts to the right if the FX market is shallow and there is an increase in total external debt, FX accumulation, or a non-fundamental capital outflow shock. ### The Complete Diagram and System of Equations - The complete IPF diagram (figure referred to) combines Panels A–D with fiscal policy and all financial frictions; configuration varies by country depending on relevant tools and frictions. - Associated system of equations (amended set, preserved exactly): - (1a’) I_1 = (1 + i^*_1) + (1−λ) Γ (C_F1 + G_F1 − X_1 + Z_1 + FXI_1 − S_1) - (1b’) B_2 = C_F1 + G_F1 − X_1 + Z_1 ( B_1 (+) , 1−λ E_1 (+) ) ≤ B^binding_2 ( κ_H (+) , E_1 (−) ) - (2a’) C_F1 = C_F2 β[I_1 + (1−λ) Γ (B_2 + FXI_1)] ( 1 − 1/α_H A_1+ν_1 ˜Y_H1 1 − 1/α_H A_1+ν_2 ˜Y_H2 ) - (2b’) C_F2 = X_2 − G_F2 + (X_1 − C_F1 − G_F1 − Z_1) I_1 − FXI_1 (1−λ) Γ (B_2 + FXI_1 − S_1) - (2c’) μ_1 = [I_1 + λΓ (B_2 + FXI_1 − S_1)] / I_1 - (2d’) (1−φ_1) (1 + θ_HH1) = I_1 μ_1 / [ I_1 + (1−λ) Γ (B_2 + FXI_1) ] ( 1 − 1/α_H A_1+ν_1 ˜Y_H1 1 − 1/α_H A_1+ν_2 ˜Y_H2 ) - (3’) ˆq_1 = (1−φ_1) μ_1 Δ C_F2 + G_R2 / I_1 - (4’) ˆq^binding_1 = ˆq^binding_1 ( κ_q (−) , B^housing_1 (+) , C_F1 + G_R1 (−) , T_GR (−) ) - (5a’) ˜Y_H1 = C_F1 / E_1 ( C_F1 / E_1 + G_H1 + Y_XH )^{ν−α_H} A_1+ν_1 , with (5b’) { ˜Y_H1 = 0 if floating regime and no binding external constraint ; E_1 = E if fixed regime. } - (5c’) ˜Y_H2 = E_2 C_F2 / (E_2 C_F2 + G_H2 + Y_XH )^{ν−α_H} A_1+ν_2 , with { ˜Y_H2 = 0 if floating regime ; E_2 = E if fixed regime. } - (6a’) E^binding_1 = E^binding_1 ( κ_H (+) , B_1 (−) , X_1 − C_F1 − G_F1 (+) ) - (6b’) ˜Y_H1 = −T + (1−λ) B_1 L if floating regime and binding external constraint. - (7’) (1 + i_1) = I_1 μ_1 (1−φ_1) E_2 / E_1 - Solution approach: inspect system given by (1a’), (2a’)–(2d’), (3’), (5a’)–(5c’), (7’); if that solution implies binding constraints, nonlinear dynamics from (1b’), (4’), and/or (6a’)–(6b’) become relevant. ### 8. Policy Mixes With Fiscal Policy (preview) - Approach: for each shock, start from a diagram in earlier sections and add specific fiscal policy changes to show how normative trade-offs and final macro outcomes alter. Diagrams and mixes are country-specific and depend on which frictions and policy tools are relevant. *Source: wpiea2024038-print-pdf - 7.2 Construction of the Diagram* ### 8.1 Commodity Price Shock ### 8.1 Commodity Price Shock ### Setup and assumptions - Consider a permanent adverse commodity price shock: X1 = X2 = X and there is a decrease in X. - Exchange-rate regime: fixed (peg). - Financial frictions: none; FX market is deep; no domestic or external borrowing constraints. - Inherited debt: B1 = Z1 = 0. - In the absence of the shock: ̃YH1 = ̃YH2 = 0 and βI1 = β(1 + i*1) = 1. - Fiscal baseline in absence of shock: GF1 = GF2 = GF > 0 and GHt = GRt = 0. - From (2a’)-(2b’): consumption is smoothed between periods 1 and 2: CF1 = CF2 = X − GF. - Additional assumptions: ν > 0 (home demand curve concave on panel C) and equation (2d’) holds. ### IPF diagram results (policy mix: decrease GF and increase GHt until ̃YHt = 0) - Panel A — Households’ imports and external financing - Supply curve: unchanged (equation (1a’) unaffected). - Demand curve: shifts to the right because GF decreases. - For the fixed regime, using GHt to ensure ̃YHt = 0 in panel C, equations (2a’)-(2b’) give: - CF1 = (X − GF)(1 + I1) / ( (1 + β) I1 ). - At I1 = (1 + i*1) = 1/β, CF1 = CF2 = X − GF, so the rightward shift equals the decrease in GF. - CF1 increases by the same amount as the decrease in GF; I1 unchanged. - No ex post capital inflow tax or household macroprudential tax required: with ̃YHt = 0, equations (2c’)-(2d’) yield μ1 = 1 and permit φ1 = θHH1 = 0. - Panel B — Housing (land price) - Land price curve shifts to the right because CF2 increases (the increase in CF2 from panel A enters equation (3’)). - ̂q1 increases at unchanged I1. - Panel C — Home goods (home output gap) - Home demand curve rotates clockwise because CF1 increases and GH1 increases (both enter equation (5a’)). - ̃YH1 = 0 can be achieved while maintaining E1 = E (equations (5a’)-(5b’)). - From equation (5c’), ̃YH2 = 0 can also be achieved due to the increase in CF2 and an increase in GH2. - Setting A1 = A2 = A, the necessary government spending is: - GH1 = GH2 = GH = ( (αH A1+ν E(X−GF))^(1/ν) ) − E(X−GF) − YXH. - (Expression preserved exactly as in source.) - Panel D — Policy rate - Modified UIP condition unchanged: equation (7’) incorporates φ1 = 0, I1 unchanged, μ1 = 1, and E2 = E. - i1 is unchanged (E1 is fixed in equation (7’)). ### Overall insights and policy recommendations - Fiscal adjustments can be especially useful under a peg following a permanent adverse commodity price shock. - For both floating and fixed regimes: - A permanent decrease in government spending on imports (GF) can mitigate the decrease in households’ consumption of imports while keeping both the trade balance and external debt in period 1 at zero. - For fixed exchange rate regimes specifically: - Increasing government spending on home goods (GHt) is a useful additional tool to stabilize the home output gap (set ̃YHt = 0). - Policymakers should weigh the stabilization benefits of these fiscal adjustments against costs of fiscal adjustment that lie outside the diagram’s scope. *Source: wpiea2024038-print-pdf - 8.1 Commodity Price Shock* ### 8.5 Di‚erences from the IS-LM Diagram ### 8.5 Differences from the IS-LM Diagram ### Key observations on fiscal policy tools and comparative impacts - The IS-LM diagram includes one kind of government spending tool; the IPF diagram includes three such tools with different positive impacts. - In the IPF diagram: - An increase in government spending on home goods has a similar impact to a traditional fiscal expansion in the IS-LM diagram: both tend to increase home output. The macroeconomic impact then depends on the monetary policy assumption. - Money supply is not fixed in the IPF diagram, so many policy rates and post-shock outcomes are feasible. If there are labor supply constraints, policymakers may increase the policy rate to mitigate some but not all of the increase in output. - Government spending on imports tends to cause a depreciation (the exchange rate moves in the opposite direction to the IS-LM diagram) because import revenues accrue to foreign firms and lump-sum taxes on domestic households reduce income available to purchase imports; if households’ imports decrease, a depreciation is needed to stabilize home output. - Government support for the housing sector stimulates domestic asset prices but does not alter output of home-produced tradable goods, so it does not affect the exchange rate. - Footnote-style quantitative remark preserved from source: - "The magnitude of the home output contraction caused by the exchange rate appreciation is larger if the fiscal expansion is more persistent. If the fiscal expansion is permanent, it causes an appreciation and no change in home output." ### Fiscal policy versus capital controls and FX intervention - The IPF diagram allows comparison of fiscal policy with capital controls and FX intervention across exchange rate regimes and frictions. - For countries with fixed exchange rate regimes: - If fiscal policy is perfectly flexible and sets all home output gaps to zero, capital controls may not be useful. - If fiscal policy is not available, the IPF diagram agrees with IS-LM that home output is destabilized after shocks; however, removal of fiscal policy does not automatically make an ex post capital inflow tax useful. - An ex post capital inflow tax redistributes aggregate demand between periods and is useful only if the home output gap is temporarily destabilized in the current period relative to future periods (example: U.S. monetary tightening shock). The tax is not useful if home output gaps are expected to be equally negative for all future periods (example: commodity price shock). - For countries with financial frictions: - For a non-fundamental outflow shock, it is unrealistic to expect fiscal policy to respond quickly enough; ex post capital controls and FX intervention may better target the source of destabilization. - For a sudden stop shock, ex post fiscal policy can help address some symptoms in practice. Ex ante capital inflow regulations can retain a role in reducing the FX mismatches that are the root cause of vulnerability. ### How the IPF diagram extends policy analysis relative to IS-LM - The IPF framework: - Recognizes heterogeneity in fiscal tools (home goods spending, import spending, housing support) and their distinct exchange rate and output effects. - Permits exploration of combinations of fiscal policy with other policy tools (capital controls, FX intervention, macroprudential measures) under different frictions and shocks. - Shows that the usefulness of capital controls, FX intervention, or fiscal measures depends on (i) the exchange rate regime, (ii) the availability and flexibility of fiscal policy, (iii) the timing and persistence of shocks, and (iv) the nature of financial frictions (e.g., FX mismatches, borrowing constraints). ### Policy implications (enumerated) - Design fiscal instruments with attention to composition: - Spending on home goods: tends to raise home output and may prompt policy-rate responses if labor constraints bind. - Spending on imports: tends to depreciate the exchange rate and can reduce domestic import demand if financed by lump-sum taxes. - Housing support: raises domestic asset prices without directly affecting tradable output or the exchange rate. - In fixed-exchange-rate regimes, evaluate whether fiscal flexibility can substitute for capital controls; where fiscal policy is constrained, consider targeted capital flow measures only if intertemporal demand imbalances justify them. - For sudden stop scenarios, combine ex post fiscal responses with ex ante capital-flow regulation to address FX mismatches and reduce vulnerability. - For shallow FX markets or occasionally binding borrowing constraints, monetary policy frameworks may need to: - Allow the policy rate to deviate from standard AE-optimal rules, or - Envisage additional tools in stressed times so the policy rate can follow a more stable path. *Source: An Integrated Policy Framework (IPF) Diagram for International Economics, Working Paper No. WP/2024/038 — section 8.5* --- _Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024038-print-pdf.pdf_