## 4.1 Policy Instruments and Wedges ## Source details **Canonical URL:** [4.1 Policy Instruments and Wedges](https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020121-print-pdf.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2020/english/wpiea2020121-print-pdf.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2020/english/wpiea2020121-print-pdf.pdf.json) --- ### Deep FX markets and UIP - Deep FX markets correspond to setting Γ = 0 in the constraints and FOCs. - Financial intermediaries face no balance sheet constraints; capacity to hold domestic currency debt is unlimited. - Country’s external debt position does not matter for the country’s gross external return, ηt. - Gamma equations reduce to the UIP conditions: E0[τΓ1] = 0 and τΓ2 = 0. (21) - UIP wedges, τΓt, generate welfare losses if a fraction of intermediaries are foreign-owned (λ∈[0,1)), but since UIP wedges average out to zero, average external premium is zero. - For simplicity the analysis sets λ = 1 (domestic households own all financial intermediaries). If domestic households own all intermediaries, the economy’s liabilities are effectively entirely in dollars. - Housing frictions assumed not to bind (either θLinear Rt ∈ R and θConcave Rt ∈ R allowed, or κL1 → ∞). - Absence of binding housing frictions implies one of the two instruments—capital controls and consumer macroprudential taxes—may be redundant because both affect the economy via altering external debt. ### Households’ Euler conditions and effectiveness of capital controls - Households’ Euler conditions (rewritten): - αF P∗F0 CF0 = β (1 + i∗0) (1 − φ0) 1 E0 [E0 E1] E0 [E0 E1 αF P∗F1 CF1] - αF P∗F1 CF1 ≥ β (1 + i∗1) (1 − φ1) αF P∗F2 CF2. (22) - Implications: - Capital controls are effective under deep FX markets because they raise the domestic policy rate above the foreign interest rate and thereby reduce domestic borrowing. - Exchange rates E0 and E1 enter the Euler condition between periods 0 and 1 because households have access to domestic currency bonds only, and not dollar bonds; the contingency of available bonds affects risk-sharing. - Exchange rates do not enter the Euler condition between periods 1 and 2 because there is no uncertainty between those periods. ### Planner’s Euler conditions and wedges - Planner’s Euler conditions for t ∈ {0,1} (equation (23) preserved in structure): - αF P∗Ft CFt [1 + (αH / αF) τHt] − IDCP · { E0[∑2 t=0 βt ωC∗t αF CFt τDCP Xt] 1 βt πt 1 P∗Ft 1 PX ∂PX ∂CFt } = β(1 + i∗t) Et { αF P∗Ft+1 CFt+1 [1 + (αH / αF) τHt+1] } + ΨBt 1 β (1 + i∗t−1) − IDCP · { E0[∑2 t=0 βt ωC∗t αF CFt τDCP Xt] Et[ (1 + i∗t) βt πt+1 1 P∗Ft+1 1 PX ∂PX ∂CFt+1 ] }. - Interpretations: - LHS first term: marginal utility of consumption in period t, accounting for the AD wedge τHt. - LHS second term: effect under DCP from period-t consumption on welfare via period-0 export-price-setting. - RHS first term: marginal utility of consumption in period t+1 with AD wedge. - RHS second term: distortion if borrowing constraint binds (multiplier ΨBt). - RHS third term: impact of period t+1 consumption on welfare via period-0 export-price-setting. - Two wedges that may justify policy intervention under deep FX markets: τHt (AD wedge) and τXt (TOT wedge). - If all wedges set to zero, household and planner Euler conditions reduce to: - αF P∗Ft CFt = β(1 + i∗t) Et[ αF P∗Ft+1 CFt+1 ] for t ∈ {0,1}, - identical to households participating without restriction in the dollar bond market; planner would set domestic policy rate consistent with zero capital controls and allow full exchange rate flexibility. - When wedges are not zero, planner may move domestic policy rate differently and add capital controls to stabilize wedges over time. ### FOCs for exchange rates: trade-offs and channels - Exchange-rate FOC (state-specific) summarized (equation (24) structure preserved): - αH τHt ︸︷︷︸ Stabilize demand for home goods = − IPCP · { ωC∗t αF CFt τPCP Xt } − IDCP · { E0[∑2 t=0 βt ωC∗t αF CFt τDCP Xt] 1 βt πt Et PX (− ∂PX ∂Et) } ︸︷︷︸ Optimize TOT on export goods + ΨBt βt (1 + i∗t−1) κH1 PH Et ︸︷︷︸ Relax bank constraint. - Planner balances: - Benefit of moving exchange rate to generate import substitution and stabilize domestic demand for home-produced tradables (AD wedge τHt). - Benefit of moving exchange rate to optimize TOT on exports by altering export volume (TOT wedges τXt), within-state (PCP) or on average via period-0 export-price-setting (DCP). - Effect of exchange rate movements on tightness of borrowing constraint (ΨBt term). - Domestic policy rate moves inversely to expected exchange rate depreciation (consistent with condition (21)). ### Capital controls: expression and interpretation - Capital controls expression (equation (25) preserved in form): - φt = { 1 − 1 Et[Et Et+1] Et[Et Et+1 αF P∗Ft+1 CFt+1] [ αF P∗Ft CFt [1 + (αH / αF) τHt] − IDCP · { E0[∑2 t=0 βt ωC∗t αF CFt τDCP Xt] 1 βt πt 1 P∗Ft 1 PX ∂PX ∂CFt } ] αF P∗Ft CFt [ Et{ αF P∗Ft+1 CFt+1 [1 + (αH / αF) τHt+1 ]} − IDCP · { E0[∑2 t=0 βt ωC∗t αF CFt τDCP Xt] Et[ 1 βt+1 πt+1 1 P∗Ft+1 1 PX ∂PX ∂CFt+1 ] } ] } if ΨBt = 0; 0 if ΨBt > 0. - Key points: - Capital controls are ineffectual (set to zero) when the banks’ borrowing constraint binds (ΨBt > 0). - Capital controls are non-zero iff numerator and denominator of the fraction are unbalanced; numerator and denominator obtained by substituting AD wedge τHt using equation (24). - Two model rationales for capital controls: 1. Pecuniary AD externality from an occasionally-binding borrowing constraint (ΨBt > 0): planner may keep AD wedge τHt higher (policy rate higher and exchange rate more appreciated) to relax constraint; monetary policy and exchange rate flexibility no longer fully address AD externality → prudential capital controls optimal. 2. TOT externality: capital controls non-zero if weighted TOT wedges τXt are not balanced over time (Costinot, Lorenzoni, Werning-type channel). - Integrated model necessary: each instrument affects several wedges; the domestic policy rate affects exchange rates and thereby optimal capital controls, and vice versa. ### Substitutability with consumer macroprudential taxes - Consumer macroprudential taxes θHHt can substitute for capital controls φt in subsections 4.2–4.3; planner uses either instrument while setting the other to zero. - Relationship (equation (26) preserved): - (1 − φt) / (1 + θHHt) = { ηt+1 Et+1 β Et{ 1 Et+1 αF P∗Ft+1 CFt+1 } αF P∗Ft CFt if ΨBt = 0; 1 if ΨBt > 0. (26) - In subsection 4.4, with unregulated sectors and/or circumvention, the two instruments become complements and need to be used together. ### Real shocks: role of initial external currency exposure - Real shocks affect real income of domestic households. - Recommendations sometimes conditioned on Bt (≡ Dt Et−1), total domestic currency debt stock at beginning of period t converted into dollar value. - With domestic households owning all intermediaries, Bt represents representative household’s effective exposure to external dollar-denominated debt. ### Productivity shocks: permanent A1 = A2 shock — policy implications - Under PCP: - Optimal to let exchange rate move to absorb shock; policy rate unchanged; ex ante and ex post capital controls are zero. - Exchange rate depreciates after positive productivity realization; with unit elastic export demand, no increase in dollar export revenues; households not wealthier in dollar terms; imports unchanged. - Employment perfectly stabilized; AD and TOT wedges fully stabilized → no case for capital controls; result independent of B0. - Under DCP: - Employment and TOT wedges not stabilized by exchange rate, but capital controls still not optimal because they do not address stickiness of dollar export price. - Result 1: Countries facing permanent productivity shocks should rely solely on exchange rate flexibility, under both PCP and DCP. - Remark 1: After permanent productivity shocks, TOT wedges are stabilized under PCP and not under DCP, but capital controls are optimally zero in both cases. ### Commodity price shocks: permanent P∗Z1 = P∗Z2 shock — policy implications - Setup compares B0 = 0 versus B0 > 0, same κH1 ∈ (0,1). - Under PCP and B0 = 0: - Capital controls optimal only insofar as intertemporal TOT externality is relevant; optimal to allow exchange rate flexibility without moving policy rate; small ex ante capital controls arise solely from intertemporal TOT externality. - When B0 high enough: - Capital controls become optimal to address pecuniary AD externalities; after low realization borrowing constraint binds due to depreciation contracting debt limit; planner keeps policy rate higher and exchange rate more appreciated than AD and TOT wedges would justify and uses ex ante capital controls. No case for ex post capital controls. - Under DCP: - Exchange rate more volatile and tradable employment destabilized. - DCP countries more vulnerable to binding borrowing constraints; for same shock and B0, constraints bind for larger set of shocks and initial conditions. - Therefore DCP countries more likely to impose ex ante capital controls to address pecuniary AD externalities and set larger ex ante capital controls than under PCP. - Result 2: Commodity exporters should not impose capital controls to address pecuniary AD externalities if there are no borrowing constraints, but should impose positive ex ante capital controls if there are borrowing constraints and external FX debt is high. Ex post capital controls are not desirable. - Remark 2: After commodity price shocks, exchange rates are more volatile under DCP than PCP. - Remark 3: For commodity-exporting countries with borrowing constraints and high initial external FX debt, ex ante capital controls are more frequently optimal and larger under DCP than PCP. Final policy takeaways from 4.1 - Capital controls are a tool to address pecuniary AD externalities (when ΨBt = 0 they can be non-zero; when ΨBt > 0 they are set to zero). - Capital controls and consumer macroprudential taxes can be substitutes if coverage is perfect (equation (26)), but become imperfect substitutes or complements when coverage is limited or circumvention is possible. - Exchange rate flexibility is the primary tool for absorbing certain real shocks (permanent productivity shocks) under both PCP and DCP; capital controls are primarily justified when borrowing constraints and FX mismatches create pecuniary externalities. - Integrated policy design matters: policy rate, exchange rate, capital controls, macroprudential taxes, and FX intervention interact through wedges τHt, τΓt, τXt and through multiplier ΨBt. *Source: 4.1 Policy Instruments and Wedges (wpiea2020121-print-pdf).* ### 4.1 Policy Instruments and Wedges ### 4.1 Policy Instruments and Wedges ### Deep FX markets and UIP - Deep FX markets case corresponds to setting Γ = 0 in the constraints and FOCs summarized in Appendix A.2. - Financial intermediaries face no balance sheet constraints; capacity to hold domestic currency debt is unlimited. - Country’s external debt position does not matter for the country’s gross external return, ηt. - Gamma equations reduce to the UIP conditions: E0[τΓ1] = 0 and τΓ2 = 0. (21) - UIP wedges, τΓt, generate welfare losses if a fraction of intermediaries are foreign-owned (λ∈[0,1)), but since UIP wedges average out to zero, average external premium is zero. - For simplicity the analysis sets λ = 1 (domestic households own all financial intermediaries). If domestic households own all intermediaries, the economy’s liabilities are effectively entirely in dollars. - Housing frictions are assumed not to bind (follows from regulation of both housing subsectors, i.e., both θLinear Rt ∈ R and θConcave Rt ∈ R are allowed, or from high housing sector debt capacity, i.e., κL1 → ∞). - Absence of binding housing frictions implies one of the two instruments—capital controls and consumer macroprudential taxes—may be redundant because both affect the economy via altering external debt. ### Households’ Euler conditions and effectiveness of capital controls - Households’ Euler conditions can be rewritten as: - αF P∗F0 CF0 = β (1 + i∗0) (1 − φ0) 1 E0 [E0 E1] E0 [E0 E1 αF P∗F1 CF1] - αF P∗F1 CF1 ≥ β (1 + i∗1) (1 − φ1) αF P∗F2 CF2. (22) - Implications: - Capital controls are effective under deep FX markets because they raise the domestic policy rate above the foreign interest rate and thereby reduce domestic borrowing. - Exchange rates E0 and E1 enter the Euler condition between periods 0 and 1 because households have access to domestic currency bonds only, and not dollar bonds; the contingency of available bonds affects risk-sharing. - Exchange rates do not enter the Euler condition between periods 1 and 2 because there is no uncertainty between those periods. ### Planner’s Euler conditions and wedges - Planner’s Euler conditions for t ∈ {0,1}: - αF P∗Ft CFt [1 + (αH / αF) τHt] − IDCP · { E0[∑2 t=0 βt ωC∗t αF CFt τDCP Xt] 1 βt πt 1 P∗Ft 1 PX ∂PX ∂CFt } = β(1 + i∗t) Et { αF P∗Ft+1 CFt+1 [1 + (αH / αF) τHt+1] } + ΨBt 1 β (1 + i∗t−1) − IDCP · { E0[∑2 t=0 βt ωC∗t αF CFt τDCP Xt] Et[ (1 + i∗t) βt πt+1 1 P∗Ft+1 1 PX ∂PX ∂CFt+1 ] }. (23) - Interpretations of terms: - Left-hand first term: marginal utility of consumption in period t, accounting for the AD wedge τHt. - Left-hand second term: effect under DCP from period-t consumption on welfare via period-0 export-price-setting. - Right-hand first term: marginal utility of consumption in period t+1 with AD wedge. - Right-hand second term: distortion if borrowing constraint binds (multiplier ΨBt). - Right-hand third term: impact of period t+1 consumption on welfare via period-0 export-price-setting. - Two wedges that may justify policy intervention under deep FX markets: τHt (AD wedge) and τXt (TOT wedge). - If all wedges set to zero, both household and planner Euler conditions reduce to: - αF P∗Ft CFt = β(1 + i∗t) Et[ αF P∗Ft+1 CFt+1 ] for t ∈ {0,1}, - identical to households participating without restriction in the dollar bond market; planner would set domestic policy rate consistent with zero capital controls and allow full exchange rate flexibility. - When wedges are not zero, planner may move domestic policy rate differently and add capital controls to stabilize wedges over time. ### FOCs for exchange rates: trade-offs and channels - FOCs for exchange rates in each state: - αH τHt ︸︷︷︸ Stabilize demand for home goods = − IPCP · { ωC∗t αF CFt τPCP Xt } − IDCP · { E0[∑2 t=0 βt ωC∗t αF CFt τDCP Xt] 1 βt πt Et PX (− ∂PX ∂Et) } ︸︷︷︸ Optimize TOT on export goods + ΨBt βt (1 + i∗t−1) κH1 PH Et ︸︷︷︸ Relax bank constraint. (24) - Planner sets exchange rate to balance: - Benefit of moving exchange rate to generate import substitution and stabilize domestic demand for the home-produced tradable good (term with AD wedge τHt). - Benefit of moving exchange rate to optimize TOT on export goods by altering export volume (term with TOT wedges τXt), either within a state (PCP) or on average via period-0 export-price-setting (DCP). - Effect of exchange rate movements on tightness of borrowing constraint (term with ΨBt). - Domestic policy rate moves inversely to expected exchange rate depreciation (in line with condition (21)). ### Capital controls: expression and interpretation - Capital controls expression: - φt = { 1 − 1 Et[Et Et+1] Et[Et Et+1 αF P∗Ft+1 CFt+1] [ αF P∗Ft CFt [1 + (αH / αF) τHt] − IDCP · { E0[∑2 t=0 βt ωC∗t αF CFt τDCP Xt] 1 βt πt 1 P∗Ft 1 PX ∂PX ∂CFt } ] αF P∗Ft CFt [ Et{ αF P∗Ft+1 CFt+1 [1 + (αH / αF) τHt+1 ]} − IDCP · { E0[∑2 t=0 βt ωC∗t αF CFt τDCP Xt] Et[ 1 βt+1 πt+1 1 P∗Ft+1 1 PX ∂PX ∂CFt+1 ] } ] } if ΨBt = 0; 0 if ΨBt > 0. (25) - Key points: - Capital controls are ineffectual (set to zero) when the banks’ borrowing constraint binds (ΨBt > 0). - Capital controls are non-zero iff numerator and denominator of the fraction are unbalanced; numerator and denominator obtained by substituting AD wedge τHt using equation (24). - Two possible rationales for capital controls in the model: 1. Pecuniary AD externality from an occasionally-binding borrowing constraint (ΨBt > 0): households do not internalize that period-t borrowing can lower aggregate demand and cause a more depreciated exchange rate in period t+1, making the borrowing constraint binding. Planner may keep AD wedge τHt higher than TOT wedges τXt would justify—policy rate higher and exchange rate more appreciated—to relax the constraint. Monetary policy and exchange rate flexibility no longer fully address the AD externality, so prudential capital controls become optimal (captures Farhi and Werning 2016 insights). 2. TOT externality: capital controls are non-zero if weighted TOT wedges τXt are not balanced over time (as in Costinot, Lorenzoni, and Werning, 2014). This channel arises in open-economy frameworks with price-setting. - Integrated model necessary: use of each policy instrument affects several wedges; level of domestic policy rate affects exchange rates and thereby optimal use of capital controls, and vice versa. ### Substitutability with consumer macroprudential taxes - In subsections 4.2–4.3, consumer macroprudential taxes θHHt are substitutes for capital controls φt; either can be used by the planner while the other set to zero. - Relationship: - (1 − φt) / (1 + θHHt) = { ηt+1 Et+1 β Et{ 1 Et+1 αF P∗Ft+1 CFt+1 } αF P∗Ft CFt if ΨBt = 0; 1 if ΨBt > 0. (26) - In subsection 4.4, with unregulated sectors and/or circumvention, the two instruments become complements and need to be used together. ### Real shocks: setup and role of initial external currency exposure - Real shocks considered affect real income of domestic households. - Recommendations sometimes conditioned on Bt (≡ Dt Et−1), the total domestic currency debt stock at beginning of period t converted into dollar value. - Since debt is sold to international financial intermediaries and domestic households own all intermediaries, Bt represents representative household’s effective exposure to external dollar-denominated debt. ### Productivity shocks: permanent A1 = A2 shock - Consider permanent productivity shock A1 = A2 in tradable production. - Parameterization to neutralize intertemporal TOT externality: E0[A0 A1] = 1. - Under PCP: - Optimal to let exchange rate move to absorb shock without moving any policy instruments. - Policy rate remains unchanged; both ex ante and ex post capital controls are zero (Figure 5 reference). - After high productivity realization: increase in domestic aggregate supply → exchange rate depreciates to close gap between demand and supply → exports more competitive. - Given unit elastic demand for exports, no increase in dollar value of export revenues, so households not wealthier in dollar terms; imports unchanged across realizations. - Households consume more home tradable good after positive productivity shock; Et At constant across states. - Employment perfectly stabilized across high and low shocks; AD and TOT wedges fully stabilized across shocks and over time → no case for capital controls; result independent of initial external debt B0. - Under DCP: - Employment and TOT wedges are not stabilized across high and low shocks by the exchange rate (Figure 6 reference). - Nevertheless, capital controls do not become optimal: instrument should only be used if it can help stabilize the wedge, and capital controls do not address the source of the stabilization problem (stickiness of dollar export price). - Result 1: Countries facing permanent productivity shocks should rely solely on exchange rate flexibility, under both PCP and DCP. - Remark 1: After permanent productivity shocks, TOT wedges are stabilized under PCP and not under DCP, but capital controls are optimally zero in both cases. ### Commodity price shocks: permanent P∗Z1 = P∗Z2 shock - Permanent commodity price shock to dollar price of commodities P∗Z1 = P∗Z2; relevant for large commodity sectors. - Simulations compare two commodity exporters with different initial conditions: B0 = 0 (no unhedged external FX debt) versus B0 > 0 (high unhedged external FX debt), assuming same κH1 ∈ (0,1). (Footnote notes alternative exercise fixing B0 and varying κH1 would yield qualitatively similar features.) - Under PCP and B0 = 0: - Capital controls optimal only insofar as intertemporal TOT externality is relevant. - Optimal to allow exchange rate flexibility without moving policy rate; small ex ante capital controls arise solely from intertemporal TOT externality (Figure 7 reference). - After low realization: aggregate demand decreases and households poorer in dollar terms; planner allows exchange rate depreciation which decreases imports; higher export demand from depreciation offsets wealth-driven decrease in domestic consumption of home traded good → tradable sector employment stabilized and insulated from commodity sector. - When B0 high enough: - Capital controls become optimal to address pecuniary AD externalities. - After low realization, borrowing constraint becomes binding because associated exchange rate depreciation causes contraction in dollar value of debt limit; forced deleveraging causes further contraction in aggregate demand. - Planner recognizes depreciation tightens constraint (19); per equation (24), planner keeps policy rate higher and exchange rate more appreciated than AD and TOT wedges would justify. - Domestic consumption of home good and tradable employment decline; planner uses ex ante capital controls to address pecuniary AD externalities. No case for ex post capital controls (Figure 8 reference). - Under DCP: - Exchange rate more volatile and tradable employment destabilized. - Without borrowing constraint, planner implements same decrease in imports under DCP as under PCP after low realization; however, depreciations do not increase export demand under DCP, so planner induces households to consume more home goods, requiring larger depreciation than under PCP; result can increase tradable employment (Figure 9 reference). - Commodity-exporting countries with DCP are more vulnerable to binding borrowing constraints: larger depreciation after low realization means debt limit contracts more under DCP; for same shock and B0, borrowing constraints bind more severely under DCP than PCP, i.e., constraints bind for a larger set of shocks and initial conditions (Figure 10 reference). - Therefore, countries with DCP are more likely to impose ex ante capital controls to address pecuniary AD externalities and set larger ex ante capital controls than under PCP. - Result 2: Countries with large commodity sectors should not impose capital controls to address pecuniary AD externalities if there are no borrowing constraints, but should impose positive ex ante capital controls for this purpose if there are borrowing constraints and external FX debt is high. Ex post capital controls are not desirable. - Remark 2: After commodity price shocks, exchange rates are more volatile under DCP than PCP. - Remark 3: For countries with large commodity sectors, borrowing constraints, and high initial external FX debt, ex ante capital controls to address pecuniary AD externalities are more frequently optimal, and larger in magnitude, under DCP than PCP. _Italic: Content derived from "4.1 Policy Instruments and Wedges" (wpiea2020121-print-pdf)._ ### 4.3 Financial Shocks ### 4.3 Financial Shocks ### 4.3.1 World Interest Rate Shocks - Definition: A world interest rate shock is a shock to the value of (1 + i∗1). It could be triggered by a change in U.S. monetary policy, expected global growth, or global risk appetite. - PCP (planner with commitment to PCP): - Optimal instruments: use the domestic policy rate combined with exchange rate flexibility; capital controls are only optimal insofar as the intertemporal TOT externality is relevant. - Allocation dynamics: if the realization of the world interest rate is high, imports decline in period 1 and increase in period 2 (consistent with households’ Euler equation between periods 1 and 2). - Response: planner allows an exchange rate depreciation and increases the domestic policy rate, but less than the increase in the world interest rate; this stimulates export demand and generates import substitution. - Employment: Employment is stabilized across the high and low shocks. - Borrowing constraints: A jump in the world interest rate on its own does not tend to make borrowing constraints binding in the simulations; depreciation contracts the debt limit, but desired debt falls more rapidly. - DCP (planner under DCP): - Exchange rate: more volatile under DCP than PCP. - Policy rate: kept unchanged in response to the shock (for the same shock under DCP relative to PCP). - Employment: becomes destabilized by the shock. - Capital controls: ex post capital controls that were optimal under PCP disappear under DCP; small ex ante capital controls are generated by the same motive. - Result 3: Countries facing world interest rate shocks should not use capital controls to address AD externalities under PCP or DCP. - Remark 4.A: After world interest rate shocks, exchange rates are more volatile under DCP than PCP. ### 4.3.2 Foreign Appetite Shocks - Definition: A foreign appetite shock is a shock to the value of S1. - Deep FX markets: - Allocations are not affected by this shock. - Further consideration deferred to section 5. - Result 4: Countries with deep FX markets do not need to respond to shocks to the foreign appetite for domestic currency debt. ### 4.3.3 Bank Debt Limit Shocks - Definition: A bank debt limit shock is a shock to the value of κH1, the pledgability parameter in the banks’ external borrowing constraint. A decline in κH1 reflects either a downgrade in the perceived credit-worthiness of banks in a particular borrower country, or a reversal in the willingness of international banks to extend credit to banks in all borrower countries. - PCP: - If initial external FX debt B0 is high enough, it is optimal to impose ex ante capital controls to address pecuniary AD externalities. - After a low realization of the shock, the borrowing constraint can become binding; the planner lowers the policy rate to support aggregate demand. - Nevertheless, the planner keeps the policy rate higher, and the exchange rate more appreciated, than price pressures from the AD and TOT wedges would justify. - Ex ante capital controls are used to address the pecuniary AD externalities. - DCP: - Exchange rate: more depreciated after the debt limit shock and ex ante capital controls are larger under DCP than PCP. - Mechanism: exchange rate is a weaker tool for import/export substitution under DCP; if exchange rate depreciation may tighten external debt limits, planner weighs depreciations’ limited benefits against equal costs of tightening the constraint under both regimes. - Planner imposes higher ex ante capital controls under DCP to relax the constraint in period 1; multiplier on external borrowing constraint is lower under DCP than PCP. - Ex post capital controls during the sudden stop: no case for ex post controls when inflows are already constrained, as controls have no effect. - Effects of allowing ex ante capital controls: - Can increase the ex post policy rate in simulation owing to two effects: - “Financial channel”: pushes for a lower ex post policy rate (capital controls reduce external debt and thereby reduce the need for a high ex post policy rate to relax the external constraint). - “Macro channel”: pushes for a higher ex post policy rate (capital controls shift aggregate demand from period 0 to period 1). - Net effect on the ex post policy rate may be ambiguous in practice. - Result 5: Countries with high external FX debt whose banks are vulnerable to external debt limit shocks should impose positive ex ante capital controls. - Remark 5: For countries with high external FX debt and vulnerability to external debt limit shocks, ex ante capital controls are larger under DCP than PCP. - Remark 6: Imposing ex ante capital controls shifts both sides of the macro-financial trade-off for monetary policy, with ambiguous results on whether the policy rate and capital controls are substitutes or complements. ### 4.4 Extension: Limits to Regulation - Baseline assumption removed: earlier subsections assumed housing sector frictions are not relevant, all households borrow only from domestic banks, and these banks are the sole domestic counterparties of international financial intermediaries; consumer macroprudential taxes can achieve full coverage and substitute for capital controls. - Two forms of imperfect coverage considered: 1. Partial coverage: consumer macroprudential taxes cover a subset of households; the remainder borrow directly from international financial intermediaries (beyond domestic macroprudential perimeter). Assumption: households who borrow directly from intermediaries face an external borrowing constraint of their own with the same formulation as the banks’ constraint. - Implication: consumer macroprudential taxes are imperfect substitutes for capital controls—they reduce external debt of regulated households, but not that of unregulated households. - Planner prescription: set consumer macroprudential taxes θHHt for domestically-regulated households pinned down by setting φt = 0 in expression (26), and set capital controls φt on intermediaries lending to the other households pinned down by setting θHHt = 0 in that expression. 2. Circumvention: all households officially regulated, but they can circumvent taxes and issue debt directly to international financial intermediaries. Assumption: households and banks face identical external borrowing constraint. - Implication: consumer macroprudential taxes and capital controls are perfect complements. If planner imposes consumer macroprudential taxes alone, households shift borrowing to intermediaries and taxes have no effect; capital controls are needed to be effective. - Planner prescription: set θHHt on all households’ borrowing from domestic banks and additionally impose φt on any intermediaries lending directly to households. - General principle: imperfect coverage by consumer macroprudential taxes should be remedied by capital controls, and vice versa. - Result 6: Capital controls and consumer macroprudential taxes are imperfect substitutes if macroprudential taxes do not cover all household borrowing, and they are perfect complements if households can circumvent the macroprudential taxes via cross-border transactions which are not intermediated through the domestic banking system. ### 4.5 Extension: FX Swap Lines - Planner can access bilateral or multilateral FX swap lines in period 1, convert FX into domestic currency, transfer proceeds to domestic banks, and make repayments at the world interest rate on those facilities in period 2 by collecting domestic currency repayments from banks in line with the domestic interest rate. - Effect on banks’ debt limit: - Augmented constraint: D2 ≤ κH1 PH1 + F2, where F2 is the total available FX summed over all swap lines. - Interpretation: Access to swap lines is isomorphic to an increase in κH1. - Value of drawing on swap lines: - Valuable during period-1 states when banks’ borrowing constraint is binding (e.g., after large commodity price declines or substantial tightening of banks’ external debt limits). - Reduces the severity of the constraint in period 1 and thus reduces the need for ex ante capital controls. ### 4.6 Summary - Key policy insight: For countries with deep FX markets, several shocks and structural characteristics can justify deviation from relying solely on the domestic policy rate and exchange rate flexibility. - Pecuniary-AD-externality rationale: - Countries should impose positive ex ante capital controls to reduce ex ante overborrowing if they have high external FX debt relative to their debt limits, combined with exposure to commodity price and/or debt limit shocks. - If external FX debt limits are irrelevant, there is no case for capital controls to address AD externalities for countries facing productivity shocks, commodity price shocks, world interest rate shocks, and foreign appetite shocks. - Role of DCP: - DCP on its own does not justify capital controls to address AD externalities. - In combination with FX mismatches and external debt limits, DCP increases incidence and severity of binding borrowing constraints. - Countries with DCP require ex ante capital controls for a larger range of initial external FX debt levels than countries with PCP, and ex ante capital controls are larger under DCP than PCP. - Mapping a retrenchment of the global financial cycle (three component shocks: rise in world interest rates, decline in foreign appetite for domestic currency debt, contraction in FX debt limits) to model implications: - Optimal policy rate response is heterogeneous across countries and retrenchment episodes. - Planner accommodates world interest rate shock by allowing exchange rate depreciation and cushioning aggregate demand: - Under PCP: raise the policy rate less than the increase in the world interest rate. - Under DCP: minimal change in the policy rate. - Planner ignores foreign appetite shock and keeps policy rate unchanged. - After debt limit shock: planner reduces policy rate but keeps it high enough to partially defend the exchange rate. - Heterogeneity: because retrenchment episodes differ in shock blends and countries have heterogeneous vulnerabilities, cross-country policy rate responses should be heterogeneous. - Capital controls: - Used in only one direction (ex ante) and not evenly across countries and episodes. - Ex ante capital controls may be welfare-improving only when the debt-limit-contraction component of the global cycle is relevant; used by countries with high FX external debt relative to their debt limits. - Macroprudential taxes vs capital controls: - Consumer macroprudential taxes substitute for capital controls if they have perfect coverage of all relevant debt transactions. - With imperfect coverage, they become imperfect substitutes or complements; in the latter case they should be used together. - FX swap lines: access reduces necessary ex ante capital controls and macroprudential taxes. *Source: wpiea2020121-print-pdf - 4.3 Financial Shocks* ### 5.2 Real Shocks ### 5.2 Real Shocks ### 5.2.1 Productivity Shocks - Setup: - Permanent shocks to productivity: A1 = A2. - Shallow FX markets: effective dollar-denominated-debt exposure at beginning of period t is λB_t−(1−λ)FXI_{t−1}; effective domestic-currency-debt exposure is (1−λ)(B_t + FXI_{t−1}). - Intertemporal TOT-neutralizing parameterization condition under shallow FX markets: - E0[ A0/A1 · ( λ(1 + i^*_0) + (1−λ) η1 (1 + i^*_0) ) ] = 1. - PCP (Planner’s Commitment Policy): - Optimal response: rely solely on exchange rate flexibility to absorb the permanent productivity shock. - Imports and employment are smoothed between periods 0 and 1 and across period-1 states, so households do not issue external debt in period 1. - Ex post capital controls and FX intervention are zero; ex ante capital controls and FX intervention are zero as well. - DCP (Discretionary Policy): - Exchange rate flexibility remains the main tool to absorb the shock. - In both period-1 states, (B2 + FXI1) is kept at zero: FX intervention is used solely to minimize external premia; capital controls are zero. - Employment is destabilized across states under DCP, producing a small ex ante motive to generate a domestic-currency-denominated asset position via (1−λ)(B1 + FXI0) < 0 (repayment contingency motive). - Implementation in simulations: elevated policy rate combined with small capital inflow subsidies and FX sales to achieve the small desired asset position. - Key statement: - Result 7. Countries facing permanent productivity shocks should rely solely on exchange rate flexibility, under both PCP and DCP, even if FX markets are shallow. - Remark 7. Permanent productivity shocks do not rationalize ex post capital controls. FX intervention should minimize premia while allowing the same degree of exchange rate flexibility as in the deep FX markets case. ### 5.2.2 Commodity Price Shocks - Setup: - Permanent shocks to dollar commodity price: P^*_Z1 = P^*_Z2. - Compare two commodity exporters with different initial unhedged external FX debt B0 and same κ_{H1} ∈ (0,1). - Cases and findings: - For B0 = 0: - Under both PCP and DCP, optimal policies identical between deep and shallow FX markets. - New domestic-currency debt should not be issued after permanent shocks → depth of FX market irrelevant for ex post policy responses. - Smoothing of imports and employment pins down ex ante policy responses. - For sufficiently high B0 such that banks’ external constraints bind after the low shock: - Optimal policies identical between deep and shallow FX markets except the steady-state level of FX intervention. - Under shallow FX markets, positive domestic-currency debt for intermediaries generates steady-state financial TOT externalities and gross external premia, reducing welfare. - Planner assumed capable of intermediation in domestic-currency debt market to reduce premia to zero; FX intervention is used solely to minimize external premia and set (B2 + FXI1) = 0. - Key statements: - Result 8. Countries with large commodity sectors should not impose capital controls to address pecuniary AD externalities if there are no borrowing constraints, but they should impose positive ex ante capital controls for this purpose if there are borrowing constraints and initial external FX debt is high. - Remark 8. Permanent commodity price shocks do not rationalize ex post capital controls. FX intervention should minimize premia while allowing the same degree of exchange rate flexibility as in the deep FX markets case. - Remark 9. For countries with large commodity sectors, borrowing constraints, high initial external FX debt, and either deep and shallow FX markets, ex ante capital controls to address pecuniary AD externalities are more frequently optimal, and they are larger in magnitude, under DCP than PCP. ### 5.3 Financial Shocks - General note: - Under shallow FX markets, financial shocks interact with occasionally-binding debt limits and always-binding intermediation frictions. Some shocks ignorable under deep FX markets cannot be ignored under shallow FX markets. ### 5.3.1 World Interest Rate Shocks - Shock: change to (1 + i^*_1). - PCP: - Planner accommodates the shock using complementary instruments: monetary policy (MP), capital controls (CC), and, when available, FX intervention. - With only MP and CC: a decline in world interest rate → imports up in period 1 and down in period 2; external borrowing increases UIP wedges earned by foreign-owned intermediaries → planner reduces domestic policy rate only slightly and uses capital controls reflecting both new financial TOT externality and intertemporal TOT externality. - Adding FX intervention: FX intervention allows more accommodation and more exchange rate volatility. Planner conducts ex post FX sales and purchases domestic-currency bonds to reduce premia; (B2 + FXI1) is pushed to zero; planner reduces ex post policy rate more and stimulates more ex post debt. - Overall: combination of looser monetary policy and expansionary FX intervention to accommodate the low world interest rate and minimize the UIP wedge. - DCP: - FX intervention used to accommodate the low shock, increasing debt and aggregate demand while minimizing UIP wedge. - Differences vs PCP: - Exchange rate more volatile under DCP than PCP. - Introduction of FX intervention reduces rather than increases ex post movement in the policy rate because it brings policy rate closer to its deep-FX-market equivalent (policy rate kept constant under deep FX markets). - Key statement: - Result 9. Countries facing world interest rate shocks should use ex post FX intervention to accommodate the shocks, rather than lean against them, under both PCP and DCP. - Remark 10. After world interest rate shocks, exchange rates are more volatile under DCP than PCP. ### 5.3.2 Foreign Appetite Shocks - Shock: change to S1 (foreign demand for domestic-currency bonds unrelated to returns). - PCP: - Domestic policy rate is a poor substitute for capital controls and FX intervention. - With only monetary policy: improved foreign appetite lowers UIP wedge; households overborrow to finance higher imports → monetary policy cannot effectively insulate economy (raising policy rate causes larger UIP wedges and hurts exports); planner reduces policy rate to limit appreciation and stabilize exports and employment. - Adding capital controls: positive ex post capital controls are more effective than monetary policy at addressing financial TOT externality and reducing overborrowing; less need for policy rate movement. - Adding FX intervention: ex post FX accumulation (sell domestic currency bonds, buy dollar bonds) absorbs some of the favorable foreign appetite shock and earns carry profits; FX intervention directly limits foreigners’ entry, reducing need for policy rate adjustment. - Combined use (MP + CC + FXI): FX intervention partially leans against the wind; (B2 + FXI1 − S1) ∈ (−|S1|,0) after high shock and ∈ (0,|S1|) after low shock. Macro allocations can be perfectly stabilized; capital controls and FX intervention are mild substitutes with each other and strong substitutes for the domestic policy rate. - Capital controls and FX intervention increase monetary autonomy by tackling appetite shocks closer to their source. - DCP: - Main PCP results on instrument use and complementarity/substitutability hold. - Key differences: - Exchange rates more volatile under DCP than PCP. - Employment destabilized under DCP and not PCP. - Policy rate increases rather than decreases after high appetite shock (no longer used to stabilize exports). - Consumption of home tradable good decreases rather than increases after high appetite shock. - Key statement: - Result 10. Countries facing foreign appetite shocks should use ex post capital controls and ex post FX intervention to insulate the domestic economy and increase ex post monetary autonomy under both PCP and DCP. - Remark 11. After foreign appetite shocks, capital controls and FX intervention are substitutes for the domestic policy rate. ### 5.3.3 Bank Debt Limit Shocks - Shock: change to κ_{H1}. - For B0 high enough so banks’ external constraints bind after the low shock: - Optimal policies identical between deep and shallow FX markets except steady-state level of FX intervention. - Under shallow FX markets, positive domestic-currency debt levels produce steady-state financial TOT externalities; FX intervention should absorb these premia and keep (B2 + FXI1) = 0. - When the banks’ debt limit binds, the interest rate ρ1 in households’ Euler condition between periods 1 and 2 is determined by overall available external funds and is no longer equal to the policy rate i1; therefore, the policy rate has no impact on aggregate demand through the Euler condition and only affects demand through the exchange rate term in the borrowing constraint. - Optimal instrument to manage the exchange rate is the policy rate (cheaper than FX intervention which has a carry cost); FX intervention is not optimal ex post except to minimize external premia. - Key statements: - Result 11. Countries with high initial external FX debt that are subject to debt limit shocks should impose positive ex ante capital controls. FX intervention should minimize premia while allowing the same degree of exchange rate flexibility as in the deep FX markets case. - Remark 12. After debt limit shocks, FX intervention is used to absorb external premia but not otherwise to influence the exchange rate. - Remark 13. For countries with high initial external FX debt and vulnerability to debt limit shocks, ex ante capital controls are larger under DCP than PCP. ### 5.4 Extension: Ban on Open FX Positions - Policy considered: ban on open FX positions for domestically owned intermediaries → mechanically removes domestic fraction λ from FX market participation; domestic-currency debt can only be absorbed by foreign-owned intermediaries. - Resulting equations (Gamma and resource constraint modifications summarized in text): - Gamma equations replaced by: - Γ(1−λ)( D1/E0 + FXI0 − S0 ) = E0[ η1 − (1 + i^*_0) ] - Γ(1−λ)( D2/E1 + FXI1 − S1 ) = η2 − (1 + i^*_1) - Economy-wide resource constraint replaced by D_{t+1} ≥ −E_t P^*_F_t [ ωC^*_t − C_{Ft} ] − E_t P^*_Zt Z_t − O_t[ (1 + ĩ_{t−1}) − (1 + i^*_{t−1}) E_t/E_{t−1} ] + (1 + ĩ_{t−1}) D_t. - Key mechanical differences vs original constraint: - No fraction λ of debt with currency mismatch → exchange rate depreciation does not increase domestic-currency value of debt repayments. - Effective carry cost of FX intervention is larger because carry profits accrue only to foreign-owned intermediaries. - Quantitative and qualitative effects (DCP case, FXI_t = 0 imposed for illustrative figures): - First key result: - Banning open FX positions reduces vulnerability to banks’ debt limit shocks and removes need for ex ante capital controls to address pecuniary AD externalities. - Transitioning from high to zero currency mismatch allows depreciations to reduce FX value of repayments and relax external debt limits in period 1; no pecuniary-AD-externality rationale for ex ante capital controls. - Second key result: - If FX markets are shallow (Γ > 0), the regulation makes FX markets effectively more shallow: effective Gamma becomes Γ/(1−λ), which is higher than Γ. - Regulation increases steady-state cost of debt financing if planner cannot use FX intervention to bypass intermediaries: the ban generates significant deleveraging when FX intervention is zero because shallower FX market → higher UIP wedges → lower equilibrium debt. - Even though ex ante capital controls are not needed for pecuniary AD externalities, there are large steady-state capital controls to mitigate financial TOT externalities. - Third key result: - Regulation increases vulnerability to foreign appetite shocks and increases marginal value of ex post FX intervention. - With ban, allocations become more volatile to foreign appetite shocks; ex post policy rate and capital controls more volatile. - Marginal value of ex post FX intervention assessed by period-1 multipliers {Θ_{H1}, Θ_{L1}} on constraint FXI_t = 0: moving from allocations without the ban to allocations with the ban increases multipliers from {Θ_{H1} = −0.03, Θ_{L1} = 0.02} to {Θ_{H1} = −0.04, Θ_{L1} = 0.12}, establishing increased value of ex post FX intervention. - Key statement: - Result 12. Banning open FX exposures reduces the country’s vulnerability to banks’ debt limit shocks and removes the need for ex ante capital controls to address AD externalities. However, it has side effects: - (i) makes debt harder to finance in steady state, and alters steady-state capital controls; - (ii) increases vulnerability to foreign appetite shocks and reliance on FX intervention. *Source: IMF Staff paper — Section 5.2–5.4 (Real Shocks, Financial Shocks, Extension: Ban on Open FX Positions).* ### 5.5 Summary ### 5.5 Summary ### Deviations from Mundell-Fleming and the role of UIP wedges - Countries with shallow FX markets have more reasons to deviate from the traditional Mundell-Fleming prescription, and to use capital controls and FX intervention, than countries with deep FX markets. - There is a case for ex post capital controls and ex post FX intervention after shocks which generate changes in external debt and UIP wedges. - Policy focus recommendation: do not focus on stabilizing the level or volatility of the exchange rate; instead monitor the level of UIP wedges which arise from imperfect arbitrage by financial intermediaries in the FX market. - Shocks that generate exchange rate fluctuations without generating changes in external debt (e.g., permanent productivity and commodity price shocks) do not rationalize ex post capital controls: - In such cases, the only use of FX intervention is to minimize external premia and thereby to facilitate the same degree of exchange rate volatility as in the deep FX markets case. - Shocks that generate changes in external debt (e.g., foreign appetite shocks) may warrant joint use of capital controls and FX intervention to: - lean against the wind, - limit some exchange rate movements, - improve monetary autonomy, - without fully eliminating the premia that the shocks generate. - Countries with both currency mismatches and shallow FX markets should carefully design macroprudential regulations to reduce external FX debt without harmful spillovers onto FX market depth: - Regulations that reduce currency mismatches while limiting participation in the FX market may reduce vulnerability to banks’ debt limit shocks only at the cost of increasing vulnerability to foreign appetite shocks. - The country may then find itself increasingly dependent on FX intervention to manage volatility in external premia. ### Mapping the global financial cycle to the model - Consider a retrenchment of the global financial cycle comprising three component shocks: - a rise in world interest rates, - a decline in foreign appetite for domestic currency debt, - a contraction in debt limits for borrower countries. - Planner objectives and implementation under shallow FX markets: - Accommodate the world interest rate shock: - under shallow FX markets, optimally use ex post FX intervention to reinforce the shock rather than lean against it. - Ignore the foreign appetite shock and set monetary policy on domestic considerations: - in shallow FX markets, these shocks compromise monetary autonomy and force the policy rate to respond to external factors. - foreign appetite shock is not return-sensitive; monetary policy is ineffective at addressing the shock at its source. - policy rate is assigned to address employment destabilization generated by the shock. - use of ex post capital controls and ex post FX intervention restores monetary autonomy so the policy rate can be set based only on domestic considerations. - Debt limit shock (banks’ external debt limits): - planner’s response is similar under deep and shallow FX markets because FX intervention cannot enhance monetary autonomy when the economy is most stressed (when the debt limit binds). - FX intervention's role is limited to reducing premia on external debt. - access to FX resources from swap lines to relax banks’ external debt limits remains useful and would reduce necessary ex ante capital controls and macroprudential taxes. ### Housing sector: framing and key mechanisms - Housing friction context: - Additional friction: housing sector borrowing constraints. - Optimal integrated use of policy rate, capital controls, FX intervention, and domestic macroprudential taxes is considered. - Domestic borrowing constraints are likely related to domestic currency value of nontraded assets; for housing, collateral is land. - Leveraged domestic borrowing matters for most advanced economies and many emerging markets. - Housing frictions in open economy: - Fire sales of land may be triggered by both domestic and external shocks, rationalizing combination of domestic (policy rate and macroprudential debt taxes) and external (capital controls and FX intervention) tools. - Conditions for housing frictions to matter: - Planner can only impose macroprudential taxes on the linear housing subsector, θ^Linear_Rt ∈ R, while the concave subsector is unregulated, θ^Concave_Rt ≡ 0. - Housing sector borrowing capacity is limited, κ_L1 is sufficiently low. - Constrained-efficient trade-offs summarized by equations: - Period-1 constrained-efficient quantity of land held by the linear subsector: equation (36). - Period-0 constrained-efficient quantity of land held by the linear subsector: equation (37). - Notation reminders in the housing context: - Ψ_R1 is the multiplier on the housing constraint in period 1. - A hat over a variable indicates the FX value of that variable. - FX gross return related to domestic interest repayments between periods t and t+1: χ_t+1 = (1 + i_t) E_t E_t+1 > 0. - If Ψ_R1 = 0 (constraint not binding): - τ_R2 = 0 and L^Linear_1 = 1. - If Ψ_R1 > 0 (constraint binding): - τ_R2 > 0 and L^Linear_1 decreases below 1, reducing period-1 land price ̂q_1 and tightening the constraint; period-0 land price effects enter via inherited debt. ### Policy instruments and wedges with housing frictions - Planner instruments to relax housing constraint: - Period-0 domestic macroprudential tax on debt of linear housing subsector can reduce L^Linear_0 below 1; housing macroprudential tax expression given in equation (38). - Reducing the policy rate and domestic borrowing rate raises land price via the concave subsector no-arbitrage. - Depreciating the exchange rate helps relax housing constraint by: - substitution in consumption from imports to home goods including housing (boosting rents and house prices), - increasing domestic currency price of land in period 2 which feeds back into period-1. - Interaction between instruments and distortions: - Use of instruments to stabilize housing creates distortions for non-housing sectors; balance required. - Whether capital controls or consumer macroprudential taxes are available matters for which distortions arise. - Housing sector FX borrowing rate depends on instrument availability: - If capital controls allowed but consumer macroprudential taxes not (φ_t ∈ R but θ^HH_t ≡ 0): housing sector’s FX borrowing rate equals borrowing rate of domestic households. - If consumer macroprudential taxes allowed but capital controls not (θ^HH_t ∈ R but φ_t ≡ 0): housing sector’s FX borrowing rate equals η_t+1, the return received by international intermediaries. - Substitutability breakdown: - Occasionally-binding housing constraint breaks the substitutability between capital controls and consumer macroprudential taxes (assuming perfect coverage). - The two instruments may be substitutable in period 0 but not in period-1 states when the housing constraint binds; this causes divergence in optimal period-0 instrument levels. - Constrained-efficient FOCs and novel terms with housing: - With capital controls allowed, exchange rate FOC in period 1 changes as in equation (39). Notable features: - planner finds it optimal to depreciate the exchange rate in period-1 states in which the housing constraint binds relative to states in which it does not bind. - depreciation raises rents and land price; distortion shows up as a reduction in τ_H1 (positive price and AD pressures). - New Euler condition between periods 0 and 1 with housing: equation (40). - New formula for ex ante capital control tax φ_0 with housing: equation (41). - Highlights: - Reducing policy rate in period 0 (via increasing C_F0, with ∂χ_1/∂C_F0 < 0) and in period-1 binding state (via increasing C_F1 in that state, with ∂χ_1/∂C^s_F1 > 0) helps relax housing constraint and reduces necessary ex ante capital controls for given UIP wedges. - Capital controls should shift consumption intertemporally to bolster rents and house prices in period-1 states when housing constraint binds; terms involving ∂̂P_Rt/∂C_Ft and ∂̂q_1/∂C_F1 capture this. - Consumer macroprudential taxes instead of capital controls: - Exchange rate and FX intervention FOCs (29) and (31) remain as in prior section. - Trade-off for optimal UIP wedge between periods 0 and 1, τ_Γ1, altered to equation (42). - New last term: Ψ_R1[(1 + i^∗_−1) B^Linear_R0 − ̂P_R0 L_−1] — planner optimally reduces UIP wedge between period 0 and period-1 states in which housing constraint binds (i.e., depreciate exchange rate in those states). - Distortion: increase in Ω_0 (international intermediaries less willing to finance domestic currency debt in period 0); planner may commit to appreciate the exchange rate in period-1 states where constraint does not bind. - Trade-off for optimal UIP wedge between periods 1 and 2, τ_Γ2, altered to equation (43). - New terms capture UIP wedge impacts on constraint via period-0 and period-1 land prices. - Constrained-efficient allocations with consumer macroprudential taxes follow Euler condition (40) with derivatives differing: - Borrowing rates for households and housing sector disconnected, so impose ∂χ_1/∂C_F0 = ∂χ_1/∂C^s_F1 = 0. - Recommendation preserved: use consumer macroprudential taxes (instead of capital controls) to alter consumption intertemporally to bolster rents and house prices in period-1 binding states. - Ex ante consumer macroprudential tax value obtained by setting φ_0 = 0 in period-0 version of equation (26). - Remaining section roadmap: - Subsequent subsections (6.2–6.4) show which real and financial shocks can cause housing constraint to bind and illustrate interactions between banks’ external debt limit and linear housing subsector’s domestic debt limit. - Focus for this section: illustrate DCP case; differences with PCP case documented in main text; one PCP figure at end encapsulates key qualitative difference relative to DCP case. *Source: wpiea2020121-print-pdf - 5.5 Summary* ### 6.2 Real Shocks ### 6.2 Real Shocks ### Productivity Shocks - Consider permanent shocks to the value of productivity, A1 = A2. - Under DCP: - After a low realization of the productivity shock, the exchange rate appreciates, reducing consumption of home goods and thereby the domestic currency value of rents and the land price, causing the housing constraint to become binding. - Planner actions: - Imposes a housing macroprudential tax in period 0. - Lowers the policy rate in the period-1 state in which the constraint binds. - Effects of policy rate reduction: - Reduces size of the necessary housing macroprudential tax and distortion in the land market. - Generates distortions elsewhere: destabilization of imports across states and periods; lower AD wedge indicates positive price and AD pressures. - Capital controls and FX interventions: - Ex ante capital controls are negative (planner induces higher consumption in period 0 to raise rents and help repay inherited debt before the shock). - Ex post capital control subsidies are provided when the constraint binds to attract inflows and limit excessive depreciation caused by policy rate reduction. - If capital controls are available, (B2 + FXI1) is kept at zero in both period-1 states (FX intervention used solely to minimize external premia). - When consumer macroprudential taxes are allowed but capital controls are not: - Advantage: planner can set a low policy rate in period 0 to reduce interest burden on inherited housing sector debt before the shock, while applying positive consumer macroprudential taxes to stabilize household consumption. - Disadvantage: without capital controls, inflow subsidies cannot be provided to limit depreciation after period-1 policy rate reduction; role for FX sales, i.e., (B2 + FXI1) < 0, to limit depreciation at a carry cost. - Under PCP, the main results from DCP continue to hold. - Result 13. Countries with high housing debt may experience fire sales in the housing sector after adverse productivity shocks. These countries should impose an ex ante housing macroprudential tax and they should lower the policy rate when the housing constraint binds. They may also need to undertake capital controls and/or FX intervention when the constraint binds. - Remark 14. FX intervention is less efficient than capital controls at limiting depreciations after policy rate reductions which are aimed at relaxing the housing constraint. ### Commodity Price Shocks - Consider permanent shocks to the dollar price of commodities, P*Z1 = P*Z2. - Focus shown for low initial level of unhedged external FX debt, B0 = 0. - Under DCP: - Housing constraint does not necessarily bind after low realizations of commodity prices. - Although the shock makes the domestic economy poorer (reducing imports and rents), the large exchange rate depreciation substantially increases the domestic currency value of rents and the land price. - In simulation (figure 33), rents and the land price are higher after low commodity price realizations than after high ones, so the housing constraint does not bind after low realizations. - Exchange rate flexibility benefits commodity exporters by optimizing import/export substitution for consumption, stabilizing non-commodity-sector employment, and helping domestic credit markets avoid binding constraints. - Under PCP: - Same qualitative mechanisms as DCP but smaller exchange rate depreciation after low commodity price realizations. - Some depreciation increases period-2 land price and filters back to higher period-1 land price, but rents may end up lower because the economy is poorer relative to the rest of the world, increasing chance of a binding housing constraint. - Result 14. Countries with large commodity sectors and DCP may not necessarily suffer from binding housing sector constraints after low realizations of commodity prices. - Remark 15. Low commodity price realizations are more likely to generate binding housing sector constraints under PCP than DCP. ### 6.3 Financial Shocks — Overview - Consider domestically- and externally-generated shocks affecting borrowing/lending: - Between domestic banks and the rest of the world. - Between different domestic agents. ### World Interest Rate Shocks - Consider a shock to the value of the world interest rate, (1 + i*1). - Under DCP: - Housing constraint does not necessarily bind after high realizations of the world interest rate. - Exchange rate response: depreciates substantially in period 1 and appreciates substantially in period 2 (figure 34). - Period-2 appreciation reduces domestic currency value of period-2 land price, filtering to a low period-1 land price and tending to tighten the constraint. - Period-1 depreciation bolsters domestic currency value of rents and tends to relax the housing constraint. - Exchange rate flexibility helps address price and AD pressures and stabilizes domestic credit markets. - Under PCP: - Similar mechanisms but smaller exchange rate depreciation after high realizations of the world interest rate, providing a smaller boost to domestic currency value of rents; housing constraint occasionally binds in simulations when world interest rate increases. - Result 15. Countries with DCP may not necessarily suffer from binding housing sector constraints after high realizations of the world interest rate. - Remark 16. High world interest rate realizations are more likely to generate binding housing sector constraints under PCP than DCP. ### Foreign Appetite Shocks - Foreign appetite shock is a shock to the value of S1. - Countries with deep FX markets are not affected by this shock (no risk of housing constraint binding); countries with shallow FX markets are affected. - Under DCP: - Capital controls are more effective than consumer macroprudential taxes in stabilizing the housing sector after foreign appetite shocks (figure 35). - With capital controls but without consumer macroprudential taxes: - Countries with shallow FX markets can fully stabilize allocations using capital controls and FX intervention. - Capital inflow subsidies after negative foreign appetite shocks raise returns to foreigners without changing the policy rate; no variation of rents and land price across period-1 states, housing sector fully stabilized with no risk of binding constraints; no need for an ex ante housing macroprudential tax. - Capital controls and FX intervention together prevent transmission of shocks into AD pressures and the housing sector, allowing the policy rate to focus on domestic price pressures only. - With consumer macroprudential taxes allowed but no capital controls: - To replicate loosening of capital controls after negative foreign appetite shocks, planner raises the policy rate for intermediaries while loosening consumer macroprudential taxes for households. - Higher policy rate causes crash in house prices and may make the housing constraint bind. - Planner optimally raises policy rate by less than needed to fully stabilize the exchange rate, leading to partially destabilized macro allocations and imposes an ex ante housing macroprudential tax. - Under PCP, main results from DCP continue to hold. - Result 16. Countries with shallow FX markets and high housing debt, but without access to capital controls, should impose higher ex ante housing macroprudential taxes if there is a possibility of foreign appetite shocks. Macro allocations are not stabilized after such shocks. - Remark 17. Countries with deep FX markets, and countries with shallow FX markets and the ability to use both capital controls and FX intervention, can set ex ante housing macroprudential taxes independently of the possibility of foreign appetite shocks. ### Housing Debt Limit Shocks - Housing sector debt limit shock is a shock to the value of κL1, the pledgability parameter in the linear housing subsector’s borrowing constraint when they borrow from domestic banks. A decline in κL1 reflects either a downgrade in perceived creditworthiness of the housing sector, or a reversal in the ability of domestic banks to extend credit to purchase land. - Under DCP: - External adjustment is necessary to handle this domestically-generated shock; open economies possess instruments in addition to domestic ones. - With exchange rate pegged and only housing macroprudential tax available (dashed line, figure 36): - Positive hedging motive after low realization of debt limit shock (shock reduces land price and tightens constraint). - Planner imposes an ex ante housing macroprudential tax to address the pecuniary production externality. - With flexible exchange rate (solid line, figure 36): - Planner allows exchange rate depreciation after low realization to relax the constraint: decline in κL1 partially offset by increase in domestic currency value of rents and land price. - Ex post depreciation may make domestic currency rents and land price similar across period-1 states or higher after the low shock, removing hedging motive and possibly eliminating need for ex ante housing macroprudential tax; in simulation the optimal tax hits its lower bound of zero. - When more instruments are available (figure 37): - Dashed lines: all instruments available except consumer macroprudential tax. Planner allows exchange rate depreciation and reduces policy rate after debt limit shock while ex ante housing macroprudential tax remains zero. - Monetary loosening reduces AD wedge (positive price and AD pressures). - Ex ante capital inflow tax sign similar to productivity shock (planner induces higher consumption in period 0). - Policy rate reduction can cause excessive exchange rate depreciation; capital control subsidies needed to attract inflows and limit depreciation. If capital controls are available, (B2 + FXI1) is kept at zero in both period-1 states. - Solid lines: consumer macroprudential taxes allowed but capital controls not. Consumer macroprudential taxes enable lower ex ante policy rate, reducing interest burden and relaxing housing constraint so much that ex post policy rate increases substantially. - For the simulation parameterization, no longer an excessive depreciation when constraint binds; instead depreciation is insufficient to optimally balance import/export substitution against housing support, so planner accumulates FX, i.e., (B2 + FXI1) > 0 to further depreciate the exchange rate. - More limited ex post support for housing market means ex ante housing macroprudential tax rises above zero. - Under PCP, the main results from DCP continue to hold. - Result 17. Countries with high housing debt that are subject to housing debt limit shocks should lower the policy rate and depreciate the exchange rate after such shocks, and may or may not need to impose an ex ante housing macroprudential tax. They may also need to undertake capital controls and/or FX intervention when the constraint binds. - Remark 18. FX intervention is less efficient than capital controls at limiting depreciations after policy rate reductions which are aimed at relaxing the housing constraint. *Source: wpiea2020121-print-pdf - 6.2 Real Shocks* ### 6.4 Domestic and External Borrowing Constraints ### 6.4 Domestic and External Borrowing Constraints ### Overview - Many countries, especially emerging markets, may face two occasionally-binding borrowing constraints: domestic (domestic-currency-denominated debt collateralized by domestic nontradable assets such as housing) and external (dollar-denominated debt collateralized by elements of domestic production). - Domestic constraints relax when the policy rate is reduced and the exchange rate depreciates; external constraints tighten when the exchange rate depreciates because the dollar value of domestic collateral declines. - The subsection analyzes interactions between domestic and external borrowing constraints within the model framework. ### 6.4.1 Housing Debt Limit Shock to Bank Constraint - An optimal exchange rate depreciation is used to relax the housing sector constraint after a low realization of κ_L1 (the linear housing subsector’s ability to pledge land as collateral). - If initial unhedged external FX debt B0 = 0, depreciation poses no external-constraint problem; if B0 > 0, depreciation may cause external constraints to bind. - Under DCP: - Depreciation can cause the external constraint to bind. - The planner limits depreciation in the binding period-1 state to relax banks’ external constraint, at the expense of tightening the housing constraint. - Ex post capital controls do not work in the binding state. - Ex post FX intervention should be used to absorb external premia but not to defend the exchange rate; once banks’ debt limit binds, the interest rate ρ1 in households’ Euler condition and the housing sector’s no-arbitrage condition becomes disconnected from the policy rate i1, so i1 can be used to manage the exchange rate. Therefore the planner sets (B2 + FXI1) to zero. - Limited ex post maneuverability strengthens the case for ex ante actions: the planner sets a low policy rate in period 0 to reduce housing sector interest burden and imposes positive ex ante capital controls to limit external FX debt. - Under PCP: - Main results from DCP continue to hold, but ex ante capital controls are lower for the same reason as in subsection 4.3.3. - Result 18: - "Countries with high housing debt and external FX debt should use the policy rate to set the ex post exchange rate to the level that balances the tightness of domestic and external constraints after housing debt limit shocks which cause all external constraints to bind. They may or may not need to impose an ex ante housing macroprudential tax, but they should impose ex ante capital controls and help reduce the housing sector’s interest burden." - Remark 19: - "After debt limit shocks, FX intervention is used to absorb external premia but not otherwise to influence the exchange rate." - Remark 20: - "For countries with high housing debt and external FX debt, ex ante capital controls are larger under DCP than PCP." ### 6.4.2 Extension: Housing Debt Limit Shock to Household Constraint - Model extension: domestic households and domestic housing firms use different banks, so some banks (those lending to households) may be externally constrained while others are not. - The external constraint for only those banks lending to households can be rearranged in equilibrium as (one equation per period-1 state): - (1 + i^* −1) B0 ≤ P^*_F0 [ωC^*_0 − C_F0] + P^*_Z0 Z0 + P^*_F1 [ωC^*_1 − C_F1] + P^*_Z1 Z1 − (1−λ)FXI0 [η1 − (1 + i^*_0)] / (λ(1 + i^*_0) + (1−λ)η1) + κ_H1 P_H E1 / (λ(1 + i^*_0) + (1−λ)η1) − α_R/α_F P^*_F1 C_F1 + χ1 α_R/α_F P^*_F0 C_F0 / (λ(1 + i^*_0) + (1−λ)η1), [Ψ_HH] - (this is the expression as presented in the source, where the last term represents housing rents no longer cancelled by aggregation over households and banks) - In this extension: - The policy rate i1 is no longer inside households’ optimization conditions but remains inside the housing sector’s optimization conditions. - Capital controls are assumed unavailable; consumer macroprudential taxes are available instead. - Under DCP: - Depreciation can cause the external constraint to bind. - There is a role for FX intervention beyond absorbing premia: because i1 still affects housing activity, lowering i1 relaxes the domestic housing constraint but also causes a depreciation that tightens the external constraint; FX sales can limit depreciation, so the planner sets (B2 + FXI1) < 0. - Under PCP: - Main DCP results continue to hold. - Result 19: - "Countries with high housing debt and external FX debt, but without access to capital controls, should use the policy rate and FX sales to set the ex post exchange rate to the level that balances the tightness of domestic and external constraints if housing debt limit shocks cause some but not all external constraints to bind." ### 6.4.3 Bank Debt Limit Shock to Housing Constraint - Consider shocks to banks’ external debt limits (to κ_H1) that may cause domestic housing constraints to bind. - Under PCP: - A banks’ debt limit shock may cause the domestic housing constraint to bind (illustrated in Figure 40). - Binding external constraint is associated with a large decrease in policy rate i1 and an exchange rate depreciation which tends to increase domestic-currency value of rents and the land price. - Simultaneously, borrowing rate ρ1 for households and the housing sector increases and household consumption decreases; if these latter effects dominate, rents and land prices fall and the housing constraint can bind (as in simulations). - The planner relaxes the housing constraint by reducing i1 and allowing more depreciation, even at the cost of tightening banks’ external constraint. - Ex post capital controls do not work in the binding state; ex post FX intervention should be used to absorb external premia but not to defend the exchange rate. - Limited ex post maneuverability increases the case for ex ante actions; the planner imposes an ex ante housing macroprudential tax. - Under DCP: - After banks’ debt limit shocks, the exchange rate is more depreciated and the external constraint is more relaxed (subsection 4.3.3). - Larger depreciation boosts domestic-currency value of rents and land price. - More relaxed external constraint lowers borrowing rate ρ1 for households and the housing sector under DCP versus PCP, supporting rents and land price. - Therefore, under DCP it is less likely that tightening external constraints cause the housing constraint to bind, and when it binds it is less severe. - Consequently, ex ante capital controls are larger under DCP than PCP, but ex ante housing macroprudential taxes are lower under DCP than PCP. - Result 20: - "Countries with high housing debt and external FX debt whose banks are vulnerable to external debt limit shocks should impose positive ex ante capital controls and ex ante housing macroprudential taxes." - Remark 21: - "For countries with high housing debt and external FX debt and vulnerability to external debt limit shocks, ex ante capital controls are larger under DCP than PCP, but ex ante housing macroprudential taxes are lower under DCP than PCP." ### Key policy implications and mechanisms - Ex post policy limits: - Ex post capital controls are ineffective in binding states. - Ex post FX intervention should primarily absorb external premia and generally should not be used to defend the exchange rate when external debt limits bind, except in the extended case where FX sales limit depreciation to balance constraints. - Ex ante policy importance: - Limited ex post maneuverability increases the value of ex ante policies: low ex ante policy rate to reduce interest burden on inherited housing debt, ex ante capital controls to limit external FX debt, and ex ante housing macroprudential taxes when appropriate. - Role of coordination: - When domestic and external constraints interact, policy instruments (policy rate, FX intervention, capital controls, housing macroprudential taxes) need to be coordinated to balance the tightness of constraints and mitigate pecuniary externalities. - Comparative dynamics DCP vs PCP: - Ex ante capital controls are larger under DCP than PCP in several scenarios (Remarks 20, 21). - Under DCP, housing constraints are less likely to bind following bank debt limit shocks and are less severe; thus ex ante housing macroprudential taxes are lower under DCP than PCP. ### Result on imperfect coverage and limits to regulation (connection to borrowing constraints) - If housing macroprudential taxes cover only a subset of linear housing subsector firms while others borrow directly from international financial intermediaries, then taxes are imperfect substitutes for housing-sector-specific capital controls. The planner should set θ^Linear_Rt for domestically-regulated firms as pinned down by (38), and capital controls φ^Linear_Rt on intermediaries lending to other firms of magnitude: - φ^Linear_Rt = θ^Linear_Rt / (1 + θ^Linear_Rt). (45) - If all linear subsector firms are officially regulated but can circumvent taxes and issue debt directly to international financial intermediaries, then taxes and sector-specific capital controls are perfect complements: housing macroprudential taxes θ^Linear_Rt need to be complemented by capital controls φ^Linear_Rt following the expression above to be effective. - Result 21: - "Capital controls and housing macroprudential taxes are imperfect substitutes if housing macroprudential taxes do not cover all housing sector firms who are vulnerable to borrowing constraints, and they are perfect complements if any housing sector firms who are vulnerable to borrowing constraints can circumvent the macroprudential taxes via cross-border transactions which are not intermediated through the domestic banking system." *Source: IMF Working Paper — section 6.4 Domestic and External Borrowing Constraints from wpiea2020121-print-pdf* ### 6.6 Summary ### 6.6 Summary ### Housing debt, frictions, and domestic borrowing constraints - Most advanced economies and a growing number of emerging markets have high levels of domestic debt which may trigger binding domestic borrowing constraints after domestic and external shocks. - Housing debt is often a large component of domestic debt. - Housing frictions are relevant for macro allocations if: - the housing sector cannot be perfectly regulated (e.g., some housing firms such as the concave subsector are beyond the regulatory perimeter), and - housing sector borrowing capacity is limited (e.g., with an upper limit given by the price of collateralized land). ### Role of small open economy analysis and external adjustment tools - Analyzing a small open economy with a housing sector identifies whether external adjustment tools should complement domestic policy tools typically recommended in closed-economy contexts. - The use of external adjustment tools may justify deviations from the traditional Mundell-Fleming prescription of relying solely on the domestic policy rate and exchange rate flexibility for some shocks and country characteristics, while bolstering that prescription in other cases. ### Key themes on constrained efficient policy responses - Exchange rate flexibility can mitigate or prevent housing constraints from binding for some shocks: - After adverse commodity price shocks, increases in world interest rates, and bank debt limit shocks, exchange rate depreciations bolster rents and the land price and help relax housing constraints if housing sector support is not offset by a reduction in rents. - Exchange rate flexibility adds benefits beyond import/export substitution and non-commodity employment stabilization: it can help domestic credit markets avoid binding constraints. - For countries vulnerable to housing sector debt limit shocks, ex post exchange rate flexibility may remove the need for housing macroprudential taxes in normal times, even though it does not eliminate the housing constraint. - Exchange rate flexibility may be insufficient or even counterproductive for other shocks: - After productivity and foreign appetite shocks, exchange rate flexibility may not relax and may tighten housing constraints. - In these cases, countries should use domestic instruments and external adjustment tools, deviating from Mundell-Fleming even if shocks originate domestically. - Countries with high housing debt may optimally use a combination of: - ex ante housing macroprudential taxes in normal times, and - policy rate reductions and exchange rate depreciations when housing constraints bind. - If a policy rate reduction causes a depreciation larger than the level optimally balancing import/export substitution against housing support, then: - capital inflow subsidies or FX sales should be used to limit depreciation (FX sales being less efficient than capital inflow subsidies). - If the depreciation is too small, then capital inflow taxes or FX purchases are appropriate. - The available instrument set matters for housing-sector stabilization: - After foreign appetite shocks, enhancing monetary autonomy through joint use of capital controls and FX intervention is further strengthened in a model with a housing market: the policy rate can focus on domestic price pressures, ignoring direct and indirect housing market effects on household borrowing and demand. - Without capital controls, the planner can try to replicate loosening of capital controls after negative foreign appetite shocks by raising the policy rate for intermediaries while loosening consumer macroprudential taxes for households; however, the higher policy rate can crash house prices and make the housing constraint bind. - Therefore, countries with shallow FX markets and no access to capital controls need higher ex ante housing macroprudential taxes because of unavoidable instability from the global financial cycle. - Interactions between domestic and external constraints when housing and FX debt are both high: - After domestic housing sector debt limit shocks, the planner optimally depreciates the exchange rate to support the domestic currency value of rents and the land price, but that depreciation may make external constraints bind and limit ex post maneuverability. - Countries should use the policy rate to set the ex post exchange rate at a level that balances the tightness of domestic and external constraints. - They may or may not need ex ante housing macroprudential taxes, but should impose ex ante capital controls and help reduce the housing sector’s interest burden. - After bank external debt limit shocks there is optimally a large exchange rate depreciation which tends to bolster the housing sector, but an increase in the borrowing rate and a decrease in household consumption tend to reduce rents and the land price; these latter effects may outweigh the depreciation’s support and make the housing constraint bind. ### Pricing paradigm and likelihood of housing constraints - The pricing paradigm (DCP versus PCP) matters for: - the likelihood of housing constraints after shocks, and - the interaction between domestic and external constraints. - Because exchange rate depreciations are optimally larger under DCP than PCP after adverse commodity price shocks and after increases in world interest rates, and since these depreciations support the housing sector, it is less likely that the housing constraint binds under DCP. - After the bank external debt limit shock: - the exchange rate is more depreciated under DCP than PCP (so there is a larger boost to domestic-currency rents and land price under DCP), - the external constraint is more relaxed under DCP (so the borrowing rate for domestic agents is lower under DCP than PCP). - Consequently, ex ante capital controls are larger under DCP than PCP, but ex ante housing macroprudential taxes are lower under DCP than PCP. ### Macroprudential taxes and capital controls: complements, not substitutes - Housing macroprudential taxes and housing-sector-specific capital controls may appear substitutable but should be used complementarily to minimize gaps in coverage. - Policy should aim to influence debt levels of any leveraged agents in the housing sector who may be vulnerable to domestic borrowing constraints in the future. ### Model construction, scope, and practical implementation challenges (summary conclusions) - The paper builds a model of a small open economy featuring real and nominal frictions and characterizes optimal integrated use of monetary policy, capital controls, FX intervention, and macroprudential policy across shocks and country characteristics. - Countries may differ in currency of trade invoicing, external debt levels, currency mismatches, borrowing constraints, and FX market depth; the workings and interactions of instruments matter and must be considered jointly. - There is no strict assignment of domestic policies to domestic shocks and external policies to external shocks. - Model limitations and caveats: - country characteristics can be endogenous to policy actions in the long term (e.g., private sector currency mismatches, development of FX markets), - imperfect policy credibility may call for using fewer instruments until credibility is built, altering policy trade-offs during transition, - the analysis is from the perspective of a small open economy; spillovers and spillbacks matter for global assessments. - Practical challenges to integrated policy implementation: - policy tools may be assigned to different agencies with imperfect coordination, - real-time identification of shocks can be difficult, - central banks must integrate multiple objectives and tools into policy, communications, and operational frameworks, - stabilization of expectations requires clear and sustained communication on how tools will be used in different states of nature and verification that promises are honored; transitional arrangements may be necessary. ### Representative numeric calibrations and parameter values (selected) - Expenditure shares: αH = 1/3, αF = 1/3, αR = 1/3. - Discount factor: β = 0.8. - Elasticity of export demand: ω = 1. - Dollar price of imports: P*F = 1. - World demand level: C* = 1. - Endowment of nontradable goods: YNT = 1. - Endowment of commodities: Z = 1. - Initial dollar price of commodity exports: P*Z = 1. - Initial world interest rate: i*0 = 1/β - 1. - Initial level of productivity: A0 = 1. - Initial debt level: B0 ∈ [0, 0.6]. - Initial housing sector debt level (in Shallow FX + housing): BR0 = 3.5. - Initial land (in Shallow FX + housing): L0 = 1. - Domestic share of intermediaries: λ = 1 (Deep FX), λ = 0.8 (Shallow FX; Shallow FX + housing). - Balance sheet friction Γ = 0 (Deep FX), Γ = 1 (Shallow FX; Shallow FX + housing). - Shock calibrations (selected): - Probability of good/bad shock: π = 0.5. - Productivity shock: A ∈ [0.75, 1.5] (Deep FX); A ∈ [0.8, 1.5] (Shallow FX; Shallow FX + housing). - Commodity price shock: P*Z ∈ [0.75, 1.5]. - World interest rate shock: i*1 ∈ [0, 0.5]; alternatively (1 + i*1) ∈ [1, 1.5] in some figures. - Bank debt limit: κH ∈ [0.025, 10]. - Housing sector debt limit (where applicable): κL ∈ [0.025, 10]. - Foreign risk appetite: S1 ∈ [−0.5, 0.5] (where applicable). *Source: wpiea2020121-print-pdf - 6.6 Summary* ### References ### References and Appendix (wpiea2020121-print-pdf - References) ### References (bibliographic sources cited) - References [1] through [23] list working papers, journal articles, manuscripts, and mimeos relevant to macroprudential policy, capital flows, exchange rates, dominant currency paradigm, credit cycles, and international liquidity. Notable cited works include: - [1] IMF Working Paper 19/66, “Digging Deeper-Evidence on the E‚ects of Macroprudential Policies from a New Database”. - [2] CEPR WP No 9223, “Optimal Policy for Macro-Financial Stability”. - [11], [12] Farhi and Werning (2014, 2016) on capital controls, exchange rates, and macroprudential policies. - [16] Gopinath et al., 2020, “Dominant Currency Paradigm,” American Economic Review, Vol. 110 (3), pp. 677-719. - [22], [23] Miranda-Agrippino & Rey (2019) and Rey (2014) on US monetary policy and the global financial cycle. ### Appendix A.1 — Price Setting Condition under DCP - Defines export price PX as: - PX = PH X1 X2 X3 X4 - Components X1, X2, X3, X4 are explicitly defined using: - A0, A1, A2; (P*F0), (P*F1), (P*F2); C*0, C*1, C*2; CF0, CF1, CF2; E0, E1, E2; i*0, i*1; and expectations E0, E1, E2. - Derivatives required for the constrained efficient allocation solution are given explicitly: - ∂PX/∂PH = PX/PH - ∂PX/∂CF0, ∂PX/∂CF1, ∂PX/∂CF2: full expressions preserve multiplicative factors π1, PH, P*Ft, A0–A2, E0–E2, and denominators with X4 and (X4)^2. - ∂PX/∂E0, ∂PX/∂E1, ∂PX/∂E2: explicit negative expressions featuring PH, PX, A0–A2, P*Ft, CFt, X4. ### Appendix A.2 — First-Order Conditions (FOCs) for Constrained Efficient Allocations - Planner problem under full commitment: maximize expected utility E0[∑_{t=0}^2 β^t V(...)] with two cases—PCP and DCP—where PX = PX(CF0,{CF1},{CF2},E0,{E1},{E2},PH) in DCP. - Binding constraints listed (preserve form and multipliers in square brackets): - Dollar-denominated intertemporal resource/budget constraints with terms (1 + i*−1) B0, P*Ft[ωC* t − CFt], P*Zt Zt, FXI terms, and I_t definitions I_t = λ(1 + i*_t) + (1−λ) η_{t+1}. - Banking-sector borrowing constraint represented with multiplier Ψ_B. - Household and housing-sector constraints with multipliers Ψ_R, Γ, Ω_0, Ω_1, Λ, Υ_0, Υ_1, Ξ_0, Ξ_1, Σ_0, Σ_1, Π_s1, Π_s2, ∆_0 as applicable. - Normalization PH = 1. - Optimal domestic policy rates and capital controls implied by optimal allocations: - (1 + \^i_t) = (1 − φ_t) (1 + i_t) = η_{t+1} E_{t+1}/E_t (1−φ_0) (1 + θ_{HH0}) = ... (explicit equalities preserved). - Special cases when Ψ_B > 0 or Ψ_B = 0 and when Ψ_R = 0 or Ψ_R > 0 are presented, with (1 + i_1) expressions depending on Ψ_B and φ_1, θ_{HH1}. - Full set of FOCs listed by choice variable: - CF0, CF1, CF2: detailed FOC equations preserving multiplicative factors I_0, I_1, I_DCP, π1, α_F, α_H, A0–A2, and multipliers Φ, Ψ_B, Γ, Ω_0, Ω_1, Υ, Σ, Ψ_R, etc. - E0, E_{H1}, E_{L1}, E2: Euler-type conditions for exchange-rate/state variables with explicit right-hand-side terms including I_PCP, I_DCP and derivatives −∂PX/∂Et. - η_{H1}, η_{L1}, η_2: first-order conditions describing intertemporal multipliers for intermediate periods, including FXI and borrowing constraint terms. - FXI0, FXI1: FOCs with explicit complementary expressions involving (1−λ), Γ, Ω_0, Ω_1. - L0, L1: labor/land-use FOCs involving G(·), G′(·), χ terms, q-hat terms and derivatives. - Complementary slackness: Θ_t ≥ 0 and ∑_{t=0}^s FXI_t ≥ 0. - Definitions for D1, D2, D3 and B1, B2, B3 in terms of initial debt and resource allocations are given explicitly. - Derivative specifications: - When capital controls are not permitted: many derivatives ∂χ/∂(CF, E) = 0, and ∂χ/∂η = 1. - When consumer macroprudential controls are not permitted: explicit nonzero derivative formulas for ∂χ^s_1/∂CF0, ∂χ^s_1/∂C^sF1, ∂χ^s_1/∂C^{-s}F1, ∂χ^s_1/∂E^s1, ∂χ^s_1/∂E^{-s}1, ∂χ2/∂CF1, ∂χ2/∂CF2, ∂χ2/∂E2, and ∂χ/∂η = 0. - Many cross-derivatives of (χ^s_1 q̂_0) with respect to CF, E, L, η, L_Linear,s1 and corresponding π^s_1 scaling factors are provided. - Derivatives for q̂1 with respect to CF1, CF2, E2, η2 and ∂̂P_R0/∂CF0, ∂̂P_R1/∂CF1, ∂̂P_R1/∂L0 are given, including negative squared-χ2 denominators. ### Appendix A.3 — Numerical Solution Procedure - Procedure to characterize numerical solution given a chosen set of policy instruments: - Instrument availability cases and corresponding simplifications: - If all instruments available: set Υ_0 = Υ_1 = Ξ_0 = Ξ_1 = Σ_0 = Σ_1 = 0. - If FX intervention not permitted: set FXI_0 = FXI_1 = 0 and remove FXI FOCs. - If capital controls and consumer macroprudential controls not permitted: set ∆_0 = Ξ_0 = Ξ_1 = Σ_0 = Σ_1 = Π_1 = Π_2 = 0. - If housing sector macroprudential controls not permitted: set Υ_0 = Υ_1 = Ξ_0 = Ξ_1 = Σ_0 = Σ_1 = Π_1 = Π_2 = 0. - If capital controls and domestic policy rate not permitted: set Σ_0 = Σ_1 = Π_1 = Π_2 = 0. - If consumer macroprudential controls and domestic policy rate not permitted: set Ξ_0 = Ξ_1 = Π_1 = Π_2 = 0. - If exchange rate is pegged: set ∆_0 = Ξ_0 = Ξ_1 = Σ_0 = Σ_1 = 0. - Iterative algorithm to convergence: 1. Fix guess on whether banks’ external borrowing constraint (19) is slack or binding in every period-1 state. For slack states set Ψ_B = 0 and remove constraint; for binding allow Ψ_B ≠ 0 and set equality. 2. Inner iteration: fix guess on whether housing-sector borrowing constraint (20) is slack or binding by setting Ψ_R = 0 (slack) or allowing Ψ_R ≠ 0 (binding). Verify consistency (Ψ_R ≥ 0 where binding; slackness elsewhere). 3. Verify household borrowing constraint guesses and Ψ_B ≥ 0 where binding. Adjust guesses and repeat until convergence. - The numerical routine requires verifying slack/binding status for three types of borrowing constraints (bank, housing sector, household) per period-1 state. ### Appendix A.4 — Ban on FX Positions (Constrained Planner Problem under FX Position Ban) - If domestically-owned intermediaries are prohibited from taking open FX positions, the planner problem changes: - The budget/resource constraints replace (1−λ)FXI_t terms with FXI_t divided by η_{t+1} or remove multiplicative (1−λ) factors; e.g., FXI_0[η_1 − (1 + i*_0)]/η_1 and similar for FXI_1. - Constraint multipliers retained: [Φ], [Ψ_B], [Ω_0], [Ω_1], [Λ], [Ψ_R]. - Normalization: fix dollar value of initial debt repayments at (1 + i*−1) B0, and set B3 = B0. - FOCs, constraints, and χ_s t+1 definitions are adjusted to reflect no open FX positions by intermediaries: - χ_s t+1 = η_s t+1 if capital controls are not permitted, or the expression involving α_F, P*Ft, CFt, βE_t { ... } if household macroprudential controls are not permitted. - The appendix preserves full set of modified constraints and the form of the constrained planner maximization under the ban on FX positions. *Source: wpiea2020121-print-pdf - References (appendix content and references list).* --- _Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020121-print-pdf.pdf_