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International Credit Flows and
Pecuniary ExternalitiesMarkus K. Brunnermeier & Yuliy Sannikov
Princeton UniversityβInternational Credit Flows,β¦β
Bank of International SettlementBasel, August 29th, 2014
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Motivation
Old βWashington consensusβ in decline Free trade: flow of goods/services intratemporal Free finance: flow of capital intertemporal
When does full capital account liberalization reduce (capital controls/macropru regulation improve) welfare?
1. Liquidity mismatch can lead to sudden stop runs Technological illiquidity: irreversibility (adjustment costs)
Market illiquidity: redeployability/specificity β not in this paper
Funding illiquidity: short-term debt, βhot moneyβ Type of capital flow matters: FDI, portfolio flows (equity), long-term debt
2. βTerms of trade hedgeβ (Cole-Obstfeld) can be undermined when Industryβs output is not easily substitutable. Consumers cannot easily
find substitutes No strong competitors in other countries
Natural resources: oil, copper for Chile, Hard drives in Thailand, Bananas in Ecuador
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Motivation
Old βWashington consensusβ in decline Free trade: flow of goods/services intratemporal Free finance: flow of capital intertemporal
When does full capital account liberalization reduce (capital controls/macropru regulation improve) welfare?
1. Sudden stop including runs due to liquidity mismatch Technological illiquidity: irreversibility (adjustment costs)
Market illiquidity: redeployability/specificity β not this paper
Funding illiquidity: short-term debt, βhot moneyβType of capital flow matters: FDI, portfolio flows (equity), long-term debt
2. βTerms of trade hedgeβ (Cole-Obstfeld) can be undermined when Industryβs output is not easily substitutable. Consumers cannot easily
find substitutes No strong competitors in other countries
Natural resources: oil, copper for Chile, Hard drives in Thailand, Bananas in Ecuador
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Ass
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Motivation
Old βWashington consensusβ in decline Free trade: flow of goods/services intratemporal Free finance: flow of capital intertemporal
When does full capital account liberalization reduce (capital controls/macropru regulation improve) welfare?
1. Sudden stop including runs due to liquidity mismatch Technological illiquidity: irreversibility (adjustment costs)
Market illiquidity: redeployability/specificity β not this paper
Funding illiquidity: short-term debt, βhot moneyβ Type of capital flow matters: FDI, portfolio flows (equity), long-term debt
2. βTerms of trade hedgeβ (Cole-Obstfeld) can be undermined when Industryβs output is not easily substitutable. Consumers cannot easily
find substitutes No strong competitors in other countries
Natural resources: oil, copper for Chile, Hard drives in Thailand, Bananas in Ecuador
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Ass
et s
ide
Liab
ility
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Motivation
Old βWashington consensusβ in decline Free trade: flow of goods/services intratemporal Free finance: flow of capital intertemporal
When does full capital account liberalization reduce (capital controls/macropru regulation improve) welfare?
1. Sudden stop including runs due to liquidity mismatch Technological illiquidity: irreversibility (adjustment costs)
Market illiquidity: redeployability/specificity β not in this paper
Funding illiquidity: short-term debt, βhot moneyβ Type of capital flow matters: FDI, portfolio flows (equity), long-term debt
2. βTerms of trade hedgeβ (Cole-Obstfeld) can be undermined when Industryβs output is not easily substitutable.
Consumers cannot easily find substitutes No strong competitors in other countries
Natural resources: oil, copper for Chile, Hard drives in Thailand, Bananas in Ecuador
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Model setup - symmetric
Preferences
πΈ 0
β
πβππ‘ππ‘1βπΎ
1 β πΎππ‘
β’ Same preference discount rate π β βsaving out of constraintβ
Two output goods π¦π and π¦π - imperfect substitutes
π¦π‘ =1
2π¦π‘
ππ β1π +
1
2π¦π‘
ππ β1π
π /(π β1)
(Comparative) advantages:
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Good π Good π
Country A πππ‘ πππ‘
Country B πππ‘ πππ‘
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Two country/sector model
World capital shares: ππ‘
π΄π + ππ‘π΄π + ππ‘
π΅π + ππ‘π΅π = 1
World supply of (output) goods:
ππ‘π = ππ‘
π΄ππ + ππ‘π΅ππ πΎπ‘ ππ‘
π = ππ‘π΅ππ + ππ‘
π΄ππ πΎπ‘
Price of output goods π and π in terms of price of π¦
ππ‘π = 1
2
ππ‘ππ‘π
1/π
and ππ‘π = 1
2
ππ‘
ππ‘π
1/π
β’ Terms of trade ππ‘π/ππ‘
π
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Two country/sector model
Capital evolution for
β’ πππ‘ = Ξ¦ ππ‘ β πΏ ππ‘ππ‘ + ππ΄ππ‘πππ‘π΄ in country π΄
β’ πππ‘ = Ξ¦ ππ‘ β πΏ ππ‘ππ‘ + ππ΅ππ‘πππ‘π΅ in country π΅
Ξ¦ concavity β technological illiquidity
Single type of capital
Investment in composite good
Shocks are β’ Two dimensional
Affect global capital stock πππ‘π΄ + πππ‘
π΅
Redistributive (initial shock + amplification) β affects wealth share, ππ‘β’ Example: Apple vs. Samsung lawsuit
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Market structures
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Markets Output π¦π, π¦π
Physical capital πΎ
Debt Equity
Complete MarketsFull integration/First Best
X X X X
Open credit account(equity home bias)
X X X
Closed credit accountX X
Trade Finance
intratemporal intertemporal
Add taxes/capital controls
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Returns on physical capital
β’ πππ‘/ππ‘ = Ξ¦ ππ‘ β πΏ ππ‘ + ππ΄ππ‘πππ‘π΄
Postulate
β’ πππ‘/ππ‘ = ππ‘πππ‘ + ππ‘
ππ΄πππ‘
π΄ + ππ‘ππ΅
πππ‘π΅
Returns from holding physical capital
β’ πππ‘π΄π =
πππ‘πβππ‘
ππ‘+ ππ‘
π+ Ξ¦ ππ‘ β πΏ + ππ΄ππ‘
ππ΄ππ‘ +
+ ππ΄ + ππ‘ππ΄
πππ‘π΄ + ππ‘
ππ΅πππ‘
π΅
β’ πππ‘π΄π =
πππ‘πβππ‘
ππ‘+ ππ‘
π+ Ξ¦ ππ‘ β πΏ + ππ΄ππ‘
ππ΄ππ‘ +
+ ππ΄ + ππ‘ππ΄
πππ‘π΄ + ππ‘
ππ΅πππ‘
π΅16
Ito product rule:π ππ‘ππ‘ = πππ‘ππ‘ + ππ‘πππ‘ + ππππππ‘
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The 3 step solution procedure
1. Derive equilibrium conditionsβ’ Optimality and asset pricing conditions (from postulated processes)
Consumptionwith log-utility: ππ‘ = πππ‘ (no precautionary savings)
Asset pricing (from above)with log-utility: Sharpe Ratio of asset = volatility of net worth
Internal investment rate ππ‘: πΞ¦β² ππ‘ β 1 = 0
β’ Market clearing conditions
2. Derive evolution of state variable ππ‘ =ππ‘
ππ‘πΎπ‘
3. Express in terms of ODE
β’ All πpostolated and πpostulated are expressed in terms of πβ²(π), πβ²β²(π), β¦
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For
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sp
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Market structures
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Markets Output π¦π, π¦π
Physical capital πΎ
Debt Equity
Complete MarketsFull integration/First Best
X X X X
Open credit account(equity home bias)
X X X
Closed credit accountX X
Trade Finance
intratemporal intertemporal
Add taxes/capital controls
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Market structures
1. Complete markets β First best
2. Incomplete markets (equity home bias)β’ Levered short-term debt financing
β’ Sudden stops: (varying technological illiquidity)
Amplification
Runs due to sunspots
3. Closed capital account: capital controls (no equity, no debt)
4. Welfare analysis
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1. Complete markets: First Best Remarks
Perfect capital allocation + perfect risk sharing
Prices are constant and independent of shocks
Economy shrinks/expands with (multiplicative) shocks
Elasticity of substitution, π , has no impact on prices
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Market structures
1. Complete markets β First best
2. Incomplete markets (equity home bias)β’ Levered (short-term) debt financing
β’ Sudden stops: (varying technological illiquidity, irreversibility)
Amplification
Runs due to sunspots
3. Closed capital account: capital controls (no equity, no debt)
4. Welfare analysis
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2. Equilibrium characterization: state variable
Equilibrium is a mapHistories of shocks prices allocation{ππ
π΄, ππ π΅ , π β€ π‘} ππ‘, ππ‘
π΄πβ¦, ππ‘π΄, ππ‘
π΅, ππ‘π΄, ππ‘
π΅
wealth distribution
ππ‘ =ππ‘
ππ‘πΎπ‘β 0,1 Aβs wealth share
ππ‘π΄π + ππ‘
π΄π + ππ‘π΅π + ππ‘
π΅π = 1 and πΆπ‘π΄ + πΆπ‘
π΅ = ππ‘ β ππ‘πΎπ‘
Portfolio weights: ππ‘
π΄π
ππ‘,ππ‘
π΄π
ππ‘, 1 β
ππ‘π΄π+ππ‘
π΄π
ππ‘
Consumption rates: ππ‘π΄ = πΆπ‘
π΄/ππ‘ ππ‘π΅ = πΆπ‘
π΅/(ππ‘πΎπ‘ β ππ‘)
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2. State variable: 3 regions
Wealth share πβ’ Three regions
β’ Symmetric
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π
Full specialization
Full specialization
π΄ produces π π π, π
π΅ produces π, π π π
0 11/2
ππ‘π΄π = ππ‘
ππ‘π΅π = 1 β ππ‘
ππ‘π΅π = ππ‘
π΄π = 0
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2. Capital share, terms of trade, price of capital
Numerical: π = 5%, π = 14%, π = 4%, πΏ = 5%, π = 2, ππ΄ = ππ΅ = 10%
Three different elasticities of substitution: π = {.5,1,β} 40
wealth share
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TOT: Supply vs. demand shock
Supply versus demand shock
TOT improve for π΄ as ππ‘ declines for ππ‘ β π, . 5can be due to
β’ πππ΄ < 0: Negative supply shock World recession
β’ πππ΅ > 0: Positive demand shock World boom
TOT: Output price
β¦but fire-sale of (physical) capital stock ππ‘
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Stationary distribution drift volatility
Three different elasticities of substitution: π = {.5,1,β}
Difference to Cole & Obstfeld 1994: persistence of capital, πΏ < β
2. Stability, Phoenix Miracle for different π
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Phoenix miracle
Masspointat {0,1}
wealth share
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Overview
1. Complete markets β First best
2. Incomplete markets (equity home bias)β’ Levered short-term debt financing
β’ Sudden stops: (varying technological illiquidity)
Amplification
Runs due to sunspots
3. Closed capital account: capital controls (no equity, no debt)
4. Welfare analysis
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2. Amplification
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ππ‘ππ΄
=
ππ‘π΄π
ππ‘(1βππ‘)
1 β [ππ‘π΄π β ππ‘]
πβ²(ππ‘)π ππ‘
ππ΄
Leverage effect ππ‘π΄π/ππ‘
Loss spiral 1/{1 β ππ‘π΄π β ππ‘
πβ² ππ‘π ππ‘
} (infinite sum)
Technological illiquidity (π , πΏ) β market illiquidity πβ² π(dis)investment adjustment cost
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2. Amplification
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ππ‘ππ΄
=
ππ‘π΄π
ππ‘(1βππ‘)
1 β [ππ‘π΄π β ππ‘]
πβ²(ππ‘)π ππ‘
ππ΄
Leverage effect ππ‘π΄π/ππ‘
Loss spiral 1/{1 β ππ‘π΄π β ππ‘
πβ² ππ‘π ππ‘
} (infinite sum)
Technological illiquidity (π , πΏ) β market illiquidity πβ² π(dis)investment adjustment cost
leverage
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2. Amplification
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ππ‘ππ΄
=
ππ‘π΄π
ππ‘(1βππ‘)
1 β [ππ‘π΄π β ππ‘]
πβ²(ππ‘)π ππ‘
ππ΄
Leverage effect ππ‘π΄π/ππ‘
Loss spiral 1/{1 β ππ‘π΄π β ππ‘
πβ² ππ‘π ππ‘
} (infinite sum)
chnological illiquidity (π , πΏ) β market illiquidity πβ² π(dis)investment adjustment cost
leverage
Market illiquidity(price impact)
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2. Amplification
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ππ‘ππ΄
=
ππ‘π΄π
ππ‘(1βππ‘)
1 β [ππ‘π΄π β ππ‘]
πβ²(ππ‘)π ππ‘
ππ΄
Leverage effect ππ‘π΄π/ππ‘
Loss spiral 1/{1 β ππ‘π΄π β ππ‘
πβ² ππ‘π ππ‘
} (infinite sum)
Technological illiquidity (π , πΏ) β market illiquidity πβ² πβ’ (dis)investment adjustment cost
leverage
Market illiquidity(price impact)
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Quadratic adjustment cost
Investment rate of Ξ¦ +1
π Ξ¦2 generates new capital
at rate Ξ¦
Ξ¦ π =1
π 1 + 2π π β 1
Three casesβ’ π = 0 β π = 1
β’ π = 2
β’ π π<0 = 100 and π π>0 = 2
2. Technological (π , πΏ) β market illiquidity πβ² π
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Sudden stops: amplification & runs
Sudden stopβ’ Adverse fundamental triggers %-decline in debt that exceeds
%-decline in net worth; π(ππ΄πβπ)
ππ
π
ππ΄πβπ> 1
πππ΄π
ππ>
ππ΄π
π
pro-cyclical leverage
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hyperbola
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Sudden stops: amplification & runs
Sudden stopβ’ Adverse fundamental triggers %-decline in debt that exceeds
%-decline in net worth; π(ππ΄πβπ)
ππ
π
ππ΄πβπ> 1
πππ΄π
ππ>
ππ΄π
π
pro-cyclical leverage
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hyperbola
Slope of tangent vs. secant
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Sudden stops: amplification & runs
Sudden stopβ’ Adverse fundamental triggers %-decline in debt that exceeds
%-decline in net worth; π(ππ΄πβπ)
ππ
π
ππ΄πβπ> 1
πππ΄π
ππ>
ππ΄π
π
pro-cyclical leverage
ππ‘π·πππ‘π΄
= 1 +π ππ‘
π΄π β ππ‘ /πππ‘ ππ‘
ππ‘π΄π β ππ‘
+
ππ‘π΄π
ππ‘(1βππ‘)
1 β [ππ‘π΄π β ππ‘]
πβ²(ππ‘)π ππ‘
ππ΄
β’ An unanticipated sunspot triggers a sudden capital price drop from π to π, accompanied by a drop in π to π.
π π = max ππ + ππ΄π π β π , 0
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Sudden stops: amplification & runs
Sudden stopβ’ Adverse fundamental triggers %-decline in debt that exceeds
%-decline in net worth; π(ππ΄πβπ)
ππ
π
ππ΄πβπ> 1
πππ΄π
ππ>
ππ΄π
π
pro-cyclical leverage
ππ‘π·πππ‘π΄
= 1 +π ππ‘
π΄π β ππ‘ /πππ‘ ππ‘
ππ‘π΄π β ππ‘
+
ππ‘π΄π
ππ‘(1βππ‘)
1 β [ππ‘π΄π β ππ‘]
πβ²(ππ‘)π ππ‘
ππ΄
β’ An unanticipated sunspot triggers a sudden capital price drop from π to π, accompanied by a drop in π to π.
π =max ππ + ππ΄π π β π , 0
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hyperbola
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Sudden stop due to sunspot
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Sudden stop due to sunspot: Zoomed in
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Overview
1. Complete markets β First best
2. Incomplete markets (equity home bias)β’ Levered short-term debt financing
β’ Sudden stops: (varying technological illiquidity)
Amplification
Runs due to sunspots
3. Closed capital account: capital controls (no equity, no debt)
4. Welfare analysis
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Market structures
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Markets Output π¦π, π¦π
Physical capital πΎ
Debt Equity
Complete MarketsFull integration/First Best
X X X X
Open credit account(equity home bias)
X X X
Closed credit accountX X
Trade Finance
intratemporal intertemporal
Add taxes/capital controls
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3. Credit account: open vs. closed
π = 5%, π = 14%, π = 4%, πΏ = 5%, π = 2, ππ΄ = ππ΅ = 10%, s = 1
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Capital price lowerβ’ Lower input priceβ’ Destabilizes
balance sheet
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3. Credit account: open vs. closed
π = 5%, π = 14%, π = 4%, πΏ = 5%, π = 2, ππ΄ = ππ΅ = 10%, s = 1
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Stability
More stabilityLess growth
Phoenix miracleslightly smaller
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Overview
1. Complete markets β First best
2. Incomplete markets (equity home bias)
3. Closed capital account: capital controls (no equity, no debt)
4. Welfare analysisβ’ Pecuniary externalities
β’ Welfare calculations + Pareto improving redistributions
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4. When are credit flows excessive?
Constrained inefficiency (in incomplete market setting)due to pecuniary externalities
β’ Price of capital: fire sale externality if leverage is high
β’ Price of output good: βterms of trade hedgeβ restrained competition
Price taking behavior undermined this hedge
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shockautomatic
hedge
Price taking behavior
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4. When are credit flows excessive?
Constrained inefficiency (in incomplete market setting)due to pecuniary externalities
β’ Price of capital: fire sale externality if leverage is high
β’ Price of output good: βterms of trade hedgeβ restrained competition
Price taking behavior undermined this hedge
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shock
Complete market insurance
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4. Welfare comparison
π = 5%, π = 14%, π = 4%, πΏ = 5%, π = 2, ππ΄ = ππ΅ = 10%,
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Full specialization
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4. Welfare comparison
π = 5%, π = 14%, π = 4%, πΏ = 5%, π = 2, ππ΄ = ππ΅ = 10%,
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Full specialization
Inefficiency at the extremes:Role for redistributive Policydefault/bail-out/debt-relief
Pareto improving
Intuition:Other countryβs output price is high
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4. Welfare comparison
π = 5%, π = 14%, π = 4%, πΏ = 5%, π = 2, ππ΄ = ππ΅ = 10%,
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Full specialization
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4. Welfare comparison
Any monotone transformation of π would be equally good state variable
Normalization: take CDF of π
β’ Uniform stationary distribution!
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Conclusion
Sudden stopsβ’ Amplification of fundamental shock β’ Runs due to sunspots β vulnerability region
Phoenix miracle Tradeoff between capital allocation & risk sharing
β’ βTerms of trade hedgeβ
When are short-term credit flows excessive?β’ When can capital controls (financial liberalization) be welfare
enhancing (reducing)? β’ Pecuniary externality
Price of physical capital fire-sales externality β technological illiquidity Price of output goods: βterms of trade hedgeβ externality
Bailout/RestructuringRedistributive policy can be Pareto improving if one country is sufficiently balance sheet impaired
β’ Reduces output good price
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