The Classics II: Borrowing Constraints Andrea Ferrero University of Oxford
Monetary Economics (IHS Vienna) Lecture 7 April 3, 2014
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Outline Last class: CSV models and applications to the crisis I
Main lesson: Potentially successful but important frictions are in right place
Today: Borrowing constraints (Kiyotaki and Moore, 1997) I
If constraint depends on value of collateral, feedback effect via asset prices
Plan: I
Model
I
Amplification
I
Applications to crisis
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
2 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
A Small Open Economy with Borrowing Constraints Based on Kocherlakota (2000) I
Small open economy version of neoclassical growth model with housing
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
3 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
A Small Open Economy with Borrowing Constraints Based on Kocherlakota (2000) I
Small open economy version of neoclassical growth model with housing
Economy populated by continuum of households of measure one I
Value consumption and housing services (proportional to housing stock)
I
Receive endowment
I
Can borrow (or lend) internationally at world interest rate (SOE)
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
3 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
A Small Open Economy with Borrowing Constraints Based on Kocherlakota (2000) I
Small open economy version of neoclassical growth model with housing
Economy populated by continuum of households of measure one I
Value consumption and housing services (proportional to housing stock)
I
Receive endowment
I
Can borrow (or lend) internationally at world interest rate (SOE)
Financial friction: Borrowing subject to fraction of value of collateral
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
3 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Households’ Problem " max
{ct +s ,ht +s ,bt +s }
= Et
∞
∑β
# s
(ln ct +s + ψ ln ht +s ) ,
β ∈ (0, 1), ψ > 0
s =0
subject to ct + qt ht − bt = qt ht −1 − (1 + rt −1 )bt −1 + yt and bt ≤ θqt ht ,
θ ∈ (0, 1)
where ct ≡ Consumption ht ≡ Housing (Price ≡ qt ) bt ≡ Debt rt ≡ World interest rate yt ≡ Endowment Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
4 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Households’ FOCs Substitute budget constraint into objective for ct Let λt /ct be Lagrange multiplier on borrowing constraint
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
5 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Households’ FOCs Substitute budget constraint into objective for ct Let λt /ct be Lagrange multiplier on borrowing constraint FOC for housing ψ 1 1 1 − qt + βEt qt +1 + θ µt qt = 0 ht ct ct + 1 ct FOC for debt 1 1 1 − β(1 + rt )Et − µt = 0 ct ct + 1 ct
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
5 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Equilibrium with Slack Constraint (µt = 0) Housing in fixed supply (normalize ht = 1 ∀t)
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
6 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Equilibrium with Slack Constraint (µt = 0) Housing in fixed supply (normalize ht = 1 ∀t) Household optimization yields
Andrea Ferrero (Oxford)
1
=
qt
=
ct β(1 + rt )Et ct +1 ct qt +1 ψct + βEt ct + 1
Classics: Borrowing Constraints
April 3, 2014
6 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Equilibrium with Slack Constraint (µt = 0) Housing in fixed supply (normalize ht = 1 ∀t) Household optimization yields 1
=
qt
=
ct β(1 + rt )Et ct +1 ct qt +1 ψct + βEt ct + 1
Resource constraint (law of motion of foreign debt)
−bt = −(1 + rt −1 )bt −1 + yt − ct Steady state level of debt undetermined
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
6 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Equilibrium with Binding Constraint (µt > 0) Housing in fixed supply (normalize ht = 1 ∀t)
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
7 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Equilibrium with Binding Constraint (µt > 0) Housing in fixed supply (normalize ht = 1 ∀t) Household optimization yields
Andrea Ferrero (Oxford)
1 − µt
=
(1 − θµt )qt
=
ct β(1 + rt )Et ct + 1 ct qt + 1 ψct + βEt ct + 1
Classics: Borrowing Constraints
April 3, 2014
7 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Equilibrium with Binding Constraint (µt > 0) Housing in fixed supply (normalize ht = 1 ∀t) Household optimization yields 1 − µt
=
(1 − θµt )qt
=
ct β(1 + rt )Et ct + 1 ct qt + 1 ψct + βEt ct + 1
Resource constraint (law of motion of foreign debt)
−bt = −(1 + rt −1 )bt −1 + yt − ct
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
7 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Equilibrium with Binding Constraint (µt > 0) Housing in fixed supply (normalize ht = 1 ∀t) Household optimization yields 1 − µt
=
(1 − θµt )qt
=
ct β(1 + rt )Et ct + 1 ct qt + 1 ψct + βEt ct + 1
Resource constraint (law of motion of foreign debt)
−bt = −(1 + rt −1 )bt −1 + yt − ct Borrowing constraint at equality bt = θqt I
Borrowing constraint determines steady state level of foreign debt
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
7 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Steady State with Binding Constraint (µ > 0) Necessary condition: 1 − β(1 + r ) > 0 ⇒ r < β−1 − 1 I
World real interest rate low enough
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
8 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Steady State with Binding Constraint (µ > 0) Necessary condition: 1 − β(1 + r ) > 0 ⇒ r < β−1 − 1 I
World real interest rate low enough
In steady state
Andrea Ferrero (Oxford)
House prices:
q
Euler equation
µ
Borrowing constraint
b
Resource constraint
c
= ψc/(1 − β − θµ) = 1 − β (1 + r ) = θq = y − rb
Classics: Borrowing Constraints
April 3, 2014
8 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Steady State with Binding Constraint (µ > 0) Necessary condition: 1 − β(1 + r ) > 0 ⇒ r < β−1 − 1 I
World real interest rate low enough
In steady state House prices:
q
Euler equation
µ
Borrowing constraint
b
Resource constraint
c
= ψc/(1 − β − θµ) = 1 − β (1 + r ) = θq = y − rb
Comparative static: Permanent increase in θ (financial deregulation)
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
8 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Steady State with Binding Constraint (µ > 0) Necessary condition: 1 − β(1 + r ) > 0 ⇒ r < β−1 − 1 I
World real interest rate low enough
In steady state House prices:
q
Euler equation
µ
Borrowing constraint
b
Resource constraint
c
= ψc/(1 − β − θµ) = 1 − β (1 + r ) = θq = y − rb
Comparative static: Permanent increase in θ (financial deregulation) I
Direct impact (increase) on b for given q (looser borrowing constraint)
I
Direct impact (increase) on q for given c (shadow value of housing)
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
8 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Steady State with Binding Constraint (µ > 0) Necessary condition: 1 − β(1 + r ) > 0 ⇒ r < β−1 − 1 I
World real interest rate low enough
In steady state House prices:
q
Euler equation
µ
Borrowing constraint
b
Resource constraint
c
= ψc/(1 − β − θµ) = 1 − β (1 + r ) = θq = y − rb
Comparative static: Permanent increase in θ (financial deregulation) I
Direct impact (increase) on b for given q (looser borrowing constraint)
I
Direct impact (increase) on q for given c (shadow value of housing)
I
Indirect impact (increase) on b via q (amplification effect)
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
8 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Steady State with Binding Constraint (µ > 0) Necessary condition: 1 − β(1 + r ) > 0 ⇒ r < β−1 − 1 I
World real interest rate low enough
In steady state House prices:
q
Euler equation
µ
Borrowing constraint
b
Resource constraint
c
= ψc/(1 − β − θµ) = 1 − β (1 + r ) = θq = y − rb
Comparative static: Permanent increase in θ (financial deregulation) I
Direct impact (increase) on b for given q (looser borrowing constraint)
I
Direct impact (increase) on q for given c (shadow value of housing)
I
Indirect impact (increase) on b via q (amplification effect)
I
Indirect impact (decrease) on c via b (repayment effect)
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
8 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Steady State with Binding Constraint (µ > 0) Necessary condition: 1 − β(1 + r ) > 0 ⇒ r < β−1 − 1 I
World real interest rate low enough
In steady state House prices:
q
Euler equation
µ
Borrowing constraint
b
Resource constraint
c
= ψc/(1 − β − θµ) = 1 − β (1 + r ) = θq = y − rb
Comparative static: Permanent increase in θ (financial deregulation) I
Direct impact (increase) on b for given q (looser borrowing constraint)
I
Direct impact (increase) on q for given c (shadow value of housing)
I
Indirect impact (increase) on b via q (amplification effect)
I
Indirect impact (decrease) on c via b (repayment effect)
I
Indirect impact (decrease) on q via c (repayment effect)
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
8 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Transition with Binding Constraint (µt > 0) Assume β = 0.96, r = 4% (think annual calibration)
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
9 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Transition with Binding Constraint (µt > 0) Assume β = 0.96, r = 4% (think annual calibration) Experiment: Permanent increase in θ from 80% to 90%
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
9 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Transition with Binding Constraint (µt > 0) Assume β = 0.96, r = 4% (think annual calibration) Experiment: Permanent increase in θ from 80% to 90% House Prices
Consumption
112
104
110
103
108 102 106 101 104 100
102 100
0
2
4
6
8
10
99
0
2
Foreign Debt
4
6
8
10
8
10
Current Account
17
1
16.5
0
16 15.5
−1
15
−2
14.5 −3
14 13.5 0
Andrea Ferrero (Oxford)
2
4
6
8
10
−4
0
Classics: Borrowing Constraints
2
4
6
April 3, 2014
9 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Amplification How big is endogenous amplification effect via asset prices (q)?
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
10 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Amplification How big is endogenous amplification effect via asset prices (q)? Same experiment with exogenous borrowing constraint: bt ≤ θ¯
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
10 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Amplification How big is endogenous amplification effect via asset prices (q)? Same experiment with exogenous borrowing constraint: bt ≤ θ¯ House Prices
Consumption
110
102
108
101.5
106
101
104
100.5
102
100
100
99.5
0
2
4
6
8
10
0
2
Foreign Debt 0
15
−0.5
14.5
−1
14
−1.5
0
Andrea Ferrero (Oxford)
2
4
6
6
8
10
8
10
Current Account
15.5
13.5
4
8
10
−2
0
Classics: Borrowing Constraints
2
4
6
April 3, 2014
10 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Amplification How big is endogenous amplification effect via asset prices (q)? Same experiment with exogenous borrowing constraint: bt ≤ θ¯ Additional 1.5% increase in debt and consumption during transition I
Consumption increases on impact because of higher borrowing
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
10 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Amplification How big is endogenous amplification effect via asset prices (q)? Same experiment with exogenous borrowing constraint: bt ≤ θ¯ Additional 1.5% increase in debt and consumption during transition I
Consumption increases on impact because of higher borrowing
What about amplification of other shocks? I
Cordoba and Ripoll (IER 2004): Productivity shocks
I
Cordoba and Ripoll (JEEA 2004): Monetary shocks
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
10 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Collateral Constraints Amplification Kiyotaki and Moore (1997) popularized collateral constraints as endogenous mechanism to generate cycles I
Closed economy (general equilibrium) with borrowers and lenders
Main result: Amplification and persistence of small, temporary shocks I
Same intuition as in small open economy example
I
Main difference: Focus on production sector
I
I
F
By assumption, credit constrained firms are more productive
F
Aggregate consequence can be severe
Main result derived under very specific assumptions F
Constrained agents fully invest any unexpected income
F
Linear preferences
F
Linear technology in collateral asset
Is main result robust to more standard preferences/technologies?
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Classics: Borrowing Constraints
April 3, 2014
11 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Amplification of Real Shocks For standard value of capital share (1/3) and elasticity of intertemporal substitution (1) ⇒ Amplification is close to zero
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
12 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Amplification of Real Shocks For standard value of capital share (1/3) and elasticity of intertemporal substitution (1) ⇒ Amplification is close to zero Amplification effect is product of four terms I
Productivity gap between borrower and savers
I
Collateral share in production
I
Production share of constrained agents
I
Redistribution of collateral to constrained agents
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
12 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Amplification of Real Shocks For standard value of capital share (1/3) and elasticity of intertemporal substitution (1) ⇒ Amplification is close to zero Amplification effect is product of four terms I
Productivity gap between borrower and savers
I
Collateral share in production
I
Production share of constrained agents
I
Redistribution of collateral to constrained agents
Redistribution of collateral is reason for amplification I
In face of aggregate shock, want to shift resources to more productive agents
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
12 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Amplification of Real Shocks For standard value of capital share (1/3) and elasticity of intertemporal substitution (1) ⇒ Amplification is close to zero Amplification effect is product of four terms I
Productivity gap between borrower and savers
I
Collateral share in production
I
Production share of constrained agents
I
Redistribution of collateral to constrained agents
Redistribution of collateral is reason for amplification I
In face of aggregate shock, want to shift resources to more productive agents
Tradeoff between productivity gap (requires little capital for productive agents) and production share (small if little capital) Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
12 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Amplification of Nominal Shocks If debt contracts are not indexed to inflation (i.e. nominal), unanticipated monetary shocks can generate large output movements
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
13 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Amplification of Nominal Shocks If debt contracts are not indexed to inflation (i.e. nominal), unanticipated monetary shocks can generate large output movements Model: Introduce cash-in-advance constraint in Kiyotaki and Moore (1997) mti −1 = pt cti + qt (kti − kti −1 )
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
13 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Amplification of Nominal Shocks If debt contracts are not indexed to inflation (i.e. nominal), unanticipated monetary shocks can generate large output movements Model: Introduce cash-in-advance constraint in Kiyotaki and Moore (1997) mti −1 = pt cti + qt (kti − kti −1 ) Intuition: Fisher effect I
Consider an unexpected monetary contraction
I
In equilibrium, inflation drops
I
With nominal debt, higher real burden of debt for borrowers
I
Redistribution of resources from borrowers to savers
I
But borrowers are productive agent
I
Amplification effect on real output
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
13 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Amplification of Nominal Shocks If debt contracts are not indexed to inflation (i.e. nominal), unanticipated monetary shocks can generate large output movements Model: Introduce cash-in-advance constraint in Kiyotaki and Moore (1997) mti −1 = pt cti + qt (kti − kti −1 ) However, if contracts are indexed to inflation, amplification largely disappears I
May even get expansionary effects of monetary contractions
I
Lower inflation increases real value of borrowers’ net worth
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
13 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Amplification of Nominal Shocks If debt contracts are not indexed to inflation (i.e. nominal), unanticipated monetary shocks can generate large output movements Model: Introduce cash-in-advance constraint in Kiyotaki and Moore (1997) mti −1 = pt cti + qt (kti − kti −1 ) However, if contracts are indexed to inflation, amplification largely disappears I
May even get expansionary effects of monetary contractions
I
Lower inflation increases real value of borrowers’ net worth
Generality of results subject to same criticisms of Kiyotaki and Moore (1997) See also Liu, Wang and Zha (2013) for additional results Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
13 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Eggertsson and Krugman (2012) Household Gross Debt % of Personal Income Country United States United Kingdom Spain
2000 96 105 69
2008 128 160 130
Debt at center-stage of crisis episodes I
Great Depression (Fisher, 1933)
I
Japan (Koo, 2008)
I
Emerging Markets (Krugman, 1999; Aghion, Bacchetta and Banerjee, 2001)
I
Great Recession (Hall, 2011; Mian and Sufi, 2011a,b)
Yet, debt irrelevant in representative agent models
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
14 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Eggertsson and Krugman (2012): Model Two types (i = {s, b }), s = savers, b = borrowers Utility U (Ct +j (i )) = Et
∞
∑ β(i )t log Ct +j (i )
j =0
with β(s ) = β > β(b ) (type b more impatient) Constant endowment Y (i ) = Y /2 ∀t. Budget constraint Ct (i ) − Dt (i ) =
Y − (1 + rt −1 )Dt −1 (i ) 2
where Dt (i ) is debt for agent i Borrowing constraint (exogenous)
(1 + rt )Dt (i ) ≤ D h with 0 < D h < βY /[2(1 − β)] Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
15 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Eggertsson and Krugman (2012): Steady State Agent b borrows up to limit in steady state, because relatively impatient C (b ) =
Y rD h − 2 1+r
Closed economy: Resource constraint is Y = C (b ) + C (s )
⇒ C (s ) =
Y rD h + 2 1+r
Savers on Euler equation because borrowing constraint not binding 1 1 = β(1 + rt )Et Ct (s ) Ct +1 (s ) I
Real interest rate in steady state is r = β−1 − 1
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
16 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Eggertsson and Krugman (2012): Deleveraging Shock Suppose debt limit falls unexpectedly from D h to D l I
Split dynamics in short- and long-run (as in Eggertsson, 2008)
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
17 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Eggertsson and Krugman (2012): Deleveraging Shock Suppose debt limit falls unexpectedly from D h to D l I
Split dynamics in short- and long-run (as in Eggertsson, 2008)
Borrowers: I
Long-run steady consumption CL ( b ) =
Y rD l Y − = − (1 − β )D l 2 1+r 2
I
Short-run adjustment
I
Y + CS (b ) 2 Suppose borrowers need to adapt in one period to new lower limit DS = D h −
DS = I
Dl 1 + rS
Short-run consumption: Plug back into short-run borrowing constraint CS (b ) =
Andrea Ferrero (Oxford)
Y Dl + − Dh 2 1 + rS
Classics: Borrowing Constraints
April 3, 2014
17 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Eggertsson and Krugman (2012): Deleveraging Shock Suppose debt limit falls unexpectedly from D h to D l I
Split dynamics in short- and long-run (as in Eggertsson, 2008)
Savers: I
Long-run consumption Y rD l Y + = + (1 − β )D l 2 1+r 2 Short-run consumption from resource constraint (Y = CS (b ) + CS (s )) CL (s ) =
I
CS ( s ) =
Y Dl − + Dh 2 1 + rS
I
Savers always on Euler equation
I
Use expressions for CL (s ) and CS (s ) from above into Euler equation
CL (s ) = β(1 + rS )CS (s )
1 + rS = Andrea Ferrero (Oxford)
Y /2 + D l β(Y /2 + D h )
Classics: Borrowing Constraints
April 3, 2014
17 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Eggertsson and Krugman (2012): Liquidity Trap Recall how to generate liquidity trap in New Keynesian model I
Large enough drop in efficient real interest rate
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
18 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Eggertsson and Krugman (2012): Liquidity Trap Recall how to generate liquidity trap in New Keynesian model I
Large enough drop in efficient real interest rate
Negative short-run real interest rate rS = I
Y /2 + D l (1 − β )Y − 1 < 0 ⇒ βD h − D l > 2 β(Y /2 + D h )
High enough “debt overhang”
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
18 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Eggertsson and Krugman (2012): Liquidity Trap Recall how to generate liquidity trap in New Keynesian model I
Large enough drop in efficient real interest rate
Negative short-run real interest rate rS = I
Y /2 + D l (1 − β )Y − 1 < 0 ⇒ βD h − D l > 2 β(Y /2 + D h )
High enough “debt overhang”
Intuition I
Borrower consumption drops due deleveraging
I
Given constant endowment, savers need to compensate
I
Real interest rate must drop enough to induce savers to consume more
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
18 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Eggertsson and Krugman (2012): Summary and Extensions Debt-deflation mechanism arises in EK with nominal asset With sticky prices get similar implications as in baseline New Keynesian model I
Main difference: Drop in efficient real interest rate endogenous
Bottom line: Deleveraging shock provides rationalization of crisis Guerrieri and Lorenzoni (2012) reach similar conclusions to EK in model with heterogenous agents and uninsurable idiosyncratic risk I
Main difference: Additional precautionary savings motive
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
19 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Empirical Evidence Evidence of tighter borrowing constraints quite pervasive I
Senior Loan Officers Opinion Survey in U.S. and E.U. (Favilukis et al., 2012)
I
Mian and Sufi (2009) on subprime mortgage expansion
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
20 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Empirical Evidence Evidence of tighter borrowing constraints quite pervasive I
Senior Loan Officers Opinion Survey in U.S. and E.U. (Favilukis et al., 2012)
I
Mian and Sufi (2009) on subprime mortgage expansion
Still tighter borrowing constraints may be not fully exogenous I
Banks may be reacting to overexposure to housing
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
20 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Empirical Evidence Evidence of tighter borrowing constraints quite pervasive I
Senior Loan Officers Opinion Survey in U.S. and E.U. (Favilukis et al., 2012)
I
Mian and Sufi (2009) on subprime mortgage expansion
Still tighter borrowing constraints may be not fully exogenous I
Banks may be reacting to overexposure to housing
Alternative: “Valuation” view (Justiniano, Primiceri and Tambalotti, 2013) I
Today focus on why debt-deleveraging story may not work
I
Will come back to valuation view later on
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
20 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Debt-Deleveraging: A Skeptical View Justiniano, Primiceri and Tambalotti (2013): Medium-scale DSGE model with borrowers and lenders and residential investment
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
21 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Debt-Deleveraging: A Skeptical View Justiniano, Primiceri and Tambalotti (2013): Medium-scale DSGE model with borrowers and lenders and residential investment Key distinctive element: Asymmetric collateral constraint ( θt qt ht if θt qt ≥ θt −1 qt −1 bt ≤ b¯ t = ¯ (1 − δh )bt −1 + θt qt Ξt if θt qt < θt −1 qt −1 where Ξt is residential investment (new houses) Idea: Mimic asymmetry in mortgage contract (although debt is one period)
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
21 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Debt-Deleveraging: A Skeptical View Justiniano, Primiceri and Tambalotti (2013): Medium-scale DSGE model with borrowers and lenders and residential investment Key distinctive element: Asymmetric collateral constraint ( θt qt ht if θt qt ≥ θt −1 qt −1 bt ≤ b¯ t = ¯ (1 − δh )bt −1 + θt qt Ξt if θt qt < θt −1 qt −1 where Ξt is residential investment (new houses) Idea: Mimic asymmetry in mortgage contract (although debt is one period) I
When prices rise, households can refinance and borrow more
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
21 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Debt-Deleveraging: A Skeptical View Justiniano, Primiceri and Tambalotti (2013): Medium-scale DSGE model with borrowers and lenders and residential investment Key distinctive element: Asymmetric collateral constraint ( θt qt ht if θt qt ≥ θt −1 qt −1 bt ≤ b¯ t = ¯ (1 − δh )bt −1 + θt qt Ξt if θt qt < θt −1 qt −1 where Ξt is residential investment (new houses) Idea: Mimic asymmetry in mortgage contract (although debt is one period) I
When prices rise, households can refinance and borrow more
I
When prices fall, F
Lenders cannot require faster payment than depreciation (= amortization)
F
Tighter credit condition apply only to new houses
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
21 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Debt-Deleveraging: A Skeptical View Justiniano, Primiceri and Tambalotti (2013): Medium-scale DSGE model with borrowers and lenders and residential investment Key distinctive element: Asymmetric collateral constraint ( θt qt ht if θt qt ≥ θt −1 qt −1 bt ≤ b¯ t = ¯ (1 − δh )bt −1 + θt qt Ξt if θt qt < θt −1 qt −1 where Ξt is residential investment (new houses) Idea: Mimic asymmetry in mortgage contract (although debt is one period) Example: Suppose ht = 1, δh = 0, θt = θ = 80%, q0 = 100 ⇒ b0 = 80 I
Suppose q1 falls to 90: Standard borrowing constraint would give b1 = 72
I
Asymmetric borrowing constraint: b1 = b¯ 0 = 80 (lower with δh > 0)
I
Sluggishness in downward debt adjustment
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
21 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
HOUSEHOLD LEVERAGING AND DELEVERAGING
Asymmetric Adjustment
(a): House prices 200 180 160 140 120 100 1970
1975
1980
1985
1990
1995
2000
2005
2010
2015
2005
2010
2015
(b): Mortgages−to−real estate ratio 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 1970
1975
Andrea Ferrero (Oxford)
1980
1985
1990
1995
Classics: Borrowing Constraints
2000
April 3, 2014
22 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
LEVERAGING AND DELEVERAGING JPT: FinancialHOUSEHOLD Deregulation Experiment
17
Figure 4.2. Cumulative LTVs. Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
23 / 28
Introduction
Small Open Economy
JPT: Results
Amplification
Applications to the Crisis
HOUSEHOLD LEVERAGING AND DELEVERAGING
(a): θ
1
(b): House prices 102.5
0.95 102 101.5 0.9
101 100.5 100
0.85 1998
2000
2002
2004
2006
2008
2010
2012
99.5 1998
2000
2002
2004
2006
2008
2010
2012
2010
2012
(d): Debt−to−GDP ratio
(c): Debt−to−real estate ratio 0.46
0.6
0.44
0.55
0.42 0.5 0.4 0.45
0.38 0.36 1998
2000
2002
2004
2006
2008
2010
2012
0.4 1998
(e): GDP 0.08
101
0.07
100
0.06
99 98 1998
2000
2002
2004
2006
2008
(f): Nominal interest rate (annualized)
102
0.05
2000
2002
2004
2006
2008
2010
2012
0.04 1998
2000
2002
2004
2006
2008
2010
2012
Figure 4.1. Credit liberalization experiment: debt and macro variables. Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
24 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
JPT: Role of Asymmetric Borrowing Constraint HOUSEHOLD LEVERAGING AND DELEVERAGING
(a): θ
20
(b): House prices 105
0.95 104 103 0.9 102 101 0.85 1998
2000
2002
2004
2006
2008
2010
2012
100 1998
2000
(c): Debt−to−real estate ratio
2002
2004
2006
2008
2010
2012
2010
2012
(d): Debt−to−GDP ratio
0.5
0.6 0.5
0.4
0.4 0.3 0.3 0.2 0.1 1998
0.2 2000
2002
2004
2006
2008
2010
2012
0.1 1998
(e): GDP
2000
2002
2004
2006
2008
(f): Nominal interest rate (annualized)
104
0.08
102
0.06
100 0.04 98 0.02
96 94 1998
2000
2002
2004
2006
2008
2010
2012
0 1998
2000
2002
2004
2006
2008
2010
2012
Figure 4.3. Credit liberalization experiment without the asymmetry of the collateral constraint : debt and macro variables. Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
25 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
HOUSEHOLD LEVERAGING AND DELEVERAGING
JPT: Redistribution
Consumption of borrowers
Consumption of lenders
115
101
110
100
105
99
100
98
95 90 1998
97 2000
2002
2004
2006
2008
2010
2012
96 1998
2000
Housing stock of borrowers
2002
2004
2006
2008
2010
2012
2008
2010
2012
2008
2010
2012
Housing stock of lenders
115
105
110
100
105 95 100 90
95 90 1998
2000
2002
2004
2006
2008
2010
2012
85 1998
2000
2002
Hours of borrowers
2004
2006
Hours of lenders
104
106 104
102
102 100 100 98 96 1998
98 2000
2002
2004
2006
2008
2010
2012
96 1998
2000
2002
2004
2006
Figure 4.4. Credit liberalization experiment: borrowers and lenders. Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
26 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
JPT: Intuition Closed economy: Almost all action is redistribution During boom: Savers downsize and consume less I
Very little evidence (savers ≈ middle-aged/old and wealthy)
Also, nominal interest rate increases during boom I
Evidence: Low interest rates during early 2000s
Bottom line: Probably underestimate importance of financial deregulation Will come back to these points later
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
27 / 28
Introduction
Small Open Economy
Amplification
Applications to the Crisis
Summary of Borrowing Constraint Models Borrowing constraints potentially powerful mechanism of amplification When constraint is endogenous, amplification occurs via asset prices I
Relaxing constraint increases borrowing
I
Pushes up asset prices
I
Further relaxes constraint
Even exogenous borrowing constraint can create severe crises Strength of amplification, however, depends on details Will revisit to several of these points later
Andrea Ferrero (Oxford)
Classics: Borrowing Constraints
April 3, 2014
28 / 28
