liquidity trap and excessive leverage · aggregate demand externalities: older literature, e.g.,...
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Liquidity Trap and Excessive Leverage
Anton Korinek (JHU and NBER) Alp Simsek (MIT and NBER)
RTF-CEPR-JFI Workshop on
Banking and Regulation: The Next Frontier
Basel, Switzerland, January 2015
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 1 / 30
Deleveraging and the recession might be related
Micro evidence: Deleveraging explains much of job losses (Mian-Sufi).
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 2 / 30
One view: Low rates and the liquidity trap
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1980q1 1985q1 1990q1 1995q1 2000q1 2005q1 2010q1 2015q1time
real rate annualized nominal rate on 3 month Tbills
Formalized by: Eggertsson-Krugman, Hall, Guerrieri-Lorenzoni...
Stimulated policy analysis. Ex-post focus. Ignored debt market.
This paper: Ex-ante/macroprudential policies.
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 3 / 30
Main results: Excessive leverage and underinsurance
Model with anticipated deleveraging and liquidity trap.
Contributing factors: Impatience, previous leverage, optimism...
Main results:
Competitive equilibrium is constrained ineffi cient.Excessive leverage and underinsurance.Pareto improvement by macroprudential policies targeted towardsreducing leverage, e.g., debt limits and mandatory insurance.
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 4 / 30
Key channel: Aggregate demand externality
Source of ineffi ciency: Aggregate demand externality.
Greater ex-ante leverage:=⇒ Lower ex-post wealth for borrowers, higher for lenders.=⇒ Lower aggregate demand.
(Since borrowers have higher MPC due to deleveraging).=⇒ Deeper recession and lower output.
Similar mechanism for underinsurance.
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 5 / 30
Interest rate policy is not the ideal tool to reduce leverage
Results on the use of monetary policy:
Common argument: Raising r can curb leverage.
Under normal circumstances: higher r may actually raise leverage!→ conventional wisdom dominated by general equilibrium effects.
Even when conventional wisdom dominates, raising r is ineffi cient.
Problem is misallocation of wealth between borrowers-lenders.Macroprudential policies target this. Interest rate policy does not.
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 6 / 30
Related literature
Deleveraging and the liquidity trap: Eggertsson-Krugman...
We focus on debt market policies and ex-ante policies.
Aggregate demand externalities:
Older literature, e.g., Blanchard-Kiyotaki (1987). Different context.
More recent work by Schmitt-Grohe-Uribe and Farhi-Werning.We focus on an application to a liquidity trap
Excessive leverage: Optimism, moral hazard, fire-sale externalities.
New mechanism. Complementary, but important differences.
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 7 / 30
Environment with anticipated borrowing constraints
Single good (dollar) and dates t ∈ {0, 1, ..}.Households h ∈ {b, l}, with equal mass normalized to 1/2.Types identical except βb ≤ β l and d0 ≡ db0 = −d l0 ≥ 0.First ingredient: Future borrowing constraints:
For each t ≥ 1, agents face borrowing constraint dht+1 ≤ φ,which is fully anticipated in baseline setup.At t = 0, they can choose d1 without constraint.
Let rt+1 denote the real interest rate between t and t + 1.
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 8 / 30
Main ingredient: Lower bound on the interest rate
Key ingredient is the lower bound on the real interest rate:
rt+1 ≥ 0 for each t ≥ 1.
In practice, the lower bound emerges from two features:1 Zero lower bound on the nominal interest rate, it+1 ≥ 0.2 Sticky nominal prices.
We remain agnostic with respect to the source of stickiness.
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 9 / 30
Demand side: Household optimization
Baseline preferences u(c̃ht − v
(nht)). (Appendix: u (c)− v (n)).
Define cht = c̃ht − v(nht)as net consumption. Households solve:
max{cht ,d ht+1,nht }t
∞∑t=0
(βh)tu(cht)
s.t. cht = eht − dht +dht+1
1+ rt+1for all t,
where eht = wtnht + Πt − v(nht)denotes net income,
and dht+1 ≤ φ for each t ≥ 1.
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 10 / 30
Supply side: Linear technology
Technology: 1 unit of labor to 1 unit of consumption good.
Effi cient level of output maximizes net income:
e∗ = maxntnt − v (nt) .
Equilibrium does not necessarily feature e∗ due to bound on rt+1.
We modify the Walrasian supply side to accommodate the bound...
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 11 / 30
Supply side: Rationing when interest rate is too high
Final good firms solve:
Πt = maxntnt − wtnt s.t.
{0 ≤ nt , if rt+1 > 0
0 ≤ nt ≤ c̃bt +c̃lt
2 , if rt+1 = 0.
If rt+1 > 0, firms optimize as usual.
If rt+1 = 0, firms are subject to additional rationing constraint.
Equilibrium is{c̃ht , n
ht , c
ht , e
ht , d
ht+1
}h,t , {wt , rt+1,Πt}t such that...
Rationing equilibrium. Isomorphic to NK model with fully stickyprices.
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 12 / 30
Equilibrium after deleveraging is complete
Dates t ≥ 2: Steady state with 1+ rt+1 = 1/β l > 0.
This implies rationing constraint does not bind: et = e∗.
Agents’consumption is given by:
c l2 = e∗ + φ(1− β l
)and cb2 = e∗ − φ
(1− β l
).
Next consider date 1, the date at which deleveraging happens...
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 13 / 30
Equilibrium during the deleveraging episode
Borrowers’(constrained) consumption: cb1 = e1 −(d1 − φ
1+r2
).
Lenders’(unconstrained) consumption: c l1 = e1 +(d1 − φ
1+r2
).
Increase mediated by reduction in real rates (Euler):
u′(c l1)
= β l (1+ r2) u′(e∗ + φ
(1− β l
)).
Constraint r2 ≥ 0, implies upper bound on lender consumption:
c l1 ≤ c l1 where u′(c l1)
= β lu′(e∗ + φ
(1− β l
)).
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 14 / 30
Equilibrium during the deleveraging episode
Equilibrium depends on:
d1 − φ︸ ︷︷ ︸leverage adjustment at 0 rate
≶ c l1 − e∗︸ ︷︷ ︸unconstrained agents’buffer at 0 rate
,
If adjustment is suffi ciently small, then r2 > 0 and e1 = e∗.
Otherwise, equivalently, if leverage is suffi ciently high
d1 ≥ d1 = φ+ c l1 − e∗,
then r2 = 0 and we are in the constrained/rationing regime...
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 15 / 30
Liquidity trap, Keynesian cross, and Keynesian multiplier
Net income is then determined by aggregate demand:
e1 =cb1 + c l12
=e1 − (d1 − φ) + c l1
2.
This is a Keynesian cross with associated Keynesian multiplier.
Solving it, we obtain the equilibrium net income:
e1 = c l1 + φ− d1.
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 16 / 30
Graphical illustration of equilibrium
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Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 17 / 30
Conditions for an anticipated recession
Date 0 equilibrium determined by Euler equations:
1+ r1 =u′(c l0)
β lu′(c l1) =
u′(cb0)
βbu′(cb1) .
Proposition
There is a recession at date 1, d1 > d1, if:(i) Borrowers are suffi ciently impatient: βb < β̄
b(d0) or
(ii) Borrowers are suffi ciently indebted: d0 > d̄0(βb).
Recession is anticipated. Is it effi cient? We turn to welfare analysis...
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 18 / 30
Pecuniary externalities hurt some, benefit others
Define agents’date 1 welfare as a function of debt:
V b
d1︸︷︷︸own
, D1︸︷︷︸aggregate
= u(e1 (D1)− d1 +
φ
1+ r2 (D1)
)+continuation.
If D1 < d̄1, then r > 0 and usual pecuniary externalities apply:
∂V h
∂D1=
{−ηu′
(ch1)< 0, if h = l
ηu′(ch1)> 0, if h = b
, where η ∈ (0, 1) .
Externalities net out. Equilibrium is constrained effi cient in this range.
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 19 / 30
Aggregate demand externalities hurt all agents
If D1 > d̄1, then e < e∗ and aggregate demand externalities apply:
∂V h
∂D1=
∂e1∂D1
u′(ch1)
= −u′(ch1)< 0, for each h ∈ {b, l} .
Unlike price externalities, AD externalities negative for all agents.Opens the door for ineffi ciencies...
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 20 / 30
Main result: Ex-ante ineffi ciency and excessive leverage
Suppose planner can impose endogenous debt limit: dh1 ≤ D1.Can also use date 0 transfer, T0, to trace the Pareto frontier.
Constrained effi cient: Can be implemented with these policies.
PropositionAn allocation is constrained effi cient iff e0 = e∗ and:(i) D1 < d̄1 and the usual Euler equations hold.(ii) D1 = d̄1 the following distorted Euler inequality holds:
β lu′(c l1)
u′(c l0) ≥ βbu′
(cb1)
u′(cb0) .
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 21 / 30
Main result: Ex-ante ineffi ciency and excessive leverage
Implication: Equilibrium with d1 > d̄1 is constrained ineffi cient.Intuition: First order gains vs. second order losses.
The result is general– except the part that recession is fully avoided...
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 22 / 30
Ineffi ciency is related to MPC differences
Version with lower MPCs for borrowers implies weaker externalities:
∂e1∂d1
= − MPC b1 −MPC l12−
(MPC b1 +MPC l1
) .Debt matters because it redistributes ex-post wealth from b to l .
Evidence, e.g., Mian-Rao-Sufi (2013), suggests MPCb>MPCl.
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 23 / 30
Required intervention is related to MPC differences
Constrained effi cient allocations in this case satisfy:
11−MPC l1
β lu′(c l1)
u′(c l0) =
11−MPC b1
βbE0[u′(cb1)]
u′(cb0) for each D1 > d1.
Planner weighs agents’consumption at date 1 by a factor 11−MPC h1
.
Do not fully alleviate the recession.
Instead create wedge between borrowers’and lenders’rates.The magnitude of optimal wedge depends on MPC differences.
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 24 / 30
Extension with underinsurance
Version with aggregate uncertainty, captured by states s ∈ {H, L}.Equilibrium determined by Euler and full-insurance:
q1,Lq1,H
=πlLπlH
u′(c l1,L)
u′(c l1,H
) =πbLπbH
u′(cb1,L)
u′(cb1,H
) .Constrained effi cient: D1,L = d1 and distorted insurance:
πlLπlH
u′(c l1,L)
u′(c l1,H
) ≥ πbLπbH
u′(cb1,L)
u′(cb1,H
) .Result: Pareto improvement with mandatory insurance.
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 25 / 30
The case for mandatory home equity insurance
Distinct policy prescription: Index debt to financial shocks.
Home equity insurance was long proposed by Shiller and Weiss (1999).
In practice, households do not seem interested (due to optimism?).
Our model: Make it mandatory, especially for large price declines.
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 26 / 30
Preventive monetary policies
Are preventive monetary policies desirable?
Raising the inflation target: Yes (Blanchard et al., 2010).
How about raising the interest rate at date 0?
We can capture with date 0 constraint r1 ≥ r1.
Proposition
Suppose u is in the CRRA family and d0 >d1(r 1)1+r 1
. Then:
e ′0 (r1) < 0 and d′1 (r1) > 0.
Increasing the interest rate can increase leverage!
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 27 / 30
Raising the ex-ante interest rate can backfire
Consider special case with u (c) = log c and φ = 0:
db1 =1
1+ βb
(e1 − βb (1+ r1) (e0 − d0)
)d l1 =
1
1+ β l
(e1 − β l (1+ r1) (e0 + d0)
).
Closed form solution illustrates three forces:
1 Substitution effect: higher r1 reduces db1 , but increases dl1
→ substitution effect leads to conflicting results2 Recession/income effect: as e0 falls, db1 increases, d
l1 falls
→ this offsets the substitution effects3 Redistribution: higher r1 transfers wealth from b to l , raising db1→ under natural assumptions, effect 3 prevails
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 28 / 30
Interest rate policy is not the right tool for the problem
Can construct variants under which conventional wisdom dominates,for example if interest rates tighten financial constraints
But even then, interest rate policy is ineffi cient.1 Ineffi cient recession at date 0.2 Usual Euler equation holds as opposed to distorted Euler inequality.
Intuitively, MP targets the wrong wedge (between date 0 and 1).Macroprudential policies target the right wedge (between b and l).
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 29 / 30
Conclusion: Liquidity trap and excessive leverage
Model with anticipated liquidity trap:
Excessive leverage and underinsurance.
Source: Aggregate demand externalities.
New rationale for macroprudential policies that regulate leverage.
Korinek and Simsek (2015) Liquidity Trap BCBS RTF Workshop 30 / 30