Liquidity Trap and Excessive Leverage · Aggregate demand externalities: Older literature, e.g.,...

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).


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.


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.


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.


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.


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.


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.


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.


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.


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...


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.


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...


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

)).


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...


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.


Graphical illustration of equilibrium

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0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.30.5

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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...


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.


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...


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) .


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...


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.


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.


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.


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.


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!


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


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).


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.


Liquidity Trap and Excessive Leverage · Aggregate demand externalities: Older literature, e.g.,...

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