A Theory of Macroprudential Policies in the Presence … · A Theory of Macroprudential Policies in...
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A Theory of Macroprudential Policies in the Presence of Nominal Rigidities
Emmanuel Farhi, HarvardIván Werning, MIT
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Tools for Macro Stabilization?
Great Moderation:soft consensusmonetary policy
Great Recession:broken consensusrising popularity of macroprudential policies
Challenge for economists: comprehensive framework encompassing monetary and macroprudential policies
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This Paper
Take up this challenge
What key market failures?
What policy interventions?
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General ModelArrow-Debreu with frictions:
price rigidities constraints on monetary policy
Instruments: monetary policymacroprudential policy: taxes/quantity restrictions in financial markets
Study constrained efficient allocations (2nd best)
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Key ResultsAggregate demand externalities from private financial decisions
Genericallymonetary policy not sufficientmacroprudential policies required
Formula for optimal policiesintuitivemeasurable sufficient statistics
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Example
Deleveraging and liquidity trap (Eggertson-Krugman)borrowers and saversborrowers take on debtcredit tightens...borrowers deleverzero lower boundrecession
Result: macroprudential restriction on ex-ante borrowing
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Growing Literature Farhi-Werning 2012a, Farhi-Werning 2012b Schmitt-Grohe-Uribe 2012 Korinek-Simsek 2013...
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ModelAgents
Goods indexed by...”state” commodity
“States”:states, periodstrade across states...financial marketstaxes or quantity controls available
i 2 I
s 2 Sj 2 Js
{Xij,s}
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Preferences and Technology
Preferences of agent
Production possibility set
i
F({Yj,s}) � 0
Âs�S
Ui({Xij,s}; s)
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Agents’ Budget Sets
{Xij,s} � Bi
s
Âs2S
DisQs Pi
Âj2Js
Pj,sXij,s �Ti
s + (1 + tiD,s)Di
s
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Agents’ Budget Sets
{Xij,s} � Bi
s
Âs2S
DisQs Pi
Âj2Js
Pj,sXij,s �Ti
s + (1 + tiD,s)Di
s
macroprudential tax
borrowing constraint
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Government Budget Set
Âs2S
Dgs Qs 0
Âi2I
(Tis � ti
D,sDis) + Dg
s = 0
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Nominal RigiditiesPrice feasibility set (vector)
Captures many forms of nominal rigidities and constraints on monetary policy
G({Pj,s}) � 0
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Market Structure...Supply of goods...follow Diamond-Mirrlees (1971):
postpone discussion of market structure“as if” government controls prices and production
Applications:spell out market structuremonopolistic competition with nominal rigiditiesenough taxes to control prices......but not enough to trivialize price rigidities...(2nd best)
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Equilibrium1. Agents optimize2. Government budget constraint satisfied3. Technologically feasible4. Markets clear5. Nominal rigidities
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Planning Problem
Planning problem
G({Pj,s}) � 0
F({Âi⇥I
Xij,s(Ii
s, Ps)}) � 0
max
Iis,Ps
Âi2I
Âs2S
liVis (Ii
s, Ps)
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Planning Problem
Planning problem
G({Pj,s}) � 0
F({Âi⇥I
Xij,s(Ii
s, Ps)}) � 0
indirect utility function
max
Iis,Ps
Âi2I
Âs2S
liVis (Ii
s, Ps)
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Wedges
Define wedges given reference good
First best...
Pj⇤(s),s
Pj,s
Fj,s
Fj⇤(s),s= 1 � tj,s
tj,s j⇤(s)
tj,s = 0
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FOCs
Incomes
social vs. private marginal utility of income
Prices
�iViI,s
1 � Âj2Js
Pj,sXij,s
Iis
IisXi
I,j,s
Xij,s
⇥j,s
=µFj⇤(s),s
Pj⇤(s),s
� · Gk,s = Âi⇥I
µFj�(s),s
Pj�(s),sÂj⇥Js
Pj,s⇥j,sSik,j,s
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Corrective InterventionsProposition (Corrective Financial Taxes).
1 + tiD,s =
1
1 � Âj2Js
Pj,sXij,s
Iis
IisXi
I,j,s
Xij,s
tj,s
Imperfect stabilization with monetary policy
Role for macroprudential policies:corrective taxation (financial taxes)quantity restrictions (financial regulation)
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Aggregate Demand Externalities
Assume “state” where a certain good is depressed
Force agents with high propensity to spend on that good to move income to that “state”...
... increases spending...income...spending....
...stabilization benefits...
...not internalized by private agents
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Aggregate Demand Externalities
Assume “state” where a certain good is depressed
Force agents with high propensity to spend on that good to move income to that “state”...
... increases spending...income...spending....
...stabilization benefits...
...not internalized by private agents
Keynesian cross
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Generic Inefficiency
Generic Inefficiency.Generically, equilibria without financial taxes are constrained Pareto inefficient.
Parallels the Geanakoplos-Polemarchakis (86) result for pecuniary externalities
Bottom line: monetary policy generically not sufficientmacroprudential policies necessary complement
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ApplicationsIn paper
liquidity trap and deleveraginginternational liquidity traps and sudden stopsfixed exchanges rates
Many others:multiplie sectors...
Map into general framework!
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ApplicationsIn paper
liquidity trap and deleveraginginternational liquidity traps and sudden stopsfixed exchanges rates
Many others:multiplie sectors...
Map into general framework!
see also Korinek-Simsek (2013)
see also Farhi-Werning (2012a,b), Schmitt-Grohe-Uribe (2012)
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Liquidity Trap and Deleveraging
Two types: borrowers and savers
Consume and work in every period
Three periods
t=1,2...deleveraging and liquidity trapas in Eggertsson and Krugman (2012)
t=0... endogenize ex-ante borrowing decisions
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Ex-Ante Borrowing RestrictionsProposition (Ex-Ante Borrowing Restrictions).
Labor wedges (inverse measure of output gap)
Impose binding debt restriction on borrowers at or equivalent tax on borrowing
Borrowers... high mpc in period 1Savers... low mpc in period 1Restricting period-0 borrowing stimulates in period 1Not internalized by agents
t0 = 0 t1 � 0 t2 0
tB0 = t1/(1 � t1)
t = 0
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Monetary vs. Macroprudential Policy
Policy debate:use monetary policy to lean against credit booms monetary policy targets full employment + no inflation, macroprudential policies targets financial stability
Model...during credit boomuse monetary and macroprudential policies togetherno tradeoff macro vs. financial stability t0 = 0
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ConclusionJoint theory:
monetary policy macroprudential policies (financial taxes or regulation)
Formula for optimal macroprudential policies:intuitivemeasurable sufficient statistics
Also implications for redistribution
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ConclusionMany applications:
liquidity trap and deleveraging
international liquidity trap and sudden stop
fixed exchange rates
...
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Liquidity Trap and Deleveraging
Two types: borrowers and savers
Three periodst=1,2...deleveraging and liquidity trapas in Eggertsson and Krugman (2012)t=0... endogenize ex-ante borrowing decisions
Main resultrestrict borrowing at t=0macroprudential regulation
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HouseholdsType-1 agents (savers), mass
Type-2 agents (borrowers), mass
f1
f2
V1 =2
Ât=0
bt[u(C1t )� v(N1
t )]
V2 =2
Ât=0
btu(C2t )
PtC1t + B1
t WtN1t + P1
t +1
1 + itB1
t+1
PtC2t + B2
t E2t +
11 + it
B2t+1
B22 P2B2B2
1 P1B1
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HouseholdsType-1 agents (savers), mass
Type-2 agents (borrowers), mass
f1
f2
V1 =2
Ât=0
bt[u(C1t )� v(N1
t )]
V2 =2
Ât=0
btu(C2t )
policy environment
PtC1t + B1
t WtN1t + P1
t +1
1 + itB1
t+1
PtC2t + B2
t E2t +
11 + it
B2t+1
B22 P2B2B2
1 P1B1
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FirmsFinal good produced competitively
Each varietyproduced monopolistically technologyprice set once and for all
Yt =
✓Z 1
0Y
e�1e
t (j)dj◆ e
e�1
Yt(j) = AtNt(j)
max
P(j)
2
Ât=0
t�1
’s=0
1
1 + isPt(j)
Pt(j) =✓
P(j)� 1 + tLAt
Wt
◆Ct
✓P(j)
P
◆�e
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GovernmentGovernment budget constraint
Type-specific lump sum taxes in period 0 to achieve any distribution of debt...
Bg0 + B1
0 + B20 = 0
Bgt =
11 + it
Bgt+1 + tLWtN1
t
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EquilibriumHouseholds optimize
Firms optimize
Government budget constraints hold
Markets clear
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Planning Problem
max Âi
lifiVi
u0(C11) = b(1 + i1)u0(C1
2)
i1 � 0
C22 = E2
2 � B2
2
Âi=1
fiCit = f1AtN1
t + E2t
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Planning Problem
max Âi
lifiVi
u0(C11) = b(1 + i1)u0(C1
2)
i1 � 0
C22 = E2
2 � B2
2
Âi=1
fiCit = f1AtN1
t + E2t
Maps to general model
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Labor Wedge
Labor wedge
First best
tt = 1 � v0(N1t )
Atu0(C1t )
tt = 0
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Ex-Ante Borrowing RestrictionsProposition (Ex-Ante Borrowing Restrictions).
Labor wedges
Impose binding debt restriction
Equivalent to tax on borrowing
Borrowers... high mpc in period 1Savers... low mpc in period 1Restricting period-0 borrowing stimulates in period 1Not internalized by agents
t0 = 0 t1 � 0 t2 0
tB0 = t1/(1 � t1)
B21 P1B1
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Capital Controls with Fixed Exchange Rates
See Farhi-Werning (2012) and Schmitt-Grohe-Uribe (2012)
Small open economy with a fixed exchange rate
Traded and non-traded goodsendowment of traded good sold competitivelynon-traded good produced from labor, sold monopolistically, rigid price
Two periods: t=0,1
Main result: use capital control to regain monetary policy autonomy
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HouseholdsPreferences
Budget constraint
Capital controls to regain monetary autonomy
1
Ât=0
btU(CNT,t, CT,t, Nt)
PNTCNT,t + EP⇤T,tCT,t +
1(1 + i⇤t )(1 + tB
t )EBt+1
WtNt + EP⇤T,tET,t + Pt � Tt + EBt
1 + it = (1 + i⇤t )(1 + tBt )
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FirmsFinal non-traded good produced competitively
Each varietyproduced monopolistically technologyprice set once and for all
YNT,t =
✓Z 1
0YNT,t(j)1� 1
e dj◆ 1
1� 1e
YNT,t(j) = AtNt(j)
PNT = (1 + tL)e
e � 1
Â1t=0 ’t�1
s=01
(1+i⇤s )(1+tBs )
WtAt
CNT,t
Â1t=0 ’t�1
s=01
(1+i⇤s )(1+tBs )
CNT,t
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Government
Government budget constraint
Tt + tLWtNt �tB
t1 + tB
tBt = 0
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EquilibriumHouseholds optimize
Firms optimize
Government budget constraints hold
Markets clear
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Indirect UtilityAssume preferences
separable between consumption and leisurehomothetic over consumption
Define indirect utility
V(CT,t, pt) = U✓
a(pt)CT,t, CT,t,a(pt)
AtCT,t
◆
CNT,t = a(pt)CT,t pt =EP⇤
T,tPNT,t
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Planning Problem
max
2
Ât=0
btV(CT,t,EP⇤
T,tPNT
)
P⇤T,0 [CT,0 � E0] +
11 + i⇤0
P⇤T,1 [CT,1 � E1] 0
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Planning Problem
Maps to general model
max
2
Ât=0
btV(CT,t,EP⇤
T,tPNT
)
P⇤T,0 [CT,0 � E0] +
11 + i⇤0
P⇤T,1 [CT,1 � E1] 0
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Labor WedgeLabor wedge
Departure from first best where
⌧t = 1 +1
At
UN,t
UCNT ,t
⌧t = 0
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Private vs. Social Value
Wedge social vs. private value of transfers:labor wedgerelative expenditure share of NT
Lemma.
VCT,t(CT,t, pt) = UCT,t
✓1 +
↵t
pt⌧t
◆
Vp(CT,t, pt) =↵p,t
ptCT,tUCT,t ⌧t
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Capital ControlsProposition (Capital Controls).Impose capital controls
Aggregate demand externalities from agents’ international borrowing and saving decisions
Corrective macroprudential capital controls
1 + ⌧B0 =1 + ↵1
p1⌧1
1 + ↵0p0⌧0
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