a theory of macroprudential policies in the presence … · a theory of macroprudential policies in...

A Theory of Macroprudential Policies in the Presence of Nominal Rigidities

Emmanuel Farhi, HarvardIván Werning, MIT

Thursday, March 20, 14

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

Thursday, March 20, 14

This Paper

Take up this challenge

What key market failures?

What policy interventions?

Thursday, March 20, 14

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)

Thursday, March 20, 14

Key ResultsAggregate demand externalities from private financial decisions

Genericallymonetary policy not sufficientmacroprudential policies required

Formula for optimal policiesintuitivemeasurable sufficient statistics

Thursday, March 20, 14

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

Thursday, March 20, 14

Growing Literature Farhi-Werning 2012a, Farhi-Werning 2012b Schmitt-Grohe-Uribe 2012 Korinek-Simsek 2013...

Thursday, March 20, 14

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}

Thursday, March 20, 14

Preferences and Technology

Preferences of agent

Production possibility set

i

F({Yj,s}) � 0

Âs�S

Ui({Xij,s}; s)

Thursday, March 20, 14

Agents’ Budget Sets

{Xij,s} � Bi

s

Âs2S

DisQs Pi

Âj2Js

Pj,sXij,s �Ti

s + (1 + tiD,s)Di

s

Thursday, March 20, 14

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

Thursday, March 20, 14

Government Budget Set

Âs2S

Dgs Qs 0

Âi2I

(Tis � ti

D,sDis) + Dg

s = 0

Thursday, March 20, 14

Nominal RigiditiesPrice feasibility set (vector)

Captures many forms of nominal rigidities and constraints on monetary policy

G({Pj,s}) � 0

Thursday, March 20, 14

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)

Thursday, March 20, 14

Equilibrium1. Agents optimize2. Government budget constraint satisfied3. Technologically feasible4. Markets clear5. Nominal rigidities

Thursday, March 20, 14

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)

Thursday, March 20, 14

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)

Thursday, March 20, 14

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

Thursday, March 20, 14

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

Thursday, March 20, 14

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)

Thursday, March 20, 14

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

Thursday, March 20, 14

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

Thursday, March 20, 14

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

Thursday, March 20, 14

ApplicationsIn paper

liquidity trap and deleveraginginternational liquidity traps and sudden stopsfixed exchanges rates

Many others:multiplie sectors...

Map into general framework!

Thursday, March 20, 14

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)

Thursday, March 20, 14

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

Thursday, March 20, 14

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

Thursday, March 20, 14

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

Thursday, March 20, 14

ConclusionJoint theory:

monetary policy macroprudential policies (financial taxes or regulation)

Formula for optimal macroprudential policies:intuitivemeasurable sufficient statistics

Also implications for redistribution

Thursday, March 20, 14

ConclusionMany applications:

liquidity trap and deleveraging

international liquidity trap and sudden stop

fixed exchange rates

...

Thursday, March 20, 14

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

Thursday, March 20, 14

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

Thursday, March 20, 14

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

Thursday, March 20, 14

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

Thursday, March 20, 14

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

Thursday, March 20, 14

EquilibriumHouseholds optimize

Firms optimize

Government budget constraints hold

Markets clear

Thursday, March 20, 14

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

Thursday, March 20, 14

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

Thursday, March 20, 14

Labor Wedge

Labor wedge

First best

tt = 1 � v0(N1t )

Atu0(C1t )

tt = 0

Thursday, March 20, 14

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

Thursday, March 20, 14

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

Thursday, March 20, 14

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 )

Thursday, March 20, 14

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

Thursday, March 20, 14

Government

Government budget constraint

Tt + tLWtNt �tB

t1 + tB

tBt = 0

Thursday, March 20, 14

EquilibriumHouseholds optimize

Firms optimize

Government budget constraints hold

Markets clear

Thursday, March 20, 14

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

Thursday, March 20, 14

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

Thursday, March 20, 14

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

Thursday, March 20, 14

Labor WedgeLabor wedge

Departure from first best where

⌧t = 1 +1

At

UN,t

UCNT ,t

⌧t = 0

Thursday, March 20, 14

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

Thursday, March 20, 14

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

Thursday, March 20, 14