Monetary Policy with Heterogeneous Agents: … Policy with Heterogeneous Agents: Insights from Tank...
Transcript of Monetary Policy with Heterogeneous Agents: … Policy with Heterogeneous Agents: Insights from Tank...
Monetary Policy with Heterogeneous Agents:Insights from Tank Models
Davide Debortoli Jordi Galí
October 2017
Davide Debortoli, Jordi Galí () Insights from TANK October 2017 1 / 23
Motivation
Heterogeneity in Monetary Models
- idiosyncratic shocks- incomplete markets- borrowing constraints- supply side as in conventional NK models ! HANK
Main lessons:
- heterogeneity in MPCs ! role of redistribution- direct vs. indirect e¤ects
Drawbacks
- computational complexity- limited use in classroom or as a policy input
Wanted: a simple tractable framework that is a good approximation
Davide Debortoli, Jordi Galí () Insights from TANK October 2017 2 / 23
Present Paper
An Organizing Framework
- heterogeneity between constrained and unconstrained households- heterogeneity within unconstrained households
Baseline Two-Agent New Keynesian model (TANK)
- constant share of hand-to-mouth households- redistribution through �scal rule
Question: How well does a TANK model capture the mainpredictions of HANK models regarding the aggregate economy�sresponse to aggregate shocks?
Davide Debortoli, Jordi Galí () Insights from TANK October 2017 3 / 23
Main Findings
A baseline TANK model with a suitably calibrated transfer ruleprovides a good approximation to a prototypical HANK model
- e¤ects of monetary policy and other shocks- role of �scal policy
Isomorphic to a modi�ed RANK model
Application: Optimal monetary policy in TANK
- heterogeneity as a source of a policy tradeo¤- calibrated model: price stability nearly optimal (as in RANK!)
Davide Debortoli, Jordi Galí () Insights from TANK October 2017 4 / 23
Some References
HANK models: Gornemann, Kuester and Nakajima (2016), Kaplan,Moll, Violante (2016), McKay and Reis (2016), McKay Nakamuraand Steinsson (2016), Werning (2015), Auclert (2016), Ravn andSterk (2013, 2017), Sterk and Tenreiro (2013), etc.
TANK models: Campbell and Mankiw (1989), Galí, Lopez-Salido,Vallés (2007), Bilbiie (2008), Cúrdia and Woodford (2010), Broer,Hansen, Krussel and Oberg (2016), Nisticó (2016), Bilbiie (2017),etc.
Davide Debortoli, Jordi Galí () Insights from TANK October 2017 5 / 23
An Organizing Framework
Continuum of heterogeneous households, indexed by s 2 [0, 1].Preferences: E0 ∑∞
t=0 βtU(C st ,Nst ;Zt) where
U(C ,N;Z) ��C1�σ � 11� σ
� N1+ϕ
1+ ϕ
�Z
Θt � [0, 1] : set of unconstrained ("Ricardian") households inperiod t
- measure 1� λt- access to one-period bonds with riskless return Rt .
Goal: derive a (generalized) Euler equation for aggregateconsumption
- in the spirit of Werning (2015), but di¤erent emphasis
Davide Debortoli, Jordi Galí () Insights from TANK October 2017 6 / 23
An Organizing Framework
Individual Euler equation: For all s 2 Θt
Zt(C st )�σ = βRtEt
�Zt+1(C st+1)
�σ
Davide Debortoli, Jordi Galí () Insights from TANK October 2017 7 / 23
An Organizing Framework
Averaging over all s 2 Θt and letting CRt � 11�λt
Rs2Θt
C st ds yields:
Zt(CRt )�σ = βRtEt
nZt+1(CRt+1)
�σVt+1o
where
Vt+1 � CRt+1jtCRt+1
!�σ "2+ σ(1+ σ)vars jtfcst+1g2+ σ(1+ σ)vars jtfcst g
#with
CRt+1jt � 11� λt
Zs2Θt
C st+1ds
vars jtfcst+kg � 11� λt
Zs2Θt
(cst+k � cRt+k )2ds
Vt : index of heterogeneity within unconstrained householdsDavide Debortoli, Jordi Galí () Insights from TANK October 2017 8 / 23
An Organizing Framework
Recall:Zt(CRt )
�σ = βRtEtnZt+1(CRt+1)
�σVt+1o
Letting Ct �R 10 C
st ds :
ZtH�σt (Ct)�σ = βRtEt
�Zt+1H�σ
t+1(Ct+1)�σVt+1
where
Ht �CRtCt
Ht : index of heterogeneity between constrained and unconstrainedhouseholds
Davide Debortoli, Jordi Galí () Insights from TANK October 2017 9 / 23
An Organizing Framework
Imposing market clearing and log-linearizing:
yt = Etfyt+1g �1σbrt � 1
σEtf∆zt+1g+Etf∆ht+1g �
1σ
Etfbvt+1gRepresentation in levels:
byt = � 1σ
�brLt � zt�� bht � bft ,brLt = EtfbrLt+1g+brt
bft = Etfbft+1g+ 1σ
Etfbvt+1gComparison to RANKHow important are �uctuations in bht and bvt (and bft)? Open questionNext: A baseline TANK model (bft = bvt = 0)Davide Debortoli, Jordi Galí () Insights from TANK October 2017 10 / 23
A Baseline TANK Model: Households
Two types of households: s 2 fK ,RgRicardian: measure 1� λ
CRt +BRtPt+QtSRt =
BRt�1(1+ it�1)Pt
+WtNRt +(Dt +Qt)SRt�1+T
Rt
Keynesian: measure λ
CKt = WtNKt + TKt
Davide Debortoli, Jordi Galí () Insights from TANK October 2017 11 / 23
A Baseline TANK Model: Policy
Fiscal Policy
- transfer rule:TKt = τ0D + τd (Dt �D)
- balanced budget:
λTKt + (1� λ)TRt = 0.
Special cases:(i) laissez-faire (τ0 = τd = 0)(ii) full steady state redistribution (τ0 = 1, τd = 0)(iii) full redistribution period by period (τ0 = 1, τd = 1) ) RANK
Monetary Policy: Taylor-type rule
Davide Debortoli, Jordi Galí () Insights from TANK October 2017 12 / 23
A Baseline TANK Model: Supply Side
Wage equationWt =MwCσ
t Nϕt
with NRt = NKt = Nt , andMw > 1.
TechnologyYt (i) = AtNt(i)1�α
In�ation equation (Rotemberg pricing):
Πt (Πt � 1) = Et
�Λt,t+1
�Yt+1Yt
�Πt+1 (Πt+1 � 1)
+ε
ξ
�1Mp
t� 1Mp
��whereMp
t � (1� α)AtN�αt /Wt andMp � εp
εp�1
Davide Debortoli, Jordi Galí () Insights from TANK October 2017 13 / 23
A Baseline TANK Model
Goods market clearing
Ct = Yt∆p(Πt)
where ∆pt (Πt) � 1� (ξ/2) (Πt � 1)2 and Ct � (1� λ)CRt + λCKt
Davide Debortoli, Jordi Galí () Insights from TANK October 2017 14 / 23
A Baseline TANK Model
Aggregate Euler equation
1 = β(1+ it)Etn(Ct+1/Ct)
�σ (Ht+1/Ht)�σ(Zt+1/Zt)Π�1t+1
owhere
Ht � CRtCt
=1
∆p(Πt)
�WtNtYt
+1
1� λ
DtYt+TRtYt
�= 1+
1∆p(Πt)
�λ(1� τd )
1� λ
�∆p(Πt)�
1� α
Mpt
��λ(τ0 � τd )
1� λ
�1� 1� α
Mp
�YYt
�Davide Debortoli, Jordi Galí () Insights from TANK October 2017 15 / 23
A Baseline TANK Model
Log-linearized equilibrium conditions
πt = βEtfπt+1g+ κeytbyt = Etfbyt+1g � 1
σ(bit � Etfπt+1g) +Etf∆bht+1g+ 1
σ(1� ρz )ztbht = χyeyt + χnbyntbit = φππt + φybyt + νt
where eyt � byt � bynt , and bynt � 1+ϕσ(1�α)+α+ϕ
at
χn �λ(τ0 � τd )
(1� λ)H
�1� 1� α
Mp
�χy � χn �
λ(1� τd )(1� α)
(1� λ)HMp
�σ+
α+ ϕ
1� α
�Davide Debortoli, Jordi Galí () Insights from TANK October 2017 16 / 23
A Baseline TANK Model
Three-equation representation
πt = βEtfπt+1g+ κeyteyt = Etfeyt+1g � 1
σ(1+ χy )(bit � Etfπt+1g �brnt )
bit = φππt + φybyt + νt
where brnt � (1� ρz )zt + σ (1+ χn)Etf∆bynt+1g) isomorphic to a modi�ed RANK model
χy ∂y/∂r
positive dampenedzero unchanged
negative ampli�ed
Davide Debortoli, Jordi Galí () Insights from TANK October 2017 17 / 23
A Baseline TANK Model: Calibration andSimulations
Preferences: β = 0.9925, σ = ϕ = 1, ε = 9
Technology: α = 0.25, ξ = 372
Financial frictions: λ = 0.21
Policy rule: φπ = 1.5, φy = 0.125
Monetary policy shocks
- the role of �scal policy- the role of �nancial frictions
Davide Debortoli, Jordi Galí () Insights from TANK October 2017 18 / 23
Monetary Policy Shocks and Transfer Rules
Monetary Policy Shocks and the Share of Constrained Households
A Baseline HANK Model
Continuum of heterogeneous households, indexed by s 2 [0, 1]Labor income: WtNt expfest g, where est = 0.966est + 0.017εstAssets: one-period nominal bond, in zero net supply.
Borrowing limit: Bst � �ψY
Alternative calibrations: ψ = f0.5, 1, 2g, implyingλ = f0.36, 0.21, 0.11gFiscal policy: government takes all pro�ts and redistributeslump-sum, same transfer rule as in TANK
Davide Debortoli, Jordi Galí () Insights from TANK October 2017 19 / 23
HANK vs. TANK Comparison
After solving HANK model (Reiter (2010)), TANK calibrated tomatch
λ : fraction of constrained householdsβ : steady state real rate
Simulations
Davide Debortoli, Jordi Galí () Insights from TANK October 2017 20 / 23
Interest Rate Elasticity of Output Type I Fiscal Policy
The Effects of a Monetary Policy Shock The Case of Rigid Prices
The Effects of a Monetary Policy Shock
The Effects of a Preference Shock
The Effects of a Technology Shock
Optimal Monetary Policy
Welfare losses (second order approximation)
Lt '12
E0
∞
∑t=0
βtn
π2t + αy y2t + αhbh2towhere αy =
�σ+ φ+α
1�α
�1ξ and αh �σ
ξ
�1�λ
λ
�Optimal monetary policy problem
min12
E0
∞
∑t=0
βtn
π2t + αy y2t + αhbh2tosubject to
πt = βEtfπt+1g+ κeytbht = χyeyt + χnbyntλ(τ0 � τd ) 6= 0) χn 6= 0 ) policy tradeo¤
Davide Debortoli, Jordi Galí () Insights from TANK October 2017 21 / 23
Optimal Monetary Policy
Representation of the optimal policy:
pt � pt � p�1 = �1κ
�αy yt + χyαhht
�Impulse responses
Davide Debortoli, Jordi Galí () Insights from TANK October 2017 22 / 23
Optimal Monetary Policy in TANK
Conclusions
A baseline TANK model with a suitably calibrated transfer ruleprovides a good approximation to a prototypical HANK model
- e¤ects of monetary policy and other shocks- role of �scal policy
Isomorphic to a modi�ed RANK model
Application: Optimal monetary policy in TANK
- heterogeneity as a source of a policy tradeo¤- price stability nearly optimal (as in RANK!)
Davide Debortoli, Jordi Galí () Insights from TANK October 2017 23 / 23