Heterogeneous Price Rigidities and Monetary Policy...(2007), Cravino et al. (2019) Our...
Transcript of Heterogeneous Price Rigidities and Monetary Policy...(2007), Cravino et al. (2019) Our...
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Heterogeneous Price Rigiditiesand Monetary Policy
Christopher Clayton 1 Xavier Jaravel 2 Andreas Schaab 1
1Harvard University
2LSE
June 27, 2019
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Introduction
What are the implications of heterogeneity for monetary policy (MP)?I MP has distributional effectsI Accounting for heterogeneity also important to understand MP transmission
Previous work:I Savers and debtorsI Incidence of unemploymentI Income compositionI Cash holdings heterogeneity
Does heterogeneity in price rigidities across sectors matter?I Price stickiness is known to be heterogeneous across sectorsI How are households exposed to this dimension of heterogeneity?I What are the implications for effects of MP?
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 1 / 26
-
Introduction
What are the implications of heterogeneity for monetary policy (MP)?I MP has distributional effectsI Accounting for heterogeneity also important to understand MP transmission
Previous work:I Savers and debtorsI Incidence of unemploymentI Income compositionI Cash holdings heterogeneity
Does heterogeneity in price rigidities across sectors matter?I Price stickiness is known to be heterogeneous across sectorsI How are households exposed to this dimension of heterogeneity?I What are the implications for effects of MP?
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 1 / 26
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Introduction
What are the implications of heterogeneity for monetary policy (MP)?I MP has distributional effectsI Accounting for heterogeneity also important to understand MP transmission
Previous work:I Savers and debtorsI Incidence of unemploymentI Income compositionI Cash holdings heterogeneity
Does heterogeneity in price rigidities across sectors matter?I Price stickiness is known to be heterogeneous across sectorsI How are households exposed to this dimension of heterogeneity?I What are the implications for effects of MP?
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 1 / 26
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This paper
1. New stylized facts (CPI/PPI/CEX/ACS data): prices are more rigid inindustries...
I ... selling to richer/more educated households (“expenditure channel”)
I ... employing richer/more educated households (“earnings channel”)
I Example: services and manufacturing
2. Heterogeneous Agent New Keynesian model with many sectors andhousehold types
I College-educated households considerably more sensitive to MP(via earnings and expenditure channels)
I Between-type debtor-saver channel pushes in opposite direction
I Aggregate effects of MP on inflation and real GDP dampened
I Structural change from goods to services implies flattening of PC (weaker MP)
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 2 / 26
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This paper
1. New stylized facts (CPI/PPI/CEX/ACS data): prices are more rigid inindustries...
I ... selling to richer/more educated households (“expenditure channel”)
I ... employing richer/more educated households (“earnings channel”)
I Example: services and manufacturing
2. Heterogeneous Agent New Keynesian model with many sectors andhousehold types
I College-educated households considerably more sensitive to MP(via earnings and expenditure channels)
I Between-type debtor-saver channel pushes in opposite direction
I Aggregate effects of MP on inflation and real GDP dampened
I Structural change from goods to services implies flattening of PC (weaker MP)
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 2 / 26
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Literature
Distributional implications of MP: Doepke and Schneider (2006), Carpenter andRogers (2004), Albanesi (2007), Williamson (2009), Ledoit (2009), Coibion et al. (2016),Auclert (2017)
Our contribution: We document and study a set of novel earnings and expenditure channels ofmonetary policy transmission
Empirical work on price stickiness: Blinder et al. (2008), Bils and Klenow (2002, 2004),Bils et al. (2003), Klenow and Kryvtsov (2008), Nakamura and Steinsson (2008), Pastenet al. (2016)
Our contribution: Two novel stylized facts about the cross-sectional exposure of households toprice rigidity (and thus monetary policy)
Models with heterogeneous price stickiness: Aoki (2001), Bils and Klenow (2002),Carlstrom et al. (2006), Carvalho (2006), Barsky et al. (2006), Nakamura and Steinsson(2007), Cravino et al. (2019)
Our contribution: We study an enriched HANK model with firm and household heterogeneity.
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 3 / 26
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Literature
Distributional implications of MP: Doepke and Schneider (2006), Carpenter andRogers (2004), Albanesi (2007), Williamson (2009), Ledoit (2009), Coibion et al. (2016),Auclert (2017)
Our contribution: We document and study a set of novel earnings and expenditure channels ofmonetary policy transmission
Empirical work on price stickiness: Blinder et al. (2008), Bils and Klenow (2002, 2004),Bils et al. (2003), Klenow and Kryvtsov (2008), Nakamura and Steinsson (2008), Pastenet al. (2016)
Our contribution: Two novel stylized facts about the cross-sectional exposure of households toprice rigidity (and thus monetary policy)
Models with heterogeneous price stickiness: Aoki (2001), Bils and Klenow (2002),Carlstrom et al. (2006), Carvalho (2006), Barsky et al. (2006), Nakamura and Steinsson(2007), Cravino et al. (2019)
Our contribution: We study an enriched HANK model with firm and household heterogeneity.
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 3 / 26
-
Literature
Distributional implications of MP: Doepke and Schneider (2006), Carpenter andRogers (2004), Albanesi (2007), Williamson (2009), Ledoit (2009), Coibion et al. (2016),Auclert (2017)
Our contribution: We document and study a set of novel earnings and expenditure channels ofmonetary policy transmission
Empirical work on price stickiness: Blinder et al. (2008), Bils and Klenow (2002, 2004),Bils et al. (2003), Klenow and Kryvtsov (2008), Nakamura and Steinsson (2008), Pastenet al. (2016)
Our contribution: Two novel stylized facts about the cross-sectional exposure of households toprice rigidity (and thus monetary policy)
Models with heterogeneous price stickiness: Aoki (2001), Bils and Klenow (2002),Carlstrom et al. (2006), Carvalho (2006), Barsky et al. (2006), Nakamura and Steinsson(2007), Cravino et al. (2019)
Our contribution: We study an enriched HANK model with firm and household heterogeneity.
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 3 / 26
-
Literature
Distributional implications of MP: Doepke and Schneider (2006), Carpenter andRogers (2004), Albanesi (2007), Williamson (2009), Ledoit (2009), Coibion et al. (2016),Auclert (2017)
Our contribution: We document and study a set of novel earnings and expenditure channels ofmonetary policy transmission
Empirical work on price stickiness: Blinder et al. (2008), Bils and Klenow (2002, 2004),Bils et al. (2003), Klenow and Kryvtsov (2008), Nakamura and Steinsson (2008), Pastenet al. (2016)
Our contribution: Two novel stylized facts about the cross-sectional exposure of households toprice rigidity (and thus monetary policy)
Models with heterogeneous price stickiness: Aoki (2001), Bils and Klenow (2002),Carlstrom et al. (2006), Carvalho (2006), Barsky et al. (2006), Nakamura and Steinsson(2007), Cravino et al. (2019)
Our contribution: We study an enriched HANK model with firm and household heterogeneity.
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 3 / 26
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Outline
1. Conceptual framework
2. Data and stylized facts
3. Quantitative analysis
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The simple model
Two periods: t = 1, 2
Two sectors: s ∈ {A,B}Finite household types i with different sectoral exposures
Household i solves:
max
2∑t=1
βt−1U [(cAi,t)1−αi(cBi,t)
αi ]
subject to
cAi,1 +cAi,2R︸ ︷︷ ︸
Spending on A
+ p1cBi,1 + p2
cBi,2R︸ ︷︷ ︸
Spending on B
=bi,1πA1︸︷︷︸
Initial wealth
+ γi(Y A1 ) +γi(Y A2 )
R︸ ︷︷ ︸Earnings from A
+ p1γi(Y B1 ) + p2
γi(Y B2 )
R︸ ︷︷ ︸Earnings from B
where pt =PBtPAt
is relative price, αi expenditure exposure and γi earnings exposure.
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 4 / 26
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The simple model
Two periods: t = 1, 2
Two sectors: s ∈ {A,B}Finite household types i with different sectoral exposures
Household i solves:
max
2∑t=1
βt−1U [(cAi,t)1−αi(cBi,t)
αi ]
subject to
cAi,1 +cAi,2R︸ ︷︷ ︸
Spending on A
+ p1cBi,1 + p2
cBi,2R︸ ︷︷ ︸
Spending on B
=bi,1πA1︸︷︷︸
Initial wealth
+ γi(Y A1 ) +γi(Y A2 )
R︸ ︷︷ ︸Earnings from A
+ p1γi(Y B1 ) + p2
γi(Y B2 )
R︸ ︷︷ ︸Earnings from B
where pt =PBtPAt
is relative price, αi expenditure exposure and γi earnings exposure.
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 4 / 26
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The simple model
Two periods: t = 1, 2
Two sectors: s ∈ {A,B}Finite household types i with different sectoral exposures
Household i solves:
max
2∑t=1
βt−1U [(cAi,t)1−αi(cBi,t)
αi ]
subject to
cAi,1 +cAi,2R︸ ︷︷ ︸
Spending on A
+ p1cBi,1 + p2
cBi,2R︸ ︷︷ ︸
Spending on B
=bi,1πA1︸︷︷︸
Initial wealth
+ γi(Y A1 ) +γi(Y A2 )
R︸ ︷︷ ︸Earnings from A
+ p1γi(Y B1 ) + p2
γi(Y B2 )
R︸ ︷︷ ︸Earnings from B
where pt =PBtPAt
is relative price, αi expenditure exposure and γi earnings exposure.
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 4 / 26
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Simple perturbation: partial equilibrium
Consider the general perturbation {dR, dY A1 , dY B1 , dp, dπA}
Define:MPCi,1 ≡ ∂
∂yipα
i
ci,1.
Proposition: Household i’s behavioral consumption response can be decomposed into
dci,1 =
Substitution effect︷ ︸︸ ︷− 1γMPSi,1ci,1
dR
R+ MPCi,1
{Interest rate exposure︷ ︸︸ ︷bi,2
dR
R−
Bond revaluation︷ ︸︸ ︷bi,1πA
dPA
PA
+γAi dYA1 + pγ
Bi dY
B1︸ ︷︷ ︸
Heterogeneous earnings channel
+ γBi p
(Y B1 +
1
RY B2
)︸ ︷︷ ︸
Relative price effect on real earnings
dp
p− αipαi
(ci,1 +
1
Rci,2
)︸ ︷︷ ︸
Relative price effect on real expenditures
dp
p
}.
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 5 / 26
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Simple perturbation: partial equilibrium
Consider the general perturbation {dR, dY A1 , dY B1 , dp, dπA}
Define:MPCi,1 ≡ ∂
∂yipα
i
ci,1.
Proposition: Household i’s behavioral consumption response can be decomposed into
dci,1 =
Substitution effect︷ ︸︸ ︷− 1γMPSi,1ci,1
dR
R+ MPCi,1
{Interest rate exposure︷ ︸︸ ︷bi,2
dR
R−
Bond revaluation︷ ︸︸ ︷bi,1πA
dPA
PA
+γAi dYA1 + pγ
Bi dY
B1︸ ︷︷ ︸
Heterogeneous earnings channel
+ γBi p
(Y B1 +
1
RY B2
)︸ ︷︷ ︸
Relative price effect on real earnings
dp
p− αipαi
(ci,1 +
1
Rci,2
)︸ ︷︷ ︸
Relative price effect on real expenditures
dp
p
}.
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 5 / 26
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Simple perturbation: partial equilibrium
Consider the general perturbation {dR, dY A1 , dY B1 , dp, dπA}
Define:MPCi,1 ≡ ∂
∂yipα
i
ci,1.
Proposition: Household i’s behavioral consumption response can be decomposed into
dci,1 =
Substitution effect︷ ︸︸ ︷− 1γMPSi,1ci,1
dR
R+ MPCi,1
{Interest rate exposure︷ ︸︸ ︷bi,2
dR
R−
Bond revaluation︷ ︸︸ ︷bi,1πA
dPA
PA
+γAi dYA1 + pγ
Bi dY
B1︸ ︷︷ ︸
Heterogeneous earnings channel
+ γBi p
(Y B1 +
1
RY B2
)︸ ︷︷ ︸
Relative price effect on real earnings
dp
p− αipαi
(ci,1 +
1
Rci,2
)︸ ︷︷ ︸
Relative price effect on real expenditures
dp
p
}.
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 5 / 26
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Simple perturbation: general equilibrium
Proposition: In response to our proposed aggregate perturbation, the change inaggregate demand can be decomposed as
dY1 =
[CovI
(µMPCi,1, bi,2
)− 1γEI(µMPSi,1ci,1)
]dR
R− CovI
(µMPCi,1,
bi,1πA
)dPA
PA
+∑s
P stPAt
(EI(MPCi,1) + CovI(µMPCi,1, γsi )
)dY s1︸ ︷︷ ︸
Heterogeneous earnings effect
+∑t
1
Rt−1p
(EI(MPCi,1) + CovI(µMPCi,1, γBi )
)Y Bt
dp
p︸ ︷︷ ︸Relative price effect on earnings
−∑t
1
Rt−1EI(µMPCi,1αipα
i
ci,t
)dp
p︸ ︷︷ ︸Relative price effect on expenditures
.
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 6 / 26
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Outline
1. Conceptual framework
2. Data and stylized facts
3. Quantitative analysis
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Data
Build 3 linked datasets with price rigidities (consumer and producerprices), expenditures and payrolls
I Covers full U.S. economy (except shelter in most cases)
CPI-ACS sample:I merge price rigidity data from Nakamura and Steinsson (2008) (at the ELI
level) to earnings data from the ACS (at the industry level)
PPI-ACS sample:I match price rigidity data from Pasten et al. (2016) (at the 6-digit NAICS level)
to ACS industries
CPI-CEX sample:I merge price rigidity data from Nakamura and Steinsson (2008) (at the ELI
level) to spending data from the CEX (at the UCC level).
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 7 / 26
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New facts
Two empirical findings:
1. Prices more rigid in product categories selling to more educated/richer households(consistent with Cravino-Lan-Levchenko, 2019)
Examples:I Services (frequency: 6.39%, share of sales to College: 37.9%)I Taxi fares (frequency: 4.41%, share of sales to College: 62.3%)I Fast food lunch (frequency: 7%, share of sales to College: 34.4%)
2. Prices more rigid in product categories employing more educated/richerhouseholds
Examples:I Computer electronics (frequency: 28.95%, payroll share to College: 72.15%)I Poultry processing (frequency: 35.1%, payroll share to College: 14.43%)
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 8 / 26
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New facts
Two empirical findings:
1. Prices more rigid in product categories selling to more educated/richer households(consistent with Cravino-Lan-Levchenko, 2019)
Examples:I Services (frequency: 6.39%, share of sales to College: 37.9%)I Taxi fares (frequency: 4.41%, share of sales to College: 62.3%)I Fast food lunch (frequency: 7%, share of sales to College: 34.4%)
2. Prices more rigid in product categories employing more educated/richerhouseholds
Examples:I Computer electronics (frequency: 28.95%, payroll share to College: 72.15%)I Poultry processing (frequency: 35.1%, payroll share to College: 14.43%)
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 8 / 26
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Earnings channel: CPI-ACS
20
40
60
80
100Pa
yrol
l Sha
re to
Col
lege
Gra
duat
es, %
ACS
(200
0-20
15)
0 10 20 30 40Frequency of price changes, % (Nakamura-Steinsson, 2008)
Notes: Includes All Prices Changes
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 9 / 26
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Earnings channel: CPI-ACS
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 10 / 26
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Earnings channel: PPI-ACS
20
40
60
80
100Pa
yrol
l Sha
re to
Col
lege
Gra
duat
es, %
ACS
(200
0-20
15)
0 20 40 60Frequency of price changes, % (Pasten-Schoenle-Weber, 2016)
Notes: Includes All Prices Changes
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 11 / 26
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Earnings channel: PPI-ACS
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 12 / 26
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Expenditure channel: CPI-CEX
0
20
40
60
80Sh
are
of S
ales
to C
olle
ge G
radu
ates
, %C
EX (2
004-
2015
)
0 20 40 60Frequency of price changes, % (Nakamura-Steinsson, 2008)
Notes: Includes All Prices Changes
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 13 / 26
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Expenditure channel: CPI-CEX
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 14 / 26
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Interaction between Earnings / Expenditure channels
20
40
60
80
100Pa
yrol
l Sha
re o
f Col
lege
Gra
duat
es, %
ACS
(200
0-20
15)
30 40 50 60 70Share of Sales to College Graduates, %
CEX (2004-2015)Notes: OLS Coeff. 0.5416*** (s.e. 0.2264), N=88
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 15 / 26
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New facts
RobustnessI Excluding sales
I Different measures of income and education
I Broad sector fixed effects (e.g. within goods)
Implications for monetary policy tightening:I NK model prediction for sector with more rigid prices:
less deflation, but bigger output gap
I More educated households suffer more: preferred goods relatively moreexpensive, stronger labor demand contraction
I Feedback loop on consumption of more educated households: demand forgoods in more rigid sector falls even more (→ relative price, labor demand)
I Monetary policy has relatively larger effect on richer, low-MPC households→ dampened aggregate effect
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 16 / 26
-
New facts
RobustnessI Excluding sales
I Different measures of income and education
I Broad sector fixed effects (e.g. within goods)
Implications for monetary policy tightening:I NK model prediction for sector with more rigid prices:
less deflation, but bigger output gap
I More educated households suffer more: preferred goods relatively moreexpensive, stronger labor demand contraction
I Feedback loop on consumption of more educated households: demand forgoods in more rigid sector falls even more (→ relative price, labor demand)
I Monetary policy has relatively larger effect on richer, low-MPC households→ dampened aggregate effect
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 16 / 26
-
Outline
1. Conceptual framework
2. Data and stylized facts
3. Quantitative analysis
-
Model overview
Start from one-asset heterogeneous-agent New Keynesian model
N intermediate goods sectors sI Different price rigidity: δs
I Sectors employ two types of workers: NsC,t and NsNC,t
I Each sector has its own, fully segmented labor market (business cycle)
Two household types i ∈ {C,NC}: college and non-collegeI Within-type heterogeneity: uninsurable earnings riskI Different sector-specific productivities: Zse (earnings shares)I Different tastes: αsC and α
sNC (expenditure shares)
I Different discount rates: ρC and ρNC (to generate plausible MPC)I Different borrowing constraints aC and aNC (purely expositional)
Policy experiment: contractionary 100bps monetary policy shock
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 17 / 26
-
Model overview
Start from one-asset heterogeneous-agent New Keynesian model
N intermediate goods sectors sI Different price rigidity: δs
I Sectors employ two types of workers: NsC,t and NsNC,t
I Each sector has its own, fully segmented labor market (business cycle)
Two household types i ∈ {C,NC}: college and non-collegeI Within-type heterogeneity: uninsurable earnings riskI Different sector-specific productivities: Zse (earnings shares)I Different tastes: αsC and α
sNC (expenditure shares)
I Different discount rates: ρC and ρNC (to generate plausible MPC)I Different borrowing constraints aC and aNC (purely expositional)
Policy experiment: contractionary 100bps monetary policy shock
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 17 / 26
-
Model overview
Start from one-asset heterogeneous-agent New Keynesian model
N intermediate goods sectors sI Different price rigidity: δs
I Sectors employ two types of workers: NsC,t and NsNC,t
I Each sector has its own, fully segmented labor market (business cycle)
Two household types i ∈ {C,NC}: college and non-college
I Within-type heterogeneity: uninsurable earnings riskI Different sector-specific productivities: Zse (earnings shares)I Different tastes: αsC and α
sNC (expenditure shares)
I Different discount rates: ρC and ρNC (to generate plausible MPC)I Different borrowing constraints aC and aNC (purely expositional)
Policy experiment: contractionary 100bps monetary policy shock
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 17 / 26
-
Model overview
Start from one-asset heterogeneous-agent New Keynesian model
N intermediate goods sectors sI Different price rigidity: δs
I Sectors employ two types of workers: NsC,t and NsNC,t
I Each sector has its own, fully segmented labor market (business cycle)
Two household types i ∈ {C,NC}: college and non-collegeI Within-type heterogeneity: uninsurable earnings risk
I Different sector-specific productivities: Zse (earnings shares)I Different tastes: αsC and α
sNC (expenditure shares)
I Different discount rates: ρC and ρNC (to generate plausible MPC)I Different borrowing constraints aC and aNC (purely expositional)
Policy experiment: contractionary 100bps monetary policy shock
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 17 / 26
-
Model overview
Start from one-asset heterogeneous-agent New Keynesian model
N intermediate goods sectors sI Different price rigidity: δs
I Sectors employ two types of workers: NsC,t and NsNC,t
I Each sector has its own, fully segmented labor market (business cycle)
Two household types i ∈ {C,NC}: college and non-collegeI Within-type heterogeneity: uninsurable earnings riskI Different sector-specific productivities: Zse (earnings shares)
I Different tastes: αsC and αsNC (expenditure shares)
I Different discount rates: ρC and ρNC (to generate plausible MPC)I Different borrowing constraints aC and aNC (purely expositional)
Policy experiment: contractionary 100bps monetary policy shock
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 17 / 26
-
Model overview
Start from one-asset heterogeneous-agent New Keynesian model
N intermediate goods sectors sI Different price rigidity: δs
I Sectors employ two types of workers: NsC,t and NsNC,t
I Each sector has its own, fully segmented labor market (business cycle)
Two household types i ∈ {C,NC}: college and non-collegeI Within-type heterogeneity: uninsurable earnings riskI Different sector-specific productivities: Zse (earnings shares)I Different tastes: αsC and α
sNC (expenditure shares)
I Different discount rates: ρC and ρNC (to generate plausible MPC)I Different borrowing constraints aC and aNC (purely expositional)
Policy experiment: contractionary 100bps monetary policy shock
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 17 / 26
-
Model overview
Start from one-asset heterogeneous-agent New Keynesian model
N intermediate goods sectors sI Different price rigidity: δs
I Sectors employ two types of workers: NsC,t and NsNC,t
I Each sector has its own, fully segmented labor market (business cycle)
Two household types i ∈ {C,NC}: college and non-collegeI Within-type heterogeneity: uninsurable earnings riskI Different sector-specific productivities: Zse (earnings shares)I Different tastes: αsC and α
sNC (expenditure shares)
I Different discount rates: ρC and ρNC (to generate plausible MPC)
I Different borrowing constraints aC and aNC (purely expositional)
Policy experiment: contractionary 100bps monetary policy shock
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 17 / 26
-
Model overview
Start from one-asset heterogeneous-agent New Keynesian model
N intermediate goods sectors sI Different price rigidity: δs
I Sectors employ two types of workers: NsC,t and NsNC,t
I Each sector has its own, fully segmented labor market (business cycle)
Two household types i ∈ {C,NC}: college and non-collegeI Within-type heterogeneity: uninsurable earnings riskI Different sector-specific productivities: Zse (earnings shares)I Different tastes: αsC and α
sNC (expenditure shares)
I Different discount rates: ρC and ρNC (to generate plausible MPC)I Different borrowing constraints aC and aNC (purely expositional)
Policy experiment: contractionary 100bps monetary policy shock
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 17 / 26
-
Model overview
Start from one-asset heterogeneous-agent New Keynesian model
N intermediate goods sectors sI Different price rigidity: δs
I Sectors employ two types of workers: NsC,t and NsNC,t
I Each sector has its own, fully segmented labor market (business cycle)
Two household types i ∈ {C,NC}: college and non-collegeI Within-type heterogeneity: uninsurable earnings riskI Different sector-specific productivities: Zse (earnings shares)I Different tastes: αsC and α
sNC (expenditure shares)
I Different discount rates: ρC and ρNC (to generate plausible MPC)I Different borrowing constraints aC and aNC (purely expositional)
Policy experiment: contractionary 100bps monetary policy shock
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 17 / 26
-
Model detailsCES consumption baskets
ci,t =
[ N∑s
(αsi )1η (csi,t)
η−1η
] ηη−1
Household budget constraint (assumptions on profit rebate important)
ȧi,t = (it − πNt )ai,t︸ ︷︷ ︸Interest income
+ zi,tni,twi,tpi,t︸ ︷︷ ︸Labor income
+ τi,tpi,t︸ ︷︷ ︸Transfer income
− ci,tpi,t,︸ ︷︷ ︸Consumption
ai,t ≥ ai
Intermediate goods producer production function
Y st (j) =
[ ∑e∈C,NC
(Zse )1κNse,t(j)
κ−1κ
] κκ−1
Two Phillips Curves (under Rotemberg pricing)
π̇st = πst
(it − πst −
Ẏ stY st
)− �− 1
δs
(�
�− 1MCst − 1
)HJB Taylor rule Kolmogorov forward equation Channel decomposition
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 18 / 26
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Calibration and estimation strategy
Heterogeneous expenditure shares: αsi → CPI-CEX data
Heterogeneous sectoral skill intensities: Zse → CPI-ACS data
Heterogeneous sectoral price stickiness: δs → CPI data
Heterogeneous discount rate: ρi → Household MPC
Heterogeneous borrowing constraint: ai → Isolate debtor-saver channel
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 19 / 26
-
Our novel earnings + expenditure channels
How can we cleanly isolate the effects of our channels?
Recall GE Proposition: It’s all about the covariance terms
CovI(MPCi, αsi ) CovI(MPCi, Zse )
We compare two models:
I Same steady state
I Same marginal distributions for: δs, αsi and Zse (also ρi and ai)
I Only difference is joint distribution (covariance terms)
We turn off between-type debtor-saver for now (turn back on later)
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 20 / 26
-
Our novel earnings + expenditure channels
How can we cleanly isolate the effects of our channels?
Recall GE Proposition: It’s all about the covariance terms
CovI(MPCi, αsi ) CovI(MPCi, Zse )
We compare two models:
I Same steady state
I Same marginal distributions for: δs, αsi and Zse (also ρi and ai)
I Only difference is joint distribution (covariance terms)
We turn off between-type debtor-saver for now (turn back on later)
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 20 / 26
-
Our novel earnings + expenditure channels
How can we cleanly isolate the effects of our channels?
Recall GE Proposition: It’s all about the covariance terms
CovI(MPCi, αsi ) CovI(MPCi, Zse )
We compare two models:
I Same steady state
I Same marginal distributions for: δs, αsi and Zse (also ρi and ai)
I Only difference is joint distribution (covariance terms)
We turn off between-type debtor-saver for now (turn back on later)
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 20 / 26
-
Our novel earnings + expenditure channels
0 5 10 15
-0.5
-0.4
-0.3
-0.2
-0.1
0
0 5 10 15
-0.5
-0.4
-0.3
-0.2
-0.1
0
0 5 10 15-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0 5 10 15-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
College
Non-College
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 21 / 26
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Consumption decomposition
0 2 4 6 8 10
-4
-3
-2
-1
0
1
2
3
Dev
iati
on f
rom
SS
in l
evel
10-3
Consumption
Savings
Earnings
Dividends
Rebates
0 2 4 6 8 10
-4
-3
-2
-1
0
1
2
3
10-3
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 22 / 26
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Between-type debtor-saver channel
0 5 10 15 20
-0.5
-0.4
-0.3
-0.2
-0.1
0
0 5 10 15 20
-0.5
-0.4
-0.3
-0.2
-0.1
0
0 5 10 15 20
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0 5 10 15 20
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
College
Non-College
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 23 / 26
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Structural change: from goods to services
Secular increase of spending share on services over time
Share of spending on goods: 60 % in 1946 to 32% in 2009 (Boppart 2014)
Effective degree of rigidity in economy increases: this leads to flattening ofPhillips curve
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 24 / 26
-
Structural change: from goods to services
0 5 10 15 20
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0 5 10 15 20
-0.45
-0.4
-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 25 / 26
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Conclusion
This paper re-evaluates the implications of heterogeneous price stickinessfor the transmission and the distributional effects of monetary policy
Establish new facts using micro data:
1. Richer/more educated households purchase in more rigid sectors
2. Richer/more educated households work in more rigid sectors
Quantitative model to assess implications of these new channelsI Real effects of MP dampened
I College-educated (richer) households significantly more sensitive to MP
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 26 / 26
-
Calibration
�
✓C✓NC
✏
�
1 � ↵NC1 � ↵C
ZNCAZCA
ZNCBZCB
�A
�B
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 1 / 13
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Baseline with 1 household type, 1 sector
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 2 / 13
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Introducing sectoral price rigidity heterogeneity
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 3 / 13
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Comparison calibration: add symmetric productivity differences
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 4 / 13
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Full calibration: asymmetric productivity differences and tastes
Differenced IRFs Asset holdings MPCs Disposable income decompositionsClayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 5 / 13
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Differenced IRFs (Full – Comparison)
Back.
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 6 / 13
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Marginal propensities to consume (MPC)
Back.
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 7 / 13
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Asset holdings and borrowing constraints
Back.
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 8 / 13
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Disposable income and its decomposition
Back.
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 9 / 13
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Households’ recursive optimization problemWe collect households’ state variables in the vector xi,t with law of motion(
dai,tdzi,t
)=
(rtai,t +
∑s z
si,tn
si,tw
si,tp
αi
t − pαi
t ci,t +Ti,t
PAt
µ(zsi,t)
)dt+
(0
σ(zsi,t)
)dBt.
This gives us the recursive, continuous-time Bellman equation
ρvi,t(xi,t) =∂tvi,t(xi,t) + maxci,t,ni,t
u(ci,t, ni,t) + θi
(v−i,t(x−i,t)− vi,t(xi,t)
)+ ∂avi,t(xi,t)
(rtai,t +
∑s
zsi,tnsi,tw
si,tp
αi
t − pαi
t ci,t +Ti,tPAt
)+ µ(zsi,t)∂zvi,t(xi,t) +
1
2σ(zsi,t)
2∂zzvi,t(xi,t)
FOCs:
c−γi,t = pαi
t ∂avi,t(xi,t)
cγi,t(nsi,t)
φ = zsi,twsi,t.
Back
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 10 / 13
-
The Taylor rule
Assumptions on the Taylor rule are important
For now, we assume equal weighting:
it = i∗t +
∑s
(φsππ
st + φ
sy(Y
st − Y )
)+ ξt, (1)
Back
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 11 / 13
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Aggregation in our model
We write Kolmogorov forward (KF) equations separately for eachhousehold type
The KF equations characterizing the evolution of these density functionsare given by
∂tgi,t(xi,t) =− ∂a([rtai,t +
∑s
zsi,tnsi,tw
si,tp
αi
t − pαi
t ci,t +Ti,tPAt
]gi,t(xi,t)
)− ∂z
(µ(zsi,t)gi,t(xi,t)
)+
1
2∂zz
(σ(zsi,t)
2gi,t(xi,t)
)− θigi,t(xi,t) + θ−ig−i,t(x−i,t).
Back
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 12 / 13
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Channel decompositions
Consider a perturbation {ξt} that corresponds to a 100bps MP shock.
We can decompose the effect on consumption as follows.
For College:
CC,0({rt, wC,t, pC,t, TC,t}t∈[0,∞), g0
)=
∫ ∞a
∫ zz
cC(a, z, {rt, wC,t, pt, TC,t}t∈[0,∞)
)g0d(z, a)
dCC,0 =
∫ ∞0
∂CC,0∂rt
drt +∂CC,0∂wC,t
dwC,t +∂CC,0∂pt
dpt +∂CC,0∂TC,t
dTC,tdt
Back
Clayton - Jaravel - Schaab Heterogeneous Price Rigidities and Monetary Policy 13 / 13
Appendix