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...

Heterogeneous Price Rigiditiesand Monetary Policy

Christopher Clayton 1 Xavier Jaravel 2 Andreas Schaab 1

1Harvard University

2LSE

June 27, 2019
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




Introduction




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)

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)

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.

Literature







Literature







Literature







Outline

1. Conceptual framework

2. Data and stylized facts

3. Quantitative analysis
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.

The simple model



Household i solves:

max

2∑t=1


αi ]

subject to


Spending on A

+ p1cBi,1 + p2

cBi,2R︸︷︷︸

Spending on B

=bi,1πA1︸︷︷︸

Initial wealth

+ γi(Y A1 ) +γi(Y A2 )


+ p1γi(Y B1 ) + p2

γi(Y B2 )


where pt =PBtPAt


The simple model



Household i solves:

max

2∑t=1


αi ]

subject to


Spending on A

+ p1cBi,1 + p2

cBi,2R︸︷︷︸

Spending on B

=bi,1πA1︸︷︷︸

Initial wealth

+ γi(Y A1 ) +γi(Y A2 )


+ p1γi(Y B1 ) + p2

γi(Y B2 )


where pt =PBtPAt


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

}.




∂yipα

i

ci,1.


dci,1 =


dR

R+ MPCi,1


dR

R−


dPA

PA

+γAi dYA1 + pγ

Bi dY

B1︸︷︷︸


+ γBi p

(Y B1 +

1

RY B2

)︸︷︷︸


dp

p− αipαi

(ci,1 +

1

Rci,2

)︸︷︷︸


dp

p

}.




∂yipα

i

ci,1.


dci,1 =


dR

R+ MPCi,1


dR

R−


dPA

PA

+γAi dYA1 + pγ

Bi dY

B1︸︷︷︸


+ γBi p

(Y B1 +

1

RY B2

)︸︷︷︸


dp

p− αipαi

(ci,1 +

1

Rci,2

)︸︷︷︸


dp

p

}.

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

.

Outline



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).

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%)

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%)

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

Earnings channel: CPI-ACS

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)


Earnings channel: PPI-ACS

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)


Expenditure channel: CPI-CEX

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

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

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

Outline



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

Model overview









Model overview





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




Model overview





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




Model overview





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)



Model overview









Model overview







I Different discount rates: ρC and ρNC (to generate plausible MPC)

I Different borrowing constraints aC and aNC (purely expositional)


Model overview









Model overview









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

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

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)






I Same steady state









I Same steady state





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

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

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

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

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

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

Calibration

�

✓C✓NC

✏

�

1 � ↵NC1 � ↵C

ZNCAZCA

ZNCBZCB

�A

�B

Baseline with 1 household type, 1 sector

Introducing sectoral price rigidity heterogeneity

Comparison calibration: add symmetric productivity differences

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
Differenced IRFs (Full – Comparison)

Back.

Marginal propensities to consume (MPC)

Back.

Asset holdings and borrowing constraints

Back.

Disposable income and its decomposition

Back.

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

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

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

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


Appendix

Heterogeneous Price Rigidities and Monetary Policy...(2007), Cravino et al. (2019) Our...

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Transcript of Heterogeneous Price Rigidities and Monetary Policy...(2007), Cravino et al. (2019) Our...