price dispersion and inflation persistence
Post on 04-Feb-2022
5 Views
Preview:
TRANSCRIPT
Price Dispersion and Inflation Persistence
Takushi Kurozumi and Willem Van Zandweghe
Bank of Japan and FRB Kansas City
SWET 2017August 5, 2017
Disclaimer: The views expressed are those of the authors and should not be interpreted as those of the Bank of Japan, theFederal Reserve Bank of Kansas City, or the Federal Reserve System.
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 1 / 27
Empirical impulse responses to a monetary policy shock
0 5 10 15 20-0.9
-0.6
-0.3
0
0.3
0.6
pp
Federal Funds Rate
0 5 10 15 20-0.4
-0.2
0
0.2
0.4
pp
Annualized Inflation Rate
0 5 10 15 20
Quarters since shock
-0.6
-0.3
0
0.3
0.6
0.9
%
Output
0 5 10 15 20
Quarters since shock
-0.6
-0.3
0
0.3
0.6
%
Labor Productivity
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 2 / 27
Intrinsic or inherited inflation inertia
The New Keynesian Phillips Curve (NKPC) governs inflationdynamics in sticky price models of monetary policy.
NKPC has difficulty accounting for inflation persistence because it ispurely forward-looking, so literature has incorporated lags of inflation.
Intrinsic inflation inertia remains controversial.
Assumptions—rule-of-thumb price setting, price indexation—are oftendeemed implausible.
Benati (2008) finds that the degree of inflation persistence varies withthe monetary policy regime across countries.
To account for inflation persistence without resorting to intrinsicinflation inertia, NKPC must inherit persistence in driving process.
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 3 / 27
Staggered pricing model with positive trend inflation hasdifficulty generating inflation persistence
Inflation dynamics in generalized NKPC depends on relative pricedistortion (RPD), reflects productivity loss due to price dispersion.
Price dispersion → demand dispersion → RPD.
Lagged RPD is an endogenous state variable, potential source ofpersistence.
However, we find the inertia of RPD has a minor effect on inflationpersistence, while it may generate a counterfactual decline in outputper hour after an expansionary shock.
⇒ Dynamics of RPD creates tension between generating plausibleresponses of inflation and output per hour.
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 4 / 27
A “smoothed-off” kink in demand curves alters therelationship between price dispersion and RPD
-100 -50 50 100Relative demand (%)
-10
-5
5
10Relative price (%)
θ=10, ϵ=0
θ=10, ϵ=-9
Generalization of Dixit-Stiglitz preferences for product diversity(Kimball, 1995; Smets and Wouters, 2007).
Kink generates strategic complementarity: large demand loss for highrelative price and small demand gain for low relative price.
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 5 / 27
Responses of inflation and output per hour consistent withVAR evidence
The kink introduces measure of price dispersion, distinct from RPD,which appears in NKPC.
Lagged price dispersion is a second endogenous state variable.
A policy shock generates a large and persistent response of pricedispersion and a muted response of RPD, allowing plausible responsesof both inflation and output per hour.
⇒ Large, persistent response of price dispersion is inherited by theresponse of inflation, which becomes persistent and hump-shaped.
⇒ Muted response of RPD prevents a counterfactual decline of outputper hour.
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 6 / 27
Credible permanent disinflation
With intrinsic inflation inertia, a permanent decline in trend inflationgenerates a gradual decline in inflation and a recession.
Without the inertia inflation jumps to its new trend rate and outputnever deviates from its trend level.
In our model with trend inflation and a kink in demand curves, acredible disinflation induces a gradual decline in inflation and arecession even absent intrinsic inflation inertia.
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 7 / 27
Overview
1 Model
2 Quantitative analysis
3 Conclusion
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 8 / 27
A model with trend inflation and kinked demand curves
Representative final-good producer combines differentiated goods intoa single product according to household preferences.
Curvature in demand curves for differentiated goods.
Continuum of monopolistically competitive intermediate-goodproducers face Calvo price rigidity.
Fixed cost of production gives rise to increasing returns to scale.
Monetary authority conducts interest rate policy and has positiveinflation target.
Representative household.
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 9 / 27
Representative final-good firm
Following Dotsey & King (2005), demand for differentiated good f is
Yt(f ) =Yt
1 + ε
[(Pt(f )
Ptdt
)−θ(1+ε)
+ ε
].
Parameter ε ≤ 0 governs curvature, which is measured as −εθ, and
dt =
[∫ 1
0(Pt(f )/Pt)
1−θ(1+ε) df
] 11−θ(1+ε)
is a measure of price dispersion.
The case ε = 0 is the familiar CES case:
Demand Yt(f ) = Yt (Pt(f )/Pt)−θ.
Price index Pt = [∫ 1
0(Pt(f ))1−θdf ]1/(1−θ) ⇔ dt = 1.
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 10 / 27
Representative final-good firm
Following Dotsey & King (2005), demand for differentiated good f is
Yt(f ) =Yt
1 + ε
[(Pt(f )
Ptdt
)−θ(1+ε)
+ ε
].
Parameter ε ≤ 0 governs curvature, which is measured as −εθ, and
dt =
[∫ 1
0(Pt(f )/Pt)
1−θ(1+ε) df
] 11−θ(1+ε)
is a measure of price dispersion.
The case ε = 0 is the familiar CES case:
Demand Yt(f ) = Yt (Pt(f )/Pt)−θ.
Price index Pt = [∫ 1
0(Pt(f ))1−θdf ]1/(1−θ) ⇔ dt = 1.
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 10 / 27
Representative final-good firm
Following Dotsey & King (2005), demand for differentiated good f is
Yt(f ) =Yt
1 + ε
[(Pt(f )
Ptdt
)−θ(1+ε)
+ ε
].
Parameter ε ≤ 0 governs curvature, which is measured as −εθ, and
dt =
[∫ 1
0(Pt(f )/Pt)
1−θ(1+ε) df
] 11−θ(1+ε)
is a measure of price dispersion.
The case ε = 0 is the familiar CES case:
Demand Yt(f ) = Yt (Pt(f )/Pt)−θ.
Price index Pt = [∫ 1
0(Pt(f ))1−θdf ]1/(1−θ) ⇔ dt = 1.
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 10 / 27
Intermediate-good firms
Minimize production costs s.t. technology
Yt(f ) =
{Nt(f )− φ if Nt(f ) ≥ φ0 otherwise.
Combining production function, intermediate-good demand, and labormarket clearing yields expression for output per hour
Yt
Nt=
(1− φ
Nt
)(st + ε
1 + ε
)−1
.
The RPD is a measure of demand dispersion:
st + ε
1 + ε=
∫ 1
0
Yt(f )
Ytdf .
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 11 / 27
Intermediate-good firms
Minimize production costs s.t. technology
Yt(f ) =
{Nt(f )− φ if Nt(f ) ≥ φ0 otherwise.
Combining production function, intermediate-good demand, and labormarket clearing yields expression for output per hour
Yt
Nt=
(1− φ
Nt
)(st + ε
1 + ε
)−1
.
The RPD is a measure of demand dispersion:
st + ε
1 + ε=
∫ 1
0
Yt(f )
Ytdf .
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 11 / 27
Intermediate-good firms
Minimize production costs s.t. technology
Yt(f ) =
{Nt(f )− φ if Nt(f ) ≥ φ0 otherwise.
Combining production function, intermediate-good demand, and labormarket clearing yields expression for output per hour
Yt
Nt=
(1− φ
Nt
)(st + ε
1 + ε
)−1
.
The RPD is a measure of demand dispersion:
st + ε
1 + ε=
∫ 1
0
Yt(f )
Ytdf .
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 11 / 27
Intermediate-good firms
Each period, a fraction α of firms keeps prices unchanged, while theremaining 1− α firms sets the price to maximize profits (p∗).
Under staggered price setting lags of price dispersion and RPD areendogenous state variables
(dt)1−θ(1+ε) = (1− α) (p∗t )1−θ(1+ε) + α
(dt−1
πt
)1−θ(1+ε)
(dt)−θ(1+ε) st = (1− α) (p∗t )−θ(1+ε) + α
(dt−1
πt
)−θ(1+ε)
st−1.
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 12 / 27
Intermediate-good firms
Each period, a fraction α of firms keeps prices unchanged, while theremaining 1− α firms sets the price to maximize profits (p∗).
Under staggered price setting lags of price dispersion and RPD areendogenous state variables
(dt)1−θ(1+ε) = (1− α) (p∗t )1−θ(1+ε) + α
(dt−1
πt
)1−θ(1+ε)
(dt)−θ(1+ε) st = (1− α) (p∗t )−θ(1+ε) + α
(dt−1
πt
)−θ(1+ε)
st−1.
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 12 / 27
Monetary authority and household
Monetary authority sets the short-term interest rate according to aTaylor-type rule with interest rate smoothing:
log it = (1− ρ) [log i + φπ (logπt−logπ)] + ρ log it−1 + εt .
Representative household chooses final-good consumption, laborsupply, and riskless bonds to maximize utility
E0
∞∑t=0
βt
(logCt −
N1+σnt
1 + σn
)
subject to budget constraint.
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 13 / 27
Generalizing the NKPC
At the zero trend inflation rate or, equivalently, with full indexation tothe trend inflation rate,
πt = βEt πt+1 +(1− α)(1− αβ)
αmct .
At a positive trend inflation rate without price indexation, theNKPC generalizes as
πt = βEt πt+1 +(1− απθ−1)(1− αβπθ)
απθ−1mct + ϕt
where ϕt = αβπθEtϕt+1
+ β(π − 1)(1− απθ−1)[θEt πt+1 + (1− αβπθ)Etmct+1
].
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 14 / 27
Generalizing the NKPC
At the zero trend inflation rate or, equivalently, with full indexation tothe trend inflation rate,
πt = βEt πt+1 +(1− α)(1− αβ)
αmct .
At a positive trend inflation rate without price indexation, theNKPC generalizes as
πt = βEt πt+1 +(1− απθ−1)(1− αβπθ)
απθ−1mct + ϕt
where ϕt = αβπθEtϕt+1
+ β(π − 1)(1− απθ−1)[θEt πt+1 + (1− αβπθ)Etmct+1
].
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 14 / 27
Adding a kink in demand, inflation inherits inertia fromprice dispersion in generalized NKPC
πt = βEt πt+1 +(1− απγ−1)(1− αβπγ)
απγ−1[1− εγ/(γ − 1− ε)]mct + ϕt + ψt
− γ(1− απγ−1)[αβπγ−1(π − 1)(γ − 1) + ε(1− αβπγ)]
απγ−1[γ − 1− ε(γ + 1)]dt
+
(Et dt+1 −
1
απγ−1dt
)− αβπγ−1
(dt −
1
απγ−1dt−1
)using shorthand γ = θ(1 + ε) and ε = f (ε, α, β, θ, π).
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 15 / 27
Adding a kink in demand, inflation inherits inertia fromprice dispersion in generalized NKPC
πt = βEt πt+1 +(1− απγ−1)(1− αβπγ)
απγ−1[1− εγ/(γ − 1− ε)]mct + ϕt + ψt
− γ(1− απγ−1)[αβπγ−1(π − 1)(γ − 1) + ε(1− αβπγ)]
απγ−1[γ − 1− ε(γ + 1)]dt
+
(Et dt+1 −
1
απγ−1dt
)− αβπγ−1
(dt −
1
απγ−1dt−1
)using shorthand γ = θ(1 + ε) and ε = f (ε, α, β, θ, π).
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 15 / 27
Effects of RPD on the dynamics of inflation and outputper hour
RPD can increase inflation persistence through real marginal cost:
mct =
(1 +
σn
1 + φY
1+εs+ε
)Yt +
σns
s+ε
1 + φY
1+εs+ε
st .
RPD can change the sign of response of output per hour:
Yt − Nt =
(φ
Y
1 + ε
s + ε
)Nt −
s
s + εst . (1)
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 16 / 27
Quarterly calibration
Preferences and technology
β Subjective discount factor 0.99
σn Inverse of the elasticity of labor supply 0.5
α Probability of no price change 0.75
θ Parameter governing the price elasticity of demand 10
ε Degree of strategic complementarity −9, 0
Monetary policy
φπ Policy response to inflation 1.5
ρ Policy response to lag of interest rate 0.9
π Annualized trend inflation rate 2.5%
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 17 / 27
Impulse responses to a monetary policy shock in the caseof no kink in demand curves
0 5 10 15 20-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
pp
Federal Funds Rate
0 5 10 15 20
0
0.2
0.4
0.6
0.8
1
pp
Annualized Inflation Rate
0 = 0;: = 2:5%
0 5 10 15 20
Quarters since shock
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
%
Output
0 5 10 15 20
Quarters since shock
-0.1
-0.05
0
0.05
0.1
%
Output Per Hour
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 18 / 27
Trend inflation has minor influence on inflation persistencebut major influence on output per hour
0 5 10 15 20-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
pp
Federal Funds Rate
0 5 10 15 20
0
0.2
0.4
0.6
0.8
1
pp
Annualized Inflation Rate
0 = 0;: = 2:5%0 = 0;: = 0
0 5 10 15 20
Quarters since shock
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
%
Output
0 5 10 15 20
Quarters since shock
-0.1
-0.05
0
0.05
0.1
%
Output Per Hour
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 19 / 27
Kink gives rise to persistent and hump-shaped response ofinflation and positive response of output per hour
0 5 10 15 20-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
pp
Federal Funds Rate
0 5 10 15 20
0
0.2
0.4
0.6
0.8
1
pp
Annualized Inflation Rate
0 = !9;: = 2:5%0 = 0;: = 2:5%0 = 0;: = 0
0 5 10 15 20
Quarters since shock
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
%
Output
0 5 10 15 20
Quarters since shock
-0.1
-0.05
0
0.05
0.1
%
Output Per Hour
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 20 / 27
Persistent rise in price dispersion with muted response ofRPD
0 5 10 15 20
Quarters since shock
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
%
Relative Price Distortion (RPD)
0 = !90 = 0
0 5 10 15 20
Quarters since shock
0
0.05
0.1
0.15
0.2
0.25
%
Relative Price Dispersion
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 21 / 27
Effect of the kink in demand curves on the slope of the(generalized) NKPC
-9 -6 -3 0
0
0
0.02
0.04
0.06
0.08
0.1
Trend inflation rate = 2.5%Trend inflation rate = 0
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 22 / 27
Effects of a credible permanent decline in trend inflation
Volcker disinflation in early 1980s: gradual decline in inflation andrecession.
NKPC generates a gradual decline in inflation and a temporary declinein output, provided the model contains intrinsic inflation inertia.
Generalized NKPC generates similar responses, provided the modelcontains a kink in demand curves.
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 23 / 27
A one percentage point decline in trend inflation:NKPC with full price indexation to past inflation
0 5 10 15 20
Quarters since disinflation
-1
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
pp d
evia
tion
from
initi
al s
tead
y st
ate
Inflation
0 = 0, indexation
0 5 10 15 20
Quarters since disinflation
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
% d
evia
tion
from
initi
al s
tead
y st
ate
Output
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 24 / 27
A one percentage point decline in trend inflation:Generalized NKPC but no kink in demand
0 5 10 15 20
Quarters since disinflation
-1
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
pp d
evia
tion
from
initi
al s
tead
y st
ate
Inflation
0 = 00 = 0, indexation
0 5 10 15 20
Quarters since disinflation
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
% d
evia
tion
from
initi
al s
tead
y st
ate
Output
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 25 / 27
A one percentage point decline in trend inflation:Generalized NKPC and a kink in demand
0 5 10 15 20
Quarters since disinflation
-1
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
pp d
evia
tion
from
initi
al s
tead
y st
ate
Inflation
0 = !90 = 00 = 0, indexation
0 5 10 15 20
Quarters since disinflation
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
% d
evia
tion
from
initi
al s
tead
y st
ate
Output
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 26 / 27
Conclusion
Models of the monetary transmission mechanism have difficultyaccounting for observed inflation inertia without assuming it isintrinsic.
A positive trend inflation rate has a minor influence on inflationpersistence and can induce a counterfactual response of productivityto a policy shock.
Combination of positive trend inflation, kink in demand curves, andfixed cost in production can generate responses of inflation andproductivity in line with empirical evidence.
Model improves responses to a transitory policy shock and apermanent disinflation.
Kurozumi (BOJ) & Van Zandweghe (FRBKC) Price Dispersion & Inflation Persistence SWET 2017 27 / 27
top related