mongey market structure slides - simon mongey - home

yyl

Market structure and monetary non-neutrality

Simon Mongey

Federal Reserve Bank of Minneapolis

ASU Junior Macroeconomics Conference

November 4, 2017

The views expressed herein are those of the authors and not necessarily those of the Federal Reserve

Bank of Minneapolis or the Federal Reserve System.

Simon Mongey, ”Market structure and monetary non-neutrality” p.0/21

Introductionyyl

Monetary economics

- How do changes in nominal spending affect output vs. inflation?

- Nominal rigidity + Firms are ‘small’ in their market (competitive)


Introductionyyl

Monetary economics



This paper

- Nominal rigidity + Firms are ‘large’ in their market (strategic)


Introductionyyl

Monetary economics



This paper


Important

1. Markets dominated by a few large firms Fig. - Distributions of concentration

e.g. Mayonnaise, Ohio, 2005:Q1 - Hellman’s 45%, Kraft 33% (IRI data)

2. “Increasing concentration” - Philippon Gutierrez ‘17, Autor et al. ‘17, Jan2 ‘17


Introductionyyl

Monetary economics



This paper


Important

1. Markets dominated by a few large firms Fig. - Distributions of concentration

e.g. Mayonnaise, Ohio, 2005:Q1 - Hellman’s 45%, Kraft 33% (IRI data)

2. “Increasing concentration” - Philippon Gutierrez ‘17, Autor et al. ‘17, Jan2 ‘17

Quantitative question

- How does market structure affect transmission of monetary shocks?


Approachyyl

Quantitative model

- Firm heterogeneity - Idiosyncratic productivity shocks

- Nominal rigidity - Menu cost of changing prices (ξ)

- Exogenous changes in nominal spending - Shocks to money supply

- New - Two ‘large’ firms in each sector. Dynamic oligopoly. Literature


Approachyyl

Quantitative model





How does market structure affect transmission of monetary shocks?

- Compare: Oligopoly vs. Monopolistic competition

- Calibrate to match same data on good-level price dynamics

- Frequency of adjustment, Size of adjustment, Average markup


Approachyyl

Quantitative model





How does market structure affect transmission of monetary shocks?

- Compare: Oligopoly vs. Monopolistic competition

- Calibrate to match same data on good-level price dynamics

- Frequency of adjustment, Size of adjustment, Average markup

Main finding

- 2.5 times larger output fluctuations under duopoly


Dynamic complementarityyl

- Consider two firms with initial prices pA > pB

- Equilibrium

- Firm A: Leave price at p′A = pA

- Firm B: Pay ξ and increase price to p′B < pA

- Why?

- Given p′A, complementarity makes a higher p′B profitable

- Given p′B , the menu cost makes a price cut unprofitable for Firm A

- Static complementarity + Frictions → Dynamic complementarity

- A higher pA yields a higher p′B in equilibrium

- A lower pA yields a lower p′B in equilibrium


Dynamic complementarityyl

- Consider two firms with initial relative prices pAM >

pBM

- Equilibrium

- Firm A: Leave price at p′A

M = pAM

- Firm B: Pay ξ and increase price to p′B

M <pAM

- Why?

- Given p′B

M , complementarity makes a higher p′B

M profitable

- Given p′A

M , the menu cost makes a price cut unprofitable for Firm A

- Static complementarity + Frictions → Dynamic complementarity

- A higher pAM yields a higher p′

B

M in equilibrium

- A lower pAM yields a lower p′

B

M in equilibrium


Market structure and monetary economicsyyl



1. Welfare

- Output is 10% higher when menu costs are zero

- 75% due to lower markups, 25% due to lower price dispersion

- Suggests a different focus for welfare analysis



1. Welfare




2. Strategic complementarity (Ball Romer ‘90, Klenow Willis ‘16, Burstein-Hellwig ‘07)

- MC menu cost models with SC can generate large real effects

- But implausible parameter values to match good-level data

- Addresses “serious challenge to Monetary econ.” (Nakamura Steinsson ‘10)



1. Welfare




2. Strategic complementarity (Ball Romer ‘90, Klenow Willis ‘16, Burstein-Hellwig ‘07)

- MC menu cost models with SC can generate large real effects

- But implausible parameter values to match good-level data

- Addresses “serious challenge to Monetary econ.” (Nakamura Steinsson ‘10)

3. Price stickiness

- Lower menu costs needed in the duopoly model

- Across-region Within-product correlations support model (IRI data)

- Better understand heterogeneity in price flexibility


Outlineyyl

1. Model

2. Simulations

3. Calibration

4. Decompose the effects of monetary shocks

5. Three additional results


Householdy

Flow utility

U(C ,N) = logC − N

C =

[∫ 1

0C

1−θθ

j dj

] θ1−θ

, θ > 1

Cj =

[

c1j1−η

η + c2j1−η

η

] η1−η

, η > θ

Total nominal expenditure

PC =∫ 1

0

[

p1jc1j + p2jc2j

]

dj ≤ M

Details - Recursive household problem with dynamic budget constraint → Discount factor


Household - Solutionyyl

Labor supply∣∣∣∣∣

W

P= −

UN (C ,N)

UC (C ,N)↔ W = PC= M

∣∣∣∣∣

Demand

dij =

(

pij

Pj

)−η(

Pj

P

)−θ

C

︸︷︷︸

Demand dij

(

pij −W

zij

)

︸︷︷︸

Per-unit profit

where Pj =

[

p1j1−η + p2j

1−η

] 11−η

P =

[∫ 1

0Pj

1−θdj

] 11−θ


Household problem - Solutionyyl

Markups∣∣∣∣∣µij =

pij

W/zij

∣∣∣∣∣

︸︷︷︸

Firm

,

∣∣∣∣∣µj =

Pj

W

∣∣∣∣∣

︸︷︷︸

Sector

,

∣∣∣∣∣µ =

P

W=

1

C

∣∣∣∣∣

︸︷︷︸

Aggregate

=1

C



Markups∣∣∣∣∣µij =

pij

W/zij

∣∣∣∣∣

︸︷︷︸

Firm

,

∣∣∣∣∣µj =

Pj

W

∣∣∣∣∣

︸︷︷︸

Sector

,

∣∣∣∣∣µ =

P

W=

1

C

∣∣∣∣∣

︸︷︷︸

Aggregate

=1

C

Profits

πij

W=

(

µij

µj

)−η(

µj

µ

)−θ1

µ︸︷︷︸

Demand dij

(

µij − 1

)

︸︷︷︸

Per-unit profit

where µj =

[

µ1j1−η + µ2j

1−η

] 11−η

µ =

[∫ 1

0µj

1−θdj

] 11−θ

Technical details



Markups ∣∣∣∣∣µij =

pij

W/zij

∣∣∣∣∣

︸︷︷︸

Choice today

,

∣∣∣∣∣µ′ij =

pij

W ′/z ′ij︸︷︷︸

State tomorrow

Profits

πij

W=

(

µij

µj

)−η(

µj

µ

)−θ1

µ︸︷︷︸

Demand dij

(

µij − 1

)

︸︷︷︸

Per-unit profit

where µj =

[

µ1j1−η + µ2j

1−η

] 11−η

µ =

[∫ 1

0µj

1−θdj

] 11−θ


Firm problemyl

Markov states

- Sector Markups µi , µ−i x = (µi , µ−i )

- Aggregate Distribution λ(x), money growth g X = (λ, g )


Firm problemyl

Markov states



Equilibrium functions

- Aggregate markup µ(X )


Firm problemyl

Markov states





Timing and Information (Doraszelski Satterthwaite, 2007)

(x ,X ) determined︸︷︷︸

Public

→ Draw menu cost ξi ∼ U[0, ξ]

︸︷︷︸

iid + Private

→ Pricing decisions︸︷︷︸

Simultaneous


Firm problemyl

Markov states





Timing and Information (Doraszelski Satterthwaite, 2007)

(x ,X ) determined︸︷︷︸

Public

→ Draw menu cost ξi ∼ U[0, ξ]

︸︷︷︸

iid + Private

→ Pricing decisions︸︷︷︸

Simultaneous

Competitor’s policies

- Markup conditional on adjustment µ∗−i (x ,X ) ∈ R+

- Markup adjustment γ−i (x ,X , ξ−i ) ∈ {0, 1}


Firm problemyl

Value

Vi (x ,X , ξi ) = maxγi∈{0,1}

γi

[

Vadji (x ,X )− ξi

]

+ (1− γi )Vstayi (x ,X )

Value of adjusting price

Vadji (x ,X ) = max

µ∗i ∈R+

∫ ξ

0

[

π(

µ∗i ,µ−i (x ,X , ξ−i ),µ(X )

)

+ βE

[

Vi

(x ′,X ′, ξ ′i

) ]]

dF (ξ−i )

µ−i (x ,X , ξ−i ) =

∥∥∥∥∥

γ−i (x ,X , ξ−i )µ∗−i (x ,X )

∥∥∥∥∥

︸︷︷︸

Competitor adjusts

+

∥∥∥∥∥

(

1− γ−i (x ,X , ξ−i ))

µ−i

∥∥∥∥∥

︸︷︷︸

Competitor stays

Solution

- Probability of price adjustment Γi (x ,X ) =∫ ξ0 γi (x ,X , ξi )dF (ξi )

- Markup conditional on adjustment µ∗i (x ,X )


Recursive equilibriumyl

- Symmetric demand, value, adjustment prob. and markup functions

d(x ,X ), V (x ,X ), Γ(x ,X ), µ∗(x ,X )

- Transition density for the distribution of sectors λ′ ∼ H(λ|X )

- Aggregate markup function µ(X )

such that

1. Firm policies and values are Markov-Perfect at the sectoral level

2. W = PC = M + Markup definitions ↔ µ(X ) = 1C (X )

3. Demand functions are consistent with household optimization

4. Transition function for λ is consistent with policies and processes

5. Aggregate mark-up is consistent with (i) mark-up policies, (ii) λ

Details - Computation


Illustrative simulationyyl

Show

- Micro MPE policies attain high markups in equilibrium

- Macro Weaker intensive and extensive response to ↑ M

Setup

- No aggregate shocks or inflation gt = 0

- Fix paths for menu costs ξit = ξ

- Fix paths for shocks zit → µit

- Plot paths for equilibrium policies(A.) Optimal markup µ∗

it = µ∗ (µit , µ−it )

(B.) Probability of adjustment Γit = Γ (µit , µ−it)

Note: Using estimated parameters (next)


Monopolistic competitionyl

20 40 60 80

Period t

-0.15

-0.10

-0.05

0

0.05

0.10

0.15

logµit−logµi0

A. Markups

Frictionless markup

Markup µit

Optimal markup µ∗

it

20 40 60 80

Period t

0

0.2

0.4

0.6

0.8B. Probability of adjustment

Markups

- Same optimal markup µ∗L = µ∗

H

—

Adjustment

- Precautionary motive ΓL > ΓH

Profit functions


Monopolistic competition - ↑ Myl

20 40 60 80

Period t

-0.15

-0.10

-0.05

0

0.05

0.10

0.15

logµit−logµi0

A. Markups

Frictionless markupFrictionless markup

Markup µit


it

20 40 60 80

Period t

0

0.2

0.4

0.6


Intensive margin

- Optimal price adjustment ∆pL = µ∗L/µL increases by ∆M

Extensive margin

- Increase in ΓL shifts distribution of price changes to price increases

Profit functions


Duopolyyl

20 40 60 80

Period t

-0.15

-0.10

-0.05

0

0.05

0.10

0.15

logµit−logµi0

A. Markups

Frictionless markup

Markup µit


it

20 40 60 80

Period t

0

0.2

0.4

0.6


Markups

- Policies support higher sectoral markup

Adjustment

- High ΓL of price increase to incentivize low ΓH of price decrease

Profit functions


Duopoly - ↑ Myl

20 40 60 80

Period t

-0.15

-0.10

-0.05

0

0.05

0.10

0.15

logµit−logµi0

A. Markups

Frictionless markup

Markup µit


it

20 40 60 80

Period t

0

0.2

0.4

0.6


Intensive margin

- Falling µH reduces µ∗L

Extensive margin

- Falling µH reduces ΓL

Profit functions


Duopoly - ↑ Myl

20 40 60 80

Period t

-0.15

-0.10

-0.05

0

0.05

0.10

0.15

logµit−logµi0

A. Markups

Frictionless markup

Markup µit


it

20 40 60 80

Period t

0

0.2

0.4

0.6


Intensive margin

- Optimal adjustment ∆pL = µ∗L/µL increases by less than ∆M

Extensive margin

- Dampened increase in ΓL

Profit functions Two low prices


Quantification - What features imply large output effects?yl

Static complementarity

- More substitutable within sectors η, less across sectors θ

Dynamic complementarity

- Which features help firms to track each other’s prices in the MPE?

- Larger menu costs ξ

- Smaller idiosyncratic shocks σz

- State-dependent (menu cost), rather than Calvo

- Lower trend money growth g?

- Lower volatility of money growth σg?


Quantification - Calibration strategy (monthly)yl

External

- Money growth parameters ρg = 0.6, σg = 0.002, g = 1.0251/12

- Cross-sector demand elasticity θ = 1.5

Internal

- Menu cost ξ, Size of shocks σz

- Within-sector demand elasticity η

Moments

- Average absolute size of regular price changes (IRI) - 10%

- Average frequency of regular price changes (IRI) - 13%

- Average markup E [µit ] = 1.30

Robustness to η in MC model Data details Identification argument for σz , ξ, η Firm vs Sector shocks


Quantification - Parameters and resultsyyl

Duopoly MC

A. ParameterCross-sector demand elasticity θ 1.5 1.5Within-sector demand elasticity η 10.5 4.5Size of menu cost ξ 0.17 0.21Size of idiosyncratic shocks (%) σz 3.80 4.00

B. Moments matchedAverage markup E [µit ] 1.30 1.30Frequency of price change 0.13 0.13Ave. absolute size of price change 0.10 0.10

C. ResultsStd. deviation consumption std [log Ct ]× 100 0.31 0.13Average minus Frictionless markup E [µit ]− µf 0.10 0.02



Duopoly MC




∗ 2.5 times larger output fluctuations (Data: US 1969-2016, std [logCt ]× 100 = 1.01)



Duopoly MC





1. 10 ppt larger markups than frictionless economy → ≈ 10% Lower output



Duopoly MC






2. Smaller shocks deliver observed size of price change



Duopoly MC






2. Smaller shocks deliver observed size of price change

3. 25 percent smaller menu costs deliver same frequency of price change

Figure - (i) ξ comp. stats., (ii) IRF of Ct Table - Alternative calibrations Figure - Comp. stats η



Duopoly MC MC′

A. ParameterCross-sector demand elasticity θ 1.5 1.5 1.5Within-sector demand elasticity η 10.5 4.5 ↑ 10.5Size of menu cost ξ 0.17 0.21 ↓ 0.17Size of idiosyncratic shocks (%) σz 3.80 4.00 ↓ 3.80

B. Moments matchedAverage markup E [µit ] 1.30 1.30 ↓ 1.12Frequency of price change 0.13 0.13 ↑ 0.19Ave. absolute size of price change 0.10 0.10 ↓ 0.05

C. ResultsStd. deviation consumption std [logCt ]× 100 0.31 0.13 ⇓ 0.06Average minus Frictionless markup E [µit ]− µf 0.10 0.02 ↓ 0.01



2. Same size shocks deliver observed size of price change

3. 25 percent smaller menu costs deliver same frequency of price change

Figure - (i) ξ comp. stats., (ii) IRF of Ct Table - Alternative calibrations Figure - Comp. stats η


Pricing frictions and firm valueyl

✓ More frictions → Higher markups

✗ More frictions → Markups further away from µ∗it

- Rationalizes why firms may want to create pricing frictions- Sep 24: Apple announces price of $999 for new iPhone on sale Nov 3

- Annual IKEA catalogue


Accounting for inflationyyl

Questions

1. Lower price response due to smaller extensive or intensive margin?

2. Which sectors (µ1j , µ2j ) dampen each margin the most?

Decomposition a la Caballero-Engel (2007)

- One-time unforeseen ∆Mt > 0

πt ≈N

∑i=1

ωi

[∣∣∣Γit

(

xit − xit

)∣∣∣

︸︷︷︸

1. Intensive

+∣∣∣xit

(

Γit − Γit

)∣∣∣

︸︷︷︸

2. Extensive

+∣∣∣

(

Γit − Γit

)(

xit − xit

)∣∣∣

︸︷︷︸

3. Covariance

]

where xit = log p∗it − log pit−1, is the desired price change


Accounting for inflationyyl

πt ≈N

∑i=1

ωi

[∣∣∣Γit

(

xit − xit

)∣∣∣

︸︷︷︸

1. Intensive

+∣∣∣xit

(

Γit − Γit

)∣∣∣

︸︷︷︸

2. Extensive

+∣∣∣

(

Γit − γit

)(

xit − xit

)∣∣∣

︸︷︷︸

3. Covariance

]

Intensive Extensive% %

Fraction of the difference: πMont − πDuo

t 36 45

Fraction of each margin by (µ1j ,µ2j )

Low-High / High-Low 142 122High-High 21 32Low-Low -63 -54

Result

- Extensive and intensive margin components dampened ≈ equally

- Low markup sectors become more flexible


Relation to some of the literatureyyl

The duopoly mechanism does not deliver amplification through

- More kurtosis in dist. of price changes (Alvarez Bihan Lippi, 2016) +

- Excess curvature in demand as under Kimball (Klenow Willis, 2016) +

... but does depend on firm’s ability to choose when to change prices

- Dynamic complementarities weaker under Calvo +

... and is qualitatively consistent with previous empirical work

- Strategic complementarities in pricing (Gopinath Itskhoki, 2010)

- Counter-cyclical µ’s and conc. (Barro Tenreyo, ‘06; Rotemburg Woodford, ‘91)

- Prices stickier for differentiated (final) goods (Bils Klenow, 2004)


Additional resultsyyl

1. Large output losses; menu costs lead to higher markups

Results

2. Strategic complementarities in the literature

Results

3. Empirical relationship between concentration and flexibility

Results


Conclusionyyl

Market structure quantitatively important for understanding

- Aggregate price flexibility following nominal spending shocks

- Firm level price flexibility following idiosyncratic shocks

- Cross-sectional heterogeneity in price flexibility

Market structure empirically important- Increasing concentration and falling labor share

Autor, Dorn, Katz, Patterson, Van Reenen (2016)

- Increasing concentration and weakening Tobin’s Q ↔ InvestmentPhilippon Gutierrez (2016)

This paper presents a framework for assessing these issues

- Relabel pit → kit delivers an oligopolistic Khan-Thomas model

- Exchange rate shocks

- Oligopsony in labor markets


yl

THANK YOU!


Household - Solutionyyl

Preferences - ↓ zij , ↑ Cost, ↑ Demand

C =

[∫ 1

0C

1−θθ

j dj

] θ1−θ

, Cj =

(c1j

z1j

) 1−ηη

+

(c2j

z2j

) 1−ηη

η1−η

Demand

dij = z1−ηij

(

pij

Pj

)−η(

Pj

P

)−θ

C

︸︷︷︸

Demand dij

(

pij −W

zij

)

︸︷︷︸

Per-unit profit

where Pj =

[(

z1jp1j

)1−η+(

z2jp2j

)1−η] 1

1−η

P =

[∫ 1

0Pj

1−θdj

] 11−θ

Back - Household solution


1. Output loss due to nominal rigidityyyl

Y =1

µ, µ =

[∫ 1

0µj

1−θdj

] 11−θ

, µj =

[

µ1j1−η + µ2j

1−η

] 11−η

Mon. Comp. Duopoly

(1) Output 0.76 0.75(2) ... under no dispersion µij = E[µij ] 0.77 0.77(3) ... with no menu costs µij = µf 0.78 0.83

(3)-(1) Output loss due to nominal rigidity 2.4% 9.7%

Result

- Nearly 10% output losses due to nominal rigidity in oligopoly

- 1st order - 75% due to higher markups

- 2nd order - 25% due to price dispersion

Back - Additional results


2. Strategic complementarities in MC modelsyyl

Strategic complementarities

“Substantial nominal rigidity can arise from a combination of strategic

complementarities and nominal frictions” - Ball Romer (1990)

Klenow Willis (2016), Burstein Hellwig (2007)

“Recent work has cast doubt on SC as a source of amplification in menu cost models,

by showing that introducing SC’s can make it difficult match size, freq. for plausible

values of ξ and σz ...this challenge is a serious one” - Nakamura Steinsson (2010)

This paper

- Smaller ξ and σz under duopoly

- Larger ↑ std [ct ] due to strategic complementarity

- How? Complementarity due to µ1jt/µ2jt , not µit/µt



3. Market concentration and price flexibilityyl



1. Oligopoly

- Lower menu cost in duopoly model

- Prices change less when firms behave strategically

- Here 1 firm = Non-strategic, 2 firms = Strategic, ∞ firms = Non-strategic



1. Oligopoly




2. Elasticity

- More competition → More elastic demand → More price changes



1. Oligopoly




2. Elasticity

- More competition → More elastic demand → More price changes

Examine correlation structure of IRI data

- U-shaped r’ship between freq of price change and concentration

- Hump-shaped r’ship between size of price change and concentration


3. Heterogeneity in market concentrationyyl

1

2

3

4

5

Effe

ctiv

e nu

mbe

r of

firm

s

2001 2003 2005 2007 2009 2011

MS AL MD NJ

A. Across−state Within−Mayonnaise

1

2

3

4

5

2001 2003 2005 2007 2009 2011

Mustketc Peanbutr Cigets Mayo

B. Across−product Within−New Jersey

- Effective number of firms = Inverse Herfindahl Index

✓ Variation across states, within product categories

✓ Variation across product categories, within states

See: Bronnenburg Dhar Dube (JPE ‘09), Bronnenburg Dube Gentzkow (AER ‘12)

Robust - Revenue share of top firm Fig. Cross/within region variation in (i) frequency, (ii) size of price changes


3. Regressionyl

Across-state w/in product Across-product w/in stateSize (%) Frequency Size (%) Frequency

Eff. number of firms 0.244*** -0.912*** 0.201*** -0.900***(0.037) (0.161) (0.043) (0.181)

Eff. number of firms2 -0.048*** 0.171*** -0.038*** 0.228***(0.010) (0.043) (0.012) (0.072)

Observations 32,016 32,016 32,016 32,016R-squared 0.100 0.106 0.036 0.031Revpst control ✓ ✓ ✓ ✓

- Standard errors clustered at State × Product level

Result

- Hump-shaped profiles of price flexibility by market concentration

- Robust to either specification

Estimating equations Unweighted Number of goods weighted No rev. control Revenue share


3. Average predicted values: Across-state w/in productyl

0.08

0.10

0.12

0.14

0.16

0.18

0.20

1 2 3 4 5 6 7 8 9 10 11 12Effective number of firms

A. Frequency of price change

0.09

0.10

0.11

0.12

1 2 3 4 5 6 7 8 9 10 11 12Effective number of firms

B. Size of price change

Note Solid lines plot the revenue weighted mean of predicted (A.) frequency (B) size of price change from across-state within-product

regression. Means are computed within Effective number of firms bins of width one. Dashed lines give 25th/75th percentiles.

Model has a causal interpretation of correlations in the data

- Oligopoly forces strong at a small handful of firms, then weaken

- Market structure important for understanding price flexibility



Extension - Endogenous entryyl

Resolve two issues

- Data Many small firms with high turnover- Theory Threat of entry may affect pricing: ↑ M , ↑ π

- Kokovin Parenti Thisee Zhelobodko (2015)



Resolve two issues



1. Preferences

C =

[

γ1η

[

(z1c1)η−1

η + (z2c2)η−1

η

]

+ (1− γ)1η Cf

η−1η

] ηη−1



Resolve two issues



1. Preferences

C =

[

γ1η

[

(z1c1)η−1

η + (z2c2)η−1

η

]

+ (1− γ)1η Cf

η−1η

] ηη−1

2. Endogenous measure δ of atomistic, one-period firms k ∈ [0, δ]

Cf =

[∫ δ

0cfk

ρ−1ρ dk

] ρρ−1

, p∗fk =ρ

ρ − 1M , Pf = δ

− 1ρ−1

ρ

ρ − 1M



Resolve two issues



1. Preferences

C =

[

γ1η

[

(z1c1)η−1

η + (z2c2)η−1

η

]

+ (1− γ)1η Cf

η−1η

] ηη−1

2. Endogenous measure δ of atomistic, one-period firms k ∈ [0, δ]

Cf =

[∫ δ

0cfk

ρ−1ρ dk

] ρρ−1

, p∗fk =ρ

ρ − 1M , Pf = δ

− 1ρ−1

ρ

ρ − 1M

3. Free-entry determines size of fringe πf(

p1, p2, z1, z2,M , δ)

− φ = 0


Extension - Exchange-rate pass-throughyl

Question in trade literature

- Question Euro devalues 10c , BMW reduces US prices by 2.5c?

- Answer BMW competes with Ford, Ford unaffected by shock






- Literature 1 Static oligopoly + Flexible prices + CES- Atkeson-Burstein, Pennings







- Literature 2 Dynamic mono. comp. + Nominal rigidities + Kimball- Itskhoki-Gopinath, Itskhoki-Mukhin, Berger-Vavra








1. Preferences

C =[

ωh

1σ (zhch)

σ−1σ + (1− ωh)

1σ (zf cf )

σ−1σ

] σσ−1








1. Preferences

C =[

ωh

1σ (zhch)

σ−1σ + (1− ωh)

1σ (zf cf )

σ−1σ

] σσ−1

2. Marginal cost

mci =W 1−αi (W ∗)αi

z+ E = log

(W

W ∗

)

→ mci =W

exp (αiE )


Data - Markets are highly concentratedyyl

- Market 31 IRI product cat. (p) × 46 states (s) × 132 months (t)

- Firm First 6 digits of barcode (within a product category)

- Example In the market for Mayonnaise in Ohio, 2005:Q1, of 14 firms,Hellmann’s had a 45% revenue share

- Example Herfindahl index of 0.43, Inverse herfindahl index of 2.3

0.00

0.05

0.10

0.15

0.20

Fra

ctio

n of

mar

kets

0 20 40 60 80 100Median = 41

A. Number of firms

0.00

0.05

0.10

0.15

0.20

1 2 3 4 5 6 7 8 9 10Median = 3.70

B. Effective number of firms

0.00

0.05

0.10

0.15

0.20

0.0 0.2 0.4 0.6 0.8 1.0Median = 0.66

B. Two firm revenue share

Back - Introduction Comparison to 6 digit NAICS


Market structure and monetary non-neutralityyl

Results

- Consumption fluctuations are 2.5 times as large

- Cumulative response of output is 2.4 times as large

Back - Calibration


Literatureyyl

1. Monopolistic competition, menu-costsMonetary Golosov Lucas (2007), Nakamura Steinsson (2010), Midrigan (2011), Vavra (2014)

Alvarez et al. (2016 ×5), Klenow Willis (2016), Burstein Hellwig (2007)

Inter’l Itskhoki Gopinath (2010), Itskhoki Mukhin (2016), Berger Vavra (2016)

New - Dynamic oligopoly

2. Oligopoly, flexible pricesTrade Atkeson Burstein (2008), Edmond Midrigan Xu (2015), Pennings (2015)

IO Hottman Redding Weinstein (2016)

New - Nominal rigidity

3. Dynamic oligopoly, nominal rigidityMaskin-Tirole ‘88, Jun Vives ‘04, Einav Somaini ‘13, Nakamura Zerom ‘10, Neiman ‘11

New - Equilibrium macroeconomic model

Back - Approach


Householdy

W(S ,B) = max{cij},N,{B(S ′)}

logC −N + βE

[

W(S ′,B(S ′)

) ]

where C =

[∫ 1

0C

θ−1θ

j dj

] 1−θθ

, θ > 1

Cj =

[

c1j1−η

η + c2j1−η

η

] ηη−1

, η > θ

subject to a nominal budget constraint

∫ 1

0

[

p1jc1j + p2jc2j

]

dj

︸︷︷︸

=M(S)

+∑S ′

Q(S , S ′)B(S ′) ≤ B(S) +W (S)N + Π(S)

Back - Household preferences


Menu cost comparative staticsyl


Calibration - Identificationyyl

Increasing ξ

- Costly to adjust. Adjust less often. Widen bounds.

- ↑ Size, ↓ Frequency

Increasing σz

(i) Given bounds. Hit bounds more often. ↑ Frequency

(ii) Hit bounds more often → Widen bounds ↑ Size

Increasing η

- Increase average markup

Back - Calibration strategy


Menu cost comparative staticsyl

0.15 0.2 0.25 0.3 0.350.05

0.1

0.15

0.2

0.25A. High µ - Frequency

0.15 0.2 0.25 0.3 0.350.05

0.1

0.15

0.2

0.25B. Low µ - Frequency

0.15 0.2 0.25 0.3 0.35Menu cost ξ

-0.12

-0.1

-0.08

-0.06C. High µ - Size

DuopolyMonopolistic competition

0.15 0.2 0.25 0.3 0.35Menu cost ξ

0.06

0.08

0.1

0.12D. Low µ - Size


Benchmarking models - Robustnessyl

(A) For each η, choose ξ and σz to match the data.

(B) Lower ↓ η → Profits less sensitive to prices → Require lower ↓ ξ

(C) Can match E [µit ] = 1.30 from duopoly model with η∗ = 4.5

(D) Result When ξ and σz are recalibrated σ(Ct) is unaffectedBack - Calibration strategy


Recursive equilibrium - Computationyl

Krussel-Smith

- Conjecture price function for µ(S)

log µ(S)− log µ = αg (log g(S)− log g) + αµ (log µ(S−1)− log µ)

- Reduces aggregate state to S = (µ−1, g)

MPE policy functions

- Approximate expected value function V e (µ1, µ2, µ,g)

V e (µ1,µ2, µ,g) =∫

V

(µ1

e ε′1+g ′(g ,ε′g ),

µ2

e ε′2+g ′(g ,ε′g ),µ,g ′(g , ε′g )

)

dF (ε′1, ε′2, ε′g )

- Cubic splines in µ1, µ2. Linear splines in µ, g

- Guess initial pricing policies µ(0)′−i (µi , µ−i ,S) and γ

(0)′−i (µi , µ−i ,S)

- Given competitor policies, use collocation algorithm to solve for value functions

- Determines new µ(1)′−i (µi ,µ−i ) and γ

(1)′−i (µi ,µ−i )

- Continue, until µ(k+1)′−i = µ

(k)′−i and γ

(k+1)′−i = γ

(k)′−i

Back - Recursive equilibrium


Profit function propertiesyl

1 1.1 1.2 1.3 1.40

0.05

0.1

A. Profit function π(µ1,µ2)

µ2 = 1.3µ2 = 1.2µ2 = 1.1

1 1.1 1.2 1.3 1.4

Mark-up µ1

1

1.2

1.4B. Static best response µ∗

2(µ1)

η = 14η = 10.5η = 6

1 1.1 1.2 1.3 1.4

Mark-up µ1

-40

-20

0

20C. Second derivative π11(µ1,µ2)

µ2 = 1.3µ2 = 1.2µ2 = 1.1

1 1.1 1.2 1.3 1.4

Mark-up µ1

-5

0

5

10D. Cross-partial derivative π12(µ1,µ2)

µ2 = 1.3µ2 = 1.2µ2 = 1.1

- Panel B - Best response slope between 0 and 1- More elastic demand ↑ η → (i) ↓ µ∗, (ii) ↑ slope

Back - Strategic complementarities


Calibration and resultsyyl

Duopoly Monopolistic

Base

A. Parameter

Within-sector elasticity of demand η 10.5 4.5Upper bound of menu cost distribution ξ ∼ U[0, ξ] 0.17 0.21Size of shocks (percent) σz 3.8 4.0

B. Moments

Markup E [µit ] 1.30 1.30Frequency of price change E [1{pit 6= pit−1}] 0.13 0.13Log absolute price change, cond. on price change E [| log(pit/pit−1)|] 0.10 0.10

C. Results

Std. deviation consumption (percent) σ (logCt) 0.31 0.13Average markup minus frictionless markup E [µit ]− µ∗ 0.10 0.02

I Parameters same as estimated duopoly model

II Same ηm = ηd re-calibrated ξm , σz,m

III Both models have flexible price markup of 1.20

Back - CalibrationSimon Mongey, ”Market structure and monetary non-neutrality” p.21/21

Robustness to target E [µit ]yl

Back - Calibration


Profit function propertiesyl

1 1.1 1.2 1.3 1.40

0.05

0.1

A. Profit function π(µ1,µ2)

µ2 = 1.3µ2 = 1.2µ2 = 1.1

1 1.1 1.2 1.3 1.4

Mark-up µ1

1

1.2

1.4B. Static best response µ∗

2(µ1)

η = 14η = 10.5η = 6

1 1.1 1.2 1.3 1.4

Mark-up µ1

-40

-20

0

20C. Second derivative π11(µ1,µ2)

µ2 = 1.3µ2 = 1.2µ2 = 1.1

1 1.1 1.2 1.3 1.4

Mark-up µ1

-5

0

5

10D. Cross-partial derivative π12(µ1,µ2)

µ2 = 1.3µ2 = 1.2µ2 = 1.1

- Strategic complementarity driven by π12 > 0

- Weird property of CES demand functions - Panel D- As markups increase, π12 falls, then becomes negative

Back - Markups ad Values


Duopoly - ↑ Myl

Intensive margin

- Optimal adjustment ∆pL = µ∗L/µL increases by more than ∆M

Extensive margin

- Larger increase in γH relative to similar MC firm

Back - Duopoly simulation


Decomposing revenue changes at large firmsyl

0.0

0.5

1.0

1.5

2.0

Firm

sha

re in

mar

ket (

1)

0.0 0.5 1.0 1.5 2.0Market share in State (2)

0.0

0.5

1.0

1.5

2.0

Firm

sha

re in

mar

ket (

1)

0.0 0.5 1.0 1.5 2.0State expenditure (3)

For each state s, product category p, decompose time-series variance in ∆ log ripst

var (∆log ripst ) = var

(

∆log

(ripst

rpst

))

︸︷︷︸

(1) Firm share in market

+ var

(

∆log

(rpst

rst

))

︸︷︷︸

(2) Market share in state

+ var (∆log rst )

︸︷︷︸

(3) State expenditure

+Covariances

Back - Calibration strategy


Relation to Kimball-style strategic complementarity yl

- Duopoly demand function super-elasticity ε ∈ [0.3, 0.7]

- Literature Klenow Willis - ε = 10, Gopinath Itskhoki - ε = 4

Back - Additional results Back - Example µ policies


Empirical - Data detailsyl

- IRI data

- An observation is at the UPC × Category × Store level

- Stores: 2,000, Years: 2001-2012, Categories: 31

- e.g. Mayonnaise, 2001. Firms: 72, UPCs: 402

- Observations removed

- Absolute size of price change greater than 99th percentile

- Data missing at t − 1

- Regular price changes

- Price change set to zero ∆ log pict = 0

- Possible measurement error: ∆| log pict | < 0.001

- Promotional flag Promoict = 1

- Items coming off promotion Promoict−1 = 1 & Promoict = 0

- Statistics

- All statistics computed monthly for each product category c

- Data is weekly, statistics reported monthly using week three of each month

- e.g. Frequency freqct is fraction of c goods changing price at t

freqct = ∑i∈c

1 [d log pict 6= 0] /Nct

Back - Empirical - Size of price changes Back - Regression specification Back - Calibration


Comparison to Census Manufacturingyyl

- Data National NAICS 6-digit revenue share of 4 largest firms

✓ Few industries are national, e.g. Manufacturing

✗ Most industries are local, e.g. Health care

0.00

0.05

0.10

0.15

0.20

Fra

ctio

n

0.0 0.2 0.4 0.6 0.8 1.0Revenue share of top 4 firms

A. Manufacturing

0.00

0.10

0.20

0.30

0.40

0.50

0.0 0.2 0.4 0.6 0.8 1.0Revenue share of top 4 firms

B. Health care / Social assistance

Source: 2007 Economic Census, 6−digit NAICS classification, national level

Back - Inverse herfindahl


Empirical - Distribution of price changesyl

0.00

0.02

0.04

0.06

0.08

0.10

Fra

ctio

n

−0.20 −0.15 −0.10 −0.05 0.00 0.05 0.10 0.15 0.20Log price change

Regular price changesAll price changes

− Regular price changes: Mean = .0396, Std dev. = .087, Skew = 1.673, Kurtosis = 11.149− All price changes: Mean = .0005, Std. dev. = .256, Skew = −.108, Kurtosis = 3.418

Regular price changes (Mayonnaise, 2005)

Back - Empirical - Size of price changes


3. Variation in market concentration - Share top firmyyl

.3

.4

.5

.6

.7

.8

Rev

enue

sha

re o

f lar

gest

firm

2001 2003 2005 2007 2009 2011

MS AL MD NJ

A. Across−state Within−Mayonnaise

.3

.4

.5

.6

.7

.8

2001 2003 2005 2007 2009 2011

Mustketc Peanbutr Cigets Mayo

B. Across−product Within−New Jersey

✗ Little time-series variation

✓ Variation across states, within product categories

✓ Variation across product categories, within states

Back - Variation in concentration


3. Variation in price flexibilityyyl

0.00

0.05

0.10

0.15

Fra

ctio

n of

mar

kets

0.00 0.10 0.20 0.30 0.40Freq_pst

1A. Frequency of price change

0.00

0.05

0.10

0.15

0.20

0 20 40 60 80 100100 x |Freq_pst−Freq_pt|/Freq_pt

1B. Variation across−s within−pt

0.00

0.05

0.10

0.15

0.20

0 20 40 60 80 100100 x |Freq_pst−Freq_st|/Freq_st

1C. Variation across−p within−st

0.00

0.05

0.10

0.15

Fra

ctio

n of

mar

kets

0.00 0.05 0.10 0.15 0.20 0.25Size_pst

2A. Average abs. size of price change

0.00

0.05

0.10

0.15

0.20

0 20 40 60 80 100100 x |Size_pst−Size_pt|/Size_pt

2B. Variation across−s within−pt

0.00

0.05

0.10

0.15

0.20

0 20 40 60 80 100100 x |Size_pst−Size_st|/Size_st

2C. Variation across−p within−st

Back - Variation in concentration


Varying nominal rigidity in a Calvo rigidity α yyl

- DC and MC models converge as α → 1



Distribution of price gaps [solid] and changes [dotted] yyl

- MC - Random ξ model is between Golosov-Lucas and Midrigan

- DC - Left skewness due to lower price flexibility at low µ firms



Regression - Estimating equationsyl

Across-state, within-product

- Remove quarter t mean for each product category, taken across states

(

ypst − y spt

)

= αt + β1

(

xpst − x spt

)

+ β2

(

xpst − x spt

)2+ εpst

Across-product, within-state

- Remove quarter t mean for each state, taken across product categories

(

ypst − ypst

)

= αt + β1

(

xpst − xpst

)

+ β2

(

xpst − xpst

)2+ εpst

Additional details

- ypst - Size and frequency of price change

- xpst - Measures of market concentration

- Standard errors clustered at State×Product levelBack - Main regression Data details


Regression results - Uniformly weightedyl



Eff. number of firms2 -0.018*** 0.014 -0.017 0.099(0.004) (0.017) (0.014) (0.070)

Observations 32,016 32,016 32,016 32,016R-squared 0.061 0.078 0.009 0.016Quarter FE ✓ ✓ ✓ ✓Revpst control ✓ ✓ ✓ ✓


Result


- Robust to either source of variation

Back - Main regression


Regression results - Number of goods weightedyl



Eff. number of firms2 -0.024*** 0.026 -0.030** 0.177**(0.007) (0.031) (0.015) (0.074)



Result





Regression results - No revenue controlyl



Eff. number of firms2 -0.048*** 0.183*** -0.041*** 0.227***(0.010) (0.050) (0.012) (0.072)

Observations 32,016 32,016 32,016 32,016R-squared 0.100 0.095 0.028 0.031Quarter FE ✓ ✓ ✓ ✓Revpst control ✗ ✗ ✗ ✗


Result





Regression results - Rev. share top firmyl


Rev. share top firm -1.411*** 7.727*** -1.436*** 6.099***(0.428) (2.015) (0.392) (2.286)

Rev. share top firm2 -9.739*** 16.939** -3.546 13.318(1.964) (7.817) (3.126) (17.419)



Result





Static Nash - Varying ω1yl

0 0.25 0.5 0.75 1

Preference weight - ω1

ηη−1=1.1

1.5

2.0

2.5

θθ−1=3.0

A. Firm 1 mark-up

Equal sized duopoly: (0.5, 1.2)

1.2 = 0.5(σ+η)0.5(σ+η)−1

0 0.25 0.5 0.75 1

Preference weight - ω1

0

0.20

0.40

0.60

0.80

1.00B. Firm 1 revenue share

Equal sized duopoly: (0.5,0.5)

Preferences

C =

[∫ 1

0C

θ−1θ

j dj

] θθ−1

Cj =

[

ω1c

η−1η

1j + (1− ω1)cη−1

η

2j

] ηη−1

- As ω1 → 1, µ1 converges to monopolistically comp. markup under θ

- As ω1 → 0, µ1 converges to monopolistically comp. markup under ηBack - Nested models


mongey market structure slides - simon mongey - home

Documents