Estimating Unequal Gains across U.S. Consumers with Supplier Trade Data Colin Hottman Ryan Monarch Board of Governors of the Federal Reserve System

November 2017

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Any opinions and conclusions expressed herein are those of the authors and do not necessarily represent the views of the U.S. Census Bureau, the Federal Reserve Board, or anyone affiliated with the Federal Reserve System. All results have been reviewed to ensure that no confidential information is disclosed.

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How has the cost of living in the United States been affected by changes in import prices over the past 20 years? How have these import price changes affected different income groups in the United States?

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How has the cost of living in the United States been affected by changes in import prices over the past 20 years? How have these import price changes affected different income groups in the United States? I

I

Matters for debate over effects of globalization on U.S. consumers/workers Implications for evolution of real income inequality

Important for policymakers to understand which economic channels drive import price changes: I I I I

Marginal cost changes Markup adjustment Product quality changes Expansion (or contraction) in the set of available varieties

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This Paper

On the theory side, we develop a new framework based on non-homothetic preferences known as the S-branch utility tree: I

Each of the four channels are flexibly allowed to contribute to changes in the price index

I

The model captures non-homotheticity both across and within sectors, while retaining exact linear aggregation (Gorman polar form) over consumers, even with variety entry and exit

I

Our framework nests the standard, homothetic, CES monopolistic competition model as special case

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This Paper

On the estimation side, we extend the GMM estimator of Feenstra (1994) to our framework, relying on the relationship between income elasticities and price elasticities to compute variety-specific demand parameters. On the data side, we apply our approach to 2 sets of U.S. data from 1998-2014 I

I

Use foreign supplier-product level prices and sales covering the universe of U.S. goods imports to define a variety. Use expenditure shares by income decile to calculate income group specific import price indices.

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Preview of today’s results: Figure: Number of Imported Varieties 3,200,000

3,000,000

2,800,000

2,600,000

2,400,000

2,200,000

2,000,000 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 Hottman and Monarch (FRB)

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Preview of today’s results: I

Markups fell from 1998-2006, but have remained flat since then: Table: Median Markup Over Time (Sales-Weighted)

I

Year 1998 2002 2006 2010 2014 Continuers 1.234 1.174 1.134 1.130 1.132 We find a U-shaped pattern for import prices from 1998-2014: Table: Aggregate Import Price Index, 1998-2014 Year

I

1998 2002 2006 2010 2014 100.0 84.9 88.4 99.6 107.8 Lowest income households experienced the most import price inflation, while the highest income households experienced the least: Table: Income-Specific Import Price Inflation (a.r.), 1998-2014 1st Decile 1.33

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Median Income 1.24

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9th Decile 0.90 7/ 45

Literature Computing Import Price Indices using Homothetic Preferences: Feenstra 1994, Broda and Weinstein 2006, Amiti et al. 2016, Hsieh et al. 2016, Feenstra and Weinstein 2017 Importance of Non-homothetic Preferences: Hunter 1991, Neary 2004, Choi et al. 2009, Fajgelbaum et al. 2011, Fieler 2011, Handbury 2013, Markusen 2013, Caron et al. 2014, Faber 2014, Simonovska 2015, Fajgelbaum and Khandelwal 2016, Jaravel 2016, Atkin et al. 2017, Borusyak and Jaravel 2017, Cravino and Levchenko 2017, Faber and Fally 2017 Theory papers on how Price Elasticities Vary with Sales: Dhingra and Morrow 2013, Zhelobodko et al. 2012, Bertoletti and Epifani 2014, Arkolakis et al. 2015, Mr´azov´a and Neary 2013 Empirical papers on Markup Adjustments from Import Competition: Levinsohn 1993, Harrison 1994, Konings and Vandenbussche 2005, Chen et al. 2009, De Loecker et al. 2014, De Loecker et al. 2015 Hottman and Monarch (FRB)

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Outline: Theory Estimation Results

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Household Preferences (S-branch utility tree) Household h has standard CES preferences over sectors s: σ X σ σ+1 σ+1 σ+1 Vht = [ ϕhst Qhst ] σ

(1)

s∈S

Consumption in sector s is: Qhst = [

X

σs s

σs

σ +1 ϕvt (qhvt − αv ) σs +1 ]

σ s +1 σs

(2)

v ∈Gs

where supplier-product varieties are indexed by v . These are Generalized CES preferences over varieties (αv can be positive, zero, or negative).

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Variety-Level Demand by Household For given Yhst , utility maximizing quantity of variety v in sector s is:    −σs −1 σs  X pvt ϕvt  qhvt = αv + Yhst − αj pjt  , (3) −σ s Pst j∈G s

−

 Pst

= 

X

1 σs

s s pjt−σ ϕjt σ 

(4)

j∈Gs

Note: I

If there is a variety that does not have a positive quantity at all measured time periods (a non-continuer), then we require αv ≤ 0. F

One interpretation of αv is the deviation from the CES benchmark quantity demanded.

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Optimal Sectoral Expenditure by Household

Substitute (3) into (2), and that into the CES cross-sector aggregator (1). Maximizing this (Brown and Heien 1972) gives utility maximizing sector expenditure:

Yhst

  X XX ϕσhst Pst −σ + Yht − =P αv pvt α p v vt σ −σ j∈S ϕhjt Pjt s∈S v ∈Gs

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v ∈Gs

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Non-Homotheticity The share of sectoral expenditure spent on a variety v varies with sectoral expenditure (within sector): ! P  s s Yhst − j∈Gs αj pjt pvt −σ ϕσvt αv pvt + P shvt = −σ s σs Yhst Yhst j∈Gs pjt ϕjt The share of total expenditure spent on a sector s varies with total expenditure (across sector): ! P P P  −σ ϕ σ α p Yht − s∈S v ∈Gs αv pvt P v vt st hst v ∈Gs Shst = + P −σ ϕσ Yht Yht j∈S Pjt hjt

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Household Indirect Utility

Some algebra (Blackorby, Primont, and Russell 1978) gives the following indirect utility function: !1

σ

Vht =

X

ϕσhst Pst −σ

(Yht −

XX

αv pvt ),

(6)

s∈S v ∈Gs

s∈S

and the expenditure function: !− 1

σ

Yht = Vht

X

ϕσhst Pst −σ

s∈S

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αv pvt .

(7)

s∈S v ∈Gs

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Household Import Price Indices

Thus for a reference utility level Vhk , the import price index at t is: !− 1

σ

Pht = Vhk

X

ϕσhst Pst −σ

s∈S

+

XX

αv pvt ,

(8)

s∈S v ∈Gs

and the change in import prices from t to t + i is:
1 P P P σ −σ − σ + Vhk ϕ P Pht+i st+i s∈S hst+i s∈S v ∈Gs αv pvt+i = (9) −1
P P P Pht σ P −σ σ + Vhk ϕ α p st v vt s∈S hst s∈S v ∈Gs

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Household Import Price Indices Using the expenditure function to substitute in for the reference utility level Vhk , we can re-write the import price index as: P P P −1   Yhk − s∈S v ∈Gs αv pvt [ s∈S ϕhst+i σ Pst+i −σ ] σ Pht+i = + P −1 Pht Yhk [ s∈S ϕhst σ Pst −σ ] σ P P  s∈S v ∈Gs αv pvt+i Yhk

Thus, households of different incomes will experience different import price inflation rates if either ∃(αv 6= 0) or the ϕhst differ with income

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Aggregate Market Demand Under simple parameter restrictions, exact linear aggregation over P consumers (Gorman polar form) is preserved: qvt = h qhvt In aggregate (over nt households):  qvt

= (αv nt ) +

s s pvt −σ −1 ϕσvt s Pst−σ







Yst −

X

(αj nt )pjt  ,

j∈Gs

 X XX ϕσst Pst −σ Yt − P (αv nt )pvt , (αv nt )pvt  + σ −σ j∈S ϕjt Pjt 

Yst

=

v ∈Gs

s∈S v ∈Gs

Pt+i Pt

=

ϕσst+i Pst+i

P

Vk

s∈S

Vk

Hottman and Monarch (FRB)

P

s∈S


1 −σ −

ϕσst Pst −σ

σ

P

+ s∈S v ∈Gs (αv nt )pvt+i P P + s∈S v ∈Gs (αv nt )pvt

σ


−1

P

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Producer Behavior Next consider each monopolistically competitive producer. The price elasticity of demand for a particular producer is:   ∂qvt pvt qvt − αv nt εvt ≡ − = (σ s + 1) ∂pvt qvt qvt

(10)

oligopoly

Income elasticity of demand: Y qvt − αv nt ∂qvt Yst P st =( )( ) ∂Yst qvt Yst − j∈Gs (αj nt )pjt qvt Producers set prices as a markup over marginal cost: εvt ωs pvt = · δvt (1 + ωs ) qvt {z } εvt − 1 |

(11)

(12)

MCvt

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Markups Note that differentiating the markup term with respect to quantity gives the following:   ∂ εvtεvt−1 − (αv nt ) (σ s + 1) = ∂qvt [(qvt − αv nt ) (σ s + 1) − qvt ]2 The markup is increasing in quantity if αv < 0. In most models, trade opening exposes producers to competition, and reduced market shares lead to reduced markups: “pro-competitive” effects of trade. In our model, we can test how common it is for markups to be decreasing in quantity (αv > 0). Markup term

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Outline: Theory Estimation Results

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Estimation We can estimate the parameters of this model in two stages I

No need for assumptions about the distribution of firm productivity or a full general equilibrium framework.

First, we estimate the parameters of the variety demand functions at the aggregate market level by extending the GMM estimator of Feenstra (1994) and applying it to supplier data. Second, we estimate the parameters of the sectoral demand functions at the household level using additional data from the BLS Consumer Expenditure Survey and an instrumental variables strategy.

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Estimation Stage One Start with market demand for variety v , pvt (qvt − αv nt ). Log, time difference, and difference rel. to variety k in same sector:   ∆k,t ln (pvt (qvt − αv nt )) = −σ s ∆k,t ln pvt + (−σ s ) ∆t ln ϕkt − ∆t ln ϕvt | {z } νvt

Do the same for the price term from the supply side:   ωs 1 εvt k,t k,t k,t ∆ ln pvt = s ∆ ln (pvt qvt ) + s ∆ ln + κvt ω +1 ω +1 εvt − 1 κvt =

1 ∆k,t ln δvt 1 + ωs

Assumption: Conditional on our double-differencing (i.e. fixed effects), the within-demand error νvt is orthogonal to the within-supply error κvt . Hottman and Monarch (FRB)

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αv =

  βsC min (qvt ) t

 βsE

min (qvt )

,

β~s = {βsC , βsE , σ s , ω s }

t

  Orthogonality condition for v : G β~s = E [vvt κvt ] = 0 which can be rewritten as:  2  h i ωs k,t = s E ∆ ln pvt E ∆k,t ln (pvt qvt ) ∆k,t ln pvt ω +1 h i 1 − s E ∆k,t ln [pvt (qvt − αv nt )] ∆k,t ln pvt σ h i ωs k,t k,t + s E ∆ ln [p (q − α n )] ∆ ln (p q ) vt vt v t vt vt (ω + 1) σ s     εvt 1 k,t k,t + s E ∆ ln ∆ ln pvt ω +1 εvt − 1     1 εvt k,t k,t + s E ∆ ln ∆ ln [pvt (qvt − αv nt )] (ω + 1) σ s εvt − 1 Hottman and Monarch (FRB)

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αv =

  βsC min (qvt ) t

 βsE

min (qvt )

,

β~s = {βsC , βsE , σ s , ω s }

t

  Orthogonality condition for v : G β~s = E [vvt κvt ] = 0 which can be rewritten as:  2  h i ωs k,t = s E ∆ ln pvt E ∆k,t ln (pvt qvt ) ∆k,t ln pvt ω +1 h i 1 − s E ∆k,t ln [pvt (qvt − αv nt )] ∆k,t ln pvt σ h i ωs k,t k,t + s E ∆ ln [p (q − α n )] ∆ ln (p q ) vt vt v t vt vt (ω + 1) σ s     εvt 1 k,t k,t + s E ∆ ln ∆ ln pvt ω +1 εvt − 1     1 εvt k,t k,t + s E ∆ ln ∆ ln [pvt (qvt − αv nt )] (ω + 1) σ s εvt − 1 Hottman and Monarch (FRB)

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Estimation Stage One Stack these and form the objective function for each sector, that can be solved via GMM:    0 βbs = arg min{G ∗ β~s WG ∗ β~s } ~s β

for a weighting matrix W (as in Broda and Weinstein 2006) and G ∗ as the sample counterpart to G , stacked over v . Identification is achieved because of heteroskedasticity: if the variance and covariance of prices and sales are not the same across varieties, pooling observations across varieties allows us to identify the common parameter values. ϕvt

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Estimation Stage Two Estimating equation (pooled across Household-Sector-Time observations): X ∆k,t ln(Yhst − αv nt pvt ) = −σ∆k,t ln(Pst ) + υhst v ∈Gs

Instrument for ∆k,t lnPst as in Hottman, Redding, and Weinstein (2016), using: S

k,t

−∆

pvt −σ 1 1 X ( ϕvt ) ) ln( σ S Nstv S p^ vt v ∈Gst ( ϕ )−σ vt

The instrument is the change in dispersion in quality-adjusted variety-level prices within a sector ϕhst Hottman and Monarch (FRB)

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Data (1): Longitudinal Firm Trade Transactions Database U.S. import data at the supplier level, studied and cleaned in Kamal and Monarch (2016) Around 1000 HS4 sectors (over 95 percent of U.S. goods imports) Nearly 40 million unique suppliers (HS10-exporter pairs) exporting to the U.S. from 1998-2014. Each transaction contains (a) Unique exporter identifier (known as Manuf. ID). (b) Value and quantity (and thus “unit value”) (c) HS 10 industry code.

Example: QUAN KAO COMPANY 1234 BEIJING LANE BEIJING, CHINA 100044 Hottman and Monarch (FRB)

CNQUAKAO1234BEI

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Data (2): Consumer Expenditure Survey

To get sector expenditure by income decile (Yhst ): 1

2

3

Use the Consumer Expenditure Survey and Census income data to obtain product-expenditure in every year for every decile. Concord the CE categories to HS4 codes (Furman, Russ, and Shambaugh 2017). Apply the import share in domestic absorption to create decile-specific imported expenditure in each HS4 category.

This leaves us with 228 HS4 sectors (about 55 percent of U.S. goods imports).

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Outline: Theory Estimation Results

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Results Figure: Number of Imported Varieties 3,200,000

3,000,000

2,800,000

2,600,000

2,400,000

2,200,000

2,000,000 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 Hottman and Monarch (FRB)

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Table: Summary of (σ s + 1)

 10% 3.06

Median 4.93

90% 8.59

εvt =

qvt − αv nt qvt



(σ s + 1)

Table: Summary of ωs

10% 0.16

Median 0.44

90% 1.59

ωs MCvt = δvt (1 + ωs ) qvt

Table: Estimates of (σ + 1)

OLS estimate 0.82 Hottman and Monarch (FRB)

IV estimate 2.78 Estimating Unequal Gains

95% C.I. (2.60 - 2.97) 31/ 45

αv = (1C βsC + 1S βsE ) · mint (qvt ) Table: Summary of βsC (Continuers)

10% 9.96 × E-5 %>0 91

Median 0.33

90% 0.39

% Significant at 95% Level 85

Table: Summary of βsE (Non-Continuers)

10% -5.97 × E-5

Median -2.55 × E-9

90% -1.08 × E-10

Markups are often decreasing in quantity sold (αv > 0). Most small firms (βsE ) behave close to CES, while the largest (βsC ) are demonstrably not CES. Hottman and Monarch (FRB)

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Estimated Markups Table: Markup Variation across HS4 Sectors ( εvtεvt−1 )

Average

10.00% 1.132

Median 1.250

90.00% 1.482

Table: Median Markup Over Time (Sales-Weighted)

Year Markup Markup- Continuers

1998 1.235 1.234

2002 1.226 1.174

2006 1.215 1.134

2010 1.215 1.130

2014 1.215 1.132

Markups fell between 1998-2006, but have been flat since.

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Aggregate Import Price Index

Next, we construct the aggregate U.S. import price index using all 1000 HS4 categories:
1 P P P σ −σ − σ + Vk Pt+i s∈S ϕst+i Pst+i s∈S v ∈Gs αv nt pvt+i = −1
P P P Pt σ −σ σ + Vk s∈S ϕst Pst s∈S v ∈Gs αv nt pvt

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Figure: Aggregate Import Price Index: 1998-2014 1.10

1.05

1.00

0.95

0.90

0.85

0.80 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 Aggregate Import Price Index

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Figure: Aggregate and BLS: 1998-2006 1.25

Figure: Aggregate and BLS: 2006-2014 1.25

1.20

1.20

1.15 1.10

1.15

1.05

1.10

1.00 0.95

1.05

0.90

1.00

0.85 0.80

1998

1999

2000

2001

Aggregate Import Price Index

2002

2003

2004

2005

2006

BLS All-Commodity Import Price Index

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2006

2007

2008

2009

Aggregate Import Price Index

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2010

2011

2012

2013

2014

BLS All-Commodity Import Price Index 36/ 45

Figure: Aggregate Import Price Index Excluding Chinese Varieties 1.15 1.1 1.05 1 0.95 0.9 0.85 0.8 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 Import Price Index Hottman and Monarch (FRB)

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Figure: Aggregate Import Price Index Excluding New Varieties 1.15 1.1 1.05 1 0.95 0.9 0.85 0.8

1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 IPI

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Finally, we use the 228 consumer product HS4 categories and our non-homothetic preference structure to estimate different import price inflation for consumers of different incomes: P P P −1   Yhk − s∈S v ∈Gs αv pvt [ s∈S ϕσhst+i Pst+i −σ ] σ Pht+i = + P −1 Pht Yhk [ s∈S ϕσhst Pst −σ ] σ P P  s∈S v ∈Gs αv pvt+i Yhk

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Figure: Income-Group Specific Import Price Indexes 1.3 1.25 1.2 1.15 1.1 1.05 1 0.95 0.9 0.85 0.8 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 1st Income Decile Hottman and Monarch (FRB)

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9th Income Decile 40/ 45

Figure: Average Annual Import Price Inflation by Decile: 1998-2014 1.50 1.40 1.30 1.20 1.10 1.00 0.90 0.80 0.70 0.60 0.50 1

2

4

5

6

8

9

Income Decile's Import Price Inflation (A.R.) Hottman and Monarch (FRB)

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Figure: Core Import Prices

Figure: Non-Core Import Prices 1.9

1.15

1.8

1.1

1.7

1.05 1.6

1

1.5

0.95

1.4

0.9

1.3 1.2

0.85

1.1

0.8 1

0.75 1998

2000

2002

1st Income Decile

2004

2006

2008

Median Income Decile

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2012

2014

0.9 1998

2000

9th Income Decile Estimating Unequal Gains

2002

1st Income Decile

2004

2006

2008

Median Income Decile

2010

2012

2014

9th Income Decile 42/ 45

Figure: Decile-Specific σh 1.3

Table: Estimates

1.25 1.2

Decile 1 2 4 5 6 8 9 Avg.

1.15 1.1 1.05 1 0.95 0.9 0.85

(σh +1) 3.26 3.11 3.02 3.18 2.49 2.66 1.93 2.81

0.8 1998

2000

2002

1st Income Decile Hottman and Monarch (FRB)

2004

2006

2008

Median Income Decile

2010

2012

2014

9th Income Decile

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Figure: Closer to Cobb-Douglas: (σ + 1) = 1.3 2.5 2.3 2.1 1.9 1.7 1.5 1.3 1.1 0.9 0.7 0.5 1998

1999

2000

2001

2002

2003

1st Income Decile Hottman and Monarch (FRB)

2004

2005

2006

2007

2008

Median Income Decile Estimating Unequal Gains

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2010

2011

2012

2013

2014

9th Income Decile 44/ 45

Conclusion

We develop a non-homothetic framework and estimate it using consumer expenditure and customs-level trade data. Our results: I I

I

I

A U-shaped pattern for aggregate U.S. import prices from 1998-2014 This patterns corresponds with significant growth, and then eventual reversal in the number of imported varieties Foreign-supplier markups fell in the first half of the time period, and then remain about flat Highest income households experienced the least import price inflation

No evidence that the consumption channel has mitigated the distributional impacts of trade over the last two decades

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Appendix

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Variety-Level Demand in Aggregate  qvt

= αv nt +

s s pvt −σ −1 ϕσvt s Pst−σ



 Yst −

 X

αj nt pjt 

j∈Gs

Note: I

Non-symmetric substitution patterns (symmetry cited as a reason why CES overstates variety gains, e.g. Hausman 1997)

p ∂qvt pjt qvt − αv nt P jt =( )( )[σs (qjt − αj nt ) − αj nt ] ∂pjt qvt qvt Yst − j∈Gs αj nt pjt ∂qvt pkt 6= ∂pkt qvt I

If αv < 0, ∃ a finite reservation price at which variety v has zero demand =⇒ matters for gains from a newly available variety

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Oligopoly

If firms internalize their impact on the sector price index, the perceived price elasticity of demand becomes:  εvt =

qvt − αv nt qvt



[(σ s + 1) + (

αv nt pvt − σ s pvt (qvt − αv nt ) P )] Yst − j∈Gs αj nt pjt

Back

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Markups Using (10), the markup term can be written as: εvt (qvt − αv nt ) (σ s + 1) = εvt − 1 (qvt − αv nt ) (σ s + 1) − qvt

Note that markups vary across: I I I

Sectors Producers Time

We also nest the constant markup model (αv = 0). Back

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ϕvt

ϕvt = exp{

ln(pvt qvt − αv nt pvt ) − ln(pkt qkt^ − αk nt pkt ) + σ s (lnpvt − lnpf kt ) } s σ

Back

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ϕhst

ϕhst = exp{

ln(Yhst −

P

v ∈Gs

P αv nt pvt ) − ln(Yhkt − ^ v ∈Gk αv nt pvt ) σ

+

(lnPst − lnPf kt )} Back

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Back

Figure: Country-Product Combinations

Figure: Consumer Product Varieties

245,000

1,900,000

235,000

1,800,000 1,700,000

225,000

1,600,000 215,000

1,500,000

205,000

1,400,000 1,300,000

195,000

1,200,000 185,000

1,100,000

Estimating Unequal Gains

2014

2013

2012

2011

2010

2009

2008

2007

2006

2005

2004

2003

2002

2001

2000

1999

2014

2013

2012

2011

2010

2009

2008

2007

2006

2005

2004

2003

2002

2001

2000

1999

1998

Hottman and Monarch (FRB)

1998

1,000,000

175,000

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