Competitive Effects of Trade: Theory and MeasurementADEMU – Pierre Werner Chair Lecture

Marc J. Melitz

Harvard University

September 20, 2016

Starting Point: Selection and Competition Effects of TradeIn models with producer heterogeneity:

Trade induces many different reallocations across firms and products:

Selection effects (extensive margin):

Which products are sold where (across domestic and exportmarkets)Which firms survive; which firms export (and where)

But also competition effects (intensive margin):

Conditional on selection (same products sold in a given market) –trade affects the relative market shares of those products

These reallocations generate (endogenous) productivity changes that areindependent of “technology”This endogenous productivity response, in turn, contributes to theaggregate gains from trade

Handout p.1

OutlineFlexible theoretical framework to jointly capture selection andcompetition effects from trade

Eschew more parametrized versions that aggregate nicely but obscurespecific transmission channelsAllows for generality in terms of trade scenarios considered:Asymmetric liberalizationWith and without balanced trade and factor price adjustments... and adjustment path over time (short run versus long run)

In particular, will emphasize departures from CES preferencesbenchmark: Variable Elasticity of Substitution (VES) preferences

Not just for sake of generality!There is very strong (and mounting) empirical support for these“departures”Greatly sharpens predictions for impact of reallocations on aggregateproductivity−→ New channel for competitive (intensive margin) effects of trade

Handout p.2

Outline (Cont.)

Examine the link between trade, reallocations and productivityempirically

Use data on French multi-product firms to measure the reallocationseffects of trade within firms (across products)−→ Highlight strong evidence for competitive effects stemming fromVES preferences

Directly measure productivity response of French firms to tradeBottom line: Can explain 1% annual growth rate for Frenchmanufacturing from 1995-2005

Connect back productivity gains to overall welfare gains from trade(theoretically)

Handout p.3

VES Monopolistic Competition and Trade

Open economy version of Zhelodbodko et al (2012)... along with long – and growing – literature on trade models withendogenous markupsAdditively separable preferences (nests CES) but most results usingresidual demand curve can be extended to non-separable preferences

Handout p.4

VES Preferences and Demand

Demand for differentiated varieties xi is generated by Lc consumers whosolve:

maxxi≥0

∫u(xi )di s.t.

∫pixidi = 1

satisfying (A1) u(xi ) ≥ 0; u(0) = 0; u′(xi ) > 0; and u′′(xi ) < 0 for xi ≥ 0

(consumer expenditures on differentiated varieties normalized to 1)

This yields inverse demand (per consumer):

p(xi ;λ) =u′(xi )

λ, where λ =

∫ M

0u′(xi )xidi > 0

is the marginal utility of income (spent on differentiated varieties)ρ(xi ;λ) ≡ [u′(xi ) + u′′(xi )xi ] /λ is the associated marginal revenueLet εp(xi ) ≡ −u′′(xi )xi/u′(xi ) and ερ(xi ) ≡ −ρ′(xi )xi/ρ(xi ) denote theelasticities of inverse demand and marginal revenue (independent of λ)

Handout p.5

Firms and Production

Single factor of production: labor (wage normalized to 1)Firm productivity ϕ (output per worker); same overhead labor cost fFirms maximize profits

π(ϕ;λ) = maxxi≥0{Lc [p(xi )xi − xi/ϕ]− f }

−→ Maximized quantity x(ϕ;λ) solves ρ(x ;λ) = ϕ−1 (MR=MC)so long as (A2) εp(x) < 1 and (A3) ερ(x) > 0 (MR positive and decreasing)

This leads to standard markup pricing

p(ϕ;λ) =1

1− εp(x (ϕ;λ))ϕ−1

and firm size

q(ϕ;λ) = Lcx(ϕ;λ) and r(ϕ;λ) = p(ϕ;λ)q(ϕ;λ)

Assume monopolistic competition: Firms take λ as outside their control

Handout p.6

Firms and Production (Cont.)

λ is a key endogenous market-level variable capturing the extent ofcompetition for a given level of market demandAnalogous to the CES price indexIncreases in λ shift down/in the firms’ demand curves, and lowers thefirms’ optimal choice of price and quantity, and resulting profits−→ Increased competition

Handout p.7

Shape of DemandAssume that VES preferences fall in “price-decreasing” competition case(Zhelobodko et al, 2012) −→ Demand becomes more elastic as move upthe demand curve

DMR

log𝑝 , log𝜌

log𝑥Consistent with vast majority of empirical evidence on firm markups andpass-through:Larger, better performing firms set higher markups

Incomplete pass-through of cost shocks to pricesAdditional evidence on ‘more’ incomplete pass-through forbetter-performing firms: Berman et al (2012) and Li et al (2015)

Handout p.8

Shape of Demand and Competition

D

Δ log𝐿

Δλ

log𝑝

log𝑥D

Δ log𝐿Δλ

log𝑝

log𝑥

Increases in competition (λ↗) shift down εp(x) −→ more elasticdemand for all firms

Handout p.9

Implications for Competition and Firm Performance

log𝜋%& , log 𝑟 , log𝑞

log𝜑

Δ log𝐿

Δλ

Increases in competition (λ↗) increase the elasticity of operatingprofits, revenues, and output −→ intensive margin reallocations

Handout p.10

Closed Economy EquilibriumIrreversible investment fE (in labor units) for firms to enter

Uncertain return: draw from a productivity distribution G (ϕ)

2 key equilibrium conditions:Endogenous exit: Zero profit cutoff productivity such thatπ(ϕ∗;λ) = 0. Firms with ϕ < ϕ∗ exitFree entry: ∫ ∞

ϕ∗π(ϕ;λ)dG (ϕ) = fE

These 2 equilibrium conditions jointly determine cutoff productivity ϕ∗

and competition level λResponse of entry and wages depend on how model is closed:

Single sector (GE): Exogenous labor supply of workers Lw = Lc .Wages adjust to ensure labor market equilibrium.Multiple sectors (PE): Exogenous expenditures on given sector (Lc

consumers). Endogenous labor supply of workers at exogenouseconomy-wide wage.

Handout p.11

Adjustment Path to Long Run Equilibrium

Re-establishing free-entry condition after a trade-shock may take time

Especially for downward response of entry!

In the short-run, the endogenous exit (zero-cutoff profit) condition wouldstill hold; but not the free-entry conditionInstead, the set of (potential) producers is fixed in the short-run−→ Mass M of firms with productivity distribution G (ϕ)

Handout p.12

Opening Economy to TradeConsider trade with destination F :

Exports to F :

Firms incur a per-unit trade cost τ and fixed export cost fX to reach FMarket size LcF and competition level λF determine export profitsπX (ϕ;λF )Only firms with ϕ ≥ ϕ∗X , such that πX (ϕ∗X ;λ) = 0 export(Zero cutoff profit condition for export market)

Free entry condition: same as in closed economy except that firmsanticipate profits

π(ϕ;λ, λF ) = 1[ϕ≥ϕ∗]πD(ϕ;λ) + 1[ϕ≥ϕ∗X ]πX (ϕ;λF )

Same modeling setup in F (generating imports into domestic economy):

Mass MF of firms with productivity distribution GF (ϕ)Firms incur trade costs τF , fF ,X and earn profits πF ,X (ϕ;λ)Only firms with ϕ ≥ ϕ∗F ,X export

Handout p.13

Predictions for the Impact of Trade

Across all different types of trade liberalization scenarios:

Import and export trade liberalizationSingle sector (GE) and multiple sector (PE)Short run and long run

... Competition effect from liberalization (λ↗) induces additionalintensive and extensive margin reallocations

Handout p.14

A Specific Example (Related to Empirical Results)

3 countries: destination D, France F , and W (ROW)Demand shock in D: LcD ↗In order to focus on demand shocks and competition in D:

Assume that D is small relative to F and W−→ Demand shocks in D do not affect country-wide equilibriumvariables in F or W (Apart from those related to exports to D)Do not model any feedback loop from changes in exports from D

−→ Focus on equilibrium response in D

Handout p.15

Impact of Demand Shocks In Destination DGE, PE, PE Short-Run trade scenarios all predict: Tougher competition(λ↗) in response to LcD ↗−→ intensive margin reallocations towards better performing products−→ Positive extensive margin response for all exporters so long as fixedexport cost is high enough

log𝜋%& , log 𝑟 , log𝑞

log𝜑

Δ log𝐿

Δλ

Handout p.16

Impact of Demand Shocks In Destination D: Productivity

Consequences for productivity:

Intensive margin effect unambiguously increases productivityExtensive margin effect increases productivity – so long as newexported products are more productive than firm average

Handout p.17

Measuring the Reallocation Effects of Trade Within Multi-Product Firms

Handout p.18

Why Within Multi-Product Firms?

It is very hard to measure the reallocation effects across firms at thecountry/industry level:

Shocks that affect trade (institutions, technology, ...) are also likely toaffect the distribution of market shares across firms

Recent theoretical models of multi-product firms highlight how tradeinduces a similar pattern of reallocations within firms as it does acrossfirms

Also fewer impediments to resource reallocation within firmsWhen measuring reallocations within multi-product firms, can:

Isolate trade shocks that are exogenous to individual firms –controlling for country/industry effectsControl for firm-level technology changesLook at same set of (narrowly defined products) sold by same firmacross destinations or time

Aside: Multi-product firms dominate world trade

Handout p.19

Similar Reallocations Across Firms and WithinMulti-Product FirmsFirms

Stable performance ranking for firms based on performance in any givenmarket (including domestic market) or worldwide salesBetter performing firms export to more destinationsWorse performing firms are most likely to exit (overall, or from any givenexport market)

Products within Firms

Stable performance ranking across destinations (and for worldwide sales)Better performing products are sold in more destinationsWorse performing products are most likely to be dropped from any givenmarket

Handout p.20

Data on French Multi-Product ExportersComprehensive customs data for firm-product exports to 229destinations (d) for 1995-2005 (t)

Exclude service and wholesale/distribution firms (keep manufacturingand agriculture)Products recorded at 8-digit level (over 10,000 product codes)

Also country, sector (ISIC-3), and product (HS6) level trade for thosedestinations:

GDP and other country level variablesImports by destination (d) at ISIC3 (M I

d ,t) and HS6 (Msd ,t) level

Handout p.21

Competition Effects: Evidence Across Destinations

110

100

1000

Mea

n G

loba

l Rat

io

5 10 15Destination GDP (log)

All countries (209)

AGO

ARE

ARG

AUSAUT

BEL

BEN

BFA

BGD

BGR

BHR

BLR

BRACAN

CHECHL

CHN

CIV

CMR

COG COL

CRI

CYP

CZE

DEU

DJI

DNK

DOM

DZA

ECU

EGY

ESP

EST

FIN

GAB

GBR

GHA

GIN

GRC

GTM

HKG

HRV

HTI

HUNIDN

IND

IRL

IRN

ISL

ISR

ITA

JOR

JPN

KAZ

KEN

KOR

KWTLBN

LBY

LKA

LTU

LUX

LVAMAR

MDG

MEX

MLIMLT

MRTMUS

MYS

NER

NGA

NLD

NOR

NZL

OMN

PAKPAN

PER

PHL

POL

PRT

QAT

ROMRUS

SAU

SEN

SGPSVKSVN

SWE

SYR

TCD

TGO

THATUN

TUR

TWN

UKR

URY

USAVEN

VNM

YEM

YUG

ZAF

110

100

1000

Mea

n G

loba

l Rat

io

6 8 10 12 14 16Destination GDP (log)

Countries with more than 250 exporters (112)

Mean Global Sales Ratio and Destination Market SizeHandout p.22

Competition Effects: Evidence Across Destinations

110

100

1000

Mea

n G

loba

l Rat

io

12 14 16 18 20Foreign Supply Potential (log)

All countries (209)

AGO

ANT

ARE

ARG

AUSAUT

BEL

BEN

BFA

BGD

BGR

BHR

BLR

BRA CAN

CHECHL

CHN

CIV

CMR

COGCOL

CRI

CYP

CZE

DEU

DJI

DNK

DOM

DZA

ECU

EGY

ESP

EST

FIN

GAB

GBR

GHA

GIN

GRC

GTM

HKG

HRV

HTI

HUNIDN

IND

IRL

IRN

ISL

ISR

ITA

JOR

JPN

KAZ

KEN

KOR

KWTLBN

LBY

LKA

LTU

LVAMAR

MDG

MEX

MLI MLT

MRTMUS

MYS

NCLNER

NGA

NLD

NOR

NZL

OMN

PAKPAN

PER

PHL

POL

PRT

PYF

QAT

ROMRUS

SAU

SEN

SGPSPM

SVKSVN

SWE

SYR

TCD

TGO

THATUN

TUR

UKR

URY

USAVEN

VNM

YEM

YUG

ZAF

110

100

1000

Mea

n G

loba

l Rat

io

12 14 16 18 20Foreign Supply Potential (log)

Countries with more than 250 exporters (112)

Mean Global Sales Ratio and Foreign Supply PotentialHandout p.23

Reallocations Over Time: Measuring Trade Shocks

Changes in the destination markets over time also induce similar patternof reallocationsFor all firms exporting to destination d , can measure change (growthrate) in

∆̃GDPd ,t

Total imports into d (in ISIC I ) excluding French exports: ∆̃M Id ,t

Both capture demand shocks for French exporters to d

... but we can also construct a firm i-specific measure of thetrade-induced demand shock:

∆̃shockIi ,d ,t ≡ ∆̃Msd ,t ∀ products s ∈ I exported by firm i to d in t − 1

All 3 trade shocks strongly predict response (growth rate) of firm i ’sexports in a destination d along both intensive and extensive margins

Handout p.24

Impact of Trade Shocks on Reallocations Over TimeDestination-level over time:

Trade shock strongly predicts increased skewness of firm’s product mixTheoretical connection with preferences satisfying previous evidence onmarkups and pass-through

Aggregating up to firm-level:Use (lagged) firm-destination export sharesTrade shocks strongly predict increased skewness of firm’s global productmix (global exports and total production)

Handout p.25

Impact of Trade Shocks on Firm Productivity

Handout p.26

New Data and Productivity

Merge trade data with production data (comprehensive annual census)

Adds firm level variables (by year) for input and output use

Measure productivity as deflated value-added per worker

Aggregates (using firm labor shares) to welfare-relevant realvalue-added per worker for French manufacturing:Firm/product level:

ΦQi =

Yi/Pi

LiΦRi =

Yi/P̃S

Li

Sector/aggregate level:

ΦQS =

YS/P̃S

LS=

∑i∈S

LiLS

ΦRi

Handout p.27

Impact of Demand Shocks on Firm Productivity: LargestFrench Exporters

Handout p.28

Counterfactual: Sector and Aggregate Productivity Effectsof Trade ShocksIndustry prod. trade shock % high exp.intens. % mfg. emp.

Radio, tv & communic. 1.8 4.94 59.77 4.31Motor vehicles & trailers 1.62 9.8 52.39 7.82Machinery 1.32 5.54 45.4 9.12Chemicals 1.15 6.58 40.55 9.63Fabricated metal .94 7.04 17.41 8.81Medical & optical instrum. .85 5.84 46.82 3.53Rubber and plastics .8 5.75 36.97 7.18Electrical machinery .73 5.83 53.12 5.17Basic metals .7 6.27 58.91 4.06Food and beverages .66 6.2 14.12 11.88Other transport equip. .65 7.25 69.14 4.3Coke, refining & nuclear -.18 5.12 25.54 .93

Agg. Manufacturing 1.17 6.2 36.66 100

Note: Yearly averages based on 1995-2005 sample

Handout p.29

Endogenous Productivity Changes and Gains From Trade

Do productivity changes generated by reallocations contribute toaggregate gains from trade?

Handout p.30

Endogenous Productivity Changes and Gains From Trade

Theoretical comparative static experiment: change the degree of firmheterogeneity holding all other structural parameters constant

CES preferences case (Melitz & Redding, 2015):

Compare a heterogeneous firm model to a model with a degenerateproductivity distribution for exporters and non-exporters−→ Welfare gains from trade liberalization are strictly higher in modelwith endogenous selection (generated by the endogenous productivityresponse)Holds for general productivity distributions under firm heterogeneity

VES preferences case (Dhingra & Morrow, 2015):

Welfare effect is even stronger as intensive margin reallocationstowards higher productivity firms and lower average markups furthercontribute to welfare gains

Handout p.31

Conclusion

Theory: Robust predictions for role of trade and competition in boostingindustrial productivity and gains from trade – especially when consideringmore general VES preferences (relative to CES)

Within class of VES preferences featuring “price-decreasing”competition

Demand shocks in export destinations induce French exporters to skewtheir export sales towards their better performing products

−→ Strong evidence for competitive effects stemming from VESpreferences−→ Substantial productivity response for French exporters mostimpacted by those demand shocks

Handout p.32