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Page 1: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

International Economics ILecture Set 5 (and 6): The Melitz model

Tomas Rodriguez Martinez

Department of Economics and BusinessUniversitat Pompeu Fabra

Page 2: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

"New" Trade Theory: Recap● n varieties of differentiated goods

– total cost functionTC = (F + βq)w

● L consumer with "love of variety"– demand

qi = (P /pi)1/(1−α)wL/P α ∈ (0,1)elasticity of substitution: 1/ (1 − α)

● equilibrium– price: from profit maximization

pi = p = βw/α (MC ∗mark-up)

– quantities: from free entry

qi = q = αF / [β (1 − α)]

– number of varieties: from labor market clearing

n = L (1 − α) /F

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Page 3: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Pattern of Trade

● each country exports its varieties and imports the foreign ones

X = L∗

L∗ +Lnq and M = L

L∗ +Ln∗q

● all firms in both countries are exporters● trade is intra-industry trade

– export and import same good (different varieties)

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Page 4: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

All Exporters?

● the model with IRS + differentiated goods predicts that all firmsexport● in reality, only few of them export

– share of exporters among manufacturing firms:- US (2007) → 17%- France (1986) → 17.4%- Japan (2000) → 20%- Chile (1999) → 20.9- Spain (2011) → 12%- Catalunya (2014) → 8%

● moreover, exporters differ from non-exporters:– exporter are bigger and more productive

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Page 5: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Exporters in the US (2007)

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Exporters Are Different

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Page 7: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Firm Heterogeneity: A Model

● Melitz (2003) modifies the previous model to account for these facts:– not all firms export– exporters are bigger and more productive than non-exporters– larger exporters export more

● new result: trade and selection– trade liberalization affects firms asymmetrically– benefit the large, more productive firms– harms small, non-exporting firms → some exit– "selection of the best fit"

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Page 8: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Melitz (2003): Assumptions

● preferences and market structure– identical to previous model– wage is again the numeraire (w = 1)

● new assumptions:1 firms draw their productivity from some distribution

- generates heterogeneity

2 there is a fixed export cost- only the most productive firms are willing to pay it

3 there is also a variable (iceberg) trade cost (not crucial)

● study reduction in trade costs between two symmetric countries

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Page 9: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Firm Heterogeneity: Closed Economy

● firms differ (exogenously) in productivity ϕ→MC = 1/ϕ– total cost of a firm with productivity ϕ:

TC = q

ϕ+ fD

– fD = fixed cost of production or serving the domestic (D) market

● firms are monopolistically competitive– usual pricing formula p = 1/αϕ– (domestic) profit of a firm with productivity ϕ:

πD = Aϕα

1−α − fD where A ≡ (1 − α)L(αP )α/(1−α)

● more productive firms:– charge lower prices, sell more, make higher profits

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Page 10: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Producing and Non-Producing Firms

● firms can shut down at no cost (free exit):– given profits

πD = Aϕα

1−α − fD– stay if π ≥ 0, otherwise exit– only the most productive firms (ϕ > ϕ∗D) survive where

A (ϕ∗D)α

1−α = fD

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Page 11: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Free Entry and Cutoff Productivity

● to jointly determine A and ϕ∗D: free entry + free exit● for given cutoff productivity ϕ∗D

– ex-ante (upon entry) expected profits are

E(πD) = ∫∞

ϕ∗D

[Aϕα/(1−α) − fD] g(ϕ)dϕ = fE

- g(ϕ) = probability of drawing productivity ϕ

– free entry: firms enter in the market until E(πD) = fE● in equilibrium, cutoff productivity is:

– increasing in fD (more difficult to cover the fixed cost of production)– decreasing in fE (need higher expected profits/survival probability for

firms to enter)– negatively correlated with A (survival is easier in more profitable

markets)

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Page 12: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Producing and Non-Producing Firms: Graph

πD = Aϕα/(1−α) − fD

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Page 13: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Exporting: Assumptions

● suppose now that a firm can sell into a foreign market, denoted by (X)● assume countries are symmetric

– same size, technology and preferences → A = AX● to serve a foreign market, there are two additional costs:

1 a new fixed cost (distribution and servicing costs) fX2 an iceberg cost: ship τ > 1 to deliver 1

- marginal cost = τ/ϕ

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Page 14: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Exporting: Prices and Profits

● price of exported goodspX = τ

αϕ

– higher because the effective productivity in the export market is ϕ/τwith τ > 1

● profits from exporting:

πX = A(ϕτ)α/(1−α)

− fX

– positive only if ϕ is high enough

● assume τα/(1−α)fX > fD– this implies that no firm prefers exporting than serving the domestic

market

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Page 15: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Exporting and Non-Exporting Firms: Graph

πD = Aϕα/(1−α) − fD and πX = A (ϕ/τ)α/(1−α) − fX

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Page 16: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Exporting and Non-Exporting Firms

● recall profits:

πD = Aϕα/(1−α) − fD and πX = A (ϕ/τ)α/(1−α) − fX

– both increase with productivity, πX by less (due to τ)

● firms partition in groups:– firms with productivity below ϕ∗D exit– firms between ϕ∗D and ϕ∗X produce in the domestic market only– firms above ϕ∗X export too

● thus, only the most productive firms export– a firm must be big enough to profitably cover the fixed export cost– note: τα/(1−α)fX > fD guarantees that ϕ∗D < ϕ∗X

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Page 17: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Trade and Selection

● cutoff productivity for the domestic market ϕ∗D increases– foreign exporters enter the domestic market

- more productive than domestic non-exporters- market becomes more competitive (A ↓)

– non-exporters:- lose domestic sales due to foreign penetration- do not gain market shares in the foreign market

– marginal (least-productive) firms are forced to exit

● selection effect:– fewer firms per country– higher average productivity of survivors

● similar effects if the costs of export (τ and/or fX) fall

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Page 18: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Trade and Welfare with Heterogeneous Firms

● variety effect:– can import foreign varieties (+)– some domestic varieties (firms) disappear (-)

● overall, welfare improves:– new imported varieties have lower marginal cost (higher productivity) →

cheaper– lost domestic varietiles have higher marginal cost (lower productivity) →

more expensive

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Page 19: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Summary

● when firms are heterogeneous in productivity (ϕ):– more productive firms charge lower price, sell more, make higher profits– the least productive exit the market

● switch to free trade (with iceberg and entry cost, τ and fX):– most productive firms become exporters– most productive foreign firms enter domestic market– least productive domestic firms exit the market (selection)– gains from variety:

- gain foreign (high-productivity) varieties- lose domestic (low-productivity) varieties

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Page 21: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Summary: Effects of Trade Liberalization

● if trade costs (τ or fX) fall bilaterally:– higher πX ↑ → more exporters ϕ∗X ↓– new and old exporters gain– more foreign competition πD ↓ → more selection ϕ∗D ↑– least productive non-exporters lose

● empirically relevant predictions– average productivity increases at industry level due to selection– increase in sales (output) of exporters– drop in sales (output) of import-competing firms

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Page 22: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Empirical Evidence: Trefler (2004)

● considers the Canada-US free trade agreement (CUSFTA,01/01/1989)

● uses data on sectors and plants (firms) in Canada during 1980-1996

● why this trade liberalization episode?– a well defined policy experiment (no confusion with macro shocks or

other reforms)

– allows to identify policy-mandated reductions in tariffs

– it is a reciprocal agreement to reduce tariffs between Canada and theUS, not vis-à-vis the rest of the world

– semi-unexpected adoption (elections with surprise outcome)

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Page 23: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Tariffs Before and After 01/01/1989

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Page 24: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Empirical Strategy

● estimate for sector i

∆yi = θ + βCA (∆τCAi ) + βUS (∆τUSi ) + controlsi + νi

– ∆ = 1988-1996 (post-liberalization) variation minus 1980-1986(pre-liberalization) variation- to identify the treatment (liberalization) effect

– y = variable of interest for Canada– τUS = tariff applied by the US on goods form Canada

- βUS quantifies the effect on (current + potential) exporters to the US

– τCAN = tariff applied by Canada on goods from the US- βCAN quantifies the effect of competition with import from the US

● repeat estimations for plant k in sector i

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Page 25: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Results

● effects on employment:– total ≃ −5% (100.000 workers) at plant and industry level, due toτCAN ↓ (competition from US exporters)

– transitory effects

– skilled/unskilled labor ↑, due to τCAN ↓ (competition from US exporters)

● effects on labor productivity:– τCAN ↓ → up to +15% at industry level, 0 at plant level (exit of the

least productive)– total effect ≃ +7.4% at industry (τCAN ↓) and plant (τUS ↓) level

● production:– τUS ↓→ +6% at plant level

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Page 26: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Summary: Evidence vs Theory

● trade liberalization:– raises productivity of each sector due to import competition (=theory)

- by inducing the least productive firms to exit

– raises productivity of exporting firms (not predicted, constant firm’s ϕ)- A ↑ → justify investment in technology upgrading → ϕ ↑

– reduces employment (not predicted, frictionless labor market)

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Page 27: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Exporters, Products and Destination Markets

● destinations per U.S. firm in 2007 (Bernard et al., 2015)– few firms export to more than one foreign market– firms exporting to many markets represent an important share of total

export

● exported products per U.S. firm in 2007 (Bernard et al., 2015)– few firms export more than one product– firms exporting many products represent an important share of total

export– firms exporting many products also export to many markets

● size matters... a lot!– larger firms much more likely to export– larger firms export much more

● firms per destination (Eaton et al., 2011 on France in 1987)– larger markets attract more exporters– larger markets imply more sales per exporter

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Page 28: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Destinations and Products per Firm: Data

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Size and Trade Participation: Data

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Size and Trade Volumes: Data

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Page 31: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Exporters and Destinations: Theory

● how to reconcile this piece of evidence?

● fixed entry cost for each product and foreign market

● more productive firms can cover more fixed costs– export to more countries– export more products– export disproportionately more

● larger markets deliver higher profits– attract more exporters– exporters choose them first– less productive exporters limit to those

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Page 32: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

An extension of Melitz (2003): Exporters vs Multinationals

● alternative to export: horizontal foreign direct investment (FDI)– firms settle in the foreign country to produce & sell there

● Helpman Melitz and Yeaple (2004)– formalize the choice beween export and FDI within the same model

● horizontal FDI entails– a fixed cost fI > fX to settle production in the foreign country– no additional variable cost → marginal cost 1/ϕ

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Page 33: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Exporters vs Multinationals: Choice

● profits from FDI:πI = Aϕα/(1−α) − fI

● profits from export:

πX = A (ϕ/τ)α/(1−α) − fX● proximity vs concentration trade-off:

– multinationals face higher fixed costs, but save transportation costs– a firm chooses FDI rather than exporting when πI > πX

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Page 34: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Multinationals, Exporting and Non-Exporting Firms

● profits from:– domestic sales, export, FDI

πD = Aϕα/(1−α) − fD πX = A (ϕ/τ)α/(1−α) − fX

πI = Aϕα/(1−α) − fI● firms partition in groups:

– firms with productivity below ϕ∗D exit– firms between ϕ∗D and ϕ∗X produce in the domestic market only– firms above ϕ∗X export too– firms above ϕ∗I become multinationals

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Page 35: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Multinationals, Exporting and Non-Exporting Firms

πD = Aϕσ−1 − fD πX = τ1−σAϕσ−1 − fX πI = Aϕσ−1 − fI

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Page 36: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Exporters vs Multinationals: Productivity

● productivity of multinationals, exporters and non-exporters is such that– ϕ∗I > ϕ∗X > ϕ∗D– Helpman et al. (2004) estimate on US data for firms of 52 sectors:

log (YL

)ij

= α + βMNEij + γEXPij + controls + εij

- (Y /L)ij = labor productivity of firm j in sector i- MNEij = 1 if j is multinational- EXP = 1 if j is exporter →- control group = non-exporters- β ≈ ϕI − ϕD, γ ≈ ϕX − ϕD and β − γ ≈ ϕI − ϕX

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Page 37: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Exporters vs Multinationals: Productivity

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Page 38: International Economics I · International Economics I LectureSet5(and6): TheMelitzmodel Tomas Rodriguez Martinez Department of Economics and Business Universitat Pompeu Fabra

Exporters vs Multinationals: Sales

● more export relative to multinational sales if:– trade iceberg cost (τ) is low– fixed FDI cost (fI) is high

● empirical evidence:– Helpman et al. (2004) estimate on the same data + subsidiaries in 38

countries:

lnSXjk

SIjk= αk+α1 lnFPj+β1 lnFREIGHTjk+β2 lnTARIFFjk+γZj+εjk

- SXjk = sales in sector j in country k by export- SIjk = sales in sector j in country k by subsidiaries (FDI)- FPj = plant-level fixed costs in sector j (represents fI)- FREIGHT = transport costs to country k (represents τ)- TARIFF = tariff rate for sector j in country k (represents τ)- Z = controls

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Exporters vs Multinationals: Sales

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