Gains from Openness Gains from Openness with Heterogenous Firms Phemelo Tamasiga 1 Gerald Willmann 2 1 Bielefeld Graduate School of Economics and Management, Germany 2 Bielefeld University, Germany June 30, 2015
Gains from Openness Overview Introduction Motivation Research Question Literature Model Assumptions Preferences and Demand Production Measure of gains from Trade Conclusion
Gains from Openness Introduction Motivation ◮ International trade research has devoted a lot of attention on trade gains, less attention has been paid to measure gains. from FDI
Gains from Openness Introduction Motivation ◮ International trade research has devoted a lot of attention on trade gains, less attention has been paid to measure gains. from FDI ◮ Arkolakis,derived gains from trade from the most commonly used quantitative trade models defined as G j = 1 − ( λ jj ) − 1 ε
Gains from Openness Introduction Motivation ◮ International trade research has devoted a lot of attention on trade gains, less attention has been paid to measure gains. from FDI ◮ Arkolakis,derived gains from trade from the most commonly used quantitative trade models defined as G j = 1 − ( λ jj ) − 1 ε ◮ The derivation is based on the observed share of a country’s trade with itself, λ j , and the elasticity of imports with respect to variable trade costs, ε
Gains from Openness Introduction Motivation ◮ International trade research has devoted a lot of attention on trade gains, less attention has been paid to measure gains. from FDI ◮ Arkolakis,derived gains from trade from the most commonly used quantitative trade models defined as G j = 1 − ( λ jj ) − 1 ε ◮ The derivation is based on the observed share of a country’s trade with itself, λ j , and the elasticity of imports with respect to variable trade costs, ε ◮ In the first quarter of 2013, the magnitude of global FDI inflows and outflows were 357 and 353 billion US dollars respectively. [OECD (2013) FDI statistics report]
Gains from Openness Introduction Motivation ◮ International trade research has devoted a lot of attention on trade gains, less attention has been paid to measure gains. from FDI ◮ Arkolakis,derived gains from trade from the most commonly used quantitative trade models defined as G j = 1 − ( λ jj ) − 1 ε ◮ The derivation is based on the observed share of a country’s trade with itself, λ j , and the elasticity of imports with respect to variable trade costs, ε ◮ In the first quarter of 2013, the magnitude of global FDI inflows and outflows were 357 and 353 billion US dollars respectively. [OECD (2013) FDI statistics report] ◮ Multinationals comprise a substantial majority of U.S. trade, roughly 90% of U.S. exports and imports (Bernard et al (2009))
Gains from Openness Introduction Research Question ◮ Are total gains from openness underestimated by omission of gains from FDI: To that effect how does the welfare measure of trade [a’la Arkolakis et al(2012)] change with FDI(gains from openess measure) ◮ Result Preview Define country j ’s gains from international trade(openess) G j ( C j ), as the absolute value of the % change in real income associated with moving from an observed equilibrium to autarky Gains from Trade Gains from Openness � � ( σ − 1) − ε − 1 G j = 1 − ( λ j ) − 1 − 1 ε + ( R µ ( σ − 1) ( σ − 1) ε λ fdi λ ex C j = 1 − − 1) ε ε j j j
Gains from Openness Introduction Research Question Example: Trade Gains ◮ In 2000, US import penetration ratio (IPR) was 7% ◮ Share of demestic expenditures on domestic goods λ = 1 − IPR = 0 . 93 ◮ Anderson and Wincoop (2004) provide estimates of trade elaticities, for US (-5,-10) ◮ Gains from trade USA: 0 . 7% − 1 . 4%
Gains from Openness Introduction Literature Proximity concentration trade off ◮ Brainard(1997) presents a simple theory to understand the trade-off between export and FDI. ◮ Markusen and Venables (2000)add factor endowment differences between countries to this simple model. ◮ Helpman, Melitz and Yeaple (2004) add firm heterogeneity Gains from Openness...? ◮ Eaton-Kortoum(2002), the only way of serving a foreign market is via exporting. ◮ Ramondo Rodriguez-Clare(2009),Trade and multinational MP in an Eaton and Kortum model. ◮ Arkolakis et al(2012)New trade models same old gains with average sectoral elasticity. ◮ Ralph Ossa (2012) Average elasticity underestimates gains from trade, different sectoral elasticities more trade gains.
Gains from Openness Model Assumptions ◮ Following Helpman et al (2004), there are N countries. ◮ Each country i is endowed with L i units of labour with wage rate w i . ◮ Each country comprises 2 sectors, sector 0 produces a homogeneous good with 1 unit of labour per unit output, ◮ H sectors produce differenciated products. ◮ The homogeneous good is freely traded with wage rate equal to 1 this ensures factor price equalisation as long as each and every country produces it. ◮ An exogenous fraction of income � h 1 − β h is spent on the homogeneous sector and, ◮ β h is spent on the differentiated goods sector
Gains from Openness Model Preferences and Demand ◮ Preferences are a Cobb-Douglas aggregate of the homogeneous good sector and differentiated traded goods ◮ CES across a continuum of differentiated goods in h = 1 , ..., H sectors, (Krugman, 1980) �� � σ h H � σ h − 1 β h σ h − 1 U = q 1 − β 0 q h ( ω ) (1) σ h 0 ω h ∈ Ω h =1 where σ > 1 is the elasticity of substitution ( ρ = σ − 1 σ ) ◮ Utility maximization implies quantity demanded in county j of good ω is q j ( ω ) = β p j ( ω ) − σ Y j (2) P 1 − σ j
Gains from Openness Model Production ◮ Exporting firm costs Exporting firms pay fixed costs ( f ex > 0) for each export ij destination. These marginal costs are given by, = w i τ ij C ex (3) ij ϕ ij ◮ FDI firm costs FDI firms pay fixed costs of FDI defined as f fdi ij . FDI marginal costs are : � � � w j � µ � w i τ ij � 1 − µ 1 C fdi = (4) ij ϕ fdi 1 − µ µ ij
Gains from Openness Model Production Zero Profit Conditions A firm will serve a foreign country if the operating profits are sufficient to cover fixed costs ◮ If firm chooses to supply foreign market via export, profits are given by: � ρ w i τ ij ) 1 − σ � 1 − σ Y j π ex ij = 0 → β P σ − 1 σ = f ex (5) j ϕ ◮ accesing foreign markets via FDI gives the following profits � � 1 − σ Y j ρ w µ j ( w i η ij ) 1 − η π fdi = 0 → β P σ − 1 σ = f fdi (6) ij j ϕ
Gains from Openness Model Production Cutoff Productivities From zero profit condition, we get cutoff productivies for export and FDI ◮ Export Productivity cutoff � f ex � 1 σ − 1 ij P − 1 ϕ ex ˜ ij = κ w i τ ij (7) j Y j � � 1 σ − 1 ρ σ such that κ = β ◮ FDI Productivity cutoff � � 1 f fdi − f ex σ − 1 ij ij ϕ fdi P − 1 ˜ = κ w i τ ij (8) ij Y j [( R ij τ ij ) µ ( σ − 1) − 1] j To ensure that the fdi cutoff productivity is higher than export productivity,i.e ϕ fdi > ϕ ex ij ,assume that ij f fdi R µ ( σ − 1) > f ex τ µ ( σ − 1) ij
Gains from Openness Model Production Entry and Exit Timing ◮ Upon entry, firms draw their initial productivity level, ϕ from a common distribution g ( ϕ ) = k ( ϕ m in ) k ϕ − ( k +1) with positive support over (0 , ϕ max ).and a continuous cumulative � ϕ mini � κ distribution G ( ϕ ) = 1 − ϕ ◮ A firm drawing a low productivity ϕ may decide to immediately exit and not produce. ◮ Produtivities are distributed Pareto ◮ Firms face a constant probability of a bad shock in every period that would force them to δ exit.
Gains from Openness Model Production Entry and Exit Continued ◮ Probability of entry in the home market, exporting (conditional on successful entry)and into FDI are given by θ iD = 1 − G ( ϕ ∗ i ) (9) θ ex = G ( ϕ ∗ fdi ) − G ( ϕ ∗ ex ) (10) 1 − G ( ϕ ∗ i ) θ fdi = 1 − G ( ϕ ∗ fdi ) (11) 1 − G ( ϕ ∗ i )
Gains from Openness Model Production Aggregation ◮ Let M be the equilibrium mass of incumbent firms in any country, ◮ Mass of firms that enter foreign country via exports and FDI M ex = θ ex M and M fdi = θ fdi M ◮ Total mass of varieties available to consumers in each country is given by the total mass of firms competing in the country, M = M + nM ex + nM fdi (12) ◮ Weighted productivity average � � 1 ϕ = 1 + nM ex τ 1 − σ � + nM fdi τ (1 − σ )(1 − η ) � ϕ σ − 1 ϕ σ − 1 ϕ σ − 1 σ − 1 � M � ex iD fdi M (13) 1 1 1 − σ p ( � σ − 1 ρ � P = M ϕ ), W = M ϕ
Gains from Openness Model Production Aggregation continued... ◮ Trade only Price Index 1 ϕ fdi 1 − σ ij = G ( ϕ ∗ fdi ) − G ( ϕ ∗ ex ) � σ P ex M ex ϕ σ − 1 ( σ − 1 w ij τ ij ) 1 − σ dG ( ϕ ij ) (14) j ij 1 − G ( ϕ ∗ i ) ϕ ex ij ◮ FDI only Price Index 1 ∞ = 1 − G ( ϕ ∗ fdi ) � σ σ − 1 ) 1 − σ [( ℜ ij τ ij ) µ ( σ − 1) − 1]( w ij τ ij ) 1 − σ dG ( ϕ ij ) P fdi i ) M fdi ϕ σ − 1 ( ij ij 1 − G ( ϕ ∗ ϕ fdi ij (15)
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