Gains from Openness with Heterogenous Firms Phemelo Tamasiga Gerald Willmann Bielefeld University June 25, 2014 Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 1 / 33
Overview Introduction 1 Model 2 Measure of gains from Trade 3 Conclusion 4 Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 2 / 33
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)) Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 3 / 33
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 Current resuslt: Gains from Openness � � ( σ − 1) − ε − 1 G j = 1 − ( λ j ) − 1 − 1 ε + ( R η ( σ − 1) ( σ − 1) ε λ fdi λ ex C j = 1 − − 1) ε ε j j j Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 4 / 33
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. Romondo(2008), variant of Eaton and Kortum, in which there are no trade flows. 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. Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 5 / 33 Melitz and Redding(2014)New trade models different welfare implications.
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 H + 1 sectors, sector 0 produces a homogeneous good with 1 unit of labour per unit output, Sectors h ≥ 1 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 Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 6 / 33
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) �� � H σ h � σ h − 1 β h σ h − 1 U = q 1 − β h σ h d ω q h ( ω ) (1) 0 ω ∈ Ω h 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 Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 7 / 33
Model Production Firms in country i can enter the domestic market by paying fixed costs of entry f E i > 0 which is thereafter sunk. Expectation of future positive profits is the only motivation for firms to pay these sunk costs. Exporting firm costs Exporting firms pay additional fixed ( f ex > 0= for each export ij destination. These marginal costs are given by, = w i τ ij C ex (3) ij ϕ ij Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 8 / 33
Model production continued... FDI firm costs FDI firms pay fixed costs of FDI defined as f fdi ij . FDI marginal costs are : � � � w j � η � w i τ ij � 1 − η 1 C fdi = (4) ij ϕ fdi η 1 − η ij Mode of Supply decisions A firm will serve a foreign country if the operating profits are sufficient to cover fixed costs. A firm can choose to supply foreign markets via exports or set up FDI plants in foreign markets. Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 9 / 33
Model production continued... If firm chooses to supply foreign market via export, profits are given by: � ρ w i τ ij ) 1 − σ � 1 − σ Y j ij = β P σ − 1 π ex σ f ex (5) j ϕ accesing foreign markets via FDI gives the following profits � � 1 − σ Y j ρ w η j ( w i η ij ) 1 − η π fdi = β P σ − 1 σ f fdi (6) ij j ϕ Cutoff Productivities From zero profit condition, we get cutoff productivies for export and FDI Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 10 / 33
Model production continued... 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 ) η ( σ − 1) − 1] j To ensure that the fdi cutoff productivity is higher than export ij ,assume that f fdi R η ( σ − 1) > f ex τ η ( σ − 1) productivity,i.e ϕ fdi > ϕ ex ij ij Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 11 / 33
Model Entry and Exit Timing Firms are identical prior to entry and must pay a xed investment cost f E to enter. 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 distribution � ϕ mini � κ 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. Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 12 / 33
Model Entry and Exit continued Pareto Distribution Good approximation of the upper tail of distribution of firm sizes (Simon and Bonini,1958). key feature 1: when truncated the random variable retains a Pareto distribution with the same shape parameter k. If entry is subject to an endogenous productivity cutoff, the distribution of the technologies that make the cut remains Pareto key feature 2: Pareto distributed random variable power functions are themselves Pareto distributed. Individual prices have a Pareto distribution, with a constant elasticity of demand, so do sales, hence firm size and variable profits are Pareto distributed. Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 13 / 33
Model 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 ) Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 14 / 33
Model Entry and Exit continued... Free Entry Condition Expectation of future profits must be equal to the fixed costs or that the probability of successful entry multiplied by average profits conditional on successful entry equal fixed costs ∞ � (1 − δ ) π = [1 − G ( ϕ ∗ )] π v ( ϕ ) = − f e (12) δ t =0 Where the average revenues and profits across all domestic firms earned from both domestic, export and FDI revenues are given as: r = π iD ˜ ( ϕ ) + n θ ex r ex ˜ ( ϕ ) + n θ fdi r fdi ˜ ( ϕ ) (13) Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 15 / 33
Model Entry and Exit continued... Taking into account the zero profit condition the previous equation becomes, r = σ ( π + f iD + n θ ex f ex + n θ fdi f fdi ) (14) π = π iD ˜ ( ϕ ) + n θ ex π ex ˜ ( ϕ ) + n θ fdi π fdi ˜ ( ϕ ) (15) These average Profits pin down the equilibrium mass of incumbent firms given as M = R L r = (16) σ ( π + f e + n θ ex f ex + n θ fdi f fdi ) Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 16 / 33
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