International Trade. Lecture 4: the extensive margin of trade. Thomas Chaney. Sciences Po. Thomas Chaney (Sciences Po) International Trade 1 / 17

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1 International Trade ecture 4: the extensive margin of trade Thomas Chaney Sciences Po Thomas Chaney (Sciences Po) International Trade / 7

2 Target of the paper Explain the observed role of the extensive margin of trade. Determin in such a model what parameters govern the elasticity of trade flows with respect to trade barriers. Thomas Chaney (Sciences Po) International Trade 2 / 7

3 New assumptions (versus Melitz) Many asymmetric countries with asymmetric trade barriers. No free entry: number of firms directly proportional to country size (can be relaxed). Pareto distributed productivity shocks (delivers closed form solutions). extranumérairesectorasinhelpman-krugmanpinsdownrelative wages (can be relaxed). Thomas Chaney (Sciences Po) International Trade 3 / 7

4 Set-up CES/Cobb-Douglas preferences, 0 ˆ U q o W q (w) s s dwa s s ( µ) N asymmetric countries: sizes ( i ) N i=,tradebarriers,(t, f ) N i,j=. Thomas Chaney (Sciences Po) International Trade 4 / 7

5 Productivity distribution and entry Pareto distribution for productivities j 2 [, + ), P (j > F) = F q with q > s. Note: Pareto distributions are invariant to truncation, P (j > F j > j ) = In country n, n potential entrants. F q j = P (j > F) j q Thomas Chaney (Sciences Po) International Trade 5 / 7

6 Ownership structure Without free entry, ownership structure matters. Aggregate world profits (P) equally distributed across workers. Aggregate income in country i, ( + P ) i Thomas Chaney (Sciences Po) International Trade 6 / 7

7 Zero cutoff profit conditions Sales by firm j from country i in country j, st r (j) = (s ) jp j Only firms with j j from i export to j, p j = 0, j = l f s µ + P j s Entry threshold into j depends on prices in j. Pj s s j t (ZCP i j) Thomas Chaney (Sciences Po) International Trade 7 / 7

8 Aggregate prices Prices in j depends on which firms able to enter j, Pj s = = = N ˆ Â k p kj (j) k= jkj ˆ s N Â k k= N Â k k= j kj s s dg (j) j s t kj q s q (s ) s dg (j) s jkj s q t kj Thomas Chaney (Sciences Po) International Trade 8 / 7

9 Aggregate prices Prices in j depends thresholds of entry into j. Threshold of entry into j depends on prices in j. Simple solution for prices, with r q j j q P j = l 2 (j ) N Â s k tkj q k= f kj s r j ( q s ) r j is an aggregate measure of j s remoteness from the rest of the world (due to both fixed and variable costs). Thomas Chaney (Sciences Po) International Trade 9 / 7

10 Equilibrium exports and selection Firm level exports (r), thresholdsofexport( j), andaggregateprofits (P), 8 < s j q rj s r (j) = l 3 t j s,ifj j : 0, otherwise j q t = l 4 s f j r j P = l 5 Note: elasticity of r w.r.t. t is (s ) as in Krugman. 2 Note: aggregate income elasticity of firm level exports <. Thomas Chaney (Sciences Po) International Trade 0 / 7

11 Gravity equation Aggregate exports from i to j, ChaneyversusKrugman, 8 >< t ( s q ) >: X Chaney X Krugman = l i j = l i j q r j f t (s ) r j Higher elasticity of trade w.r.t. variable trade barriers, q > s. 2 Elasticity does not depend on the elasticity of substitution s. 3 Elasticity w.r.t. fixed costs, q s,is negatively related to the elasticity of substitution s. 4 Both elasticities are higher in sectors where firms productivity is less dispersed (q large). Thomas Chaney (Sciences Po) International Trade / 7

12 Gravity equation Similar structure, Chaney and Krugman, 8 >< t >: with X Chaney X Krugman 8 < : = l i j = l i j r = t q f r = t (s ) q ( q r j f s ) = l s i r  N k= s k r kj j t (s ) r j = l s i r  N k= s k r j kj ( s q ) Exports from i depends on trade barriers from i relative to weighted average of trade barriers from k s. Thomas Chaney (Sciences Po) International Trade 2 / 7

13 Intensive versus extensive margins Average size of exporters versus number of exporters, 8 h i < E r (j) j j = l 0 f : t ( s q ) N = l i j l 0 f r j q f Problem : relative exports conditional on export vary a lot, r (j) r ik (j) j j,j ik = t t ik s Possible fix: t random shocks + Arkolakis (2008). Problem 2: average exports decrease with distance. Possible fix: global fixed export costs (Hanson & Xiang 2008). Thomas Chaney (Sciences Po) International Trade 3 / 7

14 Intensive versus extensive margins dx = + ˆ j ˆ j! r (j) dg (j) dt r j g j j dt t t! r (j) dg (j) r ( j ) g j j f {z } Intensive margin df f {z } Extensive margin df Thomas Chaney (Sciences Po) International Trade 4 / 7

15 Intensive versus extensive margins z x ) z s d ln X = (s ) d ln t {z } Intensive margin Elasticity d ln X d ln f = {z} 0 Intensive margin Elasticity = 0and x s < 0 +(q (s )) {z } Extensive margin Elasticity + = q q s {z } Extensive margin Elasticity = q s Thomas Chaney (Sciences Po) International Trade 5 / 7

16 Some empirics (size distribution and gravity) ln (Distance ) (.04)*** (.04)*** (.04)*** dq h s h ln (Distance ) (.002)*** (.003)*** anguage (.)*** (.2)*** (.02)** dq h s h anguage (.05)*** (.05)*** Border (.02)*** (.3)*** (.3)*** dq h s h Border (.008)*** (.08)* R 2 30% 3% 23% 25% 32% Number of obs. 65,687 65,687 65,687 65,687 65,687 Thomas Chaney (Sciences Po) International Trade 6 / 7

17 Some empirics (differentiation and gravity) ln (Distance ) (.02)*** (.02)*** (.02)*** ŝ h ln (Distance ) (.00)*** (.00)*** anguage (.04)*** (.09)*** (.05)*** ŝ h anguage (.004)*** (.004)*** Border ŝ h Border (.08)*** (.)*** (.09)*** (.006)*** (.006)* R 2 39% 40% 33% 35% 4% Number of obs. 270, , , , ,583 Thomas Chaney (Sciences Po) International Trade 7 / 7