Networks and International Trade: APractitioner sperspective

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1 Networks and International Trade: APractitioner sperspective Thomas Chaney Toulouse School of Economics Research Experience for Undergrads Becker Friedman Institute: June, 2014 Thomas Chaney (Toulouse) Networks and International Trade June, / 39

2 Questions Thomas Chaney (Toulouse) Networks and International Trade June, / 39

3 Some frontier questions in international trade 1 Gravity equations in international trade (Tinbergen 1961). 2 Firm level trade (Melitz ECMA 2003, Bernard and Jensen JIE 1999). 3 Within country trade. Thomas Chaney (Toulouse) Networks and International Trade June, / 39

4 Frontier question #1: gravity Gravity equations for aggregate bilateral trade flows, X AB µ (GDP A) a (GDP B ) b (Dist AB ) z a, b 1theoreticallywellunderstood. z 1unexplained. Thomas Chaney (Toulouse) Networks and International Trade June, / 39

5 Frontier question #2: firm level trade 1 only 18% of US manufacturing firms export. 2 more than 50% of French exporters: single export destination. 3 top 10 French exporters account for 25% of all French exports. 4 top 10 (50) exporters account for 30% (50%) of Japan s exports. Thomas Chaney (Toulouse) Networks and International Trade June, / 39

6 Frontier question #3: within country trade 1 Massive infrastructure projects: 1 India s railroad (Donaldson AER forthcoming). 2 US interstate (Allen & Arkolakis QJE forthcoming). 2 High within country barriers in developing countries. Thomas Chaney (Toulouse) Networks and International Trade June, / 39

7 Data Thomas Chaney (Toulouse) Networks and International Trade June, / 39

8 Trade data High quality data for international trade. Customs authorities are good at policing borders! Relatively easily accessible data (all things considered). Thomas Chaney (Toulouse) Networks and International Trade June, / 39

9 Aggregate trade data Good source for data: NBER: Aggregate bilateral trade data: Feenstra s World trade data: US Trade disaggregated at the product level (HS, SITC, NAICS). US tariffs... etc. Thomas Chaney (Toulouse) Networks and International Trade June, / 39

10 Firm level trade data Data collected by most countries. Typically not freely accessible to researchers. Some private providers of firm level information (expensive). Peru s firm level data are publicly available: (you need to web-crawl though...). Thomas Chaney (Toulouse) Networks and International Trade June, / 39

11 Within country trade data Sadly (or not), no (very) big brother within countries... Thomas Chaney (Toulouse) Networks and International Trade June, / 39

12 Within country trade data Sadly (or not), no (very) big brother within countries... Firm level data: US Commodity Flow Survey (random sample of shipments). Turkey firm to firm shipments (universal, for VAT purposes). Belgium firm to firm shipments (universal? VAT). COMPUSTAT data on corporations main customers. others? Thomas Chaney (Toulouse) Networks and International Trade June, / 39

13 Within country trade data Sadly (or not), no (very) big brother within countries... Firm level data: US Commodity Flow Survey (random sample of shipments). Turkey firm to firm shipments (universal, for VAT purposes). Belgium firm to firm shipments (universal? VAT). COMPUSTAT data on corporations main customers. others? Some level of aggregation: US Commodity flow survey (public). US Census of manufacturing (public). Thomas Chaney (Toulouse) Networks and International Trade June, / 39

14 Within country trade data Sadly (or not), no (very) big brother within countries... Firm level data: US Commodity Flow Survey (random sample of shipments). Turkey firm to firm shipments (universal, for VAT purposes). Belgium firm to firm shipments (universal? VAT). COMPUSTAT data on corporations main customers. others? Some level of aggregation: US Commodity flow survey (public). US Census of manufacturing (public). Create your own data: web crawling from public websites (ebay, Google shopping...). financial disclosure forms? newspaper archives? financial trail from transactions? specialized trade associations? Thomas Chaney (Toulouse) Networks and International Trade June, / 39

15 Networks, geography, trade Based on: The Network Structure of International Trade American Economic Review, forthcoming. The Gravity Equation in International Trade: An Explanation Thomas Chaney (Toulouse) Networks and International Trade June, / 39

16 The Network Structure of International Trade : set-up Space: S is a discrete set of locations. Time: discrete. Firms: discrete set of firms in each x 2S,growsatrateg. Network: each firm has contacts in various locations. Trade: 1unitoftradewitheachcontact. Thomas Chaney (Toulouse) Networks and International Trade June, / 39

17 Informational frictions Each period, a firm meets: directly searched contacts ( random friends ) remotely searched contacts ( friends of friends ) Friends of friends introduces: history dependence network effects Thomas Chaney (Toulouse) Networks and International Trade June, / 39

18 Notations f i,t : S!Nwith Â f i,t (x) = m i,t x2s Firm i of age t located in the origin (x = 0) has: m i,t contacts worldwide f i,t (x) contacts in location x. Thomas Chaney (Toulouse) Networks and International Trade June, / 39

19 Notations f i,t : S!Nwith Â f i,t (x) = m i,t x2s Firm i of age t located in the origin (x = 0) has: m i,t contacts worldwide f i,t (x) contacts in location x. Each firm trades 1 unit of output with each of its contact(s). Thomas Chaney (Toulouse) Networks and International Trade June, / 39

20 Notations f i,t : S!Nwith Â f i,t (x) = m i,t x2s Firm i of age t located in the origin (x = 0) has: m i,t contacts worldwide f i,t (x) contacts in location x. Each firm trades 1 unit of output with each of its contact(s). Average # of contacts in x among firms of age t location in the origin: f t (x) 2 R + Thomas Chaney (Toulouse) Networks and International Trade June, / 39

21 Direct contacts Number: each period, a firm receives gµ direct contacts. Geography: g (0, x), probabilitythatadirectcontactoriginating from 0 finds a contact in x. Thomas Chaney (Toulouse) Networks and International Trade June, / 39

22 Remote contacts Number: each period, a firm receives gµp remote contacts from any existing contact. Note: p measures relative importance of remote versus direct search. Geography: g (y, x), probabilitythataremotesearchoriginating from y finds a contact in x. Thomas Chaney (Toulouse) Networks and International Trade June, / 39

23 Dynamics f t+1 (x) f t (x) = gµg (0, x) {z } {z } new contacts in x direct contacts + gµp Â f t (y) g (y, x) y2s {z } remote contacts via any y Thomas Chaney (Toulouse) Networks and International Trade June, / 39

24 Total number of contacts Number of contacts at age t: m t+1 m t = gµ + gµpm t Distribution of contacts in the population: F (m) = pm 1 µp Thomas Chaney (Toulouse) Networks and International Trade June, / 39

25 Total number of contacts Number of contacts at age t: m t+1 m t = gµ + gµpm t Distribution of contacts in the population: F (m) = pm 1 µp Limit, m! 0, Limit, m!, m Exponential m Pareto 1 µ 1 µp Thomas Chaney (Toulouse) Networks and International Trade June, / 39

26 Geography of trade Special analytical case, S = Z g (y, x) only depends on the distance x y. Thomas Chaney (Toulouse) Networks and International Trade June, / 39

27 Geography of trade Special analytical case, S = Z g (y, x) only depends on the distance x y. Assumption: g ( ) has a finite second moment. Thomas Chaney (Toulouse) Networks and International Trade June, / 39

28 Notations Geography of trade for firm with m contacts, g m (x) = f m (x) m Average (squared) distance of exports, D (m) Â x 2 g m ( x ) x2z Thomas Chaney (Toulouse) Networks and International Trade June, / 39

29 Firm level geography of trade D (m) = ln (1 + pm) D g pm with D g Â x2s x 2 g ( x ) the second moment of g ( ). Thomas Chaney (Toulouse) Networks and International Trade June, / 39

30 Firm level geography of trade D (m) = ln (1 + pm) D g pm with D g Â x2s x 2 g ( x ) the second moment of g ( ). Special case, p! 0(noremotesearch), Limit, m! 0(newexporters), Limit, m! (large exporters), D (m) D (m) = D g, 8m D (m) m m=0 = 0 m! constant + D g ln (m) Thomas Chaney (Toulouse) Networks and International Trade June, / 39

31 Derivations The geographic distribution of contacts evolves recursively, f t+1 (x) = gµg (0, x) + f t (x) + gµp Â f t (y) g (x y) y2z Thomas Chaney (Toulouse) Networks and International Trade June, / 39

32 Derivations The geographic distribution of contacts evolves recursively, f t+1 (x) = gµg (0, x) + f t (x) + gµp Â f t (y) g (x y) y2z Trick #1: recognize a convolution product ( ), f t+1 = gµg + f t + gµpg f t Thomas Chaney (Toulouse) Networks and International Trade June, / 39

33 Derivations The geographic distribution of contacts evolves recursively, f t+1 (x) = gµg (0, x) + f t (x) + gµp Â f t (y) g (x y) y2z Trick #1: recognize a convolution product ( ), f t+1 = gµg + f t + gµpg f t Trick #2: take a Fourier transform, to get a simple difference equation: f t (x) F! ˆf t (s) ˆf t+1 = gµĝ + ˆf t + gµpĝ ˆf t Thomas Chaney (Toulouse) Networks and International Trade June, / 39

34 Derivations The geographic distribution of contacts evolves recursively, f t+1 (x) = gµg (0, x) + f t (x) + gµp Â f t (y) g (x y) y2z Trick #1: recognize a convolution product ( ), f t+1 = gµg + f t + gµpg f t Trick #2: take a Fourier transform, to get a simple difference equation: f t (x) F! ˆf t (s) ˆf t+1 = gµĝ + ˆf t + gµpĝ ˆf t Trick #3: easy to recover moments from Fourier transforms, D t = ĝ t (0) = ˆf t (0) m t Thomas Chaney (Toulouse) Networks and International Trade June, / 39

35 Empirical tests Thomas Chaney (Toulouse) Networks and International Trade June, / 39

36 Theoretical limitations Ionlysolvethemodelunderthesimplifyingassumptions: 1 Large population limit (LLN). 2 Simple geography (S = Z). Iusenumericalsimulationsto confirm thetheory. Thomas Chaney (Toulouse) Networks and International Trade June, / 39

37 Simulation: number of contacts Thomas Chaney (Toulouse) Networks and International Trade June, / 39

38 Simulations: geography of contacts Thomas Chaney (Toulouse) Networks and International Trade June, / 39

39 Empirical limitations Theory about firms selling to contacts. Data about firms exporting to countries. Solution: use a Simulated Method of Moments. Thomas Chaney (Toulouse) Networks and International Trade June, / 39

40 Simulated Method of Moments (SMM) Choose the parameters, Q, to estimate, Q = (µ, p, l) with g (y, x) µ e x y /l Thomas Chaney (Toulouse) Networks and International Trade June, / 39

41 Simulated Method of Moments (SMM) Choose the parameters, Q, to estimate, Q = (µ, p, l) with g (y, x) µ e x y /l Chose the vector of 120 moments, k, tomatch, number of firms exporting to 1, 2,..., 69 countries, and 70 or more. average squared distance of exports for firms exporting to 1, 2, countries. Thomas Chaney (Toulouse) Networks and International Trade June, / 39

42 Simulated Method of Moments (SMM) Choose the parameters, Q, to estimate, Q = (µ, p, l) with g (y, x) µ e x y /l Chose the vector of 120 moments, k, tomatch, number of firms exporting to 1, 2,..., 69 countries, and 70 or more. average squared distance of exports for firms exporting to 1, 2, countries. Choose a weighting matrix, W, to account for moments precision. Thomas Chaney (Toulouse) Networks and International Trade June, / 39

43 Simulated Method of Moments (SMM) Choose the parameters, Q, to estimate, Q = (µ, p, l) with g (y, x) µ e x y /l Chose the vector of 120 moments, k, tomatch, number of firms exporting to 1, 2,..., 69 countries, and 70 or more. average squared distance of exports for firms exporting to 1, 2, countries. Choose a weighting matrix, W, to account for moments precision. Minimize the distance between actual and simulated moments, 0 bq = arg min k b k (Q) W k b k (Q) Q Thomas Chaney (Toulouse) Networks and International Trade June, / 39

44 Simulated Method of Moments (SMM) Choose the parameters, Q, to estimate, Q = (µ, p, l) with g (y, x) µ e x y /l Chose the vector of 120 moments, k, tomatch, number of firms exporting to 1, 2,..., 69 countries, and 70 or more. average squared distance of exports for firms exporting to 1, 2, countries. Choose a weighting matrix, W, to account for moments precision. Minimize the distance between actual and simulated moments, 0 bq = arg min k b k (Q) W k b k (Q) Q Construct bootstrapped standard errors. Thomas Chaney (Toulouse) Networks and International Trade June, / 39

45 SMM results Thomas Chaney (Toulouse) Networks and International Trade June, / 39

46 Next step This was all about firm level trade. What about aggregate trade? This model can explain why trade µ 1/distance. Reference: The Gravity Equation in International Trade: An Explanation. Thomas Chaney (Toulouse) Networks and International Trade June, / 39

47 Amended model Get rid of direct search. Firms explicitly meet contacts of contacts. Continuous time, continuous space. b: birth rateofcontacts(fromfriendsoffriends). d: death rateofcontacts. Thomas Chaney (Toulouse) Networks and International Trade June, / 39

48 Recursive structure The geographic distribution of contacts evolves recursively, ˆ f t (x) f t (x y) = b f t (y) dy df t (x) t K t R Thomas Chaney (Toulouse) Networks and International Trade June, / 39

49 Recursive structure The geographic distribution of contacts evolves recursively, ˆ f t (x) f t (x y) = b f t (y) dy df t (x) t K t R Trick: take a Laplace transform, to get a simple ODE: f t (x) L! ˆf t (s) ˆf t (s) t = b ˆf t 2 (s) e (b d)t dˆf t (s) Thomas Chaney (Toulouse) Networks and International Trade June, / 39

50 Firm level exports Proposition g t converges to a Laplace distribution (2-sided exponential), g t (x) f t (x) K t Laplace 0, e bt/2p D 0 /2 t! Note: holds exactly for all t s if g 0 Laplace 0, p D 0 /2. Thomas Chaney (Toulouse) Networks and International Trade June, / 39

51 Firm level exports Proposition g t converges to a Laplace distribution (2-sided exponential), g t (x) f t (x) K t Laplace 0, e bt/2p D 0 /2 t! Note: holds exactly for all t s if g 0 Laplace 0, p D 0 /2. Corollary Over time, the world becomes flat for individual firms. Thomas Chaney (Toulouse) Networks and International Trade June, / 39

52 Firm level exports Proposition g t converges to a Laplace distribution (2-sided exponential), g t (x) f t (x) K t Laplace 0, e bt/2p D 0 /2 t! Note: holds exactly for all t s if g 0 Laplace 0, p D 0 /2. Corollary Over time, the world becomes flat for individual firms. Note Holds for any arbitrary initial friction g 0 (symmetric and finite variance). Thomas Chaney (Toulouse) Networks and International Trade June, / 39

53 Two intermediate results 1. Distribution of number of contacts within the population is Pareto, Pr K K K = 1 F (K ) = K 0 g b d Thomas Chaney (Toulouse) Networks and International Trade June, / 39

54 Two intermediate results 1. Distribution of number of contacts within the population is Pareto, Pr K K K = 1 F (K ) = Note: Zipf s law for (total) exports, g b d 1+. K 0 g b d Thomas Chaney (Toulouse) Networks and International Trade June, / 39

55 Two intermediate results 1. Distribution of number of contacts within the population is Pareto, Pr K K K = 1 F (K ) = Note: Zipf s law for (total) exports, g b d Average (squared) distance is power function of K, ˆ D (K ) R K 0 x 2 f K (x) K K dx = D 0 K 0 g b d b b d Thomas Chaney (Toulouse) Networks and International Trade June, / 39

56 2conditionsinthedata Source: Frenchcustoms,1992. Dataset: all French firms with exports over 1 Million FF (US$200,000). Red lines: left,d (K ) µ K.18 ; right, Zipf s law, Pr K > K µ K 1. Thomas Chaney (Toulouse) Networks and International Trade June, / 39

57 Aggregate exports: gravity Proposition Aggregate trade: total number of shipments, g e = 2min b d 1 b b d, 1. GDP A GDP B N AB µ Dist AB! (Dist AB ) 1+e Thomas Chaney (Toulouse) Networks and International Trade June, / 39

58 Aggregate exports: gravity Proposition Aggregate trade: total number of shipments, g e = 2min b d 1 b b d, 1. GDP A GDP B N AB µ Dist AB! (Dist AB ) 1+e Corollary Zipf s law ) g b d = 1+ ) 1 + e = 1 + ) Gravity in trade Thomas Chaney (Toulouse) Networks and International Trade June, / 39

59 Aggregate exports: gravity Proposition Aggregate trade: total number of shipments, g e = 2min b d 1 b b d, 1. GDP A GDP B N AB µ Dist AB! (Dist AB ) 1+e Corollary Zipf s law ) g b d = 1+ ) 1 + e = 1 + ) Gravity in trade Note Arbitrary distance friction g 0 (symmetric and finite variance). Thomas Chaney (Toulouse) Networks and International Trade June, / 39

60 Aggregate exports: numerical examples Thomas Chaney (Toulouse) Networks and International Trade June, / 39

61 Thanks Thomas Chaney (Toulouse) Networks and International Trade June, / 39

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

International Trade. Lecture 4: the extensive margin of trade. Thomas Chaney. Sciences Po. Thomas Chaney (Sciences Po) International Trade 1 / 17 International Trade ecture 4: the extensive margin of trade Thomas Chaney Sciences Po Thomas Chaney (Sciences Po) International Trade / 7 Target of the paper Explain the observed role of the extensive