International Trade: Linking Micro and Macro

Transcription

1 International Trade: Linking Micro and Macro Jonathan Eaton (The Pennsylvania State niversity) Samuel Kortum (niversity of Chicago) Sebastian Sotelo (niversity of Chicago)

2 Motivating Questions What do we learn from looking at Örm-level trade? Are we too wedded to models with a continuum of goods and/or producers? Can we handle a Önite-Örm model?

3 Motivating ata ilateral trade in 1992 from eenstra, Lipsey, and owen (1997). irm-level exports in 1992 to 92 countries from: ñ razil: Arkolakis and Muendler (2010). ñ enmark: Pedersen (2008, 2009) (1993 data). ñ rance: Eaton, Kortum, and Kramarz (2010). ñ ruguay: Raul Sampognaro (2009).

4 Macro: Zeros (one-third of bilateral observations)

5 Table 1. Trade in Manufactures Value of Trade Trade Partners in Sample (Million S) (out of a total of 91) Country Total Exports Total Imports No. estinations No. Sources 9 razil Chile enmark rance Korea (South) Nepal Nigeria nited States of America ruguay Average Variance

6 Micro and Macro: Extensive Margin

7 micro data micro data micro data micro data S$ millions razil enmark macro data macro data rance ruguay macro data macro data

8 igure 1. Micro and Macro ilateral Trade Number of bilateral exporters Volume of bilateral trade (S millions)

9 Micro: ig Exporters (1986 data)

10 Table 2. Share of Largest rench Exporters rench Exports to: Std. ev. of Shares Everywhere nited States enmark across estinations Top Top Top 1, Top 10,

11 Related Work Exporter facts: ernard and Jensen (1995), Roberts and Tybout (1997). New Örm-level theories: EJK (2003), Melitz (2003), ernard, Redding, and Schott (2007), Chaney (2008), Arkolakis (2011). inite number of producers: Gabaix (2010), Canals, Gabaix, Vilarrubia, and Weinstein (2007), di Giovanni and Levchenko (2009), Armenter and Koren (2008). Zero problem: Eaton and Tamura (1994), Santo Silva and Tenreyro (2006), Helpman, Melitz, and Rubinstein (2008),...

12 inite-irm Model

13 Overview Work with a parameterized Melitz model. ut, a countable number of Örms. Juxtapose traditional continuum model with the Önite-Örm model to emphasize similarities.

14 Technologies Each produces unique good with e ciency Z. One Örm per technology and one technology per Örm. Continuum model: Measure of Örms from country i with Z>z: z i (z) =T iz : inite-örm model: parameter z i (z). Number of such Örms is distributed Poisson with Rank them: Z (1) i >Z (2) i >Z (3) i > :::

15 Costs Wage w i taken as exogenous. Trade cost d ni 1, so that unit cost to n from i: C ni (Z) = w id ni Z : Implies C ni c i Z z = w i d ni =c:

16 Micro: Signs of Pareto

17 average sale in rance ($ millions) igure 2: omestic Sales and Entry into Export Markets rench firms selling to k or more markets

18 Costs II Continuum model: Measure of Örms from i that can supply n at cost below c: c ni (c) = nic ; where ni = T i [w i d ni ]. inite-örm model: parameter c ni (c). Number of such Örms is distributed Poisson with

19 Costs in estination Continuum model: Measure of Örms from anywhere supplying n at cost below c: c n(c) = IX i=1 c ni (c) = nc : inite-örm model: The sum of independent Poissons is Poisson with parameter c n(c). Can rank these costs: C n (1) < C n (2) < ::: < C n (k) indicate when kíth lowest cost is from i. < :::, letting I (k) ni

20 Trade Share Continuum model: Of Örms that deliver to n at cost below c, fraction from i is: ni = c ni (c) c n(c) = ni ; n for any c. inite-örm model: Now ni becomes the probability that a Örm selling in n is from i. Thus E[I (k) ni ]= ni for any k.

21 Preferences and Market Structure ixit-stiglitz preferences (elasticity of substitution >1). Monopolistic competition, ertrand competition, Örms pay an entry cost E n = w n n to sell in market n. A Örm with cost C charging price p and facing aggregate price level P n, has gross proöt n (p; C) = (1 C p ( 1) p ) Xn : P n irm takes X n as given (proöts spent elsewhere), but realizes P n may depend on p.

22 Continuum Case irm takes P n as given so sets price p n (C) = 1 C = mc. irm enters market n i C c n, the cost threshold. Closed-form solutions for price index P n and cost threshold c n, if > 1. irm sales, conditional on entry: with mean X n = Pr [X n (C) xjc c n ]= ( 1) E n. x E n =( 1) ;

23 Explaining igure 2 (with continuum model) Order countries by cost threshold: c 1 > c 2 > c 3 > ::: > c I : Measure of rench Örms with cost less than c m (hence selling to m or more): N m = m (c k )= m [c m ] = T [w ] c m d m! : Minimum sales in rance of such a Örm (proportional to mean sales): X = m [c! ( 1) m=d m ] X = [N m ] ( 1)= : P

24 inite-irm Model Consider market n with costs C n (1) <C n (2) < ::: < C (k) n < :::. Let I (k) n indicate whether the kíth lowest cost Örm actually sells in n. Assume equilibrium with I (k) n =1for k K n and 0 otherwise: 1. Given K n, ertrand competition determines price: p K n n (C n (k) ), for k =1; :::; K n : 2. Entry satisöes K n n (C (K n) n ) E n and K n+1 n (C (K n+1) n ) <E n.

25 Solving or Equilibrium ertrand conditions in Atkeson and urstein (2008) for given K n : 1. market share of the kíth Örm: s (k) n = X(k) n = X n p K n n P Kn k=1 (C n (k) ( 1) ) p K n n (C n (k) ( 1) ) 2. markup of the kíth Örm: p K n n (C n (k) ) C n (k) = ( 1)s (k) ( 1)s (k) n n 1

26 Easy to Simulate Costs Highest e ciency has extreme value distribution: Pr[Z (1) i z] =e T iz : Letting (1) i = T i Z (1) i, draw (1) as a unit exponential. Climb the order statistics: Pr[ (k+1) i (k) i u] =1 e u : Construct ordered costs: C (k) ni = w i d ni (k) 1= = i =T i (k) i n ni 11= A :

27 QuantiÖcation

28 Gravity Equation Continuum model: X ni X n = ni : se directly for calibration, ekle, Eaton and Kortum (2007, 2008). inite-irm model: E Xni X n = ni = T i [w i d ni ] Pl T l [w l d nl ] : Calibration is out.

29 Gravity Equation II Error term from randomness in K ni =K n and in sales (and location) of largest Örms X n (1), X n (2),... se Pseudo Maximum Likelihood, as in Santos Silva and Tenreyro (2006), but here multinomial likelihood. The moment condition (m n + g 0 nn dropped): E Xni X n = exp S i + m n + g 0 ni exp(s n )+ P l6=n exp S l + m n + g 0 nl Gives estimates b ni of ni, positive even if X ni =0.

30 Table 3. ilateral Trade Regressions OLS Poisson Multinomial istance (0.0379) (0.0444) (0.0511) Lack of Contiguity (0.156) (0.181) (0.136) Lack of Common Language (0.0808) (0.131) (0.106) Lack of Common Legal Origin (0.0593) (0.0778) (0.0721) Lack of Common Colonizer (0.146) (0.199) (0.204) Lack of Colonial Ties (0.126) (0.122) (0.139) Adjusted R sq Pseudo R sq Number of observations Standard errors in parentheses p<0.05, p<0.01, p<0.001

31 Mean Sales per irm Since E n is common across sources i, mean sales per Örm in n is invariant to the source country, so can be inferred from our data on exporters from just 4 countries. Let n be the subset of these 4 with Örms exporting to n: P c i2 X n = n K ni X ni P i 0 2 n K ni 0 Results in Table 4. Gives us an estimate of entry c K n = X n = c X n.

32 Table 4. Mean Sales per irm estination No. of Source Mean Sales Country Countries per irm razil Chile enmark rance Japan Jordan Kenya Korea (South) Nepal Nigeria nited States of America ruguay

33 Predicting Zeros Can use our estimates to calculate the probability of country i not selling to n: Pr [K ni =0] = (1 ni ) K n replacing ni with b ni and K n with c K n. Can also repeatedly simulate zeros over the whole matrix of country pairs, using the same draw for a single source across all destinations.

34 raction igure 2a. Probabilities of observing zero trade, given no trade Pr[K_ni = 0 X_ni = 0 ] aseline irichlet, \eta^2 =

35 raction igure 2b. Probabilities of observing zero trade, given positive trade Pr[K_ni = 0 X_ni > 0 ] aseline irichlet, \eta^2 =

36 # of estinations # of estinations igure 3a. Actual and Simulated Number of estinations ata Average of 1000 Simulations Total Absorption (S$ Millions)

37 # of Sources # of Sources igure 3b. Actual and Simulated Number of Sources ata Average of 1000 Simulations Total Absorption (S$ Millions)

38 Simulating irm Costs Replacing ni with b ni, we can follow the procedure described above for simulating costs C (1) ni <C (2) ni <C (3) ni < :::. Need a value of : estimate of 4:87 from Eaton, Kortum, and Kramarz (2011). Combine cost simulation from all sources and reorder as C (1) n <C (2) n < C (3) n < ::: Record I (k) ni to reconstruct exports.

39 Simulating irm Sales Now calculate the ertrand equilibrium, given K n with c K n. Need a value of (no longer need > 1): estimate of 2:98 in EKK (2011). Also consider values consistent with Zipf: =5:64 (so that =( 1) = 1:05) and =7:09. Recover sales of Örmís from i in n as: X (k) ni = I (k) ni X(k) n = I (k) ni s(k) n X n :

40 Results istribution of price markups among largest Örms. Contribution to total rench exports from the largest exporters (strong evidence for the middle values of ).

41 ertrand Markup igure 4. Markups of Top 10 Entrants (ertrand Competition) Percentile 95 Percentile 25 S Markup irm

42 Table 6. Share of Largest rench Exporters Average Standard eviation ( Across 10 Simulations) (Across 10 Simulations) =7:09 =5:64 =2:98 =7:09 =5:64 =2:98 Top Top Top 1, Top 10,

43 igure. Micro and Macro ilateral Trade (Simulation) Number of bilateral exporters Volume of bilateral trade (S millions)

44 Entry Costs In anticipation of doing counterfactuals, want values for the entry costs. Simulated gross proöt K b n n (C n (k) )= 2 41 C(k) n K p b n n (C n (k) ) p K b n n (C n (k) 3 ( 1) ) K P b 5 n n X n : pper bound on entry cost (see Ögures) be n = b K n n (C ( b Kn ) n ):

45 Experiments

46 Two Types Set to recompute the full equilibrium of the model under di erent scenarios. Type I: change parameters but Öx the underlying technology draws. Example: globalization, which can now open up new trade links. Type II: draw a new set of technologies but Öx all the parameters. Example: granularity so that luck-of-the-draw e ects aggregates, such as welfare.

47 Globalization Suppose all trade costs fall by 10%. As in EK (2007, 2008), this change enters the model through the ni : b 0 ni = b ni [1:1] b nn + P l6=n b nl [1:1] Can apply b 0 ni to the same realizations of the u(k) i ís. Overall 206 new trade links arise, but they account for a tiny fraction of the growth in trade.

48 Granularity Redraw (200 times) (k) i ís, each time recomputing the world equilibrium with endogenous entry. or each new set of technologies, compute the price level (for n equal to enmark and nited States): ln P 0 n = 1 1 ln 0 X Kn k=1 as well as the location of the top Örms. p K0 n n (C (k) n ) ( 1) 1 C A Results in last Ögure.

49 enmark igure 6. Variation of P n across simulations 10 Percent eviation from Mean 5 0 SA SA SA SA SA SA KOR GR GR GR ESP RA JPN -5 GTMTN GR -10 GR IRL RA VNM nited States

50 Conclusions ropping the continuum opens up new possibilities for confronting the micro data. And, we donít lose the ability to compute aggregate implications. Weíve left a lot of room to make the model richer.

51 Table 5. Source Country Coe cients Mean Sales* enmark (0.0216) razil (0.0221) ruguay (0.0680) p-value for test of joint signi cance Number of observations 282 Standard errors in parentheses *OLS Regression also includes all destination country e ects as independent variables p<0.05, p<0.01, p<0.001

52 Table 1. escriptive Statistics Total Trade ($ mil.) # of Zeros in Sample Country Exports Imports Exports Imports razil 27,212 13, Chile 7,067 7, enmark 23,624 19, rance 141, , Korea (South) 59,662 47, Nepal Nigeria 261 5, nited States 359, , ruguay 1,324 1,

53 igure 1. Micro and Macro ilateral Trade Number of bilateral exporters Volume of bilateral trade (S millions) Real data

54 Table 2. Entry Cost Estimation Country # of Source Countries Mean Sales per Market razil Chile enmark rance Korea (South) Nepal Nigeria nited States ruguay