1. Superstar Firms in International Trade
J. Peter Neary
University of Oxford and CEPR
12 September 2011

2. 1. Introduction “Two and a Half Theories of Trade”:
1.0: Perfect Competition: Comparative Advantage
2.0: Monopolistic Competition: Product Differentiation and Increasing Returns
2.5: Oligopoly
Despite growing empirical evidence: large firms matter for trade
The “2nd Wave” of micro data on firms & trade
1st wave (1995-): Exporting firms are exceptional:
Larger, older, more productive, pay higher wages, do more R&D
2nd wave: Even within exporters, large firms dominate:
[Bernard et al. (JEP 2007), Mayer and Ottaviano (2007)]
Distribution of exporters is bimodal
The firms that matter (for most questions) are different: larger, multi-product, multi-destination
Possible to model this using a Pareto distribution with high dispersion
“Granularity”: Gabaix (2005), di Giovanni and Levchenko (2009)
I prefer to try “putting the grains into granularity”

3. Bernard et al. (JEP 2007):
Data on U.S. exporting firms 2000
By # of products & export destinations
1 product,
1 destination only:
5+ products:
40.4% of firms
& 5+ dests.:
11.9% of firms
25.9% of firms
0.20% of export value
92.2% of export value
98.0% of export value
7.0% of employment
68.8% of employment
83.3% of employment

4. Why does oligopoly give only half a theory of trade?
1. Introduction (cont.)
Why does oligopoly give only half a theory of trade?
In I.O. it gets equal billing: “Two faces”
Take-home messages less than overwhelming?
Cross-hauling of identical goods [Brander JIE 1980] ...
Empirically important?
Friberg-Ganslandt (JIE 2006)
Competition effect of trade [Brander] ...
Also in monopolistic competition if s is variable
Krugman (JIE 1999), Behrens-Murata (JET 2007), Melitz-Ottaviano (REStud 2008)
Strategic trade policy [Brander-Spencer JIE 1984] ...
Non-robust to assumptions about factor mobility and firm behaviour
Dixit-Grossman (1986), Eaton-Grossman (1986)

5. Not embedded in general equilibrium?
1. Introduction (cont.)
Not embedded in general equilibrium?
This can be done: General Oligopolistic Equilibrium [“GOLE”]
Neary (JEEA 2003, REStud 2007), Bastos and Krieckemeier (JIE 2009), Grossman and Rossi-Hansberg (QJE 2010), Bastos and Straume (2010)
Trade with oligopoly interesting because there is less of it, not more
Competition effects and comparative advantage interact: profit share may rise
Suggests an explanation for non-price effects of foreign competition on wages
Allows consideration of effects of trade on market structure itself
Neary (2002, RIE 2002, REStud 2007)
Hard to combine with entry and exit?
Here: Some potential approaches
Based on work in progress with Carsten Eckel and with Kevin Roberts
… combining oligopoly with entry
… and with heterogeneous firms

6. Plan Introduction Oligopoly plus Free Entry Heterogeneous Industries
Natural Oligopoly
Superstar Firms
Conclusion

7. Plan Introduction Oligopoly plus Free Entry Heterogeneous Industries
Natural Oligopoly
Superstar Firms
Conclusion

8. 2. Oligopoly plus Free Entry
The “Integer Problem”:
Ignoring it comes close to assuming monopolistic or perfect competition:
Brander and Krugman (1983): Trade liberalization cannot lower welfare
Markusen and Venables (1988): No role for strategic trade policy
Head, Mayer and Ries (2002): No home-market effect.
Taking account of it is hard
Or is it?
Promising approach: impose restrictions on profit functions:
Bergstrom-Varian (REStud 1985): Profits depend on own costs and average of all firms’
e.g., Cournot with identical goods
Acemoglu-Jensen (CEPR WP 2009): “Aggregative games”: Profits depend on own costs and a generalised mean of all firms’:
e.g., Cournot or Bertrand with CES differentiated products
Proposition:
The number of firms in any heterogeneous-firm free-entry equilibrium of an aggregative game is the same as the integer number of firms in the corresponding “lean” homogeneous-firm non-integer equilibrium.

9. 3. Oligopoly plus Free Entry (cont.)
Heterogeneous-firm equilibrium in an aggregative game:
(i) Firms’ costs a random draw:
ci drawn from g(ci) with positive support over [c,)
(ii) Incumbents do not make losses:
(iii) A new “lean” entrant would make a loss:
Symmetric equilibrium:
i.e., assume own effect dominates cross effect
Lean symmetric equilibrium:
Non-integer lean symmetric equilibrium:
Proposition:
The number of firms in any free-entry equilibrium of an aggregative game is the same as the integer number of firms in the non-integer lean symmetric equilibrium 9 9

10. Example: The Linear Cournot Model
Solution in symmetric (homogeneous-firm) case:
ubs

13. Plan Introduction Oligopoly plus Free Entry Heterogeneous Industries
Natural Oligopoly
Superstar Firms
Conclusion

14. 3. Heterogeneous Industries
Firm heterogeneity in monopolistic competition:
[Melitz (Em 2003)]
Firms pay a sunk cost to reveal their unit cost
Draw c from g(c) with positive support over [c , )
Given c, they calculate their expected profits and choose to produce or exit
Exit if c < ce where p(ce) = 0 or r(ce) = f .
If exporting requires an additional fixed cost, only low-cost firms will engage in it
Extend to a continuum of industries/sectors:
Firms draw a unit cost and a sector: {c, z}
Sectors differ in their fixed costs: f(z), f ´ > 0
In equilibrium, sectors have different expected firm numbers

15. n Equilibrium Expected Market Structure 16 8 4 2 1 1
Monopolistic Competition 16 8
Oligopoly 4 2
Monopoly 1 1
Equilibrium Expected Market Structure
(Vertical scale is ln2n)

16. Plan Introduction Oligopoly plus Free Entry Heterogeneous Industries
Natural Oligopoly
Superstar Firms
Conclusion

17. 4. Natural Oligopoly So far: Fixed costs exogenous
Now, allow them to be chosen endogenously
Dasgupta-Stiglitz (EJ 1980), Gabszewicz-Thisse (JET 1980), Shaked-Sutton (Em 1983), Sutton (1991, 1998)
Free entry condition:
[Equilibrium operating profits a reduced-form function of firm numbers and market size]
p(n,s) = 0
Define: Market-Size Elasticity of Market Structure:
Stability requires pn < 0 for given s
Presumption (?) that ps > 0
So, E presumptively positive?
Clearly so in simple entry games: Cournot, Bertrand
Not necessarily positive in multi-stage games
“Natural Oligopoly” the case where E  0

18. Example: The Linear-Quadratic R&D+Cournot Case
Investments are unfriendly
Hence, E can be very small or negative.
Solution in symmetric non-strategic case:
ubs
[“Relative efficiency of R&D” for a unit market size]

21. Plan Introduction Oligopoly plus Free Entry Heterogeneous Industries
Natural Oligopoly
Superstar Firms
Conclusion

22. 5. Superstar Firms Distribution of ex ante identical firms:
Stage 1: Pay a fixed cost f to discover their unit cost c
Stage 2: Choose to either:
Remain as a “small” firm ; or:
Pay a further cost fL to invest (in capacity/R&D/technology adoption/ product range) and become a “large” firm
Stage 3: Competition in quantities or prices:
Strategic competition between large firms
…… facing a (monopolistically) competitive fringe

23. G(c): Cumulative distribution of unit costs
Crucial assumption:
G(c)
G(c) c
(fL )
Threshold for acquisition of
“superstar” technology
(f )
Threshold for entry
Entry condition for “superstar” firms? Same as Section 2 only!

24. 5. Superstar Firms (cont.)
So far: Advantage of “large firms” unspecified
One important case: Large firms produce a continuum of products
Consistent with earlier empirical evidence
Solves a technical problem: large firms are of finite, small ones of zero measure
Different approaches to modelling multi-product firms:
(1) I.O.: Products few and/or fixed; product line / quality competition.
(2) Symmetric demands and costs
Allanson and Montagna (IJIO 2005), Feenstra and Ma (2009), Nocke and Yeaple (2006)
(3) Stochastic market-specific costs
Bernard, Redding and Schott (AER 2009)
(4) “Flexible manufacturing”
Eckel and Neary (REStud 2010)
Empirical evidence favours (4):
Arkolakis-Muendler (2010)
(2) predicts equal sales of all varieties - rejected
(3) predicts sales ranks uncorrelated across markets - rejected
But (2) is more tractable!
Work in progress: Extend model of oligopoly with multi-product firms to allow for entry by “small” firms 24 24

25. Flexible Manufacturing
Product Range
“Core Competence”
Flexible Manufacturing

26. Output, Price, and Cost Profiles
“Core Competence”
Output, Price, and Cost Profiles 26

27. Intra-Firm Effects of Globalization
“Leaner and Meaner”:
More Competition: Scope falls
Larger Market: Scale rises
Outputs rise
Outputs fall

28. Plan Introduction Oligopoly plus Free Entry Heterogeneous Industries
Natural Oligopoly
Superstar Firms
Conclusion

29. 6. Conclusion
A road-map, not a model; hopefully with implications for:
1. Theory:
Reconcile the “Two faces of IO”
Large firms matter for more than just reciprocal dumping
2. Policy:
Hosting superstar firms, or not, may matter?
Fostering entrepreneurship / entry?
Competition policy in general equilibrium
Trade liberalization in oligopoly
3. Empirics:
Firm level data: Good news and bad
Errors at the top more costly
Ideally, think of the industry at the world level

30. Payoff to looking at the grains in granularity
6. Conclusion (cont.)
Summary:
Time for Trade Theory
Payoff to looking at the grains in granularity

31. Thank you!

32. 1. Introduction Inspiration: The Krugman Oral Tradition!
1.0: Perfect Competition: Comparative Advantage
2.0: Monopolistic Competition: Product Differentiation and Increasing Returns
2.5: Oligopoly

33. 2. How Many Theories of Trade?
Perfect versus Monopolistic Competition?
Perfect and/or Monopolistic Competition?
Similar assumptions
Similar implications with constant s : e.g., gravity equations
Both imply production efficiency, so can be represented by a GDP function:
Dixit-Norman (1980)
Dixit and Stiglitz (1977), Helpman (1984), Feenstra and Kee (JIE 2008)
Anyway: 2 full-fledged theories
So, why not trade with oligopoly too?
In I.O. it gets equal billing: “Two faces”

34. 2. How Many Theories of Trade? (cont.)
Why does oligopoly give only half a theory of trade?
Take-home messages less than overwhelming?
Cross-hauling of identical goods ...
Empirically important?
Friberg-Ganslandt (JIE 2006)
Competition effect of trade ...
Also in monopolistic competition if s is variable
Krugman (JIE 1999), Behrens-Murata (JET 2007), Melitz-Ottaviano (REStud 2008)
Strategic trade policy ...
Non-robust to assumptions about factor mobility and firm behaviour
Dixit-Grossman (1986), Eaton-Grossman (1986)
Not embedded in general equilibrium?
This can be done: General Oligopolistic Equilibrium [“GOLE”]
Neary (JEEA 2003)
Trade with oligopoly interesting because there is less of it, not more
Competition effects and comparative advantage interact: profit share may rise
Suggests an explanation for non-price effects of foreign competition on wages
Allows consideration of effects of trade on market structure itself
Neary (2002, RIE 2002, REStud 2007)

35. How Many Theories of Trade? (cont.)
One more reason why oligopoly matters for trade:
Empirics: The “2nd Wave” of micro data on firms & trade
1st wave (1995-): Exporting firms are exceptional:
Larger, more productive
2nd wave: Bernard et al. (JEP 2007): Even within exporters, big firms dominate:
[Similar results for France: Mayer and Ottaviano (2007)]
Distribution of exporters is bimodal:
40.4% of U.S. exporting firms in 2000 exported one product only; accounted for only 0.20% of export value
25.9% of U.S. exporting firms in 2000 exported 5 or more products; accounted for 98.0% of export value
11.9% of U.S. exporting firms in 2000 exported 5 + products to 5+ destinations; accounted for 92.2% of export value
The firms that matter (for most questions) are different: larger, multi-product, multi-destination
Possible to model this using a Pareto distribution with high dispersion
“Granularity”: Gabaix (2005), di Giovanni and Levchenko (2009)
I prefer to try “putting the grains into granularity”

36. How Many Theories of Trade? (cont.)
One more theoretical hurdle to be crossed:
How to combine oligopoly with entry and exit?
Here: Some potential approaches
Based on work in progress with Carsten Eckel and with Kevin Roberts
… combining oligopoly with entry
… and with heterogeneous firms

37. 3. Oligopoly plus Free Entry (cont.)
For given market size s, assume profits of firm i depend on own costs ci, on the average of rivals’ costs c–i, and on n:
[Bergstrom-Varian REStud 1985]
pi = p(ci , c–i , n)
– –
In symmetric equilibrium:
p s(c,n)  p(c, c, n)
– –
i.e., assume own effect dominates cross effect
Start with symmetric case:
We can characterise the admissible range of c and n:
(1) p s(c,n)  [Incumbents do not make losses]
(2) p s(c,n+1) < [A new entrant would make a loss]

38. (1) p s(c,n)  0 [Incumbents do not make losses]
(2) p s(c,n+1) < [A new entrant would make a loss] n*
n* is the maximum equilibrium number of firms;
BUT: A real number, not necessarily an integer ne
n*–1
p s(c,n) = 0
p s(c,n+1) = 0 c
So: “Lean” symmetric equilibrium has:
ne = int (n*–1, n*]

39. So far: Only “lean” symmetric equilibria;
Now, consider symmetric equilibria with less efficient firms: n
[A new lean entrant would make a loss] n* ne
n*–1
p s(c,n) = 0
p s(c,n+1) =0 c
So: Shaded area is the admissible region for equilibrium n in symmetric equilibria
Actual equilibrum values are on the horizontal line corresponding to the integer value:
ne = int (n*–1, n*]

40. Finally: Consider asymmetric equilibria:
Start with simplest case: monopoly vs. duopoly
Assume there is a monopoly equilibrium:
“Lean outsider” condition:
Consider a candidate duopoly equilibrium with:
Proof can be extended to oligopoly and generalised mean [mn] case:
Assume an equilibrium with n–1 firms
Replace “2” by n, c2 by mn, and cm by mn–1 in above
Conclusion: There cannot be an equilibrium with n firms
So: Equilibrium integer n is a monotonic function of (e.g.) industry size
… and, if we know the population distribution of c, we can calculate the distribution of c in free-entry oligopoly equilibrium

41. Possible Cost Configurations in Duopoly
(i) Low s
(ii) Medium s
(iii) High s c2 c2 c2 c1 c1 c1
(i) Only insider constraints bind
(iii) Only lean outsider
constraint binds
(ii) Lean outsider constraint
binds in symmetric equilibria;
insider constraint in asymmetric ones 41

42. 5. Natural Oligopoly (cont.)
With multi-stage competition:  +?
Presumption that dk/ds is positive:
Seade stability condition
Increase in market size raises investment (?)
Hence, for natural oligopoly:
Necessary condition: investments are “unfriendly”:
More likely the more investment responds to market size
… which is more likely if investments are strategic complements:

43. Sales Revenue Profiles in Home and (Larger) Foreign Market43