superstar firms in international trade j. peter neary university of oxford and cepr 12 september...
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Superstar Firms in International Trade
J. Peter Neary
University of Oxford and CEPR
12 September 2011
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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”
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5+ products:
Bernard et al. (JEP 2007):• Data on U.S. exporting firms 2000• By # of products & export destinations
83.3% of employment
25.9% of firms
98.0% of export value
7.0% of employment
40.4% of firms
0.20% of export value
1 product, 1 destination only:
& 5+ dests.:
11.9% of firms
68.8% of employment
92.2% of export value
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Why does oligopoly give only half a theory of trade?In I.O. it gets equal billing: “Two faces”
1. 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 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)
1. Introduction (cont.)
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2. 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 itselfNeary (2002, RIE 2002, REStud 2007)
3. 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
1. Introduction (cont.)
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Plan
1. Introduction
2. Oligopoly plus Free Entry
3. Heterogeneous Industries
4. Natural Oligopoly
5. Superstar Firms
6. Conclusion
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Plan
1. Introduction
2. Oligopoly plus Free Entry
3. Heterogeneous Industries
4. Natural Oligopoly
5. Superstar Firms
6. Conclusion
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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
],)(,[
nccii
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.
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3. Oligopoly plus Free Entry (cont.)
Heterogeneous-firm equilibrium in an aggregative game:
nincc ni ...,10]},{,[ )(
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
Lean symmetric equilibrium:
(i) Firms’ costs a random draw:
],)(,[),(
nccncs
0]1},,{,[ )( nccc n
(ii) Incumbents do not make losses:
(iii) A new “lean” entrant would make a loss:
0)1,(0),( ncandnc ss
Non-integer lean symmetric equilibrium:
0),( ncs
i.e., assume own effect dominates cross effect
ci drawn from g(ci) with positive support over [c,)
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Example: The Linear Cournot Model
• Solution in symmetric (homogeneous-firm) case:
fxcp iii )(
Xsap 1
sn
cax
1
fsn
cafxs
2
21
1
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Plan
1. Introduction
2. Oligopoly plus Free Entry
3. Heterogeneous Industries
4. Natural Oligopoly
5. Superstar Firms
6. Conclusion
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3. Heterogeneous Industries
Firm heterogeneity in monopolistic competition:[Melitz (Em 2003)]
• Firms pay a sunk cost to reveal their unit costDraw 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 (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
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Equilibrium Expected Market Structure(Vertical scale is ln2n)
n
z 1
Monopoly
0
Oligopoly
Monopolistic Competition
2
4
8
16
1
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Plan
1. Introduction
2. Oligopoly plus Free Entry
3. Heterogeneous Industries
4. Natural Oligopoly
5. Superstar Firms
6. Conclusion
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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]
(n,s) = 0Define: Market-Size Elasticity of Market Structure:
• Stability requires n < 0 for given s
• Presumption (?) that s > 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
s
n
ss dnE
n ds n
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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:
fkxcp iiii 2
21)(
iii kcc 0Xsap 1
xkandssn
cax
1
0
2
fscasn
sfkxs
202
21
22121 )(
)1(
1
[“Relative efficiency of R&D” for a unit market size]
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Plan
1. Introduction
2. Oligopoly plus Free Entry
3. Heterogeneous Industries
4. Natural Oligopoly
5. Superstar Firms
6. Conclusion
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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
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G(c)
cc
G(c): Cumulative distribution of unit costs
Crucial assumption:
G(c)
'( ) 0G c
(f )
Threshold for entry
(fL )
Threshold for acquisition of“superstar” technology
Entry condition for “superstar” firms? Same as Section 2 only!
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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 costsAllanson and Montagna (IJIO 2005), Feenstra and Ma (2009), Nocke and Yeaple (2006)
(3) Stochastic market-specific costsBernard, 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
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Flexible Manufacturing
ic
i
“Core Competence”
Product Range
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Output, Price, and Cost Profiles
tc 0
“Core Competence”
i
tic
ip ix
0p
0x
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Intra-Firm Effects of Globalization
ix
i
Outputs rise Outputs fall
“Leaner and Meaner”:•More Competition: Scope falls•Larger Market: Scale rises
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Plan
1. Introduction
2. Oligopoly plus Free Entry
3. Heterogeneous Industries
4. Natural Oligopoly
5. Superstar Firms
6. Conclusion
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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
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6. Conclusion (cont.)
Summary:
• Time for Trade Theory 3.0 ...
• Payoff to looking at the grains in granularity
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Thank you!
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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
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2. How Many Theories of Trade?
Perfect versus Monopolistic Competition?
Perfect and/or Monopolistic Competition?• Similar assumptions
• Similar implications with constant : 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 theoriesSo, why not trade with oligopoly too?
In I.O. it gets equal billing: “Two faces”
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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 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)
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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”
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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
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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]
i= (ci , c–i , n)
– – i.e., assume own effect dominates cross effect
Start with symmetric case:
• We can characterise the admissible range of c and n:
(1) s(c,n) 0 [Incumbents do not make losses]
(2) s(c,n1) < 0 [A new entrant would make a loss]
In symmetric equilibrium:
s(c,n) (c, c, n)
– + –
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n
c
s(c,n) = 0
c
n* n* is the maximum equilibrium number of firms;BUT: A real number, not necessarily an integer
(1) s(c,n) 0 [Incumbents do not make losses]
(2) s(c,n1) < 0 [A new entrant would make a loss]
s(c,n1) = 0
n*–1
So: “Lean” symmetric equilibrium has:ne = int (n*–1, n*]
ne
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n
c
s(c,n) = 0
c
n*
So: Shaded area is the admissible region for equilibrium n in symmetric equilibriaActual equilibrum values are on the horizontal line corresponding to the integer value:
ne = int (n*–1, n*]
So far: Only “lean” symmetric equilibria;
Now, consider symmetric equilibria with less efficient firms:
[A new lean entrant would make a loss]
s(c,n+1) =0
n*–1
ne
0)1,,( ncc
0)1,,( ncc
c
],[ ccc
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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:
],[ cccm
0)2,,( mcc
ccc 21
)2,,( 21 cc
)2,,( cc
)2,,( mcc
Proof can be extended to oligopoly and generalised mean [n] case:
• Assume an equilibrium with n–1 firms
• Replace “2” by n, c2 by n, and cm by n–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
0
)2,,( 22 cc
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Possible Cost Configurations in Duopoly
(i) Low s (ii) Medium s (iii) High s
(ii) Lean outsider constraintbinds in symmetric equilibria;
insider constraint in asymmetric ones
(i) Only insider constraints bind (iii) Only lean outsiderconstraint binds
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c2 c2 c2
c1 c1 c1
]0[ c
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5. Natural Oligopoly (cont.)
With multi-stage competition:
Presumption that dk/ds is positive:• Seade stability condition
ˆ ˆ( , ) ( , ; , ) when: argmax j
i i i j j
kn s k K n s k j
ˆ ˆ( 1)i is s K
dkn
ds
1ˆ ˆ ˆ( 1)i i ikk kK ks
dkn
ds
• Increase in market size raises investment (?)
Hence, for natural oligopoly:• Necessary condition: investments are “unfriendly”:
ˆ 0ikK
ˆ 0iK
• More likely the more investment responds to market size
• … which is more likely if investments are strategic complements:
+?
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Sales Revenue Profiles in Home and (Larger) Foreign Market
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