Raff
Trade, Heterogeneity,
Intermediation
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International Trade, Firm Heterogeneity, and
Intermediation
Horst Raff, University of Kiel
Zhejiang University
17-19 May 2011
Syllabus
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
International Trade with Heterogeneous Firms
i.
ii.
iii.
Introduction
Trade Model with Monoplistic Competition (Krugman)
Monopolistic Competition with Heterogeneous Firms (Melitz,
Ottaviano)
iv. Reciprocal Dumping Model (Brander)
v. Reciprocal Dumping Model with Heterogeneous Firms (Long,
Raff, Stähler)
vi. Trade and Innovation
vii. Intra-Industry Adjustment to Import Competition

Intermediation in International Trade
i.
ii.
iii.
iv.
Introduction
Buyer Power in International Markets
Imports and the Structure of Retail Markets
Manufacturers and Retailers in the Global Economy
Introduction
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Basic Models of International Trade
1. Comparative advantage (Ricardo, Heckscher-Ohlin)
2. Economies of Scale (Krugman)
3. Reciprocal Dumping (Brander)
Trade Models Based on Economies of Scale
• may explain why we observe a lot of intra-industry trade
between (rich) countries with similar technology and factor
endowments,
• provide a theoretical foundation for the gravity equation.
Reciprocal Dumping Model
• also features intra-industry trade (even in identical goods),
• endogenous mark-ups,
• competitive effects of trade.
Krugman Model
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I. Model
Key elements:
•
•
•
•
Dixit-Stiglitz preferences (love of variety),
L consumers/workers (labor is the only factor of production)
Monopolistic competition, general equilibrium
Economies of scale in production
Preferences:
elasticity of substitution
set of consumed varieties (endogenous)
Krugman Model
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Demand for variety i:
Constant price elasticity of demand:
Technology: labor requirement to produce y units of good i:
Krugman Model
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II. Equilibrium

Each firm chooses price to maximize its profit:

First-order condition (marginal revenue = marginal cost):

Maximized profit:
Krugman Model
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
Free-entry condition (zero profits):

Labor market clearing:

Equilibrium price index:

Indirect utility is inversely proportional to the price index.
Krugman Model
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III. Free Trade (C integrated countries)

No change in consumer prices

No change in output per firm

Greater product variety as consumers gain access to foreign varieties:

Greater welfare / lower price index due to variety effect:
Melitz-Ottaviano Model
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I. Model
Key elements:
•
•
•
•
Quadratic, quasi-linear preferences (love of variety),
L consumers/workers (labor is the only factor of production)
Monopolistic competition, partial equilibrium
Economies of scale in production
Preferences:
Melitz-Ottaviano Model
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Demand for variety i:
with average industry price:
Price elasticity of demand:
Technology:
• Constant marginal cost: c
• Fixed market entry cost:
Melitz-Ottaviano Model
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II. Equilibrium with homogeneous firms

Each firm chooses price to maximize its profit:

First-order condition:

With symmetric firms:
Melitz-Ottaviano Model
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
Free-entry condition (zero profits):

Equilibrium allocation:

Indirect utility:
Melitz-Ottaviano Model
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III. Free Trade (C integrated countries)

Consumer prices fall as competition gets tougher

Output per firm increases as firms need to sell more to break even

Product variety rises as consumers gain access to foreign varieties:

Greater welfare / lower price index due to lower prices and greater
variety
Melitz-Ottaviano Model
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IV. Firm Heterogeneity
Key changes relative to homogeneous firm model:
•
•
•
Firms draw their productivity/marginal cost from a distribution
G(c)
To obtain closed-form solutions assume a Pareto distribution
Firms enter the market and pay their (sunk) entry cost before
observing their productivity draw (expected zero-profit
condition)
Melitz-Ottaviano Model
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Optimal output of a firm has to satisfy:
Define:
Firms with a marginal cost draw greater than
produce any output
do not
The threshold
summarizes all the information required to
describe the behavior of firms that produce positive
output.
Melitz-Ottaviano Model
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Melitz-Ottaviano Model
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
Free-entry condition (zero profits):

Equilibrium allocation with Pareto distribution of productivity:
where:

Indirect utility:
Melitz-Ottaviano Model
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V. Free Trade (C integrated countries)

The threshold value of the marginal cost becomes smaller, i.e., import
competition forces the least efficient firms shut down

Demand becomes more elastic






Average prices and mark-ups fall (pro-competitive effect)
Average output rises
Higher average productivity
Surviving firms are more profitable
Greater product variety as consumers gain access to foreign varieties
Greater welfare
Melitz-Ottaviano Model
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V. Costly Trade

Additional threshold value of the marginal cost below which firms
export:

Only the most efficient firms export, less efficient firms sell only in the
domestic market, the least efficient firms produce zero output.

Expected zero-profit condition:

Threshold value of the marginal cost above which firms shut down:
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Brander Model – reciprocal dumping
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I. Model
Key elements:
•
•
•
•
Quadratic, quasi-linear preferences
2 countries: home, foreign
Segmented markets (no consumer arbitrage)
Oligopolistic competition, partial equilibrium
Preferences:
Brander Model
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Inverse demand in each country j =h,f:
The home firm sells y units at home and exports x units.
The foreign firm sells y* units in the foreign country and
exports x* units to the home country.
Brander Model
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Technology:
• Constant marginal cost: c
• Fixed cost: f
• Per-unit trade cost: t
Brander Model
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II. Equilibrium

Each firm chooses domestic sales and exports to maximize its profit:

With segmented markets and constant marginal cost we can focus on
first-order conditions in the home market:

Best-response functions:
Brander Model
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Cournot-Nash equilibrium
Brander Model
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
Equilibrium domestic sales:

Equilibrium exports
are positive as long as
Brander Model
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
Mark-up on domestic sales:

Mark-up on exports:
Reciprocal dumping: firms accept lower mark-ups on their exports.
Melitz-Ottaviano Model
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III. Trade Liberalization (reduction in t)

Reduces each firm’s domestic sales and raises exports

Raises total output in each country and lowers prices

Has non-monotonic effect on social welfare since profits
• pro-competitive effect due to import competition
• profits may fall due to trade cost (cross-hauling)

With free entry welfare effect is unambiguously positive due to procompetitive effect
Brander Model
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Welfare
0
Brander Model
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
Equilibrium with n firms in each country:

Equilibrium profits:
Long, Raff, Stähler
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I. Model
Key elements:
•
•
•
•
Brander model
Firms draw their marginal cost from a distribution F(c) as in
Melitz/Ottaviano
Firms observe only their own cost draw, but do not know the
cost draws of their competitors
Derive the Bayesian Nash equilibrium
Long, Raff, Stähler
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Inverse demand in each country j =h,f:
Marginal cost drawn from distribution
Long, Raff, Stähler
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II. Equilibrium

Firm i chooses domestic sales and exports to maximize its profit:

First-order condition for domestic sales:

Threshold value of the marginal cost above which domestic sales are
zero:

Optimal domestic sales:
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
First-order condition for exports:

Threshold value of the marginal cost above which exports are zero:

Optimal exports:

With symmetric countries every firm sells

Hence expected output of rivals at home and abroad is:
at home and exports
Long, Raff, Stähler
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
Expected domestic sales:

Expected exports:

Expected-zero-profit condition
Long, Raff, Stähler
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III. Trade Liberalization (reduction in t)

Reduces each firm’s expected domestic sales and raises expected
exports

Raises total expected output in each country and lowers expected
prices

Selection effect: the least efficient firms are forced to shut down

Has non-monotonic effect on social welfare since profits
• pro-competitive effect due to import competition
• profits may fall due to trade cost (cross-hauling)

With free entry welfare effect is unambiguously positive due to procompetitive effect
Innovation and Trade
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Innovation and Trade with
Heterogeneous Firms
Ngo Van Long (McGill University, Montreal)
Horst Raff (IfW, University of Kiel)
Frank Stähler (University of Würzburg)
Innovation and Trade
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How does trade liberalization affect productivity?


Does trade liberalization raise or reduce the incentive to invest in
R&D (specifically process R&D)?
How do changes in R&D interact with selection effects whereby the
least efficient firms are forced to shut down?
Innovation incentives and trade



Firms face tougher import competition and lose market share to
foreign competitors,
but gain better access to export markets.
Overall effect of trade on R&D incentives is non-trivial
Innovation and Trade
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What does existing theory tell us about the link between
trade liberalization and productivity?

Models with homogeneous firms (Melitz/Ottaviano,
Brander):
•

market integration leads to fewer but bigger firms, lower average
cost (scale effect)
Models with heterogeneous firms (e.g., Melitz/Ottaviano):
•
Trade liberalization raises productivity in two ways:
1. Selection effect: least efficient firms are forced to exit
2. Market-share reallocation effect: efficient firms gain market
share at the expense of less efficient firms
•
No scale effect with CES preferences (Melitz).
Innovation and Trade
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Problems with the existing literature:

Firm productivity is assumed to be exogenous: firms draw their
cost from a given distribution.

Fact is: firms may influence their productivity.
•
Trade liberalization may raise exports and productivity
simultaneously.
•
Evidence that firms raise their productivity with a view to
becoming exporters (e.g. Alvarez and Lopez, 2005).
Our paper:

Firms may invest in R&D to increase their chance of drawing a
low marginal cost.
Innovation and Trade
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Model:
1. R&D investment through which firms can increase their
chance of drawing a low marginal cost.
2. Oligopolistic competition: big firms exercise market
power.
3. Cost draws and R&D spending remain private
information.
4. Possible adjustments by firms to trade liberalization:
•
R&D decisions
•
Output adjustment
•
Entry and exit
Innovation and Trade
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•
Higher r imlies a greater chance of drawing a low cost.
•
Cost distribution with R&D (r):
•
Convex cost of R&D:
Innovation and Trade
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Innovation and Trade
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•
Timing of the game
1.
2.
3.
Firms choose R&D and make entry decision.
Each firm learns its own cost.
Firms choose domestic and export sales (Bayesian
game).
Innovation and Trade
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Expected sales:
Expected profit:
R&D choice:
.
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• How does trade liberalization affect the threshold values
of the marginal cost?
• For both fixed and endogenous market structure we can
prove:
t
Innovation and Trade
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Trade Liberalization with Homogeneous Firms
 Endogenous R&D in the Brander model
 With and without zero-profit condition
Innovation and Trade
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Trade Liberalization with Heterogeneous Firms – no entry
Innovation and Trade
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Trade Liberalization with Heterogeneous Firms – free entry
and exit (endogenous market structure)
Innovation and Trade
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Reduction in trade costs:
(i)
raises expected export sales due to
•
higher probability that any given firm will be efficient enough to
be able to export
•
those firms that do export increase their shipments abroad
(ii) reduces/raises expected local sales due to
•
greater import competition
•
greater probability that firm has to exit
•
higher R&D if trade cost is low
Innovation and Trade
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(iii) U-shaped relationship between trade cost and R&D:
•
•
A firm selling only on the domestic market would have less
incentive to invest in R&D, since trade liberalization reduces its
market share.
An exporter would have an incentive to increase R&D, since its
expected output rises and hence the marginal benefit of cost
reduction.
High trade cost: probability that the firm will be able to export is
small. Hence trade lib. reduces R&D.
Low trade cost: almost all active firms will be exporters and raise
output when trade is liberalized. Hence R&D increases.
Innovation and Trade
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Robust results (for both fixed and endogenous
market structure)
Trade liberalization:
1. raises (reduces) aggregate R&D spending if trade
costs are low (high)
2. increases firm size provided that trade costs are high
3. induces least efficient firms to exit
4. raises social welfare if trade costs are sufficiently low
Innovation and Trade
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How does our model match up with the stylized facts of trade
liberalization?
The model reproduces the stylized fact that trade liberalization
• reduces price-cost margins
• lowers domestic sales of import-competing firms (at least provided
that trade costs are high or that market structure is endogenous)
• expands markets for very efficient firms
• increases efficiency at the plant level (at least for low trade costs or
endogenous market structure)
• leads to different adjustment patterns within industries depending on
the level of sunk entry costs.
Firms that export tend to be larger and more productive than firms that do
not export.
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Intra-Industry Adjustment to
Import Competition: Theory
and Application to the German
Clothing Industry
Horst Raff (IfW, University of Kiel)
Joachim Wagner (University of Lüneburg)
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Intra-Industry Adjustment to
Import Competition: Theory
and Application to the German
Clothing Industry
Horst Raff (IfW, University of Kiel)
Joachim Wagner (University of Lüneburg)
Introduction
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1.
How do heterogeneous firms in an industry adjust to an
import shock?
2.
How does this affect industry productivity and competition
in the short and the long run?
We address these questions by constructing a
simple heterogeneous-firm model and testing its
predictions using micro-data for the German
clothing industry.
Stylized Facts
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1.
Significant increase in import penetration in the German
clothing industry 2000-2006
•
Due in part to successive elimination of import quotas under the
Multi-Fibre Arrangement.
•
Second step: Jan. 1, 2002.
Third and final step: Dec. 31, 2004.
Large changes in output, employment, market structure.
Stylized Facts
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Stylized Facts
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Stylized Facts
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2. Significant firm heterogeneity in terms of size and labor
productivity.
Stylized Facts
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Stylized Facts
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Economic Issues
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1. How does the industry adjust to import penetration?
•
•
through changes in competition between heterogeneous firms in
the industry,
i.e., changes in outputs and market structure.
2. What does this imply for competition and industry
productivity?
3. Do the competitive effects differ between the short and the
long run?
Theoretical Framework
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Long, Raff, Stähler (2009): oligopoly model with
heterogeneous firms.

Short run: fixed number of entrants in the industry.

Long run: endogenous market structure, number of
entrants determined by an expected-zero-profit condition.
(Questions 3 and 4 of the Advanced International Trade Exam 2009)
Model
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Key features:
1. Oligopoly model of a domestic industry facing import
competition.
2. Heterogeneous firms: firms draw their marginal cost after
entry, cost draws remain private information.
3. Firms play a Bayesian Cournot game.
Model
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
Home inverse demand: p=A – Q – M
M: import quota

n domestic firms

Costs:
• Entry cost: fe
• Marginal production cost: c
• Cumulative distribution function: F(c)

Timing of the game
• Entry decision.
• Each firm learns its own cost. Cost draws are private
information.
• Firms choose domestic sales (Bayesian Cournot game).
Model
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Cost level below above which a firm produces zero output:
Output of firm i:
Ex-post profit of firm i:
Expected ex-ante profit:
Model
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Nash Equilibrium: all firms have the same expected output:
Short run:
Long run:
Productivity:
Short-run effects
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Long-run effects
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.
Data
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
Panel data for enterprises from the German clothing industry (all plants
with >20 employees or belonging to an enterprise with >20 employees)
Industry, sales, total employees, hours worked by blue-collar
workers, gross wages and salaries,…

Active firms in the clothing industry:
2000: 614
2005: 310
2006: 274

Number of employees in the clothing industry:
2000: 66,881
2006: 31,420
Empirical Analysis
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Empirical Analysis
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Empirical Analysis
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Conclusions
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1.
Simple oligopoly model used to derive predictions about the
adjustment of an industry to import competition.
2.
Pro-competitive effects in the short run disappear in the
long run.
3.
Predictions of the model for the short run are supported by
data for the German clothing industry:
 The least efficient firms exit the market.
 The output of survivors decreases.
 Industry productivity rises (economically small effect
and not statistically significant)