1. Gonzague Vannoorenberghe University of Mannheim 11/12/2008
Trade between symmetric countries, heterogeneous firms and the skill premium
Gonzague Vannoorenberghe
University of Mannheim
11/12/2008

2. Motivation
Source: Autor, Katz and Kearney (2005)

3. Motivation Recent firm level evidence points out that:
Exporting firms are more skill intensive than average (Bernard and Jensen (1995,1997)).
Firms exiting the market are less skill intensive than average (Bernard and Jensen (2007)).
I build on recent heterogeneous firms literature in international trade to examine the impact of trade liberalisation on the skill premium.

4. The approach Two symmetric countries
One sector model of monopolistic competition with heterogeneous firms. I follow Melitz (2003) and the large subsequent literature.
Two factors of production: skilled and unskilled labour.
Two types of trade costs: variable and fixed costs of exporting.
Matches many empirical facts.

5. Contribution
The reallocation of productive resources between heterogeneous firms, triggered by trade liberalisation, can influence the skill premium.
Calibrating the model shows that this channel can be qualitatively important: explains up to a fourth of the rise in the U.S. skill premium.
The evolution of the skill premium is ambiguous and depends on :
the trade costs considered ⇒ policy implications
the size of the initial trade costs

6. Contribution Skill premium variable costs of trade ↓
fixed costs of trade ↓
Inverse of trade costs

7. Demand
All consumers in both countries share the same C.E.S. utility function over a continuum of varieties, with an elasticity of substitution ε>1
⇒ Love of variety
Aggregate demand for a variety in a country:
decreases in its own price
increases in the ideal price index (average price of competitors)
increases in aggregate income

8. Production
Firms produce with unskilled and skilled labour in a C.E.S. production function (σ >1):
z is the source of heterogeneity between firms. It is drawn from a continuous distribution with support [ z , ∞).
From cost minimisation: productive firms are skill intensive.

9. Profits Firms charge a constant mark-up over marginal costs.
Producing firms must pay a fixed cost in terms of capital
⇒ Not all entrepreneurs are willing to produce.
The lower the marginal costs, the larger the firm, the more skill intensive it is and the higher its profits.

10. Export Additionally, each firm decides whether to export or not.
Trade is associated with two types of costs:
iceberg costs (τ >1)
fixed costs (fx), paid in terms of capital
Both countries are perfectly symmetric in every respect.
This generates the well-known partitioning between exporters and non-exporters as long as the trade costs are large enough.

11. Partitioning z* zx* π x=0 z πd <0 πx<0 No production πd >0
Production for the domestic market only
πx>0
Production for both markets
πd =0
π x=0 z

12. Equilibrium conditions
All three factors are in fixed supply and internationally immobile. The mass of potential entrepreneurs is fixed (Chaney (2006)) and normalised to one.
Two types of conditions must hold:
the three factor markets must be in equilibrium
„cut-off“ firms must be indifferent
Existence and uniqueness require two additional (sufficient) conditions:
ε ≥ σ
K ≤ f

13. Bilateral Trade Liberalisationy
A ⇒ w ↗
B ⇒ w ↗
C ⇒ w ↗ A z z*
zx* C B

14. Bilateral Trade Liberalisationz z*
zx* y A B C
A ⇒ w ↗
B ⇒ w ↘
C ⇒ w ↗

15. Bilateral Trade Liberalisationz z*
zx* y B C
B ⇒ w ↘
C ⇒ w ↗

16. Calibration
z is Pareto distributed, with parameter a. The distribution of sales for large firms converges to a Pareto distribution.
Standard parameters in the literature:
ε = 4
σ =1.5
U/S = 1.4
τ = 1.3
Set a, K and fx such that:
Match Zipf‘s law for the distribution of sales of large firms
The skill premium is equal to 1.8
The proportion of exporting firms is 21%

17. Calibration Setting f = 1 without loss of generality, this requires:
K =
fx = 0.893
Look at the evolution of the skill premium for a change in both types of trade costs. Costs are allowed to decrease as long as partitioning holds.
Size of the effects would be higher for multilateral liberalisation.

18. Calibration

19. Calibration

20. Calibration : 3 countries

21. Calibration: 3 countries

22. Conclusion
The reallocation of resources between heterogeneous firms following trade liberalisation can affect the skill premium.
The interaction between firm size, export status and skill intensity, which is empirically well established is the core element driving the results.
This depends on the kind of trade costs considered and on their initial level.
Although the model does not provide a welfare analysis, it is of interest for policy prescriptions.