Cristiana Benedetti Fasil (UCL) Teodora Borota (Uppsala University) Bank of Estonia May 24, 2012

1. Introduction The Model Equilibrium Results Conclusion
World Trade Patterns and Prices: The Role of Productivity and
Quality Heterogeneity
Cristiana Benedetti Fasil
(UCL)
Teodora Borota
(Uppsala University)
Bank of Estonia
May 24, 2012

2. Introduction The Model Equilibrium Results Conclusion
Data on product level export and import prices has been exploited as evidence of
countries technological development, trade specialization and demand schedules
Facts on world trade patterns and prices have been established
On top of that interest, empirical studies attempt to test the validity of the new
trade theory that relies on firm heterogeneity and firm selection
We attempt to reconcile the theoretical alternatives and match two sets of
evidence:
⇒ Exporting strategies and pricing within a country
⇒ World trade patterns and prices
What is the role of firms’ productivity - quality and efficiency?

3. Introduction The Model Equilibrium Results Conclusion
Theoretical literature and Evidence (I)
Melitz (2003): higher productivity/profitability/export success - lower prices
Baldwin and Harrigan (2007): product quality
higher productivity/profitability/export success - higher prices
The truth lies somewhere in between
Baldwin and Ito (2008) identify three types of products - (1) price increases with
"difficulty" of the export market (quality-competition goods), (2) price-difficulty
relationship is negative (price-competition) and (3) can not be placed in either
category
The share of (3) lines is lower for developed countries, the share of (1) lines rises
with the development of the country
Crozet et al. (2011) find similar results and also that for highly priced product
lines (assumingly high quality ones) the price competition seems to be in place

4. Introduction The Model Equilibrium Results Conclusion
Evidence (II)
Trade patterns and intensities within and across regions of the North and the
South (developed N, and developing S)
The most intense trade flows are N-N, then N-S and S-S
Product quality as determinant of trade specialization between N and S

5. Introduction The Model Equilibrium Results Conclusion
Evidence (II)
Export prices increase with income per capita of the origin (Schott (2004) for US)
N specializes in the production of relatively higher quality
Import prices are positively related to income per capita (Fieler, 2007)
For a given exporter, import prices are positively related to income per capita
(Fieler, 2007)
N consumes relatively higher quality
Melitz (2003): negative relation between export prices and income per
capita/technology
Baldwin and Harrigan (2007): negative relationship between income per capita
and import prices, also conditional on exporter

6. Introduction The Model Equilibrium Results Conclusion
Contribution
Model of industry and a space of products distributed over efficiency and quality
dimensions
We introduce a separate measure of cost efficiency which affects the marginal
cost independently of the quality
We use homothetic preferences (standard CES, quality augmented) and turn to
supply side for the reasons of differences in demand schedules
Fixed costs result in firms partitioning and thus different demand schedules
across regions
Price distribution determined by partitioning in efficiency - quality space which
have the opposite effect on price
⇒ Generate trade patterns and prices consistent with evidence

7. Introduction The Model Equilibrium Results Conclusion
Consumer Problem - Homothetic Preferences
2 regions; 2 symmetric countries in each region: 2N-2S
Preferences are the same in all 4 countries
For J = {N, S}
1
α
max (qt (i)xt (i))α di s.t. EtJ = pt (i)xt (i)di
x i∈I J i∈I J
XtJ
where I N = I ND + I NN + 2I SN and I S = I SD + I SS + 2I NS
⇒ Demand for each good i of quality q(i):
1
PtJ qtα (i) 1−α
xt (i) = XtJ
pt (i)

8. Introduction The Model Equilibrium Results Conclusion
Production
Firm i is defined by: (a(i), q(i)),
a(i) is labor efficiency
q(i) is the quality of the variety
Production technology is
xt (i) = At (i)nt (i)
with two dimensions of productivity:
χ
At (i) = at (i)qt (i)−η
⇒ higher quality varieties are more difficult to produce
⇒ asymmetry between firm’s cost efficiency and product quality

9. Introduction The Model Equilibrium Results Conclusion
Profit Maximization
Domestic market:
πtJD (a, q) = ptJD xtD − wtJ ntD − w J cf
Foreign market:
πtJX (a, q) = ptJX xtX − wtJ ntX − w J cex
where wN = 1 numeraire
π N = π ND + max{0, π NN } + 2 max{0, π NS }
π S = π SD + max{0, π SS } + 2 max{0, π SN }

10. Introduction The Model Equilibrium Results Conclusion
Optimal Quantities
⇒ Monopolistic price - pricing quality:
wtJ qtη (i)
ptJD (a(i), q(i)) = χ
αat (i)
⇒ Production:
χ 1
αat (i)P J 1−α
xtJ (a(i), q(i)) = XtJ
qt (i)η−α w J
⇒ Profits:
χ α
αat (i)qt (i)1−η 1−α 1
πt (a(i), q(i)) = (1 − α)Pt1−α Xt − wcf .
w

11. Introduction The Model Equilibrium Results Conclusion
Entry
Sunk entry cost, ce , expressed in terms of labor
Firms draw productivity and quality from a distribution GJ (a, q), with density
g J (a, q)
g N (a, q) is log-normal and exogenous
g S (a, q|µN ) is log-normal but the mean of g S is a constant fraction θ of the
mean of the surviving firms in the North, µN
Free-entry condition
N
Π = π N (a, q)g N (a, q)dqda = w N ce ,
N
ax (q) Q
S
Π = π S (a, q)g S (a, q|µN )dqda = w S ce .
S
ax (q) Q

12. Introduction The Model Equilibrium Results Conclusion
Exit & partitioning
Firms exit when the profits are not enough to cover the fixed operational cost, cf
Exit cut-off functions for given q ∈ Q for both North and South:
For a given q:
low ’a’ firms exit
intermediate ’a’ firms sell only at home
high ’a’ sell at home and abroad (partition assured by the conditions on the fixed
costs)

13. Introduction The Model Equilibrium Results Conclusion
Firms Distribution
Density of firms conditional on successful entry
g(a,q)
1−G(ax (q),q)
if a(q) ≥ ax (q)
µ(a, q) =
0 otherwise
J J
Pin = 1 − G(ax (q), q) is the ex-ante probability of surviving
JJ,K
JJ,K 1−G(aex (q),q)
Pex = J is the ex-ante probability that successful firms export,
1−G(ax (q),q)
defined for all possible export origins and destinations (N-N, N-S, S-N and S-S)

14. Introduction The Model Equilibrium Results Conclusion
Cutoff functions
For given q ∈ Q for both North and South:
Exit cutoffs, depend on the own country aggregate:
1−α 1
J w J cf α 1 wJ χ
ax (q) = α
(1 − α)P
J 1−α
EJ α q 1−η
Export cutoffs, depend on the foreign country aggregates:
1−α 1
JJ w J cex α 1 wJτ χ
aex (q) = α
(1 − α)P
J 1−α
EJ α q 1−η
1−α 1
JK w J cex α 1 wJτ χ
aex (q) = α
(1 − α)P
K 1−α K
E α q 1−η

15. Introduction The Model Equilibrium Results Conclusion
Aggregates
The mass of incumbents in each country, I, is pinned down by the labor market
clearing condition and it represents the measure of varieties produced
The mass of exporting firms (varieties) Iex = Pex I
Mass of available varieties in each country is given by the mass of varieties
produced domestically plus the mass of varieties imported from the other three
regions, e.g. for one North region
M N = I N + Iex + 2Iex
NN SN

16. Introduction The Model Equilibrium Results Conclusion
Calibration
Targets Data Model
North-North Export Share 52.69% 54.95%
North-South Export Share 40.86% 42.49%
North Exit Rate 10% 10.43%
South Exit Rate 20% 23.43%
Wage Ratio w s /w N 0.4 0.41
Calibrated Parameters
θ 0.18
σ 0.5
cf 11.42% of avg North domestic employment
cex 29.51% of avg North domestic employment
ce 38% of avg North domestic employment
Other Parameters
α 0.73
χ 0.5
η 0.86
δ 0.5%
τ 1
gN 4.1
LN = LS 1

17. Introduction The Model Equilibrium Results Conclusion
Firms Distribution

18. Introduction The Model Equilibrium Results Conclusion
Firms Partitioning
Export to North and South
NORTH
150 Export to North
Domestic
Exit
quality 100
50
0
0 20 40 60 80 100 120 140 160 180
productivity
SOUTH
150
quality
100
50
0
20 40 60 80 100 120 140 160 180
productivity

19. Introduction The Model Equilibrium Results Conclusion
Distribution of Prices
180
160
140
120
100
quality
80 Domestic Export Export to
Exit
market to North and
North South
60
40
20
0
20 40 60 80 100 120 140 160 180 200
productivity
Average Price North South
Exports 4.0739 0.9495
Imports 1.0072 0.9101
Imports from North 4.2514 3.9861
Imports from South 1.0008 0.9054

20. Introduction The Model Equilibrium Results Conclusion
Distribution of Expenditure over Quality
5 Expenditure share per variety over quality
x 10
5
North
4.5 South
4
3.5
3
2.5
2
1.5
1
0.5
0
0 20 40 60 80 100 120 140 160 180 200
quality

21. Introduction The Model Equilibrium Results Conclusion
Total Trade Values: Imports+Exports
4 Value of total trade
x 10
16
N−N
14 S−S
N−S
12
10
8
6
4
2
0
0 20 40 60 80 100 120 140 160 180 200
quality

22. Introduction The Model Equilibrium Results Conclusion
Endogenous quality - a representative product line
a representative product line - a reduced form model, one productivity dimension
taking into account distribution of firms
quality as a function of efficiency - increasing, but at a decreasing rate for higher
values of efficiency
β
q(a) = aea−a (1)
price is not a monotonic function of efficiency (and quality)
β
p(a) = e(a−a )χ
(2)
profits are increasing in efficiency
β
Π = aea−a (3)

23. Introduction The Model Equilibrium Results Conclusion
Endogenous quality - a representative product line

24. Introduction The Model Equilibrium Results Conclusion
Conclusion
Four countries N-S trade model with two-dimensional firm heterogeneity and
firms distribution that matches stylized facts on world trade patterns
Allows to match data on the export/import prices in relation to income per capita
Positive relation between income per capita and import prices, conditional on
exporter
Generate differences between the consumption bundles of N and S even with
homothetic preferences
North consume more high quality
South consume more low quality

25. Introduction The Model Equilibrium Results Conclusion
Profits
⇒ Profits:
χ α
αat (i)qt (i)1−η 1−α 1
πt (a(i), q(i)) = (1 − α)Pt1−α Xt − wcf .
w
π(a, q) increasing and concave in a and q
Profits Distribution in Open Economy
50
45
40
35
30
productivity
25
20
15
10
5
0
0 5 10 15 20 25 30 35 40 45 50
quality