Dynamics of export share
of products in the
international trades
Matthieu Barbier and Deok-Sun Lee
Dept. Physics, Inha University
Dr. Matthieu Barbier
Now at Dept. Ecology & Evol. Biol.,
Princeton Univ. USA
International trades
• if there are comparative advantage of importing
rather than producing a product given factors of
production, politics, culture, history, etc.
D. Ricardo, On the Principles of Political Economy and Taxation (London: John Murray, 1817; retrieved 2012-12-07 via
Google Books)
• What products are the whole world producing
and exporting?
• Any fundamental “laws” there?
Products that Korea is producing and exporting
1962
2000
http://atlas.media.mit.edu/
Products the whole world is producing and
exporting
1962
3330 Petrol.oils & crude oils obt.from bitumin.minerals
0711 Coffee,whether or not roasted or freed of caffeine
2631 Cotton (other than linters),not carded or combed
2320 Natural rubber latex; nat.rubber & sim.nat.gums
2681 Seeps or lambswool,greasy or fleece-washed
2000
3330 Petrol.oils & crude oils obt.from bitumin.minerals
7810 Passenger motor cars,for transport of pass.& good
9310 Special transactions & commod.,not class.to kind
5417 Medicaments(including veterinary medicaments)
7788 Other elect.machinery and equipment
Statistics and dynamics of
“Export share” of products
- empirical observation
- what are we interested in?
NBER-UN world trade data from 1962 to 2000
•
R.C. Feenstra, R. E. Lipsey, H. Deng, A. C. Ma, and H. Mo, World Trade Flows: 19622000, NBER Working Paper No. 11040 (2005)
year
icode importer ecode
.
.
.
132627 1962 218400 USA 454100
132628 1962 218400 USA 454100
132629 1962 218400 USA 454100
.
.
.
.
.
.
exporter
.
.
.
Korea Rep.
Korea Rep.
Korea Rep.
sitc4 unit dot
.
.
.
8310
1
8420
1
8471
1
.
.
.
value quantity
1
NA
564 NA
1
NA
• Product ID
4-digit Standard International Trade Classification (SITC), revision 2
• Mainly based on the importers’ reports
• Curated and supplemented by the available data of trades of individual
countries
Export share of a product p in year t
• Export volume (value in dollars) of a product p in year t :
𝑉𝑝 𝑡
• Export share (relative export volume) of a product p in year t :
𝐴𝑝 𝑡 =
𝑉𝑝 (𝑡)
𝑝′ 𝑉𝑝′ 𝑡
This quantity is what we study here
• 508 products maintain non-zero volume from 1962 to 2000
• Normalization
•
𝑝 𝐴𝑝 𝑡 = 1, Mean 𝐴𝑝 =
1
508
= 2 × 10−3
𝐴𝑝 𝑡 | 𝑝 = 1,2,3, … , 508, 𝑡 = 1962, 1963, … , 2000
Uneven distribution of export share
𝐶𝑡 𝐴 = 𝑃𝑟𝑜𝑏. a product has 𝐴𝑝
𝑃 𝐴 ∼ 𝐴−𝛼
𝑡
≥𝐴
𝜎𝐴2 = 𝐴2𝑝 − 𝐴𝑝
2
SITC 3330 Crude oil: A = 0.14
Power law behavior with exponent between 2 and 3 is observed for 𝐴 ≿ 10−3 for all years.
The functional form of the distribution does not change with time
The second moment increases slightly with time with anomalous peaks after oil shock (1973)
Growth or decay for 39 years
• Increase or decrease?
How much?
• Growth rate
𝐴𝑝 2000
𝐺𝑝 = log10
𝐴𝑝 1962
• Skewed distribution
Coal and water
gas(3415)
8.0 × 10−5
→ 2.9 × 10−7
Invalid carriages (7853)
5.7 × 10−6 → 2.1 × 10−3
• What products increase share and what do the
opposite in the international trades?
What is the law governing it?
Variation of share for one year
- relatively microscopic view
Loss : Δ𝐴𝑝 𝑡 < 0
Gain : Δ𝐴𝑝 𝑡 = 𝐴𝑝 𝑡 + 1 − 𝐴𝑝 𝑡 > 0
Δ𝐴𝑝 (𝑡)
Δ𝐴𝑝 (𝑡)
𝐴𝑝 (𝑡)
𝐴𝑝 (𝑡)
Δ𝐴𝑝 𝑡 ≃ 𝑐𝑔 𝐴𝑝 𝑡
𝛼𝑔 = 1.0 ± 0.06
𝑐𝑔 = 0.09 ± 0.02
𝛼𝑔
Δ𝐴𝑝 𝑡 ≃ 𝑐𝑙 𝐴𝑝 𝑡
𝛼𝑙 = 0.98 ± 0.03
𝑐𝑙 = 0.07 ± 0.01
Linear scaling both for gain and loss of share !
𝛼𝑙
Our viewpoint, strategy, and goal
Hidalgo et al., Science (2007)
• Construct a particle-hopping model consistent with the linear scaling between Δ𝐴 and 𝐴
• Can the model explain the empirical observations such as the broad distribution of share?
• Can the model predict the evolution of share of individual products?
Urn model with quadratic preferential selection
- Factorized steady state
- Pseudo-condensation
Urn model (or misanthrope process)
as a model for the dynamics of export share
•
A complete graph of N sites, each site representing a product
•
A total of M particles, each particle representing the unit of share
•
Each site has 𝑚𝑖 particles and {𝑚𝑖 |𝑖 = 1,2, … , 𝑁} specifies the system’s state (𝐴𝑖 =
•
At each (microscopic) time step 𝜏, two sites i and j are selected with probability 𝑢 𝑚𝑖 , 𝑚𝑗
𝑚𝑖
)
𝑀
and a particle at site i is transferred to site j, where 𝑢 𝑚, 𝑛 = Π𝑅 𝑚 Π𝐴 𝑛 ∝ 𝑚2 𝑛2 with
𝑚𝟐
Π𝑅 𝑚 =
𝑁
𝟐
𝑖=1,2≤𝑚𝑖 ≤𝑀 𝑚𝑖
0
𝑚2
𝑁 𝑚2
(2 ≤ 𝑚𝑖 ≤ 𝑀)
𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
𝑚𝟐
Π𝐴 𝑚 =
≃
𝑚2
≃
(1 ≤ 𝑚𝑖 ≤ 𝑀 − 1)
𝑁
𝟐
2
𝑁
𝑚
𝑚
𝑖=1,1≤𝑚𝑖 ≤𝑀−1 𝑖
0
𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
Example: N=14 M=35
Every site has at least one particle
𝑚2 = 5
𝑚1 = 4
𝑚4 = 2
𝑚3 = 1
𝑚14 = 3
𝑚5 = 2
𝑚6 = 1
𝑚13 = 2
𝑚7 = 1
𝑚12 = 4
𝑚11 = 3
𝑚10 = 1
We consider the case where N is very large
𝑚9 = 2
𝑚8 = 4
Why is it quadratic, not linear?
• To be consistent with the linear relation between Δ𝐴 and 𝐴
• The annual variation of a product’s share is the sum of plus and
minus like random walk
• Suppose that particle-hopping occurs Ω times for one year. Then
m2𝑖
2Ω
N 𝑚2
Δ𝑚𝑖 = 𝑚𝑖 𝑡 + 1 − 𝑚𝑖 𝑡 =
𝜎𝑖 ∼
𝑖=1
1 or −1
• A parameter is introduced: 𝜔 =
Ω
𝑚2
Ω
𝑚
𝑁 𝑚2 𝑖
~ 0.1 (empirical)
~5
• One year corresponds to 𝜔⟨𝑚2 ⟩ times of transfer of particles
Urn model with
quadratic preferential selection
•
Different from the zero-range process in that the particle-hop probability depends on the number of
particles of the destination as well as of the source
•
Particle-hop probability is proportional to the square of the number of particles in the source and
destination site
•
Each unit of share (particle) is likely to move with probability proportional to the share of the present
product and that of the destination product
•
Our model is therefore capturing (only) the trend of a country’s economic policy towards enhancing the
likelihood of profit beyond the different abundance/deficiency of factors of production from country to
country.
•
Related works
Godrèche, Bouchaud, Mezard, JPA 28, L603 (1995) – model A, B, C
Godrèche and Luck, EPJB 23, 473 (2001) – zeta urn model
Majumdar, Evans, Zia PRL (2005); Evans, Majumdar, and Zia, JSP 123, 357 (2006) -- condensation
Barabasi and Albert, Science (1999) – (linear) preferential attachment of links
Relation to empirical results
• Distribution of share 𝑝 𝐴 corresponds to the distribution of the number
𝒑 𝑨=𝒎𝑴
of particles 𝒑 𝒎 =
, which can be obtained analytically for the
𝑴
stationary state
• Is the broad distribution of share caused by the linear scaling between Δ𝐴
and 𝐴 ?
• Can the model predict the trajectory of share of individual product?
Urn model based on
?
Factorized steady state
• 𝑃𝑡 𝑚 : Probability of a specific particle configuration 𝑚 at time t
• 𝜕𝑃𝑡
𝜕𝑡
=
𝑢 𝑚𝑖 + 1 , 𝑚𝑗 − 1 𝑃𝑡 … , 𝑚𝑖 + 1, … , 𝑚𝑗 − 1 …
− 𝑢 𝑚𝑖 , 𝑚𝑗 𝑃𝑡 {𝑚}
𝑖<𝑗
+𝑢 𝑚𝑗 + 1, 𝑚𝑖 − 1 𝑃𝑡 {… , 𝑚𝑖 − 1, … , 𝑚𝑗 + 1, … } − 𝑢 𝑚𝑗 , 𝑚𝑖 𝑃𝑡 {𝑚}
• Factorized state assumed for the stationary state 𝑃∞ 𝑚 ∝
with 𝑓 𝑚 to be determined
• Detailed balance condition
𝑢 𝑛 + 1, 𝑚 − 1 𝑓 𝑛 + 1 𝑓 𝑚 − 1 = 𝑢 𝑚, 𝑛 𝑓 𝑛 𝑓 𝑚
• Function f: 𝑓 𝑛 = 𝑓 1
𝑓 2
𝑓 1
𝑛−1
𝑛−1 𝑢 2,ℓ
ℓ=1 𝑢 ℓ+1,1
=𝑓 1
𝑓 2
4
𝑓 1
𝑖𝑓
𝑚𝑖
𝑛−1 1
𝑛2
where 𝑁 ≫ 1 is used.
𝑢 𝑚, 𝑛 ∝ 𝑚2 𝑛2
Evans and Hanney, JPA 38, R195 (2005)
Single-site particle-number distribution
• 𝑃∞ 𝑚
−1
= 𝑍𝑁,𝑀
𝑁
ℓ=1 𝑓
• Partition function 𝑍𝑁,𝑀 =
𝑚ℓ
𝑚1
𝑚2 ⋯
𝑚𝑁
𝑁
ℓ 𝑓
𝑚ℓ 𝛿 (𝑚1 + 𝑚2 + ⋯ +
Evans and Hanney, JPA 38, R195 (2005)
Partition function in our model
• Logarithmic singularity of the generating function 𝐹(𝑠) at 𝑠 = 1
∞
𝑚=1 𝑓
𝐹 𝑠 =
𝑚 𝑠𝑚 =
1
𝜁 2
𝑚
𝑠
∞
𝑚=1 𝑚2
=1+
1−𝑠 ln 1−𝑠 − 1−𝑠
𝜁 2
+ 𝑂( 1 − 𝑠
2
ln 1 − 𝑠 )
(J.E. Robinson, Phys. Rev. 83, 678 (1951))
• Partition function
𝑍𝑁,𝑀 =
𝑑𝑠
2𝜋𝑖
Steepest descent path 𝑠 = 𝑠∗ + 𝑖𝑦 | − ∞ < 𝑦 < ∞
𝑠 −𝑀−1 𝑍𝑁
𝜙 𝑠 = ln 𝐹 𝑠 − 𝜌 ln 𝑠 ≃
2𝜋 𝑟𝑖𝑒 𝑖𝜃 𝑑𝜃 𝑁𝜙 𝑠=𝑟 𝑒 𝑖𝜃
𝑒
0
2𝜋𝑖
=
1−𝑠 ln 1−𝑠 − 1−𝑠
𝜁 2
=
∞ 𝑑𝑦 𝑁𝜙 𝑠=𝑠 +𝑖𝑦
∗
𝑒
−∞ 2𝜋
+𝜌 1−𝑠 +𝑂 1−𝑠
2
ln 1 − 𝑠
𝜙 ′ 𝑠 = 0 at the saddle point 𝑠∗ , which exists within the radius of convergence
(otherwise, condensate is formed)
𝑀
𝑠∗ = 1 − 𝑒 −𝜌𝜁 2 in case 𝑒 −𝜌𝜁 2 ≪ 1 with particle density 𝜌 = 𝑁
•
𝑍𝑁,𝑀 =
1
𝑒
2𝜋
𝑁 𝑒−𝜌𝜁 2
𝜁 2
−𝜌𝜁 2 −
𝐺
𝑁𝑒 −𝜌𝜁 2
𝜁 2
∞
𝐺 𝑥 ≡
𝑒
−∞
𝑥 1−𝑖 𝑧 ln 1−𝑖 𝑧 +𝑖 𝑧
2𝜋
𝑥
𝑑𝑧 ≃
𝑐𝑜𝑛𝑠𝑡.
1
𝑥 ln 𝑥
𝑥≫1
𝑥≪1
Single-site particle-number distribution
in our model
•
𝑝 𝑚 =
•
𝜃→0
𝐺
•
𝐺
with 𝜃 =
𝜁 2 𝑒 𝜌𝜁 2
𝑁
𝑎𝑛𝑑 𝜂 =
𝑚
𝑒 𝜌𝜁 2
𝜌 ≪ ln 𝑁
𝑒 𝜃𝜂
𝜃
≃ 2𝜋𝜃 𝐺
2𝜋𝜃
𝑒 𝜃𝜂
≃
𝑝 𝑚 ≃
1
2
𝑚 𝜁 2
𝑚
−
𝑒 𝑒𝜌𝜁 2
1
𝜃
𝑒 𝜃𝜂
∼ 2𝜋𝜃 𝐺
𝜃
2𝜋𝜃
𝑒 𝜃𝜂
∼
𝑝 𝑚 ∼
1
𝑚2 𝜁
2
𝑒
𝑚
𝑚 𝑒 𝑁 −1
−
2𝑁
𝜃
𝜃 → ∞ 𝜌 ≫ ln 𝑁
𝐺
•
𝑒
𝑒𝜃𝜂
𝜃
1
𝐺
𝜃
𝑒𝜃𝜂 −1
𝜃𝜂−
𝜃
𝜃 = 𝑂(1) 𝜌 ∼ ln 𝑁
𝐺
•
1
𝜃
1 1
𝜁 2 𝑚𝟐
1
𝜃
∼
𝜃
ln 𝜃
𝐺
𝑒 𝜃𝜂
𝜃
=
𝜃𝑒 −𝜃𝜂
ln
𝜃𝑒 −𝜃𝜂
𝑝 𝑚 ≃
1
𝑚2 𝜁
2
𝑒
𝑚 𝑚
𝑒𝑁
− + 𝑁
𝜃 ln 𝜃
A bump is formed for 𝑵 ≲ 𝒎 < 𝑴 for the last two cases
Condensate-free
𝑀
𝜌= =2
𝑁
𝑁 = 50, 100, 200
𝜁 2 𝑒 𝜌𝜁
𝜃=
𝑁
2
= 0.88 𝑁 = 50 ~ 0.22 (𝑁 = 200)
Approximate
𝑚
1
− 𝜌𝜁 2
𝑝 𝑚 ≃ 2
𝑒 𝑒
𝑚 𝜁 2
Condensate …
𝑀
𝜌 = = 10
𝑁
𝑁 = 50, 100, 200
𝜁 2 𝑒 𝜌𝜁
𝜃=
𝑁
2
= 458180 𝑁 = 50 ~ 114545 (𝑁 = 200)
Approximate
𝑝 𝑚 ≃
1
𝑚2 𝜁 2
𝑚
𝑚 𝑒 𝑁 −1
−
𝑒 2𝑁 𝜃
Condensation?
•
Nature of condensation has been studied for the (continuum) mass transfer model
in 1D (Majumdar, Evans, Zia PRL (2005); Evans, Majumdar, and Zia, JSP (2006))
•
If the particle-hop probability is given by 𝑢 𝑚, 𝑛 ∝ 𝑚𝑏 𝑛𝑏 , the single-site particlenumber distribution is 𝑝 𝑚 ∼ 𝑚−𝑏
•
If 𝒃 > 𝟐, it may happen that 𝑚 = 𝑚 𝑝 𝑚 ∼
•
If 𝒃 ≤ 𝟐, 𝑚 ∼
𝑀 𝑚1−𝑏 can
𝑚
𝑀
1−𝑏
𝑚=1 𝑚
< 𝜌 even for finite 𝜌.
be infinite 𝑂(𝑀 2−𝑏 ) and can be equated to any finite
𝜌 by introducing a suitable cutoff leading to exponential decay. However, if 𝜌 is
infinite, we should compare 𝑁 and 𝜌, both of which are large numbers, and
depending on the relation between 𝜌 and 𝑁, a pseudo-condensate can appear
•
International trade dynamics is at the edge of condensation-free phase.
Application
- Does this model explain the international trade
at the aggregate level and individual level?
Yes! it does at the aggregate level
Simulate the model with 𝑁 = 508, 𝑀 = 2 × 105 , 𝜔 = 5 and the initial values from the
1962 data
Share distribution
Growth-rate distribution
Second moment
Gain versus share
Δ𝐴𝑝 𝑡 ≃ 𝑐𝑔 𝐴𝑝 𝑡
𝛼𝑔 = 0.9
𝑐𝑔 = 0.05
𝛼𝑔
Loss versus share
Δ𝐴𝑝 𝑡 ≃ 𝑐𝑙 𝐴𝑝 𝑡
𝛼𝑙 = 0.9
𝑐𝑙 = 0.04
𝛼𝑙
Evolution of export share of individual
products
• An ensemble of Κ = 300 simulation results
• The middle 80% of the simulation values for 𝐴𝑝 𝑡 is shaded
Bad…
Not bad….
Quantifying the typicality of empirical
observations among simulated trajectories
•
Values of return (one-year growth rate) 𝑅𝑝 𝑡 = ln
simulation for each p and t. That is, we have one
1
𝑅𝑝
•
(2)
𝐴𝑝 𝑡+1
𝐴𝑝 𝑡
𝑟𝑒𝑎𝑙
𝑅𝑝 (𝑡)
are compared between real and
and K=300 simulation values
(𝐾)
𝑡 , 𝑅𝑝 𝑡 , … , 𝑅𝑝 (𝑡)
Normalized rank
𝑟𝑒𝑎𝑙
𝑟𝑝 𝑡 =
rank of 𝑅𝑝
𝑡 𝑎𝑚𝑜𝑛𝑔 𝑡ℎ𝑒 𝑅𝑝𝑠 𝑡
1
1 1
− ∈ − ,
K+1
2
2 2
•
If a product p is well predicted by the model, a total of T=39 such normalized ranks at different
years 𝑟𝑝 (𝑡)|𝑡 ∈ [1962,2000] should be uniformly distributed over [-1/2, 1/2]
•
Deviation from Uniformity :
i) sort T=39 values of 𝑟𝑝 𝑡 ’s in increasing order from the smallest to the largest such that 𝑥1 =
1
𝑖
𝑟𝑝 𝑡1 ≤ 𝑥2 = 𝑟𝑝 𝑡2 ≤ ⋯ ≤ 𝑥𝑇 = 𝑟𝑝 𝑡𝑇 . If they are uniform, then one would find 𝑥𝑖 = − +
2
𝑇+1
for 1 ≤ 𝑖 ≤ 𝑇
1 𝑇
iii) Non-uniformity or Unpredictability of a product p is defined as 𝑈𝑝 =
𝑖=1 𝑥𝑖 − 𝑥𝑖
𝑇
•
𝑈𝑝 > 0.1 is observed only with probability 0.05 for 39 uniformly-distributed numbers
(Marhuenda, Morales, Pardo, Statistics 39, 315 (2005))
Classifying products
1
Mean rank 𝑟𝑝 = 𝑇 2000
𝑡=1962 𝑟𝑝 𝑡
positive: higher returns (annual growth) than expected
negative: lower returns than expected
𝑇
𝑡=1
Rank fluctuation 𝜎𝑟𝑝 =
𝑟𝑝 𝑡 − 𝑟𝑝
2
Larger than 0.29 : higher variability of rank than expected
Smaller than 0.29 :lower variability
1
Unpredictability 𝑈𝑝 = 𝑇 𝑇𝑖=1 𝑥𝑖 − 𝑥𝑖
Larger than 0.1 : deviate significantly from our model prediction
Smaller than 0.1 : predictable by the model
Predictability and mean-rank
The most unpredictable products
SITC
6589
7853
6880
2239
2640
6122
2652
6545
2231
2654
3231
9610
2742
2114
2814
2235
8996
2634
8983
7931
Description
Other_made-up_articles_of_textile_materials,n.e.s
Invalid_cariages,motorized_or_not,parts
Uranium_depleted_in_u235_&_thorium,&_their_alloys
Flours_or_meals/oil_seeds/oleag.fruit_non_defatted
Jute_&_other_textile_bast_fibres,nes,raw/processed
Saddlery_and_harness,or_any_material_for_animals
True_hemp,raw_or_processed,not_spun;tow_and_waste
Fabrics,woven,of_jute_or_of_other_textile_bast_fib
Copra
Sisal_&_other_fibres_of_agave_family,raw_or_proce.
Briouet.ovoids_&_sim.solid_fuels,of_coal_peat_lig.
Coin(other_than_gold)_not_being_legal_tender
Iron_pyrites,unroasted
Goat_&_kid_skins,raw_(fresh,salted,dried,pickled)
Roasted_iron_pyrites,whether_or_not_agglomerated
Castor_oil_seeds
Orthopaedic_appliances,surgical_belts_and_the_like
Cotton,carded_or_combed
Gramophone_records_and_sim.sound_recordings
Warships_of_all_kinds
Ap_1962
mean rank rank fluctuation unpredictability
9.81E-06
0.19632
0.4202
0.25825
5.69E-06
0.075288
0.48974
0.2515
1.50E-05
0.049059
0.47185
0.22591
1.57E-05
-0.016992
0.45334
0.20349
0.0021461
-0.20094
0.27152
0.20094
2.48E-05
0.18517
0.34404
0.19679
0.00015328
-0.16539
0.36012
0.19637
0.0026562
-0.19545
0.26332
0.19545
0.0023281
-0.1843
0.32578
0.19152
0.0013954
-0.18264
0.33049
0.18585
0.00032608
-0.17393
0.34473
0.18585
0.0001946
-0.049669
0.44353
0.18522
0.00046455
-0.17933
0.3278
0.1828
0.00061788
-0.10918
0.41458
0.17901
0.00023743
-0.13716
0.39188
0.17896
0.00020929
-0.15999
0.35708
0.17857
0.00023142
0.1768
0.19731
0.17825
3.19E-05
0.060561
0.42361
0.17805
0.00061524
0.17707
0.20675
0.17707
0.0003461
-0.080777
0.43397
0.17263
Raw materials and agricultural products
Mostly they have their share fall behind prediction.
Products with unpredictably increased share
SITC
6589
6122
8983
8996
6642
8710
8821
8959
5416
8720
7741
5530
8942
223
5161
8841
8310
1110
6647
6123
Description
Other_made-up_articles_of_textile_materials,n.e.s
Saddlery_and_harness,or_any_material_for_animals
Gramophone_records_and_sim.sound_recordings
Orthopaedic_appliances,surgical_belts_and_the_like
Optical_glass_and_elements_of_optical_glass
Optical_instruments_and_apparatus
Chemical_products_&_flashlight_materials
Other_office_and_stationery_supplies
Glycosides;glands_or_other_organs_&_their_extracts
Medical_instruments_and_appliances
Electro-medical_apparatus
Perfumery,cosmetics_and_toilet_preparations
Childrens_toys,indoor_games,etc.
Milk_&_cream,fresh,not_concentrated_or_sweetened
Ethers,alcohol_peroxides,ether_perox.,epoxides_etc
Lenses,prisms,mirrors,other_optical_elements
Travel_goods,handbags,brief-cases,purses,sheaths
Non_alcoholic_beverages,n.e.s.
Safety_glass_consisting_of_toughened/laminat.glass
Parts_of_footwear
Ap_1962
mean rank rank fluctuation unpredictability
9.81E-06
0.19632
0.4202
0.25825
2.48E-05
0.18517
0.34404
0.19679
0.00061524
0.17707
0.20675
0.17707
0.00023142
0.1768
0.19731
0.17825
7.58E-05
0.16225
0.29715
0.16343
0.00072931
0.1606
0.21861
0.16702
0.00012313
0.16025
0.18614
0.16258
0.00019894
0.14761
0.18156
0.16491
0.00048222
0.14543
0.20509
0.14688
0.0011123
0.14526
0.16567
0.15741
0.00023524
0.13707
0.24761
0.13707
0.0012252
0.13646
0.19143
0.14615
0.0025954
0.13611
0.22104
0.1435
0.00011694
0.13454
0.24441
0.13454
0.00031245
0.13332
0.20459
0.13814
0.00034402
0.13254
0.21238
0.14809
0.0010566
0.13254
0.18475
0.14231
0.00020163
0.13114
0.23304
0.13114
0.00019306
0.12949
0.24531
0.1322
0.00023262
0.12949
0.23223
0.1318
Medical appliances, toys, cosmetics
They are not exclusively subject to economic demands
Products with the largest fluctuation of rank
SITC
7853
6880
2239
9610
7931
7911
2634
7913
6589
2714
6724
2860
2114
7914
7915
7187
7933
451
541
4235
Description
Invalid_cariages,motorized_or_not,parts
Uranium_depleted_in_u235_&_thorium,&_their_alloys
Flours_or_meals/oil_seeds/oleag.fruit_non_defatted
Coin(other_than_gold)_not_being_legal_tender
Warships_of_all_kinds
Rail_locomotives,electric
Cotton,carded_or_combed
Railway_&_tramway_coaches,vans,trucks_etc.
Other_made-up_articles_of_textile_materials,n.e.s
Potassium_salts,natural,crude
Puddled_bars_and_pilings;ingots,blocks,lumps_etc.
Ores_and_concentrates_of_uranium_and_thorium
Goat_&_kid_skins,raw_(fresh,salted,dried,pickled)
Railway_&_tramway_passenger_coaches_&_luggage_van
Rail&tramway_freight_and_maintenance_cars
Nuclear_reactors_and_parts
Ships,boats_and_other_vessels_for_breaking_up
Rye,unmilled
Potatoes
Olive_oil
Ap_1962
mean rank rank fluctuation unpredictability
5.69E-06
0.075288
0.48974
0.2515
1.50E-05
0.049059
0.47185
0.22591
1.57E-05
-0.016992
0.45334
0.20349
0.0001946
-0.049669
0.44353
0.18522
0.0003461
-0.080777
0.43397
0.17263
0.00026424
-0.012199
0.4247
0.15095
3.19E-05
0.060561
0.42361
0.17805
0.00023165
0.045399
0.4203
0.15411
9.81E-06
0.19632
0.4202
0.25825
0.00030787
-0.046532
0.41845
0.15565
0.00075701
-0.039735
0.4175
0.14973
0.0026274 -0.0030498
0.41522
0.13535
0.00061788
-0.10918
0.41458
0.17901
0.00048688
-0.059167
0.41353
0.14772
0.00070004
-0.061258
0.41318
0.16395
3.72E-05
0.047839
0.40814
0.15278
0.00027311
-0.023789
0.40432
0.12718
0.00060056
-0.076246
0.40347
0.14527
0.0024874
-0.030063
0.40127
0.12806
0.0012997
0.016556
0.39846
0.13502
Railways, warships, uranium, Nuclear reactors
Offer and demand are highly variable in time and historically determined
Summary and Discussion
•
•
•
•
•
•
•
Time-evolution of the market share of products in the world trade has been studied by data
analysis and model study
Urn model with quadratic preferential selection reproduces linear scaling of annual gain and
loss of share and the power-law distribution of share with exponent 2
The model represents the pressure of directing a country’s investment towards more
popular products in the global economy
The quadratic preferential selection leads the world trade market to the edge of
condensation
The condition for the emergence of pseudo condensate has been found.
The model explains the empirical observations very successfully at the aggregate level
The share trajectory of more than 60% products are predicted by the model capturing the
pressure towards enhancing the likelihood of profit.
•
Nature of unpredictable products provides the reason of deviation from model prediction
•
For more realistic and predictive model, one should consider the network structure of
product space– hopping in product space does not happen randomly but depending on the
proximity of two products.