Dynamics of export share of products in the international trades - PowerPoint Presentation

Slide1

Dynamics of export share of products in the international trades

Matthieu

Barbier and Deok-Sun LeeDept. Physics, Inha University

Dr.

Matthieu

Barbier

Now at Dept. Ecology &

Evol

. Biol.,

Princeton Univ. USASlide2

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? Slide3

Products that Korea is producing and exporting

1962

2000

http://atlas.media.mit.edu/Slide4

Products the whole world is producing and exporting

1962

3330 Petrol.oils & crude oils obt.from bitumin.minerals0711 Coffee,whether or not roasted or freed of caffeine2631 Cotton (other than linters),not carded or combed2320 Natural rubber latex; nat.rubber &

sim.nat.gums2681 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 equipmentSlide5

Statistics and dynamics of

“Export share” of products

empirical observationwhat are we interested in?Slide6

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: 1962-2000,

NBER Working Paper No. 11040 (2005)

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

year

icode importer

ecode

exporter sitc4 unit

dot

value quantity

. . .

. . .

.

.

.

132627

1962 218400 USA 454100 Korea Rep. 8310 1 1 NA

132628 1962 218400 USA 454100 Korea Rep. 8420 1 564 NA

132629 1962 218400 USA 454100 Korea Rep. 8471 1 1

NA

.

. .

. . .

. . .Slide7

Export share of a product

p in year t

Export volume (value in dollars) of a product p in year t : Export share

(relative export volume) of a product p in year t :

508 products maintain non-zero volume from 1962 to 2000

Normalization

, Mean

This quantity is what we study hereSlide8

Time evolution of all 508 productsSlide9

Uneven distribution of export share

Power

law behavior with exponent between 2 and 3 is observed for 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)

SITC 3330 Crude oil:

 Slide10

Growth or decay for 39 years

Increase or decrease?

How much?Growth rate

Skewed distribution

What products

increase

share and what do the opposite in the international trades?

What is the law governing it?

Invalid carriages (7853)

Coal and water

gas(3415)

 Slide11

Variation of share for one year- relatively microscopic view

Gain :

Loss :

Linear scaling both for gain and loss of share !

 Slide12

Our viewpoint, strategy, and goal

Construct

a particle-hopping model consistent with the linear scaling between

and

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?

Hidalgo et al., Science (2007)Slide13

Urn model with quadratic preferential selection

Factorized steady state

Pseudo-condensationSlide14

Urn model (or misanthrope process) as a model for the dynamics of

export share

A complete graph of N sites, each site representing a productA total of M

particles, each particle representing the unit of shareEach site has

particles and

specifies the system’s

state (

)

At each (microscopic) time step

wo sites

i

and j are selected with probability

and a particle at site

i

is transferred to site j, where

with

 Slide15

Example: N=14 M=35

We consider the case where N is very large

Every site has at least one particleSlide16

Why is it quadratic, not linear?

To be consistent with the linear relation between

and The annual variation of a product’s share is the sum of plus and minus like random walkSuppose that particle-hopping occurs times for one year. Then

A parameter is introduced:

One year corresponds to

times of transfer

of particles

or

(empirical)

 Slide17

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 sourceParticle-hop probability is proportional to the square of the number of particles in the source and destination siteEach unit of share (particle) is likely to move with probability proportional to the share of the present product and that of the destination productOur 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 Slide18

Relation to empirical results

Distribution of share

corresponds to the distribution of the number of particles

,

which can be obtained analytically for the stationary state

Is

the

broad distribution of share caused by the linear scaling between

and

?

Can the model predict the trajectory of share of individual product?

?

Urn model based on Slide19

Factorized steady state

: Probability of a specific particle configuration

at time t

Factorized state

assumed for the stationary state

with

to be determined

Detailed balance condition

Function f:

where

is used.

Evans and

Hanney

,

JPA

38, R195 (2005)

 Slide20

Single-site particle-number distribution

Partition function

Grand partition function

with

Partition

function (inverse

Mellin

)

Probability

that a

single site

has m particles

Evans and

Hanney

,

JPA

38, R195 (2005)Slide21

Partition function in our model

Logarithmic singularity of the generating function

at

(J.E. Robinson, Phys. Rev

. 83

, 678 (1951))

Partition function

at the saddle point

, which exists within the radius of convergence

(otherwise, condensate is formed)

in case

with particle density

Steepest descent path

 Slide22

Single-site particle-number distribution in our model

with

A bump is formed for

for the last two cases

 Slide23

Condensate-free

Approximate

 Slide24

Condensate …

Approximate

 Slide25

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

, the single-site particle-number distribution is

If

, it may happen that

even for finite

.

If

,

can be infinite

and can be equated to any finite

by introducing a suitable cutoff leading to exponential decay. However, if

is infinite, we should compare

and

, both of which are large numbers, and depending on the relation between

and

, a pseudo-condensate can appear

International trade dynamics is at the edge of condensation-free phase.

 Slide26

Application

- Does this model explain the international trade at the aggregate level and individual level?Slide27

Yes! it does at the aggregate level

Simulate the model with

and the initial values from the

1962 data

Share distribution

Second moment

Growth-rate distribution

Gain versus share

Loss versus shareSlide28

Evolution of export share of individual products

An ensemble of

simulation resultsThe middle 80% of the simulation values for

is shaded

Bad…

Not bad….Slide29

Quantifying the typicality of empirical observations among simulated trajectories

Values of return (one-year growth rate)

are compared between real and simulation for each p and t. That is, we have one

and K=300 simulation values

Normalized rank

If a product p is well predicted by the model, a total of T=39 such normalized ranks at different years

should be uniformly distributed over [-1/2, 1/2]

Deviation from Uniformity :

i

) sort T=39 values of

’s in increasing order from the smallest to the largest such that

. If they are uniform, then one would find

for

iii) Non-uniformity or

Unpredictability

of a product p is defined as

is observed only with probability 0.05 for 39 uniformly-distributed numbers

(

Marhuenda

, Morales, Pardo, Statistics 39, 315 (2005))

 Slide30

Classifying products

Mean rank

positive: higher returns (annual growth) than expected

negative: lower returns than expected

Rank fluctuation

Larger than 0.29 : higher variability of rank than expected

Smaller than 0.29 :lower variability

Unpredictability

Larger than 0.1 : deviate significantly from our model prediction

Smaller than 0.1 : predictable by the model

 Slide31

Predictability and mean-rankSlide32

10 categoriesSlide33

The most unpredictable products

Raw materials and agricultural

productsMostly they have their share fall behind prediction.Slide34

Products with unpredictably increased share

Medical appliances, toys, cosmetics

They are not exclusively subject to economic demandsSlide35

Products with the largest fluctuation of rank

Railways, warships, uranium, Nuclear reactors

Offer and demand are highly variable in time and historically determinedSlide36

Summary and Discussion

Time-evolution of the market share of products in the world trade has been studied by data analysis and model studyUrn 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 economyThe 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 levelThe 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.