The International-Trade Network: Statistical Properties ... · Introduction This Talk: An Overview of ITN-Related Research 1 Why characterizing trade ﬂows using a network representation

The International-Trade Network:Statistical Properties and Modeling

Giorgio Fagiolo1

[email protected]://www.lem.sssup.it/fagiolo/Welcome.html

1LEM, Sant’Anna School of Advanced Studies, Pisa (Italy)

Giorgio Fagiolo (LEM) The ITN: Empirics and Models 1 / 31

Introduction

Complex-Network Approaches in Economics

A fast-growing literature. . .Many economic systems and their evolution over timecan be described and studied using complex-networktools (Schweitzer et al., 2009, Science)A better understanding of how heterogeneouseconomic agents interact in non-trivial ways and giverise to unexpected aggregate phenomenaEmpirical vs. theoretical investigations

. . . but mostly in micro and financeApplications: networks of consumers, banks, financialinstitutions, companies, traders, stocks and financialproducts, etc.

What is a network?

• A graph-theoretic representation of relationships (links) between units (nodes) of a system in a given point in time (or time interval)

• Nodes: entities, units, agents, possibly heterogeneous

• Links: existence of relation between nodes

Giorgio Fagiolo, Course on Economic Networks.

lunedì 6 febbraio 2012

What about meso/macro economics?International trade network (ITN)Product-space network (Hausmann, Hidalgo et al; Tacchella, Pietronero et al.)International financial network (Haldane; Fagiolo et al; Reyes & Minoiu)Other macro-related networks: FDI, migrations and mobility, etc.


Introduction

Complex-Network Approaches in Economics

A fast-growing literature. . .Many economic systems and their evolution over timecan be described and studied using complex-networktools (Schweitzer et al., 2009, Science)A better understanding of how heterogeneouseconomic agents interact in non-trivial ways and giverise to unexpected aggregate phenomenaEmpirical vs. theoretical investigations

. . . but mostly in micro and financeApplications: networks of consumers, banks, financialinstitutions, companies, traders, stocks and financialproducts, etc.

What is a network?

• A graph-theoretic representation of relationships (links) between units (nodes) of a system in a given point in time (or time interval)

• Nodes: entities, units, agents, possibly heterogeneous

• Links: existence of relation between nodes

Giorgio Fagiolo, Course on Economic Networks.

lunedì 6 febbraio 2012What about meso/macro economics?International trade network (ITN)Product-space network (Hausmann, Hidalgo et al; Tacchella, Pietronero et al.)International financial network (Haldane; Fagiolo et al; Reyes & Minoiu)Other macro-related networks: FDI, migrations and mobility, etc.


Introduction

This Talk: An Overview of ITN-Related Research

1 Why characterizing trade flows using a network representation may berelevant for trade economists?

2 Can the knowledge of the ITN topological properties shed new light onissues like growth, globalization and trade integration?

3 Can we separate ITN topological properties that are the sheer outcomeof randomness from those that are instead statistically significant?

4 Are standard int’l trade models (i.e. gravity) able to replicate the observedITN structure?

5 Can we explain the properties of the ITN in terms of standard economicforces such as country specialization and comparative advantage?


Introduction








Introduction








Introduction








Introduction








Introduction

This is joint work with. . .

Giorgio&&Fagiolo&

Javier&Reyes&

Stefano&Schiavo&

Giuseppe&Mangioni&

Ma9eo&Barigozzi&

Diego&Garlaschelli&

Tiziano&&Squar?ni&

Ma9eo&Chinazzi&

Marco&Duenas&

Rossana&Mastrandrea&


Introduction

The International-Trade Network (ITN)

What is it?Network where nodes are world countries and links representbilateral trade flowsTime evolution of the ITN (data from 1950 to 2010)Different empirical representations: binary/weighted, undirected/directed,aggregate/commodity-specific

Introduction

The International-Trade Network (ITN)

What is it?Network where nodes are world countries and links represent bilateral tradeflowsDifferent empirical representations: binary/weighted, undirected/directed,aggregate/commodity-specificTime evolution of the ITN (data from 1950 to 2010)

The World-Trade Web (WTW)

• Links defined as binary trade relationships: existence of non-zero trade flows

USA

LUXTrade relation

USA

LUXExport/import relations


• Links defined as binary trade relationships: existence of non-zero trade flows

USA

LUXTrade relation

USA

LUXExport/import relations


• Link weights defined by total bilateral flows (undirected) or directed import flows (always deflated)

USA

LUXTotal bilateral flow (exports plus imports) btw USA and

LUX



USA

LUXTotal Export from USA to

LUX

Total Export from LUX to

USA

USA


LUXThe World-Trade Web (WTW)


USA


LUX



USA


LUX


USA

USA


LUX



USA


LUX



USA


LUX


USA

USA


LUX

Giorgio Fagiolo (LEM) Modeling the ITN 3 / 23


• Aggregate vs commodity-specific multi-network

1

2

6

4

5

3 1

2

6

4

5

3 1

2

6

4

5

3 3 1

2

6

4

5

1

2

6

4

5

3

Colors: Commodity-

specific networks

Multi-WTW: Union of colored slices


Why Networks of International Trade?

Trade Networks. . . An old Idea

Source: De Benedictis & Tajoli (2008)



Trade Networks. . . An old Idea

Source: De Benedictis & Tajoli (2008)



From Qualitative to Quantitative Approaches

The ITN in 2000: Link weight=total trade; Node size=GDP; Node shape=Continent.Only strongest 1% of link weights are shown. See Fagiolo, 2010.




Political-Science LiteratureApplying SNA tools to extract core-periphery structure of ITN (worlddependency theories)Snyder and Kick (1979), Nemeth and Smith (1985), Breiger (1981), Smithand White (1992), Kim and Shin (2002), etc.

Complex-Network ApproachCharacterizing the time evolution of topological properties of the ITN as abinary and weighted networkCorrelation among topological measures and node attributes (pcGDP),community structure; rich-club emergence; distributional stability/persistenceover time; etc.Li et al. (2003); Serrano and Boguna (2003); Garlaschelli and Loffredo(2004, 2005); Garlaschelli et al. (2007); Serrano et al. (2007); Bhattacharyaet al. (2007, 2008); Fagiolo et al. (2008, 2009); Reyes et al. (2008); Fagioloet al. (2010); Fagiolo (2010); Barigozzi, Fagiolo and Garlaschelli (2010);Barigozzi, Fagiolo and Mangioni (2010); De Benedictis and Tajoli (2011)




Political-Science LiteratureApplying SNA tools to extract core-periphery structure of ITN (worlddependency theories)Snyder and Kick (1979), Nemeth and Smith (1985), Breiger (1981), Smithand White (1992), Kim and Shin (2002), etc.

Complex-Network ApproachCharacterizing the time evolution of topological properties of the ITN as abinary and weighted networkCorrelation among topological measures and node attributes (pcGDP),community structure; rich-club emergence; distributional stability/persistenceover time; etc.Li et al. (2003); Serrano and Boguna (2003); Garlaschelli and Loffredo(2004, 2005); Garlaschelli et al. (2007); Serrano et al. (2007); Bhattacharyaet al. (2007, 2008); Fagiolo et al. (2008, 2009); Reyes et al. (2008); Fagioloet al. (2010); Fagiolo (2010); Barigozzi, Fagiolo and Garlaschelli (2010);Barigozzi, Fagiolo and Mangioni (2010); De Benedictis and Tajoli (2011)



ITN Correlation Structure (Fagiolo et al, 2009, PRE)Correlation Structure Stationary over Time (Globalization?)

Giorgio Fagiolo, The World-Trade Web

Stability and Persistence of the WTW

Introduction Preliminaries Results Conclusions

•  Correlation structure among topological properties is stationary over time and identifies a characteristic trade structure

•  Fagiolo et al (2008, PHYSA; 2009, PRE)

Correlation Coefficients

Countries holding more partners tend to trade with countries with very few partners (strong disassortativity) and do not typically form trade triangles

Weighted WTW is only weakly disassortative: More-intensively connected countries tend to trade with relatively less connected countries

Countries with many trade partners do not necessarily trade more intensively

More-intensively connected countries are more central and tend to form highly-connected trade triangles

Binary WTW profoundly different from weighted WTW !!

See Fagiolo et al, 2008, Physica A

ND/NS=Node Degree/Strength; ANND/ANNS; Average Nearest-Neighbor Degree/Strength;BCC/WCC=Binary/Weighted Clustering Coefficient; RWBC=Random-Walk Betw Centrality



Why Should Trade Economists Care About Networks?

Generating Fresh Stylized FactsA network approach employs a holistic perspective, where trade is notviewed as a bilateral phenomenon anymore, where only direct links areimportantCountries can be characterized in terms of their global embeddedness in theITN (unlike in standard approaches)

Are Indirect-Trade Links Important?Abeysinghe and Forbes (2005): impact of shocks on a given country isexplained by indirect trade linksDees and Saint-Guilhem (2011): countries that do not trade very much withthe U.S. are largely influenced by its dominance over other trade partnerslinked with the U.S.Ward and Ahlquist (2011): bilateral trade is not independent of theproduction, consumption, and trading decisions made by firms andconsumers in third countries




Generating Fresh Stylized FactsA network approach employs a holistic perspective, where trade is notviewed as a bilateral phenomenon anymore, where only direct links areimportantCountries can be characterized in terms of their global embeddedness in theITN (unlike in standard approaches)

Are Indirect-Trade Links Important?Abeysinghe and Forbes (2005): impact of shocks on a given country isexplained by indirect trade linksDees and Saint-Guilhem (2011): countries that do not trade very much withthe U.S. are largely influenced by its dominance over other trade partnerslinked with the U.S.Ward and Ahlquist (2011): bilateral trade is not independent of theproduction, consumption, and trading decisions made by firms andconsumers in third countries




Can ITN Structure Explain Macro Dynamics?Kali et al. (2007) and Kali and Reyes (2010): country position in the tradenetwork has substantial implications for economic growth and a goodpotential for predicting episodes of financial contagion

Country Centrality and Economic DevelopmentReyes, Schiavo, Fagiolo (2010, JITED): country centrality in the ITN mayhelp to account for the evolution of international economic integration betterthan what standard statistics, like openness to trade, doExample: LATAM vs East-Asian Countries

Main IdeaITN topology describes the architecture of “real” interaction channels amongworld countries, where indirect as well as direct linkages are explicitly takeninto considerationStudying the ITN can give us insights about macro issues such as economicglobalization, internationalization, spreading of international crises,transmission of economic shocks















How Can We “Explain” ITN Statistical Properties?

Two levelsNull models of the ITNEconomic models of the ITN

Null models of the ITNCan observed properties be replicated by a null random network model thatonly preserves some local (1st-order) statistics?What is (if any) the minimal amount of information about the ITN needed toreproduce all its properties using an otherwise random model?Can one discriminate between statistically relevant and irrelevant properties?

Economic models of the ITNStandard Int’l Trade Models: Gravity Model (GM)Economics-Inspired Stochastic Models of Network Formation














Null Models of the ITN

Null Models

Main IdeaGiven observed network, define a set of local properties of the network(constraints) that must be preserved (density, degree or strength sequence,etc.)Characterize the ensemble of all networks that preserve on average theseconstraints but are otherwise purely randomObtain expected value and standard deviation of higher-order networkstatistics (assortativity, clustering, centrality, etc.) over the ensembleCompare observed vs. expected values

Application to the ITNWe study null models where we keep fixed either (in/out) degree or strengthsequences and we check higher order statistical network properties(disassortativity, clustering)By product: Are standard (local) international-trade statistics sufficient forexplaining higher-order network properties?Squartini, Garlaschelli, Fagiolo (2011a, 2011b; PRE)



Null Models

Main IdeaGiven observed network, define a set of local properties of the network(constraints) that must be preserved (density, degree or strength sequence,etc.)Characterize the ensemble of all networks that preserve on average theseconstraints but are otherwise purely randomObtain expected value and standard deviation of higher-order networkstatistics (assortativity, clustering, centrality, etc.) over the ensembleCompare observed vs. expected values

Application to the ITNWe study null models where we keep fixed either (in/out) degree or strengthsequences and we check higher order statistical network properties(disassortativity, clustering)By product: Are standard (local) international-trade statistics sufficient forexplaining higher-order network properties?Squartini, Garlaschelli, Fagiolo (2011a, 2011b; PRE)



A New Randomization Method

Features (Squartini & Garlaschelli, 2010)Fit to observed network the probability P(G) of a random graph satisfying alist of local constraints (inferred from observed network)Fully analytical method: no random variant must be generatedWorks for directed/undirected, binary/weighted, sparse/dense networksExpected properties computed in same time as empirical ones

A 3-Step MethodFind the graph probability distribution P(G;

−→θ ) that maximizes graph entropy

subject to constraintsUse observed data to estimate via ML free parameters

−→θ in the graph

probability distribution obtained aboveUse ML estimates of free parameters

−→θ∗ to compute expected values and

standard deviations of higher-order network statistics X (G)

E(X |−→θ∗) =

∑G

P(G|−→θ∗)X (G)



A New Randomization Method

Features (Squartini & Garlaschelli, 2010)Fit to observed network the probability P(G) of a random graph satisfying alist of local constraints (inferred from observed network)Fully analytical method: no random variant must be generatedWorks for directed/undirected, binary/weighted, sparse/dense networksExpected properties computed in same time as empirical ones

A 3-Step MethodFind the graph probability distribution P(G;

−→θ ) that maximizes graph entropy

subject to constraintsUse observed data to estimate via ML free parameters

−→θ in the graph

probability distribution obtained aboveUse ML estimates of free parameters

−→θ∗ to compute expected values and

standard deviations of higher-order network statistics X (G)

E(X |−→θ∗) =

∑G

P(G|−→θ∗)X (G)



The Binary ITN: Disassortativity

Orange: Observed. Green: Expected.

��

��

��

��

��

��

��

��

��

��

��

��

��

��

1950 1960 1970 1980 1990 200050

100

150

200

250

year

mktot�tot ,

m�ktot�to

t �

a

��

��

��

��

��

��

��

�

��

��

��

��

��

��

��

�

��

�

��

�

��

�

��

�

��

�

��

��

�

��

��

�

�

��

��

�

�

��

�

�

��

��

�

�

��

�

�

��

��

�

�

��

�

�

��

��

�

�

��

��

�

�

��

��

�

�

��

��

�

�

��

��

�

�

��

��

�

�

��

��

�

�

��

��

�

�

��

��

�

�

��

��

�

�

�

�

��

�

�

��

��

�

�

�

�

��

�

�

��

��

�

�

�

�

��

�

�

�

�

��

�

�

�

�

��

�

�

�

�

��

�

�

�

�

��

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

��

�

�

�

�

��

�

�

�

�

��

�

�

�

�

��

�

�

1950 1960 1970 1980 1990 20000

10

20

30

40

50

year

s ktot�tot ,

s �ktot�tot �

b

�

�

�

�

�

�

�

�

�

�

�

��

�

�

�

�

�

�

�

�

�

�

�

�

�

�

��

�

��

��

��

��

��

��

��

1950 1960 1970 1980 1990 2000�1.0

�0.5

0.0

0.5

1.0

year

r ktot�tot ,

ktot,r�ktot�to

t �,ktotc

�

�

�

�

�

�

�

�

�

�

�

�

�

�

��

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

��

��

�

��

�

��

��

��

��

��

��

1950 1960 1970 1980 1990 2000�1.0

�0.5

0.0

0.5

1.0

year

r ktot�tot ,�ktot�to

t �

d

Contraint: Degree sequenceNull model always predicts strong disassortativityITN is strongly disassortative only after 1965Null model well predicts disassortativity (when it is a robust network feature)



The Weighted ITN: Disassortativity

Orange: Observed. Green: Expected.

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

1950 1960 1970 1980 1990 20000.00

0.02

0.04

0.06

0.08

year

ms� tot�tot ,

m�s� tot�to

t �

a

�

�

�

��

�

�

�

��

�

�

�

��

�

�

�

��

�

�

�

��

�

�

�

��

�

�

�

��

�

�

�

��

�

�

�

��

�

�

�

��

�

�

�

��

�

�

�

��

��

�

��

��

�

��

��

�

��

��

�

��

��

�

��

��

�

��

��

�

��

��

�

��

��

�

��

��

�

��

��

�

��

��

��

��

��

��

��

��

��

��

��

��

�

��

��

��

��

��

��

��

��

�

��

��

�

��

��

�

��

��

��

��

�

��

��

�

��

��

�

��

��

�

��

��

�

��

��

�

��

��

�

��

��

�

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

1950 1960 1970 1980 1990 20000.0000.0050.0100.0150.0200.0250.030

year

s s� tot�tot ,

s �s� tot�tot �

b

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

�

�

�

�

�

�

�

�

�

�

�

�

��

1950 1960 1970 1980 1990 2000�1.0

�0.5

0.0

0.5

1.0

year

r s� tot�tot ,s�

tot ,r �s� tot�

tot �,s� tot

c

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

��

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

��

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

��

�

�

�

�

�

�

�

�

�

�

�

�

1950 1960 1970 1980 1990 2000�1.0

�0.5

0.0

0.5

1.0

year

r s� tot�tot ,�s�

tot�tot �

d

Contraint: Strength sequenceNull model always predicts extreme weighted disassortativityWeighted (weak) disassortativity patterns (arising consistently from 1950 to 2000)cannot be replicated



Null Models: Implications

General ResultsBinary ITN: Degrees are sufficient to reproduce all higher-order statisticsWeighted ITN: Strengths are not sufficient to reproduce higher-orderstatistics

Implications for network analysisBinary ITN: disassortativity and clustering patterns do not convey anyinteresting informationWeighted ITN: higher-order statistics convey fresh information, which is notalready contained in strength sequences

Implications for international-trade empiricsA weighted-network analysis brings value added wrt standard (local)int’l-trade statisticsDegree sequences are maximally informative: trade models should focus onexplaining new-link formation and degrees (in addition to trade flows)














Economic Models

Economic Models and the ITN

Can economic models explain/reproduce ITN architecture?

Two examples:

1 Standard Int’l Trade Models: Gravity Model (GM)

2 Stochastic Models of Network Formation


Economic Models

Economic Models and the ITN

Can economic models explain/reproduce ITN architecture?

Two examples:

1 Standard Int’l Trade Models: Gravity Model (GM)

2 Stochastic Models of Network Formation


Economic Models

The Gravity Model

The Microfounded GMThe GM explains international-trade bilateral flows as the equilibriumprediction of micro-founded models of tradeA Newton’s formula for trade

Exporta→b ∝Sizea · Sizeb

dist(a, b)

The Empirical GMAdding explanatory factors to the basic GM equationCountry-specific: population, area, land-locking effects, etc.Bilateral: geographical contiguity, common language and religion, colonyrelation, bilateral trade agreements, etc.


Economic Models

The Gravity Model

The Microfounded GMThe GM explains international-trade bilateral flows as the equilibriumprediction of micro-founded models of tradeA Newton’s formula for trade

Exporta→b ∝Sizea · Sizeb

dist(a, b)

The Empirical GMAdding explanatory factors to the basic GM equationCountry-specific: population, area, land-locking effects, etc.Bilateral: geographical contiguity, common language and religion, colonyrelation, bilateral trade agreements, etc.


Economic Models

GM Specification (Duenas & Fagiolo, 2012)Economic Models

GM Specification (Duenas & Fagiolo, 2012)

wij(t) = ↵0Yi(t)↵1Yj(t)↵2d↵3ij

"KY

k=1

Cik (t)�1k Cjk (t)�2k

#⇥

⇥ exp

HX

h=1

✓hDijh(t) +LX

l=1

(�1lZil + �2lZjl)

!⌘ij(t) = exp{Xij · �}⌘ij ,

t is the year (t = 1950, 1955, . . . , 2000)wij (t) are export flows from the observed weighted ITNi, j = 1, ..., N(t), i 6= j ; Yh(t) is year-t GDP of country h = i, j (i=exporter; j=importer)dij is geographical distance;Ch(t), h = i, j , are additional country-size effects (area and population);Dij is a vector of bilateral-relationship variables (contiguity, common language, past andcurrent colonial ties, common religion, common currency, a dummy to control if bothcountries share a generalized system of preferences, and a regional trade agreement flag);Zi and Zj are country-specific dummies (controlling for land-locking effects and continentmembership);⌘ij (t) are the errors (whose mean conditional to explanatory variables obeys E [⌘ij (t)|·] = 1).

Giorgio Fagiolo (LEM) Modeling the ITN 21 / 23

GDPGeographical

Distance

Country Vars(Area, Population)

Bilateral-relationship variables (contiguity, common language, past and current colonial ties, common religion,

common currency, regional trade agreements)

Country-specific dummies (land-locking effects, continent

membership, etc.)

Errors

Exports from i to j

at t


Economic Models

What We Do. . .

Fitting the GM to the dataTwo setups:

1 Binary structure given: estimate flows only (OLS on log-linearized model)2 Binary structure estimated together with flows (PPML, ZIP)

We employ GM predictions to build a weighted predicted ITN, whosetopological properties are compared to observed ones

Results: A Sneak-in PreviewThe GM successfully replicates the weighted-network structure of the ITN,only if one fixes its binary architectureThe GM performs very badly when asked to predict the presence of a link; orthe level of the trade flow whenever the binary structure must besimultaneously estimated


Economic Models

What We Do. . .






Economic Models

What We Do. . .






Economic Models

Weighted Correlation Structure

Weighted Disassortativity: Correlation between ANNS and NS

1970 1975 1980 1985 1990 1995 20001

0.95

0.9

0.85

0.8

0.75

0.7

0.65

0.6

0.55

0.5

Year

Corr(

NSto

t ,ANN

Stot )

ObservedOLS

1970 1975 1980 1985 1990 1995 20001

0.9

0.8

0.7

0.6

0.5

0.4

0.3

Year

Corr(

NSto

t ,ANN

Stot )

ObservedPPML

1970 1975 1980 1985 1990 1995 20001

0.9

0.8

0.7

0.6

0.5

0.4

0.3

Year

Corr(

NSto

t ,ANN

Stot )

ObservedZIP

OLS can correctly replicate observed disassortativity

PPML/ZIP always predict extreme disassortativity (as in null-model exercises, seeFagiolo, Squartini, Garlaschelli, 2011)

Why: The GM is not able to correctly predict the binary structure!


Economic Models

Stochastic Models of Network Formation

Main IdeaEmploy network-formation models ideas to replicate structure of ITN. See:Riccaboni and Schiavo (2010, NJP), Caldarelli et al. (2012, arxiv)Here: Building a model where link formation is driven by economic rationalescoming from international-trade theoriesExample: Comparative advantage and country specialization

A Sketch of the Model (Duenas and Fagiolo, fc)N countries operating in K different industries/or markets (traits)Countries are located on a ring (geographical distance)The performance of country i in industry κ is πiκ

Trade of a certain good between any pair of countries increases the morethese countries are different in their performance levelsCountry i is more likely to export product κ to j if πiκ − πjκ > 0Overall likelihood for i to export any product to j depends on

λij =∑κ

[πiκ − πjκ] · 1{πiκ−πjκ>0}


Economic Models

Stochastic Models of Network Formation

Main IdeaEmploy network-formation models ideas to replicate structure of ITN. See:Riccaboni and Schiavo (2010, NJP), Caldarelli et al. (2012, arxiv)Here: Building a model where link formation is driven by economic rationalescoming from international-trade theoriesExample: Comparative advantage and country specialization

A Sketch of the Model (Duenas and Fagiolo, fc)N countries operating in K different industries/or markets (traits)Countries are located on a ring (geographical distance)The performance of country i in industry κ is πiκ

Trade of a certain good between any pair of countries increases the morethese countries are different in their performance levelsCountry i is more likely to export product κ to j if πiκ − πjκ > 0Overall likelihood for i to export any product to j depends on

λij =∑κ

[πiκ − πjκ] · 1{πiκ−πjκ>0}


Economic Models

Link Formation

Edges are drawn independently with probability pij , the probability of having aparticular graph A = {aij} is (Park & Newman, 2004):

Γ(A) = Γ0

∏

aij∈A

(pij

1− pij

)aij

= Γ0

∏

aij∈A

Λaijij , (1)

with

Λij = βλijSiSj

dαij, with Si =

∑

k

πi,k (2)

Then,

Γ(A) = Γ0

βL

∏

aij∈A

d−α·aijij

∏

aij∈A

λaijij

∏

i

Skouti

i

∏

j

Sk in

jj

, (3)

where L is the number of edges; kouti and k in

i are in- and out-degrees; αcontrols for geographical distance; β controls for density.


Economic Models

Distribution of Perfomance P(π)

Two Extreme Scenarios1 Homogeneous Performances: Countries have similar performances in all

traits, with comparable overall “sizes” Si2 Heterogeneous Performances: Countries have very dissimilar capabilities

and overall “sizes” Si

Main IdeaComparing a world where countries do not specialize with a more realisticpicture were more competitive countries are more likely to export

Implementation1 Homogeneous Performances: Draw π from a Uniform distribution2 Heterogeneous Performances: Draw π from a Pareto distribution


Economic Models








Economic Models








Economic Models

Reproducing Node-Degree Distribution

Homogeneous Scenario Heterogeneous Scenario

The model is able to reproduce degree distributions in both scenarios


Economic Models

Reproducing Correlation Structure

Homogeneous Scenario Heterogeneous Scenario

X-axis: network density (∼ 0.45 for the ITN)

The heterogeneous scenario captures the magnitude of correlations forempirically-observed network-density values. The homogeneous scenariocannot.


Economic Models

Null vs. Economic Models: Take-Home Messages

The ITN vs. Null ModelsDegrees are responsible for higher-order binary structureMost of higher-order evidence about correlation is meaningless if one knowsdegree sequencesExplaining binary structure of first-trades (and thus degrees) is fundamental

The ITN vs. the GMThe GM turns out to be a good model for estimating trade flows, but cannotpredict the presence of a link (and thus degree sequences)However, conditional on the information that a link exists, the GM can wellpredict weighted-network properties

The ITN vs. Stochastic Models of Network FormationImportant role of specialization in explaining degree distribution andcorrelation structureWork in progress: calibration with real world data, scenario and sensitivityanalysis, etc.


Economic Models






Economic Models






Economic Models

Papers

Topological Properties of the ITN

Barigozzi, M., Fagiolo, G. and Garlaschelli, D. (2010), "The Multi-Network ofInternational Trade: A Commodity-Specific Analysis", Physical Review E, 81, 046104Fagiolo, G., Reyes, J. and Schiavo, S. (2009), "The World-Trade Web: TopologicalProperties, Dynamics, and Evolution", Physical Review E, 79, 036115 (19 pages)

Null Models

Squartini,T., Fagiolo, G. and Garlaschelli, D. (2011), “Randomizing World Trade. PartI: A Binary Network Analysis”, Physical Review E, 84, 046117.Squartini,T., Fagiolo, G. and Garlaschelli, D. (2011), “Randomizing World Trade. PartII: A Weighted Network Analysis”, Physical Review E, 84, 046118.Squartini,T., Fagiolo, G. and Garlaschelli, D. (2011), “Null Models of EconomicNetworks: The Case of the World Trade Web”, J of Econ Int & Coord, forthcoming

Gravity Models

Duenas, M. and Fagiolo, G. (2011), “Modeling the International-Trade Network: AGravity Approach”, arXiv:1112.2867 [q-fin.GN]. Also in: LEM Working Paper, 2011/25.Fagiolo, G. (2010), “The International-Trade Network: Gravity Equations andTopological Properties”, J of Econ Int & Coord, 5:1-25.


Economic Models

Thanks

Giorgio FagioloLaboratory of Economics and Management (LEM)

Institute of Economics

Sant’Anna School of Advanced Studies, Pisa, Italy

[email protected]

http://www.lem.sssup.it/fagiolo/Welcome.html


The International-Trade Network: Statistical Properties ... · Introduction This Talk: An Overview of ITN-Related Research 1 Why characterizing trade ﬂows using a network representation

Documents