ï»¿ WPS6478
Policy Research Working Paper 6478
How Many Dimensions Do We Trade In?
Product Space Geometry and Latent Comparative
Advantage
Jean-FranÃ§ois Arvis
The World Bank
Poverty Reduction and Economic Management Network
International Trade Department
June 2013
Policy Research Working Paper 6478
Abstract
This paper proposes a new quantitative implementation and 61 products, and to estimate the latent factors of
of Balassaâ€™s idea that export composition and revealed endowments by country. It formalizes a concept of latent
comparative advantage inform the relationship between comparative advantage, which has practical country
endowments in domestic factors of production and specific applications, relevant for â€œtrade competitivenessâ€?
exports. It proposes that the export composition of policies. Compared with classical revealed comparative
countries is close to a low-dimensional manifold or advantage, the model assesses how well countries are
â€œProduct Spaceâ€? within the space of export composition, matching their potential implied by the latent variables,
which has as many dimensions as product lines. The and also identifies products for which the latent
Product Space corresponds to a few latent endowments advantage is not yet revealed (extensive margin). The data
explaining the structure of the trade matrix. The model suggests that the degree of overlap between latent and
uses non-linear techniques to identify the product revealed advantage is a metric of â€œtrade competitiveness.â€?
space from the 2010 export matrix of 128 countries
This paper is a product of the International Trade Department, Poverty Reduction and Economic Management Network. It
is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development
policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.
org. The author may be contacted at jarvis1@worldbank.org.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Produced by the Research Support Team
How Many Dimensions Do We Trade In? Product Space Geometry and Latent
Comparative Advantage
Jean-FranÃ§ois Arvis 1 2
JEL C14, F11, F15, O24, O25
Keywords : Trade, Export Competitiveness, Comparative Advantage, Product Space, Non-linear
Sector Board : Economic Policy
1 Jarvis1@worldbank.org, International Trade Department, the World Bank, Washington, D.C.
2
The author would like to thank the following World Bank colleagues for useful inputs, comments and
encouragements: Daniel Saslavski, Najy Benhassine, Olivier Cadot, Amir Fouad, Mona Haddad, Bernard Hoekman,
Claire Hollweg, Daniel Lederman, Anasuya Raj, Cordula Rastogi, JosÃ© Guillerme Reis, Benjamin Shepherd, and
Daria Taglioni.
â€œSi nous comparons les nations entre elles, par quels signes certains constaterons-nous les
progrÃ¨s ou la dÃ©cadence de leur prospÃ©ritÃ© ? â€œ (*)
Antoine-Augustin Cournot â€œRecherches sur les principes mathÃ©matiques de la thÃ©orie des
richessesâ€? (1838, chapter 5)
(*)When comparing nations among themselves, by which sure signs shall we notice progress or
decadence of their wealth?
1 Introduction: What You Export Matters
What countries produce and eventually export depends upon a number of production inputs
(labor, physical and human capital) and also domestic factors that impact productivity such as
the business environment, institutions or governance (Hausmann, Hwang, & Rodrik, 2006),
(Nunn, 2007), (McMillan & Rodrik, 2011). Differences in endowments of factors largely
determine the composition of exports. Rich countries tend to export more sophisticated products.
However, even at the same level of development, as measured for instance by GDP per capita,
countries may be involved in production and exportation of more or less diversified baskets of
products.
This phenomenon is generally referred to by policy makers and the institutions advising them as
â€œexport competitivenessâ€?. Although the concept of competitiveness is intuitive to policy makers
and practitioners (WEF, 2012), there is no consensus among experts on a formal definition of
competitiveness embedded in economic theory ((Leamer, 1993)(J. P. Neary, 2003; J. Neary,
2006)); an ordinal concept of absolute competitiveness may not be easily reconciled with
classical trade theory (comparative advantage).
Even loosely defined, competitiveness may be related to cross-sector and cross-country
productivity changes that depend on factors such as cost of labor, capital, skills, logistics,
innovation, quality standards, infrastructure (availability and quality), quality of institutions,
corruption, etc. Understanding the relationship between countriesâ€™ endowments in those factors
and the potential for growth through diversification of production and exports has been a major
policy concern in rich and emerging economies, but also increasingly in poor countries willing to
reduce their dependence on a relatively small basket of commodities.
Unsurprisingly, it is an area of very active policy work, especially by organizations whose role is
to provide support to developing countries and advise on growth strategies (Reis & Farole,
2012). Disentangling competitiveness and understanding the linkages between factors of
competiveness on the one hand, and export content and its diversification on the other hand, has
been high on the practical policy research agenda in recent years. Several groups have made
substantive contributions at both the conceptual and advisory levels, including multinational
organizations (for example, the World Bank, International Trade Center, and World Economic
Forum) and academia (including the Kennedy School of Economics and MIT). This paper is a
contribution to the World Bank effort under the leadership of its International Trade Department.
The main challenge is to adequately relate trade and production outcomes by sector (i.e. export
composition) with variables that capture quantitative inputs or performance metrics of these
sectors at the country level. Such metrics would best capture the impact on production of a set of
2
domestic endowments or of relevant policies. Fortunately most of the relevant variables are now
covered by established datasets of indicators based on statistics or, very often, surveys. To meet
the expectations of policy makers to understand the differences of dynamics by industry, the
analysis had to be disaggregated at the sector level. This provides a â€œmeso-economicâ€?
description of how differences in factor endowment may be more conducive of certain products
or exports.
The insight that trade outcomes can reveal information on sources of competitiveness or
comparative advantage goes back half a century, when Balassa introduced the concept of
revealed comparative advantage. This paper follows this tradition. It proposes that the structure
of the global export matrix can be essentially explained by a few latent factors of endowments
that determine comparative advantage. Thus the position of the problem is â€œinverseâ€?: country
and product factor variables are deduced from the export outcome data, in contrast to the
traditional econometric approach whereby export outcomes are regressed against actual
endowment variables.
A nonlinear dimensionality reduction procedure (exponential-PCA or E-PCA) analyzes and
produces the few latent factors. Although based on off-the-shelf mathematical tools and intensive
computations, the main outputs consist in country specific information of practical value,
including the latent composition of trade and latent comparative advantage ratios. Ultimately the
paper proposes a scientific solution to the old problem of estimating the potential for
diversification of countries based on existing data and trade theory.
The remainder of the paper is organized as follows.
The first part of the paper (section 2) introduces the key concepts and surveys the literature.
The second part of the paper develops an alternative concept of product space (section 3) rooted
in neoclassical trade theory (section 4). It introduces the factor supply elasticity, which is a
measure of the productivity gains brought about by changes in the supply of factors across
countries. The estimation of the model requires non-linear techniques -Poisson Pseudo
Maximum Likelihood (PLM)-, in contrast to previous implementations, and corresponds to a
non-linear projection of the product space onto a one-dimensional manifold (section 5).
Implementation to trade data and various factors of competitiveness is commented on (section 6).
Finally, the third part of the paper proposes to push the model further by applying a consistent
procedure of dimensionality reduction to the product space to identify its dimensions. It
combines non-linear estimation (Poisson PLM) with principal component analysis (E-PCA)
(section 7). Country and product coordinates are estimated through this non-linear â€œprojectionâ€?.
The significance of the principal axes in this reduction and their relationship with known factors
of competitiveness are investigated (section 8), along with comparisons of latent against revealed
comparative advantage by country (section 9).
The research dataset is available at www.worldbank.org/trade -> Data
3
2 Composition Space and Revealed Comparative Advantage: A Literature Review
Following the tradition of most empirical work, this paper analyzes export data. Indeed, export
data are available across countries at a detailed sector level, more reliably than production data.
Furthermore, trade data may be more relevant for assessing cross-country competitiveness since,
by definition, this notion reflects competition between exporters from different countries.
However, the focus on export data may omit important features of production and trade. For
instance, the ability to participate in global value chains and production sharing drives much of
developing countriesâ€™ diversification towards more complex production. An analysis based
solely on export data, although already quite complex, may not capture fully the consequences of
the cross-border nature of value chains or the importance of international backward and forward
linkages (Baldwin, 2010).
Composition Space and Revealed Comparative Advantage
At an abstract level, changesâ€”or rather relative changesâ€”in factor endowments will correspond
to trajectories of countries in the composition space of exports, where coordinates are the shares
of exports by product. Composition space has many dimensions; as many as distinct product
lines in the data. A change of composition in exportsâ€”resulting from a change over time (or
across countries) of factors endowmentâ€”is naturally represented by a trajectory in a space with
as many dimensions as products, where the coordinates are the relative export composition by
country. The concept transposes to represent the position of cross-sections of countries with
different endowments in factors of production. The composition coordinates are export shares:
where is the exports of product i from country a. 3
,
Therefore, the composition space is the hyper-plane of co-dimension one (Fig 1) where the
â€œmovementâ€? takes place:
and
A perspective going back at least to Balassa (Balassa, 1979, 1986) is that the position of the
problem can be reverted. Trajectories in composition space can "reveal" information about the
importance or relative importance of factors of production for (export) competitiveness.
Balassa proposed the revealed comparative advantage (RCA) as a more meaningful
representation of the position of countries in Composition Space than the composition vector.
The RCA is the ratio of the countryâ€™s export share of a particular product against the global
3 The paper refers to a dot subscript as sums by countries or products (Einsteinâ€™s convention).
, ,
4
X ai X ..
export share of the same product, RCAai =
X a . X .i
Fig 1. Composition space (with three products)
Beyond the observation of the RCAs, a precise description of the geometry of the composition
space and the dynamics of products and countries would help inform the relationship between
endowments and composition, and ultimately how factors of â€œcompetitivenessâ€? influence the
volume of exports across countries and across products. This identification would be of high
practical relevance for understanding the potential for change of composition (synonymously
diversification) and to assess how well countries are making use of their comparative advantage.
However, this identification is quite complex because of the high dimensionality of the product
space, the non-linear nature of the relationship and the fact that many factors are relevant to
explain export compositions.
PRODY and Revealed Factor Intensity
The end of the last decade saw a fresh wave of interest in the problem, stimulated by the renewed
focus on competitiveness policies. Practical methods have been proposed to understand the
dependence of specific industries or export commodities on the endowments of different factors.
This approach yields the "PRODY" (Hausmann & Klinger, 2006), generalized in the Revealed
Factor Intensity (RFI) (Shirotori, Tumurchudur, & Cadot, 2010), available for each individual
endowment factor that is measured by a macro-index available by country, say . The revealed
factor intensity by product (or industry) , is representative of the factor endowment of
countries that have the greatest comparative advantage of producing this product i. Thus the
factor supply intensity by product is a weighted average of countriesâ€™ factor index values ,
with a weight proportional to the RCA of country a in product i
5
The original PRODY referred to the level of development classically measured by GDP per
capita. Other implementations extended the concept to RFI of capital or labor per unit of
production. The RFI concept can essentially apply to any endowments for which a cross-country
metric is available, such as the competitiveness related indicators available in the databases of
the WEF or the World Bank (Doing Business, Logistics Performance, Governance).
HHR product space as a network: economic complexity
Haussman-Hidalgo and Rodrick (HHR) put forward a more comprehensive proposal (Hidalgo &
Hausmann, 2009) that does not start from actual endowments but instead tries to understand the
structure of exports. They introduce the concept of product space and economic complexity
through a procedure akin to data analysis and dimensionality reduction. HHR views countries
and products as nodes of two dual networks or graphs. A country and a product are linked when
their RCA is more than one. This concept provides a simplified structure, thought of as a sort of
"skeleton" of the composition space. The country and product associations can be graphically
plotted. The implementation of network analysis tools, like the eigenvalue centrality (behind the
Google search engine), produces an index of economic complexity by product or country
(referred to as an atlas of economic complexity).
Other authors (Barigozzi, Fagiolo, & Garlaschelli, 2010) have similarly and independently
implemented linear, automatic classification and data clustering analysis tools to provide a
discrete, network-like description of products and countries as nodes or branches in networks or
dendrograms.
However, this "skeleton" approach based on a series of simplifications does not directly provide
country-specific information on non-revealed potential or on the linkages between composition
and endowments.
Authorâ€™s Comments
The PRODY/RFI concepts as well as product space and economic complexity have become
rather popular. However, they have some limitations stemming from their intuitive and
heuristicâ€”as opposed to model-basedâ€”nature.
First is their relation to trade theory. Factor allocations are naturally defined at the country level
(e.g. wages, investment per worker, policy variables), as they enter into the production functions,
which typically vary among products. At the micro level, industries are not characterized by
constant factor allocations worldwide but by production functions with product-dependent
parameters (e.g. elasticities in a Cobb Douglas production function). The relationship between a
product and a typical or optimal factor allocation, as in the RFI, is a statistical outcome
â€œaveragingâ€? over different factor allocations across countries within the same production
function. Implicitly, this association of an optimal level of a factor to a product relates to a life
cycle explanation of export competitiveness. The relative export level for a given product
6
increases initially and then decreases beyond a point where comparative advantage has grown
higher and the export of the product more intensive in the factor (Wells 1961). However, the
optimal or typical factor supply for an industry is a dynamical outcome resulting from
differentials in productivity across countries, products and global market demand (section 3); it is
not a primary mechanism.
The RFI does not provide an explicit predictive model that could relate change in endowments to
changes in RCAs or export composition. The "skeleton" approach in the product space
decomposition is also based on a series of simplifications and does not provide either country-
specific information on its non-revealed potential or the linkages between composition and
endowments.
Both models are univariate. The RFI takes one factor at a time, even though many factors enter
into a production function simultaneously. Economic complexity is also one dimensional.
Neither the RFI nor the product space decomposition include a metric on how well they explain
the structure of the composition matrixâ€”the equivalent of an goodness of fit in a linear
regressionâ€”making it difficult to assess quantitatively the explanatory value of the theory.
Another problem in interpreting the RFI/PRODY is that, being a weighted average of factor
variable by country, it is essentially the first iteration towards a trivial fixed point, which is the
simple average of the factor index value across countries. In fact for actual trade data it is easy to
check that the rate of convergence is relatively fast.
3 What Export Composition Tells about Factor Endowments: Product Space and Latent
Comparative Advantage
Although the original composition space has many dimensionsâ€”more than sixty if one retains a
classification with two digitsâ€”it is expected that trade composition is determined by a much
smaller number of factors of endowments. Hence the points representing countries in the
composition space should be close to a manifold (or sub-space) with relatively few dimensions
within the much larger composition space (Fig. 2).
This manifold, dubbed â€œProduct Spaceâ€?, 4 is identified from the trade data through a geometric
concept of dimensionality reduction. Modern econometric techniques yield a minimal set of
latent factors for each country that best explain the structure of the trade matrix. The
implementation of Product Space and latent factors is formalized in the forthcoming sections.
Countries have coordinates in the product space that represent latent factors and correspond to
their projection from the composition space onto the product space. Products have dual
coordinates in the same space. Thus the problem exhibits symmetry between countries and
products. These product coordinates are export elasticities to each of the countryâ€™s factor
endowment variables.
4 The author chose to use the same vocabulary as HHR to refer to the geometrical object capturing the structure
of export composition However, the parameterization of product space is very different in the two models:
â€œskeletonâ€? network in HHR vs. a continuous low dimensional manifold here.
7
The low-dimensional product space still incorporates most of the information from the entire
high-dimensional composition space and the full trade matrix. Hence the projection of countries
(Fig. 2) onto the product space encapsulates the information about its endowments and
comparative advantage. Ultimately the paper follows an â€œinverse problemâ€? approach to trade and
deduces endowments from trade outcomes.
Fig 2. Product Space and Latent Comparative Advantage
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The implementation of the model is made possible by combining two known tools in
econometric and data analysis:
â€¢ The principal component analysis (PCA) is a powerful dimensionality reduction tool. It
decomposes a cloud of data points with many dimensions into a few principal
components or dimensions that capture most efficiently the variance in the data. The PCA
is widely used in economics and social science.
â€¢ The second tool is the Poisson (pseudo) maximum likelihood. This choice is known to be
the most natural when fitting actual flows on a network, such as trade data, against
predicted values (Silva & Tenreyro, 2006).
There are several potential benefits with the proposal. The first is that the â€œprojectionâ€? technique
is itself embedded in quantitative trade theories of product differentiation. The second is that the
8
model has predictive value. For example, the expected change in export composition due to a
change in endowments in the product space can be computed. Furthermore, the projection of
countries in the low-dimensional product space corresponds to a reference latent export
composition or latent comparative advantage (LCA), .
The comparison between latent and actual compositions, or between revealed and latent
comparative advantages, carries significant country information and may help answer practical
questions. For example, how well a country realizes the potential of its position in the product
space, or whether there are opportunities of production with significant latent comparative
advantages not yet reflected in current comparative advantages.
4 Product Space in Trade Theory: Factor Supply Elasticities
This section formalizes the expected dependence of export composition on factors of
endowments and product specific elasticities, which spans the Product Space.
Effects on production or exports from changes in domestic endowments are expected to happen
through industry specific changes in productivity and eventually comparative advantage. In other
words, the export from country a in product i would depend on the individual (or the set of)
factor(s) f in the following way,
where is a positive function summarizing the impact of the factor(s) f on the advantage to
produce in industry i in country a. Furthermore, the export flow is dependent on the size of
the market for product i and on the size of the exporting economy a, yielding a bi-proportional
structure of exports
,
or ,
where the multiplicative fixed effects and account, respectively, for export country aâ€™s
size and product iâ€™s market demand.
Revealed comparative advantages are positive numbers distributed over several orders of
magnitude (Fig 3). Effects of different factors on productivity and comparative advantage are
intuitively expected to be multiplicative. It is therefore natural to look for log-linear dependence
where the expected impact of factor endowments is to enhance (or decrease depending on the
direction of the effect) production and trade with a product dependent elasticity, hereon referred
as Factor Supply Elasticity (FSE) .
9
Fig 3. the distribution of RCAs (128 countries, 61 products)
15
10
% of sample
5
0
-6 -4 -2 0 2
RCA logarithmic scale (base 10)
Hence the exports by country a of product i take the form
for one factor and
, for several independent factors
This intuitive relationship is also embedded in modern quantitative trade theory exposed by
many authors (J.E. Anderson, 2010; James E Anderson & van Wincoop, 2003; Armington,
1969). Essentially neoclassical quantitative models of trade flows suppose some degree of
country differentiation (Armingtonâ€™s hypothesis) and make use of CES preferences by importers.
They thus produce the generic multiplicative structure.
,
where represents the price of exports of product i by country a, is the Armington elasticity
of substitution for product i, and is an average price over
. Since the price would be
inversely related to factor productivity Î ai of country aâ€™s exports of product i, then the export
flow comes as
,
a formula already in the original Armington paper (Armington 1969). If factor productivity
comes in the classical Cobb-Douglas functional form of the indexes f of factor endowments,
,
10
then the export flows indeed take the expected form with factor supply elasticities related to
factor productivity through .
Elasticities of substitution are known to be relatively large (seven to eight is often retained in
practical trade empirical research). Hence even relatively modest elasticities of firm productivity
can lead to much larger effects in the trade matrix, as measured by the factor supply elasticities.
When the elasticities by products and factors are known, A and B are determined up to a factor
by the market clearance requirement in row and columns,
X a = âˆ‘ Aa Bi exp (âˆ‘ Î± ik f ak )
i k
and X i = âˆ‘ Aa Bi exp (âˆ‘ Î± ik f ak ) .
a k
Although the concept is straightforward, and the theoretical foundation known for a long time,
the actual econometric implementation is not entirely trivial, given, for instance, the presence of
zeros in the matrix and the inclusion of fixed effects. The problem is formally similar to that of
the fixed effect spatial interaction gravity equation, where the bilateral interaction coefficient - or
trade costs - takes the place of the productivity coefficient in the current problem (Anderson
2002). Recent advances in implementing the econometrics of fixed effect models of spatial
gravity models can be transposed to the empirical analysis of the export composition space.
Properties of Factor Supply Elasticities
Annex 4 includes the proof of two properties relevant to the linkage between RCA and FSE.
1. Change in factor supply: an improvement in factor supply by for country a improves the
RCA only in the export products i where the factor elasticity is above the country
weighted average elasticity . Indeed, an increase in endowment for a factor should
increase more the exports of products using this factor more intensively.
2. Approximate linear relationship between Revealed Factor Intensity (RFI) and FSE: for small
values of elasticities ,
.
The RFI is thus not only dependent on the elasticity but also on the distribution of factors
among countries. This relationship is also intuitive. Both the elasticity and the RFI are trying
to measure the same phenomenon, namely how much the export of a given product are
dependent on a given factor of endowment.
11
Invariances
The export matrix is invariant to a series of transformations of country and product market
coefficients, as well as factors and elasticities. Again, consider the case of one endowment:
. The following invariances apply (independently for each endowment):
1. Rescaling of As by the same coefficient and its inverse applied to the Bs.
and
2. Constant shift of all the factors f a by f and corresponding change for the Bs
and
3. Constant shift of all the elasticities Î± i by Î± and corresponding change for the As
Î± i â†’ Î± i + Î± and Aa â†’ Aa exp (âˆ’ f aÎ± )
Given these invariances, what is the meaning of the country and product coefficients A and B?
How do A and B differ from total export and import markets? Indeed, in a flat world without
specialization, the simple formula
would hold, and A (respectively B) would be proportional to total exports Xa (respectively Xi).
In general the proportionality does not hold and A and B are adjusted from exports and imports
by a form of the â€œmultilateral resistanceâ€? coefficient,
.
A Toy Model: Dynamic Life Cycle Effects and the Connection between Factor Supply
Elasticities andRrevealed Factor Intensity
Life cycle effects, where products are apparently associated to a typical level of factor
endowments as in HHR, are built in the model when countries have unequal factor supply. This
comes as a consequence on the one hand of unequal factor supply between countries and on the
other hand of market clearance constraints. Countries with the highest factor will concentrate
their exports in the sector with the highest FSE.
Let us consider a minimalist toy model example with two sectors, a continuum of countries with
factor f varying from 0 to 1, equal total exports per country, and equal demand for each of the
two sectors. Let the elasticity be for product 1 and zero for product 2 ( represents the
difference in elasticity with respect to f in the two sectors).
Then the relative strength of exports of product 1 as a function of f is proportional to
, and the share of product 1 in the exports of a country with endowment f has an S
shape (Fig 4)
12
.
Fig 4. Share of product 1 as a function of the factor endowment for different values of the
elasticity
100%
90%
80%
70%
0.5
60%
1
50%
2
40%
5
30%
10
20%
10%
0%
0 0.2 0.4 0.6 0.8 1
Under the assumption that countriesâ€™ total exports are the same, the RFI of product 1 will be
1
âˆ«0 f * x( f )df =
RFI1 (Î± ) =
0.5 Î± 1
0.5 + âˆ« u * tanh( (u âˆ’ ))du
.
1
âˆ« x( f )df
âˆ’0.5 2 2
0
This number ranges from 0.5 to 1. Fig 5 plots this function along with the linear approximation
of the previous section. The toy model shows that the linear relationship RFI/ FSI may hold even
for not-so-small elasticities (up to two or three).
Fig 5. Revealed factor intensity for product 1as a function of the elasticity
0.75
Revealed factor Intesity
0.7
0.65
RFI
0.6
linear approx
0.55
0.5
0 2 4 6 8 10
Elasticity
13
5 Product Space Geometry and Information Metric
This section tackles the empirical problem of fitting the original trade data against their
predicted value of in the Product Space, or latent composition, described by the log-linear
formula of section 4
ï€¥ = A B exp (âˆ‘ Î± k . f k )
X ai a i i a
k
It uses standard econometric (Poisson Pseudo Maximum Likelihood) to estimate:
â€¢ The elasticities when trade and actual variables for the factors are known (section 5-6).
â€¢ Both elasticities and latent country factors variables from only the trade matrix (section 7
onward).
The procedure leads to a natural information metric of distance of countries to their projection
(predicted value) onto the Product Space.
Poisson Pseudo Maximum Likelihood and its Information Metric
There is a strong theoretical and practical case (Silva & Tenreyro, 2006) (J. Arvis & Shepherd,
2013) to implement the Poisson pseudo maximum likelihood (PML) regression to this problem.
It is widely accepted that the Poisson pseudo log-likelihood problem is the adequate econometric
implementation to the similar gravity equation. It accepts zero values that are common in the
trade matrix and behaves well in the presence of heteroskedasticity (higher variance for smaller
flows). It also guarantees that the margin total in rows and columns are preserved and is the only
PML with this property:
, and .
Margin conservation is key to the consistent estimation of the fixed effect coefficients in the
model (coefficients A and B). It is also essential to be able to use the predicted values of the
model in further calculation, for instance to compare directly comparative advantages in the
original matrix (RCAs) with those to be estimated from the predicted export matrix, hereafter
referred to as latent comparative advantages (LCAs).
The Poisson PML compares the original trade matrix X to the latent composition
The PML is a negative or null number (it is null only when the predicted matrix equals the
original). Its opposite I is an information metric (Kullback-Leibler (KL) information distance).In
the reference case where no country has a comparative advantage ("flat world"), the trade matrix
would be simply the product of shares in line and column
14
The information distance (Kullback Leibler distance) between the flat matrix and the actual one
measures how non trivial the structure of export is, with strong specializations of countries.
X a. X .i
X ..
I0 = âˆ’âˆ‘ X ai Log ( âˆ‘
)= X ai Log ( RCAai ) , while the KL distance between actual and
a ,i X ai a ,i
LCAai
latent export composition is I = âˆ‘ X ai Log ( )
a ,i RCAai
According to McFaddenâ€˜s interpretation, the quality of a PML regression leading to the predicted
value can be quantitatively measured by the relative improvement in the log-likelihood or, in
this paperâ€™s context, the share of the information in the export matrix explained by the
regression, namely:
I I âˆ’ I0
Pseudo-R 2 =âˆ’
1 =
I0 I0
To What Degree do Countries Capture their Comparative Advantage?
The information metric I can be broken down according to the (relative) contribution of
individual countries
, with ,
and for the â€œflatâ€? composition
X ai
I 0 = âˆ‘ X a I 0 a , with I 0 a = âˆ’âˆ‘ Log ( RCAai ) .
a i Xa
The information metric Ia measures how close a countryâ€™s export composition is to the latent
0
composition estimated from the model. The smaller Ia is compared to the initial I a , the better.
Econometric Implementation
The parameters to be estimated are the fixed effect coefficients, and , and the elasticities
. The maximization conditions yield three series of equalities.
for all a (maximization in ),
for all i (maximization in ), and
15
âˆ‘f X ai = âˆ‘ f a Xï€¥ for all i (maximization in
k k
a ai ) and each factor k.
a a
These conditions are equivalent to saying that the estimator conserves i) the total in row and
column, or margins, of the trade matrix (Arvis 2011), as well as ii) the weighted average of the
country factors.
However, given the invariance properties of the estimators (section 3), there are two degrees of
indetermination in the problem:
â€¢ First the A and B are determined up to a scale factor irrelevant to elasticities
and
.
â€¢ In the numerical implementation we relieve the indetermination by imposing that the
sums of A and B are equal.
â€¢ Then the elasticities are known up to a constant. To relieve this indetermination, in the
following we choose the convention that the weighted average of elasticities is zero:
.
These conventions have no relevance to the predicted values of the model , but are needed
for the implementation of the numerical algorithm. This algorithm recursively:
â€¢ Estimates the next A and B using the line and row conditions for a given set of
elasticities ;
â€¢ Recomputes the next approximation for the elasticities using Newtonâ€™s
approximation to solve the equation of conservation of average factor.
6 Application: Estimating the Factor Supply Elasticities for Known Endowments
This section applies the model to actual trade data when factors of endowments are known, and
determines the factor supply elasticities by product.
The Poisson pseudo maximum likelihood is implemented for one year (2010) starting with 61
sectors at the 2-digit SITC rev 3 level. The independent variables used in the model are
indicators typically used to explain trade volumes or trade costs.
The following calculations have been implemented:
1. Computation of the factor supply intensity and the revealed factor intensity for each
of the variables (Table 1).
2. Computation of multivariate factor supply intensity for a combination of independent
variables (Tables 2-3).
The main findings are:
16
1. Individual indicators taken separately do not have a very strong explanatory power (max
15%). That is, no single endowment can explain the export matrix well.
2. The FSE and RFI are as expected (section 4) strongly correlated (Fig 7 and Table 5).
3. Results 1 and 2 imply that RFI/PRODY explains a small share of the information in the
export matrix. The explanatory power of such univariate indicators is more limited than
previously thought.
4. Including several variables improves the information explained by the model but not too
strongly: five variables cannot explain 50% of the information. Furthermore, the
multivariate elasticities are expectedly quite dependent on the other variables included in
the model.
Table 1. Information explained by individual selected â€œcompetitivenessâ€? variables
Source Information
Variable Countries in model
GDP per capita (current US$) log WDI 121 0.149
GDP, PPP (current international $) log WDI 119 0.0557
Liner shipping connectivity index 2010 UNCTAD 103 0.145
Time required to start a business (days) WDI 125 0.062
Natural Capital, $ per worker log WDI 100 0.136
Physical Capital Stock per Worker log UNCTAD 111 0.145
Governance: Political Stability and Absence of Violence 2011 WDI 128 0.113
Governance: Government Effectiveness 2011 WDI 128 0.118
Governance: Regulatory quality 2011 WDI 128 0.123
Governance Rule of Law 2011 WDI 128 0.136
Governance: Control of Corruption 2011 WDI 128 0.130
Governance: Voice and Accountability 2011 WDI 128 0.167
lpi score 2010 WDI 119 0.119
tons equivalent per unit of gdp log WDI 110 0.076
Table 2. Multivariate FSE estimates (two variables)
First variable is log GNI per capita.
Information
Second Variable countries content
Liner shipping connectivity index 96 0.274
Natural Capital, $ per worker 95 0.289
Physical Capital Stock per Worker 106 0.203
Governance: Political Stability and Absence of Violence 2011 121 0.163
Governance: Government Effectiveness 2011 121 0.186
Governance: Regulatory quality 2011 121 0.175
Governance: Control of Corruption 2011 121 0.180
17
Table 3. Multivariate FSE estimates (three variables or more).
First variable is log GNI per capita.
The second variable is liner shipping connectivity index (maximum value in 2004 =100).
# Variable (third and more) count information
3. Governance: Political Stability and Absence of Violence
0.290
2011 96
3. tons equivalent per unit of gdp 89 0.328
3. Physical Capital Stock per Worker 88 0.322
3. Physical Capital Stock per Worker
4. Governance: Political Stability and Absence of Violence
0.382
2011
5. tons equivalent per unit of gdp 83
3. Natural Capital, $ per worker 78 0.367
3. Natural Capital, $ per worker
4. Physical Capital Stock per Worker 0.455
5. tons equivalent per unit of gdp 69
3. Natural Capital, $ per worker
4. Governance: Political Stability and Absence of Violence
0.411
2011
5. tons equivalent per unit of gdp 72
Table 4. Correlation of Revealed Factor Intensity vs. Factor elasticity
GDP per capita (current US$) 0.536
GDP, PPP (current international $) 0.605
Liner shipping connectivity index 0.657
Time required to start a business (days) 0.101
Natural Capital, $ per worker 0.283
Physical Capital Stock per Worker 0.540
Governance: Political Stability and Absence of Violence 2011 0.597
Governance: Government Effectiveness 2011 0.645
Governance: Regulatory quality 2011 0.530
Governance Rule of Law 2011 0.584
Governance: Control of Corruption 2011 0.604
Governance: Voice and Accountability 2011 0.465
LPI score 2010 0.751
tons equivalent per unit of gdp 0.814
18
7 Dimensionality Reduction and Generalized Principal Component Analysis
This section extends the model of sections 4 and 5 to the case where the factors of endowments
are not known but are latent variables to be determined from the trade data.
Dimensionality reduction is one of the most powerful concepts in science in order to address the
complexity of problems with many degrees of freedom. It helps read data and understand
patterns. The most popular techniques of dimensionality reduction are linear techniques such as
principal component analysis (PCA) or factor analysis.
Standard linear techniques such as PCA cannot be applied directly for two rather obvious
reasons. The first is that the impact of factors is expected to be log linear as apparent in the
previous sections, not linear as in factor analysis or PCA. The second is that export matrices are
rather sparse with a large number of zeros, so log-linearization of trade data will not work as is.
Fortunately, there is a consistent way to implement the PCA concept with the previous FSE and
Poisson regression techniques. This non-linear version of the PCA is related to the exponential-
PCA (E-PCA) introduced by Collins et al. (Collins 2002) (Collins, Dasgupta, & Schapire, 2002)
for pattern recognitions algorithm. This might be the first application of this idea to economics.
This technique, in spite of the apparent algorithmic complexity, offers much insight into the
structure of the product space.
Latent competitiveness variables
What this model does is essentially invert the generic trade model of section 3 and deduce from
the actual trade flows the product elasticities and country factor indices for a few latent variables
that explain most of the information in the trade matrix. Namely, we want to transform and
decompose the trade matrix so it is ultimately explained by a series of separable factors of
competiveness by country and with elasticities by product : .
The decomposition should provide a small number d of significant dimensions, where countries
and products are represented in two dual d dimensional spaces, where the s are the coordinates
of countries and the s are the coordinates of products (Fig 2). It happens that this is a well-
conditioned problem that can be solved by iteration. The iteration extracts sequentially the latent
variables according to their decreasing contribution to the information on the trade matrix as
measured by the log-likelihood.
As before, the problem has under-determination, since it is invariant to a constant shift in factors
or elasticity as well as to an inversely proportional change of scale between factors and
elasticities. Conventions similar to that of the PCA naturally address this issue (centered and
normalized factors and centered elasticity):
is the same choice as in section 4 to fix the constant for elasticities;
fixes the constant for the factors; and
19
fixes the scale for both factors and elasticities since the product is
invariant by and .
Iterations
The E-PCA (Annex 3) generates a series of predicted matrices with an increasing number l
of dimensions/variables, beginning with the â€œflat worldâ€? no-comparative advantage value:
Each stage adds dual sets of factors and elasticities that provide the best fit with the original trade
matrix. The estimator with l number of already determined latent variables is
and should minimize:
The information improvement brought by the variable l is the improvement in log-likelihood
from l-1 to l, or
The iteration from step l to l+1 proceeds as follows.
The impact on trade and comparative advantage of the first l variables comes from the
coefficient:
, with for l= 0 and . is known from the previous iteration up
to stage l, and the predicted value at stage l+1 is
The problem is formally quasi-identical to the determination of the FSE in section 5, except that
and have to be determined simultaneously. This is achieved at each stage l+1 by:
â€¢ Seeding a randomly distributed centered and normalized (zero mean and unit
variance).
â€¢ Computing the corresponding elasticities as per the algorithm in section 5, and
centering them.
â€¢ From the elasticities, computing with the same algorithm a new iteration of .
20
â€¢ Iterating until convergence, which is experimentally rather fast.
This procedure seems to produce stable results independent of the seed. The sign of factors and
elasticities may be simultaneously changed from one trial to another, which has no relevance.
The number of dimensions to be retained is determined by procedures similar to the linear
principal component analysis such as the scree plot.
8 Results: Latent Variables and Interpretation of Latent Factors
The model of section 7 is implemented for one year (2010) starting with the 2-digit SITCS rev 3
level. Energy trade is excluded. Twelve principal components are computed in order to estimate
the number of relevant dimensions.
Number of dimensions in product space
As in PCA, the determination of the significant number of dimensions can be done by looking at
n
the contribution to the increase of the log-likelihood L or the reduction in unexplained
n
information, at stage n, I .
By construction the informational content of each successive variable J=
n
I n âˆ’ I n +1 is
decreasing
J1 > J 2 > â€¦ > J n > â€¦
hence the convex shape of the information curve and the decreasing one for the Js (see the scree
plot in Fig 9). Table 5 below provides, for the first 12 component factors, the values of the
contribution of component i as well as the cumulated contribution and the unexplained
information in the matrix.
The number of dimensions relevant to the problem corresponds to the â€œbottomâ€? of the scree
where the relative information or improvement in the log-likelihood J n +1 brought by the next
variable becomes significantly less than with the previous J n , and could be considered as
â€œnoiseâ€?. Unfortunately, as often is the case, visual inspection (Fig 6) is not enough to identify the
â€œbottomâ€? of the scree. A more rigorous criterion is to compare the contribution with the one
corresponding to a pure random â€œnoiseâ€? in the data. In such a case, the contributions are in a
geometric series with a ratio close to one. The noisy principal components are easily generated
with computer algebra software for the same number of countries and products.
Table 5. Improvement in information brought by the first 20 factors.
Information
Unexplained Contribution Explained
I J 100-I â€œNoiseâ€? level
Factor 100.00
1 67.12 32.88 32.88 4.36
2 51.99 15.13 48.01 4.01
3 42.04 9.95 57.96 3.95
4 35.12 6.92 64.88 3.75
21
5 29.98 5.13 70.02 3.65
6 26.39 3.59 73.61 3.41
7 23.38 3.01 76.62 3.32
8 20.97 2.41 79.03 3.26
9 18.84 2.13 81.16 3.23
10 16.93 1.91 83.07 3.14
11 15.46 1.47 84.54 2.92
12 14.21 1.24 85.79 2.81
Fig 6. Scree plot and explained information in the trade matrix.
35 100
C 90
30
o 80 C
n 25 u
70
t m
r 20 60 u component
i n 50 l
noise
b 15 40 a
u t cumulated
10 30
t e
20
i 5 d
o 10
0 0
1 2 3 4 5 6 7 8 9 10 11 12
In this case, the first two dimensions explain about half of the information in the trade matrix.
However, there is no sharp drop in the contribution for the following dimensions. The
determination of the bottom of the scree is somewhat arbitrary, in between the third and sixth
dimensions. We retain five dimensions, as from the sixth dimension onward the contribution of
the component is not distinguishable from the â€œnoiseâ€? value.
Latent Variables and their Interpretation
The latent variables and factors for countries and products are available in the Excel files
available in the online Annex. Unsurprisingly, compared with known variables (section 5), the
latent variables perform much better at explaining the export matrix. Unfortunately, the
interpretation of the variables is not totally obvious. The correlation between the known and
latent variables is limited. This should be expected since section 5 showed that none of the
typical variables explains much of the information structure of the actual matrix (10-20%).
The level of development, logistics and connectivity variables are better associated with the first
two factors, as well as the variables measuring government effectiveness (the latter more for the
second factor). However, the Doing Business variables do not appear as important to explaining
the structure of the export matrix. This result probably stems from the fact that trade is carried
22
out not by entrant SMEs but by large established firms, while the Doing Business indicator on
entry is relevant to the former.
Table 6. Pairwise correlation of known variables vs. latent variables
f1 f2 f3 f4 f5
GDP per capita (current US$) -0.375 -0.434 -0.072 -0.102 -0.002
GDP, PPP (current international $) -0.378 -0.288 -0.009 -0.125 0.112
Liner shipping connectivity index (maximum
value in 2004 =100) -0.325 -0.371 -0.025 -0.135 0.162
Time required to start a business (days) 0.020 0.026 -0.023 0.085 0.075
Natural Capital, $ per worker -0.001 -0.217 -0.044 -0.130 0.058
Physical Capital Stock per Worker -0.390 -0.405 -0.001 -0.089 -0.069
Average Years of Schooling for 25 years and
over -0.333 -0.256 0.015 -0.039 -0.075
Arable Land hectares per person 0.191 -0.031 -0.007 -0.123 -0.108
Arable Land hectares per worker 0.212 0.008 -0.002 -0.100 -0.097
Governance: Political Stability and Absence of
Violence 2011 -0.177 -0.374 -0.097 -0.008 -0.112
Governance: Government Effectiveness 2011 -0.309 -0.458 -0.004 -0.074 -0.123
Governance: Regulatory quality 2011 -0.294 -0.447 0.007 -0.105 -0.196
Governance Rule of Law 2011 -0.298 -0.454 -0.006 -0.047 -0.137
Governance: Control of Corruption 2011 -0.199 -0.423 -0.019 -0.027 -0.152
Governance: Voice and Accountability 2011 -0.187 -0.376 0.005 -0.056 -0.249
energy exports as % total exports 2009 0.153 0.140 -0.180 0.010 0.392
energy exports as % total exports 2011 0.090 0.115 -0.041 -0.147 0.254
lpi score 2007 -0.399 -0.505 -0.058 -0.112 -0.132
lpi score 2010 -0.377 -0.482 0.010 -0.193 -0.159
tons equivalent per unit of gdp 0.290 0.354 -0.146 0.079 0.191
A number of patterns emerge from the pairwise correlation and the inspection of the correlation
matrix as well as the reading of the distribution of countries and products in the first two
dimensions:
â€¢ The first axis essentially distinguishes between labor intensive vs. resources intensive
productions.
â€¢ The second axis distinguishes a greater degree of sophistication of manufacturing and
the need for investment.
23
Fig 7. Two First Axis Products
1.5 Articles of apparel and clothing ac
Fixed vegetable oils and fats
Footwear
Fish,crustaceans,mollucs,preparatio
Crude rubber (including synthetic a
Leather,leather manuf.,n.e.s.and dr
Textile yarn,fabrics,made-upart.,re Fertilizers,manufactured
Coffee,tea,cocoa,spices,manufacture
Animal-vegetable oils-fats,processe
Crude fertilizers and crude materia
1
Vegetables and fruit
Furniture and parts thereof Cork and wood manufactures (excl.fu
Coin(other than gold),not being leg
Travel goods,handbags and similair Crude animal Cork and
and vegetable wood
material
Non-metallic mineral manufactures,n
Non-ferrous metals
Sanitary,plumbing,heating and light Tobacco and tobaccoSugar,sugar preparations and honey
manufactures
Iron and steel chemicals
.5
Inorganic
Cereals and cereal preparations
Rubber manufactures,n.e.s. Feeding
Textile fibres stuffwool
(except tops) a
for animals,not incl.
Manufactures of metal,n.e.s. Pulp and waste paper
f2
Paper,paperboard,artic.of paper,pap
Telecommunications & sound recordin Oil seeds and Metalliferous ores and metal scrap
oleaginous fruit
0
Miscellaneous manufactured articles Animal
Live animals and
oils for
chiefly fats
food
Miscel.edible products Meat
and and
Dairy products andmeat
preparat preparations
birds'eggs
Office machines & automatic data pr General industrial
Other transport machinery &
equipment Beverages equi Hides,skins and furskins,raw
Artif.resins,plastic mat.,cellulose
Road
Power vehicles (incl.
generating air cushion
machinery ve
and equi
Dyeing,tanning and colouring materi
Chemical materials and products,n.e
-.5
Machinery Explosives pyrotechnic
andfor
specialized particula products
Electrical machinery,apparatus & ap
Essential oils & perfume mat.;toile
Professional,scientific & controlin
Metalworking machinery
Gold
Organic chemicals
-1
good and pharmaceutical produc
Medicinal
Photographic apparatus,optical
-2 -1 0 1 2
f1
24
Fig 8. Two first axis countries
2 BLZ
MUS MDG MMR
LKA ECU UGA
YEM CMR
NGA
CIV ISL
ALB MOZ RWA
PAK NPL
KHM SLV GTM KEN ETH ZMB
1
VNM MAR PAN
IDN BWA MWI
SYR BTN CHL
BIHJOR
EGY FJI BOL
TUN TGO
AZE RUS NAM DZA
TUR
DOM MDA
SEN KAZ BHR
IND BGR
GRC
NOR UKR NIC
PRT LUX
LTU LVA COL BEN MRT
0
ROM EST BLR ARM
PRY
CRI HRV TTO
IRN ZAF
VEN GEO
ARGZWE
CHN POL OMN
SUR
MYS SVK ITA
THA ISR ESP BRA
DNKFIN BHS NZL TZA PER JAM
f2
NLD SWE CAN
LBN GUY
CZE
MEX AUT
HUN SVN
COG FRA BEL AUS
USA BRB CYP
-1
PHL KOR DEU
GBR NER
JPN
KGZ
SAU
HKG
MLT ARE GHA
SGP
-2
CHE
BFA
IRL
-3
MLI
-2 -1 0 1 2
f1
25
9 Latent Comparative Advantage
This section builds on the results of the previous one, and proposes tools with practical policy
value. It follows the route sketched out in the introduction and exploits the concepts of latent
trade composition and latent comparative advantage, to propose for instance, tools to identify
the latent potential for diversification for any country. It also looks at how to interpret the
separation between actual (or revealed) values and latent values. The main hypothesis tested
here is that competitiveness is intimately associated to how well countries reveal their latent
advantages.
The concept of dimensional reduction developed in section 7 determined a limited number of
latent factors that explain most of the export composition. The projection of a country onto the
low-dimensional product space provides a direct identification of exports for which a country has
a revealed or just-latent comparative advantage, given by its position in the product space and its
endowment in factors explaining competitiveness. Indeed the projected composition
is what the export profile would be (with unchanged global demand by product), if exports were
only dependent upon latent competiveness variables independently of the â€œnoiseâ€? that makes the
actual trade matrix X ai deviate from the estimator. For instance, the estimator is always positive
while actual trade has many zeros.
Hence indicates for which products country a has a latent but not necessarily revealed
comparative advantage. It is natural to introduce the latent comparative advantage as a match to
Balassaâ€™s revealed comparative advantage.
ï€¥ X
X ï€¥ ï€¥ X
X
=
LCA = ai .. ai ..
, while
ai ï€¥ X
X ï€¥ X
a . .i a . X .i
Since the estimator is smoother product-wise than the initial matrices, the LCAs have less
dispersion than the RCAs. A direct pairwise comparison of LCAs and RCAs is not informative.
However, there are meaningful ways to compare actual and latent trade data by country.
Latent and Actual Composition Profiles by Country
It is proposed to retain the following classical indicators to compare the latent and actual trade
composition by country:
1. Theil Index of actual composition:
2. Theil Index of latent composition:
26
3. Information (Kullback Leibler) distance between the latent and actual export
compositions (sections 5-7).
4. The degree of overlap, or similarity indicator, between the latent and actual export
compositions.
The latent Theil value is expected to be higher than the actual one because the latent composition
is spread over product lines as compared to the original one. The KL distance is a positive
number, which is zero for identical composition and increases when the composition diverges,
because the latent composition is more spread out as compared to the original one. . The overlap
or similarity measure has an inverse behavior, decreasing from one for a perfect match of latent
and actual to zero for no overlap.
Cross-matrix of Latent versus Revealed Comparative Advantage by Country: Identifying the
Potential for Diversification
Another informative and intuitive way to look at the same problem is to do a double-typology of
products for each country according to whether their RCA and LCA are greater than one.
The four-category typology is the typical BCG interpretation:
Type one (RCA>1, LCA>1) represents products for which the latent comparative advantage is
realized.
Type two (RCA<1, LCA>1) are those products for which the latent advantage is not revealed.
The category is eventually an implementation of the concept of discovery (HHR) or intensive
margin.
Type three (RCA>1, LCA<1) corresponds to products where the revealed comparative
advantage is not supported by the position in the reduced product space, hence a possible
interpretation is sectors with declining competitiveness.
Type four (RCA<1, LCA<1) corresponds to products with no particular advantage, which is
typical and can represent a substantial fraction of exports.
The straightforward implementation of this typology leads to a simple tool, a â€œdiscoveryâ€? matrix
that maps for each country the products according to this typology in four categories. The matrix
is available in Annex 4. About half of the country-product pairs with a latent advantage are not
revealed (Table 8).
27
Table 7. Product typology and statistics (% of country-product pairs)
RCA > 1 RCA < 1
LCA > 1 Type 1 19.2% Type 2 19.8%
Revealed potential Untapped potential of
diversification
LCA < 1 Type 3 7.1% Type 4 53.9%
Declining sectors? Marginal sectors
For each country the following derived indicators can be produced:
1. The number of products in each of the four categories: Type 1-4 #
2. The share of latent trade in each of the four categories Type 1-4 %
Competitiveness as the Realization of the Latent Advantage
The data file provided in Annex 5 includes:
â€¢ Indices by country: Theil actual, Theil latent, KL Distance, Overlap, Type 1-4 #, Type 1-
4 %,
â€¢ The â€œdiscoveryâ€? matrix with the product typology by country.
The main observations are the following.
LCA metrics. The country-level indices of KL distance, overlap, and GL are expectedly related
as they all measure how close latent and actual export compositions are. As expected, distance or
overlap between actual and latent are also related to the relative importance of the untapped
potential for diversification (Type 2).
Most significantly, the KL distance and the overlap indices seem to capture much of the export
â€œcompetitivenessâ€?, with the KL distance being slightly better:
i. Both indicators are highly correlated with commonly accepted indicators of
competitiveness such as the WEF Global Competitiveness index (Fig 9).
ii. The ranking of countries in the sample is consistent with the general knowledge of
countriesâ€™ exports (Table 10), despite a few unintuitive cases such as the Nordic
countries.
iii. The KL distance is also associated to a higher degree of diversification of their actual
trade for countries close to their latent potential, as measured by the Theil index (Fig 10).
iv. The metric of distance between latent and actual trade is better associated with generally
accepted competitiveness outcomes than the diversification (Theil) index.
28
Table 8. Pairwise correlations
Theil actual KL distance overlap WEF CGI
KL distance -0.6177 1
overlap 0.4045 -0.8787 1
WEF CGI 0.4976 -0.6096 0.5723 1
GDP per capita 2010 0.4875 -0.5569 0.4937 0.8635
Shipping Connectivity 0.308 -0.4389 0.5233 0.5204
Capital per worker 0.5091 -0.592 0.4937 0.7952
Government effectiveness 0.3734 -0.4957 0.4981 0.891
LPI 2010 0.5577 -0.6233 0.6014 0.8715
Table 9. Ranking of countries according to the information metric (KL Distance in
increasing value)
country rank country rank country rank country rank country rank country rank
DEU 1 IRL 23 ZMB 45 CRI 67 MLT 89 FJI 111
CHN 2 SVN 24 TUN 46 NOR 68 MDG 90 DZA 112
USA 3 CHL 25 HRV 47 JAM 69 COL 91 AZE 113
KOR 4 DNK 26 ARG 48 TZA 70 CYP 92 JOR 114
JPN 5 AUS 27 PHL 49 NPL 71 MAR 93 NGA 115
GBR 6 HUN 28 BOL 50 UGA 72 OMN 94 MMR 116
CAN 7 SWE 29 FIN 51 MOZ 73 LBN 95 BLZ 117
CZE 8 THA 30 BIH 52 BWA 74 BTN 96 ETH 118
POL 9 TUR 31 ISR 53 PRY 75 MLI 97 CMR 119
ITA 10 RUS 32 ECU 54 YEM 76 NAM 98 SUR 120
SGP 11 VNM 33 IRN 55 LKA 77 NER 99 MUS 121
MEX 12 ROM 34 UKR 56 SLV 78 MDA 100 ZWE 122
AUT 13 CHE 35 GTM 57 PAK 79 GEO 101 GHA 123
NLD 14 VEN 36 LVA 58 NIC 80 MRT 102 CIV 124
FRA 15 EST 37 PAN 59 BRB 81 GUY 103 KGZ 125
BEL 16 LTU 38 KEN 60 SYR 82 TGO 104 BEN 126
ESP 17 BRA 39 EGY 61 ARE 83 HKG 105 BHS 127
IND 18 GRC 40 NZL 62 DOM 84 SEN 106 MWI 128
MYS 19 BGR 41 PER 63 ALB 85 TTO 107
SVK 20 KAZ 42 BHR 64 ISL 86 COG 108
ZAF 21 LUX 43 SAU 65 RWA 87 BFA 109
PRT 22 IDN 44 ARM 66 BLR 88 KHM 110
29
Discovery matrix (Annex 4). Under visual inspection, the matrix is consistent with expert
knowledge of countries, including developing countries targeted by World Bank assistance.
The data for European countries also provide some illustration of the differences between
countries. Table 10 below illustrates the case of Germany, France, Italy, Netherlands, Spain, and
the United Kingdom.
All countries are relatively close to their latent structure as measured by the indicators of
distance and overlap. However, Germany clearly stands out by being closer and having a very
small extensive margin of products to be revealed. Conversely, France and the Netherlands have
a rather large extensive margin. At least in the case of France, this observation and the fact that
its indicators are about the same as Spain cannot but be associated to the current debate in France
about the competitiveness and the future of its industry (Giraud & Weil, 2013).
Table 10. Latent comparative data for selected EU countries
countries DEU ESP FRA ITA GBR NLD
Theil actual 3.33 3.42 3.47 3.51 3.35 3.59
KL Distance 0.02 0.12 0.12 0.09 0.07 0.11
overlap 0.93 0.80 0.83 0.85 0.86 0.80
Type 1# 16 25 14 22 18 19
Type 2# 3 15 14 9 9 16
Type 3# 2 3 7 4 0 4
Type 4# 40 18 26 26 34 22
Fig 9. Distance between actual and real vs. WEF Global Competitiveness Indicator.
6
5
WEF CGI
43
2
0 .5 1 1.5 2
KL Distance
30
Fig 10. Degree of diversification (Theil) vs KL distance between latent an actual
4 Theil actual
trade
3.5
3
2.5
2
1.5
1
0.5
0
0 0.5 1 1.5 2 2.5
KL Distance
10 Conclusions
The model is a thorough implementation of dimensionality reduction of the export matrix. It
provides a quantitative description of dual product spaces where countries and products have
coordinates numerically estimated. Furthermore, the model provides a latent composition and
latent comparative advantage, a new concept representing the reference export composition
implied by the position of the country in the product space. This position not only depends upon
what a country actually exports (revealed comparative advantage) but also upon the export
composition of all other countries. The comparisons provide some practical indication of the
potential for diversification.
Main findings
1. The product space has relatively few dimensions (five explain 70% of the trade matrix).
2. Typical competiveness variables are weakly correlated to individual latent factors
(coordinates in the product space).
3. Latent comparative advantages are available and comparisons with RCA inform on the
extensive margins and the potential for diversification.
4. Typical competiveness variables are related to distance between latent and revealed (actual)
positions in the product space.
5. Economies with less distance, or making the most of their latent advantage, are expectedly
more â€œcompetitiveâ€? and more diversified.
6. The currently accepted concepts such as PRODY or RFI have, in fact, limited informational
power.
The model presents a number of advantages. It is not only a descriptive data analysis tool but it is
also embedded in classical trade theory. Therefore it is quantitative and eventually predictive.
For instance, it allows estimates of how trade will change a countryâ€™s latent variables and
endowments based upon known country factors. The associated information metric measures
how much of the trade structure is explained by the model (about 70%). Furthermore the model
31
does not rely on arbitrary choices of parameters or of functional structure. The only partly
subjective but not ad hoc interpretation is the reading of the scree plot, as in a standard PCA, to
determine the number of relevant dimensions of the product space.
Improvements
Several improvements are relatively straightforward:
â€¢ The model has been implemented at 2-digits. Implementation at 3- or 4-digits should be
considered.
â€¢ Improvements in the E-PCA implementation and further test of robustness.
â€¢ More detailed comparisons between latent variables and known indicators of
competitiveness.
â€¢ Inclusions of several years in the model.
Extensions
The following areas have not been considered so far.
â€¢ Inclusion of import composition as well as export composition in order to better
incorporate a value chain description of trade.
â€¢ Inclusion of geographical information in the model and how to incorporate spatial
gravity modeling.
32
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34
Annex 1 Results
Three MS Excel files are available at
www.worldbank.org/trade -> data
Annex 1 corresponds to the RFI and FSE and contains the variables used.
Annex 2 corresponds to section 8 and gives the latent variables and elasticities.
Annex 3 corresponds to section 9 and provides the â€œdiscovery matrixâ€? and the latent comparative
variables.
The core data work has been programmed in Mathematicaï›š. The notebooks can be shared upon
request.
Annex 2 Properties of the Model and Connection between Factor Supply Elasticity and
Revealed Factor Intensity
Improvement in factor supply and change in comparative advantage
Consider a small change, ceteris paribus, of the factor supply for a given country a,
Then the change in the matrix is
, or a change
, yielding the changes for total in rows and columns
, and
and for the RCA
, or
, where
is the weighted average elasticity for country a and the coefficient
35
, is in practice close to one: ,
Thus an improvement in factor supply by for country a improves the RCA only in export
products i where the factor elasticity is above the country weighted average of elasticity .
Relationship between PRODY/Revealed Factor Intensity and Factor Supply Elasticity
In this sub-section we show how the model explains the significance of the revealed factor
intensity introduced in the literature, and how it relates to factor supply elasticities. Consider a
trade matrix with relatively mild effects of factor productivity (i.e. first order deviation from a
situation of no comparative advantage). Then
Elasticities and factors can be normalized by convention with zero weighted averages
without loss of generality
, and .
At first order:
, and ,
Thus the RCA is
And the RFI is
Or at the first order in the elasticity
,
yielding a simple linear relationship between RFI and elasticity for small values of
elasticities: .
36
Annex 3 The Exponential PCA algorithm
Annex 4 The â€œDiscoveryâ€? Matrix (extraction)
The numbers in the matrix stands for the combination of RCA and LCA.
Type 1 Type 2 Type 3 Type 4
RCA and RCA <1 RCA >1 RCA <1
LCA>1 LCA>1 LCA<1 LCA<1
37
ARG AUS AUT BEL BGR BRA CAN CHL CHN CIV COL CRI CZE DEU EGY ESP FRA GBR GEO HUN IDN IND ISR
0-Live animals 2 1 2 2 1 1 1 2 4 4 2 2 3 4 4 1 1 1 3 3 4 4 4
1-Meat 1 1 1 1 1 1 1 1 4 4 2 2 4 4 4 1 1 2 2 3 4 3 4
2-Dairy prods 1 1 1 1 1 2 4 2 4 4 2 1 4 3 3 2 1 2 4 4 4 4 4
3-Seafood 1 4 4 4 2 2 1 1 4 2 1 1 4 4 2 1 4 4 2 2 1 3 4
4-Cereals 1 1 4 2 1 1 1 2 4 2 2 2 4 4 1 2 3 4 2 3 2 1 4
5-Veg&fruit 1 4 2 1 1 1 1 1 4 1 1 1 4 4 1 1 4 4 1 4 2 2 3
6-Sugar&honey 1 2 4 2 1 1 2 2 4 2 1 1 4 4 1 2 4 4 2 3 2 1 4
7-Coffee,tea, â€¦ 2 2 4 1 1 1 4 2 4 1 1 1 4 4 1 2 4 4 2 4 1 1 2
8-Animal food 1 1 4 1 1 1 2 1 4 2 2 2 4 4 1 2 3 4 2 3 2 3 4
9-Eadible prods 1 3 1 1 2 2 1 4 4 3 1 1 4 4 3 1 1 1 3 4 1 4 4
11-Bevrages 1 1 1 2 2 2 2 1 4 4 2 2 4 2 4 1 1 1 3 4 4 4 4
12-Tobacco 1 2 4 1 1 1 2 2 4 1 2 2 3 3 1 2 2 4 2 4 1 1 2
21-Hides, skins 2 1 2 4 2 2 1 2 4 4 2 2 4 4 4 1 3 2 3 2 4 4 4
22-Oil seeds 1 2 4 4 1 1 1 2 4 2 2 2 4 4 1 4 4 4 4 3 2 3 4
23-Crude rubber 2 4 4 3 2 2 4 4 4 1 2 2 4 4 2 4 4 4 4 4 1 4 4
24-Cork&wood 2 1 3 4 1 1 1 1 4 1 2 2 3 4 2 2 4 4 1 4 1 4 4
25-Pulp 2 2 4 4 1 1 1 1 4 4 2 2 4 4 2 1 4 4 2 4 1 4 4
26-Textile fibers 1 1 4 2 2 1 2 2 4 1 2 2 4 4 1 2 2 4 2 4 1 1 2
27-Fertilizers 2 2 3 1 1 1 1 1 4 2 2 2 4 4 1 1 4 4 1 4 2 1 1
28-Metal 1 1 4 2 1 1 1 1 4 2 1 4 4 4 2 4 4 4 1 4 3 3 4
29-Crude anim&veg 2 4 4 1 2 1 4 3 4 2 1 1 4 4 1 1 4 2 3 4 2 1 1
41-Animal oils 2 1 2 4 2 2 1 1 4 4 2 2 4 4 3 1 3 1 1 4 4 4 4
42-Veg oils 1 4 4 4 1 1 3 4 4 1 1 1 4 4 2 3 4 4 4 4 1 4 4
43-Animal oil 1 4 4 3 4 3 4 4 4 1 2 1 4 4 1 4 4 4 4 4 1 4 2
51-Org chems 4 4 4 1 4 4 4 4 4 4 4 4 4 4 4 4 2 1 4 4 4 3 2
52- Inorg chems 4 4 4 2 1 2 1 3 4 2 2 4 4 4 1 4 3 4 2 4 2 2 1
53-Dyeing mat 4 4 2 1 4 4 4 4 4 4 3 4 4 1 4 1 2 1 4 4 4 1 2
54-med&pharm 4 4 1 1 4 4 4 4 4 4 4 4 4 1 4 1 1 1 4 3 4 3 1
55-Essential oils 3 4 2 1 3 4 4 4 4 3 3 2 4 1 3 1 1 1 4 4 4 4 2
56-Fertlizers 2 2 4 3 1 2 1 1 4 2 2 4 4 4 1 4 4 4 1 4 2 2 3
57-Explosives 4 4 4 1 4 2 4 4 4 4 1 4 4 4 3 3 4 4 4 4 4 4 2
58-Artif. resins 4 4 1 1 4 4 2 4 4 4 3 3 1 1 4 1 2 1 4 4 4 4 3
59-Chem mats 3 4 2 1 4 4 4 4 4 4 3 2 4 1 3 2 1 1 4 4 4 4 1
61-Leather 1 2 3 2 2 1 4 2 4 2 1 1 4 4 1 1 4 4 2 4 2 1 2
62-Rubber manuf 4 4 2 4 2 4 1 4 2 4 4 1 1 1 2 1 3 4 4 1 3 4 4
63- Cork manuf 2 4 1 3 1 3 1 3 3 1 2 2 1 4 2 1 4 4 4 1 1 2 4
64-Paper 2 4 1 3 2 2 1 2 4 4 1 1 2 1 1 1 1 2 2 2 3 4 4
65-Textile yarn 4 4 4 4 1 4 4 4 1 4 3 4 4 4 1 4 4 4 4 4 1 1 2
66- Mineral man 4 4 2 1 1 4 4 4 4 2 1 4 4 4 1 1 2 1 2 4 2 1 1
67-Iron&steel 4 4 1 3 1 3 2 4 4 4 1 4 3 4 1 1 2 4 1 4 4 1 2
68-Non-ferrous 2 1 1 3 1 2 1 1 4 2 2 4 4 4 1 2 4 4 2 4 1 1 4
69- Metal manuf 4 4 1 2 2 4 4 4 1 4 4 2 1 1 3 1 2 2 4 2 4 2 4
71-Power gen. 4 4 1 4 4 4 1 4 4 4 4 4 1 1 4 1 1 1 4 1 4 4 4
72-Specialized 4 4 1 2 4 4 4 4 4 4 4 4 2 1 4 4 2 1 4 4 4 4 4
73-Metalworking 4 4 1 2 4 4 4 4 4 4 4 4 1 1 4 4 2 2 4 4 4 4 4
74-Industrial 4 4 1 2 4 4 4 4 4 4 4 4 1 1 4 2 1 1 4 2 4 4 4
75-Office 4 4 4 4 4 4 4 4 1 4 4 1 1 4 4 4 4 4 4 2 4 4 4
76-Telecom 4 4 4 4 4 4 4 4 1 4 4 4 1 4 4 4 4 4 4 1 4 4 3
77-Electrical 4 4 4 4 4 4 4 4 1 4 4 3 1 4 4 4 4 4 4 1 4 4 3
78-Road vehicle 3 4 2 3 4 4 1 4 4 4 4 4 1 1 4 1 1 1 4 1 4 4 4
79-Other transp. 4 4 2 2 4 4 3 4 4 3 4 4 4 1 4 4 1 4 3 4 4 1 1
81-Sanitary 4 4 1 4 1 4 4 4 1 4 4 2 1 1 3 2 2 2 4 1 4 4 4
82-Furniture 4 4 1 4 1 4 3 4 1 4 4 2 1 4 3 2 4 4 4 1 3 4 4
83-Travel goods 4 4 4 4 4 4 4 4 1 4 4 4 4 4 4 4 3 4 4 4 4 1 2
84-Clothing 4 4 4 4 1 4 4 4 1 4 3 2 4 4 1 3 4 4 4 4 1 1 2
85-Footwear 4 4 4 3 1 3 4 4 1 4 4 2 2 4 2 1 4 4 4 4 1 1 2
87-Professional 4 4 4 4 4 4 4 4 3 4 4 3 2 1 4 4 2 1 4 1 4 4 3
88-Photographic 4 4 4 2 4 4 4 4 4 4 4 4 4 2 4 4 2 2 4 4 4 4 2
89-Manuf artcls 4 4 1 2 4 4 4 4 1 4 4 1 1 2 4 2 1 1 4 4 4 1 2
38
ITA JPN KEN KOR LVA MAR MEXMOZ NIC NLD PAK PER PHL POL ROMRUS SGP SWE THA TUN TUR TZA USA VNM
0-Live animals 4 4 2 4 1 4 3 4 1 1 4 2 4 1 3 4 4 2 2 4 4 2 2 4
1-Meat 4 4 2 4 2 4 4 4 1 1 4 2 4 1 4 4 4 4 3 4 4 2 1 4
2-Dairy prods 1 4 2 4 1 4 4 4 1 1 4 2 4 1 4 4 4 4 4 4 4 4 2 4
3-Seafood 4 4 1 4 1 1 2 1 1 2 3 1 3 1 2 1 4 1 1 1 2 1 4 1
4-Cereals 3 4 2 4 1 2 4 2 1 2 3 2 4 2 3 1 4 2 1 4 3 1 1 3
5-Veg&fruit 1 4 1 4 2 1 3 1 1 1 3 1 3 1 2 4 4 2 1 1 1 1 3 1
6-Sugar&honey 4 4 1 4 2 2 3 3 1 2 3 2 4 4 4 2 4 4 1 4 4 2 2 4
7-Coffee,tea, â€¦ 4 4 1 4 2 2 4 2 1 1 2 1 4 3 4 2 4 4 4 2 4 1 4 1
8-Animal food 4 4 2 4 1 3 4 4 1 1 4 1 4 4 4 4 4 4 1 4 4 1 1 4
9-Eadible prods 3 4 1 4 1 4 4 4 2 1 4 4 4 1 4 4 3 1 1 3 3 4 1 4
11-Bevrages 1 4 1 4 1 4 3 4 1 1 4 4 4 2 4 4 4 2 4 4 4 4 2 4
12-Tobacco 2 4 1 4 2 2 4 3 1 1 4 2 3 1 3 1 4 4 2 2 3 1 2 1
21-Hides, skins 4 4 2 4 1 4 4 4 1 2 4 2 4 1 4 4 4 2 4 4 4 1 1 4
22-Oil seeds 4 4 2 4 1 4 4 3 1 2 4 2 4 4 3 4 4 4 2 4 4 1 1 4
23-Crude rubber 4 4 2 3 2 2 4 4 4 2 2 4 2 4 2 1 4 4 1 2 4 2 4 1
24-Cork&wood 4 4 2 4 1 2 4 1 2 4 4 2 4 1 1 1 4 1 2 4 2 1 1 1
25-Pulp 4 4 4 4 2 1 2 2 2 4 4 2 4 2 2 1 4 1 2 4 4 2 1 4
26-Textile fibers 4 4 1 3 2 2 4 3 2 2 1 1 4 4 4 2 4 4 3 4 4 1 1 4
27-Fertilizers 2 4 1 4 2 1 4 2 4 4 1 3 4 4 2 1 4 4 4 1 1 1 4 2
28-Metal 4 4 2 4 1 3 4 2 2 4 4 1 4 4 3 1 4 3 4 4 4 1 3 4
29-Crude anim&veg 2 4 1 4 1 1 4 4 2 1 3 3 3 2 4 4 4 4 2 2 4 3 2 2
41-Animal oils 4 4 2 4 2 3 4 2 2 1 4 1 4 1 4 4 4 2 4 4 4 1 1 3
42-Veg oils 4 4 1 4 2 2 4 4 1 1 2 4 1 4 4 3 4 4 2 1 4 3 4 2
43-Animal oil 4 4 1 4 4 2 4 4 2 1 1 4 2 4 4 4 4 3 2 2 3 3 4 2
51-Org chems 4 3 4 1 4 4 4 4 4 1 4 4 2 4 4 3 1 4 4 4 4 4 1 4
52- Inorg chems 4 2 3 2 2 1 4 4 4 3 2 4 3 4 2 1 4 4 2 1 2 2 1 4
53-Dyeing mat 1 3 4 4 3 4 4 4 4 1 4 3 4 4 4 4 4 3 4 4 4 4 1 4
54-med&pharm 1 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 3 4
55-Essential oils 1 4 3 4 4 4 4 4 4 2 4 4 4 3 4 4 3 4 3 4 4 4 1 4
56-Fertlizers 4 4 2 4 2 1 4 2 4 3 2 2 4 4 1 1 4 4 2 1 2 1 4 2
57-Explosives 4 2 4 1 4 4 4 4 4 1 4 4 2 4 4 4 1 4 1 4 4 4 1 4
58-Artif. resins 1 1 4 1 4 4 4 4 4 4 4 4 4 3 4 4 4 2 4 4 1 4 1 4
59-Chem mats 2 3 4 4 4 4 4 4 4 1 4 4 4 4 4 4 4 4 4 4 4 4 1 4
61-Leather 1 4 1 4 2 1 4 2 1 2 1 4 4 4 3 2 4 4 3 1 2 2 4 1
62-Rubber manuf 2 1 4 2 2 2 2 4 4 2 4 4 4 1 1 4 4 2 1 2 1 4 2 1
63- Cork manuf 2 4 2 4 1 2 2 4 4 2 2 4 3 1 1 3 4 1 2 2 1 4 2 2
64-Paper 1 4 4 4 2 2 2 4 4 2 4 4 4 1 2 1 4 1 2 3 2 3 1 4
65-Textile yarn 1 4 4 3 3 2 4 4 4 4 1 4 4 4 1 4 4 4 4 1 1 3 4 1
66- Mineral man 1 4 1 4 4 2 4 4 4 4 1 4 4 4 4 1 4 4 3 2 1 3 4 4
67-Iron&steel 1 1 4 1 3 2 4 2 4 4 2 4 4 4 1 1 4 3 4 2 1 4 4 4
68-Non-ferrous 4 4 2 4 2 2 4 1 2 4 4 1 4 3 2 1 4 2 4 4 2 2 4 4
69- Metal manuf 1 4 4 4 1 4 2 4 4 2 4 4 4 1 1 4 4 1 4 1 1 4 4 2
71-Power gen. 1 1 4 4 2 4 1 4 4 4 4 4 4 1 2 3 4 1 4 4 4 4 1 4
72-Specialized 3 1 4 1 4 4 4 4 4 3 4 4 4 4 4 4 3 1 4 4 4 4 1 4
73-Metalworking 1 1 4 1 4 4 4 4 4 4 4 4 4 4 4 4 4 1 4 4 4 4 3 4
74-Industrial 1 1 4 4 4 4 1 4 4 4 4 4 4 2 1 4 4 1 3 4 2 4 1 4
75-Office 4 4 4 4 4 4 1 4 4 1 4 4 1 4 4 4 1 4 1 2 4 4 4 2
76-Telecom 4 2 4 1 4 4 1 4 4 3 4 4 2 1 1 4 2 1 2 1 4 4 4 1
77-Electrical 4 1 4 1 4 3 1 4 4 2 4 4 1 4 3 4 1 4 1 3 4 4 2 4
78-Road vehicle 2 1 4 1 2 4 1 4 4 4 4 4 4 1 1 4 4 1 3 4 3 4 1 4
79-Other transp. 2 1 4 1 4 4 4 4 4 4 4 4 4 4 3 2 4 4 4 4 2 4 4 4
81-Sanitary 1 4 4 4 1 4 1 4 4 2 4 4 4 1 1 4 4 1 4 2 1 4 4 2
82-Furniture 1 4 4 4 1 2 1 4 4 2 4 4 4 1 1 4 4 1 2 2 1 4 4 1
83-Travel goods 1 4 4 4 4 4 4 4 4 4 2 4 4 4 4 4 4 4 4 1 2 4 4 1
84-Clothing 1 4 1 4 4 1 4 4 4 4 1 3 3 2 1 4 4 4 4 1 1 4 4 1
85-Footwear 1 4 1 4 2 1 4 4 4 4 2 4 4 2 1 4 4 4 4 1 2 4 4 1
87-Professional 4 1 4 1 4 4 3 4 4 4 4 4 2 4 4 4 1 4 2 4 4 4 1 4
88-Photographic 3 1 4 1 4 4 4 4 4 4 4 4 3 4 4 4 1 4 3 4 4 4 2 4
89-Manuf artcls 1 4 4 4 4 4 4 4 4 1 3 4 2 2 4 4 3 4 1 2 4 4 1 3
39
Annex 5 Latent comparative advantage indicators by country
Theil KL Type Type Theil KL Type Type countr Theil KL Type Type
country actual Distance 1# 2# country actual Distance 1# 2# y actual Distance 1# 2#
ALB 2.57 0.68 11 10 FRA 3.47 0.12 14 14 NER 1.81 0.79 7 11
ARE 2.23 0.66 4 8 GBR 3.35 0.07 18 9 NGA 2.80 1.05 15 11
ARG 3.16 0.40 17 13 GEO 2.52 0.82 8 15 NIC 2.62 0.66 15 9
ARM 2.09 0.54 8 15 GHA 1.43 1.20 2 7 NLD 3.59 0.11 19 16
AUS 2.52 0.18 13 9 GRC 3.49 0.29 20 21 NOR 2.95 0.56 11 17
AUT 3.44 0.11 18 12 GTM 3.12 0.48 16 18 NPL 2.59 0.60 10 14
AZE 2.79 1.03 14 13 GUY 2.05 0.87 6 12 NZL 2.96 0.51 15 7
BEL 3.40 0.12 17 16 HKG 2.35 0.91 5 8 OMN 2.78 0.75 9 17
BEN 2.24 1.39 10 20 HRV 3.47 0.39 17 15 PAK 2.20 0.65 7 10
BFA 1.18 0.99 3 4 HUN 3.03 0.18 9 6 PAN 2.44 0.50 15 11
BGR 3.43 0.31 26 13 IDN 3.36 0.34 15 12 PER 2.24 0.51 9 11
BHR 1.91 0.52 3 21 IND 3.35 0.12 19 5 PHL 2.28 0.42 3 7
BHS 1.46 1.75 3 17 IRL 2.53 0.16 11 4 POL 3.44 0.09 19 8
BIH 3.28 0.43 18 16 IRN 3.06 0.47 16 12 PRT 3.52 0.16 21 13
BLR 3.25 0.70 17 22 ISL 1.67 0.69 5 15 PRY 2.17 0.64 11 12
BLZ 1.23 1.08 5 22 ISR 2.78 0.43 7 17 ROM 3.27 0.22 14 9
BOL 2.13 0.42 13 12 ITA 3.51 0.09 22 9 RUS 3.01 0.20 14 7
BRA 3.29 0.27 17 14 JAM 1.76 0.57 8 16 RWA 1.58 0.69 8 16
BRB 2.73 0.66 9 16 JOR 2.87 1.04 8 22 SAU 2.43 0.52 5 12
BTN 1.95 0.75 6 7 JPN 2.95 0.07 12 4 SEN 2.97 0.91 13 15
BWA 1.34 0.64 3 7 KAZ 2.15 0.34 9 6 SGP 2.60 0.09 6 1
CAN 3.46 0.08 22 7 KEN 3.01 0.50 16 15 SLV 2.62 0.65 9 12
CHE 2.92 0.22 11 3 KGZ 1.83 1.34 3 10 SUR 2.62 1.14 10 24
CHL 2.22 0.17 14 11 KHM 1.28 1.00 2 10 SVK 2.99 0.13 11 3
CHN 3.10 0.03 11 1 KOR 2.93 0.05 12 2 SVN 3.26 0.17 15 9
CIV 2.04 1.22 9 14 LBN 3.06 0.75 12 21 SWE 3.32 0.18 15 10
CMR 2.19 1.10 8 18 LKA 2.19 0.65 10 10 SYR 3.11 0.66 16 20
COG 0.85 0.95 1 5 LTU 3.63 0.26 26 13 TGO 2.54 0.88 9 11
COL 3.23 0.72 13 21 LUX 3.14 0.34 12 11 THA 3.35 0.18 12 15
CRI 2.96 0.55 14 22 LVA 3.43 0.49 16 21 TTO 1.88 0.94 5 9
CYP 2.60 0.73 10 14 MAR 2.82 0.74 10 18 TUN 2.91 0.37 13 13
CZE 3.17 0.09 14 4 MDA 2.86 0.80 15 15 TUR 3.21 0.19 12 12
DEU 3.33 0.02 16 3 MDG 2.33 0.72 12 10 TZA 2.66 0.60 15 8
DNK 3.55 0.18 25 9 MEX 2.93 0.10 9 6 UGA 2.66 0.63 15 12
DOM 3.10 0.67 14 17 MLI 0.82 0.76 1 1 UKR 2.92 0.47 15 10
DZA 2.48 1.03 10 12 MLT 1.82 0.71 2 6 USA 3.55 0.04 25 10
ECU 2.52 0.43 13 17 MMR 1.90 1.06 8 17 VEN 2.56 0.24 8 8
EGY 3.35 0.50 20 10 MOZ 1.36 0.63 4 10 VNM 3.17 0.22 14 9
ESP 3.42 0.12 25 15 MRT 1.20 0.83 5 8 YEM 2.42 0.64 13 13
EST 3.52 0.26 19 18 MUS 1.91 1.16 5 16 ZAF 2.91 0.14 15 10
ETH 2.16 1.09 8 21 MWI 1.86 1.93 10 18 ZMB 1.20 0.35 2 8
FIN 3.24 0.42 17 10 MYS 2.97 0.13 8 8 ZWE 2.38 1.19 10 18
FJI 2.68 1.03 11 17 NAM 2.57 0.78 11 18
40