For Adam Smith, the secret to the wealth of nations was related

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1 The building blocks of economic complexity César A. Hidalgo 1 and Ricardo Hausmann a Center for International Development and Harvard Kennedy School, Harvard University, Cambridge, MA Edited by Partha Sarathi Dasgupta, University of Cambridge, Cambridge, United Kingdom, and approved May 1, 2009 (received for review January 28, 2009) For Adam Smith, wealth was related to the division of labor. As people and firms specialize in different activities, economic efficiency increases, suggesting that development is associated with an increase in the number of individual activities and with the complexity that emerges from the interactions between them. Here we develop a view of economic growth and development that gives a central role to the complexity of a country s economy by interpreting trade data as a bipartite network in which countries are connected to the products they export, and show that it is possible to quantify the complexity of a country s economy by characterizing the structure of this network. Furthermore, we show that the measures of complexity we derive are correlated with a country s level of income, and that deviations from this relationship are predictive of future growth. This suggests that countries tend to converge to the level of income dictated by the complexity of their productive structures, indicating that development efforts should focus on generating the conditions that would allow complexity to emerge to generate sustained growth and prosperity. economic development networks For Adam Smith, the secret to the wealth of nations was related to the division of labor. As people and firms specialize in different activities, economic efficiency increases. This division of labor, however, is limited by the extent of the market: The bigger the market, the more its participants can specialize and the deeper the division of labor that can be achieved. This suggests that wealth and development are related to the complexity that emerges from the interactions between the increasing number of individual activities that conform an economy (1 3). Now, if all countries are connected to each other through a global market for inputs and outputs so that they can exploit a division of labor at the global scale, why have differences in Gross Domestic Product (GDP) per capita exploded over the past 2 centuries? (4, 5, *) One possible answer is that some of the individual activities that arise from the division of labor described above cannot be imported, such as property rights, regulation, infrastructure, specific labor skills, etc., and so countries need to have them locally available to produce. Hence, the productivity of a country resides in the diversity of its available nontradable capabilities, and therefore, cross-country differences in income can be explained by differences in economic complexity, as measured by the diversity of capabilities present in a country and their interactions. During the last 20 years, models of economic growth have often included the assumption that the variety of inputs that go into the production of the goods produced by a country affects that country s overall productivity (3, 6). There have been very few attempts, however, to bring this intuition to the data. In fact, the most frequently cited surveys of the empirical literature do not incorporate a single reference to any measure of diversity of inputs or complexity (7). We can create indirect measures of the capabilities available in a country by thinking of each capability as a building block or Lego piece. In this analogy, a product is equivalent to a Lego model, and a country is equivalent to a bucket of Legos. Countries will be able to make products for which they have all of the necessary capabilities, just like a child is able to produce a Lego model if the child s bucket contains all of the necessary Lego pieces. Using this analogy, the question of economic complexity is equivalent to asking whether we can infer properties such as the diversity and exclusivity of the Lego pieces inside a child s bucket by looking only at the models that a group of children, each with a different bucket of Legos, can make. Here we show that this is possible if we interpret data connecting countries to the products they export as a bipartite network and assume that this network is the result of a larger, tripartite network, connecting countries to the capabilities they have and products to the capabilities they require (Fig. 1A). Hence, connections between countries and products signal the availability of capabilities in a country just like the creation of a model by a child signals the availability of a specific set of Lego pieces. Note that this interpretation says nothing of the processes whereby countries accumulate capabilities and the characteristics of an economy that might affect them. It just attempts to develop measures of the complexity of a country s economy at a point in time. However, the approach presented here can be seen as a building block of a theory that accounts for the process by which countries accumulate capabilities. A detailed analysis of capability accumulation is beyond the scope of this article but the implications of our approach will be discussed briefly in Discussion. In this article we develop a method to characterize the structure of bipartite networks, which we call the Method of Reflections, and apply it to trade data to illustrate how it can be used to extract relevant information about the availability of capabilities in a country. We interpret the variables produced by the Method of Reflections as indicators of economic complexity and show that the complexity of a country s economy is correlated with income and that deviations from this relationship are predictive of future growth, suggesting that countries tend to approach the level of income associated with the capability set available in them. We validate our measures of the capabilities available in a country by introducing a model and by showing empirically that our metrics are strongly correlated with the diversity of the labor inputs used in the production of a country s goods, approximated by using data on the use of labor inputs in the United States. Finally, we show that the level of complexity of a country s economy predicts the types of products that countries will be able to develop in the future, suggesting that the new products that a country develops depend substantially on the capabilities already available in that country. Methods We look at country product associations by using international trade data with products disaggregated according to 3 alternative data sources and classifications: First, the Standard International Trade Classification (SITC) revision 4 at the 4-digit level (see ref. 8; the data are available at udavis.edu/data/undata/undata.html, and Author contributions: C.A.H. and R.H. designed research, performed research, contributed new reagents/analytic tools, analyzed data, and wrote the paper. The authors declare no conflict of interest. This article is a PNAS Direct Submission. 1 To whom correspondence should be addressed. cesar hidalgo@ksg.harvard.edu. *In ref. 4, Maddison presents GDP per capita measures for 60 countries since In that year, the ratio of the 95th to the 5th percentile was 3.18 but it increased to by the year Today, the U.S. GDP per capita is 60 times higher than Malawi s. This article contains supporting information online at /DCSupplemental PNAS June 30, 2009 vol. 106 no cgi doi pnas

2 A Countries Capabilities Products c 1 c 2 a 1 a 2 p 1 p 2 MYS PAK c 3 a 3 p 3 Countries Products c 1 p 1 B C Node Color SITC-4 Category Name Food & live animals Beverages & tobacco Raw materials Mineral fuels, lubricants & related materials Animal & vegetable oils, fats & waxes Chemicals Manufactured goods by material Machinery & transport equipment Miscellanous manufactured articles Miscellaneous k c,1 c 2 c 3 p 2 p 3 Non-Diversified Countries Producing Standard Products Non-Diversified Countries Producing Exclusive Products k c,0 Diversified Countries Producing Standard Products Diversified Countries Producing Exclusive Products k c,1 productspace/data.html); second, the COMTRADE Harmonized System at the 4-digit level; and third, the North American Industry Classification System (NAICS) at the 6-digit level (SI Appendix, Section 1). We interpret these data as bipartite networks in which countries are connected to the products they export (Fig. 1B). Mathematically, we represent this network using the adjacency matrix M cp, where M cp 1 if country c is a significant exporter of product p and 0 otherwise. We consider country c to be a significant exporter of product p if its Revealed Comparative Advantage (RCA) (the share of product p in the export basket of country c to the share of product p in world trade) is greater than some threshold value, which we take as 1 in this exercise (RCA cp 1) (see SI Appendix, Section 2). Method of Reflections. We characterize countries and products by introducing a family of variables capturing the structure of the network defined by M cp (SI Appendix, Section 3). Because of the symmetry of the bipartite network, we refer to this technique as the Method of Reflections, as the method produces a symmetric set of variables for the 2 types of nodes in the network (countries and products). The Method of Reflections consists of iteratively calculating the average value of the previous-level properties of a node s neighbors and is defined as the set of observables: k c,n 1 k c,0 M cp k p,n 1, [1] p k p,n 1 k p,0 M cp k c,n 1, [2] c for N 1. With initial conditions given by the degree, or number of links, of countries and products: JPN MWI FJI HTI MDG WSM HND GMB NIC SLV <k GTM c,0 > GIN GUY JAM BGD CAF TGO MUS SDN MAC UGA TKM CRI DOM CMR SYR MNG ALB BDI SEN KEN NPL MOZ MAR GAB BLZ TZA ETH LVA PAK NCL BLR NGATTO TJKBHR GHA MDA LTU PNG AZE LKA BFACIV BOL EGY ECU LBN EST ZMB BEN VEN ZWE <k ARM CYP c,1 > ISL DZA BHS KGZ PHLPAN GEO JOR PER HRV RWA SLE MLT COL TUR OMN SAU KNA PRY ROM IDNGRC MLI NERIRN BRB CHL NZL PRT URY THA ZAFUKR SVKIND KAZ MEX NOR ARG HUN SVN AUSHKG CHN RUS BRADNK ISR CAN FIN KOR MYS IRL SWE SGP PHL CZE ESP AUT ITA k c,0 JPN NLD GBR POL USA DEU Fig. 1. Quantifying countries economic complexity. (A) A country will be able to produce a product if it has all of the available capabilities, hence the bipartite network connecting countries to products is a result of the tripartite network connecting countries to their available capabilities and products to the capabilities they require. (B) Network visualization of a subset of M cp in which we show Malaysia (MYS), Pakistan (PAK), Philippines (PHL), Japan (JPN), and all of the products exported by them in the year 2000 (colored circles), illustrating how countries and products are connected in M cp.(c) k c,0 k c,1 diagram divided into 4 quadrants defined by the empirically observed averages k c,0 and k c,1. k c,0 p k p,0 c M cp, [3] M cp. [4] k c,0 and k p,0 represent, respectively, the observed levels of diversification of a country (the number of products exported by that country), and the ubiquity of a product (the number of countries exporting that product). Hence, we characterize each country through the vector k c (k c,0, k c,1, k c,2...k c,n ) and each product by the vector k p (k p,0,k p,1,k p,2,...,k p,n ). For countries, even variables (k c,0,k c,2,k c,4,...) are generalized measures of diversification, whereas odd variables (k c,1,k c,3,k c,5,...) are generalized measures of the ubiquity of their exports. For products, even variables are related to their ubiquity and the ubiquity of other related products, whereas odd variables are related to the diversification of countries exporting those products. In network terms, k c,1 and k p,1 are known as the average nearest neighbor degree (9,10). Higher order variables, however, (N 1) can be interpreted as a linear combination of the properties of all of the nodes in the network with coefficients given by the probability that a random walker that started at a given node ends up at another node after N steps (see SI Appendix, Section 4). Results We can begin understanding the type of information about countries captured by the Method of Reflections by looking at where countries are located in the space defined by the first two sets of variables produced by our method: k c,0 and k c,1.fig.1c shows that there is a strong negative correlation between k c,0 and k c,1 (10, 11), meaning that diversified countries tend to export less ubiquitous products. Deviations from this behavior, however, are informative. For example, whereas Malaysia and Pakistan export the same STATISTICS ECONOMIC SCIENCES Hidalgo and Hausmann PNAS June 30, 2009 vol. 106 no

3 A Countries C ca Capabilities Countries r=0.7 Products M 80 cp Products Π pa q= Capabilities B k c,1 r=0.55 k c,1 r=0.7 q=0.05 q= N a = N a = k 35 c,0 k 70 c,0 30 N a = N a = k c, k c, k c,1 k c,1 k c,0 C r=0.55 q=0.1 N a =50 60 k c, k c,1 k c, N a r=0.7 q=0.05 N a = N a D Average Number of Labor Inputs MYS FIN SWE JPN JPN SWE MYS FIN MYS FIN SWE JPN ARM AUT CAN HUN ITA AUT ITA JOR ROMSVK CZE CAN HUN ARM CZE SVK ARM AUT ROM SEN NOR PHL DEU BLR ALB EST HRVBRA DNK POL DEU JOR CAN HUN ITA JOR ROM SVK CZE NOR PHL IRL LVA KOR SVN SGP BOL ISR IDN PRT THA BRA DNK HRVEST CHN IRL KOR SVN POL SEN SEN PHL SGP BLRALB LBN BRB LTU MEX NLD ISR CHN THA PRT LVA IDN ALB BLR ESP NLD BOL RUS GINBHS HKG UKR ESP MEX LBN BOL NOR EST HRV POL BRA DNK DEU IDN CHN IRL KOR SVN THA SGP ISRPRT LBN RUS HKGUKR BRB LTU LTU MEX NLD OMNMUS HND CRI TGO MAR CYP KNA NPL URY NZL TUR BHS CYP CRIGIN COL BEN MNG SLV GHA KAZ ZWE NZL OMN BRB RUS ESP TUR MARMUS GIN BHS HKG UKR URY HND ECU FJI GTM PRY ARG GRC IND MDA ZAF KAZ INDKNACOL ZWE NPL TGO HNDMUS OMN CRI ZMB ARG GRC PRY BENECU GHA MNG SLV TGO MAR CYP ZAF MDA GTM GHA KNA KAZ NPL NZL TUR MNG SLVZWE URY ZMB BEN ECU COL TTO CAF MLI CIV DZA ISL MLT MAC BGD MOZ MDG CHL GEO EGYAUS JAM KEN FJI NER UGA PAN MLI MLT CIV CAF AUS CHL ISL PER KGZ TTO FJI GTM PRY ARG GRC IND MDA ZAF ZMB TTO DZA MAC NER PAN CAFCIV MLI BGD NCL GUY MWI GEO EGY MOZ KEN UGA MDG DZA ISL KGZ MLT BGD MAC MDG AUS CHL TKM NIC BHR TZA BHR NCL JAM KEN MOZ CMR VEN TZA GUY MWI MWI EGY GEO VEN TKM NIC GUY NCL JAM PER UGA PAN TZA NICTKM BHR BDI GMB ETH ETHCMR BFA BFA BDI GMB CMR VEN ETH BDI GMB BFA SAU SDN BLZ SAU BLZSDN SDN BLZ SAU GAB PNGAZE PNG AZEGAB PNG GAB AZE NGA IRN IRN NGA NGA IRN k c,0 k k c,1 c,2 Fig. 2. Capabilities and bipartite network structure. (A) We model the structure of M cp by taking 2 random matrices representing the availability of capabilities in a country and the requirement of capabilities by products and consider that countries are able to produce products if they have all of the required capabilities. (B) The k c,0 k c,1 diagrams that emerge from 4 implementations of the model described in A.(C) k c,0 and k c,1 as a function of the number of capabilities (N c ) available in countries for 2 implementations of the model. (D) Average number of labor inputs required by products produced in a country as a function of the first 3 components of k c. number of products, the products exported by Malaysia (k MYS,0 104, k MYS,1 18) are exported by fewer countries than those exported by Pakistan (k PAK,0 104, k PAK,1 27.5). Combining this fact with our third level of analysis, we see that Malaysian products are exported by more diversified countries than the exports of Pakistan (k MYS,2 163 k PAK,2 142, SI Appendix, Section 8). This suggests that the productive structure of Malaysia is more complex than that of Pakistan, due, as we will show shortly, to a larger number of capabilities available in Malaysia than in Pakistan. In SI Appendix we show that the negative relationship presented in the k c,0 k c,1 diagram is not a consequence of variations in the level of diversification of countries and in the ubiquity of products. We prove this by creating 4 null models (11) that control, with increasing stringency, for the diversification of countries and the ubiquity of products and show that these distributions, per se, are not responsible for the negative relationship observed in the data (see SI Appendix, section 6). Minimalistic Model. We show that the location of countries in the k c,0 k c,1 diagram is informative about the capabilities available in a country by introducing a simple model based on the assumption that country c will be able to produce product p if it has all of the required capabilities (Fig. 2A). We implement this model by considering a fixed number of capabilities in each country and represent this by using a matrix C ca, that is equal to 1 if country c has capability a and 0 otherwise. We represent the relationship between capabilities and the products that require them by a matrix pa whose elements are equal to 1 if product p requires capability a and 0 otherwise. Using the notation introduced above, together with our only assumption, we can model the structure of the M cp matrix as: M cp 1 if a pa a pa C ca and M cp 0 otherwise [5] The simplest implementation of this model is to consider C ca 1 with probability r and 0 with probability 1 r and pa 1 with probability q and 0 with probability 1 q. An emergent property of the matrix resulting from this model is that the average ubiquity of a country s products tends to decrease with its level of diversification for a wide range of parameters (Fig. 2B). We interpret this negative relationship by considering that countries with many capabilities will be more diversified, because they can produce a wider set of products, and that because they can make products requiring many capabilities, few other countries will have all of the requisite capabilities to make them, hence diversified countries will be able to make less ubiquitous products. The model allows us to test directly whether given this set of assumptions we should expect countries with more capabilities to be more diversified and produce less ubiquitous products. Fig. 2C shows that, in the model, the diversity of a country increases with the number of capabilities it poses, whereas the ubiquity of a country s products is a decreasing function of the number of capabilities available in that country, providing further theoretical evidence that k c captures information on the availability of capabilities in a country, and therefore, about the complexity of its economy cgi doi pnas Hidalgo and Hausmann

4 STATISTICS ECONOMIC SCIENCES Fig. 3. Bipartite network structure and income (all GDPs have been adjusted by Purchasing Power Parity PPP). A E were constructed with data from the year (A C) GDP per capita adjusted by purchasing power parity as a function of our first 3 measures of diversification (kc,0,kc,2,kc,4), normalized by subtracting their respective means (具kc,N典) and dividing them by their standard deviations (stdev(kc,n)). (A) kc,0. (B) kc,2. (C) kc,4. (D) Comparison between the ranking of countries based on successive measures of diversification (kc,2n) (E) Absolute value of the Pearson correlation between the log GDP per capita at ppp of countries and theit local network structure characterized by kc,n. (F) in GDP per capita at ppp observed between 1985 and 2005 as a function of growth predicted from kc,18 and kc,19 measured in 1985 and controlling for GDP per capita at ppp in Direct Measurement of a Subset of Capabilities. We provide empir- ical evidence that the method of reflections extracts information that is related to the capabilities available in a country by looking at a measurable subset of the capabilities required by products. Fig. 2D shows the average number of different employment categories required by products exported by countries versus kc,0, kc,1, and kc,2. We measure the number of employment categories that go into a product by using the data of the U.S. Bureau of Labor Statistics (see SI Appendix, Section 1). This data should play against us, because Hidalgo and Hausmann we are disregarding the fact that other countries may use different technologies to produce goods that are similarly classified. Despite this, we find a strong positive correlation between the average Indeed, it is common for poorer countries to exchange labor for capital. For example, building a road in the US is done by a relatively small team of workers, each of them specialized to operate a different machine or technique, whereas more modest economies will tend to use more workers, yet less specialized ones, because the relative cost of machines to labor is larger in poorer economies. Hence we should expect poor countries PNAS 兩 June 30, 2009 兩 vol. 106 兩 no. 26 兩 10573

5 A <kp,1> (new exports) <kp,0> (new exports) C WSM MWI HTI NIC MDG MNG TKM TGOSDNVEN CAF PNG TJK BDI ZMB GUY GTM ETH FJI NPL SLV TZAMDABLR ARM RWA GIN BOL AZE BHRALB FIN NCL GHA BFA BEN KGZ BLZ DOM NER GMB NGA UGA SEN HNDMOZ CMR CYP BHS GEO ECU JORKEN MAC PAN SLE SVK SYR ZWE PRY LTU MAR LBNIRL MLI MLT LVA MYS BRBBGD EST GABOMN PER DZAIRN CIV KAZ CRI LKA PAK SWE TTO UKR AUS ISL MUS ZAF KNA EGY ARG PHL HKG IDN CHL COL PRT ROM SAU URY TUR NORISR CAN THA IND HRV GRC BRA JAM NZL POL HUN RUS SGP SVN MEX KOR CHN ESP AUT DNK DEU ITA NLD GBR k=-0.051k USA Pearson correlation = t-test=11.8 p-value=6x k c,0 k 1 =0.178k Pearson correlation = 0.59 t-test=8.21 p-value<3x10-13 POL NOR KOR DNK ITA NZL MEX SAU GBR JAM SVN IRL HRVNLD RUS GRC AUT GMB SVKBRB CHL IDN SWE DEU EGY EST CHN ESP SLE COL HUN GEO CAN IND IRN ISL MUS PHL TUR THA KNA LVA ARMGAB JORMOZ UKR BRA BFA BHS BHRALB MACPAN MLI CYP ISR BGDKEN CRI DOM LKALBN MDA LTU SGP ZAF URY ROM USA MAR NER NGA TTO NPL SLV PAK PRT KGZ BLR HKG OMN PRY PER ARG BEN CAF DZA SYR BDI AZE BLZ CIV FJI BOL ECU HND MLT MYS NCL KAZ GTM RWA GHA PNG SEN ZWE TJK ZMB VEN TGO ETHMNG NIC UGA TZA FIN AUS TKM MDG HTI SDN CMR GIN GUY MWI WSM k c,0 B <kp,0> (new exports) D <kp,1> (new exports) k c, k1=0.83k Pearson correlation = 0.63 WSM t-test=9.17 p-value<2x10-15 MWI HTI MDG MNG NIC VEN TKMSDN TGO PNG BLR BDI GTMCAF MDA NPL ZMB GUY TZA ETH SLV TJK FIN BHR BOL FJI AZE GHA DOM ALB GIN ARM MOZKGZ BLZ CYP BEN BFA GMB HND IRL JOR GEO LTU BHS MAC NCL NER LBN MAR MYS NGA UGA SEN RWA PAN SVK PRY ECUSYR ZWE MLT LVA CMR KEN SLE SWE AUS BRBPER EST MLI BGD HKG ARG DZA KAZ GAB PAK OMN ZAF UKR TTO IRN CIV LKA PHL ISL CRI EGY CAN HRV IDN KNA MUS PRT ROM NOR BRA ISR SAU URY TUR THA IND CHL COL SGP SVNHUN POL NZL GRC RUS JAM AUT MEX ESP CHN DEU DNK KOR ITA GBR NLD USA POL DNKNORKOR ITA MEXNZL GBR SVN IRL SAU JAM NLD RUS HRV AUT GRC DEUSWE SVK CHL BRB IDN GMB ESP CHN HUN THA PHL TUR EGY COL EST URY SLE MUS CAN IND ROM BRA GEO ISL IRN KNA LVA USA SGP ZAFJOR UKR ISR PAN MOZ BHR GAB LTU MAC CYP PRT BHS LBN ALB ARM BFA HKG BLR DOM LKA MDA MLI MAR BGD ARG NER NGA NPL TTO SLV PRY PER PAK KGZ KENCRI MYS MLT DZA SYR OMNBEN ECU BOLCIV AZE BLZ BDI GTMCAF HND KAZ ZWE NCL FJI PNG VEN GHA SEN FIN MNG ZMB RWA TGOETH TJK AUS UGATZA NIC TKMHTI MDG SDN CMR GUY GINMWI 100 k 1 =-2.99k WSM Pearson correlation = t-test=7.2 p-value<6x k c,1 Fig. 4. Path dependent development. Average network properties ( k p,0, k p,1 ; measured in 1992) of the new exports developed by a country between 1992 and 2000 as a function of the diversification of a country k c,0 and the average ubiquity of its products k c,1 measured in (A) k c,0 vs. k p,0.(b) k c,1 vs. k p,0.(c) k c,0 vs. k p,1.(d) k c,1 vs. k p,1. number of employment categories going into the export basket of countries and our family of measures of diversification (k c,0, k c,2, k c,4,...,k c,2n ). We also find a negative correlation between the average number of employment categories and measures of the ubiquity of products made by a country (k c,1, k c,3, k c,5,...,k c,2n 1 ) (Fig. 2D). This shows that more diversified countries indeed produce more complex products, in the sense that they require a wider combination of human capabilities, and that k c is able to capture this information. Complexity of the Productive Structure, Income and. We show that the information extracted by the method of reflections is connected to income by looking at the first 3 measures of diversification of a country (k c,0, k c,2, k c,4 ) versus GDP per-capita adjusted for Purchasing Power Parity (PPP) (Fig. 3 A C). To make these 3 different measures comparable we have normalized them by subtracting their respective means ( k N ) and dividing them by their respective standard deviations (stdev(k N )). As we iterate the method the relative ranking of countries defined by these variables shifts (Fig. 3D and SI Appendix, Fig. S14), making our measures of diversification and ubiquity increasingly more correlated with income (Fig. 3E and SI Appendix, Section 11). This can be illustrated by looking at the position, in the k c,n GDP diagrams, of 3 countries that exported a similar number of products in the year 2000, albeit having large differences in income (Pakistan (PAK), Chile (CHL) and Singapore (SGP) Fig. 3 A C). Higher reflections of our method are able to correctly differentiate the income level of these countries because they incorporate information about the ubiquity of the products they export and about the diversification of other countries connected indirectly to them in M cp, altering their relative rankings (Fig. 3D and SI Appendix, Fig. S14). For example, k c,2 is to use less labor inputs in the production of products than what would be reported from U.S. labor data, accentuating the effect presented in Fig. 2D. able to correctly separate Singapore, Chile and Pakistan, because it considers that in the bipartite network Singapore is connected to diversified countries mainly through nonubiquitous products, signaling the availability in Singapore of capabilities that are required to produce goods in diversified countries. In contrast, Pakistan is connected mostly to poorly diversified countries, and most of its connections are through ubiquitous products, indicating that Pakistan has capabilities that are available in most countries and that its relatively high level of diversification is probably due to its relatively large population, rather than to the complexity of its productive structure. Indeed, we find the method of reflections to be an accurate way to control for a country s population, as correlations between k c and population decrease rapidly as we iterate the method (see SI Appendix, Section 11), whereas correlations between k c and GDP increase as we iterate the method. This is another piece of evidence suggesting that the information captured by our method is related to factors that affect the ability to generate per capita income. Deviations from the correlation between k c and income are good predictors of future growth, indicating that countries tend to approach the levels of income that correspond to their measured complexity. We show this by regressing the rate of growth of income per capita on successive generations of our measures of economic complexity (i.e., k c,0, k c,1 or k c,10,k c,11 ) and on a country s initial level of income GDP t t log a b GDP t 1 GDP t b 2 k c,n t b 3 k c,n 1 t, finding that successive generations of the variables constructed in the previous section are increasingly good predictors of growth. In SI Appendix, Section 13, we present regression tables showing that these results are valid for a 20-year period ( ), two 10-year cgi doi pnas Hidalgo and Hausmann

6 periods or four 5-year periods, and that it is robust to the inclusion of other control variables such as individual country dummies (to capture any time-invariant country characteristic) and outperforms other indicators used to measure the productive structure of a country such as the Hirschman-Herfindahl (12, 13) index and entropy measures (14). A graphical example of this relationship is presented in Fig. 3f, which compares the growth predicted from the linear regression described by Eq. 6 and that observed empirically for the period and N 18. Finally, we show that the evolution of M cp exhibits strong path dependence, meaning that we can anticipate some of the properties of a country s future new exports based on its current productive structure. This observation is consistent with the existence of an unobservable capability space that evolves gradually, because the ability of a country to produce a new product is limited to combinations of the capabilities it initially possesses plus any new capabilities it will accumulate. Countries with many capabilities will be able to combine new capabilities with a wide set of existing capabilities, resulting in new products of higher complexity than those of countries with few capabilities, which will be limited by this fact. We show this using data collected between 1992 and 2000 (we choose 1992 as our starting point because the end of the Soviet Union and the unification of Germany introduce large discontinuities in the number and identity of countries) and consider as a country s new exports those items for which that country had an RCA cp 0.1 in the year 1992 and an RCA cp 1 by the year Fig. 4 shows that the level of diversification (k c,0 ) of a country and the ubiquity of its exports (k c,1 ), predicts the average ubiquity ( k p,0 ) of a country s new exports and the average level of diversification ( k p,1 ) of the countries that were hitherto exporting those products. This result is related to the idea that the productive structure of countries evolves by spreading to nearby products in The Product Space (15 17), which is a projection of the bipartite network studied here in which pairs of products are connected based on the probability that they are exported by the same countries. This last set of results suggests that the proximity between products in the The Product Space is related to the similarity of the requisite capabilities that go into a product, because countries tend to jump into products that require capabilities that are similar to those required by the products they already export. Discussion Understanding the increasingly large gaps in income per capita across countries is one of the eternal puzzles of development economics. Our view is that complexity is at the root of the explanation, as argued by both Adam Smith (1) and the recent endogenous growth theories (2, 3), yet empirical research has not advanced along these dimensions because of the absence of adequate measures of complexity. Instead, it has emphasized the accumulation of a few highly aggregated factors of production, such as physical and human capital or general institutional measures, such as rule of law, disregarding their specificity and complementarity. In this article we have presented a technique that uses available economic data to develop measures of the complexity of products and of countries, and showed that (i) these measures capture information about the complexity of the set of capabilities available in a country; (ii) are strongly correlated with income per capita; (iii) are predictive of future growth; and (iv) are predictive of the complexity of a country s future exports, making a strong empirical case that the level of development is indeed associated to the complexity of a country s economy. This article has not emphasized the process through which countries accumulate capabilities, but has instead focused on their measurement and consequences. However, the results presented here suggest that changes in a country s productive structure can be understood as a combination of 2 processes, (i) that by which countries find new products as yet unexplored combinations of the capabilities they already have, and (ii) the process by which countries accumulate new capabilities and combine them with other previously available capabilities to develop yet more products. A possible explanation for the connection between economic complexity and growth is that countries that are below the income expected from their capability endowment have yet to develop all of the products that are feasible with their existing capabilities. We can expect such countries to be able to grow more quickly, relative to those countries that can only grow by accumulating new capabilities. This perspective also suggests that the incentive to accumulate capabilities would depend, among other things, on the expected demand that new capabilities would face, and this would depend on how new capabilities can complement existing ones to create new products. This opens up an avenue for further research on the dynamics of product and capability accumulation. Development economics has tended to disregard the search for detailed capabilities and their patterns of complementarity, hoping that aggregate measures of physical capital (e.g., measured in dollars) or human capital (e.g., measured in years of schooling) would provide enough guidance for policy. Our line of research would justify and provide guidance to development strategies that look to promote products (or capabilities) as a way to create incentives to accumulate capabilities (or develop new products) that could themselves encourage the further coevolution of new products and capabilities, echoing ideas put forward by Albert Hirschman (18) more than 50 years ago, but adding the capacity to analyze them in practice. ACKNOWLEDGMENTS. We thank M. Andrews, A.-L. Barabási, B. Klinger, M. Kremer, N. Nunn, L. Pritchett, R. Rigobon, D. Rodrik, M. Yildirim, R. Zeckhauser, participants at the Center for International Development s Seminar on Economic Policy and the Harvard Kennedy School Faculty Seminar, members of the Center for Complex Network Research at Northeastern University, and the Ratatouille Seminar Series. We acknowledge support from the Lab and the Empowerment Lab at the Center for International Development. STATISTICS ECONOMIC SCIENCES 1. Smith A (1776) An Inquiry into the Nature and Causes of the Wealth of Nations (W. Strahan and T. Cadell, London). 2. Romer P (1990) Endogenous technological change. J Pol Econ 98:S71 S Grossman GM, Helpman E (1991). Quality ladders in the theory of growth. Rev Econ Stud 58: Maddison A (2001) The World Economy: A Millennial Perspective (Development Centre of the OECD, Paris). 5. Pritchett L (1997) Divergence, big time. J Econ Perspec 11: Aghion P, Howitt PW(1998) Endogenous Theory (MIT Press, Cambridge, MA) 7. Barro RJ, Sala-i-Martin X(2003) Economic (MIT Press, Cambridge, MA) 8. Feenstra RC, Lipsey RE, Deng H, Ma AC, Ma H (2005) World Trade Flows: NBER Working Paper Available at 9. Pastor-Satorras R, Vazquez A, Vespignani A (2001) Dynamical and correlation properties of the internet. Phys Rev Lett 87: Maslov S, Sneppen K (2002) Specificity and stability in topology of protein networks. Science 296: Newman MEJ (2002) Assortative mixing in networks. Phys Rev Lett 89: Hirschman AO (1945) National power and structure of foreign trade (University of California Press, Berkley, CA). 13. Herfindahl OC (1950) Concentration in the steel industry (PhD Dissertation, Columbia University, New York) 14. Saviotti PP, Frenken K (2008) Export variety and the economic performance of countries. J Evol Econ 18: Hidalgo CA, Klinger B, Barabási A-L, Hausmann R (2007) The product space conditions the development of nations. Science 317: Hausmann R, Klinger B (2006) The structure of the product space and the evolution of comparative advantage. CID Working Paper No Available at edu/cidwp/128.htm. 17. Hidalgo CA, Hausmann R (2008) A network view of economic development. Developing Alternatives 12(1): Hirschman AO (1958) The Strategy of Economic Development (Yale Univ Press, New Haven, CT). Hidalgo and Hausmann PNAS June 30, 2009 vol. 106 no

7 SUPPLEMENTARY MATERIAL FOR: THE BUILDING BLOCKS OF ECONOMIC COMPLEXITY Cesar A. Hidalgo, Ricardo Hausmann Center for International Development and Harvard Kennedy School, Harvard University TABLE OF CONTENTS SECTION 1: SOURCE DATA 2 SECTION 2: REVEALED COMPARATIVE ADVANTAGE (RCA) 3 SECTION 3: THE COUNTRY-PRODUCT NETWORK 4 SECTION 4: BIPARTITE NETWORK ANALYSIS 6 SECTION 5: BIPARTITE NETWORK STRUCTURE MEASURED IN OTHER DATASETS 13 SECTION 6: RANDOMIZING A BIPARTITE NETWORK 14 SECTION 7: THE K P,0 -K P,1 DIAGRAM 16 SECTION 8: A THIRD REFLECTION VIEW OF THE STRUCTURE OF THE COUNTRY-PRODUCT NETWORK 19 SECTION 9: NULL MODELS AND GDP 20 SECTION 10: THE METHOD OF REFLECTIONS AND COUNTRY RANKINGS (YEAR 2000) 22 SECTION 11: THE METHOD OF REFLECTIONS AND POPULATION 23 SECTION 12: SHARES OF PRODUCTS IN THE WORLD 24 SECTION 13: NETWORK STRUCTURE, INCOME AND GROWTH 25 SECTION 14: ADDITIONAL RESULTS 35 REFERENCES 42 1

8 SECTION 1: SOURCE DATA All of the figures presented in the main text of this paper were constructed using International trade data taken from Feenstra, Lipsey, Deng, Ma and Mo's "World Trade Flows: " dataset. This dataset consists of imports and exports both by country of origin and by destination, with products disaggregated to the SITC revision 4, four-digit level. The authors built this dataset using the United Nations COMTRADE database. The authors cleaned that dataset by calculating exports using the records of the importing country, when available, assuming that data on imports is more accurate than data from exporters. This is likely, as imports are more tightly controlled in order to enforce safety standards and collect customs fees. In addition, the authors correct the UN data for flows to and from the United States, Hong Kong, and China. We focus only on export data and do not disaggregate by country of destination. More information on this dataset can be found in NBER Working Paper #11040, and the dataset itself is available at and We checked the validity of our results by using two additional datasets: COMTRADE classified according to the Harmonized System at the 4-digit level (1241 products, 103 countries) and the North American Industry Classification System (NAICS) (318 products, 150 countries). We found that our results are not affected by the use of data at these different levels of aggregation. We chose to work with the Feenstra dataset because, of the three datasets available, it is the one only one that has been cleaned and checked thoroughly as part of a dedicated research project. The labor data used to construct figure 2d was downloaded from the US Bureau of Labor and Statistics at 2

9 SECTION 2: REVEALED COMPARATIVE ADVANTAGE (RCA) One way to empirically estimate whether a country is a significant exporter of a product is to calculate the Revealed Comparative Advantage (RCA) that that country has in a particular product. RCA is a measure constructed to inform whether a country s share of a product s world market, is larger or smaller than the product s share of the entire world market. Mathematically, we can rewrite the above sentence by introducing S cp, as the share that country c has of the world market for product p, and T p as the total share of product p of the world market. Using this notation, RCA can be written as RCA cp = S cp /T p (1) where (2) RCA CUTOFFS, EXPORTS AND COUNTRIES LEVEL OF DIVERSIFICATION The natural cutoff used to determine whether a country has revealed comparative advantage in a product is RCA 1. At this point the country s share of that product s market is equal or larger than the product s share of the world market. The benchmark here is a world in which countries export an amount of each product equal to the share of that product in the world market times the size of its economy. From an empirical perspective, we can study the number of products (k c,0 ) for which a country has RCA as a function of the RCA cutoff. By performing this exercise we find that the RCA cp =1 cutoff lies on the phase transition of a softened step function (Figure S1). 3

10 Fig S 1 Diversification (k c,0) as a function of the RCA cutoff for all countries in the study What is interesting about looking at k c,0 (RCA) from this empirical perspective is that we can see that there are a few countries that had exports in almost all of the 772 products exported in the year For example, Germany exported 758 products with an RCA 0.01, and 707 products with RCA 0.1, a profile similar to that of other industrialized countries like the U.K., U.S.A and Italy. Hence lowering the RCA threshold shows that industrialized countries manufacture and export products in almost all of the SITC-4 categories, and that specialization patterns are empirically driven by the lack of diversification of less developed countries, rather than by the absence of more productive economies in comparatively less sophisticated sectors. SECTION 3: THE COUNTRY-PRODUCT NETWORK Fig S 2 shows a simple visualization of the country product network for the year 2000 in which countries are located at the center of the figure and products are grouped into root SITC- 4 categories along the edges of the image. This network consists of 129 countries, 772 products and 13,470 links connecting countries and products when RCA cp 1. The large number of links in the network limits our ability to create a useful visualization of the entire set of connections. 4

11 Fig S 2 Visualization of the country product network in which all exports with an RCA>1 are shown. 5

12 SECTION 4: BIPARTITE NETWORK ANALYSIS A bipartite graph or network is a set of nodes and links in which nodes can be separated into two groups, or partitions, such that links only connect nodes in different partitions. While in principle many networks can be separated into different partitions (for example every tree is a bipartite graph), here we concentrate on examples that are bipartite, by definition, rather than as a property. One example of naturally occurring bipartite networks are publication networks, where nodes are researchers and papers, and links connect researchers to the papers they have authored. Another example is the movie-actor network in which nodes are actors and movies, and links connect actors to the movies in which they have starred.. With the exception of a few studies [ 1,2,3,4 ], bipartite networks have mostly been investigated by projecting the network into one of its partitions [ 5,6,7,8,9,10,11,12,13,14 ], typically by considering nodes to be connected if they share a neighbor in the opposite partition [ 5,6,7,8,9,10,11,12,13,14 ]. For example, co-authorship networks link scientists that have co-authored one or more papers [ 8,9,10,11 ], whereas movie-actor networks connect actors that have appeared together in one or more movies. While valuable information can be obtained from these projections, there is important information that is left out by reducing the bipartite network into either one of its partitions, regardless of the sophistication of the projection method. Here we present a method to characterize the structure of a bipartite network by iteratively considering the properties of neighboring nodes. THE METHOD OF REFLECTIONS In this section we explain in detail the method of reflections as a general technique to study the structure of bipartite networks. To shorten the math we adopt a different notation than the one used for the particular example of countries and products. Going forward, we indicate all variables that are related to nodes in each partition by either Latin or Greek characters. 6

13 Consider a bipartite network M described by the adjacency matrix M aα,where M aα =1 if node a is connected to node α and zero otherwise. We define the method of reflections as the recursive set of observables, 1,, (3), 1,, (4) for n>0,with, (5), (6) Following these definitions, the degree of nodes in the bipartite network is given by and (in this notation we can drop the a and α indices when referring to the general concept described by the variable as the alphabet already indicates if the variables refers to one partition or the other countries or products-). In the example of the main text these variables are the diversification (k a,0 ) of countries and the ubiquity (k p,0 ) of products. Following from (3) and (4), the average ubiquity of a country s exports is given by whereas the average diversification of a product s exporters is given by. The recursive nature of the method of reflections allows us to characterize the structure of the bipartite network by defining N variables for each one of its partitions. For example, continuing the characterization of the country-product network into a third layer of analysis in which, the average κ 1 of a country s exports, and,the average k1 of a product s exporter, is considered, allows us to 7

14 characterize countries and products through a three dimensional phase space spanned by,, and,,. In principle we can use the method of reflections to characterize countries and products by N variables. The method of reflections can be generalized by choosing different values for k 0 and κ 0 and iterating over them using (3) and (4). In fact, the measure of product sophistications PRODY [ 15 ] can be seen as a special case of the method of reflections in which k a,0 is the GDP(PPP) of a country and M aα is a matrix of RCAs. In such a case then PRODY=k a,1. When these variables were constructed, however, the authors were not aware that their methods were combining income information with the structure of a bipartite network. THE VARIABLES FOR THE FIRST THREE LEVELS Table S 1 shows how we interpret the first three pairs of variables describing the country-product network through the method of reflections: Definition,,,,,, Working Name Diversification Ubiquity,,,, Description: Short summary Question Form Number of products exported by country a. How many products are exported by country a? Number of countries exporting product α. How many countries export product α? Average ubiquity of the products exported by country a. How common are the products exported by country a? Average diversification of the countries exporting product α. How diversified are the countries that export product α? Average diversification of countries with an export basket similar to country a How diversified are countries exporting goods similar to those of country a? Average ubiquity of the products exported by countries that export product α. How ubiquitous are the products exported by product s α exporters? Table S 1 Interpretation of the bipartite network description obtained from the method of reflections. INTERPRETING HIGHER REFLECTIONS As we iterate the method of reflections, it becomes increasingly harder to interpret the variables generated by it. We can gain insight into what higher reflection variables stand for by analytically solving the recursion formulas presented in (3)-(6). Analytically solving the recursion requires us to be able to express k r N and r κ N as a function of the initial conditions, k r 0and r κ0. Mathematically (3)-(4) we search for solutions of the form: 8

15 k a,n r r = C k κ k κ = b r κ ab, N ( 0, 0) b,0, α,n αβ, N ( 0, 0) β,0 β C r k κ (7) To illustrate this we calculate the elements k r 2 as an example. According to the definitions of the method shown in (3)-(6) the elements of k r 2 can be expressed as: 1 = k 1 M aακα,1 = k ka,2 κα, 1 a,0 α a,0 { a} α (8) Where {a} α is the set of the α neighbors of a. We can use (4) to rewrite (8) as k a,2 1 = k a,0 { a} α 1 κ α,0 { α} b k b,0 (9) Which can be taken into the form (7) by permuting the sums and changing the index of the first summation to a sum over the second neighbors of a, and the index of the second summation to a sum over the neighbors of a and b. 1 ka,2 = kb, 0 ka,0 { a } { a b} κ α α, 0 b 1 (10) Which satisfies the form presented in (7) with C ab,2 r r 1 ( k0, κ0) = k 1 κ a,0 { a b} α α, 0 (11) We can interpret k a,2 from the form presented in (10) by noticing that k a,2 is a linear combination of the elements of k r 0 with coefficients given by product of the degrees of all nodes lying in the path connecting nodes a and b, including node a but not node b. Hence the r coefficients C, 2( 0, r ab k κ0) can be interpreted as the probability that a random walker that started at a ends up at b after two steps. The random walker interpretation of the method of reflections is true not only for k r 2but for any N. Fig S 3 shows an example of a three node network in which some of the coefficients 9

16 associated with N=4 are presented explicitly. Hence the method of reflections is a way to express the properties of a node in a network as a combination of the properties of all its neighbors, the coefficients of the linear combination being the probability that two nodes are connected by a random walker after N steps. The coefficients of the expansion can be interpreted as a measure of similarity between the nodes in the network, which is context dependent, as what matters in the expansion is the relative weight of these coefficients when compared to each other. k a,n = k a = ab, N r ( k 0, r κ ( k κ β k κ α kb b b C a 0) k b, κ γ kb κ γ +...) + k b (...) + k c (...) Fig S 3 Example showing how the method of reflections can be seen as an expansion of the properties of a node as a function of the properties of other nodes in the network with weights given by the product of the inverse of the degrees of each node traversed in the path connecting them. Finally, we would like to mention that while higher order reflections do extract increasingly more relevant information about the productive structure of a country, as measured by how they are related to income and growth, it is important to mention that as N-> all variables will progressively converge to the a similar value. Surprisingly, we find the tiny deviations of these values to be extremely informative. 10

17 A SIMPLE EXAMPLE In this section we explain the method of reflections using a simple example in which a network composed of four countries and four products is considered (Fig S 4). Countries Products p1 C1 C2 p2 C3 p3 C4 p4 Fig S 4 A simple network used to exemplify the method of reflections. In this example, the diversification of countries and the ubiquity of products is given by: k c1,0 =4 k c2,0 =1 k c3,0 =2 k c4,0 =1 k p1,0 =1 k p2,0 =2 k p3,0 =2 k p4,0 =3 Next, we calculate higher reflections of the method (or iterations). The first reflection consists of the average ubiquity of country s products and of the average diversification of a product s exporters and is given by: k c1,1 =(1/4)( )=2 k c2,1 =(1/1)(2)=2 k c3,1 =(1/2)(2+3)=2.5 k c4,1 =(1/1)(3)=3 k p1,1 =(1/1)(4)=4 k p2,1 =(1/2)(4+1)=2.5 k p3,1 =(1/2)(4+2)=3 k p4,1 =(1/3)(4+2+1)=

18 The second reflection is given by the average first reflection values of a node s neighbors. k c1,2 =(1/4)( )= k c2,2 =(1/1)(2.5)=2.5 k c3,2 =(1/2)( )=2.66 k c4,2 =(1/1)(2.333)=2.33 k p1,2 =(1/1)(2)=2 k p2,2 =(1/2)(2+2)=2 k p3,2 =(1/2)(2+2.5)=2.25 k p4,2 =(1/3)( )=2.5 We can use this example to illustrate how the method of reflections is able to differentiate between different countries based only on information regarding which country exports which product. In this example, the most diversified country is c1, which exports all four products while there are two countries, c2 and c4, that only export a single product. The sole export of c2 however, is a relatively non ubiquitous product that is exported only by c1, the most diversified country, while the sole export of c4 is a product that is exported by all countries except c2. As we iterate the method we find that there is important information encoded in the relative position of countries and products relative to one another. For example, when we look at the values characterizing countries after the second reflection (k c,2 ) we can see that country c1 comes up ahead, followed by country c3, c2 and c4. The method places country c2 ahead of c4 because by the second reflection it is already considering that country c2 produces a non ubiquitous product that is found only in diversified countries, probably signaling that country c2 has a relatively good endowment of capabilities and produces a small number of products because of other reason, such as being of relatively small size. On the contrary, c4 produces a product that is ubiquitous and it is found in diversified and non diversified countries, probably indicating that is a simple product which is accessible to countries with relatively simple productive structures. Hence while both, c2 and c4 produce the same number of products, the method can differentiate between them and considers c2 to have a more complex productive structure than c4. While small in size this example illustrates how the method of reflections can be used to characterize the structure of a bipartite network and how this can be applied to help the understanding of the productive structure of countries and the sophistication of products. 12

19 SECTION 5: BIPARTITE NETWORK STRUCTURE MEASURED IN OTHER DATASETS In this section we present two additional k c,0 -k c,1 diagrams constructed using data aggregated according to the Harmonized system and according to the North American Industry Classification System (NAICS) MDV GUY qk BDI BLZ KNA TTO PAN NCL MWI CRI NIC HND ALB MKD SDN OMN BEN MAR LCA GMB DMA VCT TGO MDA ECU BRB LVAGTM LTU HRV CYP CPV MNG NER AZE UGA SEN ZMB TZA ARM COL EST GRC MUS URY ROM BGR TUN VEN BLR ISL DNK GEO KGZ LUX PER NZL PRTUR QAT HUN CHL UKR JOR POL IRN PHL SVK SVN BOL PYF MLT MEX ARG IDNTHA ZAF ISR CAN AUT BRA NLD SAU NOR SWE IND KAZ FIN AUS IRL MYS KOR MSR GBR RUS SGP HKG TWN CHE BEL ESP CZE FRAITA CHN USA DEU JPN k 0 Fig S 5 k c,0-k c,1 diagram constructed using data containing 103 countries and 1241 products aggregated according to the Harmonized System. 13

20 55 MDV 50 BDI BLZ qk MLI GMB STP GRL NER FJI BGD GUY CUB MDG GHA BENDMA UGA LSO PNG ETH MOZ NGA MRT CMR SUR ECU VCT IRN JAM TGO KEN SDN CIV ATG MWI NPL TZA NAM NIC COM DZA FRO HND MNG PER GAB GIN CPV ZMB MAR TTO SWZ EGY LCA PAN OMN CAF BFA SEN CHL GTM KHM MDA ZWE SAU MAC GRD PRY BOL MKD NZL NCL URY BRB CYP BWA TKM TUN CRI LTU ARG AZE BHS ISL SLV MUS GEO COL EST LBN LVA JOR BGR KWT KNA MYT ALB ZAF BHR KGZ GRC TUR HRV YUG AUS ROM PHL IDN IND NOR BLR PRT POL ARM THA UKR BRA ESP NLD VEN BEL KAZ MLT LUX SVKHUN CHN RUS MYSIRL CAN SVN ISR ADO MEX PYF QAT HKG FIN KOR SWE GBR DNK FRA CZE ITA AUT 20 SGP CHE USA DEU JPN k 0 Fig S 6 k c,0-k c,1 diagram constructed using data containing 150 countries and 318 products aggregated according to the NAICS. SECTION 6: RANDOMIZING A BIPARTITE NETWORK To decide whether the structure of a network is trivial, * we need to compare it to an appropriate null model. The four null models we introduce in this section are an extension of the randomization algorithms introduced by Maslov and Sneppen [ 16 ] to analyze degree correlations in protein interaction networks. Our case differs from theirs in that we are dealing with a bipartite network rather than with a simple graph. The idea behind the randomization procedure is that we can create a null model starting from the data we want to analyze by shuffling the links of the network while conserving some of its statistical properties. The most popular version of this randomization procedure, which was designed for simple graphs, consists of randomizing the links in the network by permuting the nodes at the end of a pair of links. For example, if we consider a simple graph containing the links {a,b} and {c,d}, then an allowed randomization step would consist of replacing these two links by the pairs {a,d} and {b,c}, given that the {a,d} and {b,c} links were not already part of * Expected from chance Simple Graph is a network in which there is only one type of nodes, and connections are strictly binary (0 or 1). 14

21 the network. The randomization procedure described above conserves the number of links in the network as well as its degree sequence and degree distribution. This is because the randomization procedure conserves the exact number of connections of each node, making it a good null model to compare properties of a network while controlling for the degree of nodes, which is the most fundamental property of a network. In the case of a bipartite network, we have two separate degree sequences, one for each of its partitions. Here we introduce four null models to control for all possible combinations of degree sequences. Null Model 1 is a network with the same number of nodes and links as the original network, yet in Null Model 1 connections have been randomly assigned. Null Model 1 is the less stringent of our Null Models and represents a network with the same number of links as the original network, but with a random degree sequence for both partitions. Null Model 2 controls for the degree sequence of one partition of the network, while randomizing the target of those links in the other partition. Null Model 2 represents a network with a diversification sequence matching the one in the observed data, yet in Null Model 2 the products exported by a country have been randomly assigned. Null Model 2 also conserves the total number of links in the network. Null Model 3 is symmetric to Null Model 2 in the sense that it represents a network with the same ubiquity distribution as the one observed in the data, but where the exporters of each product have been randomly assigned. Finally, Null Model 4 is a model obtained by permuting links in the network such that the diversification of countries and the ubiquity of products are exactly the same as those observed in the empirical data. It is important to notice that as Null Models become more stringent, the number of possible permutations that can be performed in the randomization procedure drops substantially. The possible number of permutations that can be performed in a randomization procedure does not only depend on the stringency of the null model, but also on the structure of the original network. For example, if we consider a bipartite network that can be represented by a triangular adjacency matrix (for simplicity assume that the number of Degree: The number of links a node has. Degree Sequence: List containing the degrees of all nodes in the network. 15

22 products is equal to the number of countries and that M cp = 1 c<p; M cp =0 otherwise), then there is not a single possible permutation that could be performed using the fourth null model. For such a case, Null Model 4 is equivalent to the original network. NULL MODEL SUMMARY Null Model Number of links kc,0 sequence kp,0 sequence <kc,0> <kc,1> < kp,0> < kp,1> Null Model 1 = Mcp Mcp Mcp = Mcp Mcp = Mcp Mcp Null Model 2 = Mcp = Mcp Mcp = Mcp Mcp = Mcp Mcp Null Model 3 = Mcp Mcp = Mcp = Mcp Mcp =Mcp Mcp Null Model 4 = Mcp = Mcp = Mcp = Mcp Mcp =Mcp Mcp Table S 2 Summary null model behavior. <> stands for the average of a quantity. SECTION 7: THE K P,0 -K P,1 DIAGRAM We compare the k p,0 -k p,1 diagram obtained from our data with the one from our four null models (Fig S 7), finding that the structure of the country-product network is characterized by a strong negative correlation between k p,0 -k p,1 and a wide range of k p,1 values that cannot be explained by any of the four null models. This result becomes even more evident when we study higher order reflections of the method (see SM section 7). Products from different sectors are colored according to the ten root categories in the SITC-4 classification, showing that while there is a correspondence between the k p,0 -k p,1 diagram and the SITC-4 classification, there are important variations among similarly classified products. For example, this graph shows that natural resource-based products, such as minerals and fuels, exhibit a wide range of ubiquities (k p,0 ) at approximately constant diversification of its exporters (k p,1 ), meaning that 16

23 raw materials are on average exported by poorly diversified countries regardless of being relatively ubiquitous like coniferous wood (k p,0 =43, k p,1 =115), or rare as tin ore (k p,0 =8,k p,1 =109). On the other hand, products classified as machinery show variation in the level of diversification of their exporters (k p,1 ) at relatively low ubiquities (k p,0 ). Hence the k p,0 -k p,1 diagram can separate simple machines produced in less-diversified countries, such as handheld calculators, (k p,0 =7,k p,0 =144) from more complex machines produced in diversified countries such as motorcycles (k p,0 =5,k p,1 =270). 17

24 Fig S 7 Method of reflections and products characteristics. A, Schematic explanation of the k p,0 k p,1 space to characterize products. B, k p,0 k p,1 diagram for null models. C, k p,0 k p,1 diagram for the empirically observed exports data. 18

25 SECTION 8: A THIRD REFLECTION VIEW OF THE STRUCTURE OF THE COUNTRY-PRODUCT NETWORK Here we continue the analysis presented in the manuscript to a third layer of analysis in which we show figures characterizing countries by k c,0,k c,1,k c,2 and products by k p,0,k p,1,k p,2 (Fig S 8-Fig S 11). Fig S 8 Scatter plot for k c,0 and k c,2 for the original data in the year 2000 and the four null models. Fig S 9 Scatter plot for k c,1 and k c,2 for the original data in the year 2000 and the four null models. 19

26 Fig S 10 Scatter plot for κ and κ 2 for the original data in the year 2000 and the four null models. Fig S 11 Scatter plot for κ 1 and κ 2 for the original data in the year 2000 and the four null models. SECTION 9: NULL MODELS AND GDP In this section we present scatter plots between GDP per capita and the first two variables of the method of reflections characterizing the structure of bipartite networks created from our four null models (Fig S 12, Fig S 13). 20

27 Fig S 12 Scatter plot between GDP and bipartite network properties for countries (k=k c,0, k 1=k c,1) and Null Models 1 and 2 Fig S 13 Scatter plot between GDP and bipartite network properties for countries (k=k c,0, k 1=k c,1) and Null Models 3 and 4 21

28 SECTION 10: THE METHOD OF REFLECTIONS AND COUNTRY RANKINGS (YEAR 2000) Fig S 14 Relative ranking of countries based on the Method of Reflections for the year