A new metrics for the Economic Complexity of countries and products

A new metrics for the Economic Complexity of countries and products Andrea Tacchella Dept. of Physics, La Sapienza - University of Rome Istituto dei Sistemi Complessi, CNR Roma CRISISLAB ANALYTICS FOR CRISIS PREDICTION AND MANAGEMENT Rome, 8/0/013

Complex Systems and Economics So far two main approaches, mostly for Financial Markets Time-Series Analysis Agent Based Models We enter in a new field, where no quantitative method exists: A metric for the economic complexity of countries Non-Monetary Network-based

Classical Theory - Division of Labour It is the great multiplication of the productions of all the different arts, in consequence of the division of labour, which occasions, in a well-governed society, that universal opulence which extends itself to the lowest ranks of the people. Adam Smith - The Wealth of Nations

Specialization vs. Diversification Classic Theories (Smith, Ricardo): Efficiency and Specialization Block diagonal export matrix: Countries Products

Specialization vs. Diversification Real World: dynamic markets, globalized Triangular Shape Countries Complexity Products C. Hidalgo and R. Hausmann (PNAS 009)

Complexity is arising from the network An approach suggested by biological systems Far from equilibrium Countries must achieve stability trough diversification

The Building Blocks of Economic Complexity C. Hidalgo (MIT), R. Hausmann (Harvard) Countries Products C1 P1 C P C3 P3 Available Data

The Building Blocks of Economic Complexity C. Hidalgo (MIT), R. Hausmann (Harvard) Countries Products Countries Capabilities Products C1 P1 C1 A1 P1 C P C A P C3 P3 C3 A3 P3 Available Data Model

Extracting information from the matrix k c,1 ubiquity of products ALB ALB DZA DZA ARG ARG ARM ARM AUS AUS AUT AUT AZE AZE BHS BHS BHR BHR BGD BGD BRB BRB BLR BLR BLZ BLZ BEN BEN BOL BOL BRA BRA BFA BFA BDI BDI CMR CMR CAN CAN CAF CAF CHL CHL CHN CHN COL COL CRI CRI HRV HRV CYP CYP CZE CZE DNK DNK DOM DOM ECU ECU EGY EGY SLV SLV EST EST ETH ETH FJI FJI FIN FIN GAB GAB GMB GMB GEO GEO DEU DEU GHA GHA GRC GRC GTM GTM GIN GIN GUY GUY HTI HTIHND HND HKG HKG HUN HUN ISL ISL IND IND IDN IDN IRN IRN IRL IRL ISR ISR ITA ITA CIV CIV JAM JAM JPN JPN JOR JOR KAZ KAZ KEN KEN KGZ KGZ LVA LVA LBN LBN LTU LTU MAC MAC MDG MDG MWI MWI MYS MYS MLI MLI MLT MLT MUS MUS MEX MEX MDA MDA MNG MNG MAR MAR MOZ MOZ NPL NPL NLD NLD NCL NCL NZL NZL NIC NIC NER NER NGA NGA NOR NOR OMN OMN PAK PAK PAN PAN PNG PNG PRY PRY PER PER PHL PHL POL POL PRT PRT ROM ROM RUS RUS RWA RWA KNA KNA WSM WSM SAU SAU SEN SEN SLE SLE SGP SGP SVK SVK SVN SVN ZAF ZAF KOR KOR ESP ESP LKA LKA SDN SDN SWE SWE SYR SYR TJK TJK TZA TZA THA THA TGO TGO TTO TTO TUR TUR TKM TKM UGA UGA UKR UKR GBR GBR USA USA URY URY VEN VEN ZMB ZMB ZWE ZWE k c,0 k c,1 I II III IV 0 100 00 300 400 10 15 0 5 30 35 k c,0 diversification Low diversification, high ubiquity High diversification, low ubiquity First order information

Method of Reflections C. Hidalgo (MIT), R. Hausmann (Harvard) Countries Products C1 P1 C P C3 P3 Definition of the Method k c,n = 1 k c,0 X p k p,n = 1 k p,0 X c M cp k p,n 1 M cp k c,n 1 k c,0 = X p k p,0 = X c M cp M cp

Limits and inconsistencies Log K c 5.0 4.5 4.0 3.5 3.0.5 Iterations are converging to a single (trivial) value A simple model shows that correlation with capabilities is lost Log Fitness Log K c w Fitness w.0 5.0 4.5 0 4.0 3.5 4 3.0 6.5 8.0 10 0 5 10 15 0 0 4 Iteration Order kc,n kc,n Σ kc,n 4 0 4 N 0 0 10 0 30 40 50 4 0 4 N 1 0 10 0 30 40 50 4 0 4 N 4 0 10 0 30 40 50 4 0 4 N 0 10 0 30 40 50 4 0 4 N 14 0 10 0 30 40 50 4 0 4 N 6 0 10 0 30 40 50 Capabilities 4 0 4 N 4 0 10 0 30 40 50 4 0 4 N 16 0 10 0 30 40 50 4 0 4 N 8 0 10 0 30 40 50

Conceptual limits Iteration should broaden the distribution! Fitnesscountry F USA =4.1 USA F (0) c X p M cp F NGA = F USA Nigeria F NGA =0.034 0 n

An example A Small World example Imagine a world with just 4 countries: We consider a small world made up by only four countries: USA, Austria, Mexico and Kazakhistan. We assume that each of them has a fixed fitness (F): Country Fitness USA 4 Austria 3 Mexico 0.5 Kazakhistan 0.1 We then perform a single step of the Method of Reflections, thus evaluating kp=<f>, and a single step of our Quality iteration: Qp=( p(1/fc)) 1. The average and the sums are performed only over the countries producing exported the p th product. products: If we calculate Q and k for products made by every possible combination of the four countries, this is what we obtain (Q and k are both equal to F when the producer is only one): Let s look at all the possible combinations of simultaneously Linear Non-Linear Producers k Q USA, Austria 3.50 1.71 USA, Mexico.5 0.44 Austria,Mexico 1.75 0.43 USA, Austria, Mexico.5 0.39 USA, Kazakhistan.05 0.098 Austria, Kazakhistan 1.55 0.097 USA, Austria, Mexico, Kazakhistan 1.90 0.080 We clearly see that the ranking defined by Q is strongly dependent on who is the worst of the

A New Metric Intensive 5.0 Extensive 5.0 Fitness 4.5 4.0 Log K c Log Fitness Log K c w 3.5 Complexity 3.0.5.0 5.0 4.5 0 4.0 3.5 4 3.0 6.5 8.0 10 F c,n = X p Q p,n = Log@K c D 4.5 M cp Q c,n 1 F c,n = D F c,n E F 1 P c M cp 4.0 3.5 3.0 Q 1 p,n = F.5 c,n 1 Log@Fitness w D.0 0 - -4-6 -8-10 N Q p,n D QE N A weighted version can also be defined by substituting M cp! W cp = q cp P c q cp 0 ess w 0 5 10 15 0 Iteration Order 0 5 10 15 0 Iteration Order

Pareto-Zipf distributions Intensive definition correlates with intensive measure of wealth Extensive definition correlates with extensive measure of wealth Black: PerCapitaGDP - Red: Fitness 01 Dashed: Zipf's Law Black: GDP - Red: Fitness w Dashed: Zipf's Law 1 1 Rescaled Variable H1 st =1L 0.1 0.01 0.001 Rescaled Variable H1 st =1L 0.1 0.01 0.001 10-4 10-5 10-6 1 5 10 0 50 100 Ranking 1 5 10 0 50 100 Ranking

Pareto-Zipf distributions Quality is not altered by weights! Logarithm of Rescaled Variable H1 st =1L 0-1 - -3-4 -5 Black: Quality w - Red: Quality 01 Dashed: Zipf's Law -6 0 1 3 4 5 6 7 Logarithm of Ranking

Sensitivity to errors and Missing data There are errors in the data! Must clean them, and be robust with respect to the ones which are still there Countries Products

Sensitivity to errors and Missing data Surprisingly NON-LINEAR performs better than LINEAR Correlation with modeled Fitness Added Noise In collaboration with F. Battiston

DEU FRA GBR USA ITA BEL JPN AUT CHE CZE NLD ESP CHN SWE DNK POL IND SVN SVK HUN KOR FIN BLR ISR CAN THA BGR PRT MEX BRA UKR SGP ROM ZAF TUR AUS EST RUS MYS GRC HRV LVA PRK IDN LTU AND PAN NZL IRL GEO NOR LBN MKD BIH PHL COL CYP URY ARG SLV CHL GTM AZE ARM PER ALB CRI VNM JOR KAZ 1 3 4 5 6 7 8 9 10 11 1 13 14 15 16 17 18 19 0 1 3 4 5 6 7 8 9 30 31 3 33 34 35 36 37 38 39 40 41 4 43 44 45 46 47 48 49 50 51 5 53 54 55 56 57 58 59 60 61 6 63 64 65 66 67 68 69 70 DEU FRA GBR USA ITA BEL JPN AUT CHE CZE NLD ESP CHN SWE DNK POL IND SVN SVK HUN KOR FIN BLR ISR CAN THA BGR PRT MEX BRA UKR SGP ROM ZAF TUR AUS EST RUS MYS GRC HRV LVA PRK IDN LTU AND PAN NZL IRL NOR LBN MKD BIH PHL COL CYP URY ARG SLV GTM ALB VNM JOR 1 4 7 5 8 6 9 13 11 1 10 3 16 17 15 14 19 8 6 0 31 35 34 37 1 9 18 38 36 44 3 5 5 4 59 57 46 30 33 3 43 40 7 49 39 48 61 65 41 71 56 50 53 4 58 51 68 67 70 47 60 1996 009 fitness_01 Ranking DEU USA JPN CHN FRA ITA GBR NLD BEL CAN CHE ESP KOR SWE AUT MEX SGP DNK MYS IND AUS IRL BRA CZE FIN RUS THA IDN POL ZAF ISR TUR PRT NOR HUN ARG NZL PHL SVN SVK GRC UKR BLR CHL ROM COL VEN PER BGR ARE HRV VNM LTU PAK EST URY KAZ IRN MAR CRI LVA TUN SAU GTM EGY HND PAN JOR BGD MKD 1 3 4 5 6 7 8 9 10 11 1 13 14 15 16 17 18 19 0 1 3 4 5 6 7 8 9 30 31 3 33 34 35 36 37 38 39 40 41 4 43 44 45 46 47 48 49 50 51 5 53 54 55 56 57 58 59 60 61 6 63 64 65 66 67 68 69 70 DEU USA JPN CHN FRA ITA GBR NLD BEL CAN CHE ESP KOR SWE AUT MEX SGP DNK MYS IND AUS IRL BRA CZE FIN RUS THA IDN POL ZAF ISR TUR PRT NOR HUN ARG NZL PHL SVN SVK GRC UKR BLR CHL ROM COL VEN PER BGR ARE HRV VNM LTU PAK EST URY KAZ IRN MAR CRI LVA TUN SAU GTM EGY PAN JOR BGD 3 4 1 6 5 7 8 9 13 1 10 11 16 14 18 3 7 1 15 30 8 19 9 5 17 4 0 33 34 6 31 36 3 41 44 40 43 35 46 39 50 48 4 53 70 54 49 38 57 37 51 47 55 68 59 6 58 66 60 5 45 67 56 65 64 61 1996 009 fitness_w Ranking USA JPN DEU FRA GBR ITA CHN BRA CAN ESP MEX IND NLD AUS KOR ARG CHE RUS TUR BEL SWE AUT DNK POL NOR SAU GRC ZAF FIN PRT THA COL ISR IDN IRN VEN EGY IRL SGP CHL PAK MYS PHL CZE PER NZL ARE HUN DZA BGD ROM UKR MAR NGA LBY VNM KWT URY HRV ECU SVK KAZ SVN TUN SYR GTM LBN BLR UZB CRI 1 3 4 5 6 7 8 9 10 11 1 13 14 15 16 17 18 19 0 1 3 4 5 6 7 8 9 30 31 3 33 34 35 36 37 38 39 40 41 4 43 44 45 46 47 48 49 50 51 5 53 54 55 56 57 58 59 60 61 6 63 64 65 66 67 68 69 70 USA JPN DEU FRA GBR ITA CHN BRA CAN ESP MEX IND NLD AUS KOR ARG CHE RUS TUR BEL SWE AUT DNK POL NOR SAU GRC ZAF FIN PRT THA COL ISR IDN IRN VEN EGY IRL SGP CHL PAK MYS PHL CZE PER NZL ARE HUN DZA BGD ROM UKR MAR NGA LBY VNM KWT HRV ECU SVK KAZ SVN TUN SYR GTM BLR 1 4 6 5 7 3 10 9 8 14 1 16 15 13 30 1 11 17 18 19 5 7 3 4 6 9 33 35 3 36 44 0 8 34 49 31 4 45 40 38 46 39 53 51 37 48 50 59 41 47 55 43 60 58 5 61 64 56 54 63 70 67 71 65 1998 007 GDP Ranking BRIC - Time Evolution GDP is not enough GDP Extensive Intensive In the intensive measure real development emerges IND CHN BRA RUS

The potential for growth ALB ALB AND AND ARG ARG ARM ARM AUS AUS AUT AUT AZE AZE BHR BHR BGD BGD BLR BLR BEL BEL BOL BOL BIH BIH BRA BRA BGR BGR CAN CAN CHL CHL CHN CHN COL COL CRI CRI HRV HRV CYP CYP CZE CZE DNK DNK ECU ECU EGY EGY SLV SLV EST EST FIN FIN FRA FRA GEO GEO GRC GRC GTM GTM HND HND HUN HUN ISL ISL IND IND IDN IDN IRL IRL ISR ISR ITA ITA CIV CIV JPN JPN JOR JOR KAZ KAZ KEN KEN KGZ KGZ LVA LVA LBN LBN LTU LTU MKD MKD MDG MDG MYS MYS MLT MLT MEX MEX MAR MAR NPL NPL NLD NLD NZL NZL NIC NIC PRK PRK NOR NOR OMN OMN PAK PAK PAN PAN PRY PRY PER PER PHL PHL POL POL PRT PRT ROM ROM RUS RUS SAU SAU SEN SEN SGP SGP SVK SVK SVN SVN ZAF ZAF KOR KOR ESP ESP SWE SWE CHE CHE SYR SYR TZA TZA THA THA TGO TGO TUN TUN TUR TUR UKR UKR ARE ARE GBR GBR URY URY USA USA UZB UZB VEN VEN VNM VNM ZMB ZMB ZWE ZWE ARG ARG CYP CYP EGY EGY GRC GRC ISL ISL IRL IRL ITA ITA JPN JPN LBN LBN PRT PRT ESP ESP URY URY VEN VEN -3 - -1 0 1 5 6 7 8 9 10 11 1995 Log[fitness] Log[GDPPC]

The potential for growth 1995 ALB ALB AND AND ARG ARG ARM ARM AUS AUS AUT AUT AZE AZE BHR BHR BGD BGD BLR BLR BEL BEL BOL BOL BIH BIH BRA BRA BGR BGR CAN CAN CHL CHL CHN CHN COL COL CRI CRI HRV HRV CYP CYP CZE CZE DNK DNK ECU ECU EGY EGY SLV SLV EST EST FIN FIN FRA FRA GEO GEO GRC GRC GTM GTM HND HND HUN HUN ISL ISL IND IND IDN IDN IRL IRL ISR ISR ITA ITA CIV CIV JPN JPN JOR JOR KAZ KAZ KEN KEN KGZ KGZ LVA LVA LBN LBN LTU LTU MKD MKD MDG MDG MYS MYS MLT MLT MEX MEX MAR MAR NPL NPL NLD NLD NZL NZL NIC NIC PRK PRK NOR NOR OMN OMN PAK PAK PAN PAN PRY PRY PER PER PHL PHL POL POL PRT PRT ROM ROM RUS RUS SAU SAU SEN SEN SGP SGP SVK SVK SVN SVN ZAF ZAF KOR KOR ESP ESP SWE SWE CHE CHE SYR SYR TZA TZA THA THA TGO TGO TUN TUN TUR TUR UKR UKR ARE ARE GBR GBR URY URY USA USA UZB UZB VEN VEN VNM VNM ZMB ZMB ZWE ZWE ARG ARG CYP CYP EGY EGY GRC GRC ISL ISL IRL IRL ITA ITA JPN JPN LBN LBN PRT PRT ESP ESP URY URY VEN VEN -3 - -1 0 1 5 6 7 8 9 10 11 Major rating downgrades (1995-010) Log[fitness] Log[GDPPC]

The potential for growth Log[GDPPC] Log[fitness]

The potential for growth RISKY ECONOMIES DEVELOPED COUNTRIES Log(GDPpc) UNDERDEVELOPED COUNTRIES DEVELOPING COUNTRIES Log(Fitness)

Network of Products 1 1 500 1161 1 50 50 100 146 1 500 1161 100 146 Contraction: P-P network Filtering Procedure: selecting dependency links The Network of Products

Network of Products Colours: international categorization

Network of Products Colours: communities

Communities in the Network of Products Hubs of low Complexity pointing to more complex products

Network of Products Hubs of low Complexity pointing to more complex products wrong links signal completely misplaced products

Spotting wrong links 9% correct ordering 8% misplaced

Paths in product space Development of Thailand 1975 1990 009

Time evolution The network is evolving (evidences of diversification) Most of the new links remain inside the community

Thanks for your attention!