A new metrics for the Economic Complexity of countries and products

Transcription

1 A new metrics for the Economic Complexity of countries and products Andrea Tacchella, Matthieu Cristelli, Guido Caldarelli, Andrea Gabrielli, Antonio Scala, Luciano Pietronero Istituto dei Sistemi Complessi, CNR Roma Dept. of Physics, La Sapienza - University of Rome (WEB page: SAB ANALYTICS FOR SIS PREDICTION AND MANAGEMENT ETH Zurich, 1/9/1

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

3 Specialization vs. Diversification Real World: dynamic markets, globalized Triangular Shape Countries Complexity Products C. Hidalgo and R. Hausmann (PNAS 9)

4 Extracting information from the matrix k c,1 ubiquity of products DZA DZA BHS BHS BRB BRB BLZ BLZ BEN BEN BFA BFA BDI BDI CMR CMR CAF CAF DOM DOM SLV SLV EST EST ETH ETH FJI FJI GAB GAB GMB GMB GHA GHA GIN GIN GUY GUY HTI HTIHND HND HKG HKG IRN IRN CIV CIV JAM JAM JOR JOR KEN KEN KGZ KGZ MAC MAC MDG MDG MWI MWI MLI MLI MLT MLT MUS MUS MDA MDA MNG MNG MAR MAR MOZ MOZ NPL NPL NCL NCL NIC NIC NER NER NGA NGA OMN OMN PAK PAK PNG PNG RWA RWA KNA KNA WSM WSM SAU SAU SEN SEN SLE SLE LKA LKA SDN SDN SYR SYR TJK TJK TZA TZA TGO TGO TTO TTO TKM TKM UGA UGA ZMB ZMB ZWE ZWE k c, k c,1 I II III IV k c, diversification Low diversification, high ubiquity High diversification, low ubiquity First order information

5 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, X p k p,n = 1 k p, X c M cp k p,n 1 M cp k c,n 1 k c, = X p k p, = X c M cp M cp

6 Limits and inconsistencies Log K c Iterations are converging to a single (trivial) value A simple model shows that correlation with capabilities is lost Log Fitness Log K c w tness w Iteration Order kc,n kc,n Σ kc,n N N N N N N Capabilities N N N

7 Conceptual limits Iteration should broaden the distribution! Fitnesscountry F =.1 F () c X p M cp F NGA = F Nigeria F NGA =.3 n

8 An example A Small World example Imagine a world with just countries: We consider a small world made up by only four countries:, Austria, Mexico and Kazakhistan. We assume that each of them has a fixed fitness (F): Country Fitness Austria 3 Mexico.5 Kazakhistan.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, Austria , Mexico.5. Austria,Mexico , Austria, Mexico.5.39, Kazakhistan.5.98 Austria, Kazakhistan , Austria, Mexico, Kazakhistan 1.9.8

9 A New Metric 5. Fitness.5. Log K c 3.5 Complexity 3..5 F c,n = X p Q p,n = Intensive M cp Q c,n 1 F c,n = F c,n D F E 1 P c M Q 1 p,n = cp F c,n 1 N Q p,n D QE N Extensive A weighted version can also be defined by substituting M cp! W cp = q cp P c q cp Log Fitness Log K c w Log@Fitness w D ss w Iteration Order Iteration Order

10 Pareto-Zipf distributions Intensive definition correlates with intensive measure of wealth Extensive definition correlates with extensive measure of wealth Black: PerCapitaGDP - Red: Fitness 1 Dashed: Zipf's Law Black: GDP - Red: Fitness w Dashed: Zipf's Law 1 1 Rescaled Variable H1 st =1L Rescaled Variable H1 st =1L Ranking Ranking

11 Pareto-Zipf distributions Quality is not altered by weights! Logarithm of Rescaled Variable H1 st =1L Black: Quality w - Red: Quality 1 Dashed: Zipf's Law Logarithm of Ranking

12 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

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

14 EST PRK AND BIH SLV JOR EST PRK AND BIH SLV JOR fitness_1 Ranking PAK EST IRN MAR TUN SAU HND JOR PAK EST IRN MAR TUN SAU JOR fitness_w Ranking SAU IRN PAK DZA MAR NGA LBY KWT TUN SYR UZB SAU IRN PAK DZA MAR NGA LBY KWT TUN SYR GDP Ranking BRIC - Time Evolution GDP is not enough GDP Extensive Intensive In the intensive measure real development emerges

15 The potential for growth AND AND BIH BIH SLV SLV EST EST HND HND CIV CIV JOR JOR KEN KEN KGZ KGZ MDG MDG MLT MLT MAR MAR NPL NPL NIC NIC PRK PRK OMN OMN PAK PAK SAU SAU SEN SEN SYR SYR TZA TZA TGO TGO TUN TUN UZB UZB ZMB ZMB ZWE ZWE Log[fitness] Log[GDPPC]

16 The potential for growth 1995 AND AND BIH BIH SLV SLV EST EST HND HND CIV CIV JOR JOR KEN KEN KGZ KGZ MDG MDG MLT MLT MAR MAR NPL NPL NIC NIC PRK PRK OMN OMN PAK PAK SAU SAU SEN SEN SYR SYR TZA TZA TGO TGO TUN TUN UZB UZB ZMB ZMB ZWE ZWE Major rating downgrades (1995-1) Log[fitness] Log[GDPPC]

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

18 Synchronization AFG AFG AND AND BTN BTN BIH BIH KHM KHM GUY GUY HND HND KGZ KGZ LAO LAO MLT MLT MNG MNG NPL NPL NIC NIC PRK PRK TJK TJK TKM TKM UZB UZB AFG AFG AND AND BTN BTN BIH BIH KHM KHM GUY GUY HND HND KGZ KGZ LAO LAO MLT MLT MNG MNG NPL NPL NIC NIC PRK PRK TJK TJK TKM TKM UZB UZB

19 Organizers question Can economics as a scientific discipline that must extricate itself from its current conceptual crisis, benefit from concepts, methods and insights developed in other disciplines, notably the natural sciences? Yes! But greater benefits can come if not the Natural Sciences are exported, but rather Natural Scientists: their vision and their attitude can be even more valuable than their models.

20 Thanks for your attention!