The Products Space and Economic Complexity

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The Products Space and Economic Complexity
Cesar A. Hidalgo PhD
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How can we describe the economic development of
nations?
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Production Function
GDP per capita
 
Labor, Land, Capital, Technological Sophistication
Robinson, J. (1953) The production function and
the theory of capital, Review of Economic
Studies, vol XXI, 1953, pp. 81-106
Technical Change and the Aggregate Production FunctionRM Solow - The Review of Economics and Statistics, 1957
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CA Hidalgo, B Klinger, A-L Barabasi, R
Hausmann.Science (2007)
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Building the Forest
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Product
Country
Product
Product
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CA Hidalgo, B Klinger, A-L Barabasi, R
Hausmann.Science (2007)
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Where are the monkeys?
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Patterns of Comparative Advantage
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How do monkeys jump?
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Malaysia 1975
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Malaysia 1980
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Malaysia 1985
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Malaysia 1990
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Malaysia 1995
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Malaysia 2000
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China
1975
1985
2000
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Low density of Monkeys around this tree
High density of Monkeys around this tree
1985
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Countries are more likely to jump towards
products that are close by
CA Hidalgo, B Klinger, A-L Barabasi, R
Hausmann.Science (2007)
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Malaysia 1990
Chile 1990
High Densityin Chile
Low Densityin Malaysia
High Densityin Malaysia
Low DensityChile
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Malaysia 2000
Chile 2000
Exported by Chile
Not exported by Malaysia
Exported by Malaysia
Not Exported By Chile
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HAverage Density in Countries that transitioned
into the Product / Average Density in Countries
that did not transition into the product
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Convergence
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Hausmann, Hwang and Rodrik (2006), NBER Working
Paper 11905, (2006)
PRODY
34k
12k
PRODY
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Average PRODY of best 50 products after diffusing
Average PRODY of best 50 products after diffusing
Average PRODY of best 50 products now
Average PRODY of best 50 products now
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How good is yourneighborhood?
CA Hidalgo, B Klinger, A-L Barabasi, R
Hausmann.Science (2007)
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A similar story.
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What is matter made of?
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The challenge
Come up and implement the best possible numerical
description of a countrys economy

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First economic quantification
Saa
E-Sa Saa log(Saa)
HSa S2aa
DSa Saa F(Saa)
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Theory The Lego Theory Of Economic Complexity
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To create a product you need to know the
elements that go into it and how they connect
To create a Lego model you need to know the
pieces that go into it and how they connect
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How varied is your bucket of Legos.
How many Lego models can you potentially make
How many Lego models you know how to make
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Can we approach these questions without
lookingat the bucket of Legos?
How varied is your bucket of Legos.
How many Lego models you can potentially make
How many Lego models you know how to make
We do not know a priori which Lego models are
more valuable than others
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Countries
Capabilities
Products
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Countries
Products
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Methods The Method of Reflections
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Method of Reflections
Degree (Countries)
Degree (Products)
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Method of Reflections
k1 Standardness Average ubiquity of products
exported by a country
Product p1
Country C1
Product p2
Country C2
Product p3
Country C3
Product p4
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Method of Reflections
k1 Kinship Average diversification of a
products exporters
Product p1
Product p1
Country C1
Product p2
Product p2
Country C2
Product p3
Product p3
Country C3
Product p4
Product p4
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The Physics of the Method of Reflections
We characterize the system described by Maa by
using the following set of variables
(1)
(2)
We can understand what ka,n and ka,n represent by
taking them to the form
(3)
for ngt1, let us look as an example n2. We will
concentrate only on k2, as the math is symmetric
for the k s.
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We defined kn,2 as
(4)
Where aa is the set of neighbors of a indexed
by a .
We can use (2) to rewrite (4) as
(5)
We can take (5) into the form of (3) by noticing
that we can commute the summations by changing
the first sum from first two second neighbors
(6)
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Which satisfies the form of (3)
with
In this example we have been able to write ka,2
as a function of the k0s of its second nearest
neighbors. From this process we were able to
derive a new, content dependent similarity
function, that weighs in the relative value of
each of the second neighbors ks in the
expansion.
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Example
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We can solve the system for any n by reading the
similarity function from pictures
The n reflection of the method expands the
property of a node as a linear combination of the
properties of all nodes in the system with
coefficients that sum all possible paths
connecting that pair of nodes after. Each path
has a contribution which is given by the
multiplication of the inverse of the degrees of
the nodes through which the path goes through.
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Coefficient given by the probability that a
random walker that started in Spain would end up
in Panama after n steps in the bipartite network
kb,n
ka,0
kb,0
kc,0
kd,0
ke,0
kf,0
A B C D E F
Coefficient given by the probability that a
random walker that started in Spain would end up
at Sweden after n steps in the bipartite network
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Empirics Trade Data
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Complexity
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Poorly Diversified Producing Common Products
Highly Diversified Producing Common Products
Average Ubiquity of a Countrys Productsk1
Highly Diversified Producing Exclusive Products
Poorly Diversified Producing Rare Products
Diversification k0
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Dataset 1 (Year 2000)
Feenstra 129 countries 772 products (SITC-4)
How common are those Lego models
Number of Lego Models That You Make
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Dataset 2 (Year 2000)
Comtrade Data 103 countries 1241 products
(Harmonized System 4)
k1
0
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Dataset 3 (Year 2000)
152 Countries 318 products (NAICS)
k1
0
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Minimal Model Putting the Pieces together
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Le Model
Product
Country
Capabiliity
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150 countries, 1000 products, 150 capabilities
Pproducts0.05
Pcountries0.9
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132 countries, 500 products, 10 capabilities
Pcountries0.8
Pcountries0.5
Pproducts0.2
150 countries, 1000 products, 150 capabilities
Pcountries0.6
Pcountries0.9
Pproducts0.05
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132 countries, 500 products, 10 capabilities
Pcountries0.8
Pcountries0.5
Pproducts0.2
150 countries, 1000 products, 150 capabilities
Pcountries0.6
Pcountries0.9
Pproducts0.05
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132 countries, 500 products, 10 capabilities
Pcountries0.8
Pcountries0.5
Pproducts0.2
150 countries, 1000 products, 150 capabilities
Pcountries0.6
Pcountries0.9
Pproducts0.05
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Outlook Are you getting what you deserve?
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What you are getting
What you should/can get
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(k/k1)
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Conclusion
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Number of products in the data set
Number of Products Exported
RCA Cutoff
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Method of Reflections 20 year Growth
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)
PredictedVariable Growth(85,95) Growth(85,95) Growth(85,95) Growth(85,95) Growth(85,95) Growth(85,95) Growth(85,95) Growth(85,95) Growth(85,95) Growth(85,95) Growth(85,95)
Predictors
GDP per capita ppp(1985) -0.00176 0.000993 -0.00206 -0.00154 -0.00249 -0.00223 -0.00470 -0.00233 -0.00244 -0.00238 -0.00242
(-0.794) (0.533) (-0.882) (-0.497) (-0.735) (-0.688) (-1.478) (-0.758) (-0.849) (-0.804) (-0.831)
Entropy(1985) 0.00660 0.00828 0.00200 0.00322
(3.650) (2.600) (0.931) (0.896)
Herfindahl (1985) -0.0273 0.0116 -0.00414 0.00723
(-2.765) (0.760) (-0.406) (0.454)
k(1985) 6.62e-05
(2.080)
k1(1985) -0.000612
(-0.749)
k4(1985) 0.00169
(2.866)
k5(1985) 0.0321
(1.737)
k8(1985) 0.0338
(3.075)
k9(1985) 0.890
(2.713)
k18(1985) 0.401 38.88 35.05 37.26 35.57
(3.453) (2.952) (2.618) (2.849) (2.643)
k19(1985) 1127 1017 1080 1033
(2.928) (2.603) (2.829) (2.632)
Constant 0.0114 0.0137 0.00650 0.0338 -0.735 -19.29 -69.21 -23801 -21475 -22808 -21801
(0.751) (0.776) (0.437) (0.922) (-1.883) (-2.807) (-3.454) (-2.940) (-2.610) (-2.834) (-2.633)
N 97 97 97 97 97 97 97 97 97 97 97
Adjusted R2 0.195 0.115 0.192 0.118 0.206 0.247 0.202 0.274 0.274 0.268 0.268
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Method of Reflections 10 year Growth
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)
PredictedVariable Growth(85-95--05) Growth(85-95--05) Growth(85-95-05) Growth(85-95-05) Growth(85-95-05) Growth(85-95-05) Growth(85-95-05) Growth(85-95-05) Growth(85-95-05) Growth(85-95-05) Growth(85-95-05)
Predictors
GDP per capita ppp(85,95) -0.00235 0.000334 -0.00246 0.00112 -0.00395 -0.00311 0.00310 -0.00119 -0.00346 -0.00229 -0.00343
(-1.322) (0.209) (-1.349) (0.595) (-2.062) (-1.695) (2.188) (-0.707) (-1.899) (-1.327) (-1.850)
Entropy(85,95) 0.00699 0.00759 0.00458 0.00434
(4.962) (2.985) (3.002) (1.648)
Herfindahl(85,95) -0.0325 0.00422 -0.0210 -0.00162
(-3.890) (0.285) (-2.494) (-0.112)
k(85,95) 9.75e-05
(3.967)
k1(85,95) 0.000916
(2.543)
.k4(85,95) 0.00102
(5.577)
k5(85,95) 0.00329
(5.971)
k8(85,95) 0.00577
(5.056)
k9(85,95) 0.0152
(5.594)
k18(85,95) -0.000660 0.455 0.310 0.375 0.311
(-3.577) (4.306) (2.705) (3.428) (2.695)
k19(85,95) 1.158 0.789 0.954 0.792
(4.312) (2.709) (3.433) (2.699)
Constant 0.0171 0.0226 0.0153 -0.0186 -0.168 -1.178 0.102 -96.21 -65.48 -79.20 -65.78
(1.356) (1.602) (1.087) (-0.971) (-6.137) (-5.215) (3.107) (-4.308) (-2.705) (-3.428) (-2.695)
Observations 221 221 221 221 221 221 221 221 221 221 221
Adjusted R2 0.113 0.077 0.109 0.085 0.170 0.160 0.068 0.137 0.168 0.158 0.164
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Method of Reflections 5 year Growth
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)
Predicted Variable Growth(85-90-95-00-05) Growth(85-90-95-00-05) Growth(85-90-95-00-05) Growth(85-90-95-00-05) Growth(85-90-95-00-05) Growth(85-90-95-00-05) Growth(85-90-95-00-05) Growth(85-90-95-00-05) Growth(85-90-95-00-05) Growth(85-90-95-00-05) Growth(85-90-95-00-05)
Predictors
GDP per capita ppp(85,90,95,00) -0.00269 0.000292 -0.00286 0.000361 -0.00393 0.00224 0.00326 0.00310 -0.00257 0.000281 -0.00275
(-1.732) (0.211) (-1.785) (0.220) (-2.431) (1.767) (2.553) (2.479) (-1.686) (0.207) (-1.749)
Entropy(85,90,95,00) 0.00798 0.00885 0.00759 0.00851
(6.280) (3.760) (6.060) (3.680)
Herfindahl(85,90,95,00) -0.0373 0.00602 -0.0351 0.00636
(-4.970) (0.440) (-4.765) (0.474)
k(85,90,95,00) 0.000121
(5.351)
k1(85,90,95,00) 0.000953
(2.853)
k4(85,90,95,00) 0.00113
(7.074)
k5(85,90,95,00) 0.00260
(5.694)
k8(85,90,95,00) 0.00102
(3.474)
k9(85,90,95,00) 0.00312
(5.504)
k18(85,90,95,00) -0.000265 0.000632 0.000673 0.000647 0.000676
(-1.147) (2.131) (2.359) (2.234) (2.365)
k19(85,90,95,00) 0.00280 0.00259 0.00265 0.00260
(4.671) (4.494) (4.523) (4.493)
Constant 0.0166 0.0236 0.0142 -0.0160 -0.173 -0.224 0.0349 -0.163 -0.142 -0.132 -0.145
(1.497) (1.910) (1.144) (-0.933) (-7.646) (-4.198) (0.889) (-2.846) (-2.576) (-2.355) (-2.611)
Observations 451 451 451 451 451 451 451 451 451 451 451
Adjusted R2 0.090 0.062 0.089 0.071 0.136 0.071 0.013 0.057 0.127 0.101 0.125
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Method of Reflections 5 year growth, fixed
country effects
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)
Predicted Variables Growth(85-90-95-00-05) Growth(85-90-95-00-05) Growth(85-90-95-00-05) Growth(85-90-95-00-05) Growth(85-90-95-00-05) Growth(85-90-95-00-05) Growth(85-90-95-00-05) Growth(85-90-95-00-05) Growth(85-90-95-00-05) Growth(85-90-95-00-05) Growth(85-90-95-00-05)
Predictors
GDP per capita ppp(85,90,95,00) -0.0585 -0.0581 -0.0595 -0.0773 -0.0863 -0.0891 -0.0651 -0.0899 -0.0868 -0.0884 -0.0867
(-7.911) (-7.721) (-8.072) (-10.11) (-11.28) (-11.78) (-8.337) (-11.89) (-11.39) (-11.58) (-11.40)
Entropy(85,90,95,00) 0.0134 0.0247 0.00706 0.0142
(4.478) (4.037) (2.453) (2.435)
Herfindahl(85,90,95,00) -0.0390 0.0585 -0.0181 0.0360
(-2.842) (2.117) (-1.435) (1.410)
k(85,90,95,00) 0.000223
(3.710)
k1(85,90,95,00) 0.00238
(6.549)
k4(85,90,95,00) 0.000537
(2.922)
k5(85,90,95,00) 0.00366
(9.287)
k8(85,90,95,00) 0.000611
(2.801)
k9(85,90,95,00) 0.00410
(8.998)
k18(85,90,95,00) -0.000535 0.000601 0.000653 0.000618 0.000673
(-2.808) (2.801) (3.051) (2.879) (3.141)
k19(85,90,95,00) 0.00419 0.00395 0.00410 0.00389
(8.799) (8.164) (8.521) (8.031)
Constant 0.467 0.514 0.429 0.594 0.588 0.589 0.651 0.596 0.543 0.585 0.511
(7.427) (8.147) (6.592) (9.546) (8.165) (8.070) (8.203) (8.310) (7.315) (8.133) (6.583)
Observations 451 451 451 451 451 451 451 451 451 451 451
Within R2 0.2071 0.1784 0.2179 0.2991 0.3379 0.3373 0.1779 0.3372 0.3494 0.3415 0.3535
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Quantifying Economic Complexity
Maa
1 if country a exports product a
1006 product categories
132 countries
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Designer
Programmer
Hardware Knowledge
Mechanic
Webpage
Fashionable Electronic
Southern California Rich people toys
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