Page 19 - The Atlas of Economic Complexity

20 | THE ATLAS OF ECONOMIC COMPLEXITY

H ow do we go from what a country makes to words. So we can expect the diversity of words (products)

that a player (country) can make to be strongly related to the
what a country knows? If making a product
requires a particular type and mix of knowl-
number of letters (capabilities) that he (it) has. Long words
will tend to be rare, since they can only be put together by
edge, then the countries that make the
players with many letters. Hence, the number of players
product reveal having the requisite knowl-
edge (see Technical Box 2.1). From this simple
that can make a word tells us something about the variety
observation, it is possible to extract a few
of letters each word requires: longer words tend to be less
implications that can be used to construct
a measure of economic complexity. First,
Similarly, ubiquitous products are more likely to require few
countries whose residents and organizations possess more ubiquitous, while shorter words tend to be more common.
capabilities, and less ubiquitous products are more likely to
knowledge have what it takes to produce a more diverse require a large variety of capabilities.
set of products. In other words, the amount of embedded Diversity and ubiquity are, respectively, crude approxi-
knowledge that a country has is expressed in its productive mations of the variety of capabilities available in a country
diversity, or the number of distinct products that it makes. or required by a product. Both of these mappings are af-
Second, products that demand large volumes of knowledge fected by the existence of rare letters, such as Q and X. For
are feasible only in the few places where all the requisite instance, players holding rare letters will be able to put to-
knowledge is available. We define ubiquity as the number of gether words that few other players can make, not because
countries that make a product (Figure 2.1). Using this termi- they have many letters, but because the letters that they
nology, we can observe that complex products –those that have are rare. This is just like rare natural resources, such
contain many personbytes of knowledge–are less ubiqui- as uranium or diamonds. Yet, we can see whether low ubiq-
tous. The ubiquity of a product, therefore, reveals informa- uity originates in scarcity or complexity by looking at the
tion about the volume of knowledge that is required for its number of other words that the makers of rare words are
production. Hence, the amount of knowledge that a country able to form. If these players can only make a few other
has is expressed in the diversity and ubiquity of the prod- words, then it is likely that rarity explains the low ubiquity.
ucts that it makes. However, if the players that can make these rare words are,
A game of scrabble is a useful analogy. In scrabble, play- in general, able to put together many other words, then it
ers use tiles containing single letters to make words. For in- is likely that the low ubiquity of the word reflects the fact
stance, a player can use the tiles R, A and C to construct the that it requires a large number of letters and not just a few
word CAR or ARC. In this analogy, each product is repre- rare ones.
sented by a word, and each capability, or module of embed- Diversity can therefore be used to correct the informa-
ded knowledge, is represented by a letter. We assume that tion carried by ubiquity, and ubiquity can be used to cor-
each player has plenty of copies of the letters they have. Our rect the information carried by diversity. We can take this
measure of economic complexity corresponds to estimating process a step further by correcting diversity using a mea-
what fraction of the alphabet a player possesses, knowing sure of ubiquity that has already been corrected by diversity
only how many words he or she can make, and how many and vice versa. In fact, we can do this an infinite number
other players can also make those same words. of times using mathematics. This process converges after a
Players who have more letters will be able to make more few iterations and represents our quantitative measures of