Assessing Economic Complexity with Input-Output Based Measures

I a * 1 = ∑ ( ^aj 1 + a∣ 2 ) and IA * * 1 = ∑ ( a j + a 2 j ) for j = 3, 4, ■■■■ N

Based on the degree of autonomy, a degree of block dependency can be defined as:

Gd(A*)=1-Ga(A*)

It is easy to see that in a matrix A of order N there are 2ⁿ - 2 blocks A* (because there are
∑(_k^N ) blocks A* with k = 1, ... , N-1).

So, the degree of (raw) dependency of system A is defined as:

∑_kGd(Ak*)

for which k varies from 1 to 2^N - 2 and Ak* represents a square block that includes the main
diagonal.

After correcting by the scaling factor given by the maximum value of G*(A) (which is a
function of N):

2 ⁿ — 2 ^n-2 — ι

2 ⁿ — 2

the dependency degree G(A) of A is:

11

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