Sunday, February 26, 2017

A Simple Measure of Economic Complexity

Via arXive, Quantitative Finance > Statistical Finance, Jan. 2016:
We show from a simple model that a country's technological development can be measured by the logarithm of the number of products it makes. We show that much of the income gaps among countries are due to differences in technology, as measured by this simple metric. Finally, we show that the so-called Economic Complexity Index (ECI), a recently proposed measure of collective knowhow, is in fact an estimate of this simple metric (with correlation above 0.9).
1 Introduction
The standard approach to economic growth and development simplifies a country’s whole production to three aggregate s — GDP, labor and capital — thus disregarding its complexity. Complexity of production has to do with the diversity of products a country makes, which is itself a manifestation of the diversity of productive knowledge by which many products can be made — namely the various skills and technical knowledge applied by workers or automated by machines . Products differ precisely by the amount of knowledge involved in their production, which goes from zero for natural resources sold in the raw to maximum values for highly complex products such as aircrafts.

It is along such line of thought that emerged a literature , by Hausmann and Hidalgo notably, which links complexity of production to economic development [ 1 - 3 ] . Rich countries make various products, especially complex products, while poor countries make fewer and more rudimentary ones . In fact the mere number of products a country makes, or its diversification , indicates its development. Though basic , this opposes the long tradition in economics that link s international prosperity to the specialization of countries . Hausmann and Hidalgo propose a more elaborate metric called Economic Complexity Index (ECI) to quantify the amount of productive knowledge (or knowhow ) that underlies a country’s production. ECI is therefore, to use a more traditional term, a measure of a country’s technology — if technology is taken to mean precisely the sum of practical knowledge within a society . Similarly, we can define the technological sophistication of a product by the amount of knowhow involved in its production. This is measured by the Product Complexity Index (PCI) in the authors’ theory. In fact ECI and PCI are jointly computed, based on the idea that an economy’s technology is reflected in the products it makes, and, vice versa, a product reflects the technologies of the economies making it. A reformulation of the same idea was suggested by Caldarelli et al., which we shall also consider [ 4 - 6 ] . There, the metrics are named Country Fitness and Product Complexity.

Our goal in this paper is to propose a simpler and mo re natur al measure of technology : the logarithm of diversification . This metric derives from the following basic combinatorics. First, a product is but some transformed natural resources, namely some raw materials to which is applied a set of knowhow to turn it in to a valuable outcome . Second, and more fundamentally, knowledge comes in discrete units ( or ‘ bits ’) that combine to make more and more sophisticated knowledge .

Therefore with k units of knowhow , a country can make potentially 2 k d products, whose sophistication s range from zero for natural resources ( sold in the raw) to k . Thus, we can estimate the total amount of knowhow k involved in a country’s production by its log - diversification ( up to a scaling constant) . Only, bits of knowledge don’t combine such randomly: a collection of ideas is productively relevant only when it form s a coherent set of productive knowledge ( namely when they can be put together to transform a raw material ) .

So we shall develop a more realistic (yet still simple ) model of this combinatorics of knowhow . The point remains , however: log - diversification is the natural measure of technology . We show that this simple metric explains much of the income differences among countries. Finally, we show theoretically and empirically that ECI is in fact an estimate of this metric , in standardized form, while Fitness is linked to it by construction. But first we develop a simple conceptual framework and describe the data used throughout...
...MUCH MORE (14 page PDF)

Sticking with the "simple is good" theme, here's a post from 2011:
How to Predict a Nation's GDP per Capita at r=.97 Using "Economic Freedom and average citizenry IQ -- plus slight tweaks from trading block membership and oil"