The Concept of Proximity

-The intuitive definition
-Details of the measurement
-References

The Intuitive Definition

The concept of proximity formalizes the intuitive idea that the ability of a country to produce a product depends on its ability to produce other ones. For example, a country with the ability to export apples will probably have most of the conditions suitable to export pears. They would certainly have the soil and the climate, together with the appropriate packing technologies, frigorific trucks and containers. They would also have the human capital, particularly the agronomists that could easily learn the pear business. However, when we consider a different business such as mining, textiles or appliance manufacture, all or most of the capabilities developed for the apple business render useless. Unfortunately this intuitive definition of proximity is, very cumbersome to measure. It requires quantifying the overlap between the set of markets related to each product. Thus, we measure proximity by using an outcome based method founded on the assumption that similar products are more likely to be exported in tandem.

Details of the measurement

First, a stringent measure of exports is needed. We do not want to consider marginal exports, and thus we say that a country exports a product whenever they have Revealed Comparative Advantage (RCA) in it. We use the Balassa[1] definition of RCA which is given by

where x(c,i) is the value of the exports of country c in the i'th good. Basically RCA is larger than one when the share of exports of country on a given product is larger than the share of that product on the global trade. This definition of RCA allows us to set a hard threshold for a countries export. When RCA(c,i) is greater or equal to 1 we say that country c exports product i, and when RCA(c,i)<1 that country is not an effective exporter of that product.

Using RCA as an indication of a country effectively exporting a good, we define the proximity between goods i and j as

where P(RCAi|RCAj) is the conditional probability of exporting good i given that you export good j. In this definition we consider the minimum between both conditional probabilities because in the case that a country is the sole exporter of a particular good we would have that the conditional probability of exporting any other good given that one would be equal to one for all other goods exported by that country. The converse is not true and by taking the minimum we get rid of this problem and at the same time symmetrize the proximity matrix.

References

[1] B. Balassa, The Review of Economics and Statistics, 68, 315 (1986).
[2] Ricardo Hausmann and Bailey Klinger, Structural Transformation and Patterns of Comparative Advantage in the Product Space, CID Working Paper No. 128, August 2006, -abstract-