Product Space Properties

-The product space can classify products.
-Correlations between the position and value of goods.
-Changes in Time.

Using a network representation for the products space we can not only see which products are close to each other and the groups they form, but also their classifications and values. However, the network representation is nothing more than a powerful visualization technique and we still need to study the space properties using the entire proximity matrix complemented.

The Product Space Can Classify Products

The first property we study is the ability of the product space to classify goods into different classes. We compare our network representation with the clusters introduced by Leamer, as it is shown in figure 1, by using a different color for each product class. We see that the product space is not colored at random. Products in the same classes lie close to each other and tend to form clusters.

Although the classification performed by Leamer was done used a different methodology, the agreement between it and the structure of the product space is striking. Beyond the intuitive proof of Figure 7s we can tests the strength of these correlations by taking the average proximity between and within the products belonging to one of the clusters defined by Leamer (table 1s).

Table 1s. Average strength of the links between and within products as classified by Leamer.

Table 1s shows that the average proximity of products belonging to the same cluster is always higher than the proximity for products belonging to different clusters. But not all clusters have the same size, thus we look at the distribution of proximities for all links connecting products with the same or different Leamer classifications. Figure 8s shows the distribution of proximity for links connecting nodes with the same Leamer classification (blue) and for links connecting nodes annotated differently. It is clear from the figure that nodes with the same classification are connected by links with higher proximity values, and because of the large number of links present in the system (L>200'000), the difference between these two distributions is highly significant (log(P-value)<-300 ANOVA)

Figure 1. Network representation of the product space with nodes painted following the classification introduced by Leamer, sizes proportional to world trade and link strength specified as follows.

Although the classification performed by Leamer was done using a different methodology, the agreement between it and the structure of the product space is striking. Beyond the intuitive proof of figure 1 we can tests the strength of these correlation by taking the average proximity between and within the products belonging to one of the clusters defined by Leamer (table 1).

Table 1. Average strength of the links between and within products as classified by Leamer.

Table 1 shows that the average proximity of products belonging to the same cluster is always higher than the one of products belonging to different clusters. But not all clusters have the same size, thus we look at the distribution of proximities for all links connecting products with the same or different Leamer classifications. Figure 3 shows the distribution of proximity for links connecting nodes with the same Leamer classification (blue) and for links connecting nodes annotated differently. It is clear from the figure nodes with the same classification are connected by links with higher proximity values, and because of the large number of links present in the system (L>200'000), the difference between these two distributions is highly significant (log(P-value)<-300 ANOVA)

Figure 3. Distribution of proximity for links connecting products with the same Leamer classification (blue) and with a different one (red).

Correlations Between the Position and Value of the Goods.

All products have a value, which in this work we consider as the average income per-capita associated with that good or PRODY. It follows to ask: Are rich goods located in particular parts of the product space? By looking at its network representation and setting the size of the nodes proportional to the PRODY of a product (figure 9s), we see that the largest nodes are located either in the center or the down most portion of the network. At a first glance, we can say that there is a rich region of the product space, composed by machinery, electronics and chemicals, and a poor, peripheral region, made of some agricultural and labor intensive goods.

Figure 4. Network representation of the product space in which node sizes are proportional to PRODY.

We con look beyond the actual value of products and study the value of goods as a function of their distance between them. Basically we ask: Is this particular product at the top or at the bottom of the PRODY sophistication scale? To answer this we study the average PRODY of products at a given distance of a particular node. We define distance as -log(Proximity). Figure 10s shows six examples of products, three of them at the bottom of the sophistication scale (Footwear, Cotton Undergarments and Coats and Jackets) which belong to the labor intensive cluster and thus products far from them are richer or more attractive. On the other hand, chemicals such as organo sulphur compounds, phenols and cyclic alcohols appear at the top of the sophistication scale and see all other products as less sophisticated.

Figure 5. Prody as a function of distance for six different products in the space. Plots were calculated using the full proximity matrix.

We performed the same analysis for each product class and found that there are products at the top of the scale, at the bottom and in local maxima (Figure 11s). If the structural transformation only moves countries to more sophisticated goods, a local maximum would trap countries. Examples of these are cereals and animal agriculture products which are goods located in the periphery of the product space but have a relatively large PRODY compared to their neighbors.

	1.Petroleum		6. Cereals
	2. Raw Materials		7. Labor Intensive
	3. Forest Products		8. Capital Intensive
	4. Tropical Agriculture		9. Machinery
	5. Animal Agriculture		10. Chemicals

Figure 6. Average PRODY as a function fo the distance for products with a given Leamer Annotation.

Changes in Time

How fast does the product space changes in time? We can take a simple look at these by calculating the Pearson's Correlation Coefficient (PCC) between the matrices representing the product space in 1985, 1990 and 1998. Table 2s shows that the structure of the product space appears to be stable and that although links do change in time, after 10 or 13 years strong links remain strong and weak links remain weak. Thus products that are close tend to remain close and the ones that are far tend to stay far. The correlation was calculated over each pair of corresponding proximities between different time periods. Proximity values equal to zero were excluded from the calculation.

Table 2. Pearson's Correlation Coefficient between the product spaces generated with data from 1985, 1990 and 1998.