How Many Dimensions Do We Trade in? Product Space Geometry and Latent Comparative Advantage

This paper proposes a new quantitative implementation of Balassa's idea that export composition and revealed comparative advantage inform the relationship between endowments in domestic factors of production and exports. It proposes that the export composition of countries is close to a low-dimensional manifold or "Product Space" within the space of export composition, which has as many dimensions as product lines. The Product Space corresponds to a few latent endowments explaining the structure of the trade matrix. The model uses non-linear techniques to identify the Product Space from the 2010 export matrix of 128 countries and 61 products, and to estimate the latent factors of endowments by country. It formalizes a concept of latent comparative advantage, which has practical country specific applications, relevant for "trade competitiveness" policies. Compared with classical revealed comparative advantage, the model assesses how well countries are matching their potential implied by the latent variables, and also identifies products for which the latent advantage is not yet revealed (extensive margin). The data suggests that the degree of overlap between latent and revealed advantage is a metric of "trade competitiveness."