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We build on the interpretation of the Economic Complexity method as Correspondence Analysis (CA), and propose that the Canonical form of CA (CCA), which originated in the ecology literature, can be used to calculate multi-dimensional economic complexity. The traditional (CA) way of calculating economic complexity includes no "external" information such as countries' development characteristics to facilitate interpretation of "complexity". This has led to a wide range of fairly ad hoc interpretations of economic complexity on the basis of ex-post correlation to a long list of other variables. By the ex-ante inclusion of a number of country variables in the construction of the complexity indicators, CCA enables better interpretation, also in the case of multi-dimensional indicators. The analysis is further facilitated by another element of the ecologists' toolbox, the so-called biplots, which are CCA-based graph embeddings that represent a lower-dimensional product-space in which products and countries are positioned together, in mutual correspondence to each other. We show that in this way, CCA provides a richer account of development in many of its aspects, especially economic growth.

In this paper, we investigate the nature of the density metric, which is employed in the literature on smart specialization and the product space. We find that although density is supposed to capture relatedness between a country's current specialization pattern and potential products that it may diversify into, density is also correlated strongly to the level of diversification of the country, and (less strongly) to the ubiquity of the product. Together, diversity and ubiquity capture 93% of the variance of density. We split density into a part that corresponds to related variety, and a part that does not (i.e., unrelated variety). In regressions for predicting gain or loss of specialization, both these parts are significant. The relative influence of related variety increases with the level of diversification of the country: only countries that are already diversified show a strong influence of related variety. In our empirical analysis, we put equal emphasis on gains and losses of specialization. Our data show that the specializations that were lost by a country often represented higher product complexity than the specializations that were gained over the same period. This suggests that 'smart' specialization should be aimed at preserving (some) existing specializations in addition to gaining new ones. Our regressions indicate that the relative roles of related and unrelated variety for explaining loss of specialization are similar to the case of specialization gains. Finally, we also show that unrelated variety is also important in indicators that are derived from density, such as the Economic Complexity Outlook Index.

We aim to contribute to the literature on product space and diversification by proposing a number of extensions of the current literature: (1) we propose that the alternative but related idea of a country space also has empirical and theoretical appeal; (2) we argue that the loss of comparative advantage should be an integral part of (testing the empirical relevance of) the product space idea; (3) we propose several new indicators for measuring relatedness in product space; and (4) we propose a non-parametric statistical test based on bootstrapping to test the empirical relevance of the product space idea.