Hidalgo and Hausmann's Economic Complexity Index measures the complexity of national economies in terms of product groups. Analogously to economic complexity index, we develop the Patent Complexity Index on the basis of a matrix of nations versus patent classes. Using linear algebra, the three dimensions countries, product groups, and patent classes can be combined into an integrated measure of complexity. We measure ECI, PatCI, and THCI during the period from 2000 to 2014 for the 34 OECD member states, the BRICS countries, and a group of emerging economies. The positive correlation between ECI and average income claimed as an argument for the predictive value of economic complexity index cannot be confirmed using our data. The three complexity indicators are significantly correlated between themselves, yet each captures another aspect of the complexity. THCI adds the trilateral interaction terms among the three bilateral interactions, and can thus be expected to capture the extent of systems integration between the global dynamics of markets and technologies in each national system of innovation. Of the world's major economies, Japan scores highest on all three indicators, while China has been increasingly successful in combining economic and technological complexity. Our empirical results raise questions about the interpretation and empirical fruitfulness of the complexity approach.
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