||Composite Indicators are ever more diffused tools that not only measure phenomena such as innovation, but also shape discussions, policy design and implementation. The synthesis that emerges from the debate about their strengths and weaknesses recognized their intrinsic normative nature, and underlines the need for exercising conceptual and statistical clarity and transparency, and responsible use. In this paper, we consider composite indicator rankings as “fingerprints” of the values, ideas and priorities shared by the stakeholders involved in their development. Thus, we expect composite innovation indicators not only to reflect policy priorities through the underlying indicators that are the most important drivers of rankings, but also to be able to observe policy priority changes reflected in changes in the key drivers of ranks. We identify 3 key innovation policy priorities over the past two decades. By applying sensitivity analysis, we identify the statistically most important component indicators of two of the most widely used composite indices, the Summary Innovation Index and the Global Innovation Index. Examining these indicators, we find that neither of the two indices followed shifts in the innovation policy discourse from a focus on R&D to a focus on job creation. This discrepancy calls for both a better measurement of Schumpeterian Mark I entrepreneurship and firm scale-up activity at the country level, and the need for better communicating non-correlating measures of innovation.