Do AI Activity Indices Really Measure AI Activity?

AI dashboards increasingly shape economic debate, yet their headline movements often conceal what changed. For a ratio, the same rise can reflect numerator growth, denominator decline, or both. This ambiguity creates structural non-identification: adding observations or richer fixed effects cannot recover the missing information. We propose three propositions showing that a relative-index regression blends the causal effect of interest with co-movement between focal and aggregate activity and shocks shared with the outcome. These components can give the coefficient either sign under a zero effect, or erase it under a nonzero effect. Publishing denominator levels changes what can be learned by removing the co-movement channel exactly, although shared-shock confounding remains. The problem extends to power: if most identifying variation comes from a handful of units, those units determine what the design can detect, however large the nominal sample looks. At a fixed standard error, the minimum detectable effect diverges as the effective cluster count approaches one, leaving a null result uninformative. We apply this framework to OECD.AI's hiring index and Eurostat employment across 24-27 European countries, where the detection floor exceeds the reported association. In a refreshed panel, that association disappears once the 2021 survey break is excluded. Ratio indices can still reveal concentration, timing, and co-movement, but establishing displacement requires more; our framework turns that boundary into a practical standard by making denominator levels a minimum disclosure requirement.