The perennial question that a brand marketer gets asked always is what is ROI on brand investment. There are various ways one can answer that. The first order effect of that investment you can measure with the metrics of brand awareness and its reach. Second order effects of brand investment, can be mapped to down-line activities like sales volumes and sales prices.
However the problem with just relying on the measuring first order impact of brand ROI is that sometimes the impact does not carry on downstream and does not convert into incremental revenues. With just second order measurement, you can only prove co-relation and not causality.
Higher revenue is correlated to higher brand investment. Whether it is directly caused by that investment or your other marketing initiatives is very hard to prove. Trying to measure both, the direct attributes as well as the indirect attributions together and the whole analytical process of Brand ROI measurement starts to emulate a Complex Dynamic System.
The elements in first place are not linearly connected and then there is a self reinforcing dynamic feedback loop in place, which produces an emergent phenomenon which is totally unpredictable from its start state. This means what is achieved down line is never predictable from the initial conditions much like the celebrated flap of butterfly wings in amazon forest causing a storm back in New York. Though with adequate hindsight bias, any butterfly can claim to have awareness about the emergent storm however requesting for an encore might not reproduce the storm.
The central problem about measuring any complex dynamic system with a feedback loop ( like ecology, culture, markets, epidemics) is that there are no causal steps available to gain a direct measure. The moving parts are just too many to map the system into a coherent causal whole.