We compare the predictions of the stationary Kyle model, a microfounded multi-step linear price impact model in which market prices forecast fundamentals through information encoded in the order flow, with those of the propagator model, a purely data-driven model in which trades mechanically impact prices with a time-decaying kernel. We find that, remarkably, both models predict the exact same price dynamics at high frequency, due to the emergence of universality at small time scales. On the other hand, we find those models to disagree on the overall strength of the impact function by a quantity that we are able to relate to the amount of excess-volatility in the market. We reveal a crossover between a high-frequency regime in which the market reacts sub-linearly to the signed order flow, to a low-frequency regime in which prices respond linearly to order flow imbalances. Overall, we reconcile results from the literature on market microstructure (sub-linearity in the price response to traded volumes) with those relating to macroeconomically relevant timescales (in which a linear relation is typically assumed).