  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).
