Do price trajectory data increase the efficiency of market impact estimation?

Market impact is an important problem faced by large institutional investors and active market participants. In this paper, we rigorously investigate whether price trajectory data from the metaorder increases the efficiency of estimation, from the view of the Fisher information, which is directly related to the asymptotic efficiency of statistical estimation. We show that, for popular market impact models, estimation methods based on partial price trajectory data, especially those containing early trade prices, can outperform established estimation methods (e.g. VWAP-based) asymptotically. We discuss theoretical and empirical implications of such phenomenon, and how they could be readily incorporated into practice.