Why is the estimation of metaorder impact with public market data so challenging?

Transaction cost analysis is a fundamental aspect of financial trading and market impact is the main source of costs for medium and large sized investors [1]. Thus, estimating the potential impact and cost of a trading decision is important to assess its profitability. This is particularly true and challenging for metaorders, i.e. sequences of orders and trades executed gradually over a long time period and following a single investment decision. In fact, while there is a vast literature on estimating and modeling impact of individual trades (or orders) from public data, it is less clear if and how such models can be used to estimate the expected price trajectory of a metaorder and the associated impact cost. To this end, the industrial practice is to estimate market impact and the associated cost of a metaorder by using data on actual metaorder execution (for academic researches using this approach, see, for example, [2-5]). However this approach presents some pitfalls.