Before revision:  We explore its implications from the perspective of empirical market microstructure, and argue that it provides a sensible inference procedure to cure some pathologies encountered in recent attempts to calibrate cross-impact matrices. 
After revision:  We explore its implications from the perspective of empirical market microstructure, and argue that it provides a sensible inference procedure to cure some pathologies encountered in recent attempts to calibrate cross-impact matrices. As an illustration, we determine the empirical cross impact matrix of US. Treasuries, and compare the results with recent alternative calibration methods.