Statistically reliable purchases studies are very challenging. People have multiple credit cards and sometimes pay cash. If you are buying a car you don't put it on the credit card. Additionally, you have multiple cookies/MAIDS that may or may not be associate with the same person/credit card. Even companies with Google or Facebook resources can't get this to work reliably. If it is a direct response advertiser, of course, you tell Google/Facebook that a purchase is made, but these advertisers are not the bulk of the market and many advertisers don't want to give Google that data.