The NYC studies actually look halfway decent. The big problem with serological tests is that even good ones may have, say, a 2% false positive rate. So if you t

The NYC studies actually look halfway decent. The big problem with serological tests is that even good ones may have, say, a 2% false positive rate. So if you test a population where nobody is infected, the test will say that 2% have been infected. To get good numbers, you need a population where lots of people have been infected. That will allow true positives to swamp the false positives, which is what happened in the NYC study that claimed 21% of people had already been infected. Even if it's really only 19%, that doesn't change much. You also need a good random sampling procedure. IIRC, the NYC study tested people shopping for essentials at mid-day. This underrepresents essential workers, people who are really good at self-isolation, and people who are currently sick. But still, it's not too bad. The New York City numbers suggest that very roughly 1% of people infected with the virus will die, depending on how you count probable but unconfirmed COVID deaths reported by NYC. This could be off by a factor of two in either direction, depending on how good the random sampling was, and the characteristics of a given population.