As far as I'm aware, no country is doing that yet except Singapore; but fifteen minutes ago they announced that they would be supporting serological studies to

As far as I'm aware, no country is doing that yet except Singapore; but fifteen minutes ago they announced that they would be supporting serological studies to reconcile the models with the numbers. You could think of the numbers we're seeing as a diagonal 2D slice on a more complex manifold: we're either seeing spread like this because there is a large mass of asymptomatic carriers, or because there are unexpectedly-tenacious mechanisms for infection. A serological study, which you would usually only conduct post-mortem (but in light of the conditions, we may have use for an interim study), would shed light on how many people had been infected without knowledge, and give us some estimates of how infectious asymptomatic carriers are. Short of that, in countries where testing has been highly available and unconditional, you can begin to get a picture of that; it's not as good though, since people who go for testing are still self-selecting to some extent.