Professor Alan Barrett:

Not by definition, in the sense that many people are in negative equity, but their life carries on. Being in negative equity is not very pleasant, but if one can afford to repay the mortgage and pay all other bills, life goes on.

There is another practical consideration, in that given the proportion of the population in negative equity, if one were to exclude them, one could be talking about a property tax that would be double or more than it would otherwise be.