In a very short, satirical paper, James Heckman writes,

Provided conditional density (1) is assumed, we do not need to observe a variable in order to compute its conditional expectation with respect to another variable whose density can be estimated. For example, one can extend current empirical work in a variety of areas of economics to estimate the effect of income on happiness or the effect of income inequality on democracy. We conjecture that this powerful method can be extended to the more general case when X is not observed either.

Thanks to Alex Tabarrok for the pointer.