Today Tyler has a lengthy reply to my Twitter challenge:

you state your human capital/ability bias/signaling point estimates
using my typology?

Unfortunately, Tyler gets off track almost immediately:

[Bryan] does
not clearly define the denominator there: is it percentage of what you
spend on education or explaining what percentage of the variation in
lifetime earnings?  I’ll choose the latter…

The correct definition, of course, is neither.  The relevant denominator is the education premium, sometimes misleadingly called “the return to education.”  This is quite clear if you study my original post: The header for column two is “The effect of education on income.”  The whole point of the typology is to partition the observed effect of education on income into the three standard categories.

I’d love to see Tyler write a followup post using the correct denominator. 

Update: Tyler replies at length without making it any easier for me to understand his position.