Regressive free tuition

Stephen Gordon finds Canadian tuition subsidies are largely a transfer to the upper middle class.

The tuition subsidy is distributed equally across the student population. But the student population is not representative of the population as a whole; upper income groups are over-represented. If we apply Bayes' Rule (is there anything it can't do?) to the information in this graph, we can calculate the percentage of the university student population that comes from each income quartile:
Lowest:    17% 
Second:   22% 
Third:      25.5% 
Highest:   35.5%
So 61% of the tuition subsidy goes to students from the top half of the income distribution, and the proportion of the budget that goes to the top quartile is more than twice as large as the share that goes to the lowest quartile.

Once you account for that higher income people pay more in taxes (and so may expect more in benefits), it doesn't look quite as regressive. But it's hardly a great equalizer. If you care about university access for poor people, means-tested scholarships are a better way of targeting things than uniformly low tuition rates. Or, means-tested loans. Or, even better, fixing the high schools attended by lower decile students so that they want to continue with post-secondary education when they have the academic ability to do so.

I'm curious how closely NZ data tracks Canadian data here; it would be kinda fun to figure out just how regressive the Greens' proposal to provide generalized transfers to university students would wind up being.