At the meetings of the Canadian Economics Association in Montreal last month, the Innis Lecture was given by my colleague Jean-Yves Duclos. The title of his talk was 'Equity and Equality', and he offered the Quebec daycare program as a classic case of a policy that appears to be progressive, but which turns out not to be.

One of the Conservatives' election campaign promises was to provide financial support to parents directly, to the tune of $1,200 per child. Progressive-minded commentators have condemned this policy in no uncertain terms ; their preferred model runs more along the lines of the Quebec government's $7/day (formerly $5/day) program. Maybe it shouldn't.

Jean-Yves mentioned two types of equity that are generally discussed in public economics: vertical equity (which favours the redistribution from the top end of the income distribution to the lower end), and horizontal equity (which calls for identical treatment of identical individuals).

Suppose that it's been decided that public funds should be use to help parents defray the costs of child care. How does the Quebec model fit in?

First, let's consider two individuals (in practice, invariably the mother), A and B. A and B are identical in every way that matters, except for one thing: A would prefer to stay home and raise her children, while B would prefer to work. Both options are costly. A is obliged to sacrifice the income that she could have obtained by going to work, and B must deal with the financial costs of child care. (Of course, the costs are not just financial: both choices involve significant levels of stress and foregone opportunities.)

If the announced goal of a child-care policy is to help parents defray these costs, then according to the principle of horizontal equity, there's no reason for the government to choose to help one of these mothers and not the other. It turns out that the Quebec model fails this test: it chooses to help B, notwithstanding the fact that A and B are identical in every respect other than the choice of going to work or staying at home.

Since the only way to benefit from this program is to choose to go to work, it's not so much a child care program so much as a program designed to encourage mothers to return to work; Pierre Lefebvre and Phil Merrigan at UQAM have found that - unsurprisingly - the labour supply of women has increased (source - pdf file).

So the Quebec model fails the horizontal equity test. What about vertical equity? Mathieu Grenier, a MA student at UQAM wrote his thesis (available here) under the direction of Lefebre and Merrigan last year on this topic. Here are some of his findings, taken from Tables 5.5 and 5.6:

The utilisation rates and subsidies received increase with income. It's not difficult to come up with some plausible explanations for why this would be the case:

High-skilled women are more likely to choose to work than those with fewer skills.

The daycare system is almost entirely designed for those with 9-to-5 jobs, the sort that low-income workers are less likely to have.

So the Quebec model fails the vertical equity test as well.

What about the Conservatives' proposal? Since it's available to all parents, it satisfies the horizontal equity criterion. And since the payments are all equal and all subject to the (progressive) income tax, it satisfies the vertical equity criterion as well.

This doesn't mean that the Conservatives' proposal is perfect, of course. But if progressives are looking for a better alternative that satisfies the basic criteria for equity, it shouldn't be looking at the Quebec model.