I think, really, to answer your question about how much vertical equity you are giving up if you gain more efficiency, you need a good model that incorporates these things. We'd have to crunch some numbers, and clearly we don't have those numbers here today.
On the flat tax thing, I was making the point that you need to consider the marginal tax rates that are coming from other taxes in addition to the personal income tax. If we took the personal income tax and just replaced it with a flat tax and ignored what the other elements of the tax system were doing, we'd have a bad system, which I think is in agreement with what Professor Kesselman is saying.
On the deductions, I think there's a bit of a problem in Canada: we have too much of a tendency to leap to the vertical equity question and to overlook the horizontal equity question. When we switched all of the deductions over to non-refundable credits, that was a bit of a symptom of that.
For example, on the family stuff, it's more appropriate to have a deduction for dependents than it is to have a credit. The argument is that you should tax people according to their ability to pay, and kids cost something. Part of my income morally belongs to my kids, not to me, so that ought to be deducted from my taxable income.
Sometimes we should think about horizontal equity first and vertical equity second.