Kids living at home are not going to do anything to change their usage patterns. They aren't going to be using that rebate to purchase a more efficient furnace or add insulation. If they drive a car, it will be whatever they can afford. The net difference in CO2 emissions for a live at home kid between having a carbon tax and not having one is going to be as near to zero as you can imagine. It isn't going to reduce CO2 consumption.
Meanwhile, had that rebate been tied only to items the improve efficiency, like furnace rebates, insulation, transit, etc, and available to everyone, no matter their income level, I'd argue you would see much greater reductions in emissions without it being handed out to people who are marginally effected and have no means to reduce CO2.
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