There is a joke that conservatives oppose a carbon tax because they think it is a tax on capital, and liberals oppose a carbon tax because they think it is a tax on the poor; if they could just convince each other, we would have unanimous support for a carbon tax.
Joking aside, there is little dispute among economists that a carbon tax is, at the household level, regressive. The increased energy costs take up a larger fraction of a poor household’s budget than a rich one’s. But the sophisticated discussion about a carbon tax has always been about what do to with the carbon tax revenues, because that makes all the difference. Some options laid out in a 2013 Resources for the Future paper by Carbone et al, include: (A) reduction of capital taxes, including corporate income and personal income for capital investments (capital gains); (B) reduction of personal income taxes, including payroll taxes; (C) reduction of sales taxes (although these are mostly state); (D) rebate of the carbon tax proceeds as a lump-sum distribution to every household in the U.S.; and (E) deficit reduction. These are the serious options, and form the basis for further discussions about carbon taxes.
Roughly the same RFF team that authored that paper has launched a series of papers modeling the incidence of a carbon tax, along with several of the above options for carbon tax proceeds. Using a general equilibrium, overlapping generations model, Williams et al model a national $30/ton carbon tax with options A, B, and D (excluding the sales tax) for perfect revenue neutrality. In their model, the authors do not specify any specific statutory tax rate reductions or policies, but just assume the reduction of a capital or labor tax burden spends exactly the amount of carbon tax proceeds collected. In other words, they simply assume perfect revenue neutrality, without getting into the policy specifics. Taking 19 industries — 15 of them energy-intensive — 17 goods, and 8 income sources, they estimate the consumer surplus in each good market and the producer surplus from each income source. They then translate that into welfare effects for each household, in quintiles. Environmental effects are not included.
Sure enough, policy (A), a carbon tax paired with a reduction in capital taxes only favors the richest quintile; the lower 80% lose out. Policy (D), the lump-sum rebate, is steeply progressive, benefiting the three poorest quintiles, disadvantaging the second-richest quintile, and really socking it to the top quintile, saddling them with a cost of over $6,000. And reduction in income taxes (policy C) is in between, with every group losing out, but the richest quintile losing the most (only amounting to about $1500 in annual welfare loss).
This is the most recent and most comprehensive model on the impact of carbon tax proceeds on households from different income levels. It confirms what we mostly knew, but could not quantify: that a carbon tax is generally regressive, but can be made less so, and can even be made progressive, depending on how the carbon tax proceeds are used.