Does the indexing of government transfers make carbon pricing progressive?

"We analyze both the uses side and the sources side incidence of domestic climate policy using an analytical general equilibrium model, taking into account the degree of government program indexing. When transfer programs such as Social Security are explicitly indexed to inflation, higher energy prices automatically lead to cost-of-living adjustments for recipients. We show results with no indexing, 100 percent indexing, and partial indexing based on our analysis of actual transfer programs. When households are classified by annual income, the indexing of U.S. transfers is not enough to offset the regressive uses side, but when they are classified by annual expenditures as a proxy for permanent income, transfer indexing does offset regressivity across the lowest income groups"--National Bureau of Economic Research web site.