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We analyze the distributional and efficiency impacts of different allowance allocation schemes for a national cap and trade system using the USREP model, a new recursive dynamic computable general equilibrium model of the U.S. economy. We consider allocation schemes applied to a comprehensive national cap and trade system that limits cumulative greenhouse gas emissions over the control period to 203 billion metric tons. The policy target approximates national goals identified in pending legislation. We find that the allocation schemes in all proposals are progressive over the lower half of the income distribution and proportional in the upper half of the income distribution. We also find that carbon pricing by itself (ignoring the return of carbon revenues through allowance allocations) is proportional to modestly progressive. This striking result follows from the dominance of the sources over uses side impacts of the policy and stands in sharp contrast to previous work that has focused only on the uses side. Lower income households derive a large fraction of income from government transfers and, reflecting the reality that these are generally indexed to inflation, we hold the transfers constant in real terms. As a result this source of income is unaffected by carbon pricing, while wage and capital income is affected.