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Taxes can be distinguished by the effect they have on the allocation of income and wealth. A proportional tax is a tax that imposes the same relative onus on each taxpayer—i.e., in the case where tax liability and income move in the same proportion. A progressive tax is recognised by a greater than proportional rise in the tax burden in regard to the increase in income, and a regressive tax is recognisable by a less than proportional rise in the relative onus. Therefore, progressive taxes are seen as taking away a lack of equality in income distribution, while regressive taxes might increase these inequalities.

The taxes that are usually considered progressive include individual income taxes and estate taxes. Income taxes that are categorically progressive, however, could become less so for the upper-income group—in particular if a taxpayer is allowed to lower his tax base by claiming deductions or by taking some certain income parts from his taxable income. Proportional tax rates that are applied to lower-income demographics could also be more progressive if such exemptions of a personal nature are declared.

Income measured over the period of a given year might not absolutely provide the most appropriate measure of taxpaying requirements. For example, transitory rises in income can be saved, and in temporary declines in income a taxpayer may opt to provide for consumption by taking from savings. Therefore, if taxation is regarded along with “permanent income,” it would be less regressive (or more progressive) than if it is made comparable with annual income.

Sales taxes and excises (save those on luxuries) tend to be regressive, because the share of individual income consumed or spent for a specific good lessens as the amount of personal income is raised. Poll taxes (also called head taxes), calculated as a set amount per capita, clearly are regressive.

It is complicated to term corporate income taxes and taxes on business as progressive, regressive, or proportionate, principally due to the lack of certainty around the ability of businesses to shift their tax expenses (see below Shifting and incidence). This difficulty of nominating who bears the tax burden is dependant crucially on whether a national or a subnational (that is, provincial or state) tax is being debated.

In regarding the economic purpose of taxation, it is necessary to distinguish between various concepts of tax rates. The statutory rates will be dictated in law; usually these are marginal rates, but occasionally they are mean rates. Marginal income tax rates signify the fraction of incremental income demanded by taxation when income is increased by one dollar. Hence, if tax liability grows by 45 cents when income increases by one dollar, the marginal tax rate is 45 percent. Income tax legislation often contain graduated marginal rates—i.e., rates that grow as income grows. Careful analysis of marginal tax rates should review provisions other than the formal statutory rate structure. If, for example, a particular tax credit (reduction in tax) declines by 20 cents for each one-dollar rise in income, the marginal rate is 20 percentage points higher than specified within the statutory rates. Since marginal rates display how after-tax income is changed in response to changes in before-tax income, they are the relevant ones for assessing incentive effects of taxation. It is even more difficult to know the marginal effective tax rate applied to income from business and capital, since it may depend on such factors as the structure of depreciation allowances, the deductibility of interest, and the provisions for inflation adjustment. A basic economic theorem shows that the marginal effective tax rate in income from capital is nil under a consumption-based tax.

Average income tax rates display the fraction of total income that is paid in taxation. The pattern of average rates is the one that is relevant for appraising the distributional equity of taxation. Under a progressive income tax the average income tax rate increases with income. Average income tax rates commonly increase with income, both because personal allowances are permitted for the taxpayer and dependents and also because marginal tax rates are graduated; on the other side of things, preferential treatment of income received fundamentally by high-income households may dampen these effects, producing regressivity, as shown by average tax rates that fall as income increases.

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