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Taxes are categorized by the impact they have on the allocation of income and wealth. A proportional tax is the kind that applies the same relative burden on all taxpayers—i.e., in the case where tax liability and income move in relative proportion. A progressive tax is characterizable by a larger than proportional increase in the tax liability in regard to the growth in income, and a regressive tax is characterizable by a less than proportional growth in the related onus. Therefore, progressive taxes are seen as removing the lack of equality in income distribution, whereas regressive taxes can have the effect of an increase in these inequalities.

The taxes that are normally considered progressive include individual income taxes and estate taxes. Income taxes that are declarably progressive, however, could become less so for the upper-income categories—in particular if a taxpayer is permitted to lessen his tax base by claiming deductions or by excluding some income components from his taxable income. Proportional tax rates which are applied to lower-income groups will also be more progressive if exemptions of a personal nature are declared.

Income measured over the period of a given year does not definitely give the best measure of taxpaying requirement. For example, transitory growth in income can be saved, and within temporary declines in income a taxpayer may choose to pay for consumption by decreasing savings. So, if taxation is held in comparison along with “permanent income,” it can be less regressive (or more progressive) than when it is made comparable with annual income.

Sales taxes and excises (with the exception of those on luxuries) are mostly regressive, because the share of individual income consumed or spent on a specific good decreases as the amount of personal income grows. Poll taxes (also called head taxes), calculated as a standard amount per capita, clearly are regressive.

It is not simple to term corporate income taxes and taxes on business as progressive, regressive, or proportionate, principally because of the uncertainty about the ability of businesses to shift their tax expenses (see below Shifting and incidence). This difficulty of deciding who bears the tax burden rests essentially on whether a national or a subnational (that is, provincial or state) tax is being determined.

In considering the economic purpose of taxation, it is important to distinguish between several concepts of tax rates. The statutory rates are dictated in legislation; generally speaking these are marginal rates, but in some cases they are mean rates. Marginal income tax rates indicate the fraction of incremental income demanded by taxation when income rises by one dollar. Therefore, if tax burden grows by 45 cents when income increases by one dollar, the marginal tax rate is 45 percent. Income tax statutes usually contain graduated marginal rates—i.e., rates that increase as income increases. Careful analysis of marginal tax rates are required to take into account provisions as well as the formal statutory rate structure. If, for example, a particular tax credit (reduction in tax) reduces by 20 cents for each one-dollar rise in income, the marginal rate is 20 percentage points greater than indicated within the statutory rates. Since marginal rates signify how after-tax income is changed in response to changes in before-tax income, they are the necessary ones for assessing incentive effects of taxation. It is even more complicated to understand the marginal effective tax rate applicable to income from business and capital, because it may rely on factors including the structure of depreciation allowances, the deductibility of interest, and the provisions for inflation adjustment. A basic economic theorem determines that the marginal effective tax rate in income from capital is nothing under a consumption-based tax.

Average income tax rates indicate the fraction of total income that is paid in taxation. The pattern of average rates is the one that is important 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 grow with income, both because personal allowances are granted for the taxpayer and dependents and also because marginal tax rates are graduated; on the flip side, preferential treatment of income received predominantly by high-income households can dwarf these effects, forcing regressivity, as indicated by average tax rates that fall as income increases.

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