Taxes can be categorized by the impact they have on the allocation of income and wealth. A proportional tax is the kind of tax that places the same relative liability on all taxpayers—i.e., in the case where tax liability and income increase in relative scale. A progressive tax is recognised by a more than proportional growth in the tax burden in relation to the growth in income, and a regressive tax is recognised by a less than proportional increase in the relative liability. Therefore, progressive taxes are thought of as taking away the lack of equality in income distribution, whereas regressive taxes are seen to 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, can become less so in the upper-income group—in particular if a taxpayer is permitted to lessen his tax base by declaring deductions or by removing certain income parts from his taxable income. Proportional tax rates that are applied to lower-income categories can also be more progressive if personal exemptions are declared.

Income measured over a given period does not absolutely offer the most appropriate measure of taxpaying status. For example, transitory growth in income may be saved, and during temporary declines in income a taxpayer may opt to finance consumption by reducing savings. Thus, if taxation is held in comparison with “permanent income,” it can be less regressive (or more progressive) than if made comparable with annual income.

Sales taxes and excises (excepting luxuries) are usually regressive, because the spread of one’s income consumed or spent for a specific good lowers as the level of personal income rises. Poll taxes (also termed head taxes), levied as a fixed amount per capita, patently are regressive.

It is not simple to determine corporate income taxes and taxes on business as progressive, regressive, or proportionate, because of a lack of certainty about the ability of businesses to shift their tax expenses (see below Shifting and incidence). This difficulty of dictating who bears the tax burden depends crucially on whether a national or a subnational (that is, provincial or state) tax is being considered.

In considering the economic purposes of taxation, it is important to distinguish between various ideas of tax rates. The statutory rates will include those nominated in legislature; generally these are marginal rates, but occasionally they are mean rates. Marginal income tax rates note the fraction of incremental income that is demanded by taxation when income rises by one dollar. Ergo, if tax burden grows by 45 cents when income grows by one dollar, the marginal tax rate is 45 percent. Income tax legislature usually contain graduated marginal rates—i.e., rates that grow as income grows. Structured analysis of marginal tax rates are required to take into account provisions other than the formal statutory rate structure. If, for example, a particular tax credit (reduction in tax) falls by 20 cents for each one-dollar rise in income, the marginal rate is 20 percentage points higher than specified by the statutory rates. Since marginal rates signify how after-tax income changes in response to changes in before-tax income, they are the necessary ones for appraising incentive effects of taxation. It is even more difficult to understand the marginal effective tax rate applicable to income from business and capital, since it may depend on considerations such as the structure of depreciation allowances, the deductibility of interest, and the provisions for inflation adjustment. A basic economic theorem grants that the marginal effective tax rate in income from capital is nothing under a consumption-based tax.

Average income tax rates indicate the portion of total income that is paid in taxation. The pattern of average rates is the one that is relevant for judging the distributional equity of taxation. Under a progressive income tax the average income tax rate rises with income. Average income tax rates commonly increase with income, both because personal allowances are granted for the taxpayer and dependents and due to that marginal tax rates are graduated; on the other hand, preferential treatment of income received fundamentally by high-income households can dwarf these effects, allowing regressivity, as shown by average tax rates that lower as income increases.

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