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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 every taxpayer—i.e., where tax liability and income move in relative scale. A progressive tax is characterized by a greater than proportional growth in the tax liability in relation to the growth in income, and a regressive tax is characterizable by a less than proportional growth in the comparable liability. Ergo, progressive taxes are thought of as removing a lack of equality in income distribution, whereas regressive taxes are found to have the result of increasing these inequalities.

The taxes that are usually thought to be progressive include individual income taxes and estate taxes. Income taxes that are categorically progressive, however, may become less so for the upper-income categories—particularly if a taxpayer is allowed to reduce his tax base by declaring deductions or by leaving out some certain income aspects from his taxable income. Proportional tax rates when applied to lower-income groups can also be more progressive if such exemptions of a personal nature are claimed.

Income measured over the course of a given year may not definitely give the best measure of taxpaying requirement. For example, transitory growth in income could be saved, and within temporary declines in income a taxpayer might choose to pay for consumption by decreasing savings. Ergo, if taxation is compared with “permanent income,” it would be less regressive (or more progressive) than when it is compared with annual income.

Sales taxes and excises (save on luxuries) are usually regressive, because the dissemination of individual income consumed or spent for specific goods decreases as the rate of personal income rises. Poll taxes (also termed head taxes), calculated as a fixed amount per capita, obviously are regressive.

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

In analysing the economic purposes of taxation, it is relevant to distinguish between various ideas of tax rates. The statutory rates are those specified in the law; commonly these are marginal rates, but in some cases they are average rates. Marginal income tax rates denote the fraction of incremental income that is taken by taxation when income grows by one dollar. So, if tax liability grows by 45 cents when income grows 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 increases. Heavy analysis of marginal tax rates are required to take into account provisions apart from the formal statutory rate structure. If, for example, a particular tax credit (reduction in tax) reduces by 20 cents for each one-dollar growth in income, the marginal rate is 20 percentage points more than indicated in the statutory rates. Since marginal rates indicate how after-tax income moves in response to changes in before-tax income, they are the important ones for regarding incentive effects of taxation. It is even more complicated to understand the marginal effective tax rate applied to income from business and capital, as it may rely on such considerations 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 nothing under a consumption-based tax.

Average income tax rates determine the portion of total income that is paid in taxation. The pattern of average rates is the one that is important for considering the distributional equity of taxation. Under a progressive income tax the average income tax rate grows with income. Average income tax rates commonly rise with income, both because personal allowances are permitted for the taxpayer and dependents and also because marginal tax rates are graduated; on the flip side, preferential treatment of income received for the most part by high-income households could dampen these effects, forcing regressivity, as signified by average tax rates that decline as income grows.

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