Taxes are differentiated by the effect they have on the distribution of income and wealth. A proportional tax is the kind that applies the same relative burden on all taxpayers—i.e., when tax liability and income grow in the same proportion. A progressive tax is recognised by a greater than proportional growth in the tax onus relative to the growth in income, and a regressive tax is recognised by a less than proportional rise in the related onus. Hence, progressive taxes are viewed as reducing inequalities in income distribution, but regressive taxes are found to have the effect of increasing these inequalities.
The taxes that are usually considered progressive include individual income taxes and estate taxes. Income taxes that are nominally progressive, however, may become less so in the upper-income categories—especially if a taxpayer is allowed to lower his tax base by nominating deductions or by excluding certain income parts from his taxable income. Proportional tax rates if applied to lower-income categories can also be more progressive if personal exemptions are made.
Income measured over the period of a year might not absolutely give the best measure of taxpaying requirement. For example, transitory rises in income could be saved, and in temporary declines in income a taxpayer may elect to pay for consumption by reducing savings. So, if taxation is compared along with “permanent income,” it should be less regressive (or more progressive) than when it is compared with annual income.
Sales taxes and excises (excepting luxuries) are mostly regressive, because the spread of own income consumed or spent for a specific good lowers as the amount of personal income rises. Poll taxes (also termed head taxes), nominated as a flat amount per capita, patently are regressive.
It is complicated to dictate corporate income taxes and taxes on business as progressive, regressive, or proportionate, due to the uncertainty about the ability of businesses to shift their tax expenses (see below Shifting and incidence). This difficulty of determining who bears the tax burden is dependant fundamentally on whether a national or a subnational (that is, provincial or state) tax is being debated.
In analysing the economic purposes of taxation, it is important to differentiate between various points of tax rates. The statutory rates include those specified in law; generally speaking these are marginal rates, but sometimes they are average rates. Marginal income tax rates denote the fraction of incremental income that is demanded by taxation when income is increased by one dollar. Hence, if tax liability rises by 45 cents when income rises 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 rises. Careful analysis of marginal tax rates are required to regard provisions in addition to the formal statutory rate structure. If, for example, a particular tax credit (reduction in tax) declines by 20 cents for each one-dollar increase in income, the marginal rate is 20 percentage points greater than specified in the statutory rates. Since marginal rates specify how after-tax income is changed in response to changes in before-tax income, they are the appropriate ones for regarding incentive effects of taxation. It is even more difficult to realise the marginal effective tax rate applied to income from business and capital, because it may be reliant on considerations including the structure of depreciation allowances, the deductibility of interest, and the provisions for inflation adjustment. A basic economic theorem holds that the marginal effective tax rate in income from capital is zero under a consumption-based tax.
Average income tax rates display the part 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 increases with income. Average income tax rates usually grow with income, both because personal allowances are granted for the taxpayer and dependents and also because marginal tax rates are graduated; on the other hand, preferential treatment of income received fundamentally by high-income households may dampen these effects, allowing regressivity, as shown by average tax rates that lessen as income grows.
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