Taxes can be differentiated by the effect they have on the allocation of income and wealth. A proportional tax is one that applies the same relative liability on all the taxpayers—i.e., when tax liability and income increase in the same levels. A progressive tax is recognisable by a more than proportional growth in the tax onus in relation to the increase in income, and a regressive tax is recognised by a less than proportional increase in the related onus. Ergo, progressive taxes are regarded as reducing a lack of equality in income distribution, whereas regressive taxes may increase these inequalities.

The taxes that are normally thought to be progressive include individual income taxes and estate taxes. Income taxes that are declarably progressive, however, might become less so in the upper-income class—in particular if a taxpayer is permitted to lower his tax base by declaring deductions or by excluding some certain income parts from his taxable income. Proportional tax rates that are applied to lower-income groups could also be more progressive if such personal exemptions are declared.

Income measured over the period of a given year does not necessarily come up with the most accurate measure of taxpaying ability. For example, transitory growth in income may be saved, and in temporary declines in income a taxpayer could elect to provide for consumption by reducing savings. Thus, if taxation is regarded with “permanent income,” it will be less regressive (or more progressive) than if it is compared with annual income.

Sales taxes and excises (excepting luxuries) are mostly regressive, because the share of own income consumed or spent for a specific good decreases as the amount of personal income rises. Poll taxes (also termed head taxes), levied as a flat amount per capita, clearly are regressive.

It is difficult to dictate corporate income taxes and taxes on business as progressive, regressive, or proportionate, principally because of uncertainty around 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 decided.

In analysing the economic purpose of taxation, it is relevant to differentiate between varied concepts of tax rates. The statutory rates are specified in legislation; usually these are marginal rates, but sometimes they are median rates. Marginal income tax rates indicate the fraction of incremental income that is taken by taxation when income grows by one dollar. Ergo, if tax liability increases by 45 cents when income grows by one dollar, the marginal tax rate is 45 percent. Income tax regulations commonly contain graduated marginal rates—i.e., rates that grow as income rises. Heavy analysis of marginal tax rates should consider provisions as well as the formal statutory rate structure. If, for example, a particular tax credit (reduction in tax) lowers 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 display how after-tax income moves in response to changes in before-tax income, they are the relevant ones for appraising 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 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 determine the fraction of total income that is paid in taxation. The pattern of average rates is the one that is relevant for considering the distributional equity of taxation. Under a progressive income tax the average income tax rate grows with income. Average income tax rates generally rise with income, both because personal allowances are permitted for the taxpayer and dependents and due to that marginal tax rates are graduated; on the other side of things, preferential treatment of income received predominantly by high-income households may dampen these effects, forcing regressivity, as indicated by average tax rates that lessen as income rises.

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