Progressive tax

Under tax progression is defined as the increase in the tax rate depending on the taxable income or assets. There are different views on whether only the average tax rate or the marginal tax rate should rise with the tax base.

• 5.1 Indirect progression
• 5.2 Staged Progression
• 5.3 Linear Progression

• 6.1 Proportional Tariff
• 6.2 Stufig progressive tariff
• 6.3 Linear progressive tariff

• 7.1 Germany 7.1.1 calculation
• 7.1.2 Tariff History

History

A progressive income tax rate in the UK was first introduced by William Pitt the Younger in his budget of December 1798. Pitt's new graduated (progressive ) income tax began at a tax cost of 2 old pence in the pound (1/ 120) on income above £ 60 and rose to the maximum value of 2 shillings per pound ( 1/10) on incomes over £ 200.

In the Prussian local tax law of 14 July 1893 ( after the then Finance Minister Johannes Miquel also called " Miquel tax reform " ) introduced a progressive tax systems in the German -speaking world. The tax on such income tax increased from 0.62 % (for annual income 900-1050 Mark ) up to 4% ( for annual income over 100,000 dollars). Progressive tariffs have been introduced in many European countries in the following period, since 1913, for example, in the United States. How much of the tax rate increases depending on income, but is very different in different States.

Example

The tax progression can best be understood if one sets them apart from other taxation models:

• In the poll tax every citizen pays the same amount of tax, irrespective of the level of income. The tax rate is falling here in relation to income, as higher incomes are taxed proportionately lower.
• With a flat tax, ie a constant tax rate, everyone pays the same proportion of their income. The tax rate is 10%, pay someone who earns 10,000 euros, 1,000 euros in taxes and another who earns 20,000 euros, 2,000 euros in taxes ( not including the basic personal allowance ).
• With a progressive, so ( depending on income ) rising control someone who earns more than another pays a higher percentage of his income in taxes. So Worth of a 10,000 euro, and another 20,000, so for example pays the first 10% in taxes, EUR 1,000, but the second 15 %, that is 3,000 euros. Here the first 10,000 euros will be taxed at 10%, the second 10,000 Euros but with 20%.

Justification

This discrimination of those who earn more touches a fundamental principle of democracy: equality before the law. Therefore, there is agreement that requires specific reasons to justify this unequal treatment.

Politically, economically and socially progressive taxation is often justified by the diminishing marginal utility of increasing income and wealth: With the increase no longer essential to life, but only Luxury demand is increasingly being consumed.

Often, the higher tax rate is warranted for more earners by the so-called theory of sacrifice. The theory of sacrifice transmits the law of diminishing marginal utility to the taxation theory: Worth someone for example 50,000 euros, was the first euro, he deserves more useful to him than the last. Therefore, a tax on every additional euro earned is less stressful. In order to produce a stress equality between little and much earners, a progressive tax rate was necessary.

This economic science-based justification becomes increasingly questioned. Instead, considerations of justice and the welfare state principle be cited as justification.

Effects

The tax progression leads to a disproportionate increase in the tax burden on rising income or assets. Higher incomes are thus taxed not only higher in absolute terms, but also as a percentage. Simply put to a big earners leave for example, half of his income, a low-income one-tenth. This leads to a redistribution.

Effective progression

Through progressive income taxation, the unequal distribution of income is more or less reduced greatly. The effective Progressionsmaß ( Musgrave / Thin) determines the degree of unequal distribution of the Gini coefficient ( a possible unequal distribution code). The progression index Musgrave / Thin is defined for a given distribution of income before the tax deduction () and then the distribution () as follows:

This is the value of one of the Gini coefficient for total income inequality. The related thereto deviation of the Gini coefficient after taxes in proportion to the deviation of the Gini coefficient before taxes thus yields the effective Progressionsmaß.

The following relationship applies:

• Progressive Tariff:
• Proportional Tariff:
• Sliding scale:

For example, in 2004 was the Gini coefficient for the distribution of income before taxes 51.2 % and 47.3 % after tax. From the two Gini coefficients results in an effective Progressionsmaß of.

Cold progression

As cold progression is a - just to be observed over several years away and by inflation in conjunction with the related tax progression - denotes increase in real tax burden.

Species

Indirect progression

In a one-step tariff ( the flat tax or flat tax ) the interaction of the basic deduction and marginal tax rate leads (also called " limit load " ) to a rising income with the average tax rate. With increasing taxable income, the actual tax burden ( the average tax rate ) approaches flattening of the marginal tax rate. This is called an indirect progression, as the marginal tax rate itself is not progressive, but only the average tax rate. The top tax rate is in this case identical to the input tax rate and is, for example, in Bulgaria 10% or 23% in Latvia.

Staged progression

When levels marginal rate tariff, there are basic parameters ( steps), from which for each euro comes a higher marginal tax rate applied to the stage. Levels marginal rate tariffs are made up of several zones with constant (flat verlaufendem ) marginal tax rate. Again, it comes to an income-related increase in the average tax rate, however, has a dependent of the stage ripple. This follows from the nature of the calculation of the average tax rate as the ratio of tax and taxable income. The number of steps is at least two (Poland ) or three ( for example Austria ) and can be divided arbitrarily fine ( cf. Federal tax Switzerland with up to 14 steps). The greater the number of levels is chosen, the more approaches the curve of the linear progression of.

Linear progression

In the linear progression of the marginal tax rate increases in one or more areas between tax rate and top rate linearly. There are no sudden transitions here. The increase in both the marginal tax rate and the average tax rate is performed continuously ( steady). Such a tariff is used for example in the income tax in Germany.

Both the stage and in the linear progression of the top tax rate is usually much higher than the basic rate of tax. The progression in the lower income is, however, considerably slower than in the unit controller ( flat tax ).

Contrary to widespread assumptions may lead to net income losses in gross increases neither by the linear progression through the stages still marginal rate tariff. This follows from the mathematical structure of the tax amount functions in such a way that the higher marginal tax rate always applies only to the extra income.

Mathematical definition

The mathematical definitions use the following terms and variables:

= Tax amount

= Taxable income

= Basic allowance

= Average tax rate

= Tax rate

= Marginal tax rate

= Linear progression factor

Proportional rate

In the proportional tax rate and a constant tax rate, the tax increases in proportion to income without that there is a progression action ():

However, considering the basic allowance (green lines in the images ), then the tax amount calculated according to the formula:

The indirect progression of the average tax rate follows from the relation

Step-wise progressive tariff

At the stage of progressive tax rates, there are several areas where the marginal tax rate remains constant in each case. However, it is higher than in the previous (blue lines in the pictures) in the following zone. The boundaries of these zones ( basic parameters) are marked in the picture with blue arrows. Within a zone, the curve corresponds to the proportional tax rate.

With = Einkommenseckwert, where is, and = number of basic parameter directly below the CPU.

Linear progressive tariff

When linearly progressive tax scale the marginal tax rate increased linearly ( orange lines in the pictures) is:

This applies to the average tax rate of basic allowance:

Even without basic allowance occurs in the linear progression to progression impact because of the progression factor the average tax rate steadily increased depending on:

The marginal tax rate is given by:

Country overview

Germany

Calculation

Until 1989, were used for the determination of the steady increase in the marginal tax rate polynomials, with the increase leveled off at higher taxable income. Since 1990, one or more linear equations are used which result in one or more fare zones with linearly increasing marginal tax rates. The linear equations are easier to calculate. In the political debate, the linear progression (current law) and the tariff levels are discussed.

Collective history

The method for calculating the income tax rate are described in the collective history of the Federal Ministry of Finance with formulas and tables. There also took place from 1990 to simplify the calculation of the tax rate is documented.

Rate curves of the average tax rates 1990 to 2013.

Rate curves of marginal tax rates 1990 to 2013.

Rate curves for the years 1990 to 2014 ( DAS up to 30,000 euros / year).

The pictures above show the historical development of tax rates in the German income tax rate from 1990 to in 2014 in direct comparison. The significant increase in the basic personal allowance from 1996, in response to the decision of the Constitutional Court, which called for the tax exemption of subsistence. At the same time, however, the rate of tax of 19.0 % was raised to 25.9 %. In the following period the tax rate was lowered gradually again and is in the tariff in 2010 14.0%. The top tax rate was lowered from the original 53.0% to 42.0% in the tariff in 2005, but increased from 2007 for high incomes over 250,000 euros to 45.0 %.

Austria

The income tax in Austria follows a nationwide, three -stage tariff model with allowance.

Switzerland

In Switzerland, both the federal tax as well as income and wealth tax in most cantons is taxed at a progressive rate. However, especially the cantonal progression is limited in many places in the highest income and wealth to attract potent tax payer or not to sell. More recently, a few very small cantons have implemented a system change to the standard tax rate. However, this is opposed by the Social Democrats at the federal level, which wanted to force a people's initiative a minimum progression rate for the cantons. But they failed in a federal referendum on 28 November 2010.

Great Britain

In the UK there are both the " Corporation tax", a type of corporation, and in the "Income tax", ie income tax, progressive taxation. The main rate of " Corporation tax" is 28 %, affecting companies with a taxable income that is greater than £ 1.5 million. For companies with a taxable income of less than £ 300,000, the tax rate is 21%. Only with a taxable income between £ 300,000 and £ 1.5 million, there is a sliding tax rate between 21% and 28%.

Income tax is levied in the UK in four bands with three different tax rates. The " basic rate " of 20 % accesses from the first pound, the "Higher rate " of 40 % accesses from £ 37,400. As of the tax period 2010-11, there is also an "additional rate " of 50% for income over £ 150,000 parts. For dividends applies a " basic rate " of 10 %, a "Higher rate " of 32.5 % and an "additional rate " of 42.5 %. For other investment income is considered a " basic rate " of 20 % and a "Higher rate " of 40%.

Both in the UK and in the U.S. there is also a "payroll - tax" for workers who started out as a social contribution, but has developed in the meantime to a tax which - in every respect but name - is an income tax ( " stealth tax" ) and often a higher tax burden caused as the income tax. The "payroll - tax" is criticized as graduated tax.

France

A progressive income tax ( ' impôt sur ​​le revenu ') was introduced ( inter alia to promote the seven-time French Finance Minister Joseph Caillaux ) in France in 1914 after years of discussion. The law was passed on July 15, 1914; of impending or expected by many war accelerated this decision.

USA

In the U.S., the lowest tax rate of federal tax for corporations with taxable income of less than $ 50,000 is 15% and rises to 35 % with a taxable income of over 18.3 million U.S. $. The corporations are also taxed by the states, but this tax is creditable against the federal tax.

The federal income tax is levied stage with rising marginal tax rates from 10% to 39.6 %. From what taxable income reaches the next higher tax rate is different depending on whether one is assessed as an individual, as a couple together predisposed, predisposed as separated couple or a single parent. It should be noted that most states levy an additional income tax. Depending on which state you live, is a top tax rate of over 50 % is possible ( when you add federal and state income tax).

The U.S. income tax has a remarkably high effective tax progression. The index for income inequality ( here: Gini coefficient) in 2006 with respect to the taxable income at 56.47 % (income before taxes) and fell due to the strong progressive tax on 48.92 % for the after-tax income. From the two Gini coefficients is an effective progression of results ( Musgrave / Thin).