18.1 Distribution of income and income tax development

In the “Fachserie 14” of the data collection of the Federal Statistical Office, for the year 2012 the income-taxable persons are listed according to the taxable income together with the set income tax. This table summarizes the incomes in groups, whereat we also summarize the splitting- and the basic rate. The respective limits in Euro are: 0, 2,500, 5,000, 7,500, 8,005, 10,000, 12,500, 13,470, 15,000, 20,000, 25,000, 30,000, 37,500, 50,000, 52,882, 75,000, 100,000, 125,000, 175,000, 250,731, 375,000, 500,000, 1,000,000 and above.

The table below indicates the number of taxable persons, the taxable income in 1000 Euro and the income tax set within the group in 1000 Euro, as well as the average tax rate in percentage. As can be expected based on the progressive rate, the tax rate increases with income. However, in the extremely high area of income above one million Euro, the tax rate drops back to 35% from almost 39% before.

 Anzahl Steuerpflichtiger zvE in 1000 Euro festgesetzte EkSt in 1000 Euro durchschnittlicher Steuersatz in % 832.297 -6.940.108 372.049 1.015.687 1.351.910 60.759 4,5 1.682.873 6.514.624 90.694 1,4 2.501.205 15.781.163 177.908 1,1 640.092 4.969.045 59.146 1,2 2.472.358 22.252.420 584.351 2,6 3.012.467 33.900.702 1.956.230 5,8 1.179.320 15.313.790 1.205.752 7,9 1.806.793 25.711.006 2.372.394 9,2 5.572.202 97.297.032 11.765.178 12,1 4.832.332 108.387.986 16.575.284 15,3 4.371.943 120.666.641 22.307.015 18,5 3.868.201 127.591.960 27.669.035 21,7 2.636.931 112.964.269 28.102.544 24,9 345.347 17.750.726 4.819.706 27,2 1.370.411 84.684.471 25.002.928 29,5 534.515 45.729.461 14.972.535 32,7 235.755 26.185.799 9.105.759 34,8 202.385 29.522.220 10.633.004 36,0 110.240 22.756.396 8.497.485 37,3 57.337 17.227.971 6.570.031 38,1 20.539 8.802.743 3.426.041 38,9 21.734 14.640.765 5.652.296 38,6 10.945 31.866.855 11.192.548 35,1

To determine the effect of changes in tax rates and price levels, we estimate the distribution of income within the groups by means of equal distribution.

We then verify our estimate by comparing the income tax set in the group with the income tax to be set according to our estimate of the income distribution. The graph below shows how much the two values differ and how much the respective value per taxpayer is. The large variation in tax revenues per group is mainly due to the highly fluctuating size of the group. For example, the group of 37,500 Euro to 50,000 Euro includes eight times as many taxpayers as the group above, of 50,000 Euro to 52,882 Euro, which means that the total tax revenue is much higher. All in all, however, our simple approximation is quite good. The total set income tax in 2012 was 213 billion Euro. Our approximation results in 215 billion Euro.

In the following graph, we estimate how well the income distribution over time can be approximated using population figures, inflation and average income. We indicate the actual income tax rate set by the Federal Ministry of Finance and our calculations in which we adjust the taxable income for 2010 in four different ways: a) as growing with inflation (i.e. constant in real terms) and b) as growing with average income (i.e. increasing in real terms), in each case with and without consideration of the growth of the number of taxpayers. Due to problems with data consistency, we limit this presentation to the period after 1989.

Apparently, the estimate adjusted for wage growth is best suited to reflect the actual development of income tax revenue. Therefore, the entire income distribution was adjusted by the growth rate of the average income, but the number of taxpayers was not changed. Apart from the two values for 1998 and 2001, the estimate is equally good by adjusting for both the inflation rate and the change in the number of taxpayers.

(c) by Christian Bauer
Prof. Dr. Christian Bauer
Chair of monetary economics
Trier University
D-54296 Trier
Tel.: +49 (0)651/201-2743
E-mail: Bauer@uni-trier.de
URL: https://www.cbauer.de