## Chapter 16Cold Progression: Introduction

In Germany, there is a general consensus that solidarity is one of the basic principles of the social system. In the context of tax law, this means that broad shoulders can bear more. The German income tax rate is progressive, i.e. the marginal tax rate increases with increasing income. The higher the income, the higher the average tax rate.

This arrangement also has implications for increasing incomes. If the individual income increases, the individual’s performance capacity is higher and he or she can contribute more to the social burden-sharing (via a higher tax rate) - this is the idea. This is problematic, however, if income increases nominally, i.e. in terms of the euro amount, but the wage increase is eaten up by rising prices. Then the tax burden increases even though real income1 has not risen. This effect is called cold progression. In reality, average incomes usually grow faster than the inflation rate, so that the rising tax burden is partly due to actual (i.e. real) income increases and partly to cold progression. Additionally, changes in the tax tariff must also be taken into account.

The following pages aim to introduce into this topic and to present it in a clear and easily understandable way. The interactive graphics serve as a vital tool. In particular, we want to answer the following three questions:

1) The issue: What is cold progression and why should we be interested in it?

2) The sum: How much is at stake? Who wins and who loses?

3) The alternative: What would a tax rate look like that would compensate for the cold progression?

The graph below shows the inflation rate. (Source: German Federal Statistical Office). The inflation rate ${\pi }_{t}$ is the annual percentage change in the price level, i.e.

 ${\pi }_{t}=\frac{{P}_{t}-{P}_{t-1}}{{P}_{t-1}}×100$ (16.1)

The second graph shows the measured average labor income in Germany (blue) and how the average income would have developed if it had only grown with the inflation rate since 1960 (red). The red line thus corresponds to the growth of the price level. You can see that average incomes have grown much faster than prices. Consequently, the increase in income is partly due to inflation and partly to productivity gains.2

The tax rates are constantly adjusted. In the next graph, all income tax rates since 1958 can be shown. Here, the marginal tax rate and the average tax rate are displayed. The solidarity surcharge is included, but not church tax and capital returns tax. With the slider (red cross), for a chosen income also the actual tax burden can be indicated. It becomes obvious that the tax rate changes frequently and significantly. In particular, the basic tax-free allowance rose in 1996 from 2871 Euros to 6184 Euros, which provided a significant relief especially for lower incomes, while the reduction of the top tax rate from the former 53% to 42% relieved the very high incomes.

We illustrate this with two numerical examples. The average gross income per person in 1960 was the equivalent of 3156 Euros. With this income, 460 Euro or 14.6% income tax had to be paid. If the real income had remained the same, i.e. the nominal income always has increased with the inflation rate, 30 years later there would be a household gross income of 8307 Euro and the tax burden would be 1044 Euro or 12.6%. Until 2015, the tax burden for a constant real income (13689 Euro: This corresponds to only 70% of the median income, i.e. it belongs to the low-middle class), would decrease to 1000 euros or 7.3%.

If the example is calculated with a household of the upper middle class (250% of the median income), the result is an income of 54000 Euros in 2015 and a tax burden of 19210 Euros, i.e. 35.6%. With the same real income, the tax burden would have been 19.9% 25 years earlier (real equivalent gross income 32770 Euros and tax of 6506 Euros) and 26.7% in 1960 (real equivalent gross income 12450 Euros and tax of 3319 Euros). Although the household could not afford more from its gross income, the income tax to be paid has increased significantly since 1990.

Choose the tax rate for the year:

1958 1965 1975 1978 1979 1981 1986 1988 1990 1996 1998 1999
2000 2001 2002 2004 2005 2007 2009 2010 2013 2014 2015 2016

1The real income is the nominal income divided by the price level.

2It could also be discussed whether the tax burden should be based on a distribution of relative incomes by determining the proportion of the tax burden to be borne by each decile. The tax rate would then be based on median income and not on real income.

(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