# Why do we need income equality

## Influence of income inequality on gross domestic product – Theoretical considerations

Income inequality has both growth-promoting and growth-dampening effects. The most important of these are positive and negative incentive effects: 1

- The prospect of higher income can be an incentive to increase one's labor input, invest in human capital and take entrepreneurial risk. From a macroeconomic perspective, these are growth-promoting effects.
- Excessive income inequality can, however, also demotivate when performance is not worthwhile from the perspective of individual citizens. In the case of a very high inequality in income distribution, large shares of the macroeconomic income flow to a small group. Therefore, if many people have only a low income, this can have a negative effect on their willingness to perform. These demotivating performance incentives affect all aspects already mentioned (labor input, investments in one's own training and further education, implementation of innovations and investments, entrepreneurial risk).

In addition, income inequality can dampen growth through effects resulting from the collection of taxes to finance government redistribution. In addition to the welfare losses that are normally associated with the collection of taxes, political measures to reduce inequality should also be considered. For example, if the state uses more of its income for consumer transfers, fewer funds remain for public investments. In the long term, this reduces economic growth.

In the case of very high income inequality, there can also be further growth-dampening effects caused by social or political tensions. For example, the protests of the “yellow vests” led the French central bank to reduce its growth forecast for the last quarter of 2018 from 0.4% to 0.2% in December 2018.2 In addition, long-term negative growth effects can arise if low-income families are unable to provide their children with a good education and thus the growth of social human capital is weakened.3 Finally, a drop in demand should also be considered, which acts as a brake on growth when large parts of the disposable income accrue in a few households with a high disposable income and a high propensity to save .4

The answer to the question of which of the effects mentioned here predominate depends largely on the extent of the income inequality already achieved.5 This becomes clear when two theoretically conceivable extreme distribution situations and the associated performance incentives are considered:

- If at the end of a year the total of socially available income is completely evenly distributed, there are hardly any incentives for the individual members of society to intensify their work efforts, to invest in their own human capital and to take entrepreneurial risks. Why should people make an effort if they are not getting a monetary reward as a result? Only intrinsically motivated people would become economically active here. The level of economic activity is therefore low. This means that the gross domestic product (GDP) is also low. Based on this theoretical extreme distribution (equal distribution corresponds to the minimum inequality UGmin. = 0), an increase in income inequality can be expected to increase GDP as a result of the incentives associated with the higher inequality.
- In the other theoretical extreme case of income distribution, after paying taxes and transfers, only one person has the total disposable income of the country, while the incomes of all other members of society are zero. This is the maximum conceivable inequality (UGmax.). In this case, too, there are no monetary incentives for people to work, to increase their productivity through educational measures, or to do business. Hence, based on this distribution, GDP can be expected to grow as income inequality falls.

This allows the causal relationship between income inequality (UG) and the level of real GDP to be shown in the form of a simple function

[GDP = f (UG)]. Assuming a completely even distribution of disposable income (UGmin. = 0 with point Qmin. In Figure 1), an increase in income inequality leads to an increase in GDP because of the positive performance incentives. The maximum possible GDPmax. is reached at UG *. If income inequality continues to rise, the demotivating effects will predominate, so that GDP will fall. 6

##### illustration 1

Income inequality and real GDP: U-shaped relationship

GDP = gross domestic product; K = capital; L = work; TF = technical progress; UG = extent of income inequality.

Source: own illustration.

The curve of GDP depending on the level of inequality shown in Figure 1 follows between UGmin. and UG * of a neoclassical production function. It is also conceivable that an increase in income inequality initially only leads to a slight increase in real GDP, the increases then increase and then decrease again. Up to UG *, this relationship corresponds to a production function under the law of income. The resulting relationship between income inequality and GDP is bell-shaped (see Figure 2) .7

##### Figure 2

Income inequality and real GDP: bell-shaped relationship

GDP = gross domestic product; UG = extent of income inequality.

Source: own illustration.

As usual in economic models, this causal relationship - whether the reverse is U-shaped or bell-shaped - is a ceteris paribus relationship. That means: Even if the income inequality of the economy is between UG * and UGmax. society's GDP can increase over time. This is e.g. This is the case, for example, when the capital stock increases as a result of an inflow of capital from abroad or a fall in domestic interest rates (K ↑), the workforce grows (L ↑) or the technological progress induced by international competition (TF) increases production capacities . All of these factors are location parameters that shift the curve upwards.

Economic Policy Implications

If an unequal income distribution has both growth-promoting and growth-dampening effects and the assumed causal relationship between the level of income inequality and the level of real GDP, shown in Figures 1 and 2, accurately describes the economic reality, an increase in income inequality up to the extent of UG * to an increase in real GDP. The area between UGmin. and UG * can be described as “productive inequality” because rising income inequality has positive effects on real GDP. Once UG * is reached, however, rising income inequality causes GDP to decline through the dampening effects on growth. In this case, there is no contradiction between state income redistribution and economic growth. An economic policy that exclusively pursues the goal of GDP maximization would then have to strive to reduce income inequality. In the specific design of state income redistribution, however, it must be ensured that the negative growth effects of the redistribution are not greater than its positive effects

The crucial point for practical policy is how to quantify the income inequality at which “productive inequality” ends. As mentioned at the beginning, the empirical evidence is not clear. In recent years, the Organization for Economic Co-operation and Development (OECD) and the International Monetary Fund (IMF) have published studies that find a negative impact of income inequality on economic growth.9 These results sparked an extensive debate. Marcel Fratzscher, for example, agreed with these conclusions: “Scientific studies show how badly the inequality of income and wealth in Germany damages our economy and its productivity. The OECD estimates that the rise in income inequality since the 1990s has reduced German economic output by 6%. ”10 Other authors used these studies as an opportunity to carry out their own calculations on this connection. Some of them came to results that contradict the OECD and IMF studies. Galina Kolev and Judith Niehues, for example, state that their results “clearly speak against” “that income inequality in Germany is a negative growth driver” 11. A contribution by the Ifo Institute also demonstrates with "the help of an empirical analysis ... that for high-income countries there is a positive - and not a negative - relationship between inequality and growth" 12.

When evaluating the results of the estimation results, one must always pay attention to whether the influence on the absolute level of GDP or the growth rate of GDP is calculated. If the functional relationship shown in Figure 2 correctly represents reality, the GDP growth rate that depends on income inequality is represented by the slope of the GDP curve. The resulting development of the growth rate of real GDP is shown in Figure 3. This means the following: The growth rate of real GDP is ceteris paribus higher for UG1 than for UG2 (see Figure 3).

##### Figure 3

Income inequality and change in real GDP with a bell-shaped relationship

GDP = gross domestic product; UG = extent of income inequality.

Source: own illustration.

An increase in inequality over time from UG1 to UG2 thus results in a decline in the growth rate of real GDP, ceteris paribus. Nevertheless, the GDP of UG2 is greater than that of UG1 (see Figure 2). So if the income inequality rises from UG1 in year 1 to UG2 in the following year, ceteris paribus this still leads to an increase in GDP in year 2.

It is therefore always necessary to clearly distinguish whether growing income inequality reduces the growth rate of real GDP or the real volume of GDP. If the goal of society is to produce the maximum possible GDP under the given framework conditions, only the second development is problematic in the causal relationships assumed here. Therefore, even with income inequality of UG2, an increase in income inequality in the following years up to UG * makes sense from a purely economic point of view - even if the growth rate of real GDP is thereby lower ceteris paribus.

### Methodological problems

When determining the UG * distribution, numerous methodological problems arise in economic policy practice. A first challenge concerns the question of how income inequality is measured. Most empirical studies deal with disposable income inequality. This is a suitable indicator for the majority of the growth promoting and dampening effects of income inequality. At least in terms of the incentive and growth-reducing effects of tax-financed income redistribution, however, the level of market income inequality is decisive. And wealth inequality is likely to play an important role in the growth-inhibiting effects of social tensions and political unrest. Mixing income and wealth inequality results in more complex effects on GDP growth, in which, for example, growth-promoting effects of a certain level of income inequality could be overcompensated by the growth-dampening effects of high wealth inequality.

A second methodological problem relates to the fact that the growth-influencing reactions of people to the distribution of income in their society largely depend on whether the distribution is perceived as it actually is and how the subjectively perceived distribution is assessed. Research suggests that both the perception of inequality and the assessment of perceived inequality can vary widely in individual countries.13 These differences make it difficult to calculate the impact of income inequality on economic growth when working with data from many countries. Here is also a constructed example that only serves to clarify this aspect: Assume that two countries have exactly the same income distribution, which can be shown by UG * in Figure 2. Even in this case, the distributive-induced effects on the level of real GDP can be very different:

- Conceivable is z. B. that the overwhelming number of people in country 1 is of the opinion that the distribution corresponds to an inequality between UG * and UGmax. lies. If the extent of the actual inequality is overestimated, this leads to the demotivating incentives and social tensions mentioned at the beginning. If income inequality continues to rise, this would have a negative impact on real GDP if income inequality continues to be systematically overestimated. In country 2, on the other hand, there could be a systematic underestimation of inequality. For example, if the population were of the opinion that income distribution is correctly described by UG1, an increase in income inequality would have stimulating effects on growth and lead to higher real GDP.
- Even if people in both countries perceive the distribution of income exactly correctly, they can assess the extent of the income inequality achieved differently. It is - at least theoretically - conceivable that a certain income distribution, which is seen as appropriate, fair and commensurate with performance in country 1, is classified as blatant injustice in country 2 and leads there to corresponding social tensions and political unrest.

Overall, it can therefore be assumed that there is a separate UG * value for each country, which in addition does not have to be constant over time. If, however, a corresponding econometric estimate is carried out with the data from many countries, the correlations are mixed up. This can then lead to incorrect conclusions about the growth effects of income inequality in individual countries.

Because of the methodological problems mentioned, it is difficult to precisely quantify the income inequality from which the area of “productive inequality” ends. If there is an inequality, the extent of which is between UG * and UGmax. If the justification is to reduce the distribution of income, country-specific calculations would have to be carried out. However, the studies available to date on this issue usually work with data from many countries. From this, “no general statements can be made” for the specific income and economic policy of a country 14.

It is also not possible to reliably assess whether Germany is currently still in the area of productive inequality. The aforementioned calculations by the OECD and the IMF come to the conclusion that the growth-dampening effects of income inequality already predominate in Germany. Niehues and Kolev, on the other hand, refer to a global comparison of 113 countries. According to this, a positive correlation between income inequality and growth can still be assumed up to a value of the Gini coefficient of 0.35. With a Gini coefficient of 0.29, Germany is therefore still in the area of productive inequality.15 Because “the results of empirical studies on the relationship between inequality and growth are subject to great uncertainty” 16, there is undoubtedly a need for further research.

* I would like to thank Manuela Barisic, Valentina Consiglio, Lukas Nüse and Dominic Ponattu for valuable suggestions and tips. Any remaining errors are the responsibility of the author.

- 1 Cf. exemplary T. Petersen: Income inequality and economic growth, in: Das Wirtschaftsstudium, 43rd Jg. (2014), no. 10, pp. 1194-1198; M. Baur, C. Colombier, S. Daguet: Unequal distribution of income hinders economic growth, in: Die Volkswirtschaft - The magazine of economic policy, Vol. 88 (2015), H. 1/2, S. 8-11; T. van Treeck: The end of “trickle-down economics”: Inequality as a brake on growth and as a cause of the crisis ?, in: Ifo Schnelldienst, 71st year (2018), no. 15, pp. 3-6; J. Niehues, G. Kolev: Inequality and economic growth - a non-linear relationship, in: ifo Schnelldienst, 71st year (2018), no. 15, pp. 6-9.
- 2 See Reuters: Protests dampen French economy - forecast halved, https://de.reuters.com/article/frankreich-konjendung-proteste-idDEKBN1O90N4 (1.3.2019).
- 3 See G. Kolev, J. Niehues: Is inequality bad for economic growth ?, in: IW-Report, No. 14/2016, p. 6 f .; as well as B.Milanovic: Why we should be worried about high inequality, Makronom Blog, 10.12.2018, https://makronom.de/warum-uns-eine-hohe-unleichheit-sorgen-machen-sollte-28837 (4.1.2019).
- 4 Cf. H. Albig et al .: How increasing income inequality influences economic growth in Germany, in: DIW Wochenbericht, 84th year (2017), p. 160.
- 5 Another important influencing factor is the level of development of the economy, see H. Albig et al., Op. a. O., p. 161; as well as C. Fuest, F. Neumeier, D. Stöhlker: Inequality and Economic Growth: Why the OECD and the IMF are Wrong, in: ifo Schnelldient, 71st vol. (2018), no. 10, p. 23 f. With a low level of development is z. B. the public educational offer often only very weak. This means that there is a high probability that low-income families have poor access to education and that overall economic human capital formation is therefore low.
- 6 It remains to be seen whether this applies to UGmin. and UGmax. belonging GDP is the same. Possibly the demotivation at UGmax is. greater than with UGmin .. In this case, BIP (UGmax.) would be less than BIP (UGmin.).
- 7 It is also conceivable that the functional relationship between inequality and real GDP is skewed to the left or to the right. This changes little in the fundamental context.
- 8 See A. G. Berg, J. D. Ostry: Inequality and Unsustainable Growth: Two Sides of the Same Coin ?, IMF Staff Discussion Note, Washington DC 2011, p. 3.
- 9 The two best-known papers are from 2014: F. Cingano: Trends in Income Inequality and its Impact on Economic Growth, OECD Social, Employment and Migration Working Papers, No. 163, Paris 2014; and J. D. Ostry, A. Berg, C. G. Tsangarides: Redistribution, Inequality, and Growth, IMF Staff Discussion Note, Washington DC 2014.
- 10 M. Fratzscher: Germany's high inequality causes economic damage, in: Wirtschaftsdienst, 96th year (2016), special issue, p. 4-8, here: p. 7, https://archiv.wirtschaftsdienst.eu/jahr/ 2016/13 / germany-high-inequality-causes-economic-damage / (25.3.2019). Later calculations by the DIW show lower growth losses for Germany: “Since reunification, the cumulative growth of the German economy would have been around two percentage points higher if income inequality had remained constant; ... The real gross domestic product in 2015 would have been a good 40 billion euros above its actual value ", see H. Albig et al., Op. a. Cit., P. 167.
- 11 G. Kolev, J. Niehues, loc. a. Cit., P. 16.
- 12 C. Fuest, F. Neumeier, D. Stöhlker, op. a. Cit., P. 22.
- 13 Cf. J. Niehues: Inequality: Perception and Reality - an international comparison, in: Wirtschaftsdienst, 96th year (2016), special issue, pp. 13-18, https://archiv.wirtschaftsdienst.eu/jahr/2016 / 13 / perception-and-reality-an-international-comparison / (25.3.2019).
- 14 C. Fuest, F. Neumeier, D. Stöhlker, a. a. Cit., P. 23.
- 15 See J. Niehues, G. Kolev, op. a. Cit., P. 8.
- 16 T. van Treeck, op. a. Cit., P. 4.

### Title: Impact of Income Inequality on Gross Domestic Product: Theoretical Considerations

Abstract: Income inequality has both growth promoting and growth dampening effects. Up to a certain level, income inequality increases gross domestic product (GDP). In this case, there is productive inequality ’. If the inequality is too large, the GDP reducing effects dominate. Quantifying the extent of income inequality from which the area of ‘productive inequality’ ends involves numerous methodological problems. Whether Germany, for example, has already left the area of productive inequality ’cannot be clearly answered by empirical studies.

JEL Classification: D30, O15, O30

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