Declining Labour Income Share and Personal Income Inequality in Advanced Countries

Abstract

Growing income inequality currently poses a significant threat to sustainable development. Hence, it is important to monitor this phenomenon, in particular to identify determinants favouring the deepening of income inequality. One of the significant determinants in this respect is the declining labour income share in national income. The theoretical justification of the presumption of a negative relationship between the share of labour in the national income and income inequality has strong logical foundations. Existing studies indicate, however, some ambiguities as to the strength of this relationship and the existence of various factors cancelling this relationship. The following study attempts to verify the existence, direction, and intensity of the relationship between the labour income share and income inequality in a relatively homogeneous group of 33 OECD countries studied in 1990–2018. The main hypothesis verified in the study is the assumption that there is a negative relationship between labour share and income inequality. Our results show that the relationship between the share of employees’ and self-employed workers’ income in the national income and income inequality at the general level (i.e., in a group study of 33 countries in total) exists, is negative and statistically significant, but has a very small share in explaining the behaviour of income inequality.

1. Introduction

Issues related to economic inequality, especially income inequality, between citizens in individual economies have become the subject of interest when the tendency of increasing inequality in highly developed countries was observed at the end of the 20th century [1]. The observed trends seem to be a serious threat to ensuring social and political cohesion. As a result, they can lead to slower and less sustained economic growth [2].

In the second decade of the 21st century, the issue of income inequality began to be associated with the functional distribution of income that is the distribution of income between capital and labour. A significant boost in this regard was given by Piketty [3] publishing a comprehensive monograph focusing on capital and inequality, which sparked widespread interest in the topic among economists worldwide. When, in most countries, a tendency of decreasing labour income share in the national income was observed [4,5,6,7,8,9,10] which meant that the proportions of income from capital and labour were not constant, it was assumed that the growing income inequality may be a consequence of the falling labour income share. The studies conducted so far have not provided a clear answer. Most of them lead to the conclusion that there is a relationship between the two discussed issues, however, the assessment of the strength of this relationship as well as the channels of influence remain diverse [11]. The conclusions are difficult to summarise unequivocally not only because of different results, but also due to different methods of measuring both inequality and the share of labour in the national income of a given country, as well as the different selection of the countries and periods covered by the analyses. Usually, in order to capture changes in both these characteristics, long time series are needed, as these phenomena are characterised by low dynamics. It is also important to determine whether the group of the studied countries is homogeneous or whether they are at different stages of development. Recently, due to better data collection and processing systems, the possibilities of analysing the discussed issues are expanding, hence it is worth undertaking research on this subject and verifying the existing findings.

The aim of this paper is to examine whether, in highly developed countries, the declining share of income from labour is related to growing income inequality. The research hypothesis is that in these countries there is a negative relationship between the share of labour in GDP and income inequality. This paper reviews previous findings in the area of the relationship between labour share and income inequality and presents the study for 33 countries that are OECD members and meet the criteria of high-income countries. The analysis was conducted using data from 1990–2018, based on the Gini coefficient for market income and labour shares adjusted for the share of the self-employed. The study used a statistical description and regression models for panel data with fixed and random effects, estimated jointly for the entire study group, as well as a simple linear regression analysis estimated separately for each country.

2. Determinants of Changes in the Functional Income Distribution

In the vast majority of cases, the results of the conducted research indicate the tendency of declining labour share in the national income. In the majority of countries, this trend has been documented since the 1990s [7,12,13,14], and even in some cases, since the mid-1970s [15]. The phenomenon is confirmed both in most highly developed countries and in developing economies [16,17]. Only during the financial crisis of 2008–2009 was the trend reversed, which is in line with the observations about its countercyclical nature. Countercyclicality is associated with the phenomenon of “labour hoarding” in times of crisis, consisting of incomplete adaptation of employment to falling demand in order to reduce rotation costs [12]. It is worth emphasising that the declining share of income from labour is particularly noticeable in Europe and the Americas. In the United States, the decline observed between 2004 and 2016 was almost 3 percentage points [18].

There are several most likely and most common phenomena that contribute to the declining labour share. It is estimated that in highly developed countries about half of the observed decrease in the labour income share is a consequence of technological progress [16]. Attention is drawn to the fact that in the long run, technological progress contributes to the decline in the relative prices of investment goods that encourages enterprises to replace some labour with capital [4,19]. The scale of this phenomenon depends on the elasticity of substitution between labour and capital. According to the results of the conducted research, elasticity is significantly higher in the case of low-skilled workers than in the case of those with high qualifications [20,21,22]. It does not have to be constant and can vary widely between industries and countries. Moreover, it depends on the nature of the tasks performed by employees. The more routine and codable the tasks, the greater the substitutability of labour and capital is. As a result, this process leads to the job polarisation and the shrinking of the middle class [23,24,25]. Generally speaking, it can be stated that technological progress, especially related to information and communication technology (ICT), is complementary to highly skilled workers, and substitutable to those with low qualifications [26,27]. More detailed research shows that the labour share differs depending on the employee group. While among the group of low-skilled workers the phenomenon of the declining labour income share is clearly visible, among the group of highly qualified workers the phenomenon may even take the opposite direction, as is the case, for example, in the United States [28]. In particular, it does not seem to apply to the group of the highest earners (top 1%) [12,29].

Another factor, repeatedly indicated as one of the reasons for the declining labour income share, is global economic integration [6,30,31,32,33], leading to increased competition between enterprises on a global scale and the constant search for lowering production costs. A special role in this respect is played by the expansion of global value chains (GVC), which became possible as a result of a significant decrease in transport and communication costs. This enabled enterprises to divide production into many tasks, thus minimising production costs by taking advantage of the differences in the cost of factors of production between countries. Entrepreneurs from developed countries transfer tasks (fragments of production), which are highly labour-intensive, to developing countries, which are usually marked by lower labour costs. On the other hand, in developed countries, production stages characterised by high capital intensity are usually located. As a result, a decline in the labour income share is observed in developed countries.

A significant trend to reduce the range of the public sector observed in many countries, in particular in such industries as energy, transport, and communication, is also indicated as one of the reasons leading to the decrease in the labour income share. The large scale of industries privatisation could exert the impact on incentives for profit maximisation leading to strong productivity enhancements and thereby reducing labour share [12,34].

Studies typically also find the weakening bargaining power of employee organizations, in particular trade unions, as another pivotal factor for the declining labour income share. There is a decline in trade union density as well as a declining coverage of collective agreements in many OECD countries. Most workers are forced to individually negotiate their wage level, which in most cases means little bargaining power, especially for low-skilled workers. This force may be additionally weakened by the influx of immigrants with low financial expectations, at least in the initial period of their stay in a given country. As a result, these processes may contribute to the gap between the rate of wage growth and the rate of productivity growth to the detriment of wages [35,36,37].

In some studies, the authors also analyse the impact of the minimum wage institution on the labour income share. These studies highlight that in the long run, an increase in the minimum wage contributes to the reduction in the labour income share. This is because higher minimum wages encourage entrepreneurs to invest more in labour-saving innovation and training for employees that increase their productivity, but do not necessarily result in higher wages [12]. On the other hand, the widening gap between the minimum wage and the median wage may lead to an increase in income inequality.

In conclusion, it should be stated that while the tendency towards a decreasing share of labour in national income, especially in highly developed countries, is commonly confirmed, the determinants of this regularity have not been fully identified.

3. Labour Income Share and Income Inequality

The observed tendency toward decline in the labour share in national income, occurring in most OECD countries simultaneously with growing income inequality, leads to a hypothesis that these phenomena are interrelated. This hypothesis has been verified in many empirical studies. Authors typically use relatively long time series and large groups of countries for their research, or study individual economies. Daudey and García-Peñalosa (2007) [38], examining a group of developing and advanced countries, found that a higher share of income from labour is accompanied by a lower level of income inequality. Similar results in their research for the group of OECD countries were achieved by Checchi and García-Peñalosa (2010) [39]. Research conducted by the ILO, IMF, OECD, and World Bank Group (2015) [40], covering the group of G20 countries in 1995–2012, allowed for the formulation of more extensive conclusions. The observed trends indicate that the decline in the labour share is accompanied by an increase in income inequality, and in countries where the scale of the income disparity has been reduced, a renewed increase in the labour share is observed. In the G20 group, it was found that a one percent decrease in the labour share leads to an increase in inequality between 0.1 and 0.2 percent. This relationship concerns the inequalities measured with the Gini coefficient for market income. In terms of disposable income inequality that is after taxes and transfers, this relationship remains true, although its strength is weakening. This is due to the moderating effect of the government redistributive policy, however, as the authors emphasise, in most cases this impact is not sufficient to contain the increase in income inequality. It is noted that in many countries where the share of labour income is declining, wage growth lags significantly behind productivity growth. However, this regularity does not apply to all income groups. While for the top 1% of the richest, labour income increased on average by 20% in the analyzed period, for groups with low income slumped. After excluding the highest earning groups (high executive salaries and bonuses) from the research, the scale of decline in the labour income share in total income is even larger.

Extensive research covering 93 countries over 40 years on the role of functional income distribution in explaining income inequality was presented by Francese and Mulas-Granados (2015) [41]. Empirical evidence suggests that for income inequality, the distribution of labour income is much more important than the share of labour or capital income. In general, a significant portion of household income is labour income, the distribution of which is becoming increasingly uneven, causing widening income inequality. This inference is partially confirmed by the latest research presented by Erauskin (2020) [42], who, while stating a negative correlation between the labour income share and income inequality, notes that the tendency to decrease in the labour income share is closely related to the decreasing share of the lowest two income quantiles and ascending highest quantiles. In other words, income earned in society tends to accumulate in the highest income groups.

Research on the relationship between the labour income share and income inequality that affects individual economies is also being undertaken. For example, the research conducted for the US economy by Jacobson and Occhino (2012) [43] confirms the relationship between the declining labour income share and growing income inequality. However, it is additionally emphasised that not only the decreasing labour income share, which is particularly noticeable by the poorest households, is important, but also the growing share of income from capital. A disproportionately large share of income from capital is obtained by the richest households (the highest decile groups), contributing to further deepening of income inequality.

Income from capital is an important thread of research on income inequality [11,44]. Assuming that individuals can only gain income from work and from capital, the increase in the share of income from capital in national income leads to a decrease in the labour income share. This situation, in turn, will increase income inequality. This is due to the assumption that income from capital is much more unevenly distributed than income from work. This view is strongly supported by Piketti (2015) [3] who states that in the sphere of income from capital there is always a greater inequality of distribution than in the sphere of labour income. Income derived from capital is generally much more concentrated than income derived from labour. He describes labour income inequality as “mitigated”, while capital income inequality as “extreme” [3]. However, as Milanović (2018) [45] emphasises the relationship between rising income from capital and rising income inequality, even if it exists, is not as direct and unambiguous as it is usually assumed. The strength of this relationship varies depending on institutional conditions. Ultimately, however, it confirms that since the distribution of income from capital is much more diversified than labour income, an increase in the share of the former in total income leads to an increase in income inequality. Many researchers arrive at similar conclusions, regardless of the research methods used, but most emphasise that depending on other conditions, the strength of the relationship varies significantly [11].

More advanced research on the relationship between the distribution of capital income and the distribution of personal income was carried out by Randali and Milanowić (2022) [46]. An important contribution of the authors to the studied subject is the application of the income-factor concentration index (IFC) defined and developed in Randali (2022) [47], which measures the level of compositional inequality, i.e., how the shares of capital and labour income vary along income distribution. The authors emphasise that in classical political economy it was usually assumed a priori, that most of the income of people at the top of income distribution derive from capital contributing to high inter-personal inequality. Using a new indicator Randali and Milanowić found that in some cases the classical authors intuition was correct and the increase of the IFC index is associated with the increase of the Gini coefficient. However, an interesting exception are the Nordic countries, where despite high IFC, income inequality remains relatively low. A very important observation concerns the fact that, in addition to the classical vision of capitalist society, one should see the modern model of society in which people are ranked at the top of the distributional ladder not because of income from capital but because of a sizeable labour income. It is why the relationship between factorial income composition and income inequality is not unambiguous.

4. Materials and Methods

As it can be seen from the considerations, the theoretical justification of the presumption of a negative relationship between the share of labour in the national income and income inequality has strong logical foundations. The cited studies indicate, however, some ambiguities as to the strength of this relationship and the existence of various factors cancelling this relationship. The following study attempts to verify the existence, direction, and intensity of the relationship between the labour income share and income inequality in a relatively homogeneous group of countries, first focusing on the group as a whole, then on individual countries as individual study subjects. This approach aims to capture the extent to which the assumed relationship between variables is an individual phenomenon for a given country, and whether it can be generalised in the form of a universal claim that is true for all analysed countries. The main hypothesis verified in the study is the assumption that there is a negative relationship between labour share and income inequality. This hypothesis was applied for both parts of the research: for the group and for individual countries.

The study covered countries that meet three criteria: belong to OECD, meet the High Income criterion according to the World Bank classification based on gross national income per capita, and have data for a long time series available.

The aforementioned criteria were adopted in order to obtain a relatively homogeneous group in terms of the level of wealth and income. Ultimately, 33 countries were accepted for the study: Australia, Austria, Belgium, Chile, Czech Republic, Denmark, Estonia, Finland, France, Greece, Spain, Netherlands, Ireland, Iceland, Israel, Japan, Canada, Lithuania, Luxembourg, Latvia, Germany, Norway, New Zealand, Poland, Portugal, Slovakia, Slovenia, United States, Switzerland, Sweden, Hungary, United Kingdom, and Italy.

The analysed period from 1990 to 2018 was dictated by the availability of data. The Gini coefficient and the labour income share in national income were adopted as measures of income inequality. The Gini coefficient comes from the Harvard database entitled The Standardized World Income Inequality Database [48] and it is a market variant of this coefficient (The market Gini), i.e., calculated for income before tax and without social transfers.

Labour shares are taken from The Conference Board Total Economy Database^TM [49]—the database of an American organization founded at the beginning of the 20th century. The organization calculates the share of labour in income by decomposing the GDP growth rate into labour inputs and capital expenditure weighted by their respective shares in nominal GDP and the rest in the form of TFP (Total Factor Productivity), thus in accordance with the decomposition of the traditional Solow model.

Importantly, labour income includes both full-time and self-employed workers, according to the formula [50]:

$$SL=\frac{CL+MI}{Y}$$

(1)

where:

S𝐿 (Share of Labour) is the share of nominal labour income in GDP, resulting from national accounts,

𝐶𝐿 (Compensation of Employees, Compensation of Labour) are the salaries of employees,

𝑀𝐼 (Mixed Income) is a mixed income, i.e., from self-employment,

𝑌 is GDP.

The study was conducted as follows:

I. Statistical description of the studied group of countries in terms of the analysed characteristics.

II. Estimation of the parameters of a linear regression model (together for all 33 countries based on panel data from 1990–2018) with fixed and random effects according to the equation:

Yit = βXit + αi + ui, i = 1,⋯, n,

(2)

where:

Yit—matrix of explained variables, here: Gini coefficients,

Β—vector of coefficients,

Xit—matrix of explanatory variables, here: shares of labour,

αi—country-specific component,

ui—random component,

t—time (year),

i—site (country),

n—number of countries.

In the fixed effects model (FEM), unlike the random effects model (REM), it is assumed that the individual country-specific effect is correlated with the independent variable. This means that countries exhibit certain individual characteristics that may distort the analysis, and the model makes it possible to limit this impact [51]. This variant of the model was selected on the basis of the Hausman test; however, the article presents both versions of the model.

III. Estimation of the parameters of linear regression models for individual countries (separately for each country, but still for period 1990–2018), which was carried out to deepen the analysis from point II.

5. Results

Table 1. Statistical description in terms of the market Gini coefficient in the studied countries in 1990–2018.

Years	Average	Min. Value	Max. Value	Range	Standard Deviation	Coefficient of Variation
1990	43.58	35.50	55.10	19.60	4.40	10.09%
1991	43.98	36.90	55.00	18.10	4.24	9.65%
1992	44.51	38.00	54.90	16.90	4.08	9.18%
1993	45.00	38.30	55.00	16.70	4.02	8.94%
1994	45.47	38.10	54.90	16.80	3.94	8.67%
1995	45.87	38.10	54.90	16.80	3.81	8.32%
1996	46.00	37.90	54.90	17.00	3.69	8.02%
1997	46.18	37.70	55.00	17.30	3.68	7.96%
1998	46.36	37.90	55.00	17.10	3.65	7.88%
1999	46.55	38.00	55.10	17.10	3.65	7.85%
2000	46.76	38.40	55.30	16.90	3.60	7.69%
2001	46.93	38.70	55.00	16.30	3.56	7.60%
2002	47.10	39.00	54.70	15.70	3.48	7.38%
2003	47.32	39.30	54.40	15.10	3.48	7.35%
2004	47.50	39.60	53.80	14.20	3.51	7.38%
2005	47.55	39.70	53.30	13.60	3.44	7.24%
2006	47.53	39.70	53.30	13.60	3.44	7.23%
2007	47.56	39.70	53.50	13.80	3.49	7.33%
2008	47.73	39.80	54.00	14.20	3.52	7.38%
2009	47.94	40.20	55.10	14.90	3.63	7.57%
2010	48.16	39.50	55.80	16.30	3.69	7.66%
2011	48.17	38.70	56.20	17.50	3.79	7.86%
2012	48.28	38.10	56.30	18.20	3.82	7.91%
2013	48.41	37.70	56.10	18.40	3.83	7.91%
2014	48.28	37.50	55.50	18.00	3.84	7.95%
2015	48.23	37.30	54.90	17.60	3.84	7.97%
2016	48.18	37.20	54.50	17.30	3.94	8.19%
2017	47.99	37.10	54.00	16.90	3.97	8.28%
2018	47.89	37.10	53.70	16.60	3.98	8.32%
2018/ 1990	109.89%	104.51%	97.46%	84.69%	90.64%	82.49%

Source: our study based on [48].

and

Table 2. Statistical description in terms of the labour income share (%) in GDP in the studied countries in 1990–2018.

Years	Average	Min. Value	Max. Value	Range	Standard Deviation	Coefficient of Variation
1990	58.55	42.92	73.53	30.62	7.15	12.20%
1991	58.89	42.63	73.53	30.90	7.16	12.16%
1992	59.05	44.27	73.53	29.26	7.12	12.07%
1993	58.52	43.24	70.23	26.99	7.20	12.31%
1994	57.55	43.00	66.92	23.91	6.71	11.66%
1995	57.14	43.17	67.43	24.26	6.27	10.97%
1996	57.24	42.98	67.00	24.02	5.96	10.41%
1997	56.69	42.73	68.78	26.05	6.01	10.60%
1998	56.57	42.53	67.91	25.37	6.02	10.64%
1999	56.31	39.46	68.16	28.70	6.18	10.97%
2000	55.85	38.58	67.16	28.58	6.51	11.66%
2001	55.99	39.56	68.27	28.71	6.61	11.80%
2002	55.66	39.57	69.42	29.84	6.66	11.96%
2003	55.49	38.84	68.82	29.99	6.48	11.67%
2004	54.91	38.57	67.78	29.22	6.40	11.65%
2005	54.76	37.15	67.32	30.17	6.37	11.64%
2006	54.41	35.18	65.89	30.71	6.61	12.15%
2007	54.23	34.12	65.17	31.05	6.39	11.78%
2008	54.82	35.05	65.74	30.69	5.98	10.92%
2009	55.62	37.25	67.75	30.50	5.93	10.67%
2010	54.42	35.39	66.02	30.63	6.09	11.18%
2011	53.98	34.47	65.86	31.38	6.24	11.56%
2012	54.17	35.25	65.57	30.33	6.14	11.34%
2013	54.09	34.75	65.48	30.72	6.03	11.14%
2014	53.85	34.37	64.99	30.63	5.98	11.11%
2015	53.59	33.69	65.71	32.01	6.61	12.33%
2016	53.80	33.67	65.33	31.65	6.37	11.85%
2017	53.86	33.46	64.96	31.50	6.40	11.89%
2018	54.10	32.32	64.02	31.70	6.51	12.03%
2018/ 1990	92.39%	75.31%	87.07%	103.55%	91.07%	98.57%

Source: our study based on [49].

show the mean, minimum, and maximum values, as well as the range, standard deviation, and coefficient of variation for the 33 countries studied in 1990–2018. Table 1 refers to the market Gini coefficient, while Table 2 presents the characteristics in terms of the share of labour in the national income.

In the analysed period, the dynamics of the Gini coefficient (Table 1) was not high. On average, it increased by almost 10% over the 28 years. While income inequality has increased overall, the disparities between countries are narrowing: the range (the difference between the minimum and maximum value) has decreased by almost 15% in total, the average deviation from the mean has decreased from 4.4 (representing 10.09% of the average) to 3.98 (i.e., 8.32% of the average). In 1990, the lowest Gini coefficients were recorded in Slovakia, Slovenia, Czech Republic, Poland, Norway, Austria, Luxembourg, and Japan (Gini below 40 points), the highest (above 50) in Ireland, United Kingdom, Portugal, and Chile. In 2018, only two countries reached a Gini index below 40, namely Iceland and Slovakia. There were more countries with a score above 50: Hungary, Sweden, Lithuania, Portugal, Chile, Italy, the United States, Germany, and United Kingdom.

In the case of the labour share in the national income (Table 2), the dynamics is also not large, while the direction of changes is opposite to the Gini coefficient. On average, for almost 30 years, the labour income share decreased by almost 8%. The lowest (less than 50%) labour income shares wer recorded in Luxembourg, Latvia, Norway, and Chile. In 2018, labour income shares above 60% were in the following countries: Switzerland, United States, Canada, and Germany and it was, despite the relatively high value (compared to other countries), lower than that of the same countries in 1990. It is almost twice as small in Ireland (35.3%) and Luxembourg (32.3%). While the difference between the lowest value and the highest value in the group increased (by about 3.5%), in the case of the deviation and the coefficient of variation, the decrease is visible (greater in absolute values).

To achieve the main goal of the study, the parameters of linear regression models with fixed and random effects for panel data were estimated. The choice between variants of the model cannot be arbitrary but should be verified with a statistical test. In this case the models were tested with usage of the Hausman test, which made it possible to assess which variant of the model is more adequate to the specificity of the studied group of countries. Results are presented in

Table 3. Hausman test results.

	FEM	REM	Difference	SE	Ch2-Statistic	p > chi2
Labour share	−0.3392164	−0.329285	−0.0099314	0.0031496	9.94	0.0016

Source: our study based on [48,49].

.

The Hausman test is a test dedicated to verifying the type of model (fixed or random effects model) that fits better to the data and is based on a comparison of the β coefficients from the model with random effects and the model with fixed effects. As the null hypothesis (H0) it is assumed that the difference between these coefficients is not systematic. Adopting it would mean that it makes more sense to use a random effects model (a fixed effects model would give a higher standard error). In the alternative hypothesis (H1), the difference is considered systematic. If the ch2 statistic has a high value and is statistically significant (p > 0.05), H0 is rejected, which means that the model with fixed effects is more adequate. In the case of this study, the parameters are above the norms used in practice, for which H0 should be assumed, but it is not a “strong” result (the level of ch2 is relatively low), therefore

Table 4. Parameters for regression models with random and fixed effects (1990–2018, all countries together).

	Coefficient	SE	z-Statistic	p > |z|	Diagnostic Test
REM
Labour share	−0.329285	0.0191319	−17.21	0.000	R2 = 0.0261 Wald chi2 = 296.23 p > chi2 = 0.0000
Constant	65.26006	1.235745	52.81	0.000
FEM
Labour share	−0.3392164	0.0193895	−17.49	0.000	R2 = 0.0261 F(1923) = 306.07 p > F = 0.0000
Constant	65.81283	1.080648	60.90	0.000

Source: our study based on [48,49].

presents both the model with fixed effects (according to the Hausman test, more adequate) and for comparison, with random effects.

The differences between the models are slight. Both models show a negative relationship between the labour income share and the Gini coefficient (the slope factor for a linear regression equation at a level around −0.3/−0.34 with standard error at level 0.019). Both models also meet dedicated tests: in the last column both values—chi2 and F—are high, and both have strong statistical significance (p = 0.0000). However, attention is drawn to the very low level of the coefficient of determination (R2), which suggests that the model explains only 2.6% of the variability of the dependent variable (Gini coefficient). Such a low level of determination, with simultaneous good results of tests of both models and statistics for the dependent variable, suggests that the share of labour in national income is related to income inequality. This relation is consistent with the expected, i.e., negative, but it is not a strong enough factor to be able to explain the shaping of inequalities on its own. However, since it shows a statistically confirmed dependence, it is worth considering it in models with many explanatory variables as one of the characteristics with the potential to increase the degree of model fit.

In order to examine what could have caused such a low level of determination, simple linear regression models for individual countries were estimated. The results are presented in

Table 5. Parameters for linear regression models for individual countries (1990–2018, all countries separately).

Country	Labour Share: Coef. (SE)	Constant: Coef. (SE)	R2	Adjusted R2	F-Statistic	p > F
Australia	−1.03474 *** (0.1598509)	106.3371 *** (9.091347)	0.6081	0.5936	41.90	0.0000
Austria	−0.9327092 *** (0.0811191)	98.10252 *** (4.594999)	0.830	0.824	132.2	0.0000
Belgium	−0.4686334 *** (0.1404484)	75.90293 *** (8.425238)	0.2920	0.2657	11.13	0.0025
Chile	0.2768766 *** 0.0954394)	40.63256 *** (4.50028)	0.2376	0.2094	8.42	0.0073
Czech Republic	0.0775067 (0.3168863)	39.37213 * (17.0364)	0.0022	−0.0347	0.06	0.8086
Denmark	−0.6473738 *** (0.1090443)	82.35397 *** (6.24846)	0.5662	0.5502	35.25	0.0000
Estonia	−0.0725884 (0.0567448)	51.65091 *** (3.25549)	0.0571	0.0222	1.64	0.2117
Finland	−0.734248 *** (0.0974369)	86.43761 *** (5.271934)	0.6777	0.6658	56.79	0.0000
France	0.0210121 (0.2630843)	7.03618 ** (15.43569)	0.0002	−0.0368	0.01	0.9369
Greece	−0.371463 *** (0.0770267)	71.59192 *** (4.572608)	0.4628	0.4429	23.26	0.0000
Spain	−0.6168766 *** (0.0686988)	85.18468 *** (4.278329)	0.7491	0.7399	80.63	0.0000
Netherlands	−0.141726 *** (0.0341906)	54.66802 *** 2.005905)	0.3889	0.3663	17.18	0.0003
Ireland	−0.2010183 ** (0.0604841)	61.5874 *** (2.912543)	0.2903	0.2640	11.05	0.0026
Iceland	0.1013955 (0.1670907)	35.27915 ** (9.272736)	0.0135	−0.0231	0.37	0.5490
Israel	0.1706297 (0.2345409)	40.99814 ** (11.89541)	0.0192	−0.0171	0.53	0.4732
Japan	−0.6289735 *** (0.076813)	78.48913 *** (4.297838)	0.7129	0.7023	67.05	0.0000
Canada	−0.612449 *** (0.0890902)	84.28402 *** (5.611825)	0.6364	0.6229	47.26	0.0000
Lithuania	−0.6751904 *** (0.1446909)	83.10333 *** (7.4031)	0.4464	0.4259	21.78	0.0001
Luxembourg	−0.7458769 *** (0.0514136)	72.97116 *** (1.981976)	0.8863	0.8821	210.46	0.0000
Latvia	0.3233903 ** (0.1003735)	29.75222 *** (4.981302)	0.2777	0.2509	10.38	0.0033
Germany	−1.071574 *** (0.1022244)	115.0558 *** (6.254822)	0.8028	0.7954	109.88	0.0000
New Zealand	−0.0387 (0.1514395)	47.88182 *** 7.865587)	0.0024	−0.0345	0.07	0.8002
Norway	−0.4297144 * (0.1300236)	63.02844 *** (5.947308)	0.2958	0.2687	10.92	0.0028
Poland	−0.6083005 *** (0.1249551)	85.16072 *** (7.862955)	0.4674	0.4477	23.70	0.0000
Portugal	0.1280288 *** (0.0126455)	44.50369 *** (0.7560881)	0.7915	0.7838	102.50	0.0000
Slovakia	−0.7538143 ** (0.2199514)	80.35294 *** (11.42933)	0.3031	0.2773	11.75	0.0020
Slovenia	−0.5063609 *** (0.0808244)	70.72731 *** (4.978211)	0.5925	0.5774	39.25	0.0000
Sweden	0.0487104 (0.2622456)	46.16911 ** (13.01785)	0.0013	−0.0357	0.03	0.8540
Switzerland	−0.6306717 *** (0.1017738)	83.03456 *** (6.794801)	0.5872	0.5719	38.40	0.0000
United States	−0.6982114 ** (95.39485)	0.2019237 *** (13.01317)	0.3069	0.2812	11.96	0.0018
Hungary	−0.2431638 *** (0.0146908)	63.65674 *** (0.8597482)	0.9103	0.9070	273.97	0.0000
United Kingdom	0.0751177 (0.1017251)	49.03876 *** (5.6136)	0.0198	−0.0165	0.55	0.4666
Italy	−0.7517738 *** (0.119718)	89.79108 *** (6.555382)	0.5936	0.5785	39.43	0.0000

Key: * p < 0.1, ** p < 0.05, *** p < 0.01. Grey colour—models that do not meet the test requirements. Source: our study based on [48,49].

.

The estimates show that the link between the share of labour and the Gini coefficient varies greatly from country to country. For some countries, the models did not meet the tests (marked in grey). In the remaining cases, the coefficient of determination ranged from 27.8% (Latvia) to as much as 91% (Hungary). In the vast majority of cases, the relationship between the variables was negative, but there were exceptions—a positive relationship (coefficient for labour participation) can be observed in Chile, Latvia, and Portugal. The coefficient (the slope factor in the linear regression equation) also varies significantly, ranging from around zero to greater than −1.

Since the dependency shows not only a different strength, but sometimes even different directions, and that the level of R2 also varies greatly, caution should be exercised in generalising conclusions from the study of individual countries to larger groups. Only high-income and developed countries were included in the study; nevertheless, the results for individual countries varied and the general model had a very low degree of explanation for the behaviour of income inequality. Therefore, the relationship between the labour income share and the Gini coefficient should be treated individually, as potentially dependent on the idiosyncrasy of a given country. Further research is required to determine the specific factors on which the strength and direction of the relationship depend.

6. Discussion and Conclusions

Based on empirical results, it can be concluded that the relationship between the share of employees and self-employed workers’ labour income and income inequality at the general level (i.e., in a group study of 33 countries in total) exists, is negative and statistically significant, but has a very small share in explaining the behaviour of income inequality. This conclusion can be divided into two main issues:

(1) The results of the tests showing good fit of estimated models, statistical significancy of explanatory variable, and the slope of the regression function, suggests that labour share is related to income inequality, and this relation is consistent with the expected, i.e., negative. This is in line with intuition, and with the assumptions of classical political economy and results obtained by some researchers, which were described in the previous section of the paper [38,39,40,42].

(2) Although in our research the discussed relationship was confirmed, it should be emphasized that the level of determination is very low, what means that labour share in income is not a strong enough determinant to explain the behaviour of income inequality globally. It may be used as one of the characteristics in the multiple regression models, but as a single variable provides a weak explanation of income inequality.

One of the important threads that could contribute to obtaining more precise and unambiguous results is the issue of diversity of capital and labour income distribution among society. According to some researchers, this factor is more important than labour or capital income share in total income [3,45,46].

Moreover, the specific conditions of individual economies may be of key importance to the research results. One of such conditions is the level of economic development. Taking this into account, it is justified to conduct research for selected groups of countries, most often for developed and developing countries. However, this may turn out to be insufficient, as Milanović [45] has shown in his research. For this reason, we conducted additional country-specific studies in our research.

The analysis of individual cases showed that the relationship varies greatly from country to country. In the case of 22 countries, the relationship was consistent with expectations, i.e., negative, statistically significant, and with a coefficient of determination suggesting that the change in the labour income share has a noticeable significance for income inequality. In the case of 8 countries, the models did not meet the test conditions, and for 3 countries the relationship was positive. Even though only high-income and developed countries were included in the study the dependency showed not only a different strength, but sometimes even different directions, and that the level of R2 also varied greatly. Thus, caution should be exercised in generalising the conclusions from the study of individual countries to larger groups. The confirmation of the hypothesis in 2/3 cases is not sufficient to accept it without reservations, therefore we suggest that in research on the determinants of income inequality, it is not reasonable to accept a priori that a decrease in the income labour share will certainly be accompanied by an increase in income inequality. The relationship between the labour income share and the Gini coefficient should be treated individually, as potentially dependent on the idiosyncrasy of a given country. Further research is required to determine the specific factors on which the strength and direction of the relationship depend.