1
The Relation between Income Inequality and the
Business Cycle
Abstract
The aim of this thesis is to evaluate the relation between income inequality in different parts of the income distribution and the business cycle. Moreover, to evaluate the business cycle effects for different parts of the income distribution, the relation between unemployment rates for low-skilled and high-skilled workers and the business cycle is analyzed. A sample of seven OECD countries is used covering a time period from 1990-2014. First, the business cycle is extracted making use of the Hodrick-Prescott filter and the Christiano-Fitzgerald filter and thereafter a Pearson correlation analysis is done. The relation between income inequality at the top of the income distribution and at the bottom of the income distribution with the business cycle are positive and negative respectively. Only for two countries a negative significant relation is found between the business cycle and unemployment rates of low-skilled workers. However, focusing on high-low-skilled workers, a significant negative relation is found in five countries.
Edited by: Kim Boswijk, 10659129 Semester 1, 2016/2017
Bsc of Economics and Finance Supervised by: Nicoleta Ciurila
2 Statement of originality
This document is written by Student Kim Boswijk who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents
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Table Contents
Statement of Originality
1 Introduction ... 4
2 Literature review ... 5
2.1 A Brief History of Income Inequality ... 6
2.2 Income Inequality Measures... 7
2.3 Income Inequality and Economic Growth ... 7
2.3.1 Effects Economic growth on Income Inequality ... 7
2.3.2 Effects Income Inequality on Economic Growth ... 9
2.4 Income Inequality and the Business Cycle ... 10
3. Methodology ... 12 3.1 Filters ... 12 3.1.1 Hodrick-Prescott filter... 12 3.1.2 Christiano-Fitzgerald filter ... 13 3.2 Data ... 14 3.2.1 Income Inequality ... 14
3.2.2 Growth rate trend GDP ... 14
3.2.3 Unemployment rate ... 14 3.3 Hypotheses ... 14 3.3.1 Gini Coefficient ... 14 3.3.2 P90/P50, P50/P10 percentile ratios ... 15 3.3.3 Unemployment rates ... 15 4. Results ... 15
4.1 Correlations Income Inequality ... 16
4.2 Correlations Unemployment rates ... 19
5. Conclusion ... 21
5.1 Summary and Concluding Remarks ... 21
5.2 Suggestions for Further Research ... 21 Appendix
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1 Introduction
One of the most notable observations in the economic literature is the increasing income inequality in the past decades. Income inequality in the OECD countries is at its highest level for the past half century. The Gini coefficient stood at an average of 0.29 in OECD countries in the mid-1990s, and by the late 2000s, it had increased by almost 10% to 0.316 (Figure 1) (OECD, 2016) 1. Income inequality has different negative consequences for the wellbeing of people and ultimately for the functioning of society. As Wilkinson and Pickett (2006) have noted, low social status and the quality of the social environment are both know to affect the social circumstances of the country. Countries with high income inequality are likely to have a bigger problem with low social status and evidence suggest that inequality is socially corrosive. Moreover, Goodin and Dryzek (1980) found that growing income
inequality creates political instability because more individuals become discontent with their economic situation.
The long-term trend in increasing income inequality, as stated before, was interrupted only temporarily in the first years of the Great Recession. Economist has resurrected the question of how income inequality evolves over the business cycle. This question was raised long ago by economists concerned with the impact of downturns on the poor. Moreover, according to Jaumotte et al. (2008) income inequality render individuals more vulnerable to poverty because there is higher unemployment risk especially during a business cycle downturn period.
The most studies investigate the relation between income inequality and the business cycle through analyzing the economic growth and income inequality separately during the business cycle or with the use of different regressions techniques. However, this paper shows it is interesting to correlate the income inequality with the business cycle. Moreover, the unemployment rates for different skill groups are analyzed during the business cycle to see if the concerns about the downturns on the poor are compatible. Making use of a Pearson correlation analysis, and two kinds of filtering techniques to extract the business cycle, this paper finds an answer to the question whether there is a significant relation between income inequality in different parts of the income distribution and the business cycle. The relation between income inequality at the top of the income distribution and at the bottom of the income distribution with the business cycle are positive and negative respectively. Only for
1 Gini coefficient is the most common measure of inequality. It ranges between 0 in the case of perfect equality
5 two countries a negative significant relation is found between the business cycle and
unemployment rates of low-skilled workers. However, focusing on high-skilled workers, a significant negative relation is found in five countries.
The structure of this thesis is as follows. First, in section 2 existing literature will be reviewed to give a theoretical background. After that, chapter 3 provides the methodology used in this research to extract the business cycle together with a description of the data, and the hypotheses are given based on the existing literature studied. Chapter 4 discusses the results of this study. Finally, chapter 5 draws a conclusion and provides some suggestions for further research.
Figure 1: Developments Gini coefficient. Own elaborations from OECD statistics.
2 Literature review
The relation between income inequality and the business cycle has been discussed widely in academic literature over the past decades. The long-term increase of income inequality followed by a decrease in income inequality during the Great Recession has raised questions about whether there is a positive or negative relation between income inequality and the business cycle. First of all, a brief history of income inequality is given. Second, the various measurements for income inequality are discussed. Third, to gain a better understanding of income inequality and the business cycle, the two-way relation between economic growth and income inequality will be explained. Finally, the relation between income inequality in
different parts of the income distribution and the business cycle is analyzed to see if the business cycle is more harmful to the low-skilled workers than for high-skilled workers.
0,15 0,2 0,25 0,3 0,35 0,4 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 CZE GER FIN FRA HUN UK SWE
6 2.1 A Brief History of Income Inequality
The changes in income inequality have been analyzed widely in academic literature over the past decades. The Industrial Revolution was characterized by growth over the long run both in average income and income inequality. The world population growth was accompanied by an even faster rate of growth in world production. At the same time, world income inequality grew substantially (O’rourke, 2001).
Throughout the past two centuries, the world income inequality worsened according to Borguignon and Morrisson (2002). From 1820 till 1910, a period of rapid growth and
globalization, the Theil index rose 50 percent2. Between the world wars, the increase of income inequality slowed down somewhat and after 1950 even more. After 1960, another period of rapid growth and globalization, the Theil index rose slightly. Three forces caused the world income inequality to decrease in the first half of the 20TH century. The first force was the developing Asia's growth performance, which led to higher incomes in the Asian continent. Second, Borguignon and Morrison (2002) states that the equalizing effect of the Soviet revolution and the socialization of Eastern European countries offset a large part of the increase in world inequality arising from divergences in national economic growth rates. The third force behind the drop in the world income inequality is the equalization of national income distributions among European countries. Overall inequality within these countries fell to a large extent, causing a decrease in the world Theil index of 12 percentage points
(Borguignon and Morrison, 2002).
The purpose of the paper from Gottschalk and Smeeding (2000) was to summarize the empirical evidence on income inequality in 33 OECD countries since 1970. With new data resources such as Luxembourg Inequality Study (LIS), they could manage to bring a
successful summary3. While income inequality increased in 12 of the 17 countries examined from 1979 to 1995, this trend was not universal. In nearly all countries inequality decreased through the 1970s and increased in the mid-1980s through the mid-1990s. They also
concluded that differences in income inequality in OECD countries are than twice as large at
2 The Theil index allows one to decompose inequality into the part that is due to inequality within areas and the
part that is due to differences between areas, as well as the sources of changes in inequality over time. (Worldbank)
3 LIS acquires datasets with income, wealth, employment and demographic data from a large number of
7 any point in time. So far, changes in inequality do not exhibit precise trajectories, but rather erratic movements.
2.2 Income Inequality Measures
The Gini coefficient is the most common index to measure income inequality. Alternative methods, such like the Palma Ratio and the 20:20 ratio, use the percentile ratios of the poorest and the richest groups of the total population to illustrate deviance from the perfect income inequality (Yitzhaki, 1979). Unfortunately, these ratios only measure the shape of the income distribution by using outliers, and they do not represent the overall level of income inequality. The Gini coefficient is preferred over the Palma Ratio and the 20:20 ratio because it is based on the comparison of cumulative proportions of the population against cumulative proportions of income they receive. However, some critics argue that the Gini coefficient will not yield reliable results. Hoover et al. (2009) argue that if there is an increase in the Gini coefficient, it cannot be gleaned whether this is harmful to the low-skilled workers or the high-skilled workers. It can be caused by an increase in the incomes of those in the highest percentile of the income distribution while those in the bottom percentile have incomes that are stagnant or falling. Moreover, Voitchovsky (2005) states that income inequality at the top of the income distribution and a vast middle-class income inequality are on the basis of the inequality-growth relationship. She, therefore, argues for considering the ratios of the 90/50 and 50/10 percentiles of the income distribution to capture these effects separately. Each of these ratios show what is happening in different parts of the income distribution and thus provide a richer view of income inequality than a simple summary measure.
2.3 Income Inequality and Economic Growth
Economic theory does not predict the direction of the correlation in the two-way relationship between economic growth and income inequality. However, the direction and magnitude of these relations are important for policy decisions and policy evaluation. This explains the vast number of empirical studies devoted to this issue. In the empirical literature, the majority of cross-sectional studies have found a negative relationship between income inequality and economic growth. However, the negative effect seems to disappear when the models are estimated using panel data techniques.
2.3.1 Effects Economic growth on Income Inequality
The primary theoretical approach to assess the effects of economic growth on income
8 of industrial societies, he conceived a general developmental pattern in which inequality traces an inverted U-curve relation with economic development. Inequality rises in the early stages of growth due to the movement from agricultural to industrialized production. Because the agriculture sector features low per capita income and the industrial sector features higher per capita income, these movements result in a rise in per capita income for the persons who moved to the industrial sector. As the size of the agricultural sector diminishes, the
agricultural workers are enabled to join the relatively rich industrial sector. Moreover, the decreasing size of the agriculture labor force tends to drive up relative wages in that sector (Moran, 2005). Thus, in the course of industrial development, inequality first increases and then declines.
Figure 2: Kuznets Curve
Atkinson (2003) investigates the changing income inequality in nine OECD countries over the period from 1945 to 2001. In his research, he takes a 3-percentage point yardstick to see whether the changes in income inequality and the existence of the inverted U-turn are statistically significant4. The empirical findings support the hypothesis of the inverted U-curve for four of the nine countries. Moreover, for all the nine countries he found that the changes in income inequality are significant.
Thornton (2001) uses a panel of high-quality, comparable data on Gini coefficients, income quintiles and economic growth for 96 countries5. In his paper, he finds that the
relation between income inequality and economic growth corresponds to an inverted U-curve.
A more recent econometric analysis was performed by Bahmani-Oskooee and Gelan
(2008). This study uses time-series data from the US over the 1957 to 2002 period and an
4 If the Gini coefficient changes with 3 or more percent points, this change is statistically significant according to
Atkinson (2003)
9 error-correction modeling technique to distinguish the short-run effect from the long-run effects. They find that economic growth worsens income inequality in the short-run but finally improves in the long-run, supporting Kuznets inverted U-curve.
In contrast to the inverted U-curve hypothesis stands the belief that there has been little income inequality change within countries, supported by some studies. Gustaffson and Johansson (1999) find for 16 industrialized countries that there is almost no correlation between the Gini coefficient and the time-variable and there is a weak U-curve relationship.
Hsing and Smyth (1994) agree with this view. They use US data from 1947 to 1991. The methodology involves a seemingly unrelated regression (SUR) estimation method. Regressions for whites and blacks/others are estimated separately to see if they can reach different conclusions for these two population groups. They found a substantial evidence of the non-existence of the inverted U-curve for all races.
2.3.2 Effects Income Inequality on Economic Growth
The relation between income inequality and economic growth is two-sided. Initial high inequality results in lower growth rates (Galor and Zeira, 1993). There are several hypotheses for why income inequality might be associated with low economic growth rates. The main theories are about credit market imperfections, political economy and social stability (Deininger and Olinto, 1999).
According to Bourguignon (2004) and Barro (2000), the credit market imperfections typically reflect asymmetric information. This results in a higher interest rate for borrowers than for lenders. Moreover, in the presence of credit market imperfections and limited access to credit, taking advantages of investments opportunities depends on individuals' levels of income. The impossibility for poor people to obtain a loan, together with their low initial income, makes it difficult to seize potentially profitable investments. However, if there arises a shift of incomes from rich to poor, it is easier to seize an investment opportunity.
Eventually, the quantity and average productivity of investment would increase. Through this mechanism, a decline in income inequality positively influences the rate of economic growth (Barro, 2000). In contrast to this theory, Foellmi and Oechslin (2008) find an adverse result. They argue that if there arises a shift from incomes from the rich to the poor, the demand for capital will increase as will the interest rate. The poor will also be faced with the higher interest rates and will not be able to seize a profitable investment; this will have a negative impact on economic growth.
10 political economy. Attanasio and Binelli (2004), Barro (2000), and Galor (2009) hypothesized that the existence of high-income inequality in democratic countries would cause the majority voting demand for a redistribution of income from rich to poor. Thus, the majority voting will prefer a progressive taxation system. The distortion associated with the progressive taxation system, negatively affect investment in physical and human capital and capital accumulation6. The decline in investments results in a lower rate of economic growth. Furthermore, means-tested welfare payments and levies on labor income might induce less work effort, and therefore decrease productivity (Galor, 2009).
The third hypothesis about income inequality and economic growth relied on social stability. Deininger and Olinto (1999) argue that high-income inequality leads to more violence and social discontent which will affect economic growth. Firstly, through the direct damage occurred. Secondly, through the opportunity costs of resources deflected from other activities towards preventing crime. Finally, through the increase in the insecurity of property rights which will deter investment (Barro, 2000). Rodriquez (2000) empirically tested the relation between income inequality and economic growth in a two-stage analysis. He finds strong links between inequality and violent crimes and afterward between this proxy for instability and economic growth.
2.4 Income Inequality and the Business Cycle
It is widely known that the business cycle has a potential effect on income inequality (Parker, 1998). However, it is not sure which income groups are affected most and whether it is a positive or adverse effect. In this section, an overview of the relevant papers and empirical findings is given.
Barlevy and Tsiddon (2006) examine in their paper the connection between long-run trends and cyclical variation in income inequality. They find that recessions tend to increase trends in income inequality. That is, recessions contribute to more rapid growth in income inequality, but they accelerate the fall in income inequality in periods of declining inequality. At least among the workers at the top of the income distribution.
In their model income inequality is driven by technological change. If technology first arrives, those who are quick to absorb it, will increase their income and the dispersion in the income distribution will slowly increase. Eventually, the others will catch up as the new technology becomes circulated and the income inequality declines until the next technology
11 arrives (Barlevy and Tsiddon, 2006). Till what extent an individual is productive with the new technology depends on how skilled the individual is. In times of declining income inequality, the less skilled workers would absorb the new technology more quickly than to those who have already become more proficient with the new technology, so the decline in income inequality will accelerate. For empirical evidence, they used Kuznets (1953) income data. Barlevy and Tsiddon (2006) focus on a period with declining income inequality. They find income shares of the top 1% fell between 1929 and 1941, and this fall occurred mostly during the Depression between 1929 and 1932.
Mukoyama and Sahin (2006) calculate the costs of business cycles for high-skilled and low-skilled workers. In their first experiment, which assumes that business cycle fluctuations are eliminated during a boom, the gain from eliminating the business cycle is higher for low-skilled workers than for high-low-skilled workers. In their second experiment, which assumes that business cycle fluctuations are eliminated during a recession, the low-skilled workers gain again more compared to high-skilled workers. The differences in gains between the low-skilled workers and the high-low-skilled workers have two explanations (Mukoyama and Sahin, 2006) First, the high-skilled workers have already gathered enough wealth to insure
themselves against risk during the business cycle while low-skilled workers have less
opportunity to self-insure. Second, the low-skilled workers face a higher unemployment risk. According to Krusell et al. (2009), both groups gain by eliminating the business cycle because there is less wage rate risk since these fluctuate if aggregate productivity does. Due to higher sensitivity to business cycle fluctuations of the wages for low-skilled workers, the income inequality will rise.
Bonhomme and Hospido (2016) study the evolution of male income inequality and employment in Spain from 1988 to 2010.7 They use the logarithm of the 90/10 percentile ratio of male daily wages as the measure of income inequality. According to their analysis, income inequality is strongly countercyclical, and sensitivity to the business cycle is highest for low-skilled workers. Moreover, income inequality followed the same development of the
unemployment rate. This development in income inequality is partly explained by
considerable changes in the composition of employment regarding occupation, age groups, and sectoral composition. Income inequality is affected by sectoral composition due to fall in employment in the construction sector which belongs to the lower-middle part of the income distribution.
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3. Methodology
In this paper a Pearson correlation analysis is used in which the various measures of income inequality are correlated with the growth rate of trend GDP and with the business cycle (GDP gap)8. Throughout this paper, the business cycle refers to the GDP gap. In addition, the unemployment rates of the different skill groups are correlated with the growth rate of trend GDP and the business cycle to examine the difference in sensitivity to the business cycle for the different skill groups. A Pearson correlation is the most common method in the literature to quantify the strength of a linear relationship between two variables (Otto et al., 2001) 9. The correlations are calculated using pairwise deletion of observations with missing values.
The business cycle of the seven countries is obtained by analyzing the real GDP and make use of a filter technique. Due to a lack of consensus among researchers regarding the optimal detrending method, two different filters are utilized to ensure the robustness of the results. The methodology involves the use of the Hodrick-Prescott (Hodrick and Prescott, 1997) and the Christiano-Fitzgerald (Christiano and Fitzgerald, 2003) filters. With the use of different statistics, different patterns can be detected. Unfortunately, no conclusions can be made on the causality between income inequality and the business cycle.
3.1 Filters
3.1.1 Hodrick-Prescott filter
The Hodrick-Prescott (HP) filter is a widely used method for extracting the business cycle dynamics. It is a high-pass filter which means it focuses on fluctuations with higher frequency and removes the rest. The HP-filter breaks down time series, 𝑥𝑡, into a stochastic trend
(potential GDP) , 𝑥𝑡∗, and a cyclical component (GDP gap), 𝑥
𝑡𝑐, by minimizing the distance between the trend and the original series and at the same time minimizing the curvature of the trend series. The optimization problem is based on this expression as described by Hodrick and Prescott (1997):
∑𝑇 [(𝑥𝑡
𝑡=1 − 𝑥𝑡∗)2 +λ(∆𝑥𝑡+1∗ − ∆𝑥𝑡∗)2] (1)
8 The Pearson correlations are calculated following this formula: r= 1 𝑛−1
∑(𝑥−𝑥̅)(𝑦−𝑦̅) √∑(𝑥−𝑥̅)2∑(𝑦−𝑦̅)2
9 If the value is close to 1 it is said to be perfectly correlated. If the coefficient value lies between ± 0.50 and ± 1
it is said to be a high degree of correlation. If the coefficient value lies between ± 0.30 and ± 0.49, it is said to be a moderate degree of correlation, and if the coefficient value lies below + 0.29, it is said to be a low degree of correlation.
13 Where λ is a parameter controlling the smoothness of 𝑥𝑡∗, and the cyclical component in 𝑥𝑡 can be written as
𝑥𝑡𝑐 = 𝑥
𝑡− 𝑥𝑡∗ (2)
Intuitively, the solution to Equation (1) provides a mapping from 𝑥𝑡 to 𝑥𝑡∗ with the relevant ‘gap’ data series 𝑥𝑡𝑐 determined residually based on equation (2). The HP-filter was originally designed to be applied to quarterly data. Nonetheless, the data that has been used in this analysis is yearly. For quarterly data the smoothing parameter, λ, is 1600. To transform the quarterly data to yearly data the following calculation needs to be applied (Ravn and Uhlig, 2002):
1600
44 = 6.25
3.1.2 Christiano-Fitzgerald filter
The Christiano-Fitzgerald (CF) filter is shown to perform better at stopping the low-frequency fluctuations than the HP-filter does. The filter minimizes the mean squared error between the filtered series and the series filtered by an ideal band-pass filter that separates time series in a stochastic trend and a cyclical component. It assumes that the raw time series, 𝑦𝑡, follows a random-walk process without drift10. In other words, 𝑦𝑡=𝑦𝑡+1+𝜀𝑡, where 𝜀𝑡 is independent and identically distributed with mean zero and finite variance. The cyclical component is calculated as follows: 𝑐𝑡 = 𝑏0𝑦𝑡+ 𝑏1𝑦𝑡+1+ ⋯ + 𝑏𝑇−1𝑦𝑇−1+ 𝑏̃𝑇−𝑡𝑦𝑦𝑇+ 𝑏1𝑦𝑡−1+ ⋯ + 𝑏𝑡−2𝑦2+ 𝑏̃𝑇−1𝑦1, (3) for 𝑡 = 3,4 … , 𝑇 − 2 Where 𝑏𝑗 = sin(𝑗𝑐)−sin(𝑗𝑎) 𝜋𝑗 , 𝑗 ≥ 1, 𝑏0 =𝑐−𝑎 𝜋 , 𝑎 = 2𝜋 𝑝ℎ, 𝑐 = 2𝜋 𝑝𝑙 𝑏̃𝑇−𝑡 = −1 2𝑏0− ∑ 𝑏𝑗 𝑇−𝑡−1 𝑗=1
10 The formulas assume there is no drift in the random walk. If there is a drift in the raw data, we assume it has
14
𝑝𝑙and 𝑝ℎ are the cut off lengths of the cycle (Christiano and Fitzgerald (2003). That is, cycles
that are longer than 𝑝𝑙 but shorter than 𝑝ℎ are considered to be the cyclical component 𝑐𝑡.
3.2 Data11
3.2.1 Income Inequality
For the seven countries, the data on the Gini coefficient and the percentiles ratios for the years 1990-2014 is obtained from the OECD statistics. The incomes are based on disposable
incomes post taxes and post transfers. With linear interpolation the missing values are calculated. Interpolation is only possible if there are missing values in between the available values (Leigh, 2007).
3.2.2 Growth rate trend GDP
A complete data set on GDP is retrieved from the OECD statistics database. Yearly data on GDP from 1990 to 2014 is based on constant prices and constant PPP. First, the trend GDP is extracted by the use of the CF-filter and the HP-filter. Second, the growth rate of the trend GDP is calculated using the following formula:
𝐺𝑟𝑜𝑤𝑡ℎ𝑅𝑎𝑡𝑒𝑇𝑟𝑒𝑛𝑑𝐺𝐷𝑃 = (𝑇𝑟𝑒𝑛𝑑𝐺𝐷𝑃𝑡=2−𝑇𝑟𝑒𝑛𝑑𝐺𝐷𝑃𝑡=1)
𝑇𝑟𝑒𝑛𝑑𝐺𝐷𝑃𝑡=1 ∗ 100 (4)
3.2.3 Unemployment rate
The unemployment rates for the different kind of skill groups indicate the proportion of the labor force that does not have a job and is actively looking and available for work. The unemployment rate is defined as the ratio resulting from dividing the total number of
unemployed (for a country and a specific group of workers) by the corresponding labor force, which itself is the sum of the total persons employed and unemployed in the group. Low-skilled and high-Low-skilled are defined respectively as educational attainments of below upper secondary and tertiary. Due to a lack of a complete data set for all the years, the time range is from 1995 to 2014.
3.3 Hypotheses
3.3.1 Gini Coefficient
The Gini coefficient is expected to be highly correlated with the growth rate of trend GDP considering the two-way relationship between these variables as described in section 2. The
15 countries under the analysis are all developed economies. Hence the Kuznets theory assumes a negative correlation. Furthermore, income inequality is driven by technological change; that is the business cycle accelerates the decrease (increase) in income inequality in periods of declining (increasing) income inequality. Following that reasoning, the expectation is that the correlation between the Gini coefficient and the business cycle is higher than the correlation between the Gini coefficient and the growth rate of trend GDP.
3.3.2 P90/P50, P50/P10 percentile ratios
Barlevy and Tsiddon (2006) find that in times of recessions the income inequality changes accelerates for the incomes at the top of the income distribution. According to Mukoyama and Sahin (2006) and Krusell et al. (2009), the high-skilled workers (workers in the top of the income distribution) are less vulnerable to the business cycle due to the greater opportunity to self-insure and the less unemployment risks. Hence, the expectation is that the correlations with the business cycle are positive for both the income groups but for the workers on the bottom of the income distribution this correlation is expected to be even higher positively correlated.
3.3.3 Unemployment rates
The unemployment rates for the two skill groups are expected to be negatively correlated with the growth rate of trend GDP. In addition, to the expected negative correlation with the
growth rate of trend GDP, it is expected that the unemployment rates are negatively correlated with the business cycle due to a high wage risk. Moreover, according to Mukoyama and Sahin (2006), low-skilled workers have a higher unemployment risk during the business cycle compared to high-skilled workers, hence their unemployment rate is expected to be higher negatively correlated.
4. Results
In this section, the results of the analysis are summarized. The first three figures depict the correlations and the significance of these correlations between the income inequality
measures, the growth rate of trend GDP and the business cycle for the seven countries under the analysis. The next two figures depict the correlations and the significance of these correlations between the low-skilled and the high-skilled workers with the growth rate of trend GDP and the business cycle for the seven countries under the analysis.
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4.1 Correlations Income Inequality
Figure 3 depicts the correlation coefficients between the Gini coefficient, the growth rate of trend GDP, and the business cycle for the seven countries under the analysis. The data
confirms that there is a significant strong relation between the Gini coefficient and the growth rate of trend GDP for four countries. However, the data shows ambiguous results between the countries. In Czech Republic and Hungary the correlations are significantly positive and in France and Germany the correlation is significantly negative. This means that if the growth rate of trend GDP increases (decreases), the Gini coefficient increases (decreases) as well. The results from Czech Republic and Hungary are in contradiction Kuznets’ theory since the countries under the analysis are developed countries.
The results of the correlations with the business cycle using the HP-filter and the CF-filter do not show significant results for at least four countries. Remarkably, most correlations are less than the correlations with growth rate of trend GDP which is not in line with the hypotheses. A possible explanation for this finding is that the countries under the analysis are solely developed market economies, and they have on average a business cycle half as volatile as that of the emerging market economies (Aguiar and Gopinath, 2007).
Figure 3: Correlation coefficient Gini coefficient. ***Significant at 1% level, **Significant at 5% level, *Significant at 10% level. HP-filter and CF-filter are the business cycles using the Hodrick-Prescott filter technique and the Christiano-Fitzgerald filter technique respectively.
0.76*** 0.10 -0.77*** -0.55*** 0.48** -0.25 -0.13 -0.14 0.41** 0.21 -0.11 -0.43** 0.17 0.28 0.27 0.69*** 0.25 -0.30 -0.39* 0.40** 0.38* -1 -0,8 -0,6 -0,4 -0,2 0 0,2 0,4 0,6 0,8 1
CZE FIN FRA GER HUN SWE UK
% Growth Trend GDP HP-filter
17 As described in section 2.2, the Gini coefficient does not show if the changes in the Gini coefficient occurred because of changes in income inequality at the top of the income
distribution or the bottom of the income distribution. Therefore, a distinction is made between those two. Figure 4 and 5 depict the correlations for the 90/50 percentile ratio and the 50/10 percentile ratio respectively. As presented in the figures, no significant correlations were found with the growth rate of trend GDP in the top of the income distribution. Note that the results are obtained using data from the period from 1990 to 2014 which is a relatively short period, so the outcomes have little statistical power. In this matter, no hard conclusions can be drawn of any of the results whatsoever, but despite the insignificant results, we can still look at the direction of the correlation. However, opposing the previous finding, the correlations with the growth rate of trend GDP at the bottom of the income distribution are significant in five countries. In four of these countries the correlations are positive which is in line with Kuznets theory. However, there is no support for the theory of Foellmi and Oechslin (2008), in which the correlations with the growth rate of trend GDP is expected to be higher for the individuals at the top of the income distribution than at the bottom of the income distribution. The theory says that if the people in the bottom of the income distribution are faced with higher interest rate due to a higher demand for capital, they will not be able to seize profitable investments.
Focusing on the correlation coefficients of the business cycle, the results are
ambiguous. Also here the HP-filter and the CF-filter barely show significant results for the countries under the analysis. The income inequality in the top of the income distribution and the business cycle are positively correlated in the seven countries. This suggests that income inequality increases if the business cycle increases, which is in agreement with the
hypotheses. However, the correlation coefficients of income inequality at the bottom of the income distribution and the business cycle seem to be negative for five counties under the analysis. This is in disagreement with the hypotheses.
18 Figure 4: Correlation coefficient 90/50 percentile ratio. ***Significant at 1% level, **Significant at 5% level, *Significant at 10% level. HP-filter and CF-filter are the business cycles using the Hodrick-Prescott filter technique and the Christiano-Fitzgerald filter technique respectively.
Figure 5: Correlation coefficient 50/10 percentile ratio. ***Significant at 1% level, **Significant at 5% level, *Significant at 10% level. HP-filter and CF-filter are the business cycles using the Hodrick-Prescott filter technique and the Christiano-Fitzgerald filter technique respectively.
-0.17*** 0.68*** 0.42* 0.31 0.69*** 0.40** 0.21 0.39 0.21 -0.34 -0.32 -0.03 0.33 -0.03 0.56** 0.46** -0.5** -0.25 -0.03 0.42** -0.18 -0,6 -0,4 -0,2 0 0,2 0,4 0,6 0,8
CZE FIN FRA GER HUN SWE UK
% Growth Trend GDP HP-filter CF-filter -0.16 0.25 0.3 -0.19 0.3 0.12 -0.21 0.42* 0.37* 0.04 0.2 0.23 0.15 0.15 0.58*** 0.65*** 0.14 0.02 0.03 0.43** 0.31 -0,3 -0,2 -0,1 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7
CZE FIN FRA GER HUN SWE UK
% Growth Trend GDP HP-filter
19
4.2 Correlations Unemployment rates
Figure 6 and 7 depict the correlations of the unemployment rates for the low-skilled workers and the high-skilled workers respectively. It was expected that a higher growth rate of trend GDP would have a positive effect on the unemployment rate so that the correlation coefficient would be negative. Focusing on figure 6, this prediction is found in five countries under the analysis. Moreover, in two countries there is a significant correlation for both the HP-filter and the CF-filter to accept the hypotheses for low-skilled workers. If the business cycle increases (expansion), the unemployment rates decreases and if the business cycle decreases (recession), the unemployment rates increases.
Figure 6: Correlation coefficients unemployment rate low-skilled workers.***Significant at 1% level, **Significant at 5% level, *Significant at 10% level. HP-filter and CF-filter are the business cycles using the Hodrick-Prescott filter technique and the Christiano-Fitzgerald filter technique respectively.
Figure 7 depicts the correlation coefficients from the unemployment rates of the high-skilled workers. The correlation coefficients of the unemployment rates with the growth rate of trend GDP are, as expected, for most of the countries highly negative. The correlation coefficients of unemployment rates with the business cycle give supportive results to the main theories discussed in section 2. In five countries there exists a significant negative relation between the
-0.38 -0.18 -0.16 -0.29 -0.33*** 0.15 0.63*** 0.12 -0.67*** -0.86*** -0.28 -0.12 0.1 0.36 0.21 -0.77*** -0.85*** -0.29 -0.12 0.16 0.38* -1 -0,8 -0,6 -0,4 -0,2 0 0,2 0,4 0,6 0,8
CZE FIN FRA GER HUN SWE UK
Trend GDP HP-Filter CF-Filter
20 unemployment rates of high-skilled workers and the business cycle using both the filtering techniques.
The correlations with the business cycle using the HP-filter and the CF-filter show sometimes incompatible results in figure 6 and 7. A possible explanation for this fact is that the HP -filter is a high-pass filter which removes fluctuations with a frequency above a certain predetermined cutoff point and the CF-filter is a band-pass filter which also removes
fluctuations with a frequency below a certain predetermined cutoff point. Moreover, King and Rebelo (1993) demonstrate that dynamics of the HP-filtered data can differ remarkably from those based on difference operations or other detrending methods. The HP-method can generate business cycle dynamics even if none are present in the underlying data.
Figure 7: Correlation coefficients unemployment rate high-skilled workers.***Significant at 1% level, **Significant at 5% level, *Significant at 10% level. HP-filter and CF-filter are the business cycles using the Hodrick-Prescott filter technique and the Christiano-Fitzgerald filter technique respectively.
-0.63*** -0.29** 0.33 0.12 -0.29*** -0.35** -0.51*** -0.50** -0.64*** -0.53** 0.11 -0.07 -0.53** -0.59*** -0.45* -0.81*** -0.61*** 0.18 -0.04 -0.48** -0.62*** -1 -0,8 -0,6 -0,4 -0,2 0 0,2 0,4
CZE FIN FRA GER HUN SWE UK
Trend GDP HP-filter CF-filter
21
5. Conclusion
In this section a conclusion will be given based on the findings and results of the previous chapter and suggestions for future research will be discussed.
5.1 Summary and Concluding Remarks
In this paper, the relation between the income inequality, the growth rate of trend GDP, and the business cycle is evaluated. As well as the relation between unemployment rates, growth rate of the trend GDP, and the business cycle. It has attempted to explain these relations in different parts of the income distribution. The aim has been to see if there exist a significant relation between these variables and whether this relation is positive of or negative. To answer this question, seven countries are analyzed for at least the period from 1995 to 2014. First, the business cycle is extracted by using the HP-filter and the CF-filter. After that, a Pearson correlation analysis is done. The Gini coefficient, the 90/50 percentile ratio, and the 50/10 ratio were used as a measurement for income inequality.
The results show that there exists a significant strong relation between the Gini coefficient and the growth rate of trend GDP. However, it showed contradictory results. The relation between income inequality and the growth rate of trend GDP is not higher at the top of the income distribution comparing to income inequality at the bottom of the income distribution, which does not support the hypotheses. The relation between income inequality at the top of the income distribution and the business cycle is positive. Whereas this relation at the bottom of the income distribution is found to be negative. The relation between the
unemployment rates of low-skilled workers and the growth rate of trend GDP is for five countries negative as expected. However, only in two countries there is a significant negative relation found for both the HP-filter and the CF-filter. Analyzing the relation between the growth rates of trend GDP and the unemployment rates of high-skilled workers give a
negative relation for most of the countries. Moreover, the relation between the unemployment rates and the business cycle using both the filtering techniques gives a relation which was predicted by studying the literature. It is found that if the business cycle increases, the unemployment rates decreases.
5.2 Suggestions for Further Research
The literature review outlines several theories that could explain a relation between income inequality, unemployment rates, the trend GDP and the business cycle, but none has been
22 subject to rigorous empirical tests. Therefore, this paper suggests the need for not only a further careful reassessment of the relation between these variables but also further theoretical and empirical work evaluating the channels through the variables and any other variables are related. A viable explanation for the conflicting results found in the current study regarding the relations with the business cycle could be that the business cycles from the countries under the analysis are not reliable since the developed countries do not have volatile business cycles. Therefore, another suggestion for further research would be including more countries with emerging market economies in which the business cycles are twice as volatile as the countries under this analysis. A second shortcoming is the drawbacks found of using the HP-filter technique. Considering more filtering techniques such as the Baxter-King filter will generate more robustness of the results. Moreover, a larger timeframe would improve the accuracy of the HP-filter and the CF-filter. Another follow-up to this analysis could be done by using several sets of observations concerning a higher number of countries. Furthermore, measuring the income inequality at the top of the income distribution and the bottom of the income distribution could be done by considering more percentile ratios such as the 90/75 percentile. This will give more detail about where the changes in income inequality occur in the income distribution.
23
Appendix
Table 1: List of countries used in the analysis
Czech Republic Hungary
Finland Sweden
France United Kingdom
Germany
Table 2: Descriptive Statistics
Table 3: Data sources
Variable Description Source
Growth rate Trend GDP Growth rates of trend GDP are
based on constant prices, constant PPPs
OECD Statistics, National accounts
HP-Filter Business Cycle by
Hodrick-Prescott filter
Own Elaborations using STATA
CF-Filter Business Cycle by
Christiano-Fitzgerald
Own Elaborations using STATA
GINI Disposable income , post taxes
and transfers
OECD Statistics, Income Distribution and Poverty
P90/P50 Ratio: upper bound value of the
ninth decile/median income
OECD Statistics, Income Distribution and Poverty
P50/P10 Ratio: median income/upper
bound value of the first decile
OECD Statistics, Income Distribution and Poverty
UN_LOW Unemployment rate of the low
skilled workers
OECD Statistics, Labor, World Indicators of Skills for
Employment
Variable N Mean Std.Dev Min Max
GDP TREND 175 223.503 77.904 21.070 323.894 HP-filter 175 -3.20e-17 3.199 -10.567 11.614 CF-filter 175 -2.520 6.957 -14.603 20.915 GINI 175 0.284 0.035 0.211 0.361 P90/P50 164 1.870 0.208 1.516 2.431 P50/P10 164 1.656 0.209 1.312 2.055 UN_LOW 137 15.719 4.797 7.6 28.8 UN_HIGH 137 9.928 1.468 1.2 7.5
24
UN_HIGH Unemployment rate of the high
skilled workers
OECD Statistics, Labor, World Indicators of Skills for
Employment
Table 4: Correlation coefficients for Czech Republic. P-values are in parentheses below the correlation coefficients. ***Significant at 1% level, **Significant at 5% level, *Significant at 10% level.
Measure Growth Trend GDP HP-filter CF-filter
GINI 0.7555*** (0.0000) -0.1375 (0.5121) 0.2738 (0.1854) P90/P50 -0.1634 (0.5039) 0.4220* (0.0719) 0.5834*** (0.0087) P50/P10 -0.1693*** (0.0000) 0.3887 (0.1000) 0.5565** (0.0133) UN_LOW -0.3784 (0.1342) 0.1246 (0.6337) 0.2124 (0.4130) UN_HIGH -0.6263*** (0.0071) -0.4976** (0.0421) -0.4500* (0.0699)
Table 5: Correlation coefficients for Finland. P-values are in parentheses below the correlation coefficients. ***Significant at 1% level, **Significant at 5% level, *Significant at 10% level.
Measure % Growth Trend GDP HP-filter CF-filter
GINI 0.1023 (0.9974) 0.4055** (0.0443) 0.6947*** (0.0001) P90/P50 0.2515 (0.2253) 0.3661* (0.0719) 0.6528*** (0.0004) P50/P10 0.6783*** (0.0002) 0.2085 (0.3173) 0.4552** (0.0222) UN_LOW -0.175 (0.9415) -0.6747*** (0.0011) -0.8316*** (0.0000) UN_HIGH -0.2903** (0.0821) -0.6353*** (0.0026) -0.8054*** (0.0000)
25 Table 6: Correlation coefficients for France. P-values are in parentheses below the correlation coefficients. ***Significant at 1% level, **Significant at 5% level, *Significant at 10% level.
Measure % Growth Trend GDP HP-filter CF-filter
GINI -0.7685*** (0.0000) 0.2121 (0.3087) 0.2493 (0.2295) P90/P50 0.3041 (0.8832) 0.0418 (0.8610) 0.1406 (0.5543) P50/P10 0.4245* (0.0621) -0.3420 (0.1399) -0.5045** (0.0233) UN_LOW -0.1572 (0.5079) -0.8559* (0.0000) -0.8494*** (0.0000) UN_HIGH 0.3329 (0.4816) -0.5267** (0.0170) -0.6080*** (0.0045)
Table 7: Correlation coefficients for Germany. P-values are in parentheses below the correlation coefficients. ***Significant at 1% level, **Significant at 5% level, *Significant at 10% level
Measure % Growth Trend GDP HP-filter CF-filter
GINI -0.5471*** (0.0047) 0.0076 (0.9712) -0.3015 (0.1430) P90/P50 -0.1914 (0.3595) 0.1971 (0.3450) 0.0246 (0.9994) P50/P10 0.3074 (0.1349) -0.3209 (0.1178) -0.2478 (0.2324) UN_LOW -0.2891 (0.2164) -0.2840 (0.2249) -0.2928 (0.2103) UN_HIGH 0.1234 (0.7441) 0.1132 (0.8000) 0.1768 (0.4559)
Table 8: Correlation coefficients for Hungary. P-values are in parentheses below the correlation coefficients. ***Significant at 1% level, **Significant at 5% level, *Significant at 10% level.
Measure % Growth Trend GDP HP-filter CF-filter
GINI 0.4755** (0.0163) -0.4281** (0.0328) -0.3877* (0.0555) P90/P50 0.3029 (0.1411) 0.2252 (0.2790) 0.028 (0.9895)
26 P50/P10 0.6897*** (0.0001) -0.0343 (0.8706) -0.0276 (0.8959) UN_LOW -0.3262*** (0.0000) -0.1205 (0.6129) -0.1187 (0.6181) UN_HIGH -0.2923*** (0.0000) -0.0667 (0.7799) -0.0417 (0.8615)
Table 9: Correlation coefficients for Sweden. P-values are in parentheses below the correlation coefficients. ***Significant at 1% level, **Significant at 5% level, *Significant at 10% level.
Measure % Growth Trend GDP HP-filter CF-filter
GINI -0.2526 (0.8028) 0.1786 (0.6943) 0.4027** (0.0459) P90/P50 0.1207 (0.5655) 0.1524 (0.4671) 0.4226** (0.0353) P50/P10 0.4019** (0.0464) -0.3272 (0.1104) -0.4174** (0.0379) UN_LOW 0.1545 (0.8547) 0.1012 (0.7521) 0.1583 (0.5050) UN_HIGH -0.3497** (0.0606) -0.5265** (0.0171) -0.4784 (0.0329)
Table 10: Correlation coefficients for the United Kingdom. P-values are in parentheses below the correlation coefficients. ***Significant at 1% level, **Significant at 5% level, *Significant at 10% level.
Measure % Growth Trend GDP HP-filter CF-filter
GINI -0.1280 (0.5420) 0.2806 (0.1742) 0.3783* (0.0622) P90/P50 -0.2068 (0.3213) 0.1537 (0.4633) 0.3137 (0.1267) P50/P10 0.2067 (0.3215) -0.0304 (0.8852) -0.1800 (0.3892) UN_LOW 0.6339*** (0.0027) 0.3632 (0.1161) 0.3793 (0.0991) UN_HIGH -0.5093** (0.0218) -0.5937*** (0.0058) -0.6183 (0.0037)
27
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