Are changes in the dispersion of hours worked a cause of increased earnings inequality?

Checchi, Daniele; García-Peñalosa, Cecilia; Vivian, Lara Article Are changes in the dispersion of hours worked a cause of increased earnings inequality? IZA Journal of European Labor Studies Provided in Cooperation with: IZA – Institute of Labor Economics Suggested Citation: Checchi, Daniele; García-Peñalosa, Cecilia; Vivian, Lara (2016) : Are changes in the dispersion of hours worked a cause of increased earnings inequality?, IZA Journal of European Labor Studies, ISSN 2193-9012, Springer, Heidelberg, Vol. 5, Iss. 15, pp. 1-34, https://doi.org/10.1186/s40174-016-0065-2 This Version is available at: https://hdl.handle.net/10419/195011 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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IZA Journal of European Labor Studies (2016) 5:15 DOI 10.1186/s40174-016-0065-2 ORIGINAL ARTICLE Open Access Are changes in the dispersion of hours worked a cause of increased earnings inequality? Daniele Checchi1,2,3*, Cecilia García-Peñalosa4,5 and Lara Vivian4 *Correspondence: [email protected] 1University of Milan, Milan, Italy 2Irvapp-FBK, Trento, Italy 3IZA, Bonn, Germany Full list of author information is available at the end of the article Abstract Earnings are the product of wages and hours of work; hence, the dispersion of hours can magnify or dampen a given distribution of wages. This paper examines how earnings inequality is affected by the dispersion of working hours using data for the USA, the UK, Germany, and France over the period 1989–2012. We find that hours dispersion can account for over a third of earnings inequality in some countries and that its contribution has been growing over time. We interpret the expansion in hours inequality in European countries as being the result of weaker union power that led to less successful bargaining concerning working hours. JEL Classification: D31, J22 Keywords: Earnings inequality, Working hours, Inequality index decomposition 1 Introduction A vast literature has examined the evolution of wage and earnings inequality over the past three decades and, despite substantial heterogeneity across countries, has identified a major increase in the dispersion of both in many industrial economies.1An orthogonal research agenda has focused on the evolution of working hours and in particular on the divergence in working patterns between the USA and Europe since the 1970s.2Given such differences across countries, it is conceivable that the hours of work also differ in terms of their dispersion, raising the question of whether hours inequality has contributed to the increase in earnings inequality. Understanding the role and source of hours dispersion is crucial for the design of policies aimed at reducing inequality. On the one hand, policies that try to increase the hours for those with the lowest skills and wages and reduce them for those at the top of the distribution can be alternatives to ex post redistribution. On the other, the source of the dispersion is important for policy as it could be due to imposed constraints or the result of certain groups, such as women with young children, choosing to spend less time at work. This paper represents a first step in trying to understand those questions. We use data for the USA, the UK, Germany, and France to decompose earnings inequality and assess the roles played by the dispersion of wage and by inequality in hours in explaining cross-country differences and changes over time. By definition, an individual’s earnings are the product of her hourly wage rate and her hours of work. Using as our © 2016 The Author(s). Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Checchi et al. IZA Journal of European Labor Studies (2016) 5:15 Page 2 of 34 inequality index the mean log deviation (MLD), an inequality index belonging to the general entropy family, we decompose earnings inequality into the dispersion of hourly wages and a component capturing the contribution of hours. This term has itself two elements, a measure of the inequality of hours of work and a term capturing the correlation between hours and hourly wages. Hours of work can as a result magnify or dampen wage inequality depending on how dispersed hours are and of whether they are positively or negatively correlated with wages. Our sample covers the period 1989 to 2012 and considers both aggregate behavior as well as that of subgroups defined by gender and skill category. When we look at the distribution of hours, we find a surprising pattern. Figure 1 plots the distribution of hours worked by employed individuals in our four sample countries. The left-hand panels depict the USA and France, while the right-hand ones present the distributions in the UK and Germany. In order not to focus on a single, potentially unrepresentative, year, the data cover two 5-year periods, 1995–2000 and 2007–2012. The USA and France exhibit fairly concentrated distributions, with about 30 % of individuals declaring to work around 40 h a week in 1995-2000. For the latter period, this fraction falls slightly in the USA, while France exhibits twin peaks due to the introduction of the 35-h week. In sharp contrast, Germany and the UK present fairly dispersed distributions, with much thicker tails at the bottom and, especially, at the top. Fig. 1 Distribution of hours worked by country. Source: Authors’ calculations; see Section 3 below Checchi et al. IZA Journal of European Labor Studies (2016) 5:15 Page 3 of 34 These differences in dispersion are reflected in the way in which wages and hours affect the distribution of earnings, as captured by our decomposition of the mean log deviation. Although our results indicate that in all countries the dispersion of working time is an unequalizing factor that increases earnings inequality over and above that implied by wages, differences across countries are substantial. In the USA and France, the overall contribution of hours to earnings inequality is moderate, with wages accounting for at least two thirds of the inequality in earnings. In contrast, hours play a crucial role in the UK and Germany, being responsible for between 28 and 40 % of the dispersion in earnings, respectively. We pay particular attention to the covariance between wages and hours, which exhibits very different patterns across countries and over time. Wages and hours move together in the Anglo-Saxon economies, while they are negatively correlated in France and Germany at the start of the sample period, implying that part of the dispersion in wages was offset by the fact that those with the lowest earning potential spend more hours at work, the effect being particularly strong in France. These countries exhibit, however, an increase in the covariance over time, and by the end of the period, those with higher wages also work longer hours. In the case of Germany, this change has accounted for half of the increases in earnings inequality; in France, it is the major culprit. Although some of the differences are related to the skill and gender composition of employment, between-group inequality in hours is only a small part of the story. Observed changes over time are largely due to the behavior of unskilled men and skilled women. Hours inequality has increased for the two groups, and both exhibit a marked increase in the covariance which has gone from being negative at the start of the period to null or positive. As a result, the equalizing force due to those with lower wages working longer hours seems to have been eroded over time. Our paper contributes to two strands of literature. As mentioned before, there is a substantial literature on cross-country differences in working hours, and we add to this a new dimension by focusing on hours inequality. We also contribute to our understanding of what drives earnings dispersion by focusing on the neglected role of hours. Our paper is closely related to the analysis by Gottschalk and Danzinger (2005) of the relationship between individual wage rate inequality and household income inequality in the USA. They examine the various elements that determine household income inequality and emphasize, among other things, the importance of considering the distribution of hours. As in our results, they find an important role for changes in the hours worked by women. Our analysis has a very different focus as we provide an international comparison rather than the more detailed analysis of a single country that they consider. Our analysis is also related to Bell and Freeman (2001) and Bowles and Park (2005) who argue that greater wage inequality is associated with higher average hours of work, implying that the increase in wage inequality that occurred over the last decades is likely to have spurred an increase in hours worked. We argue that the impact of this mechanism on overall inequality depends on two channels, how unequal the hours response is and on the correlation of hours worked and hourly wages. The paper is organized as follows. Section 2 describes our empirical approach and presents the decomposition that we use and is followed by a section describing the data. Section 4 presents our main findings, while we conclude in Section 5. Checchi et al. IZA Journal of European Labor Studies (2016) 5:15 Page 4 of 34 2 Decomposing earnings inequality A vast literature has examined the decomposition of inequality indices by factor components.3As is well known, the various inequality indices have different merits and drawbacks, and the choice of index is consequently not trivial for the results. Two common measures are the half-squared coefficient of variation (CV), which is particularly tractable, and the Gini coefficient, with the latter providing a less tractable decomposition but being less sensitive to extreme observations than the former.4Moreover, recent work, such as Jenkins and van Kerm (2005), proposes density function decompositions which have the advantage of being independent of the choice of inequality index. These approaches have focused on decompositions over additive terms and are hence easily applicable to income factors. In the case of earnings, we are interested in decomposing total earnings inequality into a term due to wage rate inequality and one capturing hours inequality. Defining the total earnings of individual ias yi, we have that they are the product of the hourly wage, wi,andthenumberofhoursworked,hi.Thatis, yi=wihi.(1) Our two terms of interest appear multiplicatively, and as a result, there are few inequality indices that can be satisfactorily decomposed. We have chosen to employ the mean log deviation (MLD), an index belonging to the general entropy (GE) family. The MLD, also called Theil’s Lindex, is the general entropy index for α=0andsharesanumberof desirable properties of this class of indices.5The parameter αin the GE class of indices captures the weight given to income differences at various parts of the income distribution. For lower values of α,suchasα=0, GE is particularly sensitive to changes in the lower tail of the distribution. The MLD is defined as the difference between the log of the average of a variable and the average of its log and has been shown by Duro and Esteban (1998) to be decomposable. The overall inequality in earnings can hence be expressed as the sum of three components: inequality in hourly wages, inequality in hours worked, and a component capturing the correlation between hours worked and hourly wages. The MLD of earnings is denoted by Iy, which is defined as Iy=1 N N  i=1 ln ¯y yi ,(2) where Nis the number of observations and ¯yis average earnings. We can also define the index for hourly wages and hours worked, namely, Iw=1 N N  i=1 ln ¯ w wi ,(3) Ih=1 N N  i=1 ln ¯ h hi ,(4) where ¯ wand ¯ hdenote the average levels of the two variables. Using the fact that the covariance between hourly wages and hours worked, cov, can be showntobegivenbycov=y−wh , Eq. (2) can be expressed as the sum of (3) and (4) Checchi et al. IZA Journal of European Labor Studies (2016) 5:15 Page 5 of 34 plus a third term capturing the correlation between hours worked and hourly wages. That is, Iy=Iw+Ih+ln 1+cov ¯ w¯ h   ρ (5) These three terms represent the absolute contributions to inequality of the various elements. The first two terms are simply inequality in hourly wages and hours worked, and both are positive. The third term, denoted ρ, captures the correlation between hours and wages. If the covariance is negative, this term will be negative too, reducing earnings dispersion. The total contribution of hours to overall inequality hence depends on the value of the sum of the dispersion in hours and the correlation term. Whenever this sum is equal to zero, earnings inequality equals the dispersion in the hourly wage rate and hours play no role. If, instead, the sum is positive, then hours magnify the impact of wage inequality on earnings dispersion. When the correlation term is sufficiently negative, Ih+ρmay be negative, implying that hours reduce overall inequality, and the more dispersed hours are, themoretheywillreduceinequality. A convenient way of expressing Eq. (5) is to consider the relative contributions of the three terms, obtained when dividing Eq. (5) by Iy,thatis, 1=Iw Iy  RCw +Ih Iy  RCh +ρ Iy  RCρ .(6) The terms RCw,RC h,andRC ρare the relative contribution of inequality in hourly wages, of the dispersion of hours, and of the correlation term to inequality in earnings, respectively. In other words, they measure the share of earnings dispersion due to each of the three components. There are two key questions that we want to address that can be framed in terms of these contributions. The first one is how close RCwis to 1. If the relative contribution of wages is close to 1, it would indicate that most of earnings inequality is due to differences in the hourly wage rates received by individuals and that hours play a small role. In contrast, a small value of RCwwould imply that differences in hours worked magnify the dispersion of wages. Second, note that a high RCwdoes not imply that there is little inequality in hours. In fact, it may be due to hours exhibiting little dispersion or to hours being unequally distributed but negatively correlated with hourly wages. In the second case, individuals will be partly offsetting the impact of wage inequality by working more the less well-paid they are. It is in fact possible that, if the correlation is sufficiently negative, the term RCρtotally offsets RCh, implying that hours inequality makes the distribution of earnings less unequal than that of wages. The MLD index allows us to further decompose Eq. (5) into a term capturing withingroup (W) and one measuring between-group (B) inequality. If the total population is divided into Jexhaustive groups, with group j∈{1, ..., J}, then the inequality index for earnings takes the form Iy= J  j=1 pjln(¯y ¯yj )   By + J  j=1 pjIyj   Wy .(7) Checchi et al. IZA Journal of European Labor Studies (2016) 5:15 Page 6 of 34 where pj=Nj Ndenotes the proportion of individuals belonging to group j,¯yjis the mean income of group j,andIyj refers to the inequality index computed over the members of group j. This decomposition can be performed over earnings, wages, and hours; therefore, the correlation term ρcan also be written as a sum of within-group and between-group inequality. Equation (5) implies that both the within-group and the between-group terms of inequality in wages, of hours dispersion, and of the correlation term have to sum up to within and between inequality of earnings, implying that the within and between components of ρcan be calculated as Wρ=Wy−Ww−Whand Bρ=By−Bw−Bh,respectively. Combining Eqs. (5) and (7) gives a nested decomposition of overall inequality, which takes the form Iy=Bw+Bh+Bρ   By +Ww+Wh+Wρ   Wy .(8) Using a nested approach allows us to differentiate the contribution of inequality in wages, hours dispersion, and the correlation term to inequality within and between each group. 3Thedata 3.1 Databases The harmonized dataset constructed for this paper is based on different national surveys collected from national statistical institutes. We use household or labor surveys for the USA, the UK, Germany, and France, covering two decades starting around 1990. In particular, we use the Current Population Survey for the USA; the British Household Panel Survey and, from 2009, Understanding Society for the UK; the German Socio-Economic Panel for Germany; and the Enquete Emploi for France (which becomes the Enquete Emploi en temps continue in 2003), all of them surveys that have been widely used in the empirical literature on inequality. For example, CPS data was used by Murphy and Welch (1992) in their seminal paper on wage inequality in the USA, while GSOEP has been employed by Bell and Freeman (2001) and the other three surveys by Blundell et al. (2013) to perform international comparisons of hours of work. Although the design of the surveys changes over time and across countries, those datasets have a core set of questions that can be harmonized. They are, in fact, the primary source for several projects that provide harmonized data for a number of countries, such as the Luxemburg Income Study (LIS) and the Cross-National Equivalent File (CNEF) dataset.6We chose not to use the already-harmonized data provided by these projects as they were not suitable for our purposes. The LIS data are available every 5 years only, and since for several countries they start only about 25 years ago, we would have had only five observations, making it harder to identify time trends. The CNEF dataset, instead, has annual observations but covers a shorter time span than that available in the original data sources. For these reasons, we resorted to using the original surveys. For the USA, we had the choice between two datasets, CPS and the Panel Study of Income Dynamics (PSID) data. A number of papers have used PSID to examine the evolution of earnings; see, for example, Gottschalk and Moffitt (1994), Moffitt and Gottschalk (2002), and Haider (2001). The PSID data is attractive because of its panel dimension, but its small sample size is a major drawback for our purposes, specially since we intend to Checchi et al. IZA Journal of European Labor Studies (2016) 5:15 Page 7 of 34 examine time trends for disaggregated workers, implying that results for the subgroups may not be representative. A second reason to prefer CPS is that it asks the same question we find in the European surveys, namely “how many hours do you usually work per week in your current job.” PSID had traditionally not included such a question, focusing on annual hours, although the question was included in some recent surveys starting in 2003. Lastly, sample attrition in PSID may have affected its representativeness over time; see Fitzgerald et al. (1998). We hence decided to use CPS data, although a comparison of inequality in hours between the two datasets is provided below. 3.2 Variable definitions Our two key variables of interest are earnings and hours worked, from which we then compute the hourly wage. We focus on prime-age workers, i.e., those who are at least 25 years old and at most 54, who are (dependent) employees in either the private or the public sector. As is well established, employment patterns for young and for mature workers differ substantially across countries, much more than for prime-age workers. Focusing on this age group allows us to abstract for differences in the education system and in retirement possibilities. Details on sample sizes by country and year are provided in the Appendix. Both variables are measured at a particular point in time, that is, we use questions referring to the current job of the individual. This contrasts with papers that use annual hours and earnings and compute wages from those. There are good reasons for not pursuing this path, since both unemployment rates and vacation patterns vary substantially across countries and would have a major impact on measured hours. Focusing on a snapshot of weekly hours/earnings implies greater comparability of the data. 3.2.1 Earnings The measure of earnings that we employ is the usual gross income from labor that the individual receives over a week from the main current job. For employees, this means contractual wages plus overtime pay. This variable is present in all the datasets, yet some important differences need to be highlighted. Our main concern is that income from self-employment is difficult to measure in household surveys, mostly because the selfemployed tend to have high non-response and under-reporting rates; in addition, income from self-employment varies considerably over time. For these reasons, the self-employed are not asked about current usual earnings in the CPS, and in the BHPS, over one fifth of self-employed respondents either refuse to give information or do not know how much they earn.7We therefore decided to remove the self-employed from our sample.8 A second concern is that three countries report gross earnings, while France only provides earnings net of social security contributions (but not of income taxes). However, since such contributions are roughly proportional to gross earnings, this difference should have little effect on measured inequality.9 Survey frequency and the period of time covered by the questions also vary across datasets. The USA and France, for instance, collect data monthly and quarterly, respectively, and the questions concern current employment. Instead, the UK and Germany survey once a year, asking questions about current earnings and also about the employment situation during the previous year. Note that although there are differences in survey frequency (monthly, quarterly, and annual), we always use questions concerning the same Checchi et al. IZA Journal of European Labor Studies (2016) 5:15 Page 8 of 34 reference period—current job—and not questions concerning earnings last year, available in some of the surveys. Therefore, the periodicity over which the survey is conducted does not create comparability problems in terms of the variable we are using. Our selection rule is to select the month of March or the first quarter of the year, and we do so for the USA and for France. However, in the case of Germany, such a choice implies a small number of observations. Since keeping the largest possible sample is crucial given our intention of decomposing the population by gender and educational groups, we use data for the entire year. For the UK, BHPS data was collected in October/November, and thus, we are forced to use this period. In all cases, we checked that at the aggregate level (i.e., before dividing into population subsamples) annual data and first-quarter/March data gave results that were not significantly different. Finally, a more technical concern is the different policy of top-coding high incomes across countries. The USA, for instance, top-codes systematically, with a top-coding value of $2885 per week for the most recent years. We decided to follow the recommendation of the LIS project, and we top-code earnings at 10 times the weighted median of earnings. For those observations for which earnings were top-coded, the hourly wage was calculated after the top-coding was performed. Since we are interested in hourly wages, we also consider extreme values for this variable. Whenever hourly wages were above 10 times the weighted median of wages, we removed those observations.10 3.2.2 Hours worked Hours worked can be measured in different ways, capturing contract hours, actual hours, or usual hours. For most of the databases, we use the question concerning “usual hours worked in the main current job.” Some databases also ask about the number of hours actually worked during the previous week. Although this variable may have less measurement problems, we were concerned with seasonality and we hence decided against its use.11 The harmonization of this variable was not straightforward due to coding problems. First, we had to make sure that it included both contractual hours and overtime. Second, it is a variable that is often truncated. In particular, Germany truncates at 80 h per week and the USA at 99 h. Given the issue we are interested in, this may be a concern as truncation affects the upper tail of the distribution of hours worked. Inspection of the data indicates that this is not the case since we did not find a concentration of observations at the truncation points. Nevertheless, we decided to drop extreme observations and consider only workers that spend between 2 and 90 h a week working on their main job. 3.3 The USA: data sources and definitions Before proceeding to examine the data for the four countries, we consider in detail data sources for the USA. Figure 1 above presents the distribution of hours of work for the USA, with hours being highly concentrated around 40 and both the upper and lower tails being rather thin. This pattern did not match our expectations, our prior being that the USA would exhibit a fat upper tail capturing the workaholic culture that we often find discussed in the popular press; see Schor (2008). Our results raise the question of whether the data we are using is the most suitable one and if other variable definitions or data sources would yield a different picture. In order to address this concern, we consider a number of additional measures. First, we consider the CPS data and our core variable of weekly hours but do not restrict our sample Checchi et al. IZA Journal of European Labor Studies (2016) 5:15 Page 15 of 34 Fig. 4 Decomposition of earnings inequality The overall evolution of these four countries is summarized in Fig. 5, where we report inequality in wages and inequality in hours for the years reported in Table 3. It can be clearly seen that each country follows a specific pattern: the UK with the highest inequality in hours vis-à-vis the USA with the highest inequality in wages, France with the lowest inequality along both dimensions, and Germany moving from the French “model” of labor market to the British one over the two decades. 4.2 Differences in hours worked across skill and gender groups The different dynamics that we observe in the four countries may reflect compositional effects. For example, if part-time employment is a major source of hours dispersion and if this type of employment concerns mainly women, then observed cross-country differences could be the result of differences in the proportions of working women. Similarly, long-working weeks may concern only high-skilled males (the workaholic trader we find in the popular press), and consequently, the share of skilled employment may be an important determinant of hours dispersion. To address these issues, we decompose earnings inequality for four population subgroups, dividing the sample by gender and educational levels, low-skilled and high-skilled, the threshold being having at least some university education. In all countries but the USA, the share of low-skilled men declines and the share of high-skilled women is on the rise during our sample period. For France and Germany, the former group remains the largest (reaching a slightly less than 40 % at the Checchi et al. IZA Journal of European Labor Studies (2016) 5:15 Page 16 of 34 Table 3 Decomposition of earnings dispersion: absolute and relative contributions Year Country IyIwIhρRCwRChRCρ 1991 USA 0.175 0.114 0.045 0.017 0.649 0.256 0.095 (0.004) (0.002) (0.002) (0.002) UK 0.255 0.131 0.094 0.030 0.514 0.370 0.116 (0.007) (0.004) (0.004) (0.005) DE 0.174 0.118 0.055 0.000 0.680 0.319 0.001 (0.004) (0.003) (0.002) (0.003) FR 0.118 0.096 0.034 −0.013 0.818 0.292 −0.109 (0.002) (0.001) (0.001) (0.001) 1995 USA 0.225 0.165 0.039 0.021 0.734 0.174 0.092 (0.004) (0.003) (0.001) (0.002) UK 0.260 0.136 0.091 0.033 0.524 0.350 0.126 (0.009) (0.005) (0.004) (0.005) DE 0.147 0.103 0.060 −0.016 0.702 0.409 −0.111 (0.004) (0.004) (0.002) (0.004) FR 0.133 0.101 0.040 −0.008 0.759 0.300 −0.060 (0.002) (0.001) (0.001) (0.001) 2000 USA 0.218 0.161 0.034 0.022 0.742 0.156 0.102 (0.004) (0.003) (0.001) (0.002) UK 0.226 0.125 0.077 0.023 0.554 0.343 0.103 (0.007) (0.005) (0.004) (0.004) DE 0.185 0.101 0.068 0.017 0.543 0.367 0.090 (0.004) (0.002) (0.002) (0.002) FR 0.131 0.093 0.040 −0.001 0.707 0.302 −0.009 (0.002) (0.001) (0.001) (0.001) 2007 USA 0.223 0.173 0.033 0.017 0.778 0.147 0.075 (0.004) (0.004) (0.001) (0.002) UK 0.227 0.134 0.064 0.029 0.592 0.282 0.126 (0.009) (0.006) (0.003) (0.004) DE 0.230 0.123 0.082 0.025 0.535 0.358 0.107 (0.006) (0.003) (0.003) (0.003) FR 0.119 0.079 0.041 −0.001 0.664 0.346 −0.010 (0.003) (0.002) (0.002) (0.003) 2012 USA 0.247 0.183 0.037 0.027 0.741 0.151 0.109 (0.005) (0.004) (0.001) (0.002) UK 0.248 0.147 0.073 0.028 0.593 0.294 0.112 (0.004) (0.003) (0.001) (0.002) DE 0.229 0.122 0.077 0.030 0.534 0.337 0.129 (0.006) (0.004) (0.003) (0.003) FR 0.137 0.086 0.042 0.010 0.626 0.303 0.071 (0.004) (0.002) (0.001) (0.002) Note: Inequality in earnings, wages, and hours is measured by the MLD and denoted by Iy,Iw,andIh, respectively. ρdenotes the correlation term, while RCiis the relative distribution of wages, hours, and the correlation term end of the sample period), while neither of the two groups of high-skilled groups do pass the threshold of 20 % each (see Fig. 12 in the Appendix). Figure 6 depicts inequality in earnings computed for each subgroup, while Figs. 7, 8, and 9 repeat the exercise for wages, hours, and the wage-hour covariance (the corresponding figures for selected years are reported in Tables 7 to 11 in the Appendix), Checchi et al. IZA Journal of European Labor Studies (2016) 5:15 Page 17 of 34 Fig. 5 Wage inequality versus hours inequality. Note: The years reported are 1994, 2000, 2005, and 2012 Fig. 6 Earnings inequality by group Checchi et al. IZA Journal of European Labor Studies (2016) 5:15 Page 18 of 34 Fig. 7 Wage inequality by group respectively. It is interesting to observe that US inequality is pulled by the male component, while in the UK it is women that exhibit the highest dispersion. Note also that the rise of inequality in Germany is mainly attributable to low-skilled workers, with inequality among high-skilled men remaining constant and that among high-skilled women exhibiting an inverse U-shaped pattern. Lastly, for all countries and for both skill levels, the female component is characterized by higher inequality when compared to its male counterpart. Figure 7 suggests that inequality in wages remains rather constant in each subgroup over the two decades, with the exception of high-skilled workers in the USA, who experienced a rising trend in the returns to education.19 Our main interest lies in Figs. 8 and 9, depicting the evolution of inequality in hours and of the covariance term. Figure 8 highlights gender differences in working hours: while male groups experience constant patterns of hours, likely centered on full-time employment, female working hours are much more dispersed, especially in the UK and gradually also in Germany. The picture is completed by Fig. 9 reporting the covariance contribution to earnings inequality. Various comments are in order. There are striking differences between the highand the low-skilled, with the latter exhibiting a smaller covariance term. In some Checchi et al. IZA Journal of European Labor Studies (2016) 5:15 Page 19 of 34 Fig. 8 Hours inequality by group groups (low-skilled men in the USA and France), hours are likely to be fixed and therefore independent from wages. When deviating from zero, the covariance between hours and wages of the low-skilled tends to be negative for males and positive for females, although, for low-skilled males, both the UK and Germany exhibit a substantial negative correlation at the start of our sample period that disappears over time. The changes for the highskilled are striking: in both gender groups, we find a move from highly negative covariance terms to nil or positive ones, with the exception of the USA where the term is positive throughout the period. Concerning high-skilled males in the UK and France, a highly negative term reaches the same (positive) level as in the USA by the end of the period. This implies that the equalizing effect stemming from the fact that those with lower wages worked more hours has been eroded over the past two decades. The case of Germany is particularly interesting, with the transition from low to high earnings inequality being in part driven by low-skilled workers: the equalizing negative correlation that used to be apparent for men disappears while women become more and more responsive to the labor market, moving from a zero covariance to a positive one, i.e., working more hours for higher wages. Skilled individuals experienced also a substantial change in the covariance term that was particularly marked for women. Checchi et al. IZA Journal of European Labor Studies (2016) 5:15 Page 20 of 34 Fig. 9 The covariance term by group These observations are confirmed by Table 4 where we propose a standard betweenwithin decomposition of each variable under analysis (earnings, wages, hours, and covariance among the last two). Equation (8) is divided by the inequality index, which yields the relative contributions of the within-group and between-group components that are reported in the table. The table hence has a double reading. The betweengroup and within-group components of earnings inequality add up to one, while the between-group (within-group) components of wages, hours, and the covariance reported add up to the between-group (within-group) components of earnings. Not surprisingly, the largest share of earnings inequality is attributable to within-group differences, with the between-group component ranging between 15 and 27 %. Note, also, that as far as hours are concerned, between-group inequality is particularly small, accounting for only around 10 % of overall inequality in hours. This indicates that attributing the dispersion of hours to, say, female part-time employment ignores most of the sources of variation. When we consider the covariance term, its between-group component exhibits different patterns across countries, increasing substantially in France, falling in the UK, and fluctuating slightly in the USA and Germany, while the within-group component is substantially larger at the end than at the start of the period for all four countries. Checchi et al. IZA Journal of European Labor Studies (2016) 5:15 Page 21 of 34 Table 4 Withinand between-group decomposition Between Within Year Country Y W H ρYWHρ 1991 USA 15.20 9.28 1.61 4.30 84.80 55.66 23.97 5.17 UK 34.69 15.16 8.34 11.19 65.31 36.22 28.69 0.40 DE 25.25 13.44 3.58 8.23 74.75 54.55 28.33 −8.12 FR 21.68 21.11 1.82 −1.25 78.32 60.64 27.37 −9.69 1995 USA 19.28 12.50 1.28 5.50 80.72 60.88 16.14 3.70 UK 26.83 10.62 6.98 9.24 73.17 41.82 28.03 3.32 DE 20.47 8.94 4.64 6.88 79.53 61.27 36.23 −17.97 FR 23.18 20.07 2.10 1.01 76.82 55.83 27.95 −6.96 2000 USA 19.21 12.53 1.15 5.53 80.79 61.63 14.49 4.67 UK 26.56 10.91 6.40 9.25 73.44 44.54 27.88 1.01 DE 23.40 8.89 5.08 9.44 76.60 45.40 31.64 −0.44 FR 20.73 15.09 2.03 3.61 79.27 55.60 28.18 −4.52 2007 USA 16.44 11.97 0.85 3.62 83.56 65.87 13.84 3.85 UK 22.27 11.48 3.99 6.80 77.73 47.67 24.23 5.82 DE 21.00 7.69 5.34 7.97 79.00 45.84 30.43 2.73 FR 20.96 9.76 2.72 8.48 79.04 56.63 31.88 −9.48 2012 USA 17.68 12.95 0.72 4.01 82.32 61.11 14.34 6.88 UK 23.26 11.04 4.51 7.71 76.74 48.30 24.93 3.51 DE 20.29 8.57 3.97 7.75 79.71 44.82 29.75 5.14 FR 24.91 11.93 2.48 10.50 75.09 50.63 27.83 −3.38 Note: The within-between index decomposition for each component is reported as a percentage of inequality in earnings 4.3 Discussion Our results indicate that the overall contribution of hours worked to earnings inequality can be substantial, accounting for over a third of overall dispersion in some instances. Moreover, if we consider together the dispersion of hours worked and the covariance between wages and hours, they are responsible, in some countries, for half of the overall earnings dispersion. Inequality in the hours of work seems to be largely driven by the female component of employment, possibly by part-time working regimes. In the two countries with the highest inequality, the UK and Germany, women account for at least 40 % of employment and both countries are characterized by substantial parttime employment. Nevertheless, our within-between group decomposition indicates that this is only part of the story, with those two countries also exhibiting very substantial inequality in hours within groups. The changing position of Germany in cross-country comparisons of earnings inequality points to the importance of changes in the covariance between hours and wages. From a labor supply point of view, it can be read as an increasing elasticity of hours to wages (which would be consistent with a higher share of women in employment); from a labor demand point of view, it may represent a prevailing intensive margin over the extensive margin. The overall result is that some countries went from a situation in which the least-paid workers had the longest working hours to one where the best-paid also work hardest.20 Checchi et al. IZA Journal of European Labor Studies (2016) 5:15 Page 22 of 34 The immediate question that arises from our analysis is to what extent the observed time patterns are correlated with institutional changes within each country. Consider union density as a global measure of the institutionalization of the labor market.21 Figure 10 plots union density against our measure of the covariance term and indicates the well-established gradual weakening of labor standards over the past few decades which has been largely driven by the increased labor market participation of women and the up-skilling of the labor force. The figure indicates that this weakening has affected differently continental Europe (France and Germany) and the Anglo-Saxon countries (UK and USA). When unions were strong, the dominant membership of unions consisted of full-time low-skilled male workers, and this was associated with limited variation in hours and reduced inequality in wages. In the UK and USA, weaker unions led to an increase in wage inequality, while in the other two European countries, they seem to have resulted in a change in the role of hours inequality, captured by the dynamics of the correlation between hours and wages. As we can see in Fig. 10, this term is negatively correlated with union density for France and Germany but does not display a clear association in the case of the UK and USA. One way to rationalize this evidence is the distinction between intensive and extensive margins. When unions are strong, they typically oppose the use (and abuse) of intensive margins by employers, on the expectation of expanding employment opportunities (extensive margins) and increasing their bargaining power. This compresses the distribution of hours around the contractual/legal duration and leaves wages to do the adjustment to excess demand/supply. As union strength declines, employers become free to choose which margin they prefer to adjust, a decision that will depend on the relative adjustment costs per hour and per head, as well as on their expectations concerning demand. As a consequence, hours become more dispersed, the labor supply elasticity becomes positive, and the residual correlation moves from nil to positive. Although more rigorous statistical tests would be required to prove our interpretation, our hypothesis implies that earnings Fig. 10 Covariance term versus union density. Note: The years reported are the odd ones except for 2008, 2010, and 2012 Checchi et al. IZA Journal of European Labor Studies (2016) 5:15 Page 23 of 34 inequality could be attenuated by union presence which would tend to reduce both wage inequality and the positive correlation between hours and wages. The decline of unions and more generally of labor standards could represent only part of the story. The main drivers of the changes we have described consist of increased female participation and up-skilling of the labor force, both taking place at different speeds and points of time in different countries. Unions in particular have not always been able to accommodate a demand for more flexible hours arrangements, which are often expressed by the marginal segment of the labor force. We are agnostic on whether the countries under analysis have achieved “excessive” flexibility in hours, especially because we do not have information on whether the increased covariance is voluntarily accepted or imposed onto them. More careful analysis of individual answers on survey questions about the perception of working regimes could help us in better interpreting the described changes. A second question raised by our analysis concerns the population we examine, in particular when non-employment increases, as is the case during the Great Recession. Lower inequality among the employed can be the result of labor shedding at the bottom of the distribution and hence be associated with greater inequality in earnings when we consider the entire population, i.e., including those with zero earnings. We have examined the evolution of earnings and hours inequality for the entire population and report in Fig. 11 the evolution of earnings, wage, and hours inequality as well as the share of the Fig. 11 Gini index including non-employed Checchi et al. IZA Journal of European Labor Studies (2016) 5:15 Page 24 of 34 non-employed for France and Germany. In the case of France, earnings and hours dispersion behave in a similar way as when we consider only those who are employed. For example, between 2000 and 2012, earnings inequality among the employed went from 0.131 to 0.137 and from 0.551 to 0.533 for the entire population. Similarly, we found little difference for the USA and the UK (not reported in Fig. 11). In contrast, Germany exhibits a particular feature: earnings dispersion increased among the employed (from 0.185 to 0.229 over the period 2000–12) but fell for the population as a whole (from 0.474 to 0.469). These patterns are clearly the result of the mini jobs that implied an increase in inequality among the employed, but since they substantially reduced the share of nonemployed individuals (from 0.25 to 0.21 over 2000–2012), they led to lower earnings inequality among the population as a whole. This example illustrates the difficulty of designing policies aimed at reducing inequality as they are likely to be very sensitive to the question “inequality of what among whom?” 5Conclusions Our paper contributes to the literature on earnings inequality by considering the role of hours worked and not only that of hourly wages, in order to address the question of whether, for a given distribution of wages, the dispersion of working time tends to dampen or magnify initial inequalities. To do so, we decompose our inequality index to quantify the contribution of inequality in hourly wages and the dispersion in hours worked to overall inequality in earnings. Hours dispersion affects overall inequality through two mechanisms, inequality in hours and the correlation between hours worked and hourly wages. As a result, if the latter term is negative (i.e., if poorly paid workers are those that work most), hours inequality may have a substantial equalizing impact. Our results uncover a number of surprising patterns. First, we find that hours inequality is moderate in the USA and France and much larger in the UK and Germany, with the distributions presenting fat tails both at the bottom (probably associated with female part-time and “mini jobs”) and at the top. Second, the contribution of hours to inequality is always positive but varies substantially across countries and over time. In 2012, it accounted for only 15 % of earnings inequality in the USA, 29 % in the UK, 30 % in France, and 34 % in Germany. In the three European countries, we find that there is a substantial change in the covariance between wages and hours, and in some cases, notably Germany, this has been a major force behind the change in the overall contribution of hours. For several groups, mainly low-skilled males and high-skilled females, the covariance was negative at the start of the period and becomes zero or positive over time. In the case of the UK, a similar pattern is observed for high-skilled males. As a result, an important equalizing force, the longer hours worked by those with the lowest pay, seems to have disappeared, with important implications for earnings inequality. The USA presents a rather stable contribution of wages, hours, and the covariance, while Germany has witnessed major changes. Between 1991 and 2012, earnings inequality moved from being par to that of France to being close to the one observed in the USA, and this was driven by a change in the contribution of hours and, especially, of the covariance which increased by 13 percentage points. Our paper indicates that the so-far neglected question of hours inequality can help us understand the evolution of earnings dispersion in certain countries. At the same time, Checchi et al. IZA Journal of European Labor Studies (2016) 5:15 Page 31 of 34 Table 9 Decomposition of earnings dispersion by skill-gender groups: absolute and relative contributions, 2000 Group Country IyIwIhρRCwRChRCρ LowUSA 0.147 0.126 0.016 0.005 0.858 0.111 0.031 skilled (0.007) (0.006) (0.001) (0.003) males UK 0.098 0.087 0.022 −0.011 0.893 0.221 −0.114 (0.006) (0.006) (0.002) (0.003) DE 0.093 0.076 0.025 −0.007 0.809 0.268 −0.078 (0.004) (0.003) (0.002) (0.002) FR 0.076 0.065 0.014 −0.002 0.851 0.181 −0.032 (0.003) (0.002) (0.000) (0.001) HighUSA 0.169 0.139 0.021 0.008 0.824 0.127 0.049 skilled (0.005) (0.004) (0.001) (0.002) males UK 0.122 0.108 0.027 −0.013 0.885 0.218 −0.103 (0.009) (0.008) (0.005) (0.005) DE 0.119 0.090 0.024 0.005 0.755 0.200 0.045 (0.011) (0.007) (0.003) (0.005) FR 0.120 0.106 0.034 −0.021 0.887 0.285 −0.172 (0.005) (0.004) (0.001) (0.003) LowUSA 0.176 0.124 0.041 0.010 0.707 0.235 0.058 skilled (0.014) (0.013) (0.003) (0.003) females UK 0.247 0.108 0.113 0.025 0.439 0.459 0.102 (0.013) (0.010) (0.007) (0.012) DE 0.212 0.093 0.110 0.010 0.437 0.517 0.047 (0.006) (0.004) (0.004) (0.005) FR 0.131 0.065 0.061 0.005 0.494 0.465 0.041 (0.003) (0.002) (0.001) (0.001) HighUSA 0.203 0.141 0.047 0.016 0.692 0.229 0.079 skilled (0.007) (0.005) (0.003) (0.003) females UK 0.191 0.099 0.088 0.004 0.518 0.460 0.022 (0.014) (0.010) (0.009) (0.013) DE 0.157 0.086 0.087 −0.016 0.549 0.551 −0.100 (0.012) (0.007) (0.007) (0.008) FR 0.107 0.090 0.048 −0.032 0.848 0.454 −0.302 (0.003) (0.002) (0.002) (0.003) Checchi et al. IZA Journal of European Labor Studies (2016) 5:15 Page 32 of 34 Table 10 Decomposition of earnings dispersion by skill-gender groups: absolute and relative contributions, 2007 Group Country IyIwIhρRCwRChRCρ LowUSA 0.152 0.127 0.019 0.006 0.837 0.123 0.039 skilled (0.006) (0.005) (0.002) (0.004) males UK 0.125 0.109 0.024 −0.008 0.869 0.195 −0.064 (0.013) (0.013) (0.004) (0.008) DE 0.138 0.109 0.030 −0.002 0.793 0.218 −0.011 (0.008) (0.005) (0.002) (0.003) FR 0.072 0.060 0.019 −0.006 0.830 0.260 −0.089 (0.004) (0.004) (0.002) (0.003) HighUSA 0.187 0.163 0.024 0.001 0.867 0.130 0.003 skilled (0.008) (0.008) (0.002) (0.003) males UK 0.160 0.127 0.026 0.007 0.792 0.163 0.046 (0.015) (0.012) (0.004) (0.007) DE 0.104 0.079 0.026 −0.000 0.760 0.245 −0.004 (0.008) (0.006) (0.003) (0.006) FR 0.121 0.086 0.037 −0.002 0.709 0.303 −0.013 (0.008) (0.005) (0.003) (0.006) LowUSA 0.173 0.116 0.041 0.016 0.670 0.235 0.094 skilled (0.008) (0.005) (0.003) (0.003) females UK 0.207 0.084 0.088 0.035 0.407 0.426 0.167 (0.016) (0.008) (0.006) (0.008) DE 0.253 0.112 0.124 0.017 0.442 0.489 0.069 (0.008) (0.007) (0.006) (0.008) FR 0.107 0.066 0.057 −0.016 0.617 0.530 −0.147 (0.005) (0.005) (0.003) (0.006) HighUSA 0.215 0.161 0.040 0.014 0.748 0.187 0.065 skilled (0.008) (0.007) (0.002) (0.003) females UK 0.219 0.118 0.082 0.020 0.538 0.372 0.090 (0.015) (0.008) (0.007) (0.008) DE 0.196 0.098 0.092 0.006 0.499 0.471 0.031 (0.015) (0.007) (0.010) (0.008) FR 0.098 0.073 0.046 −0.021 0.746 0.472 −0.218 (0.007) (0.005) (0.004) (0.006) Checchi et al. IZA Journal of European Labor Studies (2016) 5:15 Page 33 of 34 Table 11 Decomposition of earnings dispersion by skill-gender groups: absolute and relative contributions, 2012 Group Country IyIwIhρRCwRChRCρ LowUSA 0.180 0.135 0.027 0.018 0.754 0.148 0.098 skilled (0.012) (0.011) (0.002) (0.003) males UK 0.151 0.117 0.032 0.001 0.777 0.214 0.009 (0.006) (0.005) (0.002) (0.003) DE 0.146 0.107 0.040 −0.001 0.734 0.273 −0.007 (0.008) (0.007) (0.004) (0.006) FR 0.078 0.061 0.022 −0.005 0.782 0.278 −0.060 (0.004) (0.003) (0.001) (0.003) HighUSA 0.198 0.156 0.028 0.014 0.790 0.141 0.068 skilled (0.006) (0.005) (0.002) (0.003) males UK 0.175 0.143 0.028 0.004 0.815 0.161 0.023 (0.007) (0.006) (0.001) (0.003) DE 0.117 0.082 0.028 0.008 0.699 0.235 0.067 (0.008) (0.005) (0.004) (0.003) FR 0.130 0.098 0.025 0.006 0.754 0.197 0.049 (0.008) (0.006) (0.002) (0.004) LowUSA 0.194 0.122 0.048 0.025 0.627 0.246 0.127 skilled (0.014) (0.012) (0.004) (0.004) females UK 0.222 0.096 0.102 0.024 0.433 0.458 0.109 (0.006) (0.004) (0.003) (0.004) DE 0.253 0.111 0.113 0.029 0.438 0.446 0.116 (0.008) (0.004) (0.004) (0.004) FR 0.112 0.059 0.063 −0.011 0.531 0.563 −0.094 (0.004) 0.003 (0.003) (0.003) HighUSA 0.228 0.169 0.043 0.017 0.740 0.187 0.073 skilled (0.010) (0.009) (0.002) (0.003) females UK 0.212 0.127 0.080 0.004 0.602 0.378 0.020 (0.007) (0.005) (0.003) (0.005) DE 0.153 0.086 0.064 0.003 0.563 0.415 0.022 (0.011) (0.006) (0.005) (0.005) FR 0.108 0.074 0.040 −0.005 0.680 0.368 −0.048 (0.005) (0.003) (0.002) (0.003) Competing interests The IZA Journal of European Labor Studies is committed to the IZA Guiding Principles of Research Integrity. 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