In this Section, we first present the estimates of the level of intergenerational mobility in Germany—for the entire country (Sect. 4.1), separately for East and West Germany (Sect. 4.2), and in comparison with other countries (Sect. 4.3)—and then evaluate the robustness of IEE and rank-based measures of mobility to various sample specifications and empirical approaches (Sect. 4.4).
The degree of intergenerational mobility at the national level
Table 2 presents the estimates of intergenerational mobility—intergenerational rank mobility and intergenerational elasticity in earnings— for the entire sample of children, and separately for sons and daughters. Recall that ranks of children reflect their positions in the earnings distribution of children born in the same year. Similarly, fathers’ ranks are derived based on their positions in the earnings distribution of fathers, who have children born in the same year. For gender sub-samples, ranks of both fathers and children are determined using the earnings distributions within the gender subgroups. Moreover, it is important to note that the slope-coefficients of rank-rank-correlations and IEE estimates are not directly comparable (see Sect. 2 above for more details).
The estimates of intergenerational mobility across generations are statistically significant for both rank- and elasticity-based measures of mobility implying that economic outcomes of children depend on economic outcomes of their parents. The estimates for intergenerational rank mobility show that a child born to a father at the top of the earnings distribution, on average, ranks 24 percentiles higher than a child born to a father at the bottom of the distribution. When looking at the estimates of rank mobility by gender, girls appear more mobile along the earnings ladder than boys do: on average, sons of the top percentile fathers rank 38 percentiles higher than sons of the bottom percentile fathers whereas for daughters the relative advantage is only 15 percentiles.
The estimates of IEE provide further interesting results. In particular, one can see that the gender patterns in intergenerational mobility reverse when we measure intergenerational mobility using earnings elasticity across generations. On average, a 1 percent increase in fathers’ earnings is associated with a 0.42 percent increase in daughters’ earnings and 0.27 percent increase in sons’ earnings. Hence, girls appear much less mobile than boys do as soon as we look at the intergenerational elasticities in earnings. The observed differences in the gender patterns of intergenerational mobility depending on the measure used can be partially explained by the fact that IEE estimates of mobility are sensitive to the difference in the levels of inequality in the distributions of parental and children’s earnings whereas rank-based measures are not.Footnote 7 In our sample, inequality is much higher among daughters than among sons, which drives intergenerational elasticity estimates for the former upwards.
However, gender differences in the levels of intergenerational rank mobility should be interpreted with caution. Given that ranks are derived separately for sons and daughters, the same position in the gender specific earnings distributions might be associated with highly different levels of economic resources. In our sample, a daughter occupying the 50th percentile in the daughters’ earnings distribution has annual earnings of 18,643 Euros whereas a son at the same percentile of sons’ earnings distribution earns 40,879 Euros per year (see Tabel 1 above). Similarly, the difference in economic resources associated with moving from one rank to another is not the same for sons and daughters. For instance, moving from the 5th to the 10th percentile is equivalent to an increase in gross annual earnings by almost 13,000 Euros for sons but only by 3000 Euros for daughters. This evidence implies that even a big upward move along the earnings ladder for daughters might not always bring the same gain in terms of economic resources as a small move for sons.
Regional differences in intergenerational mobility: East versus West Germany
Table 3 presents the differences in the level of intergenerational mobility between East and West Germany. To derive these differences, we assign all children to either eastern or western region of Germany taking into account the place where they lived in 1989, when the German Wall fell. The region where the children grew up is in most cases the same as the region where they lived when their earnings were measured.Footnote 8 Ranks of fathers and children living in West and East Germany are defined at the regional rather than national level (see below for a sensitivity analysis for ranking within or across regions).
Table 3 shows that rank mobility across generations is lower in East than in West Germany. On average, a child born to a father at the top of the earnings distribution ranks around 34 percentiles higher than a child born to a father at the bottom of the earnings distribution in East Germany whereas in West Germany this advantage constitutes only 24 percentiles. This evidence implies that East Germany provides lower opportunities to move along the earnings ladder than West Germany does. Based on intergenerational earnings elasticities, however, we do not obtain the same conclusion. The estimates of earnings elasticity across generations are statistically significant only in the West German sub-sample. The lack of statistical significance in the model for East Germany is most likely related to a small number of observations since only 66 child-parent pairs come from that part of the country. However, given that we do obtain statistical significant results for rank-correlations based on the very same sample, the statistical insignificance for intergenerational earnings elasticities is probably due to the much larger standard deviation of earnings, as compared to ranks. Moreover, the estimated coefficient is only 0.17, indicating that income mobility based on IEE is, if anything, higher in East than in Western Germany.
The gender specific estimates in Table 3 further indicate that regional differences in the degree of intergenerational rank mobility observed in the entire sample of children also hold in gender-specific sub-samples. In particular, rank mobility is always lower in East than in West Germany. For sons, being born to a top rather than a bottom percentile father brings them a 38-percentile higher rank in East Germany as compared to a 33-percentile higher rank in West Germany. Also for daughters, the regional differences are quite small when comparing the estimated coefficients irrespectively of the statistical insignificance of the East-German estimate (which just falls short from the statistical significance with a p value of 7%). In contrast, regarding gender-specific results for East- and West-Germany based on intergenerational earnings elasticities, the estimated coefficients vary strongly. Mobility seems to be the smallest for West-German women (with an estimated elasticity of almost 62%) and almost perfect for their East-German counterparts (8%), whereas men range in-between. However, due to the combination of small sample sizes and large earnings variance, the estimates of IEE appear unreliable for combined gender-region sub-samples.
International comparisons of intergenerational mobility
An important question to ask is how Germany compares with other countries in terms of the level of intergenerational mobility. Answering this question, however, presents a challenging exercise given that the literature on intergenerational rank mobility remains scarce and covers only a restricted number of countries (i.e. Canada, Sweden, United States). In addition, to the best of our knowledge, all available studies on intergenerational rank mobility are based on pre-tax household income rather than individual earnings, which makes the comparison of our results with the results in those studies even more challenging. In order to enable such a comparison, we re-estimate rank associations across generations using pre-tax household income as an income measure while following as close as possible sample specifications used in other studies. The results of this exercise are presented in Table 4.
Table 4 shows that intergenerational rank mobility in Germany is higher than in Canada and United States, but somewhat lower than in Sweden, if we consider all children regardless of their gender. In Germany, a child raised by parents at the top of the pre-tax household income distribution, on average, ranks 21 percentiles higher compared to a child raised by parents at the bottom of the distribution. In Canada and the USA, this difference constitutes 24 and 34 percentiles accordingly whereas in Sweden it is around 19 percentiles. This ranking seconds the more recent evidence based on the estimates of intergenerational earnings elasticity (see, among others, Corak, 2006; Schnitzlein, 2016). The ranking of countries, however, differs again if one looks at each gender separately. With no available evidence for Canada, Germany keeps its position in between Sweden and the USA in terms of mobility estimates for daughters. For sons, Germany stands as the most mobile country being followed by Sweden and the United States.
The results in Table 4 are close to Bratberg et al. (2017), who compared intergenerational mobility curves in Germany, Norway, Sweden and the USA also using pre-tax household income. In particular, they found that intergenerational rank mobility is the highest in Nordic countries with Germany standing close to them whereas it is the lowest in the USA. Similar to our study, the authors also document substantial heterogeneity in the country ranking for gender sub-samples: while Germany stands in between Nordic countries and the US regarding the level of intergenerational mobility of women, it outperforms all other countries in terms of intergenerational mobility of men.
Sensitivity of intergenerational mobility estimates
In order to test the robustness of our findings to different empirical approaches and sample specification choices, we perform a set of additional analyses. In particular, we evaluate the sensitivity of both elasticity-based and rank-based estimates of intergenerational earnings mobility to (1) the mismatch in the stages of the life-cycles at which incomes of parents and children are measured; (2) the number of years used for approximation of permanent income; (3) the treatment of zero values in income variables; (4) the choice of annual versus hourly earnings, and (5) rank specification at the national versus regional level. The results of this exercise are summarized below.
The mismatch in the stages of the life cycle at which incomes of parents and children are measured
In order to identify the sensitivity of our results to the mismatch in the stages of the life cycle at which incomes of parents and children are measured, we estimate a number of models with alternative specifications of the age at which children’s income is measured. In the first model, we consider earnings of children when they were between 30 and 32. In the subsequent models, we measure earnings of children in the second half of their 30s, i.e. when they were 35–37, 36–38, and 37–39 years old. The results of this exercise are summarized in Table 5.
The estimates reveal that rank-based measures of intergenerational mobility are much more robust to the mismatch in the stages of the life-cycle at which parental and children’s incomes are taken into account. The estimate of relative rank mobility at the age of 30–32 is a bit smaller than the baseline estimate (0.207 versus 0.242) but the difference is small compared to the difference in the estimates of IEE (0.252 versus 0.368). Moreover, the estimates of rank persistence across generations stabilize in our sample after children reach the age of 35 whereas the estimates of intergenerational elasticity of earnings keep increasing.
The number of years used for approximation of the permanent income
To test the sensitivity of the baseline estimates of intergenerational mobility to the number of years used for approximation of permanent income, we run a series of models, where we average earnings of children and parents over different number of years (Table 6).
The results show that rank-based measures of intergenerational mobility are quite robust to the number of years used for approximation of permanent earnings. In particular, decreasing the number of years over which parental earnings are averaged results into a decline in the estimates of relative rank mobility but the size of the decline is relatively small. For example, taking parental earnings for only one year yields the estimate of the rank-rank slope of 0.227 against the baseline estimate of 0.242. The estimates of relative rank mobility also do not fluctuate much depending on the number of years used for averaging earnings of children.
The estimates of intergenerational earnings elasticity, in contrast, appear very sensitive to attenuation bias. A decrease in the number of years over which parental earnings are averaged leads to an underestimation of earnings persistence across generations. For example, with only one year of fathers' earnings taken into account the elasticity of children’s earnings with respect to fathers’ earnings constitutes 0.231, which is 37 percent lower than the baseline estimate of 0.368.
Treatment of zero values in income variables
In our primary analysis, we exclude observations with earnings smaller than 1200 Euros per year. To evaluate the impact of this restriction on the mobility estimates, we perform calculations for two alternative samples (Table 7). In the first alternative sample, we include all observations with positive values of earnings. In the second sample, we also include observations with zero earnings but recode them to one before performing the logarithmic transformation.
In line with other papers in the field (e.g. Dahl and DeLeire 2008; Chetty et al. 2014a, b; Corak 2017), the results of the sensitivity analysis indicate that rank-based measures of intergenerational mobility are more robust to the treatment of zero values in income variables than elasticity-based measures. The estimates of rank mobility remain statistically significant when we include observations with low or zero values in the analysis. They also decrease in size to a much smaller extent than the estimates of IEE. In the sample with low values of earnings, the estimate of relative rank mobility is only 5 percent lower than in the baseline model whereas in the sample with zero values of earnings it is 30 percent lower. In contrast, elasticity-based measures of intergenerational mobility become insignificant as soon as we include observations with zero values in the sample.
Annual versus hourly earnings
The annual measure of earnings does not account for the intensity of labor supply at the individual level, i.e. the choice of the number of hours to work. As a consequence, one might end up comparing annual earnings of a full-time employed father with annual earnings of a part-time employed child, or the other way around. This is especially relevant for women, who are more likely than men to work part time. In order to test the sensitivity of our estimates to this issue, we repeat the analysis using hourly wages as a measure of income. The results of this exercise are provided in Table 8.
The main conclusion of this exercise is that both elasticity- and rank-based measures of mobility are sensitive to the type of earnings used but the level of sensitivity is smaller in rank-based measures. For all children together, we find relative rank mobility being 12 percent lower for hourly than for annual earnings. For IEE estimates, the difference is 30 percent and it goes in the opposite direction – we find higher mobility of children’s earnings with respect to parental earnings. This is largely due to the fact that annual earnings are more unequally distributed than hourly earnings and IEE estimates are sensitive to inequality in the earnings distribution.
Rank specification at the national versus regional level
In our analysis in Sect. 4.1 we defined individual ranks within the national distribution of earnings (either for all children together, or separately by gender). One may argue, however, that a given level of earnings can correspond to a relatively high rank in East Germany and to a relatively low rank in West Germany. In order to test the sensitivity of our main results to the different ways of computing individual ranks, we re-estimate the level of intergenerational rank mobility using ranks specified within regional distributions of earnings. The results of this exercise are presented in Table 9 below.
The main message from Table 9 is that the estimates of relative rank mobility across generations are not sensitive to the geographical level at which ranks are defined in the sample where all children are pooled together (0.242 versus 0.251). The estimates, however, differ somewhat depending on the geographical level used for definition of ranks in the gender-specific subsamples. For boys, the degree of intergenerational rank mobility increases if we define their ranks and the ranks of their fathers at the regional level. For girls, it is the other way around – defining ranks at the regional rather than national level leads to higher estimates of rank persistence across generations. Most importantly, the gender differences in intergenerational rank mobility do not change much: regardless of the definition of ranks, sons appear always less mobile than daughters do. One should keep in mind, however, that this might be a German case, which does not necessarily hold for other countries.