2.1 Institutional and Historical Background

Norway is a typical Scandinavian welfare state with a proactive labor market policy, comprehensive social security benefits, and a redistributive tax policy (see Blundell, Graber and Mogstad (2014)). Welfare provision is financed primarily through high labor and capital income taxes and, to a smaller extent, by returns from a sovereign wealth fund (which, by 2021, has a market capitalization more than three times the GDP). The labor market functions relatively well, with low unemployment and high participation rates for men and women. This is partly because of strong cooperation between unions, employers, and government that allows for wage flexibility to generate competitiveness (see Nilsen (2020)).

Although the unemployment rate is low, the number of working-age Norwegians who receive sickness or disability benefits is among the highest in the OECD (e.g. Hemmings and Prinz (2020)). While the duration of unemployment benefits and average replacement rates are relatively generous (currently two years and 62.4%, respectively), requirements for unemployment benefits are strict (Fevang, Markussen and Roed (2014)). Sickness pay is available for all employees with a 100% replacement rate up to a limit. Bratsberg, Fevang and Roed (2013) have shown that a large fraction of disability claims is triggered by job loss.

Norway experienced a remarkable increase in GDP per capita since the 1970s, which almost quadrupled from $22,000 to more than $75,000 (Figure 1a). Despite this overall outstanding performance, the economy has been subject to large cyclical variations. Until the banking crisis of the early 1990s, Norway experienced a large increase in labor force participation of women by around 25 percentage points (pp.) reaching to almost an 80% participation rate, one of the highest among developed countries (Figure 1c). The large inflow of workers contributed to the steady growth during this period. As a result, average real wages grew by only around 25% during this period (Figure 1b) compared to the 70% growth in GDP per capita. However, the banking crisis led to a sharp decline in GDP and labor force participation (especially for men, from 94% to 85%) and an increase in unemployment from around 1% to 5% (Figure 1d).

The aftermath of the recession, however, brought a quite significant resurgence of growth, with GDP per capita increasing from $40,000 to $75,000 in a span of 18 years until the Great Recession. During this period, oil prices increased sevenfold, which significantly contributed to the strong economic growth. The share of the oil sector in the economy grew from 5% to 10% in 1990 to 35% in 2007 at the peak of the oil prices (Figure 1a). Average wage growth was also strong during this period from $40,000 to $56,000 (Figure 1b). The Great Recession put a stop to this rapid economic growth, after which the Norwegian economy has been stagnating for 10 years without significant improvement, although, Norway managed to maintain high labor participation rate (above 80%) and low unemployment rate (around 4%) during this stagnation period.

(a) GDP per Capita

(b) Average Real Wage

(c) Employment Rate

(d) Unemployment Rate

2.2 Data Description

Our dataset consists of several high-quality registers covering the entire Norwegian population. All of them are collected for administrative purposes; thus, our data are less subjected to the measurement error and sample attrition that usually plague survey data. In our analysis, we use two different measures of income. The first one is labor earnings between 1993 and 2017. The second one covers a longer time span between 1967 and 2017 and includes both earnings and work-related government transfers. Below, we describe each income measure and explain how they are used in our analysis.

Labor earnings. The first income variable is a comprehensive measure of labor income from all jobs (except for self-employment income).⁴ It is obtained from annual tax records and is third-party reported by employers.⁵ This measure allows our benchmark results on earnings inequality and volatility in Sections 3.1 and 3.2 to be comparable with other articles in this issue of the journal, which also use labor earnings in their analysis.

After-transfers income. The second income variable is collected to calculate social security pension benefits since 1967 and includes all work-related pensionable income components: labor income (as described above), self-employment earnings, unemployment, sick leave, parental leave, vocational rehabilitation, and time-limited disability benefits. The long panel dimension (51 years) of this variable is key for our analysis of the intergenerational transmission of income dynamics.

Certain measurement issues warrant specific attention for this income variable. First, some observations are top-coded as a result of an earnings limit for pension accrual. Top coding was most prevalent between 1967 and 1979. From 1986 on, there is none whatsoever (see Figure A.1 in Appendix A). Second, there are changes to how benefits are included in the data throughout the sample period: (i) Paid sick leave and parental leave were included after 1978 (paid sick leave was included even before 1978 if it was more than 90% of annual income); (ii) unemployment benefits were included after 1980; and (iii) various work activity benefits were included after 2002, 2004, and 2010. Finally, a tax reform in 1992 changed the way earnings from self-employment were reported.

Since the definition of this income measure changes over time, one should be careful in interpreting the trends in inequality and volatility derived from this income measure. Therefore, in Section 3 we focus on our consistent measure of labor earnings starting in 1993. However, these measurement issues are less of a concern for our intergenerational analysis, which pertains to the comparison of earnings risk within cohorts (e.g., fathers with more volatile incomes among their peers, or sons with steeper life-cycle income growth within their cohort) and not its variation across cohorts or over time.

We complement our data on income and wages with information on families to link children to their parents (derived from the Norwegian Population Register), educational attainment (from the National Education Register), and household wealth (from tax returns since 1993), which we will explain in more detail in Section 4. All nominal incomes are deflated to their 2018 real values using the Consumer Price Index in Norway. Furthermore, to make our results comparable across countries, we convert Norwegian kroner (NOK) values to U.S. dollars using the average exchange rate in 2018.

2.3 Sample Selection and Descriptive Statistics

Our baseline sample includes all residents in Norway between ages 25 and 55 who have a personal identification number. The number of individual-year observations between 1993 and 2017 is about 51.3 million in total. As a standard practice in the literature, we trim observations below a certain time-varying annual minimum earnings threshold (\(Y_{t}^{min}\)), both to focus on workers with a meaningful labor force attachment and to avoid few observations of very low earnings affecting our results. Norway does not have a national minimum wage defined by law. Thus, we define \(Y_{t}^{min}\) as the annual earnings of an individual who works 40 hours a week for a full quarter at half the US minimum wage, which roughly equals NOK 12,000 in 2017 (see Guvenen, Ozkan and Song (2014)). 16% of the earnings observations between 1993 and 2017 are below this threshold. However, most of these individuals are out of the labor force and receive zero labor earnings during a given year, whereas only 2% of individuals with positive labor earnings are below \(Y_{t}^{min}\). Using the after-transfer income measure, only 11% of observations are trimmed, of which 1.2% have positive after-transfer income below \(Y_{t}^{min}\).

Table I shows selected statistics for earnings from our baseline sample. First, our sample is almost evenly split between men (52%) and women (48%). Second, similar to other developed economies, the Norwegian working population has become older and more educated. Third, between 1995 and 2015, the earnings of men and women across all income levels have grown (Panel B). Finally, despite high employment rates for women, the gender earnings gap is relatively high, which stems from women working shorter hours and working more in part-time jobs (see Statistics Norway (2005)).

(a)

(b)

(c)

(d)

Stata Programs for the GRID Database. To ensure the harmonization of the statistics in the GRID database, Ozkan and Salgado (2022) provide a set of Stata programs that can be easily implemented using any panel data on earnings with only minor adaptations. The common set of results presented in this issue of the journal is generated by these programs.

3.1 Earnings Inequality

We begin our analysis with the evolution of the earnings distribution (above \(Y_{t}^{min}\)) between 1993 and 2017. We also comment on longer-run trends from our 1967-2017 sample by referring to the corresponding figures in Appendix A. Throughout the paper, we present results for men and women separately (see Appendix B.2 for the results from the combined sample). The results in this section are for raw earnings without controlling for changes in educational attainment or the age composition of the population. We find qualitatively similar patterns if we control for these observable characteristics of workers (see Appendix B.3), which suggests that compositional changes are not likely to be the main driver of the evolution of earnings distribution over our sample period.

Similar to other Scandinavian countries, Norway has a relatively compressed earnings distribution compared to other developed economies. For example, the spread between the 90th and 50th percentiles (hereafter, P90-P50) and between the 50th and 10th percentiles (P50-P10) of log labor earnings for men is on average 55 and 115 log points over our sample period (Figure B.1), respectively, compared to 100 and 150 log points for a similar sample from the U.S. in 2010 (see Guvenen, Ozkan and Song (2014)). Employing a similar sample selection and methodology, Friedrich et al. (2021) and Leth-Petersen and Saverud (2021) find roughly similar levels of inequality for Sweden and Denmark, respectively. The earnings distribution for women is relatively more dispersed than for men, mainly because of the higher inequality below the median (e.g., the P50-P10 for women is around 140 log points versus 115 log points for men).

In 1993, Norway was emerging from a severe banking crisis (see Gerdrup et al. (2004)) and entering a period of relatively strong growth, partly because of high oil prices (see Bjornland and Thorsrud (2016)). Until the Great Recession, the earnings of men grew steadily at a similar pace except for those above the 90th percentile, who enjoyed relatively steeper growth (Figures 2a and 2c). This steady growth is roughly a continuation of a longer-run trend since the 1970s except for low earners, who saw large losses during the 1991 recession (Figure A.2).⁶

During and in the aftermath of the Great Recession, however, this stable earnings growth either halted or significantly slowed down for most workers, and earnings inequality grew noticeably (Figure B.1). For example, between 2008 and 2017, incomes between the 90th and 50th percentiles grew by a mere 5 log points, whereas the 10th percentile declined during this 10-year period (Figure 2). These concerning developments are partly because of a sharp drop in oil prices from 2014 to 2015, which hit the oil-rich Norwegian economy and caused another recession in 2015.

Similar to men, women in the bottom 90th percentile experienced steady earnings growth of around 40 to 50 log points between 1993 and 2008 (Figure 2b). After 2008, income growth slowed down for everyone but more so at the bottom of the distribution, thereby increasing P50-P10, albeit to a smaller extent than for men (Figure B.1). These trends are broadly in line with those from the after-transfer income, with the key exception that after-transfer income in the bottom 10% has grown faster after the banking crises of the early 1990s (Figures A.2b and A.3b), which then led to a significant reduction in inequality until the early 2000s. Furthermore, the P90-P10 of log after-transfer income reveals a slow long-run trend of decline, starting in the mid-1970s when the labor force participation of women started increasing steeply (Figure 1c).⁷

Interestingly, earnings in the top 10% evolved differently from the rest of the distribution until 2008 as they grew faster and more unequal, albeit to a lesser extent than seen for the U.S. or the U.K. (Figures 2c and 2d). For example, male workers at the 90th percentile in 2008 earn 53% (43 log points) more relative to 1993, whereas the earnings of those at the 99th, 99.9th, and 99.99th percentiles grew by around 75%, 120%, and 230%, respectively (Figure 2c).⁸ However, after 2008, high-earnings men experienced stagnant or shrinking incomes, which also led to a slight decline in top income inequality. For women, however, top income growth has not slowed as much after 2008, and inequality has continued to increase, albeit at a slower pace.⁹

Inequality within Public and Private Sectors. Income inequality in the private and public sectors has evolved quite differently over the last 20 years (see Online Appendix A). For instance, the P90-P10 for workers employed in the private sector increased by 30 log points between 1993 and 2014. Among men, most of the increase in inequality is accounted for by an expansion of the left tail of the distribution. For women, the increase in inequality is due to the stretching of both of the tails. In contrast, inequality in the public sector has remained the same among men and declined quite significantly among women, especially after 2001. These results highlight the prominent role that the public sector plays in reducing income inequality in Norway.

3.1.1 Life-Cycle Earnings Inequality

The relatively compressed earnings distribution and the changes in inequality could, in principle, be separated into two components: inequality at young ages and the life-cycle evolution of earnings dispersion. To investigate each component, we document how within-cohort inequality evolves over the life cycle and across different cohorts. Specifically, Figure 3 plots the P90-P10 of log earnings in each age for 18 cohorts of workers entering the labor market at age 25 from 1993 to 2010. The colored markers connect different ages of the same cohort, thus showing how within-cohort inequality evolves over the life cycle. Dashed lines connect the same ages of different cohorts and show how the inequality in a particular age evolves over time.

(a) Men

(b) Women

Figure 3 – Evolution of Labor Earnings Inequality by Cohorts

Notes: Figure 3 shows the P90-P10 log earnings differential over the life cycle for selected cohorts for men and women. A cohort is defined by the year in which the cohort turns 25. Dashed lines connect individuals of the same age. The plots consider cohorts born between 1969 and 1986.

Despite the lower overall earnings inequality in Norway compared to the U.S., initial dispersion at age 25 is relatively high. For example, P90-P10 of log earnings for 25-year-old men is 230 log points in 2010 versus 220 log points for the U.S. (Guvenen et al. (2018)). In fact, initial dispersion in Norway is significantly higher compared to several other countries, for example, Sweden (Friedrich et al. (2021)), Denmark (Leth-Petersen and Saverud (2021)), and Canada (Bowlus et al. (2021)).

Furthermore, newer cohorts enter the labor market more unequal, especially above the median, compared to older cohorts, and more so for men (Figure B.4). In particular, the P90-P50 of log earnings for 25-year-old men (women) is 55 (70) log points in 1993 versus 75 (80) log points in 2017. We find similar patterns for the after-transfer income measure starting in the mid-1970s (Figure A.3). The higher initial inequality for newer cohorts mirrors the change in overall earnings inequality. Guvenen et al. (2018) and Engbom et al. (2021) also document that initial inequality and overall inequality track each other very closely in the U.S. and Brazil, respectively.¹⁰

The life-cycle profile of earnings inequality is roughly similar for all cohorts: For men between 25 and 35 years old, within-cohort inequality declines by around 70 log points and remains relatively stable afterward. Women experience a slower but roughly steady decline in inequality throughout the life cycle. Using the after-transfer income measure between 1967 and 2017, we find that men and women experience a steep decline in inequality until they are 35 years old, but then income dispersion increases slightly for men and stays relatively constant for women (Figure A.4). These findings are in sharp contrast to the increasing age profile of earnings inequality seen in several developed economies (Lagakos et al. (2018)). For example, Guvenen et al. (2021) document that the variance of log earnings increases by 55 log points between ages 25 and 55 in the U.S. The decline in earnings inequality over the life cycle also explains why Norway has a relatively compressed earnings distribution.

For men, the decline in P90-P10 over the life cycle is mainly a result of the closing of the gap between the bottom and median workers. P50-P10 declines by around 70 log points between ages 25 and 35 and remains roughly constant afterward (Figure B.4a).¹¹ In comparison, the P90-P50 decreases only until age 28 and then increases steadily (Figure B.4c). These patterns are remarkably different for women, with life-cycle inequality declining at both ends of the distribution (Figures B.4b and B.4d).

In contrast to the marked decline in earnings inequality below the 90th percentile, top income inequality increases significantly over the life cycle. The difference between the 99th and 90th percentiles of log earnings (P99-P90) increases over the life cycle by around 40 log points for men and 30 log points for women (Figures B.4e and B.4f, respectively). Furthermore, P99-P90 is higher for newer cohorts at all ages compared to older cohorts. These patterns track the rise in overall top income inequality over our sample period.

Our findings suggest that different economic mechanisms may be at play in determining the inequality at different parts of the earnings distribution, which is consistent to what other studies have found. For instance, Karahan, Ozkan and Song (2022) show that in the U.S., earnings differences between the bottom and median earners are mainly a result of the differences in unemployment risk, whereas the right-skewed distribution of returns to experience explains the inequality between the top and median earners.

3.2 Distribution of Earnings Growth

In this section, we characterize income volatility by documenting the properties of the distribution of individual earnings changes in Norway. We measure income change as the log growth rate of residual earnings between years \(t\) to \(t+k\), \(g_{it}^{k}=\tilde{\varepsilon}_{it+k}-\tilde{\varepsilon}_{it}\) for \(k=\left \{1,5\right \}\). We obtain residual earnings, \(\tilde{\varepsilon}_{it}\), by regressing log earnings in each year on a set of age dummies for men and women separately.¹²

3.2.2 Trends and Business-Cycle Variation

Volatility. Overall earnings volatility for women—as measured by the P90-P10 of log income changes—is almost twice as large as the earnings volatility for men, hovering around 115 log points for women versus 60 log points for men (Figure 4a). This is likely a result of the generous maternity leave benefits provided by the Norwegian government (up to nine months of full pay), the fact that women are more likely to work in part-time jobs with more flexible hours, and an overall weaker labor market attachment (OECD, 2019). In addition, the income volatility of men has risen significantly over our sample period, with P90-P10 increasing from 54 log points in 1993 to 65 log points in 2016, whereas for women, income volatility has remained relatively stable over time (see Figure C.5 for upper- and lower-tail volatility). These findings are in contrast with the evidence from the U.S.—also based on administrative data—that volatility is roughly similar for men and women and has been trending down since the 1980s for both (Bloom et al. (2017)). Our results, however, are similar to those documented for Italy (Hoffmann, Malacrino and Pistaferri (2021)), the U.K. (Bell, Bloom and Blundell (2021)), and Sweden (Friedrich et al. (2021)).

After-transfer income volatility displays different trends relative to earnings volatility (Figure A.5). After-transfer income volatility declines steeply since the mid-1970s especially for women, when sickness benefits and unemployment insurance were added to our after-transfer income measure. In fact, in 2017 men and women face similar volatility according to the after-transfer income measure.

Skewness. Figure 4b shows the asymmetry in the distribution of earnings growth as measured by the Kelley skewness (Kelley, 1947), \(\mathcal{S_{K}}=\frac{\text{(P90-P50)}-\text{(P50-P10)}}{\text{P90-P10}}\). In Norway, Kelley skewness of log earnings growth averages -0.025 for men and -0.014 for women during our sample period. However, when measured with the third standardized moment, earnings growth displays strong negative skewness in all years (Figure C.5c), indicating a stronger asymmetry in the extreme tails of the distribution. As expected, this negative skewness is ameliorated after including public transfers in the income measure. In fact, after-transfer income changes are positively skewed (Figure A.6).

Kurtosis. Figure 4c shows the excess kurtosis of one-year earnings changes for men and women as measured by Crow and Siddiqui (1967) kurtosis, \(\mathcal{C_{K}}=\frac{\text{(P97.5-P2.5)}}{\text{P75-P25}}-2.91\), where 2.91 corresponds to \(\frac{\text{(P97.5-P2.5)}}{\text{P75-P25}}\) of a normal distribution. The kurtosis of earnings growth has remained relatively stable around at 10 over our sample period, showing only a slight increase after the Great Recession for women.¹³ Again, including public transfers makes income changes less leptokurtic, albeit only very little (Figure A.6).

(a) P90-P10

(b) Kelley

(c) Excess Crow-Siddiqui

Figure 4 – Volatility, Skewness, and Kurtosis of Earnings Changes

Notes: Figure 4 shows the P90-P10, Kelley skewness, and excess Crow-Siddiqui kurtosis of earnings growth for men and women. The shaded areas represent recession years, with unemployment growth in the rate of more than 4 pp. and an output gap of more than 5%. See Section 2 for sample selection and definitions.

Cyclical Nature of Individual Earnings Growth. To measure the business-cycle variation in income risk, we estimate time-series regressions of earnings growth moments on the unemployment rate and GDP growth (both standardized). Only some aspects of income risk seem to be cyclical (see Table C.2).¹⁴ Even when it is statistically significant, the cyclical variation in income risk is not economically significant except during the Great Recession.¹⁵ This result can be partly explained by a coordinated bargaining system between employers, unions, and the government that allows for some wage flexibility to prevent large increases in unemployment (and large declines in earnings) during recessions (Nilsen (2020)).¹⁶

3.3 Earnings Mobility

Having studied the properties of the distribution of earnings levels and growth, we now take a longitudinal perspective and turn to earnings persistence. Following our graphical approach, we plot the average rank-rank mobility that measures the expected position of an individual in the income distribution in year \(t+k\) conditional on the individual’s position in year \(t\). To isolate the persistent component of earnings, we use a slightly different version of permanent income, \(P_{it}^{*}\), defined as the average of labor earnings between periods \(t\) and \(t-2\) including earnings below the minimum earnings threshold.¹⁹ In this section, we present the average rank-rank mobility measure between \(t\) and \(t+10\). Further details and the results for 5-year average rank-rank mobility figures are presented in Appendix B, where we also report the 5-, 10-, and 15-year Markov transition matrices for \(P_{it}^{*}\) for a more complete picture of workers’ earnings dynamics.

Figure 9 shows the average rank-rank mobility for two age groups, 25-34 and 35-44, separately. Several remarks are in order. First, earnings mobility declines significantly after the first decade of working life. This finding is consistent with the previous results in the literature (see Karahan and Ozkan (2013); Guvenen et al. (2021)) in that income becomes more persistent as individuals advance in their career until around the ages of 45 to 55. Second, relative to men, earnings mobility is higher for women, and even more so for younger women in the upper half of the distribution (Panel B of Figure 9). Third, income mobility is the highest around the 10th and 90th percentiles of the income distribution, especially for younger workers. Furthermore, upward mobility in the bottom half of the income distribution is higher relative to the downward mobility in the upper half of the distribution. In fact, higher upward mobility in the bottom half leads the rank-rank measure to cross the 45-degree line below the 50th percentile.

4.1 Intergenerational Income Mobility

We start by documenting the relation between fathers’ and children’s lifetime income levels. Since our sample includes individuals who have at least 20 years of income observations, our estimates are robust to the well-known attenuation bias in measures of intergenerational elasticity of income that arises when few observations are used to calculate permanent income (see Solon (1992); Black and Devereux (2011)). Notice that our sample consists of cohorts who were born between 1928 and 1975. Furthermore, we observe some cohorts for a shorter period of time than others, either when they are young or when they are old. Thus, to make the lifetime incomes comparable across cohorts, we normalize incomes in each year and age by their corresponding year-age cell average. Then, we define the residual lifetime income of an individual \(i\) born in cohort \(c\) (birth year) as

\[ LI_{i,c}=\frac{\left [\sum _{t=\max \left \{25+c,1967\right \}}^{\min \left \{60+c,2017\right \}}\frac{I_{it}}{d_{t,h(i,t)}}\right]}{\min \left \{60+c,2017\right \} -\max \left \{25+c,1967\right \} +1}, \]

where \(I_{it}\), \(h(i,t)\), and \(d_{t,h(i,t)}\) denote the real after-transfer income, age of \(i\) in year \(t\), and the average income at age \(h(i,t)\) and in \(t\), respectively.

Figure 10 shows a binned scatter plot of the log lifetime incomes of father-son pairs (left panel) and father-daughter pairs (right panel). In particular, on the \(x\)-axis we rank fathers into 100 bins with respect to their (log) lifetime incomes and plot the average log lifetime incomes of children in each bin on the \(y\)-axis. Our results confirm the findings of the earlier literature of a strong intergenerational persistence in income. We find that the relation between fathers’ and children’s lifetime income is fairly linear, with an elasticity of intergenerational income of 0.24. For example, an increase in fathers’ log lifetime income from -0.5 to 0.5—where the bulk of the sample is—is associated with an average increase in sons’ earnings of 25 log points (Figure 10a). The results are quite similar for the father-daughter pairs, with a slightly weaker elasticity of 0.23 (Figure 10b).²²

(a) (b)

Figure: Figure 10 – Fathers and Children Income Correlation

To obtain a more granular view of the relation between fathers’ and children’s lifetime income, we construct intergenerational transition matrices (see Figure 11; for matrices with more income groups, see Appendix C.1). We rank fathers, sons, and daughters separately with respect to their lifetime incomes within age groups. These matrices then show the probability that a father in the \(ith\) income group (in the rows of the matrix) has a child in the \(jth\) income group (in the columns of the matrix) normalized by the size of the child’s quantile (i.e., population probability). For example, we find that 48% of the bottom 40% of fathers have a child in the bottom 40%. Therefore, the top left number in Figure 11 is \(1.2=\frac{48\%}{40\%}\)—the likelihood of a father in the bottom 40% having a son also in the bottom 40% relative to the population average.

The larger the numbers on the diagonal of the matrix are, the stronger the intergenerational persistence is. A diagonal of ones means that incomes of children and fathers are entirely uncorrelated as children have the same probability of being in their fathers’ income quantile as the population average. In contrast, for cells away from the diagonal the lower the numbers are, the lower the intergenerational income mobility is. For example, the likelihood of a father in the bottom 40% having a child in the top 0.1% quantile relative to the population average is only 30% (the top right number in Figure 11).

We find that all the values on the diagonal (and in most neighboring cells) are larger than 1, pointing to some degree of intergenerational persistence for all income groups. More interestingly, intergenerational persistence is highest in the top income groups: Sons of fathers in the 0.1% of the income distribution are 42.6 times and 13.1 times as likely to be in the 0.1% and next 0.9% relative to the population average, respectively. The intergenerational persistence for daughters at the top of the income distribution is lower compared to the sons.

How much upward and downward income mobility is there? The likelihood that the children (both sons and daughters) of the bottom 40% of fathers will reach the top 5% is only around 24% of the population average (i.e., 1.2% probability versus 5% probability in the population). Similarly, the probability that the sons (daughters) of the top 0.1% of fathers drop to the bottom 40% income group is 60% (90%) of the population average. These results show that even in Norway (which is known for its redistributive policies as well as free public schools and universities), upward and downward income mobility is still fairly low.

(a) Sons (b) Daughters

Figure: Figure 11 – Intergenerational Lifetime Income Mobility

4.2 Fathers’ Resources and Children’s Income Dynamics

Arguably, parents’ financial resources have a significant effect on children’s income dynamics. For example, high-income or high-wealth parents tend to spend more on their children’s education, which allows them to accumulate more human capital and enjoy high incomes from more stable jobs. Alternatively, children from rich families might be able to pursue high-risk, high-return careers or could afford to live off their inheritances without maintaining stable employment. Furthermore, parents may accumulate wealth to insure their children against income risk (e.g., Boar (2021)).

Motivated by these ideas, we investigate the relation between family resources—fathers’ lifetime income and net wealth—and children’s income dynamics. We follow the same methodology of Section 3.2.3 and analyze how the first four moments—mean, dispersion, skewness, and kurtosis—of the distribution of one-year log income changes of children vary across the distribution of fathers’ lifetime income and wealth. In particular, we rank fathers into 40 quantiles with respect to either their lifetime income, \(LI_{i,c}\), or their wealth, denoted by \(W_{i,c}\). We further group children of fathers at the top 1% of the income or wealth distribution in a separate bin. We then calculate the first four moments of residual income growth, \(g_{it}^{I,k}\), of children within each quantile.²³ Similar to the previous section, we focus on percentile-based moments for one-year income changes. We also present results from standardized moments (because higher-order moments are sensitive to the extreme observations) as well as those for the five-year changes (which capture more persistent changes in after-transfer income) in Appendices C.2 and C.3, respectively. They show qualitatively similar patterns.

To make the measures of wealth comparable across cohorts, we normalize each individual’s net wealth by a year-age cell average—similar to how we construct the lifetime income measure. The data on wealth only span from 1993 to 2014; therefore, we cannot observe the wealth of most fathers when they were young. However, this is a minor issue since wealth is a stock variable—unlike income (a flow variable)—which makes it much more persistent than income. Therefore, in our analysis we consider the average residual net worth of a household calculated between ages 45 and 54. Some cohorts either are not in our sample or have only a few observations in this age interval. For them, we use observations in years closest to these ages.

(a) By Lifetime Income (b) By Net Wealth

Figure: Figure 12 – Median Log Income Growth by Fathers’ Resources

Median Income Growth. Figure 12 shows how children’s median annual income growth varies by family resources measured by fathers’ lifetime income or wealth. We find that lifetime income growth is significantly higher for workers born into richer families. For example, median annual income growth for sons of fathers at the 90th percentile of the lifetime income distribution is almost 1% higher relative to those with parents at the 10th percentile. The corresponding difference among daughters is lower at around 0.5%. This heterogeneity is economically significant, considering that the typical estimates of the standard deviation of heterogeneous income profiles are around 2% for the U.S. (see Guvenen et al. (2021)). The variation over the father’s wealth distribution is qualitatively and quantitatively similar and slightly more pronounced.

The heterogeneity in average income growth arising from parental financial resources is even larger, with around a 2% difference between the children of parents at the 90th percentile and those from the 10th percentile (Figure OA.III.4). Furthermore, children of top earners enjoy an exceptionally steeper average income growth over the life cycle—specifically, 2% higher compared to those from the median-income families. These results indicate an increasingly right-skewed distribution of earnings growth by fathers’ income. We confirm this conjecture when we investigate the skewness of income growth.

(a) By Lifetime Income (b) By Net Wealth

Figure: Figure 13 – Dispersion of Log Earnings Growth by Fathers’ Resources

Volatility of Income Growth. Figure 13 shows that the volatility of children’s income growth—as measured by the P90-P10 differential—follows a U-shaped pattern by the fathers’ lifetime income (left panel) and wealth (right panel). This pattern is more pronounced for sons than for daughters. For example, the P90-P10 of income changes for sons (daughters) with fathers at the 1st and 99th percentiles of the lifetime income distribution is around 12 (9) log points larger than those with median-income fathers.

Children of more affluent fathers face significantly more volatile incomes. For example, the P90-P10 of income growth for workers of fathers from the top 1% of the lifetime income or wealth distributions is roughly 12 to 18 log points higher compared to those of fathers at the median. This higher income volatility for children with rich fathers, combined with their exceptionally higher median and (especially) average income growth (shown in Figures 12 and OA.III.4), suggests that they can pursue high-risk, high-return careers that children from modest backgrounds cannot.

Recall that we also find a U-shaped pattern in the dispersion of earnings growth over workers’ permanent earnings in Section 3.2.3 (Figure 5). However, the U-shaped pattern here is tilted toward the right over the fathers’ lifetime income and wealth distribution compared to the variation by workers’ own permanent earnings. That is, children of high-income, high-wealth fathers experience the most volatile incomes, whereas the volatility of earnings shocks is the highest for workers with the lowest permanent earnings. These results suggest that the relation between workers’ income volatility and their fathers’ financial resources is not due to the omitted variable of workers’ permanent earnings, which is correlated with fathers’ resources. We investigate this conjecture further in Section 4.4 when we control for a full set of children and father characteristics.

(a) By Lifetime Income (b) By Net Wealth

Figure: Figure 14 – Skewness of Log Earnings Growth by Fathers’ Resources

Skewness of Income Growth. We next turn to the variation in skewness of children’s income growth by the fathers’ lifetime income and wealth. Figure 14 shows that the distribution of income growth is right skewed regardless of fathers’ income and wealth. More importantly, we find that the distribution of income growth becomes increasingly more right skewed for both sons and daughters as we move from poorer to richer families.²⁴ This finding suggests that children from more affluent families experience higher upside income potential, lower left-tail risk, or both. Differences between high- and low-resource fathers are substantial and economically significant.

(a) Left-Tail Dispersion of \(g_{it}^{I,1}\)

(b) Right-Tail Dispersion of \(g_{it}^{I,1}\)

An important question is whether skewness becomes more positive over fathers’ resources because of a compression of the lower tail (less risk of large declines) or because of an expansion in the upper tail (more opportunities for large gains). To answer this question, we investigate how the left and right tails of the children’s income growth distribution change between poor and rich parents. In particular, Figures 15 and 16 show the P50-P10 and P90–P50 of children’s income growth. First, up to around the 85th percentile of the fathers’ income and wealth distributions, the decline in P90-P50 is relatively less pronounced than the compression of the lower tail as we move from poorer to richer parents. Therefore, the decline in income volatility in this range reflects somewhat more of a reduction in the left-tail risk of workers. However, beyond the 85th percentile, we see that both tails open up sharply, the upper tail even more so, thereby resulting in both an increase in volatility and an increase in positive skewness.

These findings are consistent with our conjecture that children from affluent families pursue high-risk high-return careers. Additional evidence from the data supports this conjecture as well. For example, we find that fraction of sons (daughters) employed in the public sector (i.e., in more stable, less risky jobs) increases from around 10% (30%) to 20% (40%) from families at the bottom of the distribution to upper-middle-class families, but then declines sharply at the top of the distribution (see Figure OA.III.8).

(a) Left-Tail Dispersion of \(g_{it}^{I,1}\) (b) Right-Tail Dispersion of \(g_{it}^{I,1}\)

Figure: Figure 16 – Left- and Right-Tail Income Volatility by Fathers’ Wealth

Kurtosis of Income Growth. Finally, Figure 17 shows the Crow-Siddiqui kurtosis of income growth conditional on fathers’ lifetime income and wealth. We find a U-shaped profile with low kurtosis of earnings growth among sons whose fathers are around the median lifetime income relative to those whose fathers were at the top or bottom of the lifetime income distribution. For daughters, we do not find any significant pattern. Children of the richest fathers face the most leptokurtic distribution of income changes. However, these results change significantly if we use the fourth standardized moment (Figure OA.III.7), which shows a hump-shaped profile with low kurtosis of earnings growth among children with bottom- and top-earning fathers relative to those from middle-income families. This result shows the importance of very large earnings changes in measurement of the higher-order moments.

(a) By Father’s Lifetime Income (b) By Father’s Net Wealth

Figure: Figure 17 – Kurtosis of Log Income Growth by Fathers’ Resources

4.3 Fathers’ and Children’s Income Dynamics

Do fathers and children have income dynamics of similar properties (for example, because of similar risk attitudes or similar jobs and occupations)? To investigate this question, we again use a permanent income measure, \(\tilde{P}_{it}=\max \left \{Y_{t}^{min},\frac{1}{3}\sum _{j=0}^{2}Y_{it-j}\right \}\), the average income between periods \(t\) and \(t-2\) winsorized at the minimum income threshold (\(Y_{t}^{min}\)).²⁵ Then, for each individual, we construct a time series of log permanent income growth (\(\Delta \tilde{P}_{it}=\log \tilde{P}_{it}-\log \tilde{P}_{it-1}\)) over their life cycle and compute the first three moments from this series. Given the relatively short length of the individual time series—between 20 and 40 years—we use percentile-based moments (the median, P90-P10, and Kelley skewness) to avoid having outliers drive our results. The results for the standardized moments display similar qualitative patterns (Appendix C.4).

Median Income Growth. Figure 18 shows a binned scatter plot of the median log permanent income growth of fathers and sons (left panel) and fathers and daughters (right panel). We find a marked non-linear relation between fathers’ and children’s lifetime income growth. Fathers’ and children’s income growth does not seem to be strongly correlated for around 10%-15% of our sample when fathers have negative or very steep life-cycle income growth. In the rest of the sample, however, the children of fathers that experienced steeper income growth during their lifetime are more likely to experience high income growth. This correlation is also economically significant: An increase in a father’s median income growth from 0 to 5 log points results in an increase of roughly 1 log point in the son’s median income growth over the life cycle. For daughters, this number is slightly lower (around 0.8 log points) but still significant. The overall intergenerational elasticity of life-cycle income growth is 0.14 for men and 0.09 for women.²⁶

(a) Sons (b) Daughters

Figure: Figure 18 – Median Income Growth of Fathers and Children

Income Growth Volatility. We now investigate whether the children of fathers with more volatile incomes also have riskier income streams. Figure 19 shows a binned scatter plot of the P90-P10 of fathers’ and children’s permanent income growth. We find a strong and economically significant correlation between fathers’ and children’s volatility of income. For example, when the father’s dispersion of income changes increases from 10 to 50 log points, where the bulk of the sample is, the son’s (daughter’s) P90-P10 of income growth increases roughly from 35 to 45 (45 to 55) log points. For more volatile incomes of fathers, the association becomes flatter, though still significant: An increase in the P90-P10 of fathers’ income from 50 to 150 log points is associated with an increase in children’s income volatility of roughly 10 log points. Together, these findings imply an elasticity between fathers’ and children’s income growth dispersion of 0.13 for sons and 0.11 for daughters.

(a) Sons (b) Daughters

Figure: Figure 19 – Dispersion of Income Growth of Fathers and Children

Skewness of Income Growth. Finally, we look at the relation between fathers’ and children’s skewness of income growth. Similar to the first two moments, Figure 20 shows a positive and strong correlation for Kelley skewness of income growth. Quantitatively, we find that an increase in fathers’ Kelley skewness from -0.25 to 0.25—where most of the distribution is found—is associated with an average increase of 0.04 (0.025) in the skewness of sons’ (daughters’) income growth.²⁷

(a) Sons (b) Daughters

Figure: Figure 20 – Skewness of Income Growth of Fathers and Children

Occupational and Educational Intergenerational Mobility. One possible explanation for the findings in this subsection is that fathers and children have similar jobs and occupations, and therefore face similar income dynamics (see also Bello and Morchio (2017) and Boar and Lashkari (2021)). Despite the lack of information on occupations in our dataset, we know workers’ education at a detailed level. We investigate the intergenerational persistence in education using 47 categories of degrees, which range from primary education to post-graduate study in law (see Appendix C.4 for a full list).

Figure OA.III.21 in Appendix C.4 shows the intergenerational transition matrix for a select group of education categories (the full matrix is available at authors’ websites). Since the Norwegian workforce has become more educated and its educational composition has changed over time, we normalize these probabilities with the corresponding population averages among children. For example, 9.7% of sons of dentists also studied dentistry, but only 0.4% of all sons are dentists. Then the value for the intergenerational persistence of dentists in this matrix is \(\frac{9.7\%}{0.4\%}=22.5\), which implies that sons of dentists are 22.5 times more likely to be dentists relative to the population average.

All of the values on the diagonal of this matrix is significantly greater than 1, with an average of 6 for sons and 4.4 for daughters. For brevity, Table II shows this statistic for the five most and least persistent education categories. According to this measure, dentists, lawyers, and doctors display the strongest intergenerational persistence along with nurses and those with a higher degree in the social sciences (which includes economists). At the other extreme, we see substantial upward intergenerational socioeconomic mobility for children of relatively low-educated fathers. For example, fathers with only a primary education are among the least likely group to have children with a similar education (after already accounting for changes in educational composition across cohorts).

Strong intergenerational persistence in education supports our conjecture that fathers and children have similar occupations, thereby exhibiting correlated income risk. In the next section, we further investigate the determinants of the transmission of income risk.

4.4 Determinants of the Transmission of Income Risk

The results presented in this section indicate that children’s income dynamics are strongly connected to their fathers through the fathers’ economic resources and nature of income dynamics. However, there are two main potential concerns with our descriptive analysis. First, simple bivariate correlations cannot quantify the relative importance of different factors (i.e., fathers’ lifetime income, net wealth, and characteristics of fathers’ income growth) on children’s income dynamics as these factors are also correlated with each other. Second, some of the strong relations documented above may simply be spurious as a result of omitted variables. For example, as we have shown in Section 3.2.3, permanent incomes are an important predictor of workers’ income risk, and fathers’ and children’s lifetime incomes are strongly correlated (Figure 10).

To address these concerns and examine the importance of different factors for workers’ income dynamics, we run a series of regressions of the form

\[ \begin{aligned} x_{i}^{c} & = & \beta _{0}+\beta _{1}x_{i}^{f}+X_{i}\Gamma +\varepsilon _{i}, \end{aligned} \]

where \(x_{i}^{c}\) is a moment from child \(i\)’s permanent income growth stream over the life cycle (i.e., median, P90-P10, and Kelley skewness) and \(x_{i}^{f}\) is the same moment but for the child’s father. The matrix \(X_{i}\) contains a set of controls for child \(i\) that includes the log of the father’s lifetime income, \(LI_{i}^{f}\), and the log of the father’s wealth, \(W_{i}^{f}\), the log of the child’s lifetime income, \(LI_{i}^{c}\). Therefore, in these regressions we have one observation for each father-child pair. The dependent variable for one such pair is computed using all permanent income observations of the child, similar to our analysis in Section 4.3.

Table III shows estimation results for equation (2) for different moments of the income growth distribution for sons and daughters. We also report the dispersion of the independent variables, measured as the standard deviation and the P90-P10 differential in columns (1) and (2). In all cases, we find that all four regressors are statistically significant at the 1% level. These results are robust to considering centralized moments instead of percentile-based measures (see Table OA.III.2) or adding quadratic terms on lifetime income and wealth (see Table OA.III.4).

Median Income Growth. Columns (3) and (4) of Table III show the results for the median income growth over the life cycle. Two points are worth noticing. First, similar to the results presented in Figure 18, we find that fathers’ and children’s median income growth is positively correlated for both sons and daughters, with an intergenerational elasticity of median income growth of 0.09 and 0.07, respectively.²⁸ This means that sons (daughters) of fathers at the 90th percentile of the median income growth distribution experience 0.54% (0.42%) higher annual income growth relative to the children of fathers at the 10th percentile, since the 90-10 differential of median income growth among fathers of sons is 0.06. Second, consistent with earlier evidence (Figure 12), the coefficients of fathers’ lifetime income and wealth are positive as children of more affluent fathers tend to experience higher income growth over their lifetime. For instance, the median growth for sons (daughters) of fathers at the 90th percentile of the lifetime income distribution is approximately 0.3% (0.1%) higher compared to sons (daughters) of fathers at the 10th percentile. These magnitudes are economically quite substantial, with 0.3% steeper annual income growth, implying a 13% higher income over a 40-year working life.

Volatility of Income Growth. We then turn to the income growth dispersion (columns (5) and (6) of Table III). We find that the P90-P10 of income growth for sons (daughters) of fathers at the 90th percentile of the income volatility distribution is 12 (8) log points higher compared to those with fathers at the 10th percentile. Quantifying the importance of family resources, we find an elasticity of 0.13 with respect to fathers’ lifetime income, which implies that sons of fathers at the 90th percentile of the lifetime income distribution face an income volatility that is 12 log points higher than the workers with fathers at the 10th percentile. For daughters, the corresponding figure is about 9 log points. These differences are quite significant, considering that the average P90-P10 of income growth among sons (daughters) is roughly 0.40 (0.51). Hence, our regression results suggest that children of more affluent families experience a more volatile income stream during their lifetime. However, recall that we find a U-shaped pattern for the volatility of income over fathers’ economic resources in Section 4.2; therefore, our linear regression results are probably a lower bound for the true effect.²⁹

Skewness of Income Growth. Finally, columns (7) and (8) in Table III present the regression results for the skewness of income growth. We find that a one standard deviation of increase in the father’s skewness of income growth implies a 2.5 pp. (2.0 pp.) increase in the Kelley skewness of the son’s (daughter’s) income growth. This magnitude is relatively small considering that the average skewness in the sample is around 0.15 for both sons and daughters. The elasticity of skewness with respect to the father’s income is also statistically significant but of a smaller magnitude.

Our empirical findings in this section can be explained, for instance, by fathers and children sharing similar careers, occupations, education, and attitudes toward risk, or children making different education and career choices depending on their parents’ financial resources. We have previously shown that there is a strong correlation between the education of fathers and children (Table II) and that children from upper middle-income families are more likely to choose public sector careers (Figure OA.III.8). To further investigate the role of education and the occupational choices of children in the intergenerational transmission of income dynamics, we estimate a model that also includes dummies for children’s education using 47 categories and an indicator variable for whether child \(i\) spent more than half of his or her career in the public sector. We find that including these additional controls in our regressions significantly reduces the coefficients of variables for fathers’ lifetime income and wealth but much less so for fathers’ features of income risk. This result shows the important roles that education and public sector employment play in workers’ income dynamics (see Table OA.III.3). More importantly, it reveals that education is a key mechanism through which fathers’ financial resources matter for children’s life-cycle earnings dynamics.

6.1 Trends in After-Transfers Income Inequality

(a)

(b)

(c)

(d)

(a)

(b)

(c)

(d)

(e) Men Age 25

(f) Women Age 25

(a) Men

(b) Women

6.2 Distribution of After-Transfer Income Growth

(a) Men

(b) Women

(a)

(b) Excess

(a) Men (b) Women

Figure: Figure A.7 – After-Transfer Income Growth Dispersion by PE and Age

(a) Men (b) Women

Figure: Figure A.8 – Skewness of After-Transfer Income Growth by PE and Age

(a) Men (b) Women

Figure: Figure A.9 – Kurtosis of After-Transfer Income Growth by PE and Age

7.1 Moments of the Earnings Distribution

(a)

(b)

(c)

(d)

(a) Men

(b) Women

(a) Men: Top 1%

(b) Women: Top 1%

(c) Men: Top 5%

(d) Women: Top 5% Figure B.3 shows the tail of the distribution of log-earnings above the 99th percentile of the distribution (panels A and B) and above the 95th percentile (panels C and D).

(a)

(b)

(c)

(d)

(e) Men: Top Income Inequality

(f) Women: Top Income Inequality

7.2 Figures for the Combined Sample (Men and Women)

(a) Percentiles

(b) Top Percentiles

(c) Dispersion

(d) Right- and Left-Tail Dispersion Figure B.5 shows the evolution of the following variables: (a) P10, P25, P50, P75, P90 (b) P90, P95, P99, P99.9, P99.99, (c) P90-P10 and 2.56*SD of log income, (d) P90-P50 and P50-P10. Percentiles in (a) and (b) are normalized to 0 in 1993. Shaded areas represent recession years as defined as years with unemployment rate growth 0.4 pp. or more and an output gap of -0.5 or less. In all figures we consider a joint sample of men and women. See Section 2 for sample selection and definitions.

7.3 Figures for Residual Earnings

(a) Percentiles

(b) Top Percentiles

(c) Dispersion

(d) Right- and Left-Tail Dispersion Figure B.6 shows the evolution of the following variables: (a) P10, P25, P50, P75, P90 (b) P90, P95, P99, P99.9, P99.99, (c) P90-P10 and 2.56*SD of log income, (d) P90-P50 and P50-P10. Percentiles in (a) and (b) are normalized to 0 in 1993. Shaded areas represent recession years as defined as years with unemployment rate growth 0.4 pp. or more and an output gap of -0.5 or less. In all figures we consider a joint sample of men and women. We residualize log-income from age fixed effects by year and gender. See Section 2 for sample selection and definitions.

8.1 Moments of Five-Years Earnings Growth

(a) Men

(b) Women Figure C.1 plot against time the following variables: (a) Men: P90-10 differential, (b) Women: P90-10 differential. Shaded areas are recessions.

(a) Skewness

(b) Excess Kurtosis Figure C.2 plot against time the following variables: (a) Men and Women: Kelley skewness, (b) Men and Women: Crow-Siddiqui kurtosis. Shaded areas are recessions.

(a) Men

(b) Women

8.2 Moments of One-Year Earnings Growth

(a) Men

(b) Women

(a) Men

(b) Women

(c)

(d) Excess

8.3 Arc-Percent Earnings Growth Distribution

(a) Men

(b) Women Figure C.6 plot against time the following variables: (a) Men: P90-10 differential, (b) Women: P90-10 differential. Shaded areas are recessions.

(a) Skewness

(b) Excess Kurtosis Figure C.7 plot against time the following variables: (a) Men and Women: Kelley skewness, (b) Men and Women: Crow-Siddiqui kurtosis. Shaded areas are recessions.

8.4 Heterogeneity in Idiosyncratic Earnings Changes

(a) Men (b) Women

Figure: Figure C.8 – Kelley Skewness (P99/P1) of Earnings Growth by PE and Age

(a) Men P50-P10 (b) Men P50-P1

(c) Women P50-P10 (d) Women P50-P1

Figure: Figure C.9 – Left-Tail Dispersion: P50-P10 and P50-P1

(a) Men P90-P50 (b) Men P99-P50

(c) Women P90-P50 (d) Women P99-P50

Figure: Figure C.10 – Right-Tail Dispersion: P90-P50 and P99-P50

(a) Men (b) Women

Figure C.11 shows the excess fourth standardized moment of log earnings changes for men and women with quantiles of the permanent income distribution, \(P_{it-1}\). Excess kurtosis is defined as the value of kurtosis minus \(3\) which is the corresponding value for a Normal distribution. In each plot, the solid markers represent the corresponding measure of kurtosis for those workers at the top 0.1% of the earnings distribution for different age groups (diamond for 25 to 34 years old, square for 35 to 44 years old, and circle for 45 to 55 years old).

Figure: Figure C.11 – Kurtosis of Earnings Growth by Earnings Level and Age

10.1 Average Rank-Rank Mobility

We calculate the average rank-rank mobility which shows the expected position of an individual in the income distribution in year \(t+k\) conditional on the individual’s position in year \(t\). We rank workers into 40 quantiles in period \(t\) within each gender and age with respect to their permanent income, \(P_{it}^{*}\), and we put the top 0.1% earners in a separate group. Then, for each income quantile, age, and gender, we calculate individuals’ average rank (out of 100) in the future permanent income distribution in \(t+k\).³⁵ In section 3.3, we present this average rank-rank mobility measure between \(t\) and \(t+10\) (10-year mobility) and the results for 5-year mobility are presented below.

(a) Men (b) Women

Figure: Figure OA.II.1 – Rank-Rank Measures by Age: Five-Years Change

10.2 Income Transition Matrices

So far, our analysis has focused on the average rank-rank mobility of permanent earnings. To capture a more complete picture of workers’ income transition dynamics, here we investigate where exactly individuals end up in the income distribution in year \(t+k\), conditional on their rank in year \(t\), by constructing first-order Markov transition matrices. In our analysis, we again use \(P_{it+k}^{*}\), as our measure of income and rank workers within age and gender groups. We then define the following states in our transition matrices: the first four quintiles of the \(P_{it+k}^{*}\) distribution, the next 15 percentiles (81st-95th percentiles), the next 4 percentiles (96th-99th percentiles), the top 1% excluding the top 0.1%, and finally, the top 0.1% of the distribution. Furthermore, instead of dropping individuals who have no significant labor income three years in a row in \(t+k\) (i.e., missing \(P_{it+k}^{*}\) observations) from our transition matrices, we explicitly investigate whether individuals have other sources of income. In particular, we add three more states that describe the status of individuals with missing \(P_{it+k}^{*}\) observations: self-employed workers (who have permanent self-employment income above the minimum income threshold \(Y_{t}^{min}\)), individuals with permanent public benefits greater than \(Y_{t}^{min}\), and individuals who do not have any significant income (i.e., total permanent income less than \(Y_{t}^{min}\)).³⁶

Figure OA.II.2 presents 10-year transition matrices for men and women between 35 and 44 years old. To understand this figure, notice that the color intensity of each cell reflects the transition probability between the corresponding row and column shown in the cell. So, the darker the cell, the more likely the transition between two quantiles. For both men and women, the diagonal cells and their close neighbors are darker than the rest, indicating that most individuals remain in their original states even after 10 years, and if they move, they do not move far. This is especially true at the top and bottom of the distribution. For instance, among men, the probabilities in the diagonal cells (i.e., probability of staying the same state) decrease from 44% for the bottom quintile to 35% for the third quintile and then increase to 49% between the 81st and 95th percentiles. More broadly, remaining in the same state or transitioning into one of the neighboring states constitutes more than 60% of the cases. These findings suggest that individual rankings in the income distribution are quite persistent. These results hold for different age groups and different transition periods (see Figures OA.II.3 and OA.II.4).

(a) Men (b) Women

Figure OA.II.2 shows a first-order transition matrix of individuals’ permanent earnings between periods \(t\) and \(t+10\) for a sample of workers between 35 and 44 years old. To construct this figure, we calculate permanent earnings for workers between the years 1995 and 2007 (the first and last years for which we can calculate permanent earnings and 10-year changes). No Emp. corresponds to individuals whose permanent earnings is below the minimum income threshold and those who do not have significant self-employment income or social security benefits in period \(t+10\). Slf Emp (Bnfts) corresponds to individuals whose permanent earnings are below the minimum income threshold but the average level of self-employment income (benefits) over the last three years is above the minimum income threshold. We then calculate the share of individuals transitioning between the predefined states for each year. Finally, we average the shares across all possible years.

Figure: Figure OA.II.2 – Permanent Earnings Mobility: Transition Matrix

(a) Men (b) Women

Figure OA.II.3 shows a first-order transition matrix of individuals’ permanent earnings between periods \(t\) and \(t+5\) for a sample of workers between 35 and 44 years old. To construct this figure we calculate permanent earnings for workers between years 1995 and 2007 (the first and last years for which we can calculate permanent earnings and 10-year changes). No Emp. correspond to individuals whose permanent earnings is below the minimum income threshold and do not have significant self employment income or social security benefits in period \(t+10\). Slf Emp (Bnfts) corresponds to individuals whose permanent earnings are below the minimum income threshold but the average level of self employment income (benefits) over the last three years is above the minimum income threshold. We then calculate the share of individuals transitioning between the predefined states for each year. Finally, we average the shares across all possible years.

Figure: Figure OA.II.3 – Permanent Earnings Mobility: Five-Year Transition Matrix

(a) Men (b) Women

Figure OA.II.4 shows a first-order transition matrix of individuals’ permanent earnings between periods \(t\) and \(t+15\) for a sample of workers between 35 and 44 years old. To construct this figure we calculate permanent earnings for workers between years 1995 and 2007 (the first and last years for which we can calculate permanent earnings and 10-year changes). No Emp. correspond to individuals whose permanent earnings is below the minimum income threshold and do not have significant self employment income or social security benefits in period \(t+10\). Slf Emp (Bnfts) corresponds to individuals whose permanent earnings are below the minimum income threshold but the average level of self employment income (benefits) over the last three years is above the minimum income threshold. We then calculate the share of individuals transitioning between the predefined states for each year. Finally, we average the shares across all possible years.

Figure: Figure OA.II.4 – Permanent Earnings Mobility: Fifteen-Year Transition Matrix

Zooming into the top 1% of the distribution, we find that persistence is even higher at the top of the income distribution. For example, 35.6% of male workers who are in the top 1% in year \(t\) appear again in the same income bracket after 10 years. More interestingly, there are very few transitions between the lower and top ends of the distribution and vice versa. For example, most (more than 99.5% of) workers in the top 0.1% of the distribution in year \(t+10\) were already in the top 5% in year \(t.\) Similarly, very few workers who are in the top 0.1% of the income distribution in year \(t\) end up outside of the top 5% in year \(t+10\). Specifically, less than 25% of the top 0.1% earners fell below the 95th percentile in year \(t+10\). This finding is inconsistent with calibrations of earnings processes with shocks that increase earnings to very high levels (e.g., the top 0.1%) but only temporarily (see Castaneda, Diaz-Gimenez and Rios-Rull (2003)). For women, top incomes are even more persistent, with a 42% probability of staying in the top 1% after 10 years.

When we say that 35.6% of workers appear again in the top 1% after 10 years we do not know whether this transition probability is the same for all workers just by looking at the results shown in Figure OA.II.5. For example, it may be that 35.6% of workers are always in the top income group and the rest temporarily appear in the top 1% only in year \(t\), or that all top earners have the same probability of staying in the top 1%. These two different income dynamics have very different implications for consumption and saving decisions and portfolio allocation. To investigate the possible heterogeneity in the persistence of top incomes, we calculate the number of years a top earner in year \(t\) reappears in the top 1% over the next 10 years. In other words, we follow the top earners for the next 10 years and document the numbers of years they stay in the top 1%.

Our results, displayed in Figure OA.II.5, show that 12% of men at the top 1% of the permanent earnings distribution (Panel A) in year \(t\) do not appear at the top again over the next 10 years, whereas 11% will appear only one more time during the same period, and so on. Interestingly, around a quarter of the top 1% earners never leave that group over the next 10 years. The results are even more striking for women (Panel B): Almost one-third of the female top earners stay in the top 1% for 10 years in a row. This finding is consistent with our results from the transition matrices for women that show a higher probability of staying in the top 1%. Whether these findings are consistent with a simple first-order Markov process or whether there are ex ante differences in income dynamics among the top earners is an open question and beyond the scope of this paper.

(a) Men (b) Women

Figure OA.II.5 shows the fraction of top 1% workers in year \(t\) that appear in the same income group between \(t+1\) and \(t+10\) for 0 years, for 1 year, for 2 years, and so on. To construct this figure, we pool all observations between the years 1995 and 2007 (the first and last years for which we can calculate permanent earnings and 10-year changes).

Figure: Figure OA.II.5 – Number of Years Staying at the Top 1% over 10 Years

When the top earners leave top 1% income group, where do they end up? How likely they never leave top 5% or top 10% income groups? Figure OA.II.6 shows the fraction of the top 1% of earners in year \(t\) that never leaves the top income groups (top 1%, 5%, and 10%) over the next ten years as well as those who never appear again in these percentiles during the same time period.

Our results show that around a quarter of the men in the top 1% the permanent earnings distribution in year \(t\) never leave that group over the next 10 years (Panel A). If we relax the definition of the top income group, then 60% and 75% of the top 1% earners never leave the top 5% and top 10% the income distribution, respectively. As for the opposite case, only 12% of the top 1% of earners do not appear at the top 1% again over the next 10 years. Almost all of them will appear again in the top 5% and top 10% the income distribution at least once during the same period.

Interestingly, the results are even more striking for women (Panel B): Almost one-third of the top earnings women stay in the top 1% for 10 years in a row. And around 75% and 85% of them never leave the top 5% and top 10% the income distribution, respectively. Whether these findings are consistent with a simple first-order Markov process or whether there are ex ante differences in income dynamics for the top earners is an interesting open question and beyond the scope of this paper.

(a) Men (b) Women

Figure OA.II.6 shows the fraction of top 1% workers in year \(t\) that appear in the same income group between years \(t+1\) and \(t+10\) for 0 years (i.e. they do not appear again in top group) or 10 years (they appear in top 1% in all years). To construct this figure, we pool all observations between the years 1995 and 2007 (the first and last years for which we can calculate permanent earnings and 10-year changes).

Figure: Figure OA.II.6 – Number of Years Staying at the Top 1% over 10 Years

11.1 Intergenerational Transition Matrices

(a) Sons (b) Daughters

Figure: Figure OA.III.1 – Fathers and Children Rank-Rank Correlation

(a) Sons (b) Daughters

Figure: Figure OA.III.2 – Intergenerational Lifetime Income Mobility

(a) Sons (b) Daughters

Figure: Figure OA.III.3 – Intergenerational Lifetime Income Mobility

11.2 Fathers’ Resources and Children’s One-Year Income Growth

(a) By Lifetime Income (b) By Net Wealth

Figure: Figure OA.III.4 – Average Log Earnings Growth by Fathers’ Resources

(a) By Lifetime Income (b) By Net Wealth

Figure: Figure OA.III.5 – Std. Dev. of Log Earnings Growth by Fathers’ Resources

(a) By Lifetime Income (b) By Net Wealth

Figure: Figure OA.III.6 – Skewness of Log Earnings Growth by Fathers’ Resources

(a) By Father’s Lifetime Income (b) By Father’s Net Wealth

Figure: Figure OA.III.7 – Kurtosis of Log Earnings Growth by Fathers’ Resources

(a) By Lifetime Income (b) By Net Wealth

Figure: Figure OA.III.8 – Share of Public Sector Workers by Fathers’ Resources

11.3 Parents and Children’s Five-Year Income Growth Moments

(a) By Lifetime Income (b) By Net Wealth

Figure: Figure OA.III.9 – Mean 5-Year Log Earnings Growth by Fathers Resources

(a) By Lifetime Income (b) By Net Wealth

Figure: Figure OA.III.10 – Dispersion of 5-Year Log Earnings Growth by Fathers Resources

(a) By Lifetime Income (b) By Net Wealth

Figure OA.III.11 shows the skewness (third standardized moment) of the one-year residual earnings growth for men and women within quantiles of the father’s lifetime income distribution (Panel A) and the fathers’ households net wealth distribution (Panel B) for a total of 41 quantiles. The top 2.5% of the distribution is further separated in two groups (97.5th to 99th percentiles and 99th percentile and above). In each plot, the lines represent are the average across all years in the sample starting in 1990. The solid markers show the corresponding value among children whose parents were at the top 1% of the corresponding distribution. We estimate residual income growth as the growth rate of the residual of a year-by-year regression of log income on a set of age dummies. We run this regression separately for men and women.

Figure: Figure OA.III.11 – Skewness of 5-Year Log Earnings Growth by Fathers Resources

(a) By Lifetime Income (b) By Net Wealth

Figure OA.III.12 shows the Kelley skewness of the one-year residual earnings growth for men and women within quantiles of the father’s lifetime income distribution (Panel A) and the fathers’ households net wealth distribution (Panel B) for a total of 41 quantiles. The top 2.5% of the distribution is further separated in two groups (97.5th to 99th percentiles and 99th percentile and above). In each plot, the lines represent are the average across all years in the sample starting in 1990. The solid markers show the corresponding value among children whose parents were at the top 1% of the corresponding distribution. We estimate residual income growth as the growth rate of the residual of a year-by-year regression of log income on a set of age dummies. We run this regression separately for men and women.

Figure: Figure OA.III.12 – Kelley of 5-Year Log Earnings Growth by Fathers Resources

(a) By Lifetime Income (b) By Net Wealth

Figure OA.III.13 shows the P50-P5 percentiles differential of the one-year residual earnings growth for men and women within quantiles of the father’s lifetime income distribution (Panel A) and the fathers’ households net wealth distribution (Panel B) for a total of 41 quantiles. The top 2.5% of the distribution is further separated in two groups (97.5th to 99th percentiles and 99th percentile and above). In each plot, the lines represent are the average across all years in the sample starting in 1990. The solid markers show the corresponding value among children whose parents were at the top 1% of the corresponding distribution. We estimate residual income growth as the growth rate of the residual of a year-by-year regression of log income on a set of age dummies. We run this regression separately for men and women.

Figure: Figure OA.III.13 – Left-Tail Dispersion of 5-Year Log Earnings Growth By Fathers Resources

(a) By Lifetime Income (b) By Net Wealth

Figure OA.III.14 shows the P95-50 percentiles differential of the one-year residual earnings growth for men and women within quantiles of the father’s lifetime income distribution (Panel A) and the fathers’ households net wealth distribution (Panel B) for a total of 41 quantiles. The top 2.5% of the distribution is further separated in two groups (97.5th to 99th percentiles and 99th percentile and above). In each plot, the lines represent are the average across all years in the sample starting in 1990. The solid markers show the corresponding value among children whose parents were at the top 1% of the corresponding distribution. We estimate residual income growth as the growth rate of the residual of a year-by-year regression of log income on a set of age dummies. We run this regression separately for men and women.

Figure: Figure OA.III.14 – Right-Tail Dispersion of 5-Year Log Earnings Growth by Fathers Income

(a) By Father’s Lifetime Income (b) By Father’s Net Wealth

Figure OA.III.15 shows the kurtosis (fourth standardized moment) of the one-year residual earnings growth for men and women within quantiles of the father’s lifetime income distribution (Panel A) and the fathers’ households net wealth distribution (Panel B) for a total of 41 quantiles. The top 2.5% of the distribution is further separated in two groups (97.5th to 99th percentiles and 99th percentile and above). In each plot, the lines represent are the average across all years in the sample starting in 1990. The solid markers show the corresponding value among children whose parents were at the top 1% of the corresponding distribution. We estimate residual income growth as the growth rate of the residual of a year-by-year regression of log income on a set of age dummies. We run this regression separately for men and women.

Figure: Figure OA.III.15 – Kurtosis of 5-Year Log Earnings Growth by Fathers Income

(a) By Father’s Lifetime Income (b) By Father’s Net Wealth

Figure OA.III.16 shows the Crow-Siddiqui kurtosis of the one-year residual earnings growth for men and women within quantiles of the father’s lifetime income distribution (Panel A) and the fathers’ households net wealth distribution (Panel B) for a total of 41 quantiles. The top 2.5% of the distribution is further separated in two groups (97.5th to 99th percentiles and 99th percentile and above). In each plot, the lines represent are the average across all years in the sample starting in 1990. The solid markers show the corresponding value among children whose parents were at the top 1% of the corresponding distribution. We estimate residual income growth as the growth rate of the residual of a year-by-year regression of log income on a set of age dummies. We run this regression separately for men and women.

Figure: Figure OA.III.16 – Crow-Siddiqui Kurtosis of 5-Year Log Earnings Growth by Fathers Income

11.4 Fathers’ and Children’s Income Dynamics: Extra Results

(a) Men (b) Women

Figure: Figure OA.III.17 – Average of Income Growth of Fathers and Children

(a) Men (b) Women

Figure: Figure OA.III.18 – Standard Deviation of Income Growth of Fathers and Children

(a) Men (b) Women

Figure: Figure OA.III.19 – Skewness of Income Growth of Fathers and Children

(a) Men (b) Women

Figure: Figure OA.III.20 – Crow-Siddiqui of Income Growth of Fathers and Children

(a) Sons

(b) Daughters

Figure: Figure OA.III.21 – Intergenerational Educational Mobility