Disposable income is defined as an individual’s income after the deduction of taxes and social security contributions. It includes: (i) working income: salaries, self-employed income, etc.; (ii) income from household worth: dividends, interest, rent, etc., to which we add the imputed rents; (iii) social security benefits, including pension and unemployment benefits; and (iv) current transfers, particularly insurance indemnities minus premiums and transfers between households.

We first compute disposable income using data from the French Household Expenditure Survey (Budget de famille, referred to hereafter as BdF) waves conducted in 1979, 1984, 1989, 1995, 2000, 2005, and 2010. With more than 10,000 participating households, the aim of these surveys was to reconstitute all household accounts by gathering information on the respondents’ income and expenditure levels. It is worth noting that in the BdF, a household refers to any group of people who ordinarily share a dwelling and a budget, and who may or may not be related.

We estimate each household’s disposable income by adding up all sources of income and deducting any direct taxes paid (income tax, council tax, property tax). As the BdF surveys conducted between 1979 and 1995 did not provide figures for imputed rents, these figures were estimated using the characteristics of housing; as in d’Albis and Badji (2017). All of the variables are deflated using the consumer price index.

Unlike in d’Albis and Badji (2017), in the current analysis we individualise the disposable income following the recommendations made by the National Transfer Accounts (United Nations 2013). The BdF surveys provide some income data at the household level (such as property income, imputed rents, family benefits, transfers between households, and direct taxes paid), and other income data at the individual level. The household-level data are allocated between the members of the household using a sharing rule. Property income, transfers between households, direct taxes, and family benefits¹ are allocated equally between the household reference person and his or her spouse. Imputed rents are allocated using the NTA rule.

To enable us to compare data within a consistent time frame, we adjust the survey data to the French System of National Accounts aggregates. This adjustment, which is similar to the adjustment carried out for the National Transfer Accounts (d’Albis et al. 2015; 2017), ensures that the aggregate disposable income of individuals is equal to the National Accounts aggregates. Our sample is restricted to ordinary households residing in Metropolitan France. Finally, the rescaled individual variables are split by sex.

Figure 1 shows the disposable income by age for 16 generations. These generations are established using the seven cross-sectional databases we created from the seven BdF surveys. We first built 79 annual cohorts, defined according to the reference individual’s date of birth. The first cohort was born in 1901, while the last cohort was born in 1979. The generations are then defined using the mean of five consecutive cohorts (except for the first generation, which consists of four cohorts). Each line in Figure 1 represents a generation (e.g. 1947 represents all cohorts born between 1945 and 1949) at different ages (e.g. 57 represents the 55–59 age bracket).

Both for the whole population (Figure 1(a)) and for men alone (Figure 1(b)), income over the life-cycle forms an inverted U. Moreover, since the curves often cross, it is hard to come to any conclusion about income variation from one generation to the next. However, for women alone (Figure 1(c)), income appears to rise throughout an individual’s lifetime, and clearly improves from generation to generation. But regardless of the age or generation, women’s income is lower than men’s income. Figure 1(d) shows the ratio between men’s and women’s disposable income obtained from the data presented in Figures 1(b) and 1(c), except for the data from the 1979 survey. We can see that, for all ages and for all generations, this ratio is greater than one. Inequalities appear to decline from one generation to the next, with a sharp division emerging between those born before and after the Second World War.

The mortality-adjusted disposable income indicator is designed to include longevity gains by assigning them a monetary value. This value is determined by the reduction in income that would theoretically be accepted in exchange for enjoying a longer lifespan. Here, we adapt the method described in d’Albis and Bonnet (2018) by calculating the willingness to pay for a longer life at each age, and not just at birth.

Let us start with a life-cycle model with an uncertain lifespan, like those developed by Yaari (1965) and Barro and Friedman (1977), among others. The program of a representative agent of age a = {0,1,...,T} at date t is to maximise an intertemporal utility: Va,t=∑i=aT1(1+θ)i−ali,tla,tu(ci,t+i−a),  (1)

subject to an intertemporal budget constraint: ∑i=aT1(1+r)i-ali,tla,tci,t+i-a=wa,t+∑ i=aT1(1+r)i-ali,tla,tyi,t+i-a.  (2)

Variables ca,t, ya,t, and wa,t represent consumption income and wealth at age a and date t. Moreover, li,t/la,t is the probability of surviving to age i for an individual of age a, which is here approximated with period life tables. Finally, θ and r are the discount rate and interest rate, respectively. Assuming θ=r, zero initial wealth and yi,t+i-a=ya,t, we find that the optimal consumption is constant and equal to income. The intertemporal utility can thus be written as: Va,t=u(ya,t)a(li,tla,t),  (3)

which corresponds to the product of the utility of income and the value of an annuity calculated using survival functions,

Following Fleurbaey and Gaulier (2009) and d’Albis and Bonnet (2018), we defined a mortality-adjusted income. The principle behind this approach is to calculate a willingness to pay, denoted xa,t, by comparing for a given date the life expectancy at age a with the life expectancy that prevails at a late date, denoted t*. This willingness to pay corresponds to the income an individual at date t would be willing to forego in order to enjoy the life expectancy at date t*. It is calculated as follows:

where ya,t-xa,t corresponds to our mortality-adjusted income, which solves:

The greater the gap in life expectancy between t and t*, the lower the mortality-adjusted income. Like Becker et al. (2005) and d’Albis and Bonnet (2018), we use a Constant Relative Risk Aversion utility function:

and choose the following parameter values: r=0.03, γ=1.25, and α=-16.2. The last two parameters are used in Becker et al. (2005), and enable us to match Murphy and Topel (2003)’s estimates of the Value of a Statistical Life. A robustness check for an alternative set of parameters reveals that the evaluation of the willingness to pay is sensitive to those parameters, but that estimations of age and cohort effects remain qualitatively robust (see Appendix B). Moreover, the dates we consider are those of the BdF surveys; i.e. t=1979,1984,…,2010; while the ages are: a=25,26,…,84.

The life expectancy by age statistics come from the Human Mortality Database. For reasons of data availability, we use the cross-sectional data. This approach probably underestimates the rise in life expectancy, and, consequently, the benefit to the youngest generations of this rise in life expectancy. As we shall see below, this approach does not undermine our econometric results. Indeed, because it is based cautious assumptions, it strengthens them.

Figure 2 shows the increase in life expectancy at each age from 1979 to 2010 for the whole population, men alone, and women alone. In line with recent mortality trends in most other developed countries, life expectancy in France rose with age, reaching 77 for men and 82 for women (Wilmoth and Horiuchi 1999). The increase was close to 40% by these ages, and then declined. At all ages between 25 and 80, the increase was significantly greater for men than for women.

As calculated, willingness to pay was higher for men than for women, most likely because women’s life expectancy increased less than that of men. Furthermore, although the willingness to pay declined from one survey to another, it was relatively constant from one age group to another. For example, the share of disposable income men said they were willing to pay in exchange for enjoying a 2010 life expectancy was around 20% in 1979, and more than 10% in 1995. The corresponding shares for women were just over 9% and 4%. Figures 3(a), 3(b), and 3(c) show mortality-adjusted disposable income for, respectively, the whole population, men alone, and women alone. While the age profiles for income do not differ greatly from those in Figures 1(a), 1(b), and 1(c), the differences between the generations are clearer. Figure 3(d) also shows that the differences between men and women are smaller.

Individual data can be used to distinguish the effects of age, cohort, and period, provided these are panel data that follow individuals throughout their entire life-cycle. Since our data are cross-sectional, we have built pseudo panels that group individuals belonging to the same cohort. We defined our cohorts using the “date of birth” variable, which resulted in 79 annual cohorts. The first cohort is made up of individuals who were born in 1901, and the last cohort cohort is made up of individuals who were born in 1979. Our pseudo panel includes 407 observations of our cohorts, because not all cohorts were observed in each survey, and the sizes of cohorts depended on the samples used (see Table 1). The observation numbers were small mainly for the older cohorts, and particularly for men, as their life expectancy was lower.

The simultaneous introduction of the “age”, “cohort”, and “period” variables in the estimation creates a collinearity problem because the survey year is equal to the sum of the “age” and “cohort” variables. As was noted in d’Albis and Badji (2017), various solutions to this problem have been proposed in the literature. We have chosen to follow the most common strategy: namely, that of Deaton and Paxson (1994). This approach imposes restrictions on the estimated parameters based on the assumption that period effects sum to zero, and are orthogonal to the long-term trend.

We assume that the three effects (age, cohort, and period) that we are seeking to estimate are additive. The model equation is written as follows:

where ȳjt represents the explained variable related to cohort j=1901,1902,…,1979 and survey dates t=1979,1984,…,2010,1ajt represent the indicators of the five-year age brackets from 25–29 years old to 80–84 years old associated with cohort j at date t, 1j=c represent the indicators of the cohorts, and 1t=p represent the indicators associated with survey dates t.

We estimated our equation for each of the variables of interest: disposable income and mortality-adjusted disposable income, both for the whole population and for men and women separately. Looking at Table 2, we can see that in all instances, the tests for fixed individual effects (which in our case are cohort effects, given by the term ∑cβc1j=c) were positive, which justifies our choice of a fixed effects model. More precisely, we estimated a Least Square Dummy Variable type fixed effects model.

Figures 4, 5, and 6 represent the logarithm of the two incomes we consider as functions of the birth date when we control for age and period effects. Figure 7 covers the whole population, whereas Figures 8 and 9 refer to men and women, respectively. In each figure, panel (a) is the logarithm of the disposable income, and panel (b) is the logarithm of the mortality-adjusted disposable income. The results are expressed as a deviation from a reference cohort; i.e. the cohort born in 1946. Moreover, the grey lines delimit the confidence interval at the 5% level.

When we consider the whole population (Figure 4), we can discern two major periods in the development of disposable income by date of birth. Among the cohorts born before the Second World War, incomes increased significantly from generation to generation: from the 1926 cohort to the 1946 cohort, incomes rose 40%. But among the post-war cohorts, there were no significant changes. A slight increase can be observed for the latest cohorts. However, since there is less information on these cohorts in our databases, this finding should not be given too much importance. The observation that disposable income has stagnated suggests that that the baby boom cohorts in particular have not had higher living standards than subsequent cohorts (d’Albis and Badji 2017). When the gains from higher life expectancy are added, the distinction between these two periods becomes much less clear. Mortality-adjusted disposable income increased throughout the study period. In particular, we can see that all of the cohorts born after 1960 have enjoyed significantly higher incomes than the cohort born in 1946. We find, for example, that mortality-adjusted disposable income rose 28.6% from the 1946 cohort to the 1966 cohort, compared to 49.4% from the 1926 to the 1946 cohort. It thus appears that, ultimately, all of the post-baby boom cohorts had a higher adjusted income than the baby boomers. Note that our results are reinforced when using private consumption rather that disposable income (see Appendix B).

The breakdown by sex is also highly instructive. The variation in disposable income has been much flatter for the male population (Figure 5) than for the population as a whole. The increase observed among the pre-war cohorts is less pronounced, and no further relative improvement can be seen from the 1946 cohort to the 1970s cohorts. Including life expectancy gains hardly alters this observation, although we do find that the increase was greater for the pre-war cohorts, and that some post-baby boom cohorts had a significantly higher mortality-adjusted income than the 1946 cohort.

The results for the female population differ dramatically from those for the male population (Figure 6). Even before we include life expectancy gains, we see a considerable increase. For example, we find that disposable income for women rose 27% from the 1946 cohort to the 1966 cohort, compared to 71.9% from the 1926 cohort to the 1946 cohort. Furthermore, we can see that all of the cohorts born after 1961 had significantly higher incomes than the 1946 cohort. When life expectancy gains are included, these increases are slightly greater: i.e. mortality-adjusted disposable income for women rose 38.8% from the 1946 cohort to the 1966 cohort, and 76.6% from the 1926 cohort to the 1946 cohort.

It is of interest to note that recent studies of intergenerational mobility have focused on men alone. Lefranc (2018) has shown that the intergenerational persistence of income has increased starting with the cohorts born in the 1950s; while Alesina et al. (2018) has found that the French, like other Europeans, are pessimistic about intergenerational mobility. Our results suggest that the positions of men are not representative of the positions of the population as a whole; and, thus, that focusing on men’s experiences conceals the improvements women have enjoyed. Moreover, as those two studies used data from the same survey (Formation et Qualification Professionnelle), which does not contain explicit information on income, the authors had to estimate income. Using the same survey to study intergenerational mobility through social classes, Vallet (2017) concluded that mobility increased for the younger cohorts, and that improvements were larger for women than for men; while Ben-Halima et al. (2014) showed that the degree of intergenerational persistence was less pronounced for daughters than for sons. The findings of both of these studies complement our results, which highlight the role of education in the reduction in intergenerational inequalities.

Figures 7, 8, and 9 represent the logarithm of the two incomes we consider as functions of the age when we control for cohort and period effects. Figure 7 covers the whole population, whereas Figures 8 and 9 display the findings for men and women, respectively. In each figure, the left panel is the logarithm of the disposable income, and the right panel is the logarithm of the mortality-adjusted disposable income. The results are expressed as a deviation from a reference age group of 45–49-year-olds. As above, the grey lines delimit the confidence interval at the 5% level.

Looking at the population as a whole (Figure 7), we can see that disposable income by age increased sharply (+43.7%) from ages 27 to 47, ² levelled out up to age 62, and then rose moderately (+27:9%) up to age 82. Note that this general increase in disposable income differs greatly from the pattern implied by the descriptive statistics in Figure 1(a). After controlling for cohort and period effects, the perceived dip in income after age 50 disappears, and indeed turns into an improvement. The rise in income after age 62 may be explained by a composition effect similar to the one described in the literature on the missing poor in the poverty statistics (Kanbur and Mukherjee 2007). Since longevity correlates with income, the proportion of low-income people tends to decline from one higher age group to the next.

When longevity gains are included, we find that income growth was continuous over a lifetime; and, indeed, rose later in life. Adjusted growth was 53% from ages 27 to 47, 7.3% from ages 47 to 62, and 50.1% from ages 62 to 82. Thus, we can see that the gains have been particularly large for the oldest people. These observations are in line with evidence indicating that since the late 1970s, life expectancy gains in France have occurred mainly at higher ages.

The breakdown of these results by sex uncovers wide disparities between men and women. Men’s disposable income (Figure 8) stopped rising after age 52, and was even significantly lower from ages 57 to 77 than at age 47. By age 67, men’s income had declined 9.5%. By contrast, women’s disposable income (Figure 9) rose continuously, increasing 46.3% from ages 27 to 47, 20.3% from ages 47 to 62, and 123% from ages 62 to 82. Including longevity gains greatly alters the curve of men’s income by age, which was significantly higher after age 67 than it was at age 47. Taking these gains into account also increases the slope of the curve of women’s income.

A number of conclusions may be drawn from our estimates. The first is that there can be inequality between age groups without any generation losing out. None of the income by age curves presented in Section 3.2 slopes downwards: in most cases, the slopes rise, and a few level out (or fall slightly) during part of the life-cycle. This observation implies that, on average, a person of a given age has an income that is higher than or equal to that of a younger person, after controlling for cohort and period effects. But the finding that young people are less rich than current seniors does not mean that they lose out: in all of our estimates, their income was always found to be higher than or equal to that of members of previous generations at the same age. d’Albis and Badji (2017) attributed this pattern to economic growth. Although the growth in real per capita GDP was less vigorous between 1979 and 2010 than it was during the 30 years that followed the Second World War, it still increased 50% over this period.

Including longevity gains only supported this observation. After these gains were added, hardly any periods of stagnation in mortality-adjusted disposable income remained: in all of our models, that indicator rose as a function both of age and year of birth. This is likely because life expectancy at birth rose from 1979 to 2010 (10% to 40%, depending on age and sex), which added to the effect of economic growth. Thus, it is clear that well-being, which was measured here by combining an economic and a demographic indicator, improved both over a lifetime and from one generation to the next. If we assume that equity between generations is ensured as long as their well-being does not deteriorate (Stavins et al. 2003; Arrow et al. 2004), we can conclude that the relative positions of the French cohorts born from 1901 to 1979 have been equitable.

However, our breakdown of the population into men and women has led us to qualify this observation. It is clear that most of the gains in mortality-adjusted disposable income have gone to women, whose economic positions greatly improved over this period. Conversely, the mortality-adjusted disposable income levels of men varied little for all of the cohorts born after the Second World War. Thus, while men’s well-being has not worsened, it has not improved as much as that of women. This point in no way detracts from the reality that men continue to have much higher disposable income than women (for example, among 52-year-olds in 2010, men’s income levels were 60% higher than women’s). Our observations merely reveal that women’s earnings are catching up to those of men.