The analysis above was based on important normative assumptions regarding what individuals were held responsible for. We assumed that individuals were responsible for four variables (4var); their education, work hours, and whether they are self-employed or work in the public sector. We also assumed that individuals should not be held responsible for the part of these variables that could be accounted for by circumstance variables. That is, the correlation (cor) between circumstances and effort was itself considered outside the control of individuals. We further assumed that the part of individual well-being that was unaccounted for by circumstance or effort variables (residual) was within individual control. Next, we implicitly considered well-being differences across different age groups (age) as unfair. Finally, for the equivalent income measure, we assumed that individuals were not responsible for well-being differences due to preference heterogeneity arising from circumstances (pref).
Our baseline effort set contained 4var and residual. In this section, we try to shift the responsibility cut by altering what goes into the effort set. First, we look at whether the characteristics of the opportunity-deprived change as we change the effort set. This is analyzed in Figures5and 6. Figure5uses our most narrow effort set, only4var, while Figure 6uses the widest possible effort set, 4var, residual, cor, age, pref.
The figures show the same overall pattern as our main results. For the most part, the opportunity-deprived share the same characteristics across all four measures.
The only disputes are, once again, for individuals born abroad and for different age groups. The responsibility cut does matter for quantifying the degree to which a particular group is opportunity-deprived. For example, individuals born in East Germany have an average opportunity rank of about 40 with the smallest effort set and 15 with the largest effort set. In other words, East Germans are not doing too poorly if we only hold individuals responsible for four variables (which almost mimics just looking at outcomes), but the more we hold individuals responsible for, the more disadvantaged they are. This suggests that East Germans have relatively high effort levels.
Figure 5: Changing the Responsibility Cut: Effort = {4var}
Log Income Life Satisfaction Multidim. Index Log Eq. Income
Notes: The figure shows the average opportunity rank for people sharing a particular circumstance using a narrow effort set. Bars indicate boot-strapped 95thpercentile confidence bands.
Next, we look at whether the developments over time depend on where we place the responsibility cut. We try six different specifications, which gradually expand the effort set. Results are displayed in Figure7. Our primary interest is not whether the trends change as we change the responsibility cut, but rather whether the four well-being measures follow similar trends regardless of where we place the cut.
Our baseline results are displayed in panel (c). If we no longer hold individuals responsible for the four variables we had deemed effort (panel (b)), then our main results become more clear; inequality of opportunity increased until about 2005 and then decreased for all four measures. If we only hold individuals responsible for the four variables and shift the residual to the other side of the responsibility cut (panel (a)) then the picture looks very different, particularly for log income. Since the four effort variables only are able to explain very little of the variance, the measure almost boils down to the development in inequality over time, which we already
Figure 6: Changing the Responsibility Cut: Effort ={4var, residual, cor, age, pref}
Log Income Life Satisfaction Multidim. Index Log Eq. Income
Notes: The figure shows the average opportunity rank for people sharing a particular circumstance using a wide effort set. We no longer report dif-ferences in the average opportunity rank by age groups, as age is not con-sidered a circumstance in this specification. Bars indicate bootstrapped 95thpercentile confidence bands.
established follows different trends. Other studies that have switched the residual to the other side of the responsibility cut likewise found this to have a great impact on the results (see for example Alm˚as et al. (2011) and Devooght(2008)).
If we also hold individuals responsible for the correlation between effort and circumstances (panel (d)), then we still see an increase in inequality of opportunity in all measures from 1992-2005, but from then on the multidimensional index diverges from the rest. In the other cases where we add more to the responsibility cut (panel (e) and (f)), the overall trend changes, but stays broadly similar across the four well-being measures. In these cases, inequality of opportunity has remained rather flat or decreased a little from 1992 to 2016.
In sum, we find that when characterizing the opportunity-deprived, neither the
Figure 7: Altering the Responsibility Cut
(a) Effort: 4var
80100120140160Inequality of opp. (1992=100)
1995 2000 2005 2010 2015
Log Income Life Satisfaction Multidim. Index Log Equivalent Incomes
(b) Effort: Residual
80100120140160Inequality of opp. (1992=100)
1995 2000 2005 2010 2015
Log Income Life Satisfaction Multidim. Index Log Equivalent Incomes
(c) Effort: 4var, residual
80100120140160Inequality of opp. (1992=100)
1995 2000 2005 2010 2015
Log Income Life Satisfaction Multidim. Index Log Equivalent Incomes
(d) Effort: 4var, residual, cor
80100120140160Inequality of opp. (1992=100)
1995 2000 2005 2010 2015
Log Income Life Satisfaction Multidim. Index Log Equivalent Incomes
(e) Effort: 4var, residual, cor, age
80100120140160Inequality of opp. (1992=100)
1995 2000 2005 2010 2015
Log Income Life Satisfaction Multidim. Index Log Equivalent Incomes
(f) Effort: 4var, residual, cor, age, pref
80100120140160Inequality of opp. (1992=100)
1995 2000 2005 2010 2015
Log Income Life Satisfaction Multidim. Index Log Equivalent Incomes
Notes: Development in inequality of opportunity in each well-being variable from 1992-2016 for different responsibility cuts. 4var: The four variables work hours, education, self-employed, and works in public sector are considered effort. Residual: The residuals from the regressions of the well-being variables on circumstance and effort variables are considered effort. Age: Age is considered effort (implying we are equalizing lifetime opportunities).Cor: The correlation between effort and circumstance variables is not considered a circumstance. Pref: Individuals are fully held responsible for their preferences (only applies to the equivalent income measure). Our baseline specification used4var andresidual as effort.
measure of welfare nor the precise location of the responsibility cut is of great im-portance. When analyzing developments in equality of opportunity over time, where we place the residual matters quite a bit, while enlarging the effort set further has few implications. Although the trend may change depending on what we hold indi-viduals responsible for, for a given responsibility cut, the well-being measures follow broadly the same trend.