Existing sources of publicly available data are rather limited with respect to these three criteria. We resorted to the LIS Cross-National Data Center in Luxembourg (http://www.lisdatacenter.org/), which allowed us to process data from four countries (Italy, Germany, France and Switzerland), while a fifth country was obtained from accessing the original provider (United Kingdom – <u>https://www.understandingsociety.ac.uk/).</u> The surveys we have used are therefore the following:

- **Italy:** Survey on Household Incomes and Wealth (SHIW), collected by the Bank of Italy – 11 surveys, covering the period 1993-2014 (information on parental background is not available before the starting date – originally consisting of 112,690 individuals, which reduces to 107,846 when considering non-missing information.

- **Germany:** German Socio-economic Panel (SOEP) – 11 surveys, covering the period 1984-2013 – originally including 156,338 individuals, then reduced to 133,467 in case of non-missing information.

- **France:** Household Budget Survey (HBS), conducted by the Banque de France) – 6 surveys, covering the period 1978-2005 – originally consisting of 97,306 individuals, declining to 89,119 when missing information is excluded.

- **Switzerland:** Swiss Household Panel (SHP) – 6 surveys, covering the period 1999-2014 – originally consisting of 43,102 individuals, which then decline to 31,273 valid observations.

- **United Kingdom:** starts as British Household Panel (BHPS), replaced after 2009 by the Understanding Society-Household Longitudinal Survey (UKHLS) – considers 24 waves over the period 1991-2014 – originally consisting of 434,253 individuals, which then decline to 308,625 valid observations.

Our selection rules include individuals aged 25-80 with a positive disposable income, harmonized according to the LIS procedure (variable DPI).<sup>7</sup> Incomes are converted to constant prices using the national consumer price index. Parental education is typically a categorical variable recording the highest educational attainment in the parental couple. In order to estimate a unique coefficient associated to the intergenerational transmission of education, we have converted them into years of education.<sup>8</sup> Descriptive statistics at survey/country disaggregation are reported in tables 1 to 5 in the Appendix.

Using these data, total inequality, absolute inequality of opportunity (namely inequality computed over incomes predicted according to circumstances) and relative inequality of opportunity (see equation (13)) have been estimated for each country and for each survey/year. These measures are reported in tables 6 to 10, including two indicators of inequality (standard deviation of logs and mean

> 7 To avoid negative values associated to logs, we have excluded all individuals with yearly incomes below 10. Data for the United Kingdom were rather volatile with respect to top incomes: in order to avoid confounding factors associated to differences in sampling procedures, we have trimmed them excluding incomes exceeding the 99.5 centile.

> 8 In the Italian file, recoding implies the following conversion: [1] illiterate=0 years; [2] primary=5 years; [3] lower secondary=8 years; [4] upper secondary=13; [5] tertiary=18. In the German file, recoding implies the following conversion: [1] school not attended =0 years; [2] no school degree =4; [3] Secondary General School ( _Hauptschule_ )=9 years; [4] Intermediate School ( _Realschule_ )=10 years; [5] Technical High School ( _Fachoberschule_ )=12 years; [6] Upper Secondary School ( _Abitur_ )=13 years. In the Swiss file, recoding implies the following conversion: [1]1: Primary or first stage of basic education=6 years; [2] 2: Lower secondary or Second stage of basic education=9 years; [3] 3A&B Upper secondary education (preparation for tertiary education & voc.educ)=12 years; [4] 3C: Upper secondary education (entrance into the labor market)=11 years; [5] 4A: Post-secondary education non-tertiary (preparation for an institution for higher education)=13 years; [6] 5B: First stage of tertiary education (professional education)=15 years; [7] 5A/6 tertiary education (general education)=16 years. In the UK file recoding implies the following conversion: [1] no qualification =8 years; [2] some qualification=10 years; [3] post school qualification=12 years; [4] university degree=18 years. Eventually, in the case of France there is no information on parental education, but only on parental occupation. In order to retain the country, we have created a dummy variable corresponding to either [5] intermediate profession (foreman, nurse, etc.) or [6] executive, liberal profession. We interpret this variable as the (likely) completion of secondary or tertiary education.

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