incomes, poverty, and living conditions on an annual basis and covers a cross-section of 31 European countries in the 2011 wave.<sup>10</sup> We draw on the 2011 wave since it contains an ad-hoc module about the intergenerational transmission of (dis)advantages, which allows us to construct finely-grained type partitions. The set of observed circumstances Ωand<sup>ˇ</sup> their respective expressions _x_<sup>_p_</sup> are listed in Table 1 whereas descriptive statistics concerning circumstances are reported in Appendix A.2. As an additional advantage, EU-SILC has been extensively studied by the empirical literature on inequality of opportunity and thus provides appropriate benchmarks against which we can compare our method (Checchi et al., 2016; Marrero and Rodr ́ıguez, 2012; Palomino et al., 2016).

The unit of observation is the individual, whereas the outcome of interest is equivalent disposable household income. Aware that inequality statistics tend to be heavily influenced by outliers (Cowell and Victoria-Feser, 1996) we adopt a standard winsorization method according to which we set all non-positive incomes to 1 and scale back all incomes exceeding the 99.5th percentile of the country-specific income distribution to this lower threshold. Our analysis is focused on the working age population. Therefore, we restrict the sample to respondents aged between 30 and 59. To assure the representativeness of our country samples all results are calculated by using appropriate individual cross-sectional weights.

Table 2 shows considerable heterogeneity in the income distributions of our country sample. While households in Norway (NO) and Switzerland (CH) on average obtained incomes above e40,000 in 2010, the average households in Bulgaria (BG), Romania (RO) and Lithuania (LT) did not exceed the e5,000 mark. The lowest inequality prevails in the Nordic countries of Norway (NO), Sweden (SE) and Iceland (IS), all of which are characterized by Gini coefficients of below 0 _._ 22. At the other end of the spectrum we find the Eastern European countries of Latvia (LV), Lithuania (LT) and Romania (EL) with Gini coefficients well above the level of 0.33.

# **4.2 Benchmark Methods**

We compare our estimates from trees and forests against three benchmark methods that have been proposed in the extant literature.

First, we draw on the parametric approach as proposed by Bourguignon et al. (2007) and Ferreira and Gignoux (2011). In line with equation (3), estimates are obtained by a Mincerian regression of equivalent household income on the following controls: father occupation (10 categories), father and mother education (five categories), area of birth (three categories), and tenancy status of the household (two categories). The model specification therefore includes 20 binary variables and resembles the specification used in Palomino et al. (2016).<sup>11</sup> Second, we draw on the non-parametric approach as proposed by Checchi and Peragine (2010). Non-parametric estimates are obtained by partitioning the sample into 40 types. Individuals in type _tm_ have parents of equivalent education (five categories), share their migration status (a binary variable whether the respondent is a first or second generation immigrant), and have fathers working in the same occupation. To minimize the frequency of sparsely populated

> 10The sample consists of Austria (AT), Belgium (BE), Bulgaria (BG), Switzerland (CH), Cyprus (CY), Czech Republic (CZ), Germany (DE), Denmark (DK), Estonia (EE), Greece (EL), Spain (ES), Finland (FI), France (FR), Croatia (HR), Hungary (HU), Ireland (IE), Iceland (IS), Italy (IT), Malta (MT), Lithuania (LT), Luxembourg (LU), Latvia (LV), Netherlands (NL), Norway (NO), Poland (PL), Portugal (PT), Romania (RO), Sweden (SE), Slovenia (SI), Slovak Republic (SK), and Great Britain (UK).

> 11We have estimated the predicted outcomes both as the exponential of the predicted log outcome, _yiEA_ = _P_ ˇ exp _p_ =1<sup>_β_ˆ</sup><sup>_pC_</sup> _i_<sup>_p_</sup> , and by introducing, assuming a normally distributed error term, the correction _yi_<sup>_EA_</sup> = �� � _P_ ˇ exp _p_ =1<sup>_β_ˆ</sup><sup>_pC_</sup> _i_<sup>_p_+</sup><sup>_σ_2</sup><sup>_/_2</sup> , where _σ_<sup>2</sup> is the estimated variance of the error term. We do not find any signifi�� � cant differences in the level of estimated inequality of opportunity when introducing the correction. This may explain why the need of such correction has never been explicitly discussed in previous contributions.

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