# **II. THE EMPIRICAL ANALYSES**

This section investigates the distributional changes that occurred in Italy and Brazil in the last decade. These analyses pursue two additional aims: (i) assessing the main consequences of the actual economic crisis on the Italian distribution of income according to the EOp perspective and (ii) assessing the distributional implications of the most recent economic development experienced by Brazil in terms of EOp.

For both applications, we first provide an assessment of growth according to the equality of outcome perspective. We then move to the analysis of growth according to the EOp perspective.<sup>21</sup>

## **_Opportunity and Growth in Italy: The Data_**

Italy is the first country considered in this section. This analysis is developed using the Bank of Italy’s “Survey on Household Income and Wealth” (SHIW), a representative sample of the Italian resident population interviewed every two years. Three waves of the survey are considered: 2002, 2006, and 2010 (the latest available).

The unit of observation is the household, defined as all persons sharing the same dwelling. The individual outcome is, then, measured as the household equivalent income in 2010 euro.<sup>22</sup> Income includes all household earnings, transfers, pensions, and capital incomes, net taxes, and social security contributions. The richest and poorest 1% of the households in each wave are dropped to avoid the effect of outliers. To identify the types, the distribution is partitioned into 18 types using information about three characteristics of the head of the family: the highest educational

> 21We calculate confidence intervals for the difference between individual OGIC, type OGIC, and indexes in the two growth processes. The resampling procedure that we use is in line with the approach proposed by Lokshin (2008) for the GIC. We assume that the income distributions observed at the two points in time, _y_<sup>_t_</sup> _, y_<sup>_t_+1</sup> , are independent and identically distributed observations of the unknown probability distributions _F_ ( _y_<sup>_t_</sup> ) _, F_ ( _y_<sup>_t_+1</sup> ). _γ_ is the statistic of interest, and its standard error is _σ_ ( _F_ ( _y_<sup>_t_</sup> ) _, F_ ( _y_<sup>_t_+1</sup> )) = ~~�~~ _V arγ_ ˆ( _y_<sup>_t_</sup> _, y_<sup>_t_+1</sup> ). Our bootstrap estimate of the standard error is _σ_ ˆ = _σ F_ ˆ( _y_<sup>_t_</sup> ) _, F_ ˆ( _y_<sup>_t_+1�</sup> , where _F_<sup>ˆ</sup> ( _y_<sup>_t_</sup> ) _, F_<sup>ˆ</sup> ( _y_<sup>_t_+1</sup> ) are the empirical distributions observed. The 95% � confidence interval is obtained by resampling _B_ = 1 _,_ 000 ordinary non parametric bootstrap replications of the two distributions _yt_<sup>_∗, y_</sup> _t_<sup>_∗_</sup> +1<sup>.Thestandarderrorofparameter</sup><sup>_γ_ˆisobtainedusing</sup><sup>_σ_ˆ</sup><sup>_B_=</sup> ~~�~~ <u>�</u> _Bb_ =1<sup>_{γ_ˆ</sup><sup>_∗_(</sup><sup>_b_)</sup><sup>_−γ_ˆ(</sup><sup>_._)</sup><sup>_}_2</sup><sup>_/_(</sup><sup>_B −_1),</sup> wherenormally _γ_ ˆ( _._ ) =distributed,� _Bb_ <u>=1</u> _B_<sup>_<u>γ∗</u>_</sup><sup><u>(</u></sup> we<sup>_b_</sup><sup><u>)</u></sup> . calculateWe know confidencethat _σ_ ˆ _B →_ intervals: _σ_ ˆ when _Bγ_ ˆ _→∞_ = _γ_ ˆ, _±_ and, _z_ 1 _−_ under _α/_ 2 _σ_ ˆ _B_ the. Ourassumptionestimate thatquality _γ_ isreliesapproximatelyon strong assumptions. However, as will be clear in the discussion of the results, dominances appear rather reliable for the illustrative purpose of the exercise.

> 22We use the OECD equivalence scale given by the square root of the household size.

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