<table><caption>Table 18: Estimates of the growth elasticities of FGT indices for Brazil, 1981–2022.</caption><thead><tr><th rowspan="2">Year</th><th colspan="3">z = $3.65</th><th colspan="3">z = $6.85</th></tr><tr><th>Θ<sub>0</sub></th><th>Θ<sub>1</sub></th><th>Θ<sub>2</sub></th><th>Θ<sub>0</sub></th><th>Θ<sub>1</sub></th><th>Θ<sub>2</sub></th></tr></thead><tbody><tr><td>1981</td><td>-0.92</td><td>-1.18</td><td>-1.31</td><td>-0.51</td><td>-0.82</td><td>-0.99</td></tr><tr><td>1982</td><td>-0.90</td><td>-1.17</td><td>-1.31</td><td>-0.52</td><td>-0.81</td><td>-0.98</td></tr><tr><td>1983</td><td>-0.76</td><td>-1.08</td><td>-1.24</td><td>-0.41</td><td>-0.70</td><td>-0.88</td></tr><tr><td>1984</td><td>-0.78</td><td>-1.10</td><td>-1.28</td><td>-0.41</td><td>-0.72</td><td>-0.91</td></tr><tr><td>1985</td><td>-0.87</td><td>-1.17</td><td>-1.32</td><td>-0.49</td><td>-0.78</td><td>-0.96</td></tr><tr><td>1986</td><td>-1.24</td><td>-1.44</td><td>-1.51</td><td>-0.79</td><td>-1.08</td><td>-1.25</td></tr><tr><td>1987</td><td>-0.96</td><td>-1.20</td><td>-1.31</td><td>-0.60</td><td>-0.87</td><td>-1.03</td></tr><tr><td>1988</td><td>-0.90</td><td>-1.13</td><td>-1.22</td><td>-0.56</td><td>-0.81</td><td>-0.96</td></tr><tr><td>1989</td><td>-0.95</td><td>-1.16</td><td>-1.24</td><td>-0.58</td><td>-0.84</td><td>-0.99</td></tr><tr><td>1990</td><td>-0.85</td><td>-1.13</td><td>-1.29</td><td>-0.52</td><td>-0.79</td><td>-0.96</td></tr><tr><td>1992</td><td>-0.93</td><td>-1.12</td><td>-1.19</td><td>-0.62</td><td>-0.84</td><td>-0.97</td></tr><tr><td>1993</td><td>-0.94</td><td>-1.15</td><td>-1.23</td><td>-0.60</td><td>-0.85</td><td>-0.99</td></tr><tr><td>1995</td><td>-1.10</td><td>-1.32</td><td>-1.38</td><td>-0.75</td><td>-1.00</td><td>-1.14</td></tr><tr><td>1996</td><td>-1.04</td><td>-1.21</td><td>-1.26</td><td>-0.74</td><td>-0.96</td><td>-1.07</td></tr><tr><td>1997</td><td>-1.06</td><td>-1.25</td><td>-1.29</td><td>-0.73</td><td>-0.97</td><td>-1.09</td></tr><tr><td>1998</td><td>-1.11</td><td>-1.33</td><td>-1.37</td><td>-0.77</td><td>-1.02</td><td>-1.15</td></tr><tr><td>1999</td><td>-1.10</td><td>-1.33</td><td>-1.38</td><td>-0.77</td><td>-1.01</td><td>-1.14</td></tr><tr><td>2001</td><td>-1.12</td><td>-1.34</td><td>-1.43</td><td>-0.79</td><td>-1.03</td><td>-1.17</td></tr><tr><td>2002</td><td>-1.20</td><td>-1.47</td><td>-1.56</td><td>-0.82</td><td>-1.08</td><td>-1.25</td></tr><tr><td>2003</td><td>-1.17</td><td>-1.39</td><td>-1.50</td><td>-0.79</td><td>-1.06</td><td>-1.21</td></tr><tr><td>2004</td><td>-1.27</td><td>-1.51</td><td>-1.59</td><td>-0.83</td><td>-1.12</td><td>-1.29</td></tr><tr><td>2005</td><td>-1.33</td><td>-1.56</td><td>-1.64</td><td>-0.89</td><td>-1.17</td><td>-1.34</td></tr><tr><td>2006</td><td>-1.40</td><td>-1.61</td><td>-1.66</td><td>-0.98</td><td>-1.25</td><td>-1.41</td></tr><tr><td>2007</td><td>-1.41</td><td>-1.55</td><td>-1.51</td><td>-1.00</td><td>-1.26</td><td>-1.38</td></tr><tr><td>2008</td><td>-1.48</td><td>-1.65</td><td>-1.63</td><td>-1.09</td><td>-1.35</td><td>-1.47</td></tr><tr><td>2009</td><td>-1.50</td><td>-1.63</td><td>-1.59</td><td>-1.13</td><td>-1.35</td><td>-1.47</td></tr><tr><td>2011</td><td>-1.55</td><td>-1.53</td><td>-1.47</td><td>-1.22</td><td>-1.41</td><td>-1.49</td></tr><tr><td>2012</td><td>-1.62</td><td>-1.60</td><td>-1.68</td><td>-1.27</td><td>-1.51</td><td>-1.59</td></tr><tr><td>2013</td><td>-1.69</td><td>-1.77</td><td>-1.84</td><td>-1.32</td><td>-1.56</td><td>-1.68</td></tr><tr><td>2014</td><td>-1.71</td><td>-1.83</td><td>-1.89</td><td>-1.39</td><td>-1.64</td><td>-1.74</td></tr><tr><td>2015</td><td>-1.64</td><td>-1.70</td><td>-1.78</td><td>-1.34</td><td>-1.56</td><td>-1.66</td></tr><tr><td>2016</td><td>-1.54</td><td>-1.56</td><td>-1.62</td><td>-1.24</td><td>-1.46</td><td>-1.53</td></tr><tr><td>2017</td><td>-1.44</td><td>-1.45</td><td>-1.51</td><td>-1.23</td><td>-1.41</td><td>-1.46</td></tr><tr><td>2018</td><td>-1.42</td><td>-1.44</td><td>-1.51</td><td>-1.21</td><td>-1.42</td><td>-1.45</td></tr><tr><td>2019</td><td>-1.41</td><td>-1.37</td><td>-1.46</td><td>-1.19</td><td>-1.38</td><td>-1.41</td></tr><tr><td>2020</td><td>-2.04</td><td>-1.98</td><td>-1.90</td><td>-1.75</td><td>-1.97</td><td>-1.98</td></tr><tr><td>2021</td><td>-1.43</td><td>-1.39</td><td>-1.55</td><td>-1.28</td><td>-1.43</td><td>-1.45</td></tr><tr><td>2022</td><td>-1.67</td><td>-1.70</td><td>-1.73</td><td>-1.40</td><td>-1.61</td><td>-1.68</td></tr><tr><td>mean</td><td>-1.25</td><td>-1.41</td><td>-1.48</td><td>-0.91</td><td>-1.15</td><td>-1.28</td></tr></tbody></table>
<table><caption>Table 19: Estimates of the observed values of $\pi_{\alpha,\mu_z}$, $\pi_{\alpha,GE_{2z}}$, $\zeta$ and $\nu_{\alpha}$ for Brazil, 1981–2022.</caption><thead><tr><th rowspan="2">Year</th><th colspan="5">z = $3.65</th><th colspan="5">z = $6.85</th></tr><tr><th>π<sub>1,μ<sub>z</sub></sub></th><th>π<sub>2,μ<sub>z</sub></sub></th><th>ζ</th><th>π<sub>2,GE<sub>2z</sub></sub></th><th>ν<sub>2</sub></th><th>π<sub>1,μ<sub>z</sub></sub></th><th>π<sub>2,μ<sub>z</sub></sub></th><th>ζ</th><th>π<sub>2,GE<sub>2z</sub></sub></th><th>ν<sub>2</sub></th></tr></thead><tbody><tr><td>1981</td><td>-1.18</td><td>-1.31</td><td>-0.99</td><td>0.24</td><td>0.87</td><td>-0.82</td><td>-0.99</td><td>-1.64</td><td>0.18</td><td>3.32</td></tr><tr><td>1982</td><td>-1.17</td><td>-1.31</td><td>0.19</td><td>0.24</td><td>-2.69</td><td>-0.81</td><td>-0.98</td><td>-1.31</td><td>0.17</td><td>-0.88</td></tr><tr><td>1983</td><td>-1.08</td><td>-1.24</td><td>-1.16</td><td>0.22</td><td>4.92</td><td>-0.70</td><td>-0.88</td><td>-1.72</td><td>0.15</td><td>4.15</td></tr><tr><td>1984</td><td>-1.10</td><td>-1.28</td><td>-0.23</td><td>0.22</td><td>0.32</td><td>-0.72</td><td>-0.91</td><td>-0.68</td><td>0.15</td><td>0.49</td></tr><tr><td>1985</td><td>-1.17</td><td>-1.32</td><td>-0.45</td><td>0.24</td><td>0.84</td><td>-0.78</td><td>-0.96</td><td>-0.41</td><td>0.17</td><td>0.92</td></tr><tr><td>1986</td><td>-1.44</td><td>-1.51</td><td>-1.88</td><td>0.28</td><td>5.88</td><td>-1.08</td><td>-1.25</td><td>-1.77</td><td>0.22</td><td>5.86</td></tr><tr><td>1987</td><td>-1.20</td><td>-1.31</td><td>-1.07</td><td>0.25</td><td>3.33</td><td>-0.87</td><td>-1.03</td><td>-1.08</td><td>0.19</td><td>2.71</td></tr><tr><td>1988</td><td>-1.13</td><td>-1.22</td><td>-0.55</td><td>0.24</td><td>0.59</td><td>-0.81</td><td>-0.96</td><td>-0.98</td><td>0.18</td><td>1.34</td></tr><tr><td>1989</td><td>-1.16</td><td>-1.24</td><td>-1.13</td><td>0.25</td><td>4.10</td><td>-0.84</td><td>-0.99</td><td>-1.03</td><td>0.19</td><td>2.88</td></tr><tr><td>1990</td><td>-1.13</td><td>-1.29</td><td>-0.49</td><td>0.23</td><td>-0.17</td><td>-0.79</td><td>-0.96</td><td>-1.01</td><td>0.17</td><td>1.28</td></tr><tr><td>1992</td><td>-1.12</td><td>-1.19</td><td>-0.19</td><td>0.25</td><td>0.14</td><td>-0.84</td><td>-0.97</td><td>-0.38</td><td>0.19</td><td>0.60</td></tr><tr><td>1993</td><td>-1.15</td><td>-1.23</td><td>-1.27</td><td>0.25</td><td>6.71</td><td>-0.85</td><td>-0.99</td><td>1.29</td><td>0.19</td><td>4.02</td></tr><tr><td>1995</td><td>-1.32</td><td>-1.38</td><td>-7.09</td><td>0.27</td><td>23.88</td><td>-1.00</td><td>-1.14</td><td>-4.19</td><td>0.22</td><td>16.98</td></tr><tr><td>1996</td><td>-1.21</td><td>-1.26</td><td>-10.51</td><td>0.26</td><td>27.72</td><td>-0.96</td><td>-1.07</td><td>-5.75</td><td>0.22</td><td>15.43</td></tr><tr><td>1997</td><td>-1.25</td><td>-1.29</td><td>-5.34</td><td>0.27</td><td>23.46</td><td>-0.97</td><td>-1.09</td><td>-6.34</td><td>0.22</td><td>18.17</td></tr><tr><td>1998</td><td>-1.33</td><td>-1.37</td><td>-0.93</td><td>0.28</td><td>2.46</td><td>-1.02</td><td>-1.15</td><td>-0.46</td><td>0.22</td><td>2.15</td></tr><tr><td>1999</td><td>-1.33</td><td>-1.38</td><td>1.99</td><td>0.27</td><td>1.40</td><td>-1.01</td><td>-1.14</td><td>2.13</td><td>0.22</td><td>-1.57</td></tr><tr><td>2001</td><td>-1.34</td><td>-1.43</td><td>-6.87</td><td>0.27</td><td>24.02</td><td>-1.03</td><td>-1.17</td><td>-2.85</td><td>0.22</td><td>15.82</td></tr><tr><td>2002</td><td>-1.47</td><td>-1.56</td><td>1.25</td><td>0.28</td><td>-4.77</td><td>-1.08</td><td>-1.25</td><td>-0.44</td><td>0.22</td><td>-1.27</td></tr><tr><td>2003</td><td>-1.39</td><td>-1.50</td><td>-1.93</td><td>0.27</td><td>4.91</td><td>-1.06</td><td>-1.21</td><td>-1.33</td><td>0.22</td><td>4.74</td></tr><tr><td>2004</td><td>-1.51</td><td>-1.59</td><td>-2.80</td><td>0.28</td><td>9.97</td><td>-1.12</td><td>-1.29</td><td>-3.04</td><td>0.22</td><td>6.77</td></tr><tr><td>2005</td><td>-1.56</td><td>-1.64</td><td>-0.39</td><td>0.29</td><td>0.40</td><td>-1.17</td><td>-1.34</td><td>-1.04</td><td>0.23</td><td>2.46</td></tr><tr><td>2006</td><td>-1.61</td><td>-1.66</td><td>1.29</td><td>0.30</td><td>-10.17</td><td>-1.25</td><td>-1.41</td><td>0.63</td><td>0.24</td><td>-3.28</td></tr><tr><td>2007</td><td>-1.55</td><td>-1.51</td><td>-1.44</td><td>0.31</td><td>6.73</td><td>-1.26</td><td>-1.38</td><td>-1.23</td><td>0.25</td><td>3.97</td></tr><tr><td>2008</td><td>-1.65</td><td>-1.63</td><td>0.79</td><td>0.32</td><td>-4.47</td><td>-1.35</td><td>-1.47</td><td>0.08</td><td>0.26</td><td>-1.57</td></tr><tr><td>2009</td><td>-1.63</td><td>-1.59</td><td>0.69</td><td>0.32</td><td>-6.38</td><td>-1.35</td><td>-1.47</td><td>-0.81</td><td>0.26</td><td>-0.25</td></tr><tr><td>2011</td><td>-1.53</td><td>-1.47</td><td>2.21</td><td>0.31</td><td>-18.07</td><td>-1.41</td><td>-1.49</td><td>1.76</td><td>0.27</td><td>-7.28</td></tr><tr><td>2012</td><td>-1.60</td><td>-1.68</td><td>-2.21</td><td>0.29</td><td>9.40</td><td>-1.51</td><td>-1.59</td><td>-0.48</td><td>0.28</td><td>4.97</td></tr><tr><td>2013</td><td>-1.77</td><td>-1.84</td><td>-0.77</td><td>0.31</td><td>2.65</td><td>-1.56</td><td>-1.68</td><td>-1.26</td><td>0.28</td><td>3.13</td></tr><tr><td>2014</td><td>-1.83</td><td>-1.89</td><td>11.91</td><td>0.31</td><td>-39.52</td><td>-1.64</td><td>-1.74</td><td>4.34</td><td>0.29</td><td>-31.19</td></tr><tr><td>2015</td><td>-1.70</td><td>-1.78</td><td>-0.92</td><td>0.30</td><td>4.71</td><td>-1.56</td><td>-1.66</td><td>-0.89</td><td>0.28</td><td>4.14</td></tr><tr><td>2016</td><td>-1.56</td><td>-1.62</td><td>31.01</td><td>0.29</td><td>-102.90</td><td>-1.46</td><td>-1.53</td><td>13.26</td><td>0.28</td><td>-87.48</td></tr><tr><td>2017</td><td>-1.45</td><td>-1.51</td><td>-0.41</td><td>0.28</td><td>0.67</td><td>-1.41</td><td>-1.46</td><td>-0.50</td><td>0.28</td><td>1.14</td></tr><tr><td>2018</td><td>-1.44</td><td>-1.51</td><td>2.95</td><td>0.28</td><td>-7.25</td><td>-1.42</td><td>-1.45</td><td>1.82</td><td>0.29</td><td>-4.89</td></tr><tr><td>2019</td><td>-1.37</td><td>-1.46</td><td>-2.35</td><td>0.27</td><td>9.49</td><td>-1.38</td><td>-1.41</td><td>-1.95</td><td>0.28</td><td>6.84</td></tr><tr><td>2020</td><td>-1.98</td><td>-1.90</td><td>0.03</td><td>0.35</td><td>-1.53</td><td>-1.97</td><td>-1.98</td><td>-1.33</td><td>0.33</td><td>4.08</td></tr><tr><td>2021</td><td>-1.39</td><td>-1.55</td><td>-5.28</td><td>0.26</td><td>11.43</td><td>-1.43</td><td>-1.45</td><td>-1.74</td><td>0.29</td><td>10.45</td></tr><tr><td>2022</td><td>-1.70</td><td>-1.73</td><td></td><td></td><td></td><td>-1.61</td><td>-1.68</td><td></td><td></td><td></td></tr><tr><td>mean</td><td>-1.41</td><td>-1.48</td><td>-0.12</td><td>0.28</td><td>-0.19</td><td>-1.15</td><td>-1.28</td><td>-0.60</td><td>0.23</td><td>0.25</td></tr><tr><td>mean*</td><td>-1.39</td><td>-1.46</td><td>-1.35</td><td>0.27</td><td>3.87</td><td>-1.13</td><td>-1.26</td><td>-1.14</td><td>0.23</td><td>3.65</td></tr></tbody></table>

Note: Elasticities are computed for yearly changes in the Lorenz curves; * is for the average value without the years 2014 and 2016.
<table><caption>Table 20: Estimates of the between-Gini elasticities of FGT indices ($\epsilon_{\alpha,q}^B$) for Brazil, 1981–2022, $q = 0, 4$.</caption><thead><tr><th rowspan="2">Year</th><th colspan="3">$z = \$3.65$</th><th colspan="3">$z = \$6.85$</th></tr><tr><th>Θ<sub>0</sub></th><th>Θ<sub>1</sub></th><th>Θ<sub>2</sub></th><th>Θ<sub>0</sub></th><th>Θ<sub>1</sub></th><th>Θ<sub>2</sub></th></tr></thead><tbody><tr><td>1981</td><td>-0.32</td><td>3.63</td><td>4.57</td><td>-0.18</td><td>0.87</td><td>1.95</td></tr><tr><td>1982</td><td>-0.31</td><td>3.69</td><td>4.71</td><td>-0.18</td><td>0.90</td><td>2.01</td></tr><tr><td>1983</td><td>-0.26</td><td>2.44</td><td>4.02</td><td>-0.14</td><td>0.62</td><td>1.50</td></tr><tr><td>1984</td><td>-0.27</td><td>2.47</td><td>4.01</td><td>-0.14</td><td>0.61</td><td>1.49</td></tr><tr><td>1985</td><td>-0.29</td><td>2.99</td><td>4.18</td><td>-0.17</td><td>0.72</td><td>1.68</td></tr><tr><td>1986</td><td>4.46</td><td>5.19</td><td>5.43</td><td>-0.27</td><td>2.50</td><td>4.01</td></tr><tr><td>1987</td><td>3.79</td><td>4.78</td><td>5.20</td><td>-0.21</td><td>1.41</td><td>2.81</td></tr><tr><td>1988</td><td>3.92</td><td>4.91</td><td>5.31</td><td>-0.20</td><td>1.32</td><td>2.70</td></tr><tr><td>1989</td><td>4.52</td><td>5.52</td><td>5.92</td><td>-0.21</td><td>1.71</td><td>3.31</td></tr><tr><td>1990</td><td>-0.30</td><td>4.31</td><td>5.32</td><td>-0.18</td><td>1.10</td><td>2.37</td></tr><tr><td>1992</td><td>-0.31</td><td>3.26</td><td>3.63</td><td>-0.21</td><td>0.77</td><td>1.71</td></tr><tr><td>1993</td><td>3.69</td><td>4.48</td><td>4.82</td><td>-0.21</td><td>1.11</td><td>2.36</td></tr><tr><td>1995</td><td>4.26</td><td>5.10</td><td>5.31</td><td>-0.26</td><td>2.13</td><td>3.66</td></tr><tr><td>1996</td><td>4.22</td><td>4.91</td><td>5.09</td><td>-0.26</td><td>2.13</td><td>3.61</td></tr><tr><td>1997</td><td>4.23</td><td>5.01</td><td>5.18</td><td>-0.25</td><td>2.08</td><td>3.59</td></tr><tr><td>1998</td><td>4.30</td><td>5.16</td><td>5.28</td><td>-0.27</td><td>2.25</td><td>3.77</td></tr><tr><td>1999</td><td>4.11</td><td>4.97</td><td>5.16</td><td>-0.27</td><td>1.99</td><td>3.48</td></tr><tr><td>2001</td><td>4.18</td><td>4.98</td><td>5.32</td><td>-0.27</td><td>2.60</td><td>3.99</td></tr><tr><td>2002</td><td>4.31</td><td>5.28</td><td>5.62</td><td>-0.28</td><td>2.73</td><td>4.16</td></tr><tr><td>2003</td><td>4.13</td><td>4.90</td><td>5.28</td><td>-0.27</td><td>2.47</td><td>3.87</td></tr><tr><td>2004</td><td>4.16</td><td>4.95</td><td>5.23</td><td>-0.28</td><td>2.60</td><td>3.95</td></tr><tr><td>2005</td><td>4.30</td><td>5.03</td><td>5.29</td><td>-0.30</td><td>2.96</td><td>4.17</td></tr><tr><td>2006</td><td>4.35</td><td>5.00</td><td>5.14</td><td>-0.33</td><td>3.63</td><td>4.35</td></tr><tr><td>2007</td><td>4.29</td><td>4.70</td><td>4.59</td><td>3.03</td><td>3.82</td><td>4.20</td></tr><tr><td>2008</td><td>4.26</td><td>4.75</td><td>4.67</td><td>3.14</td><td>3.88</td><td>4.23</td></tr><tr><td>2009</td><td>4.22</td><td>4.61</td><td>4.48</td><td>3.20</td><td>3.81</td><td>4.16</td></tr><tr><td>2011</td><td>4.20</td><td>4.14</td><td>3.98</td><td>3.30</td><td>3.81</td><td>4.04</td></tr><tr><td>2012</td><td>4.42</td><td>4.38</td><td>4.59</td><td>3.47</td><td>4.13</td><td>4.34</td></tr><tr><td>2013</td><td>4.44</td><td>4.67</td><td>4.85</td><td>3.47</td><td>4.11</td><td>4.44</td></tr><tr><td>2014</td><td>4.36</td><td>4.67</td><td>4.80</td><td>3.53</td><td>4.18</td><td>4.42</td></tr><tr><td>2015</td><td>4.19</td><td>4.33</td><td>4.53</td><td>3.41</td><td>3.97</td><td>4.24</td></tr><tr><td>2016</td><td>4.25</td><td>4.30</td><td>4.47</td><td>3.42</td><td>4.02</td><td>4.24</td></tr><tr><td>2017</td><td>4.01</td><td>4.04</td><td>4.20</td><td>3.42</td><td>3.92</td><td>4.04</td></tr><tr><td>2018</td><td>4.05</td><td>4.12</td><td>4.32</td><td>3.47</td><td>4.05</td><td>4.13</td></tr><tr><td>2019</td><td>4.00</td><td>3.90</td><td>4.14</td><td>3.38</td><td>3.90</td><td>4.00</td></tr><tr><td>2020</td><td>4.16</td><td>4.03</td><td>3.88</td><td>3.57</td><td>4.02</td><td>4.04</td></tr><tr><td>2021</td><td>3.86</td><td>3.76</td><td>4.18</td><td>3.45</td><td>3.86</td><td>3.90</td></tr><tr><td>2022</td><td>4.24</td><td>4.31</td><td>4.39</td><td>3.56</td><td>4.08</td><td>4.27</td></tr><tr><td>mean</td><td>3.36</td><td>4.41</td><td>4.77</td><td>1.20</td><td>2.65</td><td>3.51</td></tr></tbody></table>
<table><caption>Table 21: Estimates of the bottom-Gini elasticities of FGT indices ($\bar{\varepsilon}_{\alpha,q}$) for Brazil, 1981–2022, $q = 0, 4$.</caption><thead><tr><th rowspan="2">Year</th><th colspan="3">$z = $3.65</th><th colspan="3">$z = $6.85</th></tr><tr><th>Θ<sub>0</sub></th><th>Θ<sub>1</sub></th><th>Θ<sub>2</sub></th><th>Θ<sub>0</sub></th><th>Θ<sub>1</sub></th><th>Θ<sub>2</sub></th></tr></thead><tbody><tr><td>1981</td><td>0.00</td><td>0.00</td><td>0.65</td><td>0.00</td><td>0.00</td><td>0.09</td></tr><tr><td>1982</td><td>0.00</td><td>0.00</td><td>0.35</td><td>0.00</td><td>0.00</td><td>0.05</td></tr><tr><td>1983</td><td>0.00</td><td>0.00</td><td>0.19</td><td>0.00</td><td>0.00</td><td>0.03</td></tr><tr><td>1984</td><td>0.00</td><td>0.00</td><td>0.18</td><td>0.00</td><td>0.00</td><td>0.03</td></tr><tr><td>1985</td><td>0.00</td><td>0.00</td><td>0.26</td><td>0.00</td><td>0.00</td><td>0.04</td></tr><tr><td>1986</td><td>-0.09</td><td>0.58</td><td>1.18</td><td>0.00</td><td>0.00</td><td>0.21</td></tr><tr><td>1987</td><td>-0.46</td><td>0.08</td><td>0.64</td><td>0.00</td><td>0.00</td><td>0.09</td></tr><tr><td>1988</td><td>3.41</td><td>-0.22</td><td>0.56</td><td>0.00</td><td>0.00</td><td>0.08</td></tr><tr><td>1989</td><td>-0.40</td><td>0.08</td><td>0.66</td><td>0.00</td><td>0.00</td><td>0.09</td></tr><tr><td>1990</td><td>0.00</td><td>0.00</td><td>0.39</td><td>0.00</td><td>0.00</td><td>0.05</td></tr><tr><td>1992</td><td>0.00</td><td>0.00</td><td>0.46</td><td>0.00</td><td>0.00</td><td>0.07</td></tr><tr><td>1993</td><td>-0.36</td><td>0.01</td><td>0.50</td><td>0.00</td><td>0.00</td><td>0.07</td></tr><tr><td>1995</td><td>-0.35</td><td>0.40</td><td>1.03</td><td>0.00</td><td>0.00</td><td>0.17</td></tr><tr><td>1996</td><td>-0.50</td><td>0.42</td><td>1.01</td><td>0.00</td><td>0.00</td><td>0.17</td></tr><tr><td>1997</td><td>-0.14</td><td>0.36</td><td>0.98</td><td>0.00</td><td>0.00</td><td>0.16</td></tr><tr><td>1998</td><td>-0.13</td><td>0.51</td><td>1.12</td><td>0.00</td><td>0.00</td><td>0.18</td></tr><tr><td>1999</td><td>-1.21</td><td>0.76</td><td>0.56</td><td>0.00</td><td>0.00</td><td>0.12</td></tr><tr><td>2001</td><td>-0.26</td><td>0.60</td><td>1.30</td><td>0.00</td><td>0.00</td><td>0.23</td></tr><tr><td>2002</td><td>-0.55</td><td>0.65</td><td>1.51</td><td>0.00</td><td>0.00</td><td>0.24</td></tr><tr><td>2003</td><td>-0.30</td><td>0.65</td><td>1.21</td><td>0.00</td><td>0.00</td><td>0.23</td></tr><tr><td>2004</td><td>-0.18</td><td>0.73</td><td>1.51</td><td>0.00</td><td>0.00</td><td>0.26</td></tr><tr><td>2005</td><td>0.62</td><td>0.61</td><td>0.44</td><td>0.00</td><td>0.00</td><td>0.31</td></tr><tr><td>2006</td><td>-0.12</td><td>0.93</td><td>2.36</td><td>0.00</td><td>0.00</td><td>0.45</td></tr><tr><td>2007</td><td>-0.15</td><td>1.03</td><td>2.38</td><td>-0.52</td><td>0.03</td><td>0.55</td></tr><tr><td>2008</td><td>0.02</td><td>1.52</td><td>2.76</td><td>-0.51</td><td>0.07</td><td>0.69</td></tr><tr><td>2009</td><td>-13.28</td><td>7.82</td><td>35.48</td><td>6.64</td><td>-1.85</td><td>1.96</td></tr><tr><td>2011</td><td>0.65</td><td>1.85</td><td>3.80</td><td>-0.64</td><td>0.31</td><td>1.10</td></tr><tr><td>2012</td><td>0.35</td><td>2.93</td><td>4.93</td><td>0.11</td><td>0.30</td><td>1.23</td></tr><tr><td>2013</td><td>1.09</td><td>1.94</td><td>2.45</td><td>-0.35</td><td>0.70</td><td>1.26</td></tr><tr><td>2014</td><td>1.14</td><td>2.89</td><td>3.94</td><td>0.13</td><td>0.69</td><td>1.45</td></tr><tr><td>2015</td><td>1.32</td><td>2.32</td><td>3.23</td><td>-0.05</td><td>0.60</td><td>1.33</td></tr><tr><td>2016</td><td>0.98</td><td>2.66</td><td>3.77</td><td>-0.25</td><td>0.40</td><td>1.28</td></tr><tr><td>2017</td><td>1.18</td><td>1.93</td><td>2.06</td><td>0.26</td><td>0.71</td><td>1.06</td></tr><tr><td>2018</td><td>0.15</td><td>1.78</td><td>2.67</td><td>-0.44</td><td>0.62</td><td>1.19</td></tr><tr><td>2019</td><td>0.87</td><td>1.98</td><td>2.80</td><td>-0.10</td><td>0.60</td><td>1.22</td></tr><tr><td>2020</td><td>2.56</td><td>2.57</td><td>2.41</td><td>0.06</td><td>1.07</td><td>1.70</td></tr><tr><td>2021</td><td>0.40</td><td>2.29</td><td>3.15</td><td>-0.15</td><td>0.39</td><td>1.16</td></tr><tr><td>mean</td><td>-0.10</td><td>1.15</td><td>2.56</td><td>0.11</td><td>0.12</td><td>0.56</td></tr></tbody></table>
<table><caption>Table 22: Estimates of the bottom income share elasticities of FGT indices ($\rho_{\alpha,q}$) for Brazil, 1981–2022, $q = 0, 4$.</caption><thead><tr><th rowspan="2">Year</th><th colspan="3">$z = $3.65</th><th colspan="3">$z = $6.85</th></tr><tr><th>Θ<sub>0</sub></th><th>Θ<sub>1</sub></th><th>Θ<sub>2</sub></th><th>Θ<sub>0</sub></th><th>Θ<sub>1</sub></th><th>Θ<sub>2</sub></th></tr></thead><tbody><tr><td>1981</td><td>-0.79</td><td>-1.18</td><td>-1.29</td><td>-0.10</td><td>-0.54</td><td>-0.82</td></tr><tr><td>1982</td><td>-1.41</td><td>-1.28</td><td>-0.85</td><td>-0.54</td><td>-1.22</td><td>-1.27</td></tr><tr><td>1983</td><td>-0.53</td><td>-0.90</td><td>-1.27</td><td>-0.03</td><td>-0.38</td><td>-0.66</td></tr><tr><td>1984</td><td>-0.98</td><td>-1.18</td><td>-1.26</td><td>-0.51</td><td>-0.88</td><td>-1.04</td></tr><tr><td>1985</td><td>-0.74</td><td>-1.14</td><td>-1.34</td><td>-0.52</td><td>-0.77</td><td>-0.94</td></tr><tr><td>1986</td><td>-1.17</td><td>-1.88</td><td>-2.40</td><td>-0.32</td><td>-0.88</td><td>-1.34</td></tr><tr><td>1987</td><td>-0.74</td><td>-1.24</td><td>-1.61</td><td>-0.36</td><td>-0.72</td><td>-0.99</td></tr><tr><td>1988</td><td>-0.87</td><td>-1.13</td><td>-1.21</td><td>-0.44</td><td>-0.79</td><td>-0.96</td></tr><tr><td>1989</td><td>-0.73</td><td>-1.20</td><td>-1.61</td><td>-0.42</td><td>-0.73</td><td>-0.99</td></tr><tr><td>1990</td><td>-0.89</td><td>-1.14</td><td>-1.15</td><td>-0.40</td><td>-0.76</td><td>-0.93</td></tr><tr><td>1992</td><td>-0.96</td><td>-1.12</td><td>-1.15</td><td>-0.61</td><td>-0.85</td><td>-0.97</td></tr><tr><td>1993</td><td>0.15</td><td>-1.17</td><td>-2.77</td><td>-1.32</td><td>-0.36</td><td>-0.92</td></tr><tr><td>1995</td><td>-0.60</td><td>-1.90</td><td>-2.86</td><td>-0.06</td><td>-0.65</td><td>-1.24</td></tr><tr><td>1996</td><td>0.04</td><td>-2.13</td><td>-3.47</td><td>0.38</td><td>-0.60</td><td>-1.29</td></tr><tr><td>1997</td><td>-0.91</td><td>-1.62</td><td>-2.32</td><td>0.04</td><td>-0.61</td><td>-1.11</td></tr><tr><td>1998</td><td>-1.06</td><td>-1.54</td><td>-1.82</td><td>-0.84</td><td>-0.99</td><td>-1.20</td></tr><tr><td>1999</td><td>-7.21</td><td>2.50</td><td>1.43</td><td>-11.74</td><td>-3.75</td><td>-1.50</td></tr><tr><td>2001</td><td>-0.65</td><td>-2.41</td><td>-3.75</td><td>-0.21</td><td>-0.78</td><td>-1.52</td></tr><tr><td>2002</td><td>-1.83</td><td>-0.72</td><td>0.17</td><td>-0.81</td><td>-1.10</td><td>-0.98</td></tr><tr><td>2003</td><td>-0.96</td><td>-1.86</td><td>-2.37</td><td>-0.44</td><td>-0.91</td><td>-1.33</td></tr><tr><td>2004</td><td>-1.14</td><td>-2.03</td><td>-2.67</td><td>-0.32</td><td>-1.03</td><td>-1.46</td></tr><tr><td>2005</td><td>-1.42</td><td>-1.65</td><td>-1.70</td><td>-0.64</td><td>-1.09</td><td>-1.37</td></tr><tr><td>2006</td><td>-1.64</td><td>0.16</td><td>2.84</td><td>-2.01</td><td>-1.33</td><td>-0.56</td></tr><tr><td>2007</td><td>-1.33</td><td>-2.18</td><td>-2.96</td><td>-0.68</td><td>-1.28</td><td>-1.72</td></tr><tr><td>2008</td><td>-1.48</td><td>-0.84</td><td>-0.14</td><td>-1.37</td><td>-1.31</td><td>-1.10</td></tr><tr><td>2009</td><td>-1.88</td><td>-1.41</td><td>-0.56</td><td>-0.94</td><td>-1.40</td><td>-1.42</td></tr><tr><td>2011</td><td>0.38</td><td>3.97</td><td>9.81</td><td>-3.10</td><td>-0.49</td><td>1.77</td></tr><tr><td>2012</td><td>-1.86</td><td>-3.60</td><td>-5.04</td><td>-1.34</td><td>-1.71</td><td>-2.43</td></tr><tr><td>2013</td><td>-2.47</td><td>-3.16</td><td>-3.60</td><td>-1.07</td><td>-2.06</td><td>-2.59</td></tr><tr><td>2014</td><td>-19.06</td><td>-46.31</td><td>-62.53</td><td>-3.28</td><td>-12.18</td><td>-24.06</td></tr><tr><td>2015</td><td>-2.60</td><td>-3.38</td><td>-4.12</td><td>-1.30</td><td>-1.99</td><td>-2.62</td></tr><tr><td>2016</td><td>-7.86</td><td>-18.75</td><td>-25.98</td><td>0.39</td><td>-4.02</td><td>-9.80</td></tr><tr><td>2017</td><td>-1.88</td><td>-2.18</td><td>-2.29</td><td>-1.33</td><td>-1.68</td><td>-1.86</td></tr><tr><td>2018</td><td>-1.06</td><td>3.81</td><td>6.38</td><td>-2.54</td><td>0.41</td><td>2.08</td></tr><tr><td>2019</td><td>-2.29</td><td>-3.35</td><td>-4.26</td><td>-1.09</td><td>-1.98</td><td>-2.64</td></tr><tr><td>2020</td><td>-4.54</td><td>-4.50</td><td>-4.26</td><td>-1.81</td><td>-3.02</td><td>-3.65</td></tr><tr><td>2021</td><td>-2.05</td><td>-4.96</td><td>-6.46</td><td>-1.05</td><td>-2.04</td><td>-3.25</td></tr><tr><td>mean</td><td>-2.08</td><td>-3.10</td><td>-3.80</td><td>-1.15</td><td>-1.53</td><td>-2.13</td></tr><tr><td>mean*</td><td>-1.43</td><td>-1.42</td><td>-1.48</td><td>-1.14</td><td>-1.15</td><td>-1.28</td></tr></tbody></table>

Note: Elasticities are computed for yearly changes in the Lorenz curves; * is for the average value without the years 2014 and 2016.
<table><caption>Table 23: Correlates of the Gini elasticity of poverty in Brazil, 1981–2022, $z = \$3.65$.</caption><thead><tr><th rowspan="3"></th><th colspan="12">Dependent variable</th></tr><tr><th colspan="4">ε<sub>0</sub></th><th colspan="4">ε<sub>1</sub></th><th colspan="4">ε<sub>2</sub></th></tr><tr><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th><th>(7)</th><th>(8)</th><th>(9)</th><th>(10)</th><th>(11)</th><th>(12)</th></tr></thead><tbody><tr><td>μ</td><td>-0.227<br>(0.447)</td><td>0.228<sup>*</sup><br>(0.124)</td><td>0.283<br>(0.244)</td><td>0.219<sup>*</sup><br>(0.112)</td><td>-0.513<br>(1.002)</td><td>0.502<sup>*</sup><br>(0.286)</td><td>0.487<br>(0.624)</td><td>0.305<br>(0.237)</td><td>-0.641<br>(1.376)</td><td>0.732<br>(0.444)</td><td>0.661<br>(0.888)</td><td>0.397<br>(0.361)</td></tr><tr><td>G</td><td>0.819<br>(64.709)</td><td>-5.058<br>(17.719)</td><td>40.721<br>(32.835)</td><td>-6.340<br>(15.636)</td><td>64.248<br>(145.024)</td><td>52.604<br>(40.882)</td><td>138.715<br>(84.026)</td><td>14.672<br>(33.039)</td><td>120.157<br>(199.142)</td><td>105.798<br>(63.400)</td><td>214.504<sup>*</sup><br>(119.476)</td><td>41.075<br>(50.320)</td></tr><tr><td>ΔG/G</td><td>-1.021<br>(36.595)</td><td>2.464<br>(9.999)</td><td></td><td></td><td>5.420<br>(82.017)</td><td>13.577<br>(23.071)</td><td></td><td></td><td>12.138<br>(112.622)</td><td>23.561<br>(35.779)</td><td></td><td></td></tr><tr><td>|ΔG/G|<sup>-1</sup></td><td></td><td></td><td>-0.028<sup>***</sup><br>(0.004)</td><td>-0.001<br>(0.003)</td><td></td><td></td><td>-0.057<sup>***</sup><br>(0.009)</td><td>0.016<sup>**</sup><br>(0.006)</td><td></td><td></td><td>-0.075<sup>***</sup><br>(0.013)</td><td>0.026<sup>***</sup><br>(0.009)</td></tr><tr><td>Const.</td><td>4.437<br>(41.824)</td><td>2.813<br>(11.443)</td><td>-21.411<br>(21.186)</td><td>3.734<br>(9.972)</td><td>-27.498<br>(93.736)</td><td>-31.957<br>(26.402)</td><td>-75.727<br>(54.217)</td><td>-9.403<br>(21.072)</td><td>-57.367<br>(128.714)</td><td>-64.217<br>(40.945)</td><td>-118.464<br>(77.092)</td><td>-25.702<br>(32.094)</td></tr><tr><td>Obs.</td><td>37</td><td>35</td><td>37</td><td>35</td><td>37</td><td>35</td><td>37</td><td>35</td><td>37</td><td>35</td><td>37</td><td>35</td></tr><tr><td>R<sup>2</sup></td><td>0.022</td><td>0.257</td><td>0.653</td><td>0.257</td><td>0.063</td><td>0.092</td><td>0.567</td><td>0.238</td><td>0.078</td><td>0.094</td><td>0.543</td><td>0.267</td></tr><tr><td>Adj. R<sup>2</sup></td><td>-0.067</td><td>0.185</td><td>0.621</td><td>0.185</td><td>-0.022</td><td>0.004</td><td>0.527</td><td>0.164</td><td>-0.005</td><td>0.006</td><td>0.502</td><td>0.196</td></tr><tr><td>Res. Std. Err.</td><td>7.439</td><td>2.031</td><td>4.431</td><td>2.032</td><td>16.673</td><td>4.687</td><td>11.338</td><td>4.293</td><td>22.895</td><td>7.269</td><td>16.122</td><td>6.538</td></tr><tr><td>F Stat.</td><td>0.24</td><td>3.58<sup>**</sup></td><td>20.69<sup>***</sup></td><td>3.57<sup>**</sup></td><td>0.74</td><td>1.04</td><td>14.39<sup>***</sup></td><td>3.22<sup>**</sup></td><td>0.93</td><td>1.07</td><td>13.07<sup>***</sup></td><td>3.76<sup>**</sup></td></tr></tbody></table>

Note: For column (2), (4), (6), (8), (10) and (12), the observations for the years 2014 and 2016 have been dropped. *p<0.1; **p<0.05; ***p<0.01.
<table><caption>Table 24: Correlates of the Gini elasticity of poverty in Brazil, 1981–2022, $z = \$6.85$.</caption><thead><tr><th rowspan="3"></th><th colspan="12">Dependent variable</th></tr><tr><th colspan="4">ε<sub>0</sub></th><th colspan="4">ε<sub>1</sub></th><th colspan="4">ε<sub>2</sub></th></tr><tr><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th><th>(7)</th><th>(8)</th><th>(9)</th><th>(10)</th><th>(11)</th><th>(12)</th></tr></thead><tbody><tr><td>μ</td><td>0.059<br>(0.075)</td><td>0.098<sup>*</sup><br>(0.052)</td><td>0.138<sup>**</sup><br>(0.057)</td><td>0.157<sup>***</sup><br>(0.034)</td><td>-0.054<br>(0.264)</td><td>0.210<sup>**</sup><br>(0.093)</td><td>0.212<br>(0.168)</td><td>0.176<sup>**</sup><br>(0.082)</td><td>-0.214<br>(0.552)</td><td>0.339<sup>*</sup><br>(0.180)</td><td>0.329<br>(0.350)</td><td>0.232<br>(0.152)</td></tr><tr><td>G</td><td>-12.975<br>(10.791)</td><td>-16.232<sup>**</sup><br>(7.360)</td><td>-5.112<br>(7.645)</td><td>-4.787<br>(4.690)</td><td>9.192<br>(38.209)</td><td>4.351<br>(13.335)</td><td>29.751<br>(22.585)</td><td>-2.295<br>(11.382)</td><td>34.794<br>(79.862)</td><td>28.026<br>(25.685)</td><td>75.228<br>(47.087)</td><td>7.177<br>(21.156)</td></tr><tr><td>ΔG/G</td><td>-3.463<br>(6.103)</td><td>-3.910<br>(4.153)</td><td></td><td></td><td>0.052<br>(21.609)</td><td>1.692<br>(7.525)</td><td></td><td></td><td>2.876<br>(45.165)</td><td>7.209<br>(14.495)</td><td></td><td></td></tr><tr><td>|ΔG/G|<sup>-1</sup></td><td></td><td></td><td>-0.003<sup>***</sup><br>(0.001)</td><td>-0.005<sup>***</sup><br>(0.001)</td><td></td><td></td><td>-0.015<sup>***</sup><br>(0.002)</td><td>0.003<br>(0.002)</td><td></td><td></td><td>-0.031<sup>***</sup><br>(0.005)</td><td>0.009<sup>**</sup><br>(0.004)</td></tr><tr><td>Const.</td><td>7.912<br>(6.975)</td><td>9.371<sup>*</sup><br>(4.753)</td><td>2.814<br>(4.933)</td><td>2.581<br>(2.991)</td><td>-2.549<br>(24.696)</td><td>-2.666<br>(8.612)</td><td>-15.866<br>(14.573)</td><td>1.231<br>(7.260)</td><td>-14.728<br>(51.618)</td><td>-16.915<br>(16.588)</td><td>-40.916<br>(30.383)</td><td>-4.539<br>(13.493)</td></tr><tr><td>Obs.</td><td>37</td><td>35</td><td>37</td><td>35</td><td>37</td><td>35</td><td>37</td><td>35</td><td>37</td><td>35</td><td>37</td><td>35</td></tr><tr><td>R<sup>2</sup></td><td>0.228</td><td>0.547</td><td>0.466</td><td>0.763</td><td>0.015</td><td>0.246</td><td>0.526</td><td>0.294</td><td>0.048</td><td>0.113</td><td>0.544</td><td>0.227</td></tr><tr><td>Adj. R<sup>2</sup></td><td>0.158</td><td>0.503</td><td>0.418</td><td>0.741</td><td>-0.075</td><td>0.173</td><td>0.483</td><td>0.226</td><td>-0.039</td><td>0.027</td><td>0.503</td><td>0.152</td></tr><tr><td>Res. Std. Err.</td><td>1.241</td><td>0.844</td><td>1.032</td><td>0.609</td><td>4.393</td><td>1.529</td><td>3.048</td><td>1.479</td><td>9.181</td><td>2.945</td><td>6.354</td><td>2.749</td></tr><tr><td>F Stat.</td><td>3.25<sup>**</sup></td><td>12.45<sup>***</sup></td><td>9.60<sup>***</sup></td><td>33.35<sup>***</sup></td><td>0.16</td><td>3.36<sup>**</sup></td><td>12.19<sup>***</sup></td><td>4.30<sup>**</sup></td><td>0.55</td><td>1.31</td><td>13.12<sup>***</sup></td><td>3.03<sup>**</sup></td></tr></tbody></table>

Note: For column (2), (4), (6), (8), (10) and (12), the observations for the years 2014 and 2016 have been dropped. *p<0.1; **p<0.05; ***p<0.01.
<table><caption>Table 25: Counterfactual estimates of the Gini elasticities of FGT indices for Brazil, 1981–2022.</caption><thead><tr><th rowspan="2">Year</th><th colspan="5">z = $3.65</th><th colspan="5">z = $6.85</th></tr><tr><th>min<sub>0</sub></th><th>max<sub>0</sub></th><th>min<sub>1</sub></th><th>max<sub>1</sub></th><th>min<sub>2</sub></th><th>max<sub>2</sub></th><th>min<sub>0</sub></th><th>max<sub>0</sub></th><th>min<sub>1</sub></th><th>max<sub>1</sub></th><th>min<sub>2</sub></th><th>max<sub>2</sub></th></tr></thead><tbody><tr><td>1981</td><td>4.28</td><td>112.39</td><td>-109.30</td><td>146.52</td><td>-223.50</td><td>164.13</td><td>-119.68</td><td>29.99</td><td>-13.59</td><td>13.88</td><td>-64.46</td><td>92.92</td></tr><tr><td>1982</td><td>3.12</td><td>94.11</td><td>-94.41</td><td>124.41</td><td>-192.40</td><td>141.15</td><td>-107.35</td><td>25.53</td><td>-12.60</td><td>16.84</td><td>-56.41</td><td>82.79</td></tr><tr><td>1983</td><td>-72.03</td><td>-12.65</td><td>-100.17</td><td>61.88</td><td>-113.18</td><td>139.07</td><td>-22.01</td><td>61.96</td><td>4.91</td><td>10.64</td><td>-42.04</td><td>37.44</td></tr><tr><td>1984</td><td>-14.70</td><td>-1.98</td><td>-18.86</td><td>15.52</td><td>-20.23</td><td>33.39</td><td>-4.55</td><td>12.51</td><td>1.81</td><td>3.39</td><td>-6.88</td><td>9.43</td></tr><tr><td>1985</td><td>2.23</td><td>18.49</td><td>-13.67</td><td>27.14</td><td>-29.98</td><td>32.47</td><td>-15.04</td><td>5.13</td><td>-0.81</td><td>0.53</td><td>-7.79</td><td>14.11</td></tr><tr><td>1986</td><td>-29.59</td><td>63.41</td><td>-105.81</td><td>77.54</td><td>-178.75</td><td>84.66</td><td>7.43</td><td>38.93</td><td>-27.80</td><td>55.57</td><td>-64.25</td><td>65.79</td></tr><tr><td>1987</td><td>-4.25</td><td>35.60</td><td>-44.12</td><td>47.81</td><td>-83.36</td><td>54.76</td><td>8.20</td><td>21.53</td><td>-8.80</td><td>32.70</td><td>-27.26</td><td>40.03</td></tr><tr><td>1988</td><td>-1.76</td><td>32.13</td><td>-37.08</td><td>43.26</td><td>-72.13</td><td>49.37</td><td>8.03</td><td>19.30</td><td>-6.92</td><td>29.58</td><td>-23.37</td><td>36.22</td></tr><tr><td>1989</td><td>-18.17</td><td>6.93</td><td>-18.83</td><td>38.28</td><td>-17.08</td><td>68.72</td><td>-12.05</td><td>-3.85</td><td>-15.67</td><td>10.31</td><td>-17.00</td><td>25.21</td></tr><tr><td>1990</td><td>-4.80</td><td>1.63</td><td>-3.74</td><td>12.34</td><td>-2.00</td><td>22.81</td><td>-1.46</td><td>9.76</td><td>-1.64</td><td>3.18</td><td>-3.43</td><td>8.11</td></tr><tr><td>1992</td><td>1.18</td><td>9.09</td><td>-4.97</td><td>12.95</td><td>-11.24</td><td>15.80</td><td>-7.35</td><td>2.63</td><td>0.16</td><td>1.35</td><td>-2.68</td><td>7.84</td></tr><tr><td>1993</td><td>-100.43</td><td>6.64</td><td>-119.56</td><td>124.28</td><td>-126.01</td><td>241.07</td><td>-28.43</td><td>164.61</td><td>-46.32</td><td>21.57</td><td>-98.08</td><td>77.14</td></tr><tr><td>1995</td><td>-86.08</td><td>210.90</td><td>-369.18</td><td>256.43</td><td>-639.46</td><td>270.58</td><td>34.77</td><td>142.99</td><td>-95.39</td><td>192.42</td><td>-230.77</td><td>220.33</td></tr><tr><td>1996</td><td>-692.25</td><td>296.95</td><td>-801.73</td><td>1298.64</td><td>-827.07</td><td>2264.23</td><td>-491.42</td><td>-118.18</td><td>-639.96</td><td>353.56</td><td>-711.52</td><td>843.80</td></tr><tr><td>1997</td><td>-327.93</td><td>138.27</td><td>-384.93</td><td>609.04</td><td>-394.32</td><td>1059.74</td><td>-227.12</td><td>-55.98</td><td>-300.20</td><td>162.80</td><td>-336.06</td><td>390.76</td></tr><tr><td>1998</td><td>-103.21</td><td>51.74</td><td>-120.13</td><td>204.89</td><td>-119.46</td><td>349.23</td><td>-73.17</td><td>-15.69</td><td>-94.64</td><td>55.42</td><td>-104.39</td><td>129.04</td></tr><tr><td>1999</td><td>-108.54</td><td>46.03</td><td>-127.77</td><td>199.43</td><td>-129.41</td><td>345.37</td><td>-77.58</td><td>-19.64</td><td>-99.72</td><td>50.92</td><td>-110.44</td><td>124.37</td></tr><tr><td>2001</td><td>-213.33</td><td>128.55</td><td>-250.42</td><td>461.84</td><td>-264.13</td><td>781.03</td><td>-151.34</td><td>-23.30</td><td>-195.92</td><td>133.98</td><td>-221.22</td><td>294.24</td></tr><tr><td>2002</td><td>-121.48</td><td>80.27</td><td>-145.04</td><td>270.94</td><td>-150.76</td><td>449.82</td><td>-84.30</td><td>-11.00</td><td>-109.54</td><td>77.38</td><td>-124.71</td><td>167.07</td></tr><tr><td>2003</td><td>-57.67</td><td>36.96</td><td>-64.94</td><td>128.64</td><td>-66.50</td><td>216.67</td><td>-40.30</td><td>-6.25</td><td>-52.20</td><td>36.72</td><td>-58.12</td><td>80.62</td></tr><tr><td>2004</td><td>-436.73</td><td>269.51</td><td>-516.37</td><td>882.79</td><td>-542.08</td><td>1462.78</td><td>-288.10</td><td>-41.08</td><td>-387.49</td><td>243.84</td><td>-445.00</td><td>534.74</td></tr><tr><td>2005</td><td>-106.78</td><td>80.36</td><td>-121.18</td><td>238.69</td><td>-123.74</td><td>388.11</td><td>-72.70</td><td>-6.31</td><td>-94.23</td><td>68.68</td><td>-105.94</td><td>144.52</td></tr><tr><td>2006</td><td>-102.37</td><td>94.72</td><td>-113.60</td><td>253.70</td><td>-112.71</td><td>401.47</td><td>-73.26</td><td>-0.05</td><td>-91.66</td><td>77.05</td><td>-101.15</td><td>154.17</td></tr><tr><td>2007</td><td>-81.48</td><td>85.58</td><td>-84.91</td><td>216.30</td><td>-78.52</td><td>336.72</td><td>-59.53</td><td>3.32</td><td>-72.79</td><td>69.51</td><td>-78.02</td><td>135.25</td></tr><tr><td>2008</td><td>-217.66</td><td>246.76</td><td>-238.52</td><td>593.79</td><td>-229.87</td><td>907.35</td><td>-162.76</td><td>19.65</td><td>-198.66</td><td>193.85</td><td>-214.31</td><td>365.61</td></tr><tr><td>2009</td><td>-101.66</td><td>130.24</td><td>-106.27</td><td>301.92</td><td>-98.57</td><td>457.82</td><td>-79.38</td><td>14.10</td><td>-92.14</td><td>101.95</td><td>-98.31</td><td>188.63</td></tr><tr><td>2011</td><td>-223.51</td><td>174.37</td><td>-471.06</td><td>176.80</td><td>-713.29</td><td>175.07</td><td>-32.37</td><td>133.81</td><td>-171.09</td><td>157.31</td><td>-307.02</td><td>169.27</td></tr><tr><td>2012</td><td>-105.77</td><td>177.80</td><td>-99.32</td><td>356.94</td><td>-98.95</td><td>546.30</td><td>-86.06</td><td>32.32</td><td>-99.60</td><td>134.88</td><td>-102.15</td><td>233.31</td></tr><tr><td>2013</td><td>-126.01</td><td>230.13</td><td>-126.83</td><td>458.72</td><td>-126.39</td><td>685.01</td><td>-101.79</td><td>46.29</td><td>-117.64</td><td>170.39</td><td>-124.29</td><td>290.31</td></tr><tr><td>2014</td><td>-872.72</td><td>1553.91</td><td>-928.95</td><td>3087.07</td><td>-949.63</td><td>4556.91</td><td>-711.08</td><td>336.94</td><td>-836.77</td><td>1156.08</td><td>-884.02</td><td>1938.05</td></tr><tr><td>2015</td><td>-94.68</td><td>68.42</td><td>-191.37</td><td>76.21</td><td>-289.57</td><td>85.08</td><td>-18.50</td><td>52.13</td><td>-71.44</td><td>63.69</td><td>-122.77</td><td>70.71</td></tr><tr><td>2016</td><td>-1709.75</td><td>2747.64</td><td>-1720.98</td><td>5674.30</td><td>-1786.51</td><td>8688.22</td><td>-1379.01</td><td>532.17</td><td>-1616.13</td><td>2169.89</td><td>-1701.97</td><td>3749.23</td></tr><tr><td>2017</td><td>-211.56</td><td>143.36</td><td>-453.49</td><td>149.99</td><td>-702.57</td><td>161.46</td><td>-42.19</td><td>118.98</td><td>-176.53</td><td>139.62</td><td>-306.06</td><td>146.68</td></tr><tr><td>2018</td><td>-193.95</td><td>338.38</td><td>-191.66</td><td>725.79</td><td>-195.47</td><td>1123.83</td><td>-169.27</td><td>73.51</td><td>-194.48</td><td>289.00</td><td>-195.74</td><td>494.09</td></tr><tr><td>2019</td><td>-8.21</td><td>31.99</td><td>-2.21</td><td>65.42</td><td>3.08</td><td>101.61</td><td>-10.17</td><td>7.95</td><td>-8.65</td><td>27.43</td><td>-5.87</td><td>45.93</td></tr><tr><td>2020</td><td>-42.15</td><td>36.38</td><td>-73.79</td><td>41.15</td><td>-104.95</td><td>45.50</td><td>-9.40</td><td>26.55</td><td>-28.07</td><td>32.99</td><td>-45.61</td><td>36.23</td></tr><tr><td>2021</td><td>-74.41</td><td>124.49</td><td>-67.19</td><td>265.37</td><td>-70.11</td><td>423.22</td><td>-69.60</td><td>25.06</td><td>-75.00</td><td>104.84</td><td>-73.18</td><td>182.01</td></tr></tbody></table>

Note: $min_{\alpha} := \min\{\varepsilon_{\alpha}^{R}, \varepsilon_{\alpha}^{AR}\}$ and $max_{\alpha} := \max\{\varepsilon_{\alpha}^{R}, \varepsilon_{\alpha}^{AR}\}$.
References

AABERGE, R. (2000): "Characterizations of Lorenz Curves and Income Distributions," *Social Choice and Welfare*, **17**, 639–653.

ADAMS, R. (2004): “Economic Growth, Inequality and Poverty: Estimating the Growth Elasticity of Poverty,” *World Development*, **32**, 1989–2014.

ALVAREDO, F., F. BOURGUIGNON, F. FERREIRA, AND N. LUSTIG (2024): “Inequality Bands: Seventy-five Years of Measuring Income Inequality in Latin America,” Working Paper 672, ECINEQ.

ANDREWS, C. (2004): “Anti-Poverty Policies in Brazil: Reviewing the Past Ten Years,” *International Review of Administrative Sciences*, **70**, 477–488.

ARISTONDO, O., C. D'AMBROSIO, AND C. LASSO DE LA VEGA (2023): “Decomposing the Changes in Poverty: Poverty Line and Distributional Effects,” *Bulletin of Economic Research*, **75**, 1048–1063.

ARISTONDO, O., C. LASSO DE LA VEGA, AND A. URRUTIA (2010): “A New Multiplicative Decomposition for the Foster-Greer-Thorbecke Poverty Indices,” *Bulletin of Economic Research*, **62**, 259–267.

ATHEY, S. AND G. IMBENS (2006): “Identification and Inference in Nonlinear Difference-in-Differences Models,” *Econometrica*, **74**, 431–497.

ATKINSON, A. (1987): “On the Measurement of Poverty,” *Econometrica*, **55**, 749–764.

BANERJEE, A. V. AND E. DUFLO (2003): “Inequality and Growth: What Can the Data Say?” *Journal of Economic Growth*, **8**, 267–299.

BERGSTROM, K. (2022): “The Role of Income Inequality for Poverty Reduction,” *World Bank Economic Review*, **36**, 583–604.

BESLEY, T. AND R. BURGESS (2003): “Halving Global Poverty,” *Journal of Economic Perspectives*, **17**, 3–22.

BLUHM, R., D. DE CROMBRUGGHE, AND A. SZIRMAI (2018): “Poverty Accounting,” *European Economic Review*, **104**, 237–255.

BOURGUIGNON, F. (1979): “Decomposable Income Inequality Measures,” *Econometrica*, **47**, 901–920.

——— (2003): “The Growth Elasticity of Poverty Reduction: Explaining Heterogeneity across Countries and Time Periods,” in *Inequality and growth: Theory and policy implications*, ed. by T. Eicher and S. Turnovsky, MIT Press, 3–26.

——— (2004): “The Poverty-Growth-Inequality Triangle,” in *Poverty, Inequality and Growth, Proceedings of the AFD-EUDN Conference*, AFD, no. 10 in Notes et Documents, 69–111.

BOURGUIGNON, F. AND A. ATKINSON (2000): “Pauvreté et inclusion dans une perspective mondiale,” *Revue d'Économie du Développement*, **1-2**, 13–32.

BRESSON, F. (2010): “A general class of inequality elasticities of poverty,” *Journal of Economic Inequality*, **8**, 71–100.
CERRA, V., R. LAMA, AND N. LOAYZA (2022): “Links Between Growth, Inequality, and Poverty,” in *How to Achieve Inclusive Growth*, ed. by V. Cerra, B. Eichengreen, A. El-Ganainy, and M. Schindler, Oxford University Press, chap. 2, 32–73.

CHEN, S. AND M. RAVALLION (1997): “What Can New Survey Data Tell us about Recent Changes in Distribution and Poverty?” *World Bank Economic Review*, 11, 357–82.

— (2007): “China’s (Uneven) Progress Against Poverty,” *Journal of Development Economics*, 82, 1–42.

— (2011): “Weakly Relative Poverty,” *Review of Economics and Statistics*, 93, 1251–1261.

CIASCHI, M., R. DAMASCENO COSTA, R. RUBIÃO, A. L. PAFFHAUSEN, AND L. SOUSA (2020): “A Reversal in Shared Prosperity in Brazil,” *Poverty and Equity Global Practice*, LAC Report No.1, World Bank, 15 p.

COWELL, F. (1980): “Generalized Entropy and the Measurement of Distributional Change,” *European Economic Review*, 13, 147–159.

DAĞDEVIREN, H., R. VAN DER HOEVEN, AND J. WEEKS (2004): “Redistribution Does Matter: Growth and Redistribution for Poverty Reduction,” in *van der Hoeven and Shorrocks (2004)*, chap. 7, 125–153.

DASGUPTA, P., A. SEN, AND D. STARRETT (1973): “Notes on the Measurement of Inequality,” *Journal of Economic Theory*, 6, 180–187.

DATT, G. AND M. RAVALLION (1992): “Growth and Redistribution Components of Changes in Poverty Measures: A Decomposition with Applications to Brazil and India in the 1980s,” *Journal of Development Economics*, 38, 275–295.

DE SCHUTTER, O. (2024): “Eradicating Poverty Beyond Growth,” Report A/HRC/56/61, United Nations.

DE SOUZA, P. (2012): “Poverty, Inequality and Social Policies in Brazil, 1995-2009,” Working Paper 87, International Policy Centre for Inclusive Growth.

DEATON, A. (2005): “Measuring Poverty in a Growing World (or Measuring Growth in a Poor World),” *Review of Economics and Statistics*, 87, 1–19.

DEININGER, K. AND L. SQUIRE (1996): “A New Dataset Measuring Income Inequality,” *World Bank Economic Review*, 10, 565–591.

DOLLAR, D., T. KLEINEBERG, AND A. KRAAY (2015): “Growth still is good for the poor,” *European Economic Review*, 81, 68–85.

DOLLAR, D. AND A. KRAAY (2002): “Growth is good for the poor,” *Journal of Economic Growth*, 7, 195–225.

DONALDSON, D. AND J. WEYMARK (1980): “A Single Parameter Generalization of the Gini Indices of Inequality,” *Journal of Economic Theory*, 22, 67–86.

EPAULARD, A. (2003): “Macroeconomic Performance and Poverty Reduction,” Working Paper 03/72, IMF.

FERREIRA, F., P. LEITE, AND J. LITCHFIELD (2006): “The Rise and Fall of Brazilian Inequality: 1981-2004,” World Bank Policy Research Working Paper Series 3867, World Bank.
FERREIRA, F., P. LEITE, AND M. RAVALLION (2010): “Poverty Reduction without Economic Growth? Explaining Brazil’s Poverty Dynamics, 1985–2004.” *Journal of Development Economics*, 93, 20–36.

FOSTER, J. (1998): “Absolute versus Relative Poverty,” *American Economic Review*, 88, 335–341.

FOSTER, J., J. GREER, AND E. THORBECKE (1984): “A Class of Decomposable Poverty Measures,” *Econometrica*, 52, 761–766.

FOSU, A. (2017): “Growth, Inequality, and Poverty Reduction in Developing Countries: Recent Global Evidence,” *Research in Economics*, 71, 306–336.

FUCHS, V. (1967): “Redefining Poverty and Redistributing Income,” *The Public Interest*, 8, 88–95.

GASTWIRTH, J. (1971): “A General Definition of the Lorenz Curve,” *Econometrica – Notes and Comments*, 39, 1037–1039.

GOH, C.-C., X. LUO, AND N. ZHU (2009): “Income Growth, Inequality and Poverty Reduction: A Case Study of Eight Provinces in China,” *China Economic Review*, 20, 485–496.

HARTMANN, V. AND K. WACKER (2023): “Poverty Decompositions with Counterfactual Income and Inequality Dynamics,” *Review of Development Economics*, 27, 1746–1768.

HELTBERG, R. (2004): “The Growth Elasticity of Poverty,” in *van der Hoeven and Shorrocks (2004)*, chap. 4, 81–91.

HUPPI, M. AND M. RAVALLION (1991): “Measuring Changes in Poverty: A Methodological Case Study of Indonesia during an Adjustment Period,” *World Bank Economic Review*, 5, 57–82.

JENKINS, S. AND P. LAMBERT (1997): “Three Types of Poverty Curves, with an Analysis of UK Poverty Trends,” *Oxford Economic Papers*, 49, 317–327.

JOLLIFFE, D., D. GERSZON MAHLER, C. LAKNER, A. ATAMANOV, AND S. KOFI TETTEH-BAAH (2022): “Assessing the Impact of the 2017 PPPs on the International Poverty Line and Global Poverty,” *Policy Research Working Paper 9941*, World Bank.

KAKWANI, N. (1993): “Poverty and Economic Growth with Application to Côte d’Ivoire,” *Review of Income and Wealth*, 39, 121–139.

——— (2000): “On Measuring Growth and Inequality Components of Poverty with Application to Thailand,” *Journal of Quantitative Economics*, 16, 67–79.

KAKWANI, N. AND K. SUBBARAO (1990): “Rural Poverty and its Alleviation in India,” *Economic and Political Weekly*, 31/06, A2–A16.

KALWIJ, A. AND A. VERSCHOOR (2007): “Not by Growth Alone: The Role of the Distribution of Income in Regional Diversity in Poverty Reduction,” *European Economic Review*, 51, 805–829.

KILPATRICK, R. (1973): “The Income Elasticity of the Poverty Line,” *Review of Economics and Statistics*, 55, 327–332.

KLASEN, S. AND M. MISSELHORN (2006): “Determinants of the Growth Semi-Elasticity of Poverty Reduction,” *Proceedings of the German Development Economics Conference*, Berlin 2006 15, Verein für Socialpolitik, Research Committee Development Economics.
KRAAY, A. (2006): "When is Growth Pro-Poor? Evidence from a Panel of Countries," *Journal of Development Economics*, 80, 198-227.

KRAAY, A., C. LAKNER, B. ÖZLER, B. DECERF, D. JOLLIFFE, O. STERCK, AND N. YONZAN (2023): "A New Distribution Sensitive Index for Measuring Welfare, Poverty, and Inequality," Working Paper 10470, World Bank, 48 p.

KUZNETS, S. (1955): "Economic Growth and Income Inequality," *American Economic Review*, 45, 1-28.

LAKNER, C., D. MAHLER, M. NEGRE, AND E. PRYDZ (2022): "How Much does Reducing Inequality Matter for Global Poverty?" *Journal of Economic Inequality*, 20, 559-585.

LAKNER, C., M. NEGRE, AND E. PRYDZ (2014): "Twinning the Goals: How Can Promoting Shared Prosperity Help to Reduce Global Poverty?" Policy Research Working Paper 7106, World Bank.

LUSTIG, N., L. LOPEZ-CALVA, AND E. ORTIZ-JUAREZ (2013): "Declining Inequality in Latin America in the 2000s: The Cases of Argentina, Brazil, and Mexico," *World Development*, 44, 129-141.

——— (2016): "Deconstructing the Decline in Inequality in Latin America," in *Inequality and Growth: Patterns and Policy*, ed. by K. Basu and J. Stiglitz, Palgrave Macmillan, vol. II of *International Economic Association Series*, chap. 7, 212-247.

RAM, R. (2007): "Roles of Income and Equality in Poverty Reduction: Recent Cross-Country Evidence," *Journal of International Development*, 19, 919-926.

RAVALLION, M. (1995): "Growth and Poverty: Evidence for developing countries in the 1980s," *Economic Letters*, 48, 411-417.

——— (2001): "Growth, Inequality and Poverty : Looking Beyond Averages," *World Development*, 29, 1803-1815.

——— (2003): "Measuring Aggregate Welfare in Developing Countries: How Well do National Accounts and Surveys Agree?" *Review of Economics and Statistics*, 85, 645-652.

——— (2007): "Inequality is Bad for the Poor," in *Inequality and Poverty Re-Examined*, ed. by J. Micklewright and S. Jenkins, Oxford University Press, chap. 2, 37-61.

——— (2011): "A Comparative Perspective on Poverty Reduction in Brazil, China, and India," *World Bank Research Observer*, 26, 71-104.

——— (2013): "How Long Will it Take to Lift One Billion People Out of Poverty?" *World Bank Research Observer*, 28, 139-158.

——— (2016): *The Economics of Poverty: History, Measurement, and Policy*, Oxford University Press, 736 p.

——— (2020): "SDG1: The Last Three Percent," Working Paper 527, Center for Global Development.

——— (2022): "Growth Elasticities of Poverty Reduction," Working Paper 30401, NBER.

RAVALLION, M. AND S. CHEN (2003): "Measuring Pro-Poor Growth," *Economic Letters*, 78, 93-99.

——— (2019): "Global Poverty Measurement when Relative Income Matters," *Journal of Public Economics*, 177.
SEN, A. (1976): "Poverty: An Ordinal Approach to Measurement," *Econometrica*, 44, 219-231.

SHORROCKS, A. (2013): “Decomposition Procedure for Distributional Analysis: A Unified Framework Based on the Shapley Value,” *Journal of Economic Inequality*, 11, 99–126.

SHORROCKS, A. AND G. WAN (2008): “Ungrouping Income Distributions: Synthetising Samples for Inequality and Poverty Analysis,” *Research Paper 2008/16*, UNU WIDER.

SOTOMAYOR, O. (2021): “Can the Minimum Wage Reduce Poverty and Inequality in the Developing World? Evidence from Brazil,” *World Development*, 138, 14 p.

VAN DER HOEVEN, R. AND A. SHORROCKS, eds. (2004): *Growth, Inequality, and Poverty: Prospects for Pro-Poor Economic Development*, UNU-WIDER Studies in Development Economics, Oxford University Press.

WANG, Z. AND J. SUN (2021): “Has Recent Economic Growth/Recession in Brazil been Pro-Poor?” *Applied Economic Letters*, 28, 1317–1320.

WATTS, H. (1968): “An Economic Definition of Poverty,” in *On Understanding Poverty*, ed. by D. P. Moynihan, Basic Books.

WORLD BANK (2015): *A Measured Approach to Ending Poverty and Boosting Shared Prosperity: Concepts, Data, and the Twin Goals*, no. 91350 in Policy Research Report, The World Bank, 299 p.

— (2016): *Taking on Inequality*, Poverty and Sahred Prosperity Report, The World Bank.

— (2020): *Reversals of Fortune*, Poverty and Sahred Prosperity Report, The World Bank.

— (2022): *Correcting Course*, Poverty and Shared Prosperity Report, The World Bank.

— (2024): *Pathways out of the Polycrisis*, Poverty and Shared Prosperity Report, The World Bank.

ZHENG, B. (1997): “Aggregate Poverty Measures,” *Journal of Economic Surveys*, 11, 123–162.