More on Lorenz Curve Interpolation

In the previous post the interpolation was demonstrated using a simulated data. Here we do an application to a real data set. The Data is for Urban China 2004-2005 obtained from PovcalNet website. In what follows we plot the Spline-interpolated curves vs their estimation using GB2 and we also compare the computed Gini coefficient and head-count ratios. Below are the plots: To naked eyes the Lorenz curves are almost indistinguishable (except for the last group) but CDF and PDF are visibly different.Rplot_1Rplot_2Rplot_3Computing Gini coeff for interpolated model is very easy based on formula Gini=1-2 \int L(c)dc and the computed head-count ratio are based on the interpolated CDF function (for poverty line 38$). The numbers from GB2 comes from my papers. Gini coefficient from interpolated model is 0.346  vs  0.345 from GB2. This should be expected because as we can see the two Lorenz curves are almost indistinguishable but for the poverty measure the estimates are different: H=0.012 for interpolated model vs 0.019 for GB2. Again from the graphs this should be expected .

 

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