Estimation of Lorenz curves based on dummy variable regression

We propose a new estimation method of the Lorenz curve based on dummy variable regression for granting clear economic connotations to parameters in the estimation of the Lorenz curve. The dummy variable regression model of the Lorenz curve is established by introducing dummy variables to group data about income level. On this basis, it is proved that the regression function is endowed with the convexity that the Lorenz curve should have. To verify the effectiveness of the new method, empirical study is carried out taking the income data of urban and rural residents in the Chinese Household Income Project Survey (CHIP) database as examples. In the empirical study, the proposed model is compared with several existing classical parameter models. The results indicate that the slope parameter of the model represents the cumulative income–population resilience of corresponding residents, and reflects the income structure of residents to some extent. Meanwhile, compared with classical parameter models, the newly proposed method has advantages of higher fitting precision and stronger adaptability.