Package GiniWegNeg. January 13, 2016

Transcription

1 Type Package Package GiniWegNeg January 13, 2016 Title Computing the Gini Coefficient for Weighted and Negative Attributes Version 1.0 Imports graphics Date Author Emanuela Raffinetti, Fabio Aimar Maintainer Emanuela Raffinetti Computation of the Gini coefficient in the presence of weighted and/or negative attributes. Two different approaches are considered in order to fulfill, in the case of negative attributes, the normalization principle, that is a value of the Gini coefficient bounded into the close range [0,1]. The first approach is based on the proposal by Chen, Tsaur and Rhai (1982) and Berebbi and Silber (1985), while the second approach is based on a recent proposal by Raffinetti, Siletti and Vernizzi (2015). The plot of the curve of maximum inequality, defined in the contribution of Raffinetti, Siletti and Vernizzi (2015), is provided. License GPL-3 NeedsCompilation no Repository CRAN Date/Publication :50:09 R topics documented: GiniWegNeg-package BI Gini Gini_CTR_BS Gini_RSV GRSVc RSVc Index 13 1

2 2 GiniWegNeg-package GiniWegNeg-package Computing the Gini Coefficient for Weighted and Negative Attributes Computation of the Gini coefficient in non-traditional scenarios, i.e. in the cases of non-negative weighted data, negative non-weighted data and weighted negative data. The computation of the Gini coefficient in the case of non-negative or negative weighted data involves, in addition to the vector of attributes (typically incomes), the vector of weights associated with each statistical unit (typically households). Two functions are made available for the computation of the Gini coefficient in the case of negative attributes. A first function is based on the contribution by Chen, Tasur and Rhai (1982), further improved by Berebbei and Silber (1985). Recently, a more appropriate normalization factor was introduced by Raffinetti, Siletti and Vernizzi (2015), who specified a new definition of the "polarized" scenario, where the total negative attribute amount is assigned to one unit, the total positive to another unit, while all the other units have a zero amount of attribute. Also the plot of the corresponding curve of maximum inequality (RSV curve), both by considering the attribute values in absolute and relative terms, is provided. Package: GiniWegNeg Type: Package Version: 1.0 Date: License: GPL-3 Author(s) Emanuela Raffinetti, Fabio Aimar Maintainer: Emanuela Raffinetti <emanuela.raffinetti@unimi.it> Z.M. Berrebi, J. Silber (1985), The Gini coefficient and negative income: a comment, Oxford Economic Papers 37, C.N. Chen, T.W. Tsaur, T.S. Rhai (1982), The Gini coefficient and negative income, Oxford Economic Papers 34, F.A. Cowell (1995), Measuring Inequality, Prentice Hall/Harvester Wheatshef E. Raffinetti, E. Siletti, A. Vernizzi (2014), Inequality measures and the issue of negative income. Italian Statistical Society Conference (SIS), Book of Short Papers: "SIS th Scientific

3 BI Meeting of the Italian Statistical Society", CUEC (Cooperativa Universitaria Editrice Cagliaritana), June 2014 E. Raffinetti, E. Siletti, A. Vernizzi (2015), On the Gini coefficient normalization when incomes with negative values are considered, Statistical Methods & Applications, 24(3), See Also Gini, Gini_CTR_BS, Gini_RSV, GRSVc, RSVc BI2012 A Sample of Income Data from the Bank of Italy (2012) A sample of the data collected by the Survey of Household Income and Wealth (SHIW) of the Bank of Italy in 2012 (Banca d Italia, 2012). Usage data("bi2012") Format A data frame with 200 observations on the following 8 variables. weight weights associated to each household Y total net income (all non-negative values) YL income from employment (all non-negative values) YTP income from pensions (all non-negative values) YTA income from transfers (some negative values) YM income from self-employment (all non-negative values) YCA income from capital gain (all non-negative values) YCF income from financial capital gain (some negative values) The Survey on Household Income and Wealth (SIHW) includes wealth and other aspects of households economic and financial behaviour such as, for instance, which payment methods are used. The original 2012 survey covered 8,151 households and 20,022 units, distributed over about 300 Italian municipalities. Here, a sample of 200 randomly selected units from the original 2012 survey was considered. We remark that the weight associated to each selected household was obtained by multiplying the scale suggested by Kakwani and Lambert (1998) and the weight given in SHIW.

4 4 Gini Source Survey of Household Income and Wealth (SHIW) of the Bank of Italy in 2012: bancaditalia.it/statistiche/tematiche/indagini-famiglie-imprese/bilanci-famiglie/ distribuzione-microdati/documenti/ind12_ascii.zip, where also the whole dataset may be obtained. N. Kakwani, P.J. Lambert (1998), On measuring inequality in taxation: a new approach, European Journal of Political Economy, 14, Gini Classical Gini coefficient for weighted attributes computes the classical Gini coefficient for weighted data Usage Gini(y,p) Arguments y p a vector of attributes typically containing non-negative elements a vector containing the weights associated to the elements of the attribute vector Value Note Gini(y,p) is the Gini coefficient for weighted data. Thus, the vector of attributes is considered togheter with the vector of weights associated to each statistical units (typically households). If the vector of attributes contains even negative values, the Gini coefficient for weighted data may take values greater than one. the value of the classical Gini coefficient If the vector p contains unitary weights, compute Gini as Gini(y). Moreover, if the vector of attributes does not contain negative elements, Gini(y) has the same value of the classical Gini coefficient computed with the package ineq. Author(s) Emanuela Raffinetti, Fabio Aimar

5 Gini_CTR_BS 5 F.A. Cowell (1995), Measuring Inequality, Prentice Hall/Harvester Wheatshef C.Gini (1936), On the measure of concentration with special reference to income and wealth, In: Abstracts of Papers presented at the Cowles Commission Research conference on economics and statistics. Colorado Springs, Colorado College Press, 1936, See Also ineq Examples # generate the vector of non-negative attributes y<-c(25,12,5,3,2,10,45) # generate the vector of weights p<-c(1.5,2.2,1.9,3.8,4.7,5,2.3) # compute the classical Gini coefficient as Gini(y,p) # generate the vector of even negative attributes y<-c(10,-25,-12,3,2,-5,45) # generate the vector of weights p<-c(1.5,2.2,1.9,3.8,4.7,5,2.3) # compute the classical Gini coefficient as Gini(y,p) data(bi2012) # define the vector of weights # select the vector of incomes (e.g., the incomes from employment YL) y<-bi2012$yl # compute the classical Gini coefficient Gini(y,p) Gini_CTR_BS The Gini coefficient adjusted for negative attributes (Chen, Tsaur and Rhai, 1982, and Berebbi and Silber, 1985) computes the Gini coefficient adjusted for negative (even weighted) data. Usage Gini_CTR_BS(y,p)

6 6 Gini_CTR_BS Arguments y p a vector of attributes containing even negative elements a vector containing the weights associated to the elements of the attribute vector Value Note Gini_CTR_BS(y,p) is the Gini coefficient for negative weighted data proposed by Chen, Tsaur and Rhai (1982) and subsequenty improved by Berebbi and Silber (1985). It is based on a normalization factor adding the part of the concentration area lying below the x-axis and provides a values always included into the close range [0,1]. the value of the Gini coefficient adjusted for negative attributes. If the vector p contains unitary weights, compute Gini_CTR_BS as Gini_CTR_BS(y). Moreover, if the vector of attributes does not contain negative elements, Gini_CTR_BS(y) takes the same value of the classical Gini coefficient computed with the package ineq. Finally, if the the vector of attributes does not contain negative elements but the vector p contains non-unitary weights, Gini_CTR_BS(y,p) has the same value of Gini(y,p). Author(s) Emanuela Raffinetti, Fabio Aimar Z.M. Berrebi, J. Silber (1985), The Gini coefficient and negative income: a comment, Oxford Economic Papers 37, C.N. Chen, T.W. Tsaur, T.S. Rhai (1982), The Gini coefficient and negative income, Oxford Economic Papers 34, See Also ineq Examples # generate the vector of attributes with even negative elements y<-c(-7,-15,11,-10,2,4,40) # generate the vector of weights p<-c(2.5,1.1,3.6,4.4,0.8,2.7,1.9) # compute the Gini coefficient of Chen, Tsaur and Rhai (1982), Berebbi and Silber (1985) as Gini_CTR_BS(y,p) data(bi2012) # define the vector of weights

7 Gini_RSV 7 # select the vector of incomes (e.g., the incomes from transfers YTA) y<-bi2012$yta # compute the Gini coefficient adjusted for negative values Gini_CTR_BS(y,p) Gini_RSV The Gini coefficient adjusted for negative attributes (Raffinetti, Siletti and Vernizzi, 2015) computes the Gini coefficient adjusted for negative (even weighted) data. Usage Gini_RSV(y,p) Arguments y p a vector of attributes containing even negative elements a vector containing the weights associated to the elements of the attribute vector Gini_RSV(y) is the Gini coefficient for income negative weighted data proposed by Raffinetti, Siletti and Vernizzi (2015) and based on a new definition of the "polarized" scenario, where the total negative attribute amount is assigned to one unit, the total positive to another unit, while all the other units have a zero amount of attribute. It provides a values always included into the close range [0,1]. Value the value of the Gini coefficient adjusted for negative attributes. Note If the vector p contains unitary weights, compute Gini_RSV as Gini_RSV(y). Moreover, if the vector of attributes does not contain negative elements, Gini_RSV(y) takes the same value of the classical Gini coefficient computed with the package ineq. Finally, if the the vector of attributes does not contain negative elements but the vector p contains non-unitary weights, Gini_RSV(y,p) has the same value of Gini(y,p). Author(s) Emanuela Raffinetti, Fabio Aimar

8 8 GRSVc E. Raffinetti, E. Siletti, A. Vernizzi (2014), Inequality measures and the issue of negative income. Italian Statistical Society Conference (SIS), Book of Short Papers: "SIS th Scientific Meeting of the Italian Statistical Society", CUEC (Cooperativa Universitaria Editrice Cagliaritana), June 2014 E. Raffinetti, E. Siletti, A. Vernizzi (2015), On the Gini coefficient normalization when incomes with negative values are considered, Statistical Methods & Applications, 24(3), See Also ineq Examples # generate the vector of attributes with even negative elements y<-c(-7,-15,11,-10,2,4,40) # generate the vector of weights p<-c(2.5,1.1,3.6,4.4,0.8,2.7,1.9) # compute the Gini coefficient of Raffinetti, Siletti and Vernizzi (2015) as Gini_RSV(y,p) data(bi2012) # define the vector of weights # select the vector of incomes (e.g., the incomes from transfers YTA) y<-bi2012$yta # compute the Gini coefficient adjusted for negative values Gini_RSV(y,p) GRSVc Generalized RSV (Raffinetti, Siletti and Vernizzi, 2015) curve of maximum inequality for negative attributes Usage computes the x-axis and y-axis values of the generalized RSV curve of maximum inequality for weighted and negative attributes. GRSVc(z, p = rep(1, length(z)), plot = FALSE) Arguments z p a vector of attributes containing negative elements a vector containing the weights associated with the elements of the attribute vector

9 GRSVc 9 plot logical. If TRUE the generalized RSV curve of maximum inequality will be plotted Value Note GRSVc(z,p) provides the points of the generalized RSV curve of maximum inequality. A list of class GRSVc with the following components: Generalized RSV (maximum inequality) x-axis points vector with the x-axis values of the generalized RSV curve of maximum inequality Generalized RSV (maximum inequality) y-axis points vector with the y-axis values of the generalized RSV curve of maximum inequality. The plot of the generalized Lorenz curve, for both non-negative and negative attributes, can be obtained by the ineq package. If the vector of attributes z does not contain negative elements, the generalized RSV curve of maximum inequality corresponds to the generalized Lorenz curve of maximum inequality provided by the package ineq. Author(s) Emanuela Raffinetti, Fabio Aimar E. Raffinetti, E. Siletti, A. Vernizzi (2014), Inequality measures and the issue of negative income. Italian Statistical Society Conference (SIS), Book of Short Papers: "SIS th Scientific Meeting of the Italian Statistical Society", CUEC (Cooperativa Universitaria Editrice Cagliaritana), June 2014 E. Raffinetti, E. Siletti, A. Vernizzi (2015), On the Gini coefficient normalization when incomes with negative values are considered, Statistical Methods & Applications, 24(3), See Also ineq Examples # generate the vector of attributes with even negative elements z<-c(-7,-15,11,-10,2,4,40) GRSVc(z,plot=TRUE) # generate the vector of even negative attributes

10 10 RSVc z<-c(10,-25,-12,3,2,-5,45) # generate the vector of non-unitary weights p<-c(1.5,2.2,1.9,3.8,4.7,5,2.3) GRSVc(z,p,plot=TRUE) data(bi2012) # define the vector of non-unitary weights # select the vector of incomes (e.g., the incomes from financial capital gain YCF) z<-bi2012$ycf GRSVc(z,p,plot=TRUE) # define the vector of non-unitary weights # select the vector of incomes (e.g., the incomes from employment YL) z<-bi2012$yl GRSVc(z,p,plot=TRUE) RSVc Ordinary (empirical) RSV (Raffinetti, Siletti and Vernizzi, 2015) curve of maximum inequality for negative attributes computes the x-axis and y-axis values of the ordinary RSV curve of maximum inequality for weighted and negative attributes. Usage RSVc(z, p = rep(1, length(z)), plot = FALSE) Arguments z p plot a vector of attributes containing negative elements a vector containing the weights associated with the elements of the attribute vector logical. If TRUE the ordinary RSV curve of maximum inequality will be plotted RSVc(z,p) provides the points of the ordinary RSV curve of maximum inequality.

11 RSVc 11 Value Note A list of class RSVc with the following components: RSV (maximum inequality) x-axis points vector with the x-axis values of the ordinary RSV curve of maximum inequality RSV (maximum inequality) y-axis points vector with the y-axis values of the ordinary RSV curve of maximum inequality. The plot of the ordinary (empirical) Lorenz curve, for both non-negative and negative attributes, can be obtained by the ineq package. If the vector of attributes z does not contain negative elements, the ordinary RSV curve of maximum inequality corresponds to the ordinary Lorenz curve of maximum inequality provided by the package ineq. Author(s) Emanuela Raffinetti, Fabio Aimar E. Raffinetti, E. Siletti, A. Vernizzi (2014), Inequality measures and the issue of negative income. Italian Statistical Society Conference (SIS), Book of Short Papers: "SIS th Scientific Meeting of the Italian Statistical Society", CUEC (Cooperativa Universitaria Editrice Cagliaritana), June 2014 E. Raffinetti, E. Siletti, A. Vernizzi (2015), On the Gini coefficient normalization when incomes with negative values are considered, Statistical Methods & Applications, 24(3), See Also ineq Examples # generate the vector of attributes with even negative elements z<-c(-8,-11,9,-12,7,6,35) RSVc(z,plot=TRUE) # generate the vector of even negative attributes z<-c(12,-21,-10,6,1,-3,40) # generate the vector of non-unitary weights p<-c(1.2,2.3,1.6,3.5,4.7,4,2.2) RSVc(z,p,plot=TRUE) data(bi2012) # define the vector of non-unitary weights # select the vector of incomes (e.g., the incomes from transfers YTA)

12 12 RSVc z<-bi2012$yta RSVc(z,p,plot=TRUE) # define the vector of non-unitary weights # select the vector of incomes (e.g., the incomes from capital gain YCF) z<-bi2012$yca RSVc(z,p,plot=TRUE)

13 Index Topic datasets BI2012, 3 BI2012, 3 Gini, 3, 4 Gini_CTR_BS, 3, 5 Gini_RSV, 3, 7 GiniWegNeg (GiniWegNeg-package), 2 GiniWegNeg-package, 2 GRSVc, 3, 8 ineq, 4 9, 11 RSVc, 3, 10 13