R: Matrix for testing Generalized Lorenz dominance

OmegaGL {rtip}

R Documentation

Matrix for testing Generalized Lorenz dominance

Description

The auxiliary function OmegaGL computes the (empirical) vector of Generalized Lorenz (GL) curve ordinates and its corresponding covariance matrix. Given two income distributions, this matrix will be used to test the null hypothesis that one distribution dominates the other in the Generalized Lorenz sense.

Usage

OmegaGL(dataset, ipuc = "ipuc", hhcsw = "DB090", hhsize = "HX040",
  samplesize = 10, generalized = TRUE)

Arguments

`dataset`	a data.frame containing the variables.
`ipuc`	a character string indicating the variable name of the income per unit of consumption. Default is "ipuc".
`hhcsw`	a character string indicating the variable name of the household cross-sectional weight. Default is "DB090".
`hhsize`	a character string indicating the variable name of the household size. Default is "HX040".
`samplesize`	An integer representing the number of GL ordinates to be estimated. Default is 10. These ordinates are estimated at points `p_i`, where `p_i=i/samplesize, \quad i=1, \dots, samplesize`.
`generalized`	logical; if FALSE the matrix for testing Lorenz dominance will be calculated.

Details

Estimation of GL curve ordinates and their covariance matrix are calculated following Beach and Davidson (1983) and Beach and Kaliski (1986).

Calculations are made using the equivalised disposable income. The equivalence scales that can be employed are the modified OECD scale or the parametric scale of Buhmann et al. (1988). The default is the modified OECD scale (see setupDataset).

Value

A list with the following components:

Omega, covariance matrix for the estimated vector of GL curve ordinates.
gl.curve, estimated vector of GL curve ordinates.
p, vector with components p_i=i/samplesize, \quad i=1,..., samplesize.
quantiles, estimated vector of quantiles of income corresponding to these p_i.
gamma, vector of estimated conditional means of income less than the quantile corresponding to p_i=i/samplesize, \quad i=1, \dots, samplesize.

Author(s)

A. Berihuete, C.D. Ramos and M.A. Sordo

References

C. M. Beach and R. Davidson (1983) Distribution-free statistical inference with Lorenz curves and income shares, Review of Economic Studies, 50, 723–735.

C. M. Beach and S. F. Kaliski (1986) Curve inference with sample weights: and application to the distribution of unemployment experience, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 35, No. 1, 38–45.

B. Buhmann et al. (1988) Equivalence scales, well-being, inequality and poverty: sensitivity estimates across ten countries using the Luxembourg Income Study (LIS) database, Review of Income and Wealth, 34, 115–142.

K. Xu (1997) Asymptotically distribution-free statistical test for generalized Lorenz curves: An alternative approach, Journal of Income Distribution, 7, 45–62.