OmegaGL: Matrix for testing Generalized Lorenz dominance

In AngelBerihuete/laeken2: Calculate the TIPs and Lorenz curves

Description

The auxiliary function OmegaGL computes the (empirical) vector of Generalized Lorenz (GL) curve ordinates and its corresponding covariance matrix. This matrix will be used to compute the test-statistic to test for the Generalized Lorenz dominance relation between two GL curves.

Usage

OmegaGL(dataset, samp)

Arguments

dataset	a data.frame containing variables obtained by using the setupDataset function.
samp	an integer which represents the number of the GL ordinates to be estimated. These ordinates will be estimated at points p_i, where p_i=i/samp, \quad i=1, …, samp.

Details

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

Calculations are made using the equivalized 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_i vector with components p_i=i/samp, i=1, ..., samp.

quantile_i estimated vector of quantiles of income corresponding to these p_i's.

gamma.i vector of estimated conditional means of income less than the quantil corresponding to p_i=i/samp, i=1, ..., samp.

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.

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.

See Also

testGL, setupDataset

Examples

data(eusilc2)
ATdataset <- setupDataset(eusilc2, country = "AT", s = "OECD")
omega.gl <- OmegaGL(ATdataset, samp = 10)
str(omega.gl)

AngelBerihuete/laeken2 documentation built on May 5, 2019, 6:02 a.m.