testGL: Test for Lorenz and Generalized Lorenz dominance
In AngelBerihuete/laeken2: Calculate the TIPs and Lorenz curves

Description Usage Arguments Details Value Author(s) References See Also Examples

Statistical test procedure given by Xu (1997) to study Generalized Lorenz dominance from sample Generalized Lorenz curve estimates. Lorenz dominance from sample Lorenz curve estimates can also be studied (Beach and Davidson, 1983).

1	testGL(dataset1, dataset2, generalized = FALSE, samplesize = 10)

`dataset1`	a data.frame containing variables obtained by the using setupDataset function.
`dataset2`	a data.frame containing variables obtained by the using setupDataset function.
`generalized`	logical; if TRUE the test will be applied to compare two Generalized Lorenz curves. In another case Lorenz curves will be compared.
`samplesize`	an integer which represents the number of Lorenz (Generalized Lorenz) curve ordinates to be estimated for comparison. The default is 10.

The null hypotesis to be tested is if the Lorenz (Generalized Lorenz) curve calculated from dataset1 dominates the one calculated from dataset2.

A list with the following components:

Tvalue the value of the test-statistic

p.value simulated p-value of the test-statistic Tvalue (Wolak, 1989). It is calculated only when the Tvalue falls into an inconclusive region.

decision if the Tvalue is less than the lower-bound of the critical value at the 5 percent significance level the decision is "Do not reject null hypothesis". If the Tvalue is greater than the upper-bound of the critical value at the 5 percent significance level the decision is "Reject null hypothesis". Lower and upper-bounds critical values are obtained from Kodde and Palm (1986). If Tvalue falls into an inconclusive region (between the lower- and upper-bounds) the p-value will be estimated following Wolak (1989).

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

C. M. Beach and R. Davidson (1983) Distribution-free statistical inference with Lorenz curves

D.A. Kodde and F.C. Palm (1986) Wald criteria for jointly testing equality and inequality restrictions, Econometrica, 50, 1243–1248.

F.A. Wolak (1989), Testing inequality constrains in linear econometric models, Journal of Econometrics, 41, 205–235.

K. Xu (1997) Asymptotically distribution-free statistical test for generalized Lorenz curves: An alternative approach, Journal of Income Distribution, 7(1), 45–62.

OmegaGL, setupDataset

data(eusilc2)
ATdataset1 <- setupDataset(eusilc2, country = "AT", region = "Burgenland")
ATdataset2 <- setupDataset(eusilc2, country = "AT", region = "Carinthia")
testGL(ATdataset1, ATdataset2, generalized = TRUE, samplesize = 10)