帮忙翻一下这两段话呗？In all cases, we make the comparisons statistically. We use a distribution-free estimator
of the standard errors of a set of ordinates on each curve to test the null that the ordinates for
each curve are the same (Davidson and Duclos, 1998). Following Howes (1996), we reject the
null hypothesis of non-dominance only if the tests at each ordinate differ significantly and are of
the same sign. We also reject the null in favor of crossing concentration curves if there are two
or more significant t-statistics with opposite signs.
Because the dominance tests are quite general, there are many instances in which we
cannot reject the null of no dominance, even though tax incidence might differ for some indices
of inequality. To allow for this possibility, we also use another comparison of tax incidence
based on extended gini coefficients (Yitzhaki, 1983; Younger, et.al, 1999). In particular, we
check for differences in extended ginis for a wide range of parameter values (1.01 to 4, an upper
limited suggested by Duclos’ (2000) leaky bucket experiments) that allow for increasing weight
of poorer households in the underlying social welfare function. If we find that one tax is more
concentrated among the poor than another for the entire range of parameter values, we conclude
that the second tax “dominates” the first by the e-gini criterion. This not as general a statement as
the standard dominance result, because it does not guarantee preference with respect to other
social welfare functions. But given the range of parameter values that we use, the results
reasonably robust and therefore of interest.