It will be negative if the change in the effect of households characteristics is such that for children with same characteristics and same position in the income distribution, their income decreased. Regression coefficients then reflect the effect of characteristics on the conditional quantile but cannot be read as the unconditional effects, in which case the interpretation is limited (unless one estimates quantiles regressions for all quantiles). It turns then that one needs to know the entire conditional distribution of the outcome Y in each group g given X to compute the group-specific quantiles.