Hi,

I am trying to use the following model: UTPr,s = Pr (Yt > s+r | Yo < s) to calculate upward transition probability (UTP).

UTP: Child's income percentile (Yt) exceeds a given percentile s in the child's income distribution by an amount r, conditional on the parent's income percentile (Yo) being at or below s in the parent's income distribution. However, at the same time, I want to calculate it differently for two religious groups Hindus and Muslims. These two groups are in the form of a dummy variable taking value 1 if Hindu and 0 if Muslim.

How should I introduce the non-overlapping percentile intervals of the parent income distribution (for example, s ˂ 10th percentile,
10th percentile > s ˂ 20th percentile ... 40th percentile > s ˂ 50th percentile)?