# Diff-in-diff parallel trends with a positive outcome

I am trying to test for parallel trends when using diff-in-diffs, where my outcome variable is nonnegative (basically a percentage -- the share of subjects with some property). I run into a simple-looking problem which I never saw addressed in the standard literature.

Suppose that for all $$t < T$$, the value of the outcome variable for the untreated group is $$x_t$$ and for the treated group it is $$x_t-\delta$$. Then, for $$t=T$$, it is $$x_T$$ for the untreated group, but it cannot be $$x_T-\delta$$ for the treated group, because this value is negative. So in practice the difference between the values at $$t=T$$ is less than $$\delta$$.

Strictly speaking, this is a rejection of parallel trends, but are there ways around it, given that the assumption is only in one data point, where there is a strict limit on the value?

Any suggestions?

Thanks!