Hello everyone,

I am currently running fixed effects model to see the relationship between program participation and child outcomes. There are two waves and the FE is at the individual level. I want to test whether this relationship varies by a child's poverty status in a prior wave and to do so, I added an interaction term of poverty status & program participation variable. But since this poverty status variable comes from a prior wave (say, wave 1 when FE model includes wave 2 and wave 3), I was not sure how I should interpret the coefficient on this interaction term.

This is the code I used: xtreg y i.x1##i.x2 covariates i.year, fe (when x1 is program participation var and x2 is poverty status)

First, is it correct to say that the poverty status is a time-invariant variable here? I am pretty positive it is, since it gets omitted in the model, but wanted to double check.

Second, Is it correct to interpret the coefficient on the interaction term as how the relationship between program participation and child outcomes varies depending on a child's poverty status in a prior wave?

And if the coefficient is positive and significant, can we say the program is more strongly related to child outcomes for children living in poverty in a prior wave compared to children who are not poor? I was confused whether I can make this comparison between children in poverty and those who are not, since the FE is a within-entity estimator.

I'd highly appreciate if any of you can give me some help on this. Thank you in advance!!