# Difference-in-differences parallel trends for treatment and control groups of uneven size

I am confused about how to run a formal parallel trends test for my DiD study. Here is an overview of my data.

There are 25 districts in the treatment group. Each district has data on district-level average income for five periods (P1, P2, P3, P4, P5) each year from 1900 to 1910.

There are 60 districts in the control group. As in treatment, each of the 60 districts have district-level average income for five periods each year from 1900 to 1910.

The intervention happened in 1905. I want to estimate its effect on the income at the district-level using difference-in-differences. To this end, I want to first ensure that parallel trends assumption is fulfilled. Namely, I need to test that evolution of income in the treatment group would have followed the same trend as in control group if there was no intervention.

I have read several posts about parallel trends on this forum, but confusion does not go away. I read a paper that does a t-test (to compare the means of two groups) as a formal test for parallel trends assumption. Not sure I can simply average the incomes of all districts in both treatment and control groups for each time period. This way I think I can also do a t-test. I do not know if this way of averaging is a good idea in my case. Any suggestions?

• I’m not an econometrician but you can estimate the treatment difference by a mixed model, using a random intercept for each district. Commented Nov 13, 2022 at 5:23
• Could you elaborate in an answer? Commented Nov 13, 2022 at 6:05
• There are 11 years from 1900 to 1910, so the statement "five periods (P1, P2, P3, P4, P5) each year from 1900 to 1910" is somewhat confusing. Commented Nov 13, 2022 at 13:53
• see my answer to another similar question here and let me know. Commented Nov 13, 2022 at 20:17
• Perhaps the OP is referring to the 5 post-treatment periods, or the 5 periods after the immediate intervention year? Commented Nov 13, 2022 at 20:38