# Difference-in-Difference, different group size

Is there a specific rule to the number of units in the treatment and control group. I am trying to carry out a difference-in-difference estimation and in the treatment group I have about 9000 individuals and in the control group I have about 800 individuals.

There is no direct rule but it will be more difficult to find a treatment effect if the two groups are very different in size. For example, if your outcome $Y$ is a normal random variable then the minimum detectable effect for the average treatment effect is $$\sqrt{\frac{\text{Var}(\widehat{Y})}{n}}\sqrt{\frac{1}{p(1-p)}}(q_{1-\frac{\alpha}{2}}+q_\lambda)$$ where $p$ is the proportion of individuals in the treatment group, $n$ is the sample size, $q$ are the quantiles from a standard normal, and $\alpha$ and $\lambda$ are the level and power that are chosen by the econometrician. The smallest minimum detectable effect is achieved if the number of treated individuals is equal to the number of control group individuals, i.e. $p=0.5$.