I have matched my sample using propensity score matching such that each individual has an estimated propensity score of being assigned to a treatment group. Let $T_i$={0,1} be the actual treatment group of each individual. And $score_i$ be the estimated propensity score for each individual. I ran a log-linked gamma model with the following model specification: $$log(\mu)=\beta_0+\beta_1*score+\beta_2*T+\beta_3*score*T$$
Average Treatment Effect (ATE) is esimated using: $$ATE=exp(\hat{\beta_0}+\hat{\beta_1}*\overline{score}+\hat{\beta_2}*1+\hat{\beta_3}*\overline{score}*1)-exp(\hat{\beta_0}+\hat{\beta_1}*\overline{score}+\hat{\beta_2}*0+\hat{\beta_3}*\overline{score}*0)$$
where $\overline{score}$ is the average propensity score. How do I calculate the variance of the ATE?