definition of average causal effect $$ ACE = E(C_1) - E(C_0) $$ $$ ACE = E(Y|X=1) - E(Y|X=0) $$ given the condition that $$ X \bot (Y(0), Y(1)) $$
So if I have a regression
m <- lm(y~x)
whose residual is perfectly normally distributed:
Can I assert that coefficient of $X$ is the average causal effect of $X \rightarrow Y$ ?
If so, how can I test whether that $m\$redisuals$ is normally distributed along $X$?
Thank you a lot!
If you mean that, given your experimental design, you can justify the statements about independence of assignment of treatment from treatment outcome, you can assert the coefficient of X to be the average causal effect of X on Y.
If you mean that you can't necessarily assert the independence of assignment of treatment from treatment outcome, you cannot identify the coefficient of X as the causal effect.
The question of normality of residuals is covered here
`
