Randomisation and balance in experiments Suppose we are interested in the effect of some 'treatment' on some outcome of interest. A common practice is to select a group of people and then randomly choose some fraction (often half) to receive the treatment. The remaining people are untreated (i.e. the 'control'). As shown in (e.g.) Angrist and Pischke, the difference in mean outcomes between the groups is then an unbiased estimate of the average causal effect of the treatment.

While such a procedure does give us an unbiased estimate, it does not ensure that the treatment and control group are 'balanced' on observable criteria. For example, although on average there will be the same fraction of men in the treated and untreated groups, in our actual sample there are likely to be a higher fraction of men in one group. In such a situation, it seems natural to simply take some men from the 'overly male' group and place them in the 'overly female group' until the gender ratio is the same in both groups. (If we wanted, we could select the men we choose randomly.)

Some questions:


If we do this, will the difference in mean outcomes between treated and untreated groups remain an unbiased estimate of the causal effect?
If so, why is this not done in all RCTs?
If not, how do we trade-off the benefits of achieving 'balance' against the possible bias that we are introducing?


Optional extra: I am aware that this procedure seems rather similar to 'stratification'. However, my understanding is that, after stratifying, people do not compare mean outcomes for the treated and untreated groups (rather, they compare mean outcomes for every subsample on which they stratified, or equivalently run a regression with stratification dummies). If my proposal is indeed equivalent to stratification, my question is then equivalent to the question why we need these dummies and what are the costs and benefits of stratification.
Ok, I am far from an econometrician, but my train of thought would be as follows:

By using random assignment we have two groups that are on average equal to one another on all aspects. As you rightly point out due to sampling variation there will be differences.

My worry would be that if I start "correcting" those after randomization (as per your example with gender distribution) I introduce other differences between the groups in say age or even an unobserved but important characteristic.

Stratification is different as it is done upfront. You have a characteristic that you know is different for different groups so you take the random samples within those groups. As a rather naive example: we know that the effect of taking anticonception pills is rather different for men and women, so if you wanted to test the effect of the pill on fertility you could stratify by sex and then do a random assignment within the sexes.