Estimating multiplicative treatment effect

[amedury]

I am interested in obtaining a multiplicative treatment E[Y=1]/E[Y=0] within the causal tree framework.

One potential way was that if the potential outcomes at the bottom of the sample are unbiased, then by obtaining the sample estimates of the treated and control groups separately, perhaps I could take the ratio instead.

Is there a way to obtain the potential outcomes at the end of each leaf separately?

[susanathey]

The simplest approach is to first create predictions from the causal tree; then create a factor variable based on those predictions, which gives you a different value of the factor for each leaf (double check there are no ties, but ties would be unlikely). You can then create means of any variable grouped by the new factor variable, or run a regression of your outcomes on the factor variable.