The notation on pg 3935 in the handbook is quite sloppy, and so is the statement:

"In general, controlling for variables that have a large effect on the outcome can help

reduce standard errors of the estimates and thus the sample size needed. This is a reason

why baseline surveys can greatly reduce sample size requirement when the outcome

variables are persistent."

This statement seems to imply that they're suggesting this regression is correct:

y=alpha+beta*dummy_1+....+z*dummy_z+gamma*Treatment_dummy+error

No. The correct regression is:

y=alpha+beta*dummy_1xTreatment+....+z*dummy_zxTreatment+error

where each dummy is interacted with the treatment. The ATE is now the sum of the coefficients on the dummies interacted with the treatment.

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