Thursday, December 12, 2013

Update on strata and heterogenous assignment

In my last post I was dealing with an issue where the assignment to treatment differed across strata. Duflo et. al. in the Handbook note that an OLS regression with indicators for the strata is comparable to averaging the difference between treatment vs. control across strata, where the weights are the probability of treatment conditional on being in particular strata.

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:


No. The correct regression is:


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

Also, Macartan Humphreys has a well written paper on hetero effects:

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