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I want to conduct a simple propensity score estimation where the treatment $D_i$ is a binary variable ($D_i=1$ individual $i$ participates in the labor market program, zero otherwise). I estimate the propensity score using a simple probit model using various explanatory variables (including gender).

Then I want to calculate the average treatment effect (ATE) (and the average treatment effect on the treated, ATET) using e.g. caliper matching with replacement or a simple 1:1 matching with replacement.

The question: how can I check whether the ATEs of e.g. male and female individuals differ, i.e. whether $$(\text{ATE|i is male} - \text{ATE|i is female}) = 0$$

How can I make inference (whether the difference between the ATEs is different from zero)? Would you recommend bootstrap? If this was the case how would I do it?

Carlos Cinelli
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user21156
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  • You can create your matched pairs, then apply a model based upon [this paper](http://cgibbons.us/research/papers/Gibbons--FixedEffects.pdf) that I've written with coauthors. – Charlie Feb 25 '13 at 18:04
  • Are you using or have access to Stata 13? – dimitriy May 09 '14 at 03:53
  • I haven't read it, but this article may offer a perspective: https://eng.uber.com/analyzing-experiment-outcomes/ – Cam.Davidson.Pilon Nov 14 '18 at 03:57
  • This is late, but for those who may run into this in the future. What OP wants is actually the difference in difference in difference, see discussion here: https://stats.stackexchange.com/questions/99140/difference-in-difference-in-differences-estimator – Jason Goal Apr 19 '19 at 11:37

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