Heterogeneity test in CATE

[Denzil Fiebig]

The test for whether treatment effects are heterogeneous in the CATE suite of commands in Stata19 (estat heterogeneity) is not fully documented. Instead there is reference to an NBER working paper Chernozhukov et al. (2006). The associated link takes you to the revised version of the paper (subsequently published in Econometrica) which does not contain the test. In my searching I have been unable to find the exact form and motivation for the test. Any help would be appreciated.

[Di Liu (StataCorp)]

Hi Denzil!

You can take a look at Section 3.1 of Chernozhukov, Demirer, Fuflo, and Fernandez-Val (2025) for motivation and intuition. In -cate-, we apply the same type of regression to both the PO and AIPW estimators. For details, see Page 16 in -cate postestimation- manual.

Reference:

Chernozhukov, Victor, Mert Demirer, Esther Duflo, and Iván Fernández‐Val. “Fisher–Schultz Lecture: Generic Machine Learning Inference on Heterogeneous Treatment Effects in Randomized Experiments, With an Application to Immunization in India.” Econometrica, 93, .no 4, (Econometric Society: 2025), 1121-1164. https://doi.org/10.3982/ECTA19303