Oster's (2016) delta test after ivreg2

[Junida Mulla]

Hello,
I am writing because I am trying to apply Oster's (2016_ delta test, using the psacalc commend. However, my setting seems not to be covered by the models psacalc supports. For more context, I am running a 2SLS model (using ivreg2), where I am instrumenting my endogenous variable of interest (X) with instrument (Z). From the feedback received, discussants of our paper pointed out certain channels through which our instrument may be threatened. We have hence constructed proxies P1, P2, P3, to account for those channels, and we include them as additional controls in our main specification. We would like to use Oster's delta test, to verify that our results are robust. However, psacalc can not be run after ivreg2. Would it be valid to run 2SLS by hand, that is 1) get fitted values of X, X_hat, from the first stage regression; 2) Run the second stage using reg Y X_hat P1, P2, P3 3) Run Oster'sdelta test. Advice would be greatly appreciated.

[Sebastian Kripfganz]

The following article on our kinkyreg command might be helpful:

• Kripfganz, S., and J. F. Kiviet (2021). kinkyreg: Instrument-free inference for linear regression models with endogenous regressors. Stata Journal 21 (3), 772-813.

In this article, we describe a procedure that can be used to assess the robustness of your 2SLS estimates. It is linked to Oster's approach, and we illustrate how.

[Junida Mulla]

Thank you so much, Sebastian - I will read your paper with great interest.Do you or any other members of the community know if my suggestion using manual implementation would give credible results? Or just generally if it is conceptually OK to use psacalc in this manner?

[Sebastian Kripfganz]

Oster's delta already can be difficult to interpret. Applied to the second stage of a 2SLS procedure, it becomes even less clear how to interpret it. For this approach to be meaningful, you need to justify which bounds on delta are acceptable. I would not feel confident doing this for your procedure.

If you want to assess the plausibility of the exogeneity assumption on your instruments, a better approach might be the "plausibly exogenous" procedure implemented in the plausexog command by Clarke and Matta. We also talk about this command in our article referenced above.