Time-invariant Instrumental Variable with First Difference Regression

[Guest]

Dear All,

I have been using a time-invariant instrumental variable with fixed effects in my article. A reviewer has asked me to try the first difference approach to make sure my results hold. However, as my instrumental variable is time-invariant I am not sure how I can use that with a first difference estimation. I asked ChatGPT and it suggested this approach:

"Using Original Instrument in FD-IV Framework: If you prefer to use the FD model, but you have a time-invariant instrument, you can implement a two-stage least squares (2SLS) approach within the differenced data framework: First Stage: Regress the endogenous variable on the instrument in levels, as the instrument itself does not vary over time. Second Stage: Use the fitted values from the first stage in the differenced outcome equation."

Is this approach correct? If so, could you please refer me to an actual reference that endorses this approach?

[Sebastian Kripfganz]

As with many ChatGPT recommendations, this one does not seem to make much sense.

In principle, you can use a time-invariant instrument for the first-differenced model if it is reasonable to assume that it is sufficiently correlated with the first-differenced endogenous regressor. In practice, it might be difficult to find supportive arguments.

[George Ford]

This is from Jeff Wooldridge:

"This is why we can't let Stata do identification analysis for us. It's clear that a time-constant IV cannot be used in fixed effects, so one shouldn't try. As Sebastian noted, Stata will drop collinear variables, but not always the one that it should. Whenever one does fixed effects manually, this can happen."

https://www.statalist.org/forums/forum/general-stata-discussion/general/1618845-can-i-use-time-invariant-instrument-variable-and-country-fixed-effects-in-pooled-cross-sectional-analysis

You got bigger problems.

[Guest]

This is from Jeff Wooldridge:

"This is why we can't let Stata do identification analysis for us. It's clear that a time-constant IV cannot be used in fixed effects, so one shouldn't try. As Sebastian noted, Stata will drop collinear variables, but not always the one that it should. Whenever one does fixed effects manually, this can happen."

https://www.statalist.org/forums/forum/general-stata-discussion/general/1618845-can-i-use-time-invariant-instrument-variable-and-country-fixed-effects-in-pooled-cross-sectional-analysis

You got bigger problems.

Thanks for this reply. But indeed time-invariant instrument variables along with fixed effects have been widely-used in academic articles published in impactful journals.

[Sebastian Kripfganz]

It is all a matter of assumptions and whether they can be reasonably justified. Unfortunately, many published articles (even in impactful journals) remain vague about their assumptions.

[George Ford]

What command did you use to estimate the model?