Talk:Instrumental variables

3SLS

A group of PhD students were made to write a number of articles on econometrics topics. Encyclopedia quality is poor and they were blocked for not disclosing that they made paid edits, but to make at least some use of their work maybe someone can look at Draft:Three-Stage Least Squares Estimator and see what if any of it can be used. Antimanipulator (talk) 16:28, 28 September 2017 (UTC)

Endogeneity with an exponential regression function

The same group from #3SLS also wrote Endogeneity with an exponential regression function, which contains salvageable material on instrumental variables estimation in Poisson regression. I suggest that the usable material be merged into a new section here. Wikiacc (¶) 14:57, 22 May 2019 (UTC)

Pretty ugly stuff. Nevertheless, support merge and suggest some refinement in situ.   Y Merge completed Klbrain (talk) 07:06, 6 July 2020 (UTC)

Another merge proposal

Similar to the previous section, Binary response model with continuous endogenous explanatory variables might be worth merge here, if not deleting. Thoughts? Klbrain (talk) 21:31, 19 July 2020 (UTC)

I created a header Instrumental variables#Methods for generalized linear models under which it could go. As with the Poisson section, a merge is worthwhile, though serious cleanup will be needed. Wikiacc (¶) 00:32, 26 July 2020 (UTC)

@Klbrain and Wikiacc: The article in question, Binary response model with continuous endogenous explanatory variables, describes a residual inclusion, not an IV method. If anything, it should be merged into control function (econometrics). --bender235 (talk) 22:51, 2 August 2020 (UTC)

Fair point. But isn't Instrumental variables#Poisson regression also a residual inclusion method? I'm inclined to think the two should stick together, but that could be at the control function article. Wikiacc (¶) 23:12, 2 August 2020 (UTC)

You're right. Unfortunately, the definition of IV is very fuzzy. In the narrow sense, the term "IV estimation" only describes the special case of just-identified two-state least squares (2SLS). But since the "idea" of an instrumental variable (a variable that is excluded from the main equation of a model, or "second" stage of a regression) can be extended into non-linear models, the term is now used rather loosely in the literature. I'm not sure whether we should follow that trend.

In the end, the "classic" projection version of 2SLS, of which IV is the aforementioned special case, can also be expressed as residual inclusion (i.e., both approaches give the same estimate). However, only the residual inclusion works also in non-linear models. So again, calling this an "IV method" only leads to confusion, especially among those just learning econometrics. But then again, the excluded variable(s) from the first stage of residual inclusion methods are often referred to as "instrument(s)" nonetheless.

Long story short: I'm not quite sure whether it's best for us to adopt a narrow IV definition (which the risk of potentially contradicting some textbooks) or stick to the wide IV definition (with the risk of this article turning into a hodge podge of vaguely related methods). --bender235 (talk) 01:53, 3 August 2020 (UTC)

This article is messy at present, but I agree that focusing on the linear model will help keep the article from sprawling further. (I'd keep keep overidentified IV here, though.) I support limiting this article to the linear model and developing a section at the control function article about residual inclusion in nonlinear models (both Poisson and probit). Wikiacc (¶) 02:20, 3 August 2020 (UTC)

I like the idea of splitting the topic along linear vs. non-linear models ("projection inclusion" vs. residual inclusion). But it's going to be some work to reorganize and rewrite these articles. Unfortunately, giving each of the technical terms that being thrown around in the context of IV estimation at large its own article will lead to a lot of overlap and redundancy (endogeneity, exclusion restriction, identification, reduced form, etc.), not to mention the number of related techniques that almost synonymous with IV (indirect least squares, limited information maximum likelihood). So I guess some detailed planning would be great. --bender235 (talk) 18:19, 3 August 2020 (UTC)

The tricky part will be separating "instrumental variables estimation" from simultaneous equations model. I'm not sure what the solution is there. But fortunately the linear/nonlinear split won't affect that at all. Wikiacc (¶) 01:36, 4 August 2020 (UTC)

Wow, I didn't even think of that one. But you're right, that's another article with overlap and redundancy potential. Unfortunately I won't have time to get more involved in any large-scale reorganization any time soon. --bender235 (talk) 02:20, 5 August 2020 (UTC)

Rebooted merge proposal

As a result of the discussion above, I have revised the merge proposal to the following: Binary response model with continuous endogenous explanatory variables and Instrumental variables#Poisson regression both get merged to a new section in control function (econometrics) about residual inclusion methods in nonlinear models. Wikiacc (¶) 02:44, 5 August 2020 (UTC)

At the binary response model article, there is a method estimated purely by conditional MLE. Separating that from the residual inclusion method seems silly. Therefore, I suggest the following revision. Instead of control function (econometrics), how about making the target a new article? Say, nonlinear simultaneous equations model (by analogy with simultaneous equations model). This new page could also contain material on the "forbidden regression" (see above) and other related topics, focusing more on the setting than on the particular method. Wikiacc (¶) 03:33, 14 August 2020 (UTC)

Scratch that new proposal—too ambitious. I have moved the Poisson regression section to control function (econometrics). Not exactly sure what to do with Binary response model with continuous endogenous explanatory variables. Wikiacc (¶) 04:29, 11 December 2020 (UTC)

Article title

Closed Limelike Curves: I'm seeing last December you moved this page from Instrumental variables estimation to Instrumental variable. I'd propose we either move it back to the earlier title or to Instrumental variables (with an s). The method itself is primarily referred to as "instrumental variables", where an instrumental variable (without additional qualifier) would refer to a specific use of that method. See e.g. the sources listed here; the only two which don't use the "s" qualify it somehow, with "Instrumental Variable Estimates" or "Instrumental Variable Regression". Vermont (🐿️—🏳️‍🌈) 18:07, 23 May 2026 (UTC)

I'm ok with either, but went with the singular since WP:PLURAL. – Closed Limelike Curves (talk) 02:41, 26 May 2026 (UTC)

Makes sense. I think in this case, it falls under a similar exception as Skew coordinates. I'll move the page to the title with an s. Best, Vermont (🐿️—🏳️‍🌈) 02:05, 29 May 2026 (UTC)