Timeline for A 2SLS when the instrumented variable has two interactions in the model
Current License: CC BY-SA 4.0
22 events
| when toggle format | what | by | license | comment | |
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| Jun 26, 2020 at 8:09 | vote | accept | Tom | ||
| S Jun 25, 2020 at 18:02 | history | bounty ended | Tom | ||
| S Jun 25, 2020 at 18:02 | history | notice removed | Tom | ||
| Jun 25, 2020 at 12:09 | answer | added | Ale | timeline score: 3 | |
| Jun 25, 2020 at 9:00 | history | tweeted | twitter.com/StackStats/status/1276077700470517761 | ||
| S Jun 18, 2020 at 14:32 | history | bounty started | Tom | ||
| S Jun 18, 2020 at 14:32 | history | notice added | Tom | Draw attention | |
| Jun 16, 2020 at 16:06 | comment | added | Adrian Keister | Everything's clearer in causal diagrams. I would STRONGLY recommend drawing up as accurate and full a causal diagram as you can. | |
| Jun 16, 2020 at 16:04 | comment | added | Tom | @AdrianKeister Yes, that part is clear to me. But how do I deal with the instrumented variable $x_1$ being an interaction with two other variables $x_2$ and $x_3$? My suggest model is $y=ax_1x_2+bx_1x_3+cx_4+e$ . My problem is not how to carry out a 2SLS. My problem is how to carry out this particular 2SLS, The first stage would suggest that my dependent variable (or variables) would be interaction term(s).. My question is how to deal with that (without losing the information from the factors). | |
| Jun 16, 2020 at 15:35 | comment | added | Adrian Keister | The standard 2SLS would be this: $y=r_1z+\varepsilon$ and $x=r_2z+\varepsilon.$ Then the ratio $r_1/r_2$ provides the coefficient $\alpha$ of the true causal effect of $X$ on $Y.$ So the IV $z$ is always on the RHS of all the regressions. I'm not an R guy, so I can't help with your R syntax. | |
| Jun 16, 2020 at 15:31 | comment | added | Tom | Thank you for your comment @AdrianKeister. I get your point, but this post is just a simplified example I made up. The actual situation is a bit more complicated. As a results, I would really like to stick to the 2SLS. Is there anything you can do for me with regard to answering the main question? | |
| Jun 16, 2020 at 15:16 | comment | added | Adrian Keister | So actually, the best causal diagram would simply be $Z\to X\to Y,$ right? When a variable does not affect another, you simply don't have any edges between them. In this case, I do not see why 2SLS is necessary; there is no confounding, because there is no backdoor path from $X$ to $Y.$ 2SLS is more for a confounding situation, particularly when there is an unmeasured backdoor path from $X$ to $Y.$ | |
| Jun 16, 2020 at 14:06 | comment | added | Tom | Y is the dependent/effect variable. The main point is that the z, provide an exogenous shock to x. Furthermore, the z do not affect y other than through x (hence the red cross). The correlation between the z and x should therefore lead to an exogenous change in y. Which I assume answer the question what the causal effect of x on y is. Does that clear anything up? | |
| Jun 16, 2020 at 13:58 | comment | added | Adrian Keister | Causal diagrams can make a LOT of causal concepts much clearer - I would always start with them. Your diagram still leaves me with a couple questions: 1. Is $Y$ the effect variable? 2. Is $X$ the causal variable? 3. What is the big red X in your diagram? One comment: your diagram is not the usual setup for 2SLS. Instrumental variables can be useful for certain diagrams, but other techniques, such as the backdoor adjustment or the frontdoor adjustment formulas, are oftentimes more useful. | |
| Jun 16, 2020 at 7:05 | history | edited | Tom | CC BY-SA 4.0 |
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| Jun 16, 2020 at 7:00 | comment | added | Tom | @AdrianKeister I have added a diagram:) | |
| Jun 16, 2020 at 6:59 | history | edited | Tom | CC BY-SA 4.0 |
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| Jun 16, 2020 at 6:30 | comment | added | Tom | @AdrianKeister I am not very familiar with using causal diagrams, but I noticed that my example was very unclear. Did I by improving the example perhaps take away your confusion? If not, could you tell me what exactly is unclear? I will then try to make that clear using a causal diagram. | |
| Jun 16, 2020 at 6:26 | history | edited | Tom | CC BY-SA 4.0 |
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| Jun 16, 2020 at 6:04 | history | edited | Tom | CC BY-SA 4.0 |
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| Jun 15, 2020 at 14:25 | comment | added | Adrian Keister | Can you add a causal diagram to your question, please? | |
| Jun 11, 2020 at 7:25 | history | asked | Tom | CC BY-SA 4.0 |