Timeline for Linear regression, good and bad controls, omitted variable error, and causal graphs
Current License: CC BY-SA 4.0
15 events
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| Oct 12, 2020 at 8:21 | comment | added | curious | I understand the pedagogical points and I think Wooldridge is excellent. I know the bad controls section in MHE, thanks. I'd also recommend this paper offering a nice overview. I agree with what is written in these references, I just wanted to understand it from the notation of intro econometrics textbooks, and here I apparently took the definition of the error term too literally. In their Primer Pearl et al. (2016, p. 81) define the error term as "factors ... that influence Y and are not themselves affected by X" which confirms our rephasing. | |
| Oct 11, 2020 at 23:51 | comment | added | Michael | Not really, no. (Perhaps someone else does and can share.) Starting with precise general first principles is usually not the style/priority of empirical econometrics. Rather it's communicated through empirical examples. You can find more discussion on bad control in Section 3.2.3 of "Mostly Harmless Econometrics". There, "...Bad controls are variables that are themselves outcome variables in the notional experiment at hand" is offered as a type of empirical description of bad control. | |
| Oct 9, 2020 at 23:02 | history | edited | curious | CC BY-SA 4.0 |
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| Oct 9, 2020 at 23:00 | comment | added | curious | Do you know a reference that uses a more precise definition of the error term along the lines you suggested? | |
| Oct 9, 2020 at 22:56 | history | edited | curious | CC BY-SA 4.0 |
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| Oct 9, 2020 at 22:53 | comment | added | curious | Not sure I understand exactly what you mean by "It is a point of empirical semantics" but since what I believe I'm trying to say is the same as your rephrasing, I added the latter to the edit in the original post, so your suggested rephrasing can be directly seen. Thanks again! | |
| Oct 9, 2020 at 22:35 | comment | added | Michael | It is a point of empirical semantics. The point here is that if $y(z(x))$ describes the relationship between $x$, $y$, and $z$, then $z$ is a bad control in the regression of $y$ on $x$. You provided an example above where all function forms are linear. Some of the partial effect of $x$ would be mistakenly captured by the coefficient on $z$, whose partial effect derives solely from that of $x$. | |
| Oct 9, 2020 at 22:32 | vote | accept | curious | ||
| Oct 9, 2020 at 22:32 | history | edited | curious | CC BY-SA 4.0 |
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| Oct 9, 2020 at 22:27 | comment | added | curious | Thanks, I see! I have edited this in the post above. Concerning the more precise definition of the error term. I think "... and that themselves are not affected by x." and "are not channels of the effect of x on y" are the same, no? I think it does not preclude correlated with x because it still allows x and u to be correlated due to u causing x? | |
| Oct 9, 2020 at 22:18 | comment | added | Michael | That is very good, except you need to move $g_2*a_0$ into the intercept, so the error term in the final regression has mean zero (another reason to always include an intercept term). Your phrase "...and that themselves are not affected by x..." is too strong a requirement. It also excludes "correlated with x", which is the definition of omitted variable bias. Indeed in your wage on education regression, there's a bias b/c the omitted variable---part of $u$---is correlated with education. One can rephrase that as, e.g. "variables which are not channels of the effect on x on y". | |
| Oct 9, 2020 at 22:02 | history | edited | curious | CC BY-SA 4.0 |
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| Oct 9, 2020 at 19:26 | answer | added | Michael | timeline score: 1 | |
| Oct 9, 2020 at 10:17 | review | First posts | |||
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| Oct 9, 2020 at 10:08 | history | asked | curious | CC BY-SA 4.0 |