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I am confused about the exact definitions here.

Assuming I have a cross-sectional regression, let's say, Wage on Education and I additionally control for observable characteristics with a set of dummies or variables like intelligence level, age, parent's education level, urbanization area, gender, race, work experience etc.

  1. Does this mean I used dummies/variables to "control for observable fixed effects" that I obtained through my data collection? (Is, for example, parent's education level thus an observable fixed effect?)

  2. Do unobservable fixed effects like ability (as often quoted in the literature) are then said to be "controlled" by proxies through my dummies like intelligence level, experience etc.?

In a way I'd like to know the exact difference between controlling for a variable, observable and unobservable characteristics, observable and unobservable fixed effects. Thanks.

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  • $\begingroup$ I am slightly confused by the wording you use (probably it's just me.) Do you by cross-sectional regression mean a simple linear regression without random effects? Where did you get the quotation "control for observable fixed effects"? Using your example: Yes, parent's education level is a fixed effect as you set them to be 3, 5, 14 levels, I don't know how many levels you can/want to use. There is no "randomness" regarding the levels, you fix them, you fully observe them. Can you please give some literature examples you try to follow? $\endgroup$
    – usεr11852
    Oct 27, 2013 at 15:08
  • $\begingroup$ Thanks for considering. Yes, no panel data, just plain vanilla cross section. Look at Currie and Yellowitz (1999) - Are public housing projects good for kids. They write the following: "We find that after controlling for observable characteristics...". Look at Nunn and Wantchekon (2011) - The Slave Trade, they write: "X denotes.. five fixed effects for the respondent's living condition", "controlling for these observable characteristics..", "we control for a number of proxies for income [...] and living conditions fixed effects". $\endgroup$
    – user31766
    Oct 27, 2013 at 16:08
  • $\begingroup$ Right. The Nunn & Wantchekon article is a good clarification for what you want. I am no expert on the matter but I think your intuition is correct. Ultimately it is an OLS; the way they test for significance is somewhat specialized but otherwise nothing crazy. So... "Yes" is also your second question's answer. In the paper you mention they strive to have a somewhat rigorous falsification of their findings, checking of their "unknown unknowns" but yes, otherwise nothing too exotic. $\endgroup$
    – usεr11852
    Oct 27, 2013 at 17:34
  • $\begingroup$ So you control for observable fixed effects in an OLS regression by adding dummies? Is this correctly phrased? $\endgroup$
    – user31766
    Oct 27, 2013 at 18:44
  • $\begingroup$ I think not. If there is an observable fixed effects you can include it in the OLS to start with. You try to control the unobservable ones by adding dummies, surrogate variables if you like. $\endgroup$
    – usεr11852
    Oct 29, 2013 at 8:43

1 Answer 1

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Using your example for your first question: Yes, parent's education level is a fixed effect as you set them to be at any arbitrary number you can/want to use. There is no "randomness" regarding the levels, you fix them, you fully observe them.

Regarding your second question: The Nunn & Wantchekon article is a good clarification for what you want. I am no expert on the matter but I think your intuition is correct. Ultimately it is an OLS; the way they test for significance is somewhat specialized but otherwise nothing crazy. So... "Yes" is also your second question's answer. Ν. & W. strive to have a somewhat rigorous falsification of their findings, checking of their "unknown unknowns" but yes, otherwise nothing too exotic. In general, if there is an observable fixed effects you can include it in the OLS to start with. If you suspect there are some unobservable ones you try to control for them by adding dummies; surrogate variables if you like.

As mentioned, I am not an expert on panel data and I haven't work in economics ever so take it with a grain of salt. I believe your statistical intuitions are not wrong though.

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