Very short question. What exactly is the difference between an instrumental variable and a proxy variable when building a regression model?

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    $\begingroup$ please do a simple proof-reading before posting the question. Putting caps and spaces between words is language independent. I am writing this purely because, every question you ask is poorly formatted. $\endgroup$ – mpiktas Jul 28 '11 at 13:09

An instrumental variable is used to help estimate a causal effect (or to alleviate measurement error). The instrumental variable must affect the independent variable of interest, and only affect the dependent variable through the independent variable of interest. The second part (only effecting the dependent variable through the independent variable) is called an exclusion restriction.

A proxy variable is a variable you use because you think it is correlated with the variable you are really interested in, but have no (or poor) measurement of.

  • $\begingroup$ Hey Alex, when you talk about instrumental variables and you say "affect the independent variable of interest", does affect mean 'correlated', or does affect mean you know that this instrumental variable has a casual affect on your interested ind. variable $\endgroup$ – Siddharth Gopi Dec 28 '13 at 2:12
  • $\begingroup$ @SiddharthGopi You need that the IV is not correlated with the main dependent variable of interest. So ideally if you think it might be, then you are required to control for that variable in your two stage regressions $\endgroup$ – karsha Apr 5 '17 at 16:41

One way to think about what an instrumental variable is doing is to say you are first regressing X on the instrument Z. What you then have are the predicted values for X - say, X*. So intuitively this is sort of the part of X that you get from Z. Then you take Y and regress it on those X* (and correct for standard errors). This is different from deciding to use Z as a proxy directly and regressing Y on Z. Intuitively, you then have all of Z in the regression instead of Z's relationship to X.

  • $\begingroup$ @SiddharthGopi - it means correlated. As to what karsha said - I'm not sure what you mean. I think usually one does expect that X is correlated with Y (and a regression is pretty pointless otherwise). You would not control for the variable you are trying to instrument for. $\endgroup$ – user186072 Nov 25 '17 at 1:07

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