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Say I'm estimating a regression of several variables through FE estimator,

$$ y_{it} = \alpha + v_i + \sum_{j} \beta_j x^j_{it} + \epsilon_{it} $$

and I have reason to suspect the $k$-th variable to be endogenous, hence I expect its coefficient to be biased.

But, the focus of my analysis is not on the $k$-th variable, rather on a different one, I am including variable $k$ only because I think it is an important variable in relation to $y_i$.

How bad will not including an instrument be? Will this bias other coefficients? If I picture the geometry of this, trying to fit a (hyper)plane through a set of points, the answer should be yes, altering one of the coefficient will have repercussion in how the other one fits.

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  • $\begingroup$ I think this is a duplicate, just need to find the correct older thread. $\endgroup$ – Richard Hardy May 10 at 14:58
  • $\begingroup$ Be happy to read it, could not find a similar one when posting. $\endgroup$ – Three Diag May 11 at 11:12
  • $\begingroup$ Right, I could not either, though my search was pretty quick. $\endgroup$ – Richard Hardy May 11 at 11:17
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YES

In the extreme, omit an important variable. That biases the coefficient by forcing it to be zero.

When you do that, you can get incorrect signs on the remaining variables...major bias, indeed.

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