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For example, if I have an equation $$ y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + u $$

Where $x_1$ and $x_2$ are simultaneously determined, say

$$ x_1 = \gamma_0 + \gamma_1 x_2 + \gamma_2 z_1 + e $$

$$ x_2 = \delta_0 + \delta_1 x_1 + \delta_2 z_2 + v $$

Should I estimate using 2SLS or is this effect already contained when adding both variables to the main regression?

The concrete example I was thinking was for tax collection and drug cartels in Mexico:

$$ collection = \beta_0 + \beta_1 cartel_{memebers}+ \beta_2 GDP{per \ capita} + u $$

Where the presence of drug cartels negatively affects GDP but cartels choose to settle on richer towns.

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    $\begingroup$ probably the first $u$ is not the same as the second error term $u$, right? $\endgroup$
    – Regio
    Commented May 9, 2019 at 22:12
  • $\begingroup$ Yeah, should be different erros. I've corrected it. $\endgroup$
    – Pablo Derbez
    Commented May 10, 2019 at 3:18
  • $\begingroup$ Do you know anything about $E[ux_1]$ and $E[ux_2]$? $\endgroup$
    – Bertrand
    Commented Oct 7, 2019 at 10:08

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In your concrete example, I think 2SLS is something worth considering because the error term u (of $y$, i.e. of tax collection) is plausible in theory to be affected by presence of cartels in ways that make it more unreliable in reporting (e.g. via increased corruption). Of course you can/should test this endogeneity.

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