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

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

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

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.

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.