# Does it matter if there's simultaneous determination between two dependent variables?

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.

• probably the first $u$ is not the same as the second error term $u$, right? – Regio May 9 '19 at 22:12
• Yeah, should be different erros. I've corrected it. – Pablo Derbez May 10 '19 at 3:18
• Do you know anything about $E[ux_1]$ and $E[ux_2]$? – Bertrand Oct 7 '19 at 10:08

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.