<p>In your concrete example, I think 2SLS is something worth considering because the error term <em>u</em> (of <span class="math-container">$y$</span>, 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 <a href="https://en.wikipedia.org/wiki/Endogeneity_(econometrics)" rel="nofollow noreferrer">endogeneity</a>.</p>

CC BY-SA 4.0
2019-05-09T22:42:47.457Z
2019-05-09T22:42:47.457Z
fantastic peace and prosperity
<p>For example, if I have an equation
<span class="math-container">$$
y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + u
$$</span></p>

<p>Where <span class="math-container">$x_1$</span> and <span class="math-container">$x_2$</span> are simultaneously determined, say</p>

<p><span class="math-container">$$
x_1 = \gamma_0 + \gamma_1 x_2 + \gamma_2 z_1 + e
$$</span></p>

<p><span class="math-container">$$
x_2 = \delta_0 + \delta_1 x_1 + \delta_2 z_2 + v
$$</span></p>

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

<p>The concrete example I was thinking was for tax collection and drug cartels in Mexico:</p>

<p><span class="math-container">$$
collection = \beta_0 + \beta_1 cartel_{memebers}+ \beta_2 GDP{per \  capita} + u
$$</span></p>

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

CC BY-SA 4.0
2019-05-09T22:12:43.647Z
probably the first $u$ is not the same as the second error term $u$, right?
Regio
CC BY-SA 4.0
2019-05-10T03:18:19.343Z
Yeah, should be different erros. I've corrected it.
Pablo Derbez
CC BY-SA 4.0
2019-10-07T10:08:19.470Z
Do you know anything about $E[ux_1]$ and $E[ux_2]$?
Bertrand
<econometrics>
Does it matter if there's simultaneous determination between two dependent variables?
Pablo Derbez
# Does it matter if there's simultaneous determination between two dependent variables?

(Asked by: username_0 on 2019-05-09)

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.

**Tags:** econometrics
> **Comments:**
> **username_1**: probably the first $u$ is not the same as the second error term $u$, right?  
> **username_0**: Yeah, should be different erros. I've corrected it.  
> **username_2**: Do you know anything about $E[ux_1]$ and $E[ux_2]$?  

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## 1 answers

### Answer by username_3 on 2019-05-09. Score: 1 | Accepted answer

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](https://en.wikipedia.org/wiki/Endogeneity_(econometrics)).


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