<p>If you have endogeneity between a dependent variable and error term the use of Instrument variables are the way to go.</p>

<p>as long as $\mathbf{COV}(x_1,z_1)\ne0,\mathbf{COV}(x_2,z_2)\ne0,\mathbf{COV}(z_2,e)=0$ and $\mathbf{COV}(z_1,e)=0$ you can do so.</p>

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2017-11-16T22:46:20.150Z
Isn't it also required that $z_1,z_2$ are uncorrelated with $X_{other}$?
Adam Bailey
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2017-11-17T01:16:09.707Z
@AdamBailey the issue is _perfect_ multicollinearity. as long as the correlation between all combinations of $z_1,z_2$  and $X_{other}$ are not 1 or -1, its good.
https://en.wikipedia.org/wiki/Multicollinearity#Definition
EconJohn
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2017-11-17T02:03:24.453Z
@EconJohn I think you meant to say COV(z2,e)=0 whereas you said COV(z1,e)=0 twice. Also more generally you could allow for Cov(x1, z2)≠0 and Cov(x2, z1)≠0. The point is as long as there are as many instruments that are informative as there are variables that are endogenous (ie the rank condition)
Andrew M
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2017-11-17T03:25:20.600Z
@AndrewM you are correct.  edited
EconJohn
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2017-11-17T14:25:29.860Z
Thanks @EconJohn for your time.  what is your comments on "**Models with multiple endogenous variables are indeed hard to identify and the results can be hard to interpret.

So we don’t usually like to see them – for one thing it’s not clear why you’re tackling two causal questions at the same time; one is hard enough.**" from http://www.mostlyharmlesseconometrics.com/2010/02/multiple-endogenous-variables-what-now/
Max Shang
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2017-11-17T15:12:03.087Z
@MaxShang  The blog post is valid. However if you have strong instruments, I don;t think it should be an issue with using more than one.
EconJohn
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2017-11-17T20:07:01.707Z
@EconJohn Thanks again for your time. I really appreciate your help.
Max Shang
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2017-11-16T18:56:41.400Z
2017-11-17T03:24:45.857Z
2017-11-17T03:24:45.857Z
EconJohn
<p>Can you use two instrumental variables $z_1$ and $z_2$ at the same time for $x_1$ and $x_2$, in the following regression model</p>

<p>$y=a+bx_1+cx_2+dX_{other}+e$, where</p>

<p>$y$ is the explained variable,</p>

<p>$x_1$ and $x_2$ are two variables of interest that you want to study but are endogenous,</p>

<p>$X_{other}$ are other exogenous control variables,</p>

<p>$e$ is the error term.</p>

CC BY-SA 3.0
2017-11-17T02:21:30.793Z
Yes. In that case, technically, the instrumental variables are $z_1$, $z_2$ and $X_{other}$. The exogeneity requirement is clear. The relevance condition is more complicated when there are multiple (in your case, two) endogenous regressors. See `help ivregress_postestimation` (`estat firststage`) of Stata.
chan1142
<econometrics><instrumental-variable>
Can you use more than one instrumental variables in an Econometric model?
Max Shang
# Can you use more than one instrumental variables in an Econometric model?

(Asked by: username_0 on 2017-11-16)

Can you use two instrumental variables $z\_1$ and $z\_2$ at the same time for $x\_1$ and $x\_2$, in the following regression model

$y=a+bx\_1+cx\_2+dX\_{other}+e$, where

$y$ is the explained variable,

$x\_1$ and $x\_2$ are two variables of interest that you want to study but are endogenous,

$X\_{other}$ are other exogenous control variables,

$e$ is the error term.

**Tags:** econometrics, instrumental-variable

> **Comments:**
> **username_1**: Yes. In that case, technically, the instrumental variables are $z_1$, $z_2$ and $X_{other}$. The exogeneity requirement is clear. The relevance condition is more complicated when there are multiple (in your case, two) endogenous regressors. See `help ivregress_postestimation` (`estat firststage`) of Stata.  

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## 1 answers

### Answer by username_2 on 2017-11-16. Score: 4 | Accepted answer

If you have endogeneity between a dependent variable and error term the use of Instrument variables are the way to go.

as long as $\mathbf{COV}(x\_1,z\_1)\ne0,\mathbf{COV}(x\_2,z\_2)\ne0,\mathbf{COV}(z\_2,e)=0$ and $\mathbf{COV}(z\_1,e)=0$ you can do so.

> **Comments:**
> **username_3**: Isn't it also required that $z_1,z_2$ are uncorrelated with $X_{other}$?  
> **username_2**: @username_3 the issue is _perfect_ multicollinearity. as long as the correlation between all combinations of $z_1,z_2$  and $X_{other}$ are not 1 or -1, its good. https://en.wikipedia.org/wiki/Multicollinearity#Definition  
> **username_4**: @username_2 I think you meant to say COV(z2,e)=0 whereas you said COV(z1,e)=0 twice. Also more generally you could allow for Cov(x1, z2)≠0 and Cov(x2, z1)≠0. The point is as long as there are as many instruments that are informative as there are variables that are endogenous (ie the rank condition)  
> **username_2**: @username_4 you are correct.  edited  
> **username_0**: Thanks @username_2 for your time.  what is your comments on "**Models with multiple endogenous variables are indeed hard to identify and the results can be hard to interpret.  So we don’t usually like to see them – for one thing it’s not clear why you’re tackling two causal questions at the same time; one is hard enough.**" from http://www.mostlyharmlesseconometrics.com/2010/02/multiple-endogenous-variables-what-now/  
> **username_2**: @username_0  The blog post is valid. However if you have strong instruments, I don;t think it should be an issue with using more than one.  
> **username_0**: @username_2 Thanks again for your time. I really appreciate your help.  

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