<p>I don't think you need anything like a 3SLS. Just run the first stage for the two endogenous variables separately:</p>

<p>$$\tilde{X}=\alpha_1+\beta_1X'+\beta_2Y'+\beta_3C+\epsilon$$
$$\tilde{Y}=\kappa_1+\gamma_1X'+\gamma_2Y'+\gamma_3C+\delta$$</p>

<p>Then run a regression of Z on the predicted value of $\tilde{X}$, $\tilde{Y}$ as and $C$. If the assumptions are all satisfied, this should give a consistent estimate of the coefficients.</p>

<p>I also found this thread online. It might be helpful.
<a href="https://www.stata.com/statalist/archive/2012-08/msg01238.html" rel="nofollow noreferrer">https://www.stata.com/statalist/archive/2012-08/msg01238.html</a> </p>

CC BY-SA 4.0
2021-05-24T18:10:58.690Z
I have a related question; https://stats.stackexchange.com/questions/525706/if-i-have-two-endogenous-variables-for-which-i-each-have-an-instrument-do-i-abs?noredirect=1#comment967613_525706 Would you have any idea?
Tom
CC BY-SA 4.0
2018-08-16T08:35:42.523Z
2018-08-16T08:35:42.523Z
displayname2
<p>I have a model $Z = \alpha X + \beta Y + \gamma C + \epsilon$. I am interested in the relative effects of $X$ and $Y$ on $Z$. However, $X$ and $Y$ are endogenous. I have identified two instruments $X'$ and $Y'$ respectively. $C$ is an exogenous control variable (fixed effect). </p>

<p>How do I go about estimating the model with these two instruments for the two endogenous variables? Do I need to use 3SLS? I am fairly new to this field. Any resources that address this would be very helpful, thank you. </p>

CC BY-SA 4.0
2018-08-16T14:49:30.420Z
No need for 3sls, you can just run 2sls as you normally would.
BB King
<econometrics>
Two Endogenous Variables and Two Instruments
esperanto
# Two Endogenous Variables and Two Instruments

(Asked by: username_0 on 2018-08-13)

I have a model $Z = \alpha X + \beta Y + \gamma C + \epsilon$. I am interested in the relative effects of $X$ and $Y$ on $Z$. However, $X$ and $Y$ are endogenous. I have identified two instruments $X'$ and $Y'$ respectively. $C$ is an exogenous control variable (fixed effect).

How do I go about estimating the model with these two instruments for the two endogenous variables? Do I need to use 3SLS? I am fairly new to this field. Any resources that address this would be very helpful, thank you.

**Tags:** econometrics
> **Comments:**
> **username_1**: No need for 3sls, you can just run 2sls as you normally would.  

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## 1 answers

### Answer by username_2 on 2018-08-16. Score: 4 | Accepted answer

I don't think you need anything like a 3SLS. Just run the first stage for the two endogenous variables separately:

$$\tilde{X}=\alpha\_1+\beta\_1X'+\beta\_2Y'+\beta\_3C+\epsilon$$
$$\tilde{Y}=\kappa\_1+\gamma\_1X'+\gamma\_2Y'+\gamma\_3C+\delta$$

Then run a regression of Z on the predicted value of $\tilde{X}$, $\tilde{Y}$ as and $C$. If the assumptions are all satisfied, this should give a consistent estimate of the coefficients.

I also found this thread online. It might be helpful.
<https://www.stata.com/statalist/archive/2012-08/msg01238.html>

> **Comments:**
> **username_3**: I have a related question; https://stats.stackexchange.com/questions/525706/if-i-have-two-endogenous-variables-for-which-i-each-have-an-instrument-do-i-abs?noredirect=1#comment967613_525706 Would you have any idea?  

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