# Two Endogenous Variables and Two Instruments

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.

• No need for 3sls, you can just run 2sls as you normally would. – BB King Aug 16 '18 at 14:49

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