<p>I have  the following structural equations where <span class="math-container">$G,Z$</span> are endogenous and <span class="math-container">$X,Y$</span> are exogenous</p>

<p><span class="math-container">$$ G_d=B_0+B_1Z+B_2X+u_1\\
G_s=a_0 +a_1Z+a_2Y+u_2 \\
G_d=G_s
$$</span></p>

<p>Now, I would like to perform 2SLS, thus, I started off by obtaining the reduced-form equations</p>

<p><span class="math-container">$$
Z=c_1+c_2Y+c_3X+v_1 \\
G=d_1+d_2Y+d_3X+v_2
$$</span></p>

<p>Now how do I proceed to test for weak instruments? should I consider the overall F test for the two reduced form equations? or consider the individual t statistics?</p>

CC BY-SA 4.0
2020-03-28T11:47:27.237Z
There's no error term in the reduced form equations? Which equation are you estimating? Which variable is being instrumented?
Michael
CC BY-SA 4.0
2020-03-28T12:53:53.273Z
I just added the error term, I am following 2SLS estimation, whereby I would like to use an instrumental variable instead of Z.
Anna
CC BY-SA 4.0
2020-03-28T12:56:52.290Z
Z is the only endogenous variable on the RHS of the equation which will cause it be correlated with the error term leading to simulatenous equation bias. As a result, I need an instrument variable for Z which is usually the fitted values obtained from the reduced form equation. My problem is how to test whether the instrument variables are weak or not
Anna
<instrumental-variable>
Weak Instrument - Stock and Yogo
Anna
# Weak Instrument - Stock and Yogo

(Asked by: username_0 on 2020-03-28)

I have the following structural equations where $G,Z$ are endogenous and $X,Y$ are exogenous

$$ G\_d=B\_0+B\_1Z+B\_2X+u\_1\\
G\_s=a\_0 +a\_1Z+a\_2Y+u\_2 \\
G\_d=G\_s
$$

Now, I would like to perform 2SLS, thus, I started off by obtaining the reduced-form equations

$$
Z=c\_1+c\_2Y+c\_3X+v\_1 \\
G=d\_1+d\_2Y+d\_3X+v\_2
$$

Now how do I proceed to test for weak instruments? should I consider the overall F test for the two reduced form equations? or consider the individual t statistics?

**Tags:** instrumental-variable

> **Comments:**
> **username_1**: There's no error term in the reduced form equations? Which equation are you estimating? Which variable is being instrumented?  
> **username_0**: I just added the error term, I am following 2SLS estimation, whereby I would like to use an instrumental variable instead of Z.  
> **username_0**: Z is the only endogenous variable on the RHS of the equation which will cause it be correlated with the error term leading to simulatenous equation bias. As a result, I need an instrument variable for Z which is usually the fitted values obtained from the reduced form equation. My problem is how to test whether the instrument variables are weak or not  

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## 0 answers

