IV regression help

#1
Hello everyone,

Im confused about endogeneity and how to approach this problem in a case of one equation and multiple equations that are jointly determined (simultaneous)

One equation

D = Endogenous, Z1 = instrument, E = error

Equation: Y = D + X2 + X3 + E
The first stage: D = Z1 + X2 + X3 + E
Reduced form: Y = Z1 + X2 + X3 + E

The first stage is OLS regression of endogneous on all exogenous and IV. It is used to check whether the IV a good instrument (high t-value). The fitted values are substituted in the second stage. I get this part.

Question 1: But: what does the reduced form tell us (in non-mathematical language)? What is the function of the reduced form?

simultaneous equation (2 equations)

For example supply and demand.

Demand equation: Qd = D1(price) + X2 + X3 + X4 + E
Supply equation: Qs = D1(price) + X2 + E
X3 does not appear in the supply equation (Use it as IV), hence supply is identified.

First stage: D1(price) = X3 + X4 + E
Reduced form: Qs = X3 + X4 + X2 + E
Question 2: is the first stage correctly specified?

Question 3: is the reduced form correctly specified?

In general, I do not know how to specify the model in case of simultaneous equations, like supply and demand. That is the reason for asking question 2 and 3.

If someone can explain the above I would really appreciate that!!

I posted this question on stackexchange to. But I get the feeling there are more people around here that can help. If I receive an answer on stackexchange I will post it here :)
 

hlsmith

Omega Contributor
#3
Are the Xs confounders of D and Y? So you are using Z to go further up stream to get past the confounding?


I have only ran locally average treatment effects before and simple mediation analyses, so I would help more if I could in regards to the modeling. I would imagine there are some good economics or social science YouTube videos out there on IVs. It may help if you draw out a graph showing the assumed relationships between variables and post it. We have one regular on this site that is familiar with SEM that may be able to help. If I see him around I will direct him to this post.


Thanks.
 
#4
To get past the confounding I use indeed the instrument Z1. The other Xs are not confounders, they are exogenous. In the SEM model X3 is used as IV and is exogenous. The other Xs are exogenous to. However, only the independent variable D is endogenous.
A graphical representation of the above is as follows:


The D variable is problematic in equation one and two.

I watched all the videos available on youtube and read a lot of papers. But it appears that the terms reduced form and first stage are used interchangeably. It makes it difficult to gasp this subject.

Thanks for your time and effort.