Is Simultaneous Equation Model (SEM) a Right Approach When the Two Equations Have the Same Independent Variables?

[Ryan Kim]

Hi,

I was wondering whether I should fit my models in SEM or not.
My models look like below:

(Price)it = (DD)it + (Product_Reviews)it + (Product_Rating)it + (Seller_Reviews)it + (Product_Characteristics_as_Control_Vars)i + (Product Fixed Effects)i + (Time Fixed Effects)t + eit
(Demand)it= (Price)it + (DD)it + (Product_Reviews)it + (Product_Rating)it + (Seller_Reviews)it + (Product_Characteristics_as_Control_Vars)i + (Product Fixed Effects)i + (Time Fixed Effects)t + eit

Where
DD refers the difference-in-difference(DD) interactions (post-treat*treated). My models have staggered DD where treatment occurs at multiple time periods.
Product_Reviews & Seller_Reviews are the number of reviews
Product_Rating is the rating from 1 to 5 by 0.5 scale.

To simply put, I'm trying to look at the effects of DD on Price and the effects of DD on Demand (Please understand that I can't disclose what my DD is yet).

However, one of the reviews I'd received was that I needed to put Demand Var as one of the independent variables in the 1st equation and set the models as SEM.

After I searched SEM and studied about it, I noticed that the right hand side of the two models should have different set of independent variables. For example, I can use one independent var that is not shown in the 1st model but shows in the 2nd model as an instrument (IV) for the endogenous var (If I set my models as SEM, then the endogenous var is going to be Demand var in this case) in the 1st model and vice versa.

But in my case, I just intended to measure the effect of DD on two different outcome variables (Price & Demand) and I thought all the variables (reviews, rating, and other control vars) may affect price and demand so I include the same set of independent vars on both of the equations.

My Questions are:
1. Do I really need to use SEM approach?
2. If so, which vars should I include or exclude from each model given that those vars are all I have.
3. If not, what would be the good arguments to say that I do not need SEM?

I tried to find out the answers for these questions but I couldn't.
All I've found was that this is an example of SEM setting and how to address simultaneity in SEM (2SLS or 3SLS)..
Could anyone please help me out? I would be greatly appreciated.

[Jenny Williams]

Hi,

I'm not sure you "have" to do either. It depends on your research question.

If you're just interested in looking at the effect of your independent variables on each of the two outcomes then you might be interested in multivariate modelling which you can do with mvreg, sureg or SEM. See Stata 13 help manual, entry "Structural models 11: Multivariate regression", for example. For this question, you don't have to do SEM, or even multivariate regression. You can just run the separate outcome models and it will give you the same point estimate. However, the added value of SEM or multivariate modelling is to allow for cross model testing of equality of coefficients.

Or, it sounds like the reviewer was asking you to include demand as an independent variable for the price equation? If so, then you're looking at a mediation model, which you can do in SEM.

But these are for two very different research questions and you need to decide which is most appropriate.