Recursive system, OLS and Stata estimation

[Arjen Steiner]

Hello everyone, I replicate a study on migration and I would like to know how to correctly estimate the paper's equation system with Stata.

In fact, the insufficient information they give does not allow us to know which command we should use in order to perform the following operations correctly :


The system :

(1) M_i= β₀ + β₁D_i + β₂P_i + β₃E +εi

(2) H_i= β₀ + β₁M_i + β₂M_i *G_i + β₃E +εi

_{(3) GDPi}= β₀ + β₁M_i + β₂H_i + β₃R +ε_i

The additional informations are the following:

• "The three equation system is a recursive one, so there is no simultaneity bias."
• "Recursive one so there is no simultaneity bias"
• "we use OLS"

My question is: should I use sem or gsem command to estimate it, as it is a recursive system? (note that there is an interaction term in (2)).

They explicitly said that they use OLS:

- Shoud I use a simple OLS and put the predicted values of Mi & Hi in the next equations (2) & (3) ?
If so, is there a way to correct for the variance of the generated regressors?

I am confused regarding the right command to use, I will appreciate your precious help !

[Richard Williams]

You might link to the article you are citing. Anything we say will be speculation as to what the authors did.

I find it odd that the main effect of G is not included in model 2.

Based on what you say, I see no reason to substitute the predicted values.

They say they use OLS, so you should probably use OLS. Unless you think OLS is sub-optimal. In which case, you might use SEM.

In short, just from the info given, it sounds like you run 3 OLS regressions to replicate. Whether that is the optimal way, or whether you've fully described what the authors did, I don't know.

[Arjen Steiner]

Hi Mr Williams, thank very much you for your answer !

• Link: https://www.sciencedirect.com/scienc...jscEJlzXM#FN11

I think about 2sls because at point4.2 Specification issue (p 284), the talk about addressing the endogeneity of M_i by instrumenting it as other papers did. However, they not explicitly say that they use 2sls.

At point 4.3 Estimation results (p 285), the display their "equation system".