Instrumental-variables regression for multilevel mixed-effects models

[Sophie Dibbern]

Dear Statalist users,

I am working with multilevel data using the xtmixed command. I have observations nested in individuals (ID) nested in teams (TeamID). It is not panel data. My model has a quadratic term.

xtmixed DV IV IV2 || TeamID: || ID: , mle cov(unstr)

I am considering that my independent variable (IV) could be endogenous, which is why I would like to run an instrumental-variables regression. I have used the Two Stage Least Squares (2SLS)
approach before using the ivreg2 command in Stata. Following this approach, I would run the following:

ivreg2 DV IV IV2 (IV IV2 = Instrument Instrument2) , first endog(IV)

(any comment on whether I instrumented the quadratic term correctly is highly appreciated, too)

However, I suspect that my multilevel data violates assumptions of the estimator. The between-group variation in my data is quite high (ICC=0.29). So my question is: Is there any specific command in Stata to run an instrumental-variables regression with multilevel data? I would highly appreciate any advice.

[wbuchanan]

Assuming you don’t care as much about the team random effects, you could xtset your data on ID and use xtivreg which may allow you to correct the standard errors via cluster robust errors where you’d use the TeamID to define the clustering.

[Sophie Dibbern]

Thank you for your advice! I will try that. With "random effects", are you referring to random coefficients or slopes or both?

[wbuchanan]

I think xtivreg only includes random intercepts, but would definitely be best to consult the documentation. The only other potential option would be to fit your model using gsem. It would definitely provide much more flexibility with regards to the model itself, but will definitely require more work to specify exactly what you might want.

[Sophie Dibbern]

Thank you very much for your help. I used a likelihood ratio test to find out whether I need to run a random coefficient model instead of a random intercept model with my data. The estimates are not significantly different, so I would choose a random intercept over a random coefficient model. Thus, xtivreg appears a reasonable option. I will check the xtivreg documentation for more details..