Endogeneity from dep. variable in a multilevel model

[Doris Rivera]

Dear Statalist, I have a panel data of firm-year for which I know the region each firm belong to, therefore, I study how a regional characteristic relates with firm’s innovation using a multilevel approach. However, I have received a strong recommendation for including into the model a dynamic structure, that is, including the dependent variable lagged as a firm-level characteristic into the model. I am aware of these models for panel data (Arellano-Bond model, or Arellano-Bover, or Blundell-Bond estimator in order to control for the endogeneity coming ffrom this inclusion).

I am wondering if there is any way to perform such a dynamic model in a three-level Logit multilevel analysis. I can imagine that just including the dependent variable lagged in my model, without further corrections will imply a serious endogeneity problem. My main model is logit model:

melogit y L.x1 L.x2  L.mn_x1 L.mn_x2 i.year i.sector mn_z1 mn_z2 if year>=2008 ||region: ||firm: , or vce(robust) intpoints(15)

Here mn_z1 is the regional variable of interest, while the rest are regional- and firm-level controls (I also include Mundlak approach for firm-level for avoiding endogeneity with firm's heterogeneity).

Can you give me some references or point me to the right command I should use?

Any help will be much appreciated!

[Doris Rivera]

I really don't remember having read anything about Multilevel model (3 levels in fact) using the correction for including the lagged dependent variable as a regressor. This is something we see in panel data only (two level e.g., firm-year). Maybe you know about a possible way to address this? That would be really helpful.

The model I am working with is:

 
 melogit y L.x1 L.x2  L.mn_x1 L.mn_x2 i.year i.sector mn_z1 mn_z2 if year>=2008 ||region: ||firm: , or vce(robust) intpoints(15)

While the recommendation I received was:

 
 melogit y L.y L.x1 L.x2  L.mn_x1 L.mn_x2 i.year i.sector mn_z1 mn_z2 if year>=2008 ||region: ||firm: , or vce(robust) intpoints(15)

So, my question would be, if there is any way for correcting for the endogeneity coming from the inclusion of the lagged dep. variable as a regressor in this 3-level model.