OK to include lagged DV as a control?

[Franz Hopp]

Hello,

I was wondering whether it is OK to include a lagged DV as a control?

In the current project we are working on, we believe that a certain firm_strategy affects firm_performance. But we have a reverse causality problem, and fear that our DV firm_performance might influence our independent variable firm_strategy.

We do plan to conduct a 2SLS regression at a later point in the paper. I am sure that only a 2SLS can really address the problem of reverse causality.

• But for several reasons, we prefer to have a simple Fixed Effects regression in the main Data/Findings section of our paper.
• So in the beginning of the paper, in the main Data/Findings section, we plan to report the results from a simple FE regression. And later on, at the end of the paper in a separate "Robustness Check" section, we plan to report 2SLS results
• Now, for the main Data/Findings section section in the beginning of the paper (where we don't have 2SLS, but only FE regression) we are of course left with the problem of reverse causality:
  • We could do "nothing" here (and just say that later on we provide additional results from 2SLS in a robustness check section. And leave the FE results as they are in the beginning of the paper.). But I am sure that reviewers might be a bit unhappy about this.
  • So instead, we plan to address reverse causality in the main Data/Findings section of the paper by including the lagged DV firm_performance as a control variable.

So in this context, we are wondering about the following question: Is it just OK to include the lagged DV as a control variable in a regression specification? Or could this lead to some problems? E.g. could including the lagged DV as a control lead to endogeneity problems of some sort?

Thank you so much in advance!

Franz

[Sebastian Kripfganz]

A lagged dependent variable in a fixed-effects model is correlated by construction with the unobserved fixed effects. This correlation is a decreasing function of the number of time periods. So, if you are having a reasonably large time horizon in your sample, you might be fine. Otherwise, you will have to look into the literature on the estimation of fixed-T dynamic panel data models. Potential estimators include GMM and ML:

• XTDPDGMM: new Stata command for efficient GMM estimation of linear (dynamic) panel models
• XTDPDQML: new Stata command for quasi-maximum likelihood estimation of linear dynamic panel models

among others.