Seeking Advice on Models for Controlling Lagged Dependent Variables in Panel Data

[Cooper Felix]

Hi All,

I'm working with panel data and looking for model suggestions to control for lagged dependent variables. Currently, I'm considering dynamic panel data models such as xtabond2 (given some potential variables of interest are either predetermined or endogenous) but am open to other effective alternatives. My understanding is that directly including the lagged dependent variable into a panel fixed effects model such as "xtreg, fe" is incorrect. Would appreciate any insights or experiences on suitable models and key considerations for this kind of analysis.

[Sebastian Kripfganz]

Unless your time dimension is very large, adding a lagged dependent variable yields biased estimates with the conventional fixed-effects (or random-effects) estimator. Alternatives include the following:

• xtdpdqml: Quasi-maximum likelihood estimation of linear dynamic panel data models
• xtdpdbc: Bias-corrected estimation of linear dynamic panel data models
• xtdpdgmm: Generalized method of moments estimation of linear dynamic panel data models

The first two approaches require that your regressors (aside from the lagged dependent variable) are strictly exogenous. This is the same requirement as for the conventional fixed-effects estimator, but it can often be hard to justify. The third approach is very flexible as it allows for endogeneity of any of the regressors, but it tends to require larger sample sizes for reliable inference due to potential weakness of the instruments. Note that xtdpdgmm is an alternative to xtabond2, which is more flexible and (in my opinion) offers a more intuitive syntax. (Also have a look at the xtdpdgmmfe command, which is part of the same package.) The following presentation might be helpful as well:

• Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference.

In any case, it is indispensable to get a good methodological understanding of the respective methods before using them.