What are the statistical reasons of choosing between a static and dynamic panel data model?

[Olaf Hotte]

Dear all,

I would like to know more about the relation between serial correlation/autocorrelation and static vs. dynamic panel data models to decide between a static or dynamic model.

Currently, I am analyzing an unbalanced panel data set with individual and time fixed effects. Based on the theory, I do not have strong reasons to apply dynamic panel models (e.g. lagged dependent variable / Arellano-Bond estimator). However, I would like to exclude the possibility of misspecification/inconsistency/ inefficiency.

Because serial correlation in linear panel-data models biases the standard errors and causes the results to be less efficient, researchers need to identify serial correlation in the idiosyncratic error term in a panel-data model. If serial correlation is present, the model is inefficient and I need to correct a least my standard error that is robust to serial correlation.

• If serial correlation IS present, under which circumstances is a dynamic panel model (e.g. Arellano-Bond estimator) more appropriate than just correcting the standard errors?
• If serial correlation IS NOT present, does this confirm my assumption of static panel data?

Correcting the standard error will increase efficiency. What is about consistency?

• What are statistical reasons to add the lagged dependent variable?
• If I have a dynamic process and leave out the lagged dependent variable, would I expect autocorrelation of my error?
• If I add the lagged dependent variable to my fixed-effect model and the coefficient does/does not get significant, what does it tell me?

Best regards, Olaf

[Sebastian Kripfganz]

• If serial correlation IS present, under which circumstances is a dynamic panel model (e.g. Arellano-Bond estimator) more appropriate than just correcting the standard errors?

The question to be asked is: What is the underlying reason for the serial correlation? If your theory does not suggest that there are neglected dynamics, then a dynamic model would not do the job for you. After all, you want to estimate a model that aligns well with your theory to be able to interpret the coefficients accordingly.

• If serial correlation IS NOT present, does this confirm my assumption of static panel data?

Statistically speaking, you cannot "confirm" an assumption. All you can hope for is not the reject an assumption. With that in mind, yes, no serial correlation can be seen as supportive evidence in favor of a static model.

Correcting the standard error will increase efficiency. What is about consistency?

It depends. If you are using the fixed-effects estimator, you need to assume that all variables are strictly exogenous. Strict exogeneity implies that serial correlation does not affect consistency. If you are using instrumental variables (similar to dynamic panel data GMM) because some of your variables are predetermined or endogenous, then serial correlation might invalidate your instruments and cause inconsistency.

• What are statistical reasons to add the lagged dependent variable?

Reasons should be primarily theoretical. Statistical evidence of serial correlation can be a reason to estimate a dynamic model if there is as well a theoretical justification for it (e.g. imperfect adjustment processes, habit formation).

• If I have a dynamic process and leave out the lagged dependent variable, would I expect autocorrelation of my error?

Usually yes.

• If I add the lagged dependent variable to my fixed-effect model and the coefficient does/does not get significant, what does it tell me?

Assuming that you are estimating this model by GMM or any other consistent estimator for dynamic panel models, an insignificant AR coefficient would provide evidence that a static model might be sufficient.

[Olaf Hotte]

You are my hero! Thank you so much for your very detailed and clear explanations. They help me a lot.