m2 statistic (Arellano and Bond 1991)

[Prateek Bedi]

Hi,

I recently came across a test for serial correlation for dynamic panel models in this video: https://youtu.be/A2B5kJFLTXU?list=PL...6Rce7dK&t=1748

I would like to know if this test can be performed in Stata and if yes, how?

Thanks

[Sebastian Kripfganz]

This is just the familiar Arellano-Bond AR(2) test that is reported as a postestimation result by any of the GMM commands for linear dynamic panel model estimation.

[Prateek Bedi]

Thanks a lot Sebastian Kripfganz!

[Prateek Bedi]

I would also like to know how can we statistically check that our dependent variable depends on its own lag before applying dynamic panel (or is it just a theoretical call?). I ask this also because we are required to specify lag structure of dependent variable (and for independent variables as well) in GMM panel estimations. So how do we statistically prove whether dependent variable is an AR(1) process or AR(2) process and so on. This can help me to justify the application of dynamic panel instead of FE model.

[Sebastian Kripfganz]

You can estimate a model with an AR(1) or AR(2) structure and check whether the respective coefficients are statistically significant.

If you are estimating a static FE model first, you can check for residual serial correlation as a hint for potentially omitted dynamics. See the community-contributed Stata command xtserial.

[Prateek Bedi]

I performed FE and xtserial showed presence of high serial correlation in the error term. I have the following questions:

1. If the error term is serially correlated, can we confidently conclude that our dependent variable is autoregressive? Is there no other potential cause of this serial correlation other than absence of a lagged dependent variable term in our model?
2. How do I estimate an AR(1) or AR(2) model for a panel data set? I know how to do it for time series but l am not able to comprehend intuitively the mechanics of an AR model in panel framework. Basically, I have 700 cross-sectional units (firms) and 16 years of data (I have an unbalanced panel though). Is the coefficient averaged across cross-sectional units (firms) and then reported? Please guide me how to do this in STATA.

Thanks

[Sebastian Kripfganz]

1. There could be many kinds of model misspecification that yield a serially correlated error term. An omitted lagged dependent variable is just one possibility. Similarly, it could be omitted lags of the regressors, other omitted variables, an incorrect functional form, ...

2. Not sure what you want to do. A panel AR(1) model with homogeneous coefficient would just be a dynamic panel model with a lagged dependent variable. In the AR(2) case, you add the second lag of the dependent variable. With 16 time periods, you cannot really estimate separate time series models for each firm.