About the Arellano-Bond test for autocorrelation

[Hoang Luong]

Dear all,
I'm working on a project about innovation and market concentration.
I'm using GMM with the command xtabond2 to estimate the model of R&D expenditures on market concentration and some corporate governance variables at firm level (T = 9, N = 10022)
The table of results can be seen in attached file.
I have two questions:
_ About the robust standard error: it is proved that two-step GMM standard errors are already robust, but in the paper "How to do xtabond2", in the example page 127, the authors still applied robust standard error for two-step GMM. So I'm wondering whether I should add robust standard error in two-step GMM (because with my case when I use both options "small" and "robust", the results will change completely and not significant anymore in comparison with the good results if applied only "small" option).
_ The second question is about Arellano-Bond test for autocorrelation: as you can see in the table of results, I cannot reject the no autocorrelation null hypotheses for both AR(1) and AR(2), but the lag 1 of dependent variable is obviously very important and should be added in the model. So can anyone explain to me why I get this wrong test result and do i need to really care about it or how to solve it?

Thank you very much for reading and all contributions are appreciated.
Hoang Luong

[Eric de Souza]

Look carefully at your output. You have effectively 204 observations only divided over 116 groups. This gives you1.76 observations per group on average. Some groups have 5 effective observations and others only one. Probably a number of groups have dropped out. This means that your results are not reliable. Examine your data carefully.

[Hoang Luong]

Dear Eric!
Thank you very much Sir for you advice. I'm still in the cleaning and considering step with my dataset, so of course I will take more time to look and investigate it, and try to improve the number of obs and groups as much as possible.
How about the two question that I've raised. Do you have any idea of when should I apply the robust standard error to two-step GMM and how to solve the unexpected wrong results of Arellano-Bond test for autocorrelation?
Any other contributions will be appreciated Sir.

Hoang Luong

[Eric de Souza]

1. From D. Roodman, How to do xtabond2, The Stata Journal (2009) 9, Number 1, pp. 86–136:
robust triggers the Windmeijer finite-sample correction to the reported standard errors in two-step estimation, without which those standard errors tend to be severely downward biased.

2. What the AR(1) test is telling you is that the (idiosyncratic) residuals in first differences are not serially correlated. Therefore, the residuals themselves are serially correlated. This invalidates the model. This result could come from (I) insufficient lags [AR residuals] or from (ii) instruments that have not been lagged enough [MA residuals] You would need a not too small number of observations for each n to try and correct for this

[David Roodman]

Eric's first point is right, but I think not the second. As for the first, yes, the two-step standard errors are already robust, but that is a statement about what happens as the sample size goes to infinity. In practice, they are often biased. As for the second, you should ignore the "AR(1)" test because if the residuals are uncorrelated, we expect their first differences to be correlated, and so that's not interesting. The "AR(2)" test is suggesting that you errors are serially correlated or order 1, and this is a cause for concern, as I discuss the xtabond2 paper and help file.
Note also that this regression has 1 instrument for every two observations, which is way too high, so you'll need to reduce that. See my paper, "A Note on the Theme of Too Many Instruments."
--David

[Eric de Souza]

David:

As for the second, you should ignore the "AR(1)" test because if the residuals are uncorrelated, we expect their first differences to be correlated, and so that's not interesting

You are, of course, right. The important test is the AB AR(2) test or the m2 test as they call it.

[Hoang Luong]

Dear Eric and David!
Thank both of you very much for these clear answers and explanations. I really appreciate your help.

Hoang Luong