xtabond2 without the lagged dependent variable

[Maria Reyes Retana]

Hello fellow statalists, I need your help.

I am currently working on my thesis and I am using the system GMM, with the comand xtabond2 in Stata15.1. I am using these method because I have a case with small T large N case, T= 7 and N = 32 ( I know is not that large). The dependent variable is GDP per capita, the principal explanatory variables are development in telecommunications sector including mobile, fixed and internet, I add some other control variables identified by economic theory, primary enrollment rate, ,exports and investment.
After reading the paper How to do xtabond2: An introducttion to difference and system GMM in Stata by Roodman I was able to perform xtabond2 but I have a few questions.

I am implementing the command as follows:

xtabond2 LOGPIBPCIM INT MOV FIJ PRIM LABIM EXPIM IEDIM, gmmstyle(L.LOGPIBPCIM, collapse laglimits(1 3) eq(level)) gmmstyle(L.MOV, laglimits(1 3) collapse eq(level)) gmmstyle(L.INT, laglimits(1 3) collaprse eq(level)) gmmstyle(L.FIJ, laglimits(1 3) collapse eq(level)) ivstyle(PRIM EXPIM LABIM IEDIM, equation (level)) robust noconstant

LOGPIBPCIM is the log of GDP per capita, INT MOV FIJ are my main variabes and LABIM EXPIM IEDIM are control variables.
I copy here my results as an image:

As you can see I am not ussing the lagged dependent variable as a regressor just as a gmm style instrument, I want to know if this practice is valid. I have a lot of reasons to use this method and when I add the lagged dependent variable as a regressor the hansen test goes to .002 and AR2 test to .012, added to this the signs of the main and control variables are not in line with the economic literature and without the dependent variable as a regressor my signs and coefficients are as expected and to the best of my knowledge the hansen and AR2 test indicate that my instruments are valid.

Please feel free to comment on any other irregularities you see, or suggestions they will be very appreciated.

Thanks in advance, María Reyes Retana

References
Roodman, David, "A Note on the Theme of Too Many Instruments." Oxford Bulletin of Economics and Statistics, (2009):135-158.
Roodman, David, “How to do xtabond2: An introducttion to difference and system GMM in Stata.” The Stata Journal 9, No.1 (2009): 86-136.

[Sebastian Kripfganz]

The insignificance of the AR1 test for no serial correlation in the first-differenced errors indicates that there is strong serial correlation in the level errors which in turn is a sign of model misspecification.

You are comparing two different models here. If economic theory tells you that you should include a lagged dependent variable (as in the literature on economic convergence), then leaving out the lagged dependent variable would potentially introduce a bias. At least, the interpretation of your coefficients changes.

It is not a question of how to estimate the model, but of how to specify the model correctly in the first place. It still could be that a static model is appropriate for your research question, but this should in general be an ex ante decision before you run the estimations.

That said, I wonder why you are still including the lagged dependent variable in the set of instruments after removing it from the set of regressors.

After all, a problem with your (dynamic) specification might just be that your number of instruments (despite being small in absolute terms) is relative large in comparison to your very small sample size. You may not want to use GMM-type instruments for the other regressors. Essentially, you are assuming that all of your regressors are endogenous. While in theory it is possible to instrument all of them, in practice that hardly ever yields reasonable results (in particular in small samples). You are demanding too much from your data and would be better off imposing some stronger assumptions about the exogeneity of your regressors (besides the lagged dependent variable).

[Maria Reyes Retana]

Thank you very much for you answer, I understand my problem now. The other problem is that my 3 vairable of interest are consider endogenous in almost every study I have read. I will remove the lagged dependent variable of the set of instruments but after that I do not know how to proceed. Do you have any kind of advice about a correct form to specify the model correctly using this method because since my T is very small using another econometric method like fixed effect would yield inconsistent results.

Thank you again for your very helpful answer.

[Hamid muili]

Sebastian Kripfganz , I am using xtabond command for system gmm, however, the Ar(1) test shows significance at 1% but the lags of dependent variable is not significant at any level, what could be the possible reason for this

[Sebastian Kripfganz]

The AR(1) is expected to be significant if there is no serial correlation in the idiosyncratic level errors. The AR(2) should not be significant.