I don't remember the literature or the GMM method clearly but to use GMM T needs to be at least 3. You can also use GMM when you have a long T and small N but this may cause problems due to presence of many instrumental variables. But if T is very large for example 20, 30 or more and N is smaller I think you can or it may be better to use panel time series techniques.
A good solution is to apply the Bootstrap Method generally used for estimation in finite samples.
Could work well depending on the exact problem! Here is the code. http://www.mathworks.com/matlabcentral/fileexchange/12114-gmm
Generalized method of moments
From Wikipedia, the free encyclopedia
In econometrics, the generalized method of moments (GMM) is a generic method for estimating parameters in statistical models. Usually it is applied in the context of semiparametric models, where the parameter of interest is finite-dimensional, whereas the full shape of the distribution function of the data may not be known, and therefore maximum likelihood estimation is not applicable.
The method requires that a certain number of moment conditions were specified for the model. These moment conditions are functions of the model parameters and the data, such that their expectation is zero at the true values of the parameters. The GMM method then minimizes a certain norm of the sample averages of the moment conditions.
The GMM estimators are known to be consistent, asymptotically normal, and efficient in the class of all estimators that don’t use any extra information aside from that contained in the moment conditions.
GMM was developed by Lars Peter Hansen in 1982 as a generalization of the method of moments which was introduced by Karl Pearsonin 1894. Hansen shared the 2013 Nobel Prize in Economics in part for this work.
if your data's time dimension is large enough to test time series properties of panel data, surely you can use unit root test, cointegration tests and cointegration estimators for research long run relationships of variables. Those are also dynamic panel data methods as well.
You may want to use a different approach from GMM. For example the SEM-ML (Allison, Moral-Benito among others). It performs fantastically with dynamic panel data when the endogenous regressors are supposed to be normally distributed. But it is superior to the GMM approaches (xtabond in Stata) even in small samples. The command is xtdpdml. Easy to use and simpler to code compared to the SEM (Stata 13 and later versions).
The command has been presented in February 2018.
You should use the least squares dummy variables bias corrected... the code is xtlsdvc in stata software! 😁
Dear Researchers/Professors
my n=5 and t=30
i first check the stationarity of the data. on the basis of stationarity test results
i applied ARDL. Is it the correct method? I also want to know that can i use fixed effect and random effect for this type of data or not?
Can anyone suggest me an econometric book for dealing with this different nature of panel data
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