Panel Data & IV I have a panel data, and need to run an IV. I have only 1 endogenous variable. 
1) Should I use a Two-stage least squares or a GMM?
2) I understand that GMM is only for dynamic panel data. What is a dynamic panel data?
Thank you
 A: Answer 1: Should I use 2SLS or GMM?
To answer your first question a number of clarification should be made concerning the terminology


*

*The question "Shoud I use 2SLS or GMM" is not valid because 2SLS or IV estimation is essentially a special case of GMM! so there is no either or here.

*IV and 2SLS estimation is in principal the same, the only difference being that 2SLS allows us to deal with the case where there are more instruments than there are regressors in the original matrix $X$. In fact, 2SLS also encompasses the case in which the number of regressors to instrument and the number of instruments are the same, so one could loosely say that IV is really more the term of the general approach while 2SLS is the actual estimation method (first regress the endogenous variable on the instruments, and second run a regression of $y$ on all the fitted values)

*Therefore: if you have to "run an IV" it isn't a question of whether to use 2SLS or not. If you really have to use IV as you said, than 2SLS is basically what your statistical program would do anyway.


Answer 2: What is dynamic panel data?
The term dynamic panel data includes all methods, ideas and estimators related to the estimation of dynamic relationships in the framework of a panel data analysis. So "What is dynamic panel data" is not that easy to answer unless you get more specific. Although its hard to tell without any more information I am guessing that in your case you you dont need dynamic panel data estimators since -- so i understand -- you just want to use IV since you have an endogeneity problem and fixed effects would be to costly in terms of efficiency losses.
I think the confusion probably arose because in a panel data context GMM is usually only mentioned in relation to dynamic panel data estimators such as the Arellano Bond or Arellano Bover-type estimators. So to be clear then: despite the fact that the term GMM is mostly used in the dynamic panel data framework it is not something that is intrinsically dynamic. 
I hope this helps to clarify some of the misunderstandings.
Kind regards
A: I think Manuel's answer is overall useful but wrong in stating that it is not easy to answer what dynamic panel data models are. This is relatively simple. Dynamic panel models are models where lags of the outcome variable are included amongst the explanatory variables.
For example:
$$F_{i,t} = aF_{i,t-1} + Bx_{i,t} + u_{i,t}$$
is a dynamic panel model because F appears on the left hand side and a lag of it appears on the right.
