I have 25 quarterly observations and I want to estimate price elasticity of demand. I intented to use GMM-IV estimator. However, I read that it is not good for small samples. What can you suggest me? Please keep in mind that I am not econometrician by profession.
Unfortunately for your case all GMM estimators suffer from finite sample bias. In the presence of an endogenous explanatory variable the GMM estimator is only consistent.
There's not much you can do to remedy this issue, except collect more data. Check for consistency of sign and magnitude of estimates between OLS and GMM, as well as sensitivity to instrument choice (if your model is over-identified).
Price elasticity of demand is computed as follows:
Percent Change in Quantity Demanded (Qd) / Percent Change in Price (P)
Say you have price and demand quantity data from two years (t=1,2). To calculate change in Q demanded you would do the following:
[(Qd in t=2)-(Qd in t=1)] / (Qd in t=1)
The process is the same for price (substitute P for Qd above).
Elasticity may be calculated for other variables as well; not just price and demand. For example, if you wanted to see how a 1% change in IQ affects the relative change in a student's GRE score you could. This is done by messing with logs and regression functions.
Hopefully this helps you out a bit.