st: Dynamic panel data with very short panels

["Sebastian van Baal" <s.vanbaal@arcor.de>]

Dear Stata List Users: 
 
I have a problem involving dynamic panel data and I hope that you can point
me in the right direction. My panels are very short and therefore, I am
unsure if I can use the typically recommended approaches. 
 
I am trying to estimate a model of the following type: 
 
y[it] = ay[i,t-1] + bx[it]
 
The index i corresponds to about 2,000 subject sessions (my data are
experimental) and t (= 1,2,...T) are discrete points in time. The horizon T
differs by subject session, so my panel is unbalanced. There is serial
correlation in the residuals within subject sessions. 
 
The model appears to be a standard problem often dealt with in the
literature on panel data analysis. Due to the lagged dependend variable on
the right-hand side, simple estimators are regarded as inconsistent, so an
alternative approach is needed. In the literature, IV-estimators (and
GMM-estimators) are mentioned. In Stata, the corresponding commands are
xtabond, xtdpdsys and xtdpd. 
 
However, my panels are very short: Most T's are 3 or less. Hence, the IV-
and GMM-estimators appear to be problematic, since with these, the first few
observations are lost because instruments are constructed based on lags. In
order to test my model, I need all observations -- because the beginning of
the process is what is most important. 
 
Did I missunderstand something? Can I still use, e.g., xtdpd to estimate the
model? Is there an alternative approach? 
 
I will be very grateful for any hints you can give me. 
 
Sebastian van Baal
University of Cologne, Germany

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