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st: question on xtabond2
I’m working with an unbalanced panel and want to use xtabond2 to estimate individual labour supply over a period of (up to) eight waves.
I applied the estimator without correcting for people who were not observed at least for three periods, which the estimator assumes by construction:
The formula is
Yit = aYit-1 + Ai + Eit
taking first differences leads to
dYit = a(dYit-1) + dEit
and than I use for example the lagged level Yit-2 as an instrument for the first difference dYit-1 It is easy to see, why the estimator needs at least three periods if I want to use lagged levels as instruments.
My first model uses only lagged levels and only up to one lag (six instruments for eight periods), but the number of observations seems too high. Than I read in the syntax of xtabond2 that “Missing values are always replaced by zeros.” in the gmm-option, i.e. the instrument matrix.
My question is: is it right, that the estimator uses also data on individuals if they are only observed for two periods by replacing the missing third period by zero in the instruments, i.e. in the example above xtabond2 would replace Yit-2 by zero if that observation is missing? And if it does so, why? To me it seems to be a very strong assumptions about the first period.
My first solution will be to condition on the length an individual is observed in the sample, but I’m a bit confused.
Any help would be appreciated. Cheers.