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st: Individual effect identification in Blundell-Bond system GMM


From   robystr <[email protected]>
To   [email protected]
Subject   st: Individual effect identification in Blundell-Bond system GMM
Date   Mon, 22 Nov 2010 06:42:46 -0800 (PST)

Dear Statalisters,

I'm using your the xtabond2 to estimate a dynamic model with system GMM.
However, I would need to obtain estimates of the individual (fixed) effects
to go on with my analyses.

My structural model is defined as:

y_i,t = gamma*y_i,t-1+beta*x_i,t+v_i+e_i,t

where vi is the fixed component I'm interested in.

Since there is no option in "predict" after xtabond to obtain the estimates
I need, while I can obtain the estimated residuals, what I think I might do
is to take time-series averages of  y_it, of the preditermined variables in
x_it and of the estimated residuals e_it, and to work out the fixed-effects
v_i as follows:

v_i = (1-gamma)*mean(y_it) - beta*mean(x_it) - mean(e_it)

This produce estimates, but I don't think it is appropriate for a few
reasons:

1) I imposed no restrictions in order to identify v_i and this sounds
strange, but maybe xtabond2 does it in order to estimate the constant term
in beta

2) For each firm-year observation, v_it = y_it - gamma*y_it,-1 - beta*x_it -
e_it is equal to a variable that is not constant for each firm (so the above
formula for v_i would not work) . This makes me think that Blundell and Bond
GMM assumes random effects.

3) In system GMM in might include time-invariant variables in the level
equation, because moment conditions are used in order to estimate
parameters. How might this be consistent with estimating an individual fixed
component from the level equation itself?

Hence, I would be tempted to conclude that while system GMM allows to obtain
consistent estimates of coefficients and to make inferences on marginal
effects, in case you need to estimate individual fixed effects it doesn't
help. Hence, I would use LSDV although it is biased (after providing some
simulation evidence that the bias is not a serious issue for my specific
problem).

However, the puzzle is complicated by two recent papers that estimate my
very same model and claim they obtain the fixed-effects estimates from
Blundell-Bond system GMM (they also claim they use xtabond2). 

What do you think? Is there a way to obtain individual fixed-effects
estimates from system GMM? Are these papers doing something wrong?

Thanks.

Best Regards,
Roberto

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