Dear Bean,
in Stata the Arellano-Bond dynamic panel model is available in xtabond. With the variable of your datatset if you want to model the following dynamic relationship
Y = Y(t-1) + X1 + X2 + X3,
taping
"xtabond y X1 X2 X3"
you say that X1, X2, X3 are strictly exogenous, so that they enter as instruments in first-difference. If you want to use also lags of explicative variables as instruments you have to tape
"xtabond y, pre(X1 X2 X3)"
the command prestates that the variables in varilist are predetermined so that they enter as instruments if levels from t-p-1, where p is the maximum lag of the dependent variable used as explanatory variable. If you think that X1, X2 and X3 are endogenous, so that they enter in the instrument matrix in levels from t-p-2, you have to write
"xtabond y, pre(X1 X2 X3, endog)" (P.S. this command is available only if your stata is updated!)
Another alternative is to use xtabond2 command (ssc install xtabond2), a new stata routine to implement also the Blundell and Bond system of GMM estimators for dynamic panel (1998).
The problem with Arellano and Bond first difference estimator is that the lags of predetermined (= not strictly exogenous) variables used as instruments are orthogonal to the transformed error term (in first difference) but are not strictly correlated with the variable instrumented. The idea is to improve the Arellano and Bond estimators with a linear GMM model where tha variable l.y in level is instrumented with t-p-1 lags of y and predeterminde variable in first difference and the exogenous variable in level. The system of GMM is the system of the Arellano-Bond first difference estimator with this linear GMM. This improve the correlation of matrix instruments with instrumented variable. The commanda xtabond2 allow to replicate the results of xtabond (conditionally to the updated verdion of Stata!)
For example
xtabond y X1 X2 X3, noconst (where X1, X2, X3 are strictly exogenous)
is equal to
xtabond2 y l.y X1 X2 X3, noleveleq gmm(l.y) iv(X1 X2 X3).
Note: you have to drop the constant in xtabond to replicate the xtabond results with xtabond2. In xtabond2 the iv option display the variables that you consider as strictly exogenous that enter in first difference equation in first difference and the command gmm specifies the endogenous variable (l.y!) and the predetermined variables (that enter in the fd equation in levels from t-p-1). In xtabond2 the option noleveleq drop the level equation from the system, replicating the A-B fd model.
xtabond y, pre( X1 X2 X3) noconst ==
xtabond2 y l.y X1 X2 X3, gmm(l.y X1 X2 X3) noleveleq.
xtabond2 is more useful as in gmm option you can specifies the number of instruments to use. A problem in the AB fd estimators is that the number of instruments increase with the number of variables, so that the GMM performs not very well with a big matrix of instruments. Different from xtabond, in xtabond2 you can exactly set the number of instrument. For example:
you want to use onfl t-2 and t-3 level of y, X1, X2 and X3 as additional instrument
xtabond2 y l.y X1 X2 X3, gmm (l.y X1 X2 X3, lag (2 3)) noleveleq
if you want to use all the level of y and only t-2 and t-3 of Xs
xtabond2 y l.y X1 X2 X3, gmm (l.y) gmm(X1 X2 X3, lag (2 3)) noleveleq
or if you want to use all the level of Xs but only t-2 and t-3 level of y
xtabond2 y l.y X1 X2 X3, gmm (l.y, lag(2 3)) gmm(X1 X2 X3) noleveleq
Dropping the option noleveleq the system of GMM is estimated.
I hope my mail is of some use,
sincerly
Andrea Sisto
University of Eastern Piedmont (Italy)
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