Fixed effects and lagged variables in IV estimation - valid? [xtivreg2 / xtabond2]

[Olaf Hotte]

Hi,

I found following statement in lecture notes:

Source: Panel Analysis Bruederl_Ludwig 1.pptx (uni-muenchen.de)

In particular, I am interested in applying lagged variables as instruments in a panel data setting. The function xtivreg2 offers fixed effects and first difference transformation. If I read the above statement a possible interpretation could be that lagged variables are valid instruments in first difference IV estimation only - not for fixed effects IV estimation. Is this interpretation correct? What is the reason for this?

(Is this the reason why there is no Arellano-Bond GMM estimator [e.g. xtabond2] with fixed effects?)

[Sebastian Kripfganz]

Yes and yes. The fixed-effects transformation requires "strict exogeneity" because it subtracts the within-group average from all variables. If variables are only "sequentially exogenous", i.e. they might be correlated with future errors, then their within-group averages (which are a function of all time periods) would be correlated with the error term. In contrast, first-differencing only subtracts the value from the previous period instead of an average over all periods. Thus, lagged values would retain their exogeneity.

Btw: You could combine the traditional lagged instruments for the first-differenced model (Arellano-Bond) with instruments in the style of a "fixed-effects" transformation, if you have some variables which are sequentially exogenous and others which are strictly exogenous. This can be done with my xtdpdgmm command.