Dear everyone,

I had noticed a very interesting phenomenon in GMM estimation, which I can't figure out why. Hope you can give me some hints. Great thanks.

Take the following equation (the one listed in the help file of the code xtdpdgmm) as an example:

************************************************** ******************************************
webuse abdata

//gen new variable by minus a constant
gen w_new=w-2

//OLS
reg n l.n w k
reg n l.n w_new k

//GMM
xtdpdgmm L(0/1).n w k, gmm(L.n w k, l(1 4) c m(d)) iv(L.n w k, d) two vce(r)
xtdpdgmm L(0/1).n w_new k, gmm(L.n w_new k, l(1 4) c m(d)) iv(L.n w_new k, d) two vce(r)

************************************************** ***********************************************

Logically, when the independent variable minus a constant, we should expect the coefficients won't change, that is the case of OLS estimation. However, the coefficients vary for all independent variables in the GMM estimation (both in code xtdpdgmm and xtabond2). That's really hard for me to understand. Could anyone enlighten me on what leads to this outcome?

Best,
Haiyan