I am currently delving into Professor Kripfganz's presentation slides from the London Stata Conference, aiming to implement both Two-step difference Generalized Method of Moments (diff-GMM) estimation and Two-step system GMM estimation in Stata. In this context, suppose I have a strongly balanced panel with N=120, T=9. Thus, I want to regress yit on yi,t-1 x1i,t-1 x2i,t-1 w1it w2it , t
Notably, x1 and x2 represent two predetermined regressors, with the caveat that I would regress them individually on their respective lagged levels of order one.Furthermore, w1 and w2 are suspected to be endogenous (alongside yi,t-1). Finally, t denotes time dummy.
To conduct a two-step difference Generalized Method of Moments (diff-GMM) estimation with corrected standard errors (Windmeijer, 2005), while addressing the issue of instrument proliferation through collapsing instruments, I employ the following STATA code:
xtdpdgmm y L.y L.x1 L.x2 w1 w2 i.year, model(diff) collapse gmm(y w1 w2, lag(2 8)) gmm(d.(L.x1) d.(L.x2), lag(0 0)) nocons two vce(r) nolog
Regarding a specific concern: given that x1 and x2 are predetermined and enter as lagged values in the first difference equation, it is theoretically plausible not to require additional instruments for them. This is grounded on the fact that they are not correlated with the first difference error, and the first difference lagged one levels for x1 and x2 should serve as self-own instruments. Is my interpretation theoretically correct? Is my Stata code consistent with this interpretation?
After estimating the model, I conduct the Sargan-Hansen test, yielding a p-value of 0.04. This result leads me to reject the hypothesis, at a 5% significance level, that the overidentifying restrictions are valid. Can I interpret this rejection as indicative of potential model mis-specification?
In the case of sys-GMM, I have a similar uncertainty regarding the specification of instruments. Should the instruments for the lagged predetermined variables be d.(L.x1) d.(L.x2) for the equation in first difference and L.x1 and L.x2 for the equation in levels?
Notably, x1 and x2 represent two predetermined regressors, with the caveat that I would regress them individually on their respective lagged levels of order one.Furthermore, w1 and w2 are suspected to be endogenous (alongside yi,t-1). Finally, t denotes time dummy.
To conduct a two-step difference Generalized Method of Moments (diff-GMM) estimation with corrected standard errors (Windmeijer, 2005), while addressing the issue of instrument proliferation through collapsing instruments, I employ the following STATA code:
xtdpdgmm y L.y L.x1 L.x2 w1 w2 i.year, model(diff) collapse gmm(y w1 w2, lag(2 8)) gmm(d.(L.x1) d.(L.x2), lag(0 0)) nocons two vce(r) nolog
Regarding a specific concern: given that x1 and x2 are predetermined and enter as lagged values in the first difference equation, it is theoretically plausible not to require additional instruments for them. This is grounded on the fact that they are not correlated with the first difference error, and the first difference lagged one levels for x1 and x2 should serve as self-own instruments. Is my interpretation theoretically correct? Is my Stata code consistent with this interpretation?
After estimating the model, I conduct the Sargan-Hansen test, yielding a p-value of 0.04. This result leads me to reject the hypothesis, at a 5% significance level, that the overidentifying restrictions are valid. Can I interpret this rejection as indicative of potential model mis-specification?
In the case of sys-GMM, I have a similar uncertainty regarding the specification of instruments. Should the instruments for the lagged predetermined variables be d.(L.x1) d.(L.x2) for the equation in first difference and L.x1 and L.x2 for the equation in levels?
