xtabond2 for difference and system GMM; Wald test is missing; 2SLS

[Aneta Joanna]

Hi everyone,

Are these commands equivalent if I want to compare estimates from difference and system GMM? Why Wald test is missing in two-step difference GMM? How can I write command to calculate an analogous model 2SLS (Anderson and Hsiao)?

Two-step difference GMM: xi: xtabond2 lnr_fpl L.lnr_fpl i.year, gmm(L.lnr_fpl, collapse) iv(i.year) noleveleq nodiffsargan twostep robust orthogonal small

Two-step system GMM: xi: xtabond2 lnr_fpl L.lnr_fpl i.year, gmm(L.lnr_fpl, collapse) iv(i.year) nodiffsargan twostep robust orthogonal small

[Sebastian Kripfganz]

I guess that the Wald test is missing because you have specified the noleveleq option, which suppresses the intercept. That's not a concern.

Note that iv(i.year) is not equivalent to iv(i.year, eq(level)) iv(i.year, eq(diff)). If this comes as a surprise, then I would recommend to always explicitly specify the model equation to which the instruments are referring. In a balanced panel model, there is no need to specify the time dummies separately for the two model equations. Just iv(i.year, eq(diff)) is sufficient, which also helps with the comparability of the system and difference GMM estimator.

For the Anderson-Hsiao estimator, you would simply use the ivregress command:

ivregress 2sls D.lnr_fpl (LD.lnr_fpl = L2.lnr_fpl) D.(i.year), noconstant vce(robust)

More on the GMM estimation of linear dynamic panel models:

• Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference.