I have an unbalanced panel dataset (N=504, T=3) and I am trying to run instrumental variable regression given that there are 3 endogenous variables in my model. I checked for heteroskedasticity using xttest3 (proposed by Greene, 2000) command and also using White's test commands for panel data similar to the ones used for cross-sectional data and found that there is heteroskedasticity in my dataset. I am using 2 instruments for the first endogenous variable and one each for the other two endogenous variables, so that the number of endogenous variables is 3 and the number of instruments is 4. There is also a case of weak instruments in my analysis and 2SLS is inconsistent in that case. Furthermore, 2SLS, LIML, Fuller's (1977) estimators are not robust to heteroskedasticity and biasness in 2SLS increases with number of over identifying restrictions even with a fixed sample size.

Given the above scenario, I wish to use the HFUL estimators as proposed in paper titled 'Instrumental variable estimation with heteroskedasticity and many instruments' by Hausman, Newey, Woutersen, Chao and Swanson (2012) since they are consistent with heteroskedasticity, weak instruments and many instruments. Additionally, they have same efficiency as LIML under many instruments and homoskedasticity.

Could anyone please help me with Stata command/code of estimating HFUL given panel data structure?