Dear all,

I am studying the relationship between Economic growth and FDI inflow. Due to the endogenous issue, I choose two step system of GMM to solve this. The variables used in the model as follows: growth for dependent var, FDI for independent var, control vars including log of real gdp/capita, population growth, capital formation and explanatory variables including inflation, external debt and institution and the interaction between these factors and FDI. When reading the literature, I found that previous study usually used the lag2 and futher for transformed equation delta yi,t−1 and others for level equation. Here is original text: "lagged differences of yit as instruments for equations in levels and lagged levels of yit as instruments for equations in first differences. We use lagged two and/or three periods of y and X as valid instruments to generate consistent and efficient parameters estimates". Another article uses yit-2 and lag2 of other variables as instrument and futher lag for transformed equation and the delta of yit-2 and others for level equation.
I want to check the effect of independent variable gradually so I analysis the first model with FDI and other control variables. In model 2, 3 and 4, I will add 3 explanatory variables, respectively. The last model will include all variables of the model. Here is my code for the first one and the last one:

Model 1. xtabond2 Growth ln_gdp Popul Capiform FDI y*, gmm(ln_gdp FDI Popul Capiform, lag (2 3) equation(diff) collapse) gmm(ln_gdp FDI Popul Capiform, lag(1 1) equation(level) collapse) iv (y*) twostep nodiffsargan robust small
Model 5. xtabond2 Growth ln_gdp Popul Capiform FDI exdebt infl freedom FDIxExdebt FDIxInfl FDIxEcoFre y* , gmm(ln_gdp FDI Popul Capiform exdebt infl freedom, equation(diff) lag(2 3) collapse) gmm(ln_gdp FDI Popul Capiform exdebt infl freedom , lag(1 1) equation(level) collapse) iv ( FDIxExdebt FDIxInfl FDIxEcoFre y*, equation(level)) twostep nodiffsargan robust small

Model 5 have to struggle with the problem that the instruments is much more than the number of groups although I have added collapse suboptions in gmmstyle. Could anyone please help me in explaning these following questions:

1. Whether the code which I use for model 1 is correct or not?
2. Is these instruments valid compared to the previous studies?
3. How can I solve the problem of model 6 when I have a lot of instruments?
4. Whether I can use this code for model 6 when I use the deep lag of these variable to modify the instruments to make the results more significant and decrease the number of instruments?

xtabond2 Growth ln_gdp Popul Capiform FDI exdebt infl freedom FDIxExdebt FDIxInfl FDIxEcoFre y*, gmm(l3.ln_gdp l2.FDI l4.Popul l3.Capiform l2.exdebt l3.infl l3.freedom, equation(diff) lag(2 .) collapse) gmm(ln_gdp FDI Popul Capiform exdebt infl freedom , lag(1 1) equation(level) collapse) iv ( FDIxExdebt FDIxInfl FDIxEcoFre y*, equation(level)) twostep nodiffsargan robust small Array

Thank you very much for your help!

Regards,
Margaret