GMM - lagged dependent variable as instrumental variable

[Ronan Mack]

Hello, my name is Ronan and this is my first Statalist post (apologies, I didn't know how to export output from stata). I am currently researching an analysis of ESG and bank value in developed countries. My aim is to two step system GMM, with the lagged dependent variable as an instrumental variable. My dependent variable is Tobin's Q and my main independent variable is ESG (using 1 period lag of Tobin's Q to address endogeneity), with Size-Inflation as control variables. I am concerned that my AR(2) is a bit high and that my code does not target the lag of Tobin's Q as an instrumental variable. Could anyone kindly help me out with the code? I am treating GDP_Annual_Growth, Financial_Development, and Inflation as exogenous.

[Sebastian Kripfganz]

In your option gmm(Tobins_Q ..., lag(1 1) collapse), you are specifying the first lag of Tobins_Q as an instrument. This is not a valid instrument for the first-differenced model because it is correlated by construction with the first-differenced error term. You would need to replace the dependent variable in this option by the lagged dependent variable. Also note that your instruments in the iv() option are implicitly assumed to be uncorrelated with the unobserved group-specific effects (akin to a random-effects assumption). This is a very strong assumption, which is often not justified.

More on GMM estimation of dynamic panel models:

• Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference.
• XTDPDGMM: new Stata command for efficient GMM estimation of linear (dynamic) panel models

[Ronan Mack]

Hi Sebastian, thank you for your response. I have changed Tobins_Q to L1.Tobins_Q and this was my outcome. Would you suggest testing some of my presumed exogenous variables as endogenous, and vice versa? The AR(2) value seems okay but the Sargan/Hansan test do not. Also, when using the lagged dependent variable as an instrumental variable, does it necessarily matter whether it is included in gmm() or iv()?

[Sebastian Kripfganz]

The lagged dependent variable is correlated by construction with the unobserved group-specific effect. As a general rule, you therefore cannot put it into the iv() option. As I mentioned earlier, some of your instruments in the iv() option might be invalid, which could be a reason for the failure to satisfy the Hansen test. Another reason could be that some of your variables in the gmm() option are endogenous and not just predetermined. In this case, you would need to start at least with lag 2 in the lags() suboption for those variables.

[Ronan Mack]

Thank you kindly. I have 18 different models, and for them some of the variables are endogenous/exogenous, and in other models more of a lag is taken. Is that okay to do, where each model's lags are viewed separately?