I am investigating conditional convergence across Indian states using panel data. I include the state name, year, SDP per capita, and a number of conditioning variables such as Public Expenditure, Literacy, Rural Banks per Capita. I hypothesize that I will find weak evidence of conditional convergence when controlling for some of the production fundamentals of each state.
I wanted to check that I have done the correct robustness checks for my model. I am using R, and the plm package in particular. The conditional convergence regression will include a specification with a pooled OLS and controlling variables, a specification with state fixed effects and controlling variables, and a specification with state fixed effects as well as time fixed effects and controlling variables.
I attempted to do a Hausman test for fixed vs. random effects, but it was unsuccessful as I believe my regressors are too dependent.
I did a Breusch-Pagan test for heteroskedasticity
I also used the Ramsey RESET test for functional form.
I will be using SEs clustered at the state level.
Are there any R tests I am missing for pooled OLS and state/time fixed effects? What assumptions have I left out?
I also was interested in adding a more sophisticated specification: the GMM model. I found in the literature that OLS estimates are inconsistent (biased upwards) in the presence of a lagged dependent variable and fixed effects. GMM was used in a number of the papers I read, but I dismissed it initially. Then I started to think that including a lagged growth rate variable would be prudent. The plm package appears to support GMM models.
I understand that the GMM estimator allows past realizations of the dependent variable to affects its current value, and I think it would add a lot of value, but I am unsure of the assumptions/robustness tests I need to perform. If it is relatively straightforward I would like to move forward with it, but I would appreciate any thoughts.
Also please let me know if any more detail is needed!