I want to accurately estimate a production function lnY=alpha*lnK+beta*lnL+idiosyncratic error+fixed effect.

As per Blundell and Bond (2000), I intend to use system GMM to address potential omitted variable bias and/or simultaneity bias.

I have read that the proper way to implement this in Stata is to use the -xtabond2- command.

My question is: what are the theoretical assumptions needed to execute this command?

My understanding is that if a) unit root testing indicates my data is stationary; and b) there is no AR(2) autocorrelation indicated in the -xtabond2- results, my procedure is valid. Is this correct? Are there other assumptions I require?

Relatedly, for Arellano-Bond estimation, I've read that there there is a necessary initial condition that E[y_{i1}e_{i2}]=0. I don't understand what this is saying, though. What does this mean intuitively?