Generating full Solow data

I'm spending much time setting up a Monte Carlo program which will generate reasonable data for global growth models. When testing estimation methods, many papers have looked at very simple data from models like Y(t)=a + b.Y(t-1) + error. My model introduces endogenous variables in the right hand side too, for multiple countries and time periods.

It doesn't sound too complex, but when one tries to implement it, there are complexities of what sort of standard errors should be used, how to generate the endogenous terms, and so on. Sometimes simple tasks demonstrate many different knots such as the differences between prediction standard error (the uncertainty in the difference between a model's predictions and expected observed data) and the forecast standard error (the uncertainty between a model's predictions and actual observed data, so the prediction error plus the data's error). Another point the task has clarified is why so many papers on growth do not report any constants in their regressions. It would seem to be because the country specific constants are not zero mean, so if they are not reported then the country specific constants are meaningless. It is not a great reason.