Differential Growth Rates in Two Country Models

Hi all
I am planning to estimate a 2-country model.
I have the following problem.
The growth rates of the C, I, Y for both countries are different. I do not want to impose the standard ‘world’ technology shock with a unit root, so that all these variables grow at the same rate ( thereby preventing the demeaning of the growth rates in the data that enter the observation equation since the growth rate are internally generated by the model).
I would like to have the 2 countries growing at different rates. Is this possible? Have you seen any paper do this? I cannot think of any solution that will not violate balanced growth.