End of period convention and decision lag

Actually, from what you describe, I think the law of motion for n should be

n_t =(1-rho_{t})n_{t-1}+m_{t}

You inherit employment n_{t-1} from the previous period, some matches dissolve based on rho_t and you get new matches m_t. This is similar to the law of motion for capital. Alternatively, you could shift the whole equation by 1 period:

n_{t+1} =(1-rho_{t})n_{t}+m_{t}

and use

predetermined_variables n

Regarding the limited information assumption, you need to change the information set of the expectations operator in Dynare. You can use the EXPECTATION(-2) operator for that (see the manual). You can see the change in timing in the working paper version at