Implementation of additional shock processes

General DSGE Modeling
1

I have a basic New Keynesian DSGE model with households exhibiting a utility function like this:

\mathbb{E}_0 \sum_{t=0}^\infty \beta^t \left( \frac{c_t^{o(1-\sigma)}}{1-\sigma} - \kappa_L \frac{h_t^{o(1+\varphi)}}{1+\varphi} \right).

However, in another publication I find a utility function like this:

\mathbb{E}_0 \sum_{t=0}^\infty \beta^t \nu_t^b \left( \frac{c_t^{o(1-\sigma)}}{1-\sigma} - \nu_t^n \kappa_L \frac{h_t^{o(1+\varphi)}}{1+\varphi} \right) ,

where \nu_t^b and \nu_t^n denote shocks to the discount rate and the labor supply respectively and are defined as stationary white noise processes. Attempting to implement these kinds of shocks via additional AR(1) processes for the discount factor and the hours however will yield two more equations than endogenous variables. How can I implement these additional shocks to my existing model and ultimately in Dynare?

2

You are confusing something. An AR1 \nu_t=\rho \nu_{t-1}+\varepsilon_t introduces one additional endogenous variable \nu_t, while the shock \varepsilon_t is an exogenous variable. Thus, the number of equations and endogenous variables remains the same.