Equation with variances


I am trying to solve a model that looks like

Ay_t + E_t (y_{t+1}) = Var_t(y_{t+1})

where y_t = Bz_t + \varepsilon_{t+1} and z_t is a vector of state variables that follows an AR(1) process. I would like to solve for B.

Is there a paper or code that I can refer to that uses Dynare to solve a problem similar to this one?

Many thanks in advance.

  1. Why does y_t contain a shock dated t+1?
  2. This will be a problem for standard perturbation techniques. They approximate the model around the deterministic steady state where the variance is 0. The problem is similar to the portfolio choice problems where the (co)-variance is required.

Thank you for the prompt reply!

  1. This is a typo. Sorry about that. It should be y_t = Bz_t + \varepsilon_t.
  2. Yes, you pin-pointed what I am trying to do. Essentially I am solving for a rational expectations equilibrium of a portfolio model. Is there any references that you can point me towards that solves portfolio choice problems with Dynare?

There is the work by Devereux/Sutherland that comes to mind, e.g. Steady state impossible to find after 2nd order stochastic simulation