Hi,

I am hoping to clarify my understanding of allowing for correlated structural shocks in my DSGE model when I estimate the model. In particular I want to know if the following is how Dynare specifies the correlations in the variance-covariance matrix. Given a transition equation with my model variables given by

s_t = \Phi s_{t-1} + R \epsilon_t,

where \epsilon_t is my vector of structural shocks, composed of a monetary policy shock and a demand shock (\varepsilon_t^{m}, \varepsilon_t^{d}) which is distributed \epsilon_t \sim N(0,QQ). If I allow monetary policy shocks to be correlated with the demand shock, does Dynare specify the variance-covariance matrix as the following?

QQ = \begin{bmatrix} \sigma_m^{2} & \rho_{m,d} \sigma_m \sigma_d \\ \rho_{m,d} \sigma_d \sigma_m & \sigma_{d}^{2} \end{bmatrix}

where \rho_{m,d} is the correlation coefficient between the shocks. My rationale for this var-cov matrix is coming from the fact that the off diagonal elements are covariance terms and the correlation can be rewritten as

\rho_{m,d} = \frac{cov(\varepsilon_t^{m},\varepsilon_t^{d})}{\sigma_m \sigma_d} \Rightarrow \rho_{m,d} \sigma_m \sigma_d = cov(\varepsilon_t^{m},\varepsilon_t^{d})

Just want to make sure I understand the inner-workings of the Dynare package, otherwise my estimation is running great.

Thanks to everyone for all your work.

J.