# Variance-covariance matrix with correlated structural shocks

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.

Have a look at
https://www.dynare.org/manual/the-model-file.html#shocks-on-exogenous-variables
There you can see that for calibration you can either specify the correlation of the covariance. In your notation, if you specify the correlation and the standard deviations, Dynare will fill the off-diagonal of QQ with the computed covariance. If you specify the covariance, these will directly be put on the off-diagonal. For estimation, you specify the correlation and Dynare will compute the required covariance.

Thanks, Johannes! This answers my question perfectly.