Equation Estimation

Hi, for the priors in Bayesian estimation, I should estimate the following equations but I do not know how, because of the two error terms which are present in both equations.
Could anyone help me?
(eq. 20 & 21, “When does government debt crowd out investment?”
N Traum, SCS Yang, Journal of Applied Econometrics )

What exactly is your problem?

I do not know how to estimate \sigma _{k}, \sigma _{l} and \sigma _{kl}.
The simple OLS regression does not work here, right?
Is it something like structural VAR?

In that paper the whole model was estimated using Bayesian techniques. OLS won’t work here easily. But essentially, this is a VAR.