Hi @brianleblanc, would that be a correct representation of your model:
\Pi_i\sim \text{Some Prior}\\
\alpha \sim \text{Some Prior}\\
\lambda_i \sim \text{Some Prior}\\
y_{1,t} \sim N(\Pi_1 X_t, \lambda_1) \\
y'_{2,t} \sim N(\Pi_2 X_t , \lambda_2) \\
y_{2,t} = y'_{2,t} - \alpha(y_{1,t} - \Pi_1 X_t)