\begin{align}
    \boldsymbol{X}_{i,t} &= \boldsymbol{\gamma}_i^x\boldsymbol{F}_t+\boldsymbol{\theta}_i^x\boldsymbol{G}_t + \boldsymbol{\chi}_{i,t} \label{eq:emp3}\\ 
     \boldsymbol{G}_{t} &= \boldsymbol{\xi}\boldsymbol{F}_t+ \boldsymbol{\omega}_{t}\label{eq:emp4}.
\end{align}
