\begin{align}
    y_{i,t} &= \rho_i y_{i,t-1} +\boldsymbol{X}_{i,t}\boldsymbol{\beta}_i +  \boldsymbol{G}_t\boldsymbol{\theta}_i +  u_{i,t} \label{eq:emp1}\\ 
    u_{i,t} &= \boldsymbol{\gamma}_i\boldsymbol{F}_t + \epsilon_{i,t}\label{eq:emp2}.
\end{align}
