\begin{align}
y_{i,t} =& \rho_i y_{i,t-1} +\boldsymbol{\beta}_i\boldsymbol{\chi}_{i,t} + \left(\boldsymbol{\beta}_i\boldsymbol{\theta}_i^x + \boldsymbol{\theta}_i\right)\boldsymbol{\omega}_{t} \label{eq:FinalModel}\\
&+ \left[\boldsymbol{\beta}\left(\boldsymbol{\gamma}_i^x+\boldsymbol{\theta}_i^x\boldsymbol{\xi}\right)+\boldsymbol{\gamma}_i+\boldsymbol{\theta}_i\boldsymbol{\xi}+\epsilon_{i,t}\right].
\end{align}
