\begin{eqnarray}
\Delta \log       \mathbf{C} _{t+1} & = & \alpha_{0} + \alpha_{1} \mathbf{E} _{t-n}[\Delta \log       \mathbf{C}_{t} ] + \alpha_{2} \mathbf{E} _{t-n}[\Delta \log       \mathbf{Y} _{t+1}] + 
\alpha_{3} \mathbf{E} _{t-n}[ {     A }_{t}]     \label{eq:CGrowTime} \\ 
\Delta \log  \bar{\mathbf{C}}_{t+1} & = & \alpha_{0} + \alpha_{1} \mathbf{E} _{t-n}[\Delta \log \bar{\mathbf{C}}_{t}] + \alpha_{2} \mathbf{E} _{t-n}[\Delta \log \bar{\mathbf{Y}}_{t+1}] + 
\alpha_{3} \mathbf{E} _{t-n}[ {\bar{A}}_{t}]     \label{eq:CGrowBarTime}
\end{eqnarray}
