   \newcommand{\CGrowCross}{\Delta \log       \mathbf{c} _{t+1,i} & = & \alpha_{0} + \alpha_{1} \Delta \log       \mathbf{c} _{t,i} + \alpha_{2} \mathbf{e} _{t,i}[\Delta \log             \mathbf{y} _{t+1,i}] + \alpha_{3}            {     a }_{t,i}    \\}
\newcommand{\CGrowCrossBar}{\Delta \log  \bar{\mathbf{c}}_{t+1,i} & = & \alpha_{0} + \alpha_{1} \Delta \log \bar{\mathbf{c}}_{t,i} + \alpha_{2} \mathbf{e} _{t,i}[\Delta \log       \bar{\mathbf{y}}_{t+1,i}] + \alpha_{3}            {\bar{a}}_{t,i}    }
