RDP 8610: Equilibrium Exchange Rates and a Popular Model of International Asset Demands: An Inconsistency Equation (27)

\begin{array}{l} 0 = Σ_{i} π_{i} (σ_{i} d z_{i} - σ_{1} d z_{1}) + (π_{0} - {\hat{Σ}}_{i} {\hat{π}}_{i}) ({\hat{σ}}_{1} d {\hat{z}}_{1} + σ_{e} d z_{e} - σ_{1} d z_{1}) \\ + {\hat{Σ}}_{i} {\hat{π}}_{i} ({\hat{σ}}_{1} d {\hat{z}}_{i} + σ_{e} d z_{e} - σ_{1} d z_{1}) \end{array}