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

\begin{array}{l} π_{0} \equiv ({\hat{a}}_{\hat{s} + 1} + Σ {\hat{a}}_{\hat{s} + j}) (1 - {\hat{a}}_{\hat{s} + 1} - Σ {\hat{a}}_{\hat{s} + j}) e \hat{w} + (1 - a_{s + 1} - \hat{Σ} a_{s + j}) (a_{s + 1} + \hat{Σ} a_{s + j}) w \\ π_{i} \equiv - (1 - {\hat{a}}_{\hat{s} + 1} - Σ {\hat{a}}_{\hat{s} + j}) {\hat{a}}_{\hat{s} + i} e \hat{w} - (a_{s + 1} + \hat{Σ} a_{s + j}) a_{i} w & i = 2, \dots, s \\ {\hat{π}}_{i} \equiv ({\hat{a}}_{\hat{s} + 1} + Σ {\hat{a}}_{\hat{s} + j}) {\hat{a}}_{i} e \hat{w} + (1 - a_{s + 1} - \hat{Σ} a_{s + j}) a_{s + i} w & i = 2, \dots, \hat{s} \end{array}