RDP 2009-01: Currency Misalignments and Optimal Monetary Policy: A Re-examination Equation (B47)

\begin{matrix} {\tilde{c}}_{t} + {\tilde{c}}_{t}^{*} = {\tilde{y}}_{t} + {\tilde{y}}_{t}^{*} + Ω ({\tilde{y}}_{t}^{2} + 2 {\bar{y}}_{t} {\tilde{y}}_{t} + {\tilde{y}}_{t}^{*_{2}} + 2 {\bar{y}}_{t}^{*} {\tilde{y}}_{t}^{*} - 2 {\bar{y}}_{t} {\tilde{y}}_{t}^{*} - 2 {\bar{y}}_{t}^{*} {\tilde{y}}_{t} - 2 {\tilde{y}}_{t} {\tilde{y}}_{t}^{*}) \\ - \frac{ν}{2} (\frac{2 - ν}{2}) \frac{1}{D^{2}} Δ_{t}^{2} - \frac{ν}{2} (\frac{2 - ν}{2}) (\frac{2 (1 - ν) (1 - σ)}{D^{2}}) Δ_{t} (y_{t} - y_{t}^{*}) + o (‖ a^{3} ‖) . \end{matrix}