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

y ˜ t R = ν ( 2 − ν ) ( s t − ( a t − a t ∗ ) ) − ( ν − 1 ) π t R y ˜ t = 1 2 ( y ˜ t W + y ˜ t R ) y ˜ t ∗ = 1 2 ( y ˜ t W − y ˜ t R ) Δ t = − ξ σ π t R − ( ν − 1 ) ( s t − ( a t − a t ∗ ) ) π H t = 1 2 ( π t W + π t R ) − ( 2 − ν 2 ) ( s t − s t − 1 ) π F t = 1 2 ( π t W + π t R ) + ν 2 ( s t − s t − 1 ) π F t ∗ = 1 2 ( π t W + π t R ) + ( 2 − ν 2 ) ( s t − s t − 1 ) π H t ∗ = 1 2 ( π t W − π t R ) − ν 2 ( s t − s t − 1 ) MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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@08B7@