RDP 8702: Open Market Operations in Australia: A U.S. Perspective Appendix

The purpose of this appendix is to derive the reduced form expression for interest rates in (13). From (11) the information contained in .

Further, postulate the following undetermined coefficient solution for the interest rate.

The coefficients α₁, α₂ can be thought of coefficients in a population regression given by (12). Therefore

or

where the last equality makes use of the fact that one can show that (ψ₃m₁+ψ₅) = (ψ₃m₂−ψ₇)=0. Δ is the determinant of the 2×2 matrix in equation (A2) and is given by .

The undetermined coefficients are then solved for by equating their value on each side of (10). The result is , ψ₃ = −(d₃/d₂)ψ₂θ, ψ₄, ψ₄ = −m₁ψ₃, ψ₅ = m₂ψ₃, and where and .