Estimated Open Economy New Keynesian Phillips Curves for the G7

(20)

(21)

br d

pb_t = pb_t-1 + πb_t-1.

Substituting equation (22) into (21) gives,

pb_t^r =(1- ω)xbt + ωpb_t^r_-1 + ωpb_t^d_-1 - ωpb_t^d_-2 .

Inserting equation (20) into this expression then yields,

Pt

1-α

^αPt-1

1-α

(1 - ^ω)xt+^ω μ t^- 1—
1-α

^αP*-2

1-α

+ωpbt-1 ^{- ωpb}t-2.

(22)

(23)

(24)

This can be rearranged in terms of xb_t, substituted into equation (22) and solved
using the definition of output price inflation, πbt = pb_t^d - pb_t^d_-1 to give,

d
πb_t

^βα E bd ₊^ωbd ₊(¹ - ^ω)(¹ - ^a)(1 - ^αβ) (dC     f₂₅⁴)

λ Etbt+1 + λbt-1 ⁺ (1 + (ψ - 1)θ)λ (^MC*    (²⁵⁾

+(ψ - 1)^bye_t + P^bt - pb_t^d).

where λ = ω + βωα + α - ωα .

2.4 Open Economy NKPC

We next reformulate the above specification in a form more appropriate for
estimation. To do so consider the element of marginal cost which is independent
of the firm’s actions,

1-ρ

M^gCt =

+ α_m

(26)

This can be log-linearised as,

_____

M^gCt

pf wff αm∖^ρ

______w_______w. + P-V ONl____(pf _ P )
W + pf (wf Om ´'´ ‘ ⁺ (w + pf W Om П (p*   ')

₄ P ∖ ^αN JJ      ∖ P ∖ ^αN J J

(27)