Estimated Open Economy New Keynesian Phillips Curves for the G7

where

MCt = bt ^- (^ψt ^{- 1})(ι + (ιi- ψt)it) ^{bt -}

(<i - ρ) μ.)+ρ μ ■ '     ) μτ⅛)) (c - pf)

st + i_t        1+(1- ψ_t)i_t    st +i_t

⁺ (1 + (11 ψt)is )  ^{t- pf} )

ff

ψ≠ =    `- ^μ_d—^--/(1 + is ); is = p^t_dm^t ; λ = ω + βωα + α — ωα; z_t is a vector

^t     (WtNt/p_t^dyt)+i_t^{s          t t}     p_t^dyt                                      ^t

of instruments⁹ , including 4 lags of demeaned price inflation, πb^d, wage inflation,
πb^w , commodity price inflation, πb^c, the labour share, sb the output gap, yb and a
constant term; all other variables are defined as in Section 2. Further note that
hatted rates are calculated as deviations away from a constant mean and hatted
levels and relative prices are calculated as deviations away from a quadratic
trend¹⁰ . Finally we assume that Et (zt , ut )=0 .

3.2 Interpretation of Results

We next turn to the GMM estimates of (33). Table 1 gives the results for our
central estimates of the NKPC across four model variants. Model M1 represents
the closed-economy estimates which are comparable with the figures for the US
in Gali et al (op. cit.). M2 introduces the open economy effects considered
above and freely estimates, ρ, the elasticity of substitution between imports
used in production and labour. As for all economies, except the US, this co-
efficient is not significantly different from 1.InmodelM3 we replace the CES
production function with a Cobb-Douglas formulation by imposing ρ =1.Fi-
nally, in variant M₄ we reduce the elasticity of substitution between imported
production imports and labour to 1/3 in line with the assumption of McCallum
(2001).

If we consider the closed economy estimates first, we can see the estimates
of the degree of nominal inertia, α, and the proportion of firm’s which follow
backward-looking rules of thumb, ω are all highly significantly and economically
plausible. We can estimate the average time it takes for all prices to adjust in an
economy as ι-1α and this implies that the country with least inertia is Italy with
average price adjustment taking only 6 months, closely followed by the US at 6.5
months, the UK at just under 7 months, Canada at slightly less than 9 months,

⁹Our instruments set is based on the one used in Gali and Gertler (1999). We conduct
Hansen’s J-test below to test the validity of our overidentifying restrictions since we have more
instruments than parameters to estimate.

¹⁰ Both these transformations are common in this literature, see e.g. Gali et al (1999 and
2001). The rates include: π^p, π^w, π^c and, s and the levels and relative prices include: y,
W - p^f and p^d - p^f .

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