3.1 Empirical Considerations and Estimator
Prior to estimating (29) for the G7 economies it is necessary to obtain data for
the steady-state ratio of imported goods used in production relative to GDP,
ρfmf Tj1 1 — τj ∙ 1∙1 j1∙ j1
^Pdy , and the steady-state labour share s. It is readily apparent from the
data that the ratio of imported intermediate goods relative to GDP has been
growing in line with the ratio of imports to GDP. Accordingly, estimating an
open economy NKPC assuming that the importance of imports in production
was constant, would imply too great a weight on open economy effects in the
1970s and too small a weight in the 1990s, ceteris paribus. To account for this
we replace this ratio with actual data rather than an average across the sample.
This has the desired effect of appropriately capturing the increasing importance
of imported goods in production over time. For consistency we also use actual
data for the labour share and in calibrating ψ to calculate the weights on the
open economy terms in our NKPC7 . To obtain the latter, consider the labour
and intermediate goods share under imperfect competition,
WN + pf mf θ
(31)
pde ψ(θ — i)
which, by noting the definition of GDP can be used to derive an estimate of ψ
from labour share and imported intermediate goods data,
ψ = (θ⅛ /
pf mf
pdy
pf mf
pdy
(32)
To calculate ψ and when estimating (29) we follow the literature and adopt
values for the elasticity of demand facing the firm, θ. The parameter, θ implies
a mark-up of prices over marginal costs, μ of j—ɪ which we assume to be 10%,
so that θ =11. We also consider the robustness of our results to changing this
assumed parameter by reducing θ to 3.5 which implies a mark-up of 40%8 . Note
that this is a similar range of values to those considered in Gali et al (2001) and
encompasses the values adopted in the literature.
Given that our model incorporates forward looking rational expectations
(RE), we employ Hansen’s (1982) generalised method of moments (GMM) es-
timator which easily handles the set of orthogonality conditions suggested by
the RE hypothesis. In this context and incorporating time-varying measures of
—f—f
ppdy , s and ψ discussed above, our econometric specification can be expressed
as follows,
d βα d ω d (1 — ω)(1 — α)(1 — αβ) d
Et t - t. - λbt-1--(ι + (ψt — I)θ)λ (MCt)]z9 =0 (33)
7 However, we also considered the implications for our results of adopting straightforward
averages for these ratios and these are discussed below.
8 See Appendix III for detailed results.
11