Estimated Open Economy New Keynesian Phillips Curves for the G7

so that changes in the price of imported intermediate goods relative to labour
costs will result in a substitution between labour and intermediate import goods.
This can then be substituted back into the production function to obtain,

N(z)t = (y(z)t)ψ

ρ-1

m(z)_t^f = (y(z)t)ψ

Wt am
p_t^f αN

1-ρ

and after substituting for ^dN(^z)^t and ^dm(z)^t

∂y(z)t         ∂y(z)t

decompose marginal cost into two elements - one which is independent of the

firms actions and the other which depends upon the position they are operating
on their production function, such that marginal cost equals,

(y(z)t)ψ^-1MgCt.

The first multiplicative term captures the increase in firm specific marginal costs
through increasing production given the fixed stock of capital³ and decreasing
marginal returns to the remaining factors. The second element reflects the
labour and intermediate goods costs that enter into the costs of production and
are constant across firms. We label this second term, MCt .

2.3  Profit Maximising Price Setting

We can now start to consider the problem facing a firm which chooses to set
its price in order to maximise profits. The real variable profits⁴ (deflated by

³ An alternative modelling strategy would be to allow capital to be reallocated across firms
so as to equate the shadow value of capital, implying that each firm’s marginal cost is identical
to the economy-wide average cost (see Sbordone (2002) for a discussion). However, the pos-
sibility that firms can reallocate capital without friction, but cannot reset prices continuously
seems implausible.

⁴ We ignore the fixed costs of utilising the capital stock in formulating the firm’s problem
and we assume that all shocks are sufficiently small that firms continue to earn positive profits
at all points in time.

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