Estimated Open Economy New Keynesian Phillips Curves for the G7



2 The Model

In this section we analyse a model of firms’ price setting behaviour which takes
account of open economy terms of trade effects in two main ways. Firstly, we
assume that imperfectly competitive firms sell their goods both at home and
abroad and, therefore, that they take into account the price they set relative to
the prices set by other firms, both at home and abroad. Secondly, we also assume
that firms utilise imported intermediate goods in production so that changes in
the price of imported intermediate goods relative to domestic labour costs can
affect the marginal costs of production. We further assume that firms face the
constraints in price-setting implied by the use of Calvo (1983) contracts, in that
they can only change their prices after a random interval of time. Within this
constraint, we also allow firms to adopt two forms of price-setting behaviour.
Some firms set prices by maximising the expected discounted value of future
profits, while the remaining firms choose to follow a simple rule of thumb which
updates their prices in line with inflation and the price changes they observed
in the previous period.

2.1 Product Demand

We first turn to consider the demand for the firm’s product1 . We allow for the
possibility that goods produced at home and abroad are not identical in the
impact they have on utility. Specifically, we assume that consumers maximise
the utility generated by the following consumption bundle,

ct = (<tf (cf)^                       (1)

where, ctd is a CES index of consumer goods produced in the home country,
Г 1        θ-1    1 θ-^τ

cd = R0 cd(z)~s~dz   and cf is a CES index of consumer goods produced in

I-                                          -I θ

the foreign country, cf = [R01 cf (z) --^ dz^ . There are price indices associated
with each of these consumption bundles, such that we can define the index of

1 In doing so it should be borne in mind that there is an implicit model of utility max-
imisation which allocates an individual’s consumption sp ending across time. This can be the
usual consumption Euler equation or can include more complex dynamics, such as those aris-
ing from habits effects as in Leith and Malley (2001). However, in analysing firms’ pricing
decisions, we only require knowledge of how consumer’s allocate this consumption spending
across domestic and foreign goods.



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