Estimated Open Economy New Keynesian Phillips Curves for the G7

consumer prices as² ,

The price index associated with the consumer goods produced at home is defined

while the same index for imported goods is given by,

The Cobb-Douglas form of the aggregate utility function implies relative
shares of home and foreign goods in consumption given by, cd = χ-Pd c_t, and

^t      P_t

cf = (1 — χ) Ptf c_t. There are corresponding equations for the foreign economy,
P_t

where foreign variables are denoted by a ‘*’. If we assume that the government
allocates spending across goods in the same pattern as consumers then the
total demand for domestically produced goods for the purposes of domestic and
foreign public and private consumption are given by the sum of the following
demands,

There is an additional source of demand for domestically produced goods - we
assume that foreign firms utilise a bundle of domestically produced goods in pro-
duction, just as domestic firms employ a bundle of foreign produced goods in do-
θ

mestic production. Accordingly, we define m(i)f * =

being the bundle of domestically produced products used in foreign production,
by foreign firm i. As this composite intermediate good possesses the same de-
gree of substitutability between goods as the government and consumers’ con-
sumption bundles, foreign firms, domestic consumers and foreign consumers will

² This price index is derived by minimising the cost of purchasing a single unit of the
composite consumption bundle, ct . The Cobb-Douglas form of the utility function implies
that to minimise costs consumers will allocate spending across the home and foreign goods
in the following patter, Pfc^f = y^χχΡt^dcd. Utilising the fact that c_t = (c^d}^x (ʃŋ = 1
f                                                         P^{d -χ}

allows us to eliminate ct from this relationship and solve in terms of c^d = f γ-^χχ ptf )   ∙

f χ — 1

The consumer price level is then defined as, Pt = Pt (cd) ^χ  + Ptd cd. Replacing cd in this

expression yields the consumer price index defined above.

<<   <   1   2   3   4   5   6   7   >   >>