Exchange Rate Economics: Theories and Evidence

80 The economics of the PPP puzzle
in the importer’s currency,the exporter maximises the expected utility of profits
in its own currency as:
Max E t−1 {U [(s t p t − c ∗ t )x(p t, v t , Z t ) + y t ( f t
t−1 − s t)]},(3.22)
where U is the firms utility function, p t is the price in the importing country set in
period t − 1 for t, c ∗ cost of production (average and marginal) in the exporters
currency, x is the demand function for imports where v (a scaler) is the price of
import-competing goods 4 and Z is consumer expenditure. The last term in (3.22)
represents the cost of forward cover where y is the amount of the importers currency
sold on the forward market. The nominal exchange rate, s,defined in units of the
exporter’s currency,is assumed to be the only stochastic term entering (3.22). The
first-order condition from this maximising problem is:
p t
(
1 − 1 η t
)
=
(
Et−1 ct
∗ )
,(3.23)
t−1f t
where the price elasticity of demand, η, ≡−δ ln(E t−1 x t )/δ ln p t . In this expression
the exporter’s marginal costs, E t−1 ct ∗ ,are converted to the importing country’s
currency using the forward exchange rate and so the forward rate,along with
the elasticity of demand,is now a determinant of the optimal price. This is an
illustration of the separation theorem of Ethier (1973) that the variance of the spot
rate does not affect the optimal price. Feenstra and Kendal (1997) demonstrate
that the comparable first order condition for a firm which invoices in its own
(i.e the exporters) currency is:
(
pt
∗ 1 − 1 )
ηt
∗ = ( E t−1 ct
∗ )
,(3.24)
where pt ∗ is the price in the exporters currency, ηt ∗ ≡−δ ln[E t−1 x(pt ∗z t−1f t , q t , z t )]/δ
where the forward rate enters the elasticity formula and,again,as in the case of
invoicing in the importing country’s currency,the variance of the exchange rate
does not affect the optimal price chosen by the exporting firm.
3.3.3 Pricing to market: some empirical evidence
Mann (1986) analysed a data set consisting of the movement of four-digit industry
US import prices relative to a trade weighted average of foreign production costs
and found that profit margins are adjusted to mitigate the impact of exchange rate
changes on dollar prices of US imports. Interestingly,she found that US exporters
did not adjust mark-ups in response to exchange rate changes. The latter finding
was confirmed by Knetter (1989).
Knetter (1989) presents an empirical framework which is capable of distinguishing
between three alternative hypotheses: the fully competitive integrated market
model and two non-competitive alternatives. These hypotheses may be motivated
using the following panel regression equation:
ln p it = θ t + λ t + β i ln s it + u it ,(3.25)