Exchange Rate Economics: Theories and Evidence

Purchasing power parity and the PPP puzzle 53
of regression equation (2.17) α 0 and α 1 need not equal plus and minus unity,
respectively.
A further explanation for why α 0 and α 1 need not equal unity,in absolute
terms,relates to the construction of the price series (see Patel 1990). Assume a
representative agent, i,for whom PPP prevails. Therefore:
s t = ζ p i t − ζ ∗ p ∗i
t ,(2.25)
where pt i and pt
∗i are the ‘true’ prices facing the representative agent in the home
and foreign country and,by definition,ζ = ζ ∗ = 1. In terms of measured price
indices, p t and pt ∗ ,the weights used to construct them will differ from country to
country:
p t =
p ∗ t =
N∑
ω jt p jt ,(2.26)
j=1
N∑
ωjt ∗ p∗ jt ,(2.27)
j=1
where ω j denotes the weight given to commodity j in the construction of the price
index and this will differ from country to country; that is, ω j ̸= ωj
∗ (the potential
time-variation of ω implies that the α terms are also potentially time-varying).
Hence if the weights are not equal across countries,the only inference that may
be tested on the α’s in (2.17) is that they are positive (because the weights are,by
definition,positive).
The basic message from cointegration-based tests of (2.17) is that the estimator
used matters. For example,the application of the two-step Engle–Granger method,
in which symmetry is generally imposed,produces little or no evidence of cointegration
– see,for example,Baillie and Selover (1987),Enders (1988),Mark (1990)
and Patel (1990) for evidence of a variety of bilateral currencies from the recent
floating period. MacDonald (1995a) applies this test to a consistent data base for
nine bilateral US dollar exchange rates for the recent floating experience and for
illustrative purposes his results are presented in Table 2.1. This table contains a set
of point estimates of the coefficients in (2.17),along with augmented Dickey–Fuller
statistics. The sample period used to construct these numbers runs from March
1973 to December 1992 and both wholesale and consumer prices (WPI and CPI)
are used as the price measures.
Using the WPI as the price measure we note that all of the α 0 and α 1 coefficients
are correctly signed (positive and negative,respectively) while with the CPI,7 of the
9 currencies produce correctly signed values of these coefficients and this seems to
suggest that the WPI measure is the more appropriate. However,it is clear that most
of the estimated coefficients are far from their hypothesised values of +1 and −1
(although as we have seen this is not particularly damaging to the PPP hypothesis in
the presence of transaction costs). Of more concern,however,is the fact that none