A Principal Components Approach to Cross-Section Dependence in Panels



factor included in the US$ panel regressions is quite high. In the DM panels
where
τ = 3 and 2, the t-ratio on the first factor is dramatically larger than
that for the other two. Since — as suggested by the Monte Carlo simulations
for the monthly panel dimensions — the conventional standard errors for
these panel estimators underestimate the true ones by almost 50%, these
results can be taken as prima facie evidence that just one factor is signi
ficant
in the DM panels also.14 This is clearly corroborated by the Bai and Ng
(2002) criteria (16) and (17). For instance, using RII residuals in
V (τ, Wτ),
for the ADF model ICp1 gives 3.655(τ =3), 3.611(τ =2) and 3.550(τ =1)for
the CPI-DM panel and 3.608(
τ =2) and 3.552(τ =1) for the WPI-DM panel.
Inspection of the factors graphs does not suggest any obvious interpretation.

Tables 5(A-B) summarise the estimation results.15 While the restrictions
-2 < ρi < 0 (ADF model) and γi = 0 (ARDL) both imply long-run PPP,
there is a subtle di
fference between them. The latter restriction only implies
that changes in relative prices are re
flected one-for-one in nominal exchange
rates, but the former is more restrictive. It additionally requires real exchange
rates to be I(0) variables.16 The regression results indicate that the inclusion
of factors has a small but consistent impact on the coe
fficient estimates.17 In
11 out of 12 cases, the inclusion of factors makes
ρ more negative strength-
ening the evidence in favour of PPP. In 10 out of the 12 cases, the included
factors move
γ closer to zero, again making the evidence more favourable
toward PPP. The e
ffects seem stronger for the dollar than the DM panels.

How do our PPP results compare with those from panel unit root or
cointegration approaches accounting for cross section dependence? On one
hand, our
findings contrast with the results of both Moon and Perron (2001)
and O’Connell (1998) which strongly reject the PPP hypothesis. On the
other, they are in line with those of Pedroni (1997) whose panel cointegration
tests support weak PPP and with those of Bai and Ng (2001a) who
find some
evidence for PPP using a common-idiosyncratic decomposition.

14 Repeating the simulations with the panel dimensions of our PPP data, N =13and
T = 324, gives a qualitatively similar ratio SM(SEb)/SSD(b) of 0∙56 (FE) and 0.57 (POLS).

15Note that the nominal exchange rate is normalized on the base year (1995) for the
POLS regression to prevent biases arising from pooling observations in di
fferent metrics.

16 On the basis of panel regressions of spot rates on price differentials a consistent esti-
mator may suggest a long-run slope coe
fficient equal to one while real exchange rates are
non-stationary. This issue is discussed in Coakley, Fuertes and Smith (2001).

17This is probably related to the high correlation between regressors in PPP equations
due to a common numeraire which, as with SURE-GLS, erodes the gains from our ap-
proach.

17



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