A Principal Components Approach to Cross-Section Dependence in Panels



observations for the nominal exchange rate and price index variables, 1972:1-
1998:12, giving T
= 324 observations. Four panels are constructed which
represent di
fferent combinations of price indexes and numeraire currencies.
The CPI-DM and CPI-US$ panels use consumer price index data and nom-
inal exchange exchange rates against the German mark and US dollar, re-
spectively. The WPI-DM and WPI-US$ panels are based on wholesale price
indexes.13

The following two PPP equations are considered:

i) Augmented Dickey-Fuller (ADF) type regression:

k

qit = α0i + α1it + ρiqi,t-1 +    γj qi,t-j + uit           (18)

j=1

where qit = eit dit represents the real exchange rate, dit = pit pt is the
price di
fferential between domestic country i and the foreign country, and all
variables are in logarithms.

ii) Autoregressive distributed lag (ARDL) regression:

kk

eit = αi + βidt + δ1iqi,t-1 + γidi,t-1 +    γj1iei,t-j +    γj2idi,t-j + uit

j=1              j=1             (19)

which is a reparameterization of an analogous equation with ei,t-1 as regressor
instead of
qi,t-1, where the coefficients on the former and on di,t-1 are δ1i and
δ2i , respectively, with γi = δ1i + δ2i .

The average correlations between the cross-section OLS (standardized)
residuals are shown in Table 3 together with the condition number and
p-
values of a diagonality test. All these indicate a considerable degree of cross-
section dependence. This is especially so for the dollar panels where the
depdendence may well re
flect the large swings in the dollar during the 1980s.
The number of retained factors (
λi > 1) is also reported in Table 3.

Panel regressions are estimated with and without factors. Table 4 reports
the estimated coe
fficients and t-ratios on the factors. The t-ratio on the single

13The CPI panels comprise N = 17 countries, Austria, Canada, Denmark, Finland,
Germany, Greece, Japan, Netherlands, Sweden, Spain, Switzerland, United Kingdom,
United States, Belgium, France, Italy, Norway, Portugal. The WPI panels exclude the
latter five countries and instead include Ireland to make N =13.

16



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