I've conducted the IPSHIN test on two variables, one of which
appears to be
nonstationary (log of the minimum wage, or "lnmin1") and the
other appears
to be stationary (log of the 5th wage percentile, or "lnq5").
When I create
a third variable (log of 5th wage percentile - log of minimum wage,
or"lngap"), the IPSHIN test indicates that it is stationary.
How can it be
that the ratio of a stationary and nonstationary variable is
stationary?
(Some background info: the panels in this dataset are US
states -- all 50,
the time points are 6 month intervals over 20 years).
Here are my results:
. ipshin lnmin1 if gestcen~=53, lags(17) trend
Im-Pesaran-Shin test for cross-sectionally demeaned lnmin1
Deterministics chosen: constant & trend
t-bar test, N,T = (50,40) Obs = 1593
Augmented by 17 lags (average)
t-bar cv10 cv5 cv1 W[t-bar] P-value
-1.456 -2.320 -2.360 -2.440 . .
. ipshin lnq5 if gestcen~=53, lags(17) trend
Im-Pesaran-Shin test for cross-sectionally demeaned lnq5
Deterministics chosen: constant & trend
t-bar test, N,T = (50,40) Obs = 1593
Augmented by 17 lags (average)
t-bar cv10 cv5 cv1 W[t-bar] P-value
-3.087 -2.320 -2.360 -2.440 . .
. ipshin lngap if gestcen~=53, lags(17) trend
Im-Pesaran-Shin test for cross-sectionally demeaned lngap
Deterministics chosen: constant & trend
t-bar test, N,T = (50,40) Obs = 1593
Augmented by 17 lags (average)
t-bar cv10 cv5 cv1 W[t-bar] P-value
-3.585 -2.320 -2.360 -2.440 . .
