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Is the insufficient number of observations statement in regards to the length of time series or the number of cross-sections? I am receiving the statement with the Kao tests but not with the Pedroni tests.

Yes, I was unclear. What I mean to ask is in the Dickey-Fuller Unit Root Test which hypothesis is being tested? a=0 or p=1.

For the unit root test, what is the hypothesis being tested? Is it,
yt = pyt-1 + et
H0: p=1 v. Ha: p<1
or
Δyt = ayt-1 + et where a = p-1
H0: a=0 v. Ha: a<0

Thanks for any help!