Selecting maximum lag length for LLC unit root test

[Noah Spencer]

I am using an LLC unit root test to determine whether the variables in my N = 10, T = 20 panel data set are stationary. However, the results of the test seem to be very sensitive to the maximum lag length I let AIC select.

For example, when I set the maximum lag length for this variable to 4, I reject the null of a unit root

xtunitroot llc dcaptolab, lags(aic 4)

Levin-Lin-Chu unit-root test for dcaptolab
------------------------------------------
Ho: Panels contain unit roots               Number of panels  =     10
Ha: Panels are stationary                   Number of periods =     20

AR parameter: Common                        Asymptotics: N/T -> 0
Panel means:  Included
Time trend:   Not included

ADF regressions: 0.50 lags average (chosen by AIC)
LR variance:     Bartlett kernel, 8.00 lags average (chosen by LLC)
------------------------------------------------------------------------------
                    Statistic      p-value
------------------------------------------------------------------------------
 Unadjusted t       -13.9013
 Adjusted t*        -10.8931        0.0000
------------------------------------------------------------------------------

, but when I allow the maximum lag length to be 8, I cannot reject the null:

xtunitroot llc dcaptolab, lags(aic 8)

Levin-Lin-Chu unit-root test for dcaptolab
------------------------------------------
Ho: Panels contain unit roots               Number of panels  =     10
Ha: Panels are stationary                   Number of periods =     20

AR parameter: Common                        Asymptotics: N/T -> 0
Panel means:  Included
Time trend:   Not included

ADF regressions: 6.70 lags average (chosen by AIC)
LR variance:     Bartlett kernel, 8.00 lags average (chosen by LLC)
------------------------------------------------------------------------------
                    Statistic      p-value
------------------------------------------------------------------------------
 Unadjusted t        -5.8614
 Adjusted t*          8.1148        1.0000
------------------------------------------------------------------------------

Furthermore, when I include the "trend" option, I get unit roots with pretty much all variables.

I'm not very familiar with time-series data analysis, so I'm not really sure theoretically why I'm getting such different results here, what they mean, and which options to proceed with. Any help would be greatly appreciated!