Panel Unit Root Tests and Cointegration - Lag Problem

[Kate Sunderland]

Hello! I am a fresh Stata user and not very excellent on econometrics. My data is consisted of N=8 and T=16 in years. I have 13 independent variables and 1 dependent variable. My dependent variable is specified in t, and all my independents are in t-1. First, for all of them I checked cross-sectional dependence, and two of my independent variables are cross-sectionally independent and the rest is dependent. I use Pescadf to test unit root for my cross sectionally dependent variables and Fisher dfuller and pperron for my cross sectionally independent variables. All before, I tried to use "pvarsoc" command to specify the lags for all my variables, but I cannot succeeded in it. So, for 7 of my independent variables in the pescadf side, I reject the null of unit root using 0 lags. For 2 of my independent variables in the pescadf side, I reject the null using 1 lags, and for 1 using 2 lags (As I am using yearly data in a lagged form, I am abstaining to use 2 lags). For the rest two, when I used 1st differencing, all seem OK. For the Fisher side, when I apply 1st differencing into the one variable having unit root, it is also OK.
So, my question is choosing lags in such a way is OK or do I have to use any command to choose the lags?
My second question is, now, could I run Panel Cointegration (Westerlund) test as including my all level variables and variables in difference together? Or do I have to separate my cases and variables from each other?
Thanks in advance!

[John Riveros]

Greetings, As far as I understood your post, you're using lags in different orders to establish a stationary properties in the regression right? . Theory might give you an example of what number of lags should be used, and remember that varsoc commands just gives you an "ideal" of the optimal lag. Depending of the conditions and problems associate to your model, differente lags can be chosen with right different criteria like BIC, AIC, etc. So picking up specific lags might be able to me.

And concerning to your second questoin, i'm not sure how appropiate would it be to test together the level and differenced variables, I'd believe it's better in separate cases and variables, one for series and one for first differences.