Greetings Stata Users.

I'm trying to estimate the public spending role over economic growth. So basically i'm using an inverse Wagner Law to see how those two variables are correlated.

I have checked either GDP (PIB) and Public Spending, and both of them have unit roots. Integrated in order 2.
This is consistent with higher R^2 value and probably a spurious regression that shows ahead.

Code:
reg PIB_nominal_bm total_gasto_nom

      Source |       SS           df       MS      Number of obs   =        28
-------------+----------------------------------   F(1, 26)        =  11070.25
       Model |  2.0580e+30         1  2.0580e+30   Prob > F        =    0.0000
    Residual |  4.8334e+27        26  1.8590e+26   R-squared       =    0.9977
-------------+----------------------------------   Adj R-squared   =    0.9976
       Total |  2.0628e+30        27  7.6400e+28   Root MSE        =    1.4e+13

---------------------------------------------------------------------------------
 PIB_nominal_bm |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
total_gasto_nom |   5.04e+09   4.79e+07   105.22   0.000     4.94e+09    5.14e+09
          _cons |   3.52e+13   4.05e+12     8.68   0.000     2.69e+13    4.35e+13
---------------------------------------------------------------------------------
Then next codes were

Code:
predict u, res
dfuller u

Dickey-Fuller test for unit root                   Number of obs   =        27

                               ---------- Interpolated Dickey-Fuller ---------
                  Test         1% Critical       5% Critical      10% Critical
               Statistic           Value             Value             Value
------------------------------------------------------------------------------
 Z(t)             -3.732            -3.736            -2.994            -2.628
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.0037
Maybe i'm reading wrong the p-value, but i suppose the null hypothesis it's unit roots behaviour.


So when i ran the stationary test of the residuals of that regression. dfuller test says it's stationary. So i'm a bit confused, does this mean that relation is not spurious and it's telling me the long-term relationships?.