hello everyone, I use a panel data and do after running the regression I get the residual and to follow my adviser I did the test of stationarity, but even after first differences the non-stationarity still remains, I hope I recieve your advice:
Code:
 xtset ifscode year
       panel variable:  ifscode (strongly balanced)
        time variable:  year, 1996 to 2019
                delta:  1 unit
Code:
. reghdfe f(0)lnfertility l(0/2)dum_recession l(1/2)lnfertility , absorb( i.ifscode year) vce(cluster ifscode) residuals(res)
(MWFE estimator converged in 3 iterations)

HDFE Linear regression                            Number of obs   =      3,116
Absorbing 2 HDFE groups                           F(   5,    141) =    6592.37
Statistics robust to heteroskedasticity           Prob > F        =     0.0000
                                                  R-squared       =     0.9998
                                                  Adj R-squared   =     0.9998
                                                  Within R-sq.    =     0.9493
Number of clusters (ifscode) =        142         Root MSE        =     0.0190

                               (Std. Err. adjusted for 142 clusters in ifscode)
-------------------------------------------------------------------------------
              |               Robust
  lnfertility |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
dum_recession |
          --. |  -.0013254   .0015998    -0.83   0.409    -.0044881    .0018372
          L1. |  -.0015468   .0011184    -1.38   0.169    -.0037579    .0006642
          L2. |    .000273   .0010136     0.27   0.788    -.0017309    .0022769
              |
  lnfertility |
          L1. |   1.316072   .0545001    24.15   0.000     1.208329    1.423815
          L2. |    -.36521   .0512967    -7.12   0.000    -.4666201      -.2638
              |
        _cons |   .8267416   .1036365     7.98   0.000     .6218594    1.031624
-------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
     ifscode |       142         142           0    *|
        year |        22           0          22     |
-----------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation
Code:
. predict r, resid
(292 missing values generated)

. xtunitroot fisher r, dfuller lags(0)
(292 missing values generated)

Fisher-type unit-root test for r
Based on augmented Dickey-Fuller tests
--------------------------------------
Ho: All panels contain unit roots           Number of panels       =    142
Ha: At least one panel is stationary        Avg. number of periods =  21.94

AR parameter: Panel-specific                Asymptotics: T -> Infinity
Panel means:  Included
Time trend:   Not included
Drift term:   Not included                  ADF regressions: 0 lags
------------------------------------------------------------------------------
                                  Statistic      p-value
------------------------------------------------------------------------------
 Inverse chi-squared(284)  P      2180.3843       0.0000
 Inverse normal            Z       -34.7407       0.0000
 Inverse logit t(714)      L*      -49.9196       0.0000
 Modified inv. chi-squared Pm       79.5705       0.0000
------------------------------------------------------------------------------
 P statistic requires number of panels to be finite.
 Other statistics are suitable for finite or infinite number of panels.
------------------------------------------------------------------------------
now after first differences :
Code:
. reghdfe f(0)dlnfertility l(0/2)dum_recession l(1/2)lnfertility , absorb( i.ifscode year) vce(cluster ifscode) residuals(res)
(MWFE estimator converged in 3 iterations)

HDFE Linear regression                            Number of obs   =      3,116
Absorbing 2 HDFE groups                           F(   5,    141) =      52.36
Statistics robust to heteroskedasticity           Prob > F        =     0.0000
                                                  R-squared       =     0.4073
                                                  Adj R-squared   =     0.3735
                                                  Within R-sq.    =     0.1755
Number of clusters (ifscode) =        142         Root MSE        =     0.0190

                               (Std. Err. adjusted for 142 clusters in ifscode)
-------------------------------------------------------------------------------
              |               Robust
 dlnfertility |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
dum_recession |
          --. |  -.0013254   .0015998    -0.83   0.409    -.0044881    .0018372
          L1. |  -.0015468   .0011184    -1.38   0.169    -.0037579    .0006642
          L2. |    .000273   .0010136     0.27   0.788    -.0017309    .0022769
              |
  lnfertility |
          L1. |   .3160717   .0545001     5.80   0.000     .2083288    .4238146
          L2. |    -.36521   .0512967    -7.12   0.000    -.4666201      -.2638
              |
        _cons |   .8267416   .1036365     7.98   0.000     .6218594    1.031624
-------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
     ifscode |       142         142           0    *|
        year |        22           0          22     |
-----------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation
Code:
. predict r, resid
(292 missing values generated)

. xtunitroot fisher r, dfuller lags(0)
(292 missing values generated)

Fisher-type unit-root test for r
Based on augmented Dickey-Fuller tests
--------------------------------------
Ho: All panels contain unit roots           Number of panels       =    142
Ha: At least one panel is stationary        Avg. number of periods =  21.94

AR parameter: Panel-specific                Asymptotics: T -> Infinity
Panel means:  Included
Time trend:   Not included
Drift term:   Not included                  ADF regressions: 0 lags
------------------------------------------------------------------------------
                                  Statistic      p-value
------------------------------------------------------------------------------
 Inverse chi-squared(284)  P      2180.3843       0.0000
 Inverse normal            Z       -34.7407       0.0000
 Inverse logit t(714)      L*      -49.9196       0.0000
 Modified inv. chi-squared Pm       79.5705       0.0000
------------------------------------------------------------------------------
 P statistic requires number of panels to be finite.
 Other statistics are suitable for finite or infinite number of panels.
------------------------------------------------------------------------------
also , I use lag(0) in both, and if I use lag(5) it is station.

many thanks for your valuable time and advice,

best regards .