ı have N:12 T:31 panel data about EU agricultural. My variables inputcosts, totaloutput and totalsubsidies.All of my variables I(1). ı have CD and Heterojens. Results of Gengenbach,urbain and westerlunds ;

xtcaec y1 x1 x2, lags(0 3) select


Mean-group error correction models with variable cross-sectional averages
Following Chudik & Pesaran (2015); Gengenbach, Urbain & Westerlund (2015); Eberhardt & Presbitero (2015)

Group-specific lag selection enabled
Dependent variable y: y1



Panel EC-test:
-------------------------------------------------
d.y | Coef T-bar P-val*
---------------+---------------------------------
y(t-1) | -0.708 -3.554 <=0.01
-------------------------------------------------

Long-run average coefficients:
------------------------------------------------------------------------------
y1 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | .4697346 .0823996 5.70 0.000 .3082343 .631235
x2 | 2.278555 .7347663 3.10 0.002 .8384392 3.71867
------------------------------------------------------------------------------

Pesaran (2015) CD-test:
--------------------------------------
Variable | CD P-val
---------------+----------------------
y1 | 43.358 0.000
x1 | 25.804 0.000
x2 | 42.152 0.000
e | 0.392 0.695
--------------------------------------

Root mean square error: 3.3e+03
Number of observations: 358
Number of groups: 12

the series have long run relations. I performed CCE and AUGMENT with xtmg commands. My results;


. xtmg y1 x1 x2, cce robust


Pesaran (2006) Common Correlated Effects Mean Group estimator

All coefficients present represent averages across groups (code)
Coefficient averages computed as outlier-robust means (using rreg)

Mean Group type estimation Number of obs = 372
Group variable: code Number of groups = 12

Obs per group:
min = 31
avg = 31.0
max = 31

Wald chi2(2) = 41.89
Prob > chi2 = 0.0000

---------------- --------------------------------------------------------------
y1 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+ ------------------------------- ---------------------------------
x1 | .4346822 .0752134 5.78 0.000 .2872668 .5820977
x2 | 1.051112 .3606741 2.91 0.004 .3442035 1.75802
__00000M_y1 | .4522446 .1511749 2.99 0.003 .1559472 .748542
__00000L_x1 | -.0334324 .0389326 -0.86 0.390 -.1097389 .042874
__00000L_x2 | -.5905111 .2416771 -2.44 0.015 -1.064189 -.1168328
_cons | -964.8573 1753.616 -0.55 0.582 -4401.882 2472.168
------------------------------------------------------------------------------
Root Mean Squared Error (sigma): 5.3e+03
(RMSE uses residuals from group-specific regressions: unaffected by 'robust').
Cross-section averaged regressors are marked by the suffix:
_y1, _x1, _x2 respectively.



. xtmg y1 x1 x2, aug robust


Augmented Mean Group estimator (Bond & Eberhardt, 2009; Eberhardt & Teal, 2010)

Common dynamic process included as additional regressor
All coefficients present represent averages across groups (code)
Coefficient averages computed as outlier-robust means (using rreg)

Mean Group type estimation Number of obs = 372
Group variable: code Number of groups = 12

Obs per group:
min = 31
avg = 31.0
max = 31

Wald chi2(2) = 48.84
Prob > chi2 = 0.0000

------------------------------------------------------------------------------
y1 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | .4699278 .0923345 5.09 0.000 .2889555 .6509001
x2 | .7348895 .153431 4.79 0.000 .4341702 1.035609
__00000R_c | .4387439 .1377632 3.18 0.001 .168733 .7087547
_cons | 9258.004 4347.401 2.13 0.033 737.2543 17778.75
------------------------------------------------------------------------------
Root Mean Squared Error (sigma): 6.4e+03
(RMSE uses residuals from group-specific regressions: unaffected by 'robust').
Variable __00000R_c refers to the common dynamic process.

. xtmg y1 x1 x2, aug trend


Augmented Mean Group estimator (Bond & Eberhardt, 2009; Eberhardt & Teal, 2010)

Common dynamic process included as additional regressor
All coefficients present represent averages across groups (code)
Coefficient averages computed as unweighted means

Mean Group type estimation Number of obs = 372
Group variable: code Number of groups = 12

Obs per group:
min = 31
avg = 31.0
max = 31

Wald chi2(2) = 51.35
Prob > chi2 = 0.0000

------------------------------------------------------------------------------
y1 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | .4479802 .0702805 6.37 0.000 .310233 .5857275
x2 | .8870072 .4680652 1.90 0.058 -.0303837 1.804398
__00000R_c | .649198 .3349802 1.94 0.053 -.0073511 1.305747
__000007_t | -163.1971 934.6178 -0.17 0.861 -1995.014 1668.62
_cons | 17404.05 5798.292 3.00 0.003 6039.609 28768.5
------------------------------------------------------------------------------
Root Mean Squared Error (sigma): 4.8e+03
Variable __00000R_c refers to the common dynamic process.
Variable __000007_t refers to a group-specific linear trend.
Share of group-specific trends significant at 5% level: 0.250 (= 3 trends)


MY QUESTİONS;

1) I would like to know here, what does mean _00000M_y1, ____0000000L_x1 and ____0000000L_x2 ? What Should ı understant for these variables result here ?
2) Same questions about augment result, what does mean _0000R_c, __0007_t ? What Should ı understant for these variables result here ?
3) did ı do correct apllications?