Allin Cottrell <cottrell@wfu.edu> replied:

You can get that quite easily if you want it. Example:

open greene14_1.gdt
logs C Q PF
list X = l_Q l_PF LF
panel l_C 0 X --fixed
series ai = $ahat
# correlation matrix of ai and regressors
corr ai X
matrix b = $coeff[2:]
series Xb = {X}*b
# correlation reported by Stata
corr ai Xb

The last correlation is the one that is reported by Stata as
corr(u_i, Xb). I'm not aware of programs that print the first
correlation matrix.

Thank you for this: it did indeed work for the example you gave (including Jack's later correction). 

However, when I ran this for my own (unbalanced) panel dataset (N=47, T-36, NT=823), -gretl- choked:

---------------------------------------------------------------------------------------------------------------------------------------------------------------------
? logs lavggdp pop
Listing 67 variables:
  0) const              1) country            2) year             
  3) score              4) max                5) adjscore         
  6) order              7) first              8) size             
  9) visits            10) language          11) host             
 12) border_countrie   13) links             14) eu               
 15) nato              16) icc               17) kyoto            
 18) fh_pr             19) fh_cl             20) fhscore          
 21) iraq1             22) iraq2             23) polindex         
 24) lagwbgdp          25) lagungdp          26) lavggdp          
 27) pop               28) l_lavggdp         29) l_pop            
 30) dt_1              31) dt_2              32) dt_3             
 33) dt_4              34) dt_5              35) dt_6             
 36) dt_7              37) dt_8              38) dt_9             
 39) dt_10             40) dt_11             41) dt_12            
 42) dt_13             43) dt_14             44) dt_15            
 45) dt_16             46) dt_17             47) dt_18            
 48) dt_19             49) dt_20             50) dt_21            
 51) dt_22             52) dt_23             53) dt_24            
 54) dt_25             55) dt_26             56) dt_27            
 57) dt_28             58) dt_29             59) dt_30            
 60) dt_31             61) dt_32             62) dt_33            
 63) dt_34             64) dt_35             65) dt_36            
 66) dt_37            

Warning: generated missing values
? list X = order first visits language host links fhscore l_lavggdp l_pop dt_2-dt_36
Generated list X
? panel adjscore 0 X --robust

Model 4: Fixed-effects, using 823 observations
Included 47 cross-sectional units
Time-series length: minimum 1, maximum 37
Dependent variable: adjscore
Robust (HAC) standard errors
Omitted due to exact collinearity: dt_37

              coefficient   std. error    t-ratio    p-value 
  -----------------------------------------------------------
  const       −275.214      1101.01       −0.2500    0.8027  
  order          1.08344       0.259419    4.176     3.32e-05 ***
  first          8.12990      14.4472      0.5627    0.5738  
  visits        −4.30177       0.973728   −4.418     1.15e-05 ***
  language     −18.4580        6.61705    −2.789     0.0054   ***
  host          15.3185        8.62230     1.777     0.0760   *
  links         11.3360        2.38579     4.751     2.43e-06 ***
  fhscore        4.84832       4.56374     1.062     0.2884  
  l_lavggdp    −14.6571       10.3819     −1.412     0.1584  
  l_pop          5.48696      66.0810      0.08303   0.9338  
  dt_1         119.389        41.8247      2.855     0.0044   ***
  dt_2         132.488        40.3803      3.281     0.0011   ***
  dt_3         141.034        40.5656      3.477     0.0005   ***
  dt_4         123.957        35.0240      3.539     0.0004   ***
  dt_5         143.473        36.8987      3.888     0.0001   ***
  dt_6         154.050        34.4538      4.471     9.01e-06 ***
  dt_7         145.373        33.1778      4.382     1.35e-05 ***
  dt_8         179.338        35.8883      4.997     7.29e-07 ***
  dt_9         150.118        31.1913      4.813     1.81e-06 ***
  dt_10        165.977        29.3945      5.647     2.34e-08 ***
  dt_11        169.547        32.2387      5.259     1.90e-07 ***
  dt_12        164.780        32.7179      5.036     5.98e-07 ***
  dt_13        143.035        27.0339      5.291     1.61e-07 ***
  dt_14        162.187        27.7669      5.841     7.81e-09 ***
  dt_15        154.748        23.8133      6.498     1.50e-10 ***
  dt_16        159.761        22.4501      7.116     2.65e-12 ***
  dt_17        165.958        24.1232      6.880     1.29e-11 ***
  dt_18        156.266        19.6676      7.945     7.33e-15 ***
  dt_19        135.978        22.1994      6.125     1.48e-09 ***
  dt_20        149.205        19.2219      7.762     2.82e-14 ***
  dt_21        177.119        19.9124      8.895     4.54e-18 ***
  dt_22        187.884        18.3915     10.22      5.42e-23 ***
  dt_23        157.278        17.5641      8.955     2.79e-18 ***
  dt_24        167.432        14.2153     11.78      1.92e-29 ***
  dt_25        188.551        16.9743     11.11      1.34e-26 ***
  dt_26        185.966        15.8267     11.75      2.54e-29 ***
  dt_27        184.989        17.7171     10.44      6.97e-24 ***
  dt_28        178.747        15.4103     11.60      1.13e-28 ***
  dt_29        154.438        18.2544      8.460     1.45e-16 ***
  dt_30         57.9160       19.2844      3.003     0.0028   ***
  dt_31         25.7587       18.6302      1.383     0.1672  
  dt_32         45.6746       18.4930      2.470     0.0137   **
  dt_33          3.04816      16.8308      0.1811    0.8563  
  dt_34         −5.74523      15.7867     −0.3639    0.7160  
  dt_35         13.7708       18.4558      0.7461    0.4558  
  dt_36         42.4965       14.1809      2.997     0.0028   ***

Mean dependent var  −236.0365   S.D. dependent var   98.53478
Sum squared resid     1796860   S.E. of regression   49.57908
R-squared            0.774854   Adjusted R-squared   0.746827
F(91, 731)           27.64603   P-value(F)           2.3e-182
Log-likelihood      −4331.643   Akaike criterion     8847.287
Schwarz criterion    9280.879   Hannan-Quinn         9013.630
rho                 −0.029294   Durbin-Watson        1.923296

Test for differing group intercepts -
  Null hypothesis: The groups have a common intercept
  Test statistic: F(46, 731) = 3.12977
  with p-value = P(F(46, 731) > 3.12977) = 1.00693e-10

? series ai = $ahat
Generated series ai (ID 67)
? corr ai X

Correlation Coefficients, using the observations 1:01 - 47:37
(missing values were skipped)

            ai         order         first        visits      language
        1.0000       -0.1228       -0.2883        0.7048        0.3867  ai
                      1.0000        0.0955       -0.0049       -0.1280  order
                                    1.0000       -0.2844       -0.0242  first
                                                  1.0000        0.0600  visits
                                                                1.0000  language

[...]

         dt_36         dt_37

[...]

       -0.0278       -0.0278  dt_33
       -0.0278       -0.0278  dt_34
       -0.0278       -0.0278  dt_35
        1.0000       -0.0278  dt_36
                      1.0000  dt_37

? series Xb = lincomb(X, $coeff[2:])
Data error
? matrix b = $coeff[2:]
Generated matrix b
? series Xb = {X}*b
Matrices not conformable for operation
---------------------------------------------------------------------------------------------------------------------------------------------------------------------

Difficult to know how to fix this - my data is what it is! 

 
> Also, no information is given on the standard deviations of
> these FE error components which are used to compute \rho
> (which is shown): any reason as to why?

In the gretl output "rho" is the first-order autocorrelation
of the residuals. Perhaps you're thinking of the random
effects model, for which we have to calculate the within and
between error variances (to get what gretl calls "theta", the
quasi-demeaning coefficient). In that case we do print both
variances.

Sorry, but I don't see reference to a 'quasi-demeaning coeffiecent' anywhere in the results, and any reference to 'theta' in the manual is in the context of ARMA models, Kalman filters and matrices; I also looked at the command reference as well - also nothing.
 
Clive Nicholas (clivenicholas.posterous.com)

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