[Carlo Lazzaro]

Nils:
the statistical significance of -xttest0- outcome rules out pooled OLS only.
You should check via -xtoverid- if -re- is the way to go for your regression model #2.

[Nils Edgren]

Carlo Lazzaro

After running xtoverid, I get this result:

xi: xtreg GREENPREMIUM MATURITY logISSUEAMOUNT i.CURRENCY_n i.RATING_n i.PROJECTTYPE_n, re robust
i.CURRENCY_n      _ICURRENCY__1-11    (naturally coded; _ICURRENCY__1 omitted)
i.RATING_n        _IRATING_n_1-6      (naturally coded; _IRATING_n_1 omitted)
i.PROJECTTYPE_n   _IPROJECTTY_1-8     (naturally coded; _IPROJECTTY_1 omitted)

Random-effects GLS regression                   Number of obs     =     54,402
Group variable: RIC_2                           Number of groups  =        166

R-sq:                                           Obs per group:
     within  = 0.0000                                         min =         18
     between = 0.1362                                         avg =      327.7
     overall = 0.1798                                         max =      1,180

                                                Wald chi2(21)     =          .
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =          .

                                  (Std. Err. adjusted for 166 clusters in RIC_2)
--------------------------------------------------------------------------------
               |               Robust
  GREENPREMIUM |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
      MATURITY |   .0031035   .0013315     2.33   0.020     .0004938    .0057131
logISSUEAMOUNT |  -.0034405   .0035123    -0.98   0.327    -.0103245    .0034435
 _ICURRENCY__2 |   .0008916   .0078046     0.11   0.909    -.0144051    .0161884
 _ICURRENCY__3 |  -.0324914   .0122286    -2.66   0.008    -.0564589   -.0085239
 _ICURRENCY__4 |  -.0129723   .0084138    -1.54   0.123    -.0294631    .0035185
 _ICURRENCY__5 |  -.0415893   .0269605    -1.54   0.123    -.0944309    .0112522
 _ICURRENCY__6 |   .0278079   .0240035     1.16   0.247    -.0192382    .0748539
 _ICURRENCY__7 |   .0021348   .0158619     0.13   0.893     -.028954    .0332236
 _ICURRENCY__8 |  -.0271689   .0142142    -1.91   0.056    -.0550283    .0006905
 _ICURRENCY__9 |  -.0329504   .0121408    -2.71   0.007    -.0567458   -.0091549
_ICURRENCY__10 |  -.0030497   .0086104    -0.35   0.723    -.0199258    .0138263
_ICURRENCY__11 |  -.0010443   .0071359    -0.15   0.884    -.0150303    .0129418
  _IRATING_n_3 |  -.0023062   .0086004    -0.27   0.789    -.0191627    .0145503
  _IRATING_n_4 |  -.0014689   .0067198    -0.22   0.827    -.0146395    .0117016
  _IRATING_n_5 |   .0009454   .0082851     0.11   0.909     -.015293    .0171839
  _IRATING_n_6 |   .0046709   .0128373     0.36   0.716    -.0204898    .0298317
 _IPROJECTTY_2 |   .0012968   .0087217     0.15   0.882    -.0157975    .0183911
 _IPROJECTTY_3 |  -.0037861   .0132794    -0.29   0.776    -.0298132     .022241
 _IPROJECTTY_5 |   -.009492   .0116256    -0.82   0.414    -.0322778    .0132938
 _IPROJECTTY_6 |   .0035156   .0082554     0.43   0.670    -.0126646    .0196958
 _IPROJECTTY_7 |   .0213694   .0275832     0.77   0.439    -.0326927    .0754315
 _IPROJECTTY_8 |   .0393904     .01969     2.00   0.045     .0007987     .077982
         _cons |   .0780195   .0665256     1.17   0.241    -.0523682    .2084073
---------------+----------------------------------------------------------------
       sigma_u |  .03484352
       sigma_e |  .01669494
           rho |  .81328881   (fraction of variance due to u_i)
--------------------------------------------------------------------------------

. xtoverid

Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re  robust cluster(RIC_2)
Sargan-Hansen statistic 2004.515  Chi-sq(21)  P-value = 0.0000

I interpret this as saying that the random effects model is not suitable for my data, given the statistical significance of the xtoverid test?

Do you have any advice on how to go forward with the step 2 regression? I've emailed the authors of the paper I'm drawing inspiration from to inquire about how they performed their regressions but haven't received a reply yet. Is it correct that there is no way to run a fixed effect xtreg with factor variables that are constant for the entire time-series for each separate bond? As the data does not support neither pooled OLS nor -re-, if I've interpreted the results correctly, I'm not quite sure how to proceed.

[Carlo Lazzaro]

Nils:
the only way seems to go -re-.

[Nils Edgren]

Carlo Lazzaro
Ok, thank you for your input. Just for my own learning, if you care to expand on it, what are the drawbacks from going with the -re- specification when -xtoverid- has high statistical significance?

[Carlo Lazzaro]

Nils:
the drawback is that your model is misspecified.

[Nils Edgren]

Carlo Lazzaro
It does seem like a misspecified model is quite the drawback, and it's strange that the author of the original paper doesn't expand on this issue. However, performing regressions on panel data with time-invariable factor variables doesn't seem very rare to me. Is the method used in research to use misspecified models, or can you analyze panel data with factor variables in another way/another method of regression?

[Carlo Lazzaro]

Nils:
I cannot say whether the model reported in the paper you mention is misspecified or not.
What I can say is that sometimes published articles are not that clear on the applied quantitative methods.
Recently, I've spotted a squared-chi to test the difference between the mean of two continuous variables.
As far as regression models are concerned, it may well be that reserachers start out with a given research assumption (say, let's use -fe- in panel data regression) but do not check whether that assumption is ok for the dataset on hand.

[Nils Edgren]

Carlo Lazzaro
Hi again Carlo,

I have taken some time to think through my model and speak with my supervisor. I have also been in touch with the author of the paper I have previously mentioned as a source of inspiration. The reason that I have had trouble with the step 2 regression is that I have generated the wrong values for the dependent variable in the step 2 regression, GREENPREMIUM. Recall that this variable is the fixed effect for each bond from the step 1 regression. Since there are 166 bonds, I should have 166 observations for GREENPREMIUM. The step-2 regression will then not be a panel regression, but a cross-sectional regression on what is now cross-sectional data, not longitudinal. As can be seen in the following code, I did not generate these values correctly as I have a single observation for each time period for each bond:

. predict GREENPREMIUM, xb
(248,876 missing values generated)


    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
GREENPREMIUM |     54,402    .0134972    .0434479  -.2865282   .2611284

I think this is what is causing me some problems. I have googled how to obtain a single value for each group (i.e. each bond) but I can't seem to find the correct command to do so. Do you know of a way to go about doing this? To clarify, the outcome I'm trying to achieve is a single value for the variable GREENPREMIUM which is the fixed effect of the step 1 regression for each bond.

Is it as simple as obtaining the average of the fixed effect for each bond (although I didn't manage to do this either using egen, since I still ended up with one observation for each time period per bond)?

Would I then run a simple -reg- on the same variables with robust standard errors?

Many thanks,

Nils

[Nils Edgren]

To add on to my previous post as I can no longer edit it: You mentioned earlier that I should use -predict, xb- to retrieve the values for GREENPREMIUM. After reading -help predict- and -help xtreg-, is it not -predict,u- that I should be running to obtain the value of the fixed effect?

[Carlo Lazzaro]

Nils:
it depends on what you're interested in predicting.
The fitted values of the regressand (-predict, xb) are sometimes used as a predictor for secon-step regression models (eg, hurdle models): that was my idea concerning your research goal.
Conversely, if you're interested in the fixed effect, you are correct with going -predict <fixed_effect>, u-.
As far as your second-to-last post is concerned, fixed effect it changes between panels but not within panels: hence it remain constant and the mean of a constant is still a constant.

[Lu Westfield]

Nils:
1) the result of the F-test appearing as a footnote of the outcome table tells you that your dataset shows evidence of panelwise effect; hence a pooled OLS would not be appropriate given your data.

I read the presentation from Princeton to interpret my results from FE-model.
I think there is written that the F-Test is above on the right side. what is correct?
Furtermore I missed some explanations for my output and hope anyone can help me with this:

1. I think that I have very high Coef. and Std.Err./Robust Std. Errors compariny my results with other results. Is this a mistake or how can I interpret this?
2. How to interpret - corr(u_i, xb)= - ?
3. How to interpret -cons- ?

Thanks in advance

 xtset Unternehmen Jahr
       panel variable:  Unternehmen (unbalanced)
        time variable:  Jahr, 2014 to 2018, but with gaps
                delta:  1 year

. xtreg  Y x1 x2 x3 x4 x5 x6 x7 x8 EnSc SoSc GoSc i.Jahr, fe vce(cluster Unternehmen)

Fixed-effects (within) regression               Number of obs     =        342
Group variable: Unternehmen                     Number of groups  =         79

R-sq:                                           Obs per group:
     within  = 0.7509                                         min =          1
     between = 0.4127                                         avg =        4.3
     overall = 0.5609                                         max =          5

                                                F(15,78)          =      37.55
corr(u_i, Xb)  = -0.1701                        Prob > F          =     0.0000

                           (Std. Err. adjusted for 79 clusters in Unternehmen)
------------------------------------------------------------------------------
             |               Robust
           Y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          x1 |   .0091464   .0133006     0.69   0.494     -.017333    .0356259
          x2 |  -4.252209   5.415393    -0.79   0.435    -15.03343     6.52901
          x3 |   -.473511   .3681172    -1.29   0.202    -1.206376    .2593541
          x4 |  -12.73621    3.07371    -4.14   0.000     -18.8555   -6.616927
          x5 |    11.2182   4.267745     2.63   0.010     2.721767    19.71462
          x6 |   10.09346   .9198481    10.97   0.000     8.262186    11.92474
          x7 |   .0046431    .008961     0.52   0.606    -.0131968    .0224831
          x8 |   .0455602   .2953716     0.15   0.878    -.5424795    .6335998
        EnSc |  -.0980529   .1633973    -0.60   0.550    -.4233519    .2272461
        SoSc |   .2070221   .1437574     1.44   0.154    -.0791769    .4932211
        GoSc |    .102173   .0929156     1.10   0.275    -.0828077    .2871538
             |
        Jahr |
       2015  |   15.09593   3.107805     4.86   0.000     8.908765     21.2831
       2016  |   21.15731   5.616581     3.77   0.000     9.975561    32.33907
       2017  |   17.33039   5.899157     2.94   0.004     5.586071    29.07471
       2018  |   23.44871   3.764808     6.23   0.000     15.95355    30.94387
             |
       _cons |   17.31959   65.53958     0.26   0.792    -113.1597    147.7989
-------------+----------------------------------------------------------------
     sigma_u |  21.567956
     sigma_e |  12.179949
         rho |  .75819981   (fraction of variance due to u_i)
------------------------------------------------------------------------------

[Carlo Lazzaro]

Lu:
1) The F-test you refer to (the one in the upper right corner of -xtreg,fe- output) is the usual F-test (that is reported by -regress-, too). Basically, it is a test of all your coefficients being jointly zero (which is not your case).
2) That said, my guess is that you refer to another F-test, that appears as a footnote of the -xtreg,fe- outcome table (see -xtreg- entry in Stata .pdf manual for further details). Unoforunately, it is not reported when non-default standard errors are invoked.
3) Your within R-sq = 0.7509 is good. Have you already ruled out potential quasi-extreme multicollinearity issues via -estat vce, corr-?
4) corr(u_i, Xb) = -0.1701 expresses the correlation of the panel-wise effect u_i term of the composite error) with the vector of regressors (a form of weak endogeneity allowed by the -fe- machinery).
5) The _cons in -fe- is basically immaterial: so stop worrying about it and read https://www.stata.com/support/faqs/s...effects-model/.

As most of your questions refer to the building blocks of the (theoretical demanding) panel data regression methods, I would recommend you to take a comprehensive tour of the whole stuff in any decent panel data econometrics textbook. Stata users like https://www.stata.com/bookstore/micr...metrics-stata/ , coupled with Jeff Wooldridge 's https://mitpress.mit.edu/books/econo...second-edition.

[Lu Westfield]

Thank you Carlo!
I see in different analysis always under all independent variables a "Constant" in the Table. This is my "_cons" in stata? And I don´t have to worry about this when "_cons" isn´t significant?

My results from estat vce,corr are following:

. estat vce, corr

Correlation matrix of coefficients of xtreg model

             |                                                                                                    
        e(V) |       x1        x2        x3        x4        x5        x6        x7        x8      EnSc      SoSc 
-------------+----------------------------------------------------------------------------------------------------
          x1 |   1.0000                                                                                           
          x2 |   0.3189    1.0000                                                                                 
          x3 |   0.1569    0.0519    1.0000                                                                       
          x4 |   0.2888    0.2945   -0.3075    1.0000                                                             
          x5 |  -0.1585    0.0164    0.0046    0.1107    1.0000                                                   
          x6 |   0.0368   -0.0914    0.2009    0.0455   -0.0477    1.0000                                         
          x7 |  -0.3010   -0.2711    0.0802   -0.1098    0.3394   -0.0346    1.0000                               
          x8 |  -0.3803   -0.2050   -0.0585    0.0110    0.5135   -0.1670    0.6543    1.0000                     
        EnSc |  -0.0353    0.0723    0.2646   -0.1092    0.1595    0.0631    0.0981   -0.0557    1.0000           
        SoSc |   0.1788    0.1240    0.0527    0.2197    0.0468   -0.1515   -0.0065    0.0364    0.0279    1.0000 
        GoSc |  -0.0937   -0.1394    0.1172   -0.3607    0.0240    0.1171   -0.0630    0.0579   -0.0523   -0.1047 
   2015.Jahr |   0.0592    0.0311   -0.0661    0.1296    0.5468    0.0553   -0.2804   -0.0053   -0.0215   -0.2482 
   2016.Jahr |  -0.2148   -0.0847   -0.0050    0.0582    0.9116   -0.0774    0.3254    0.6054    0.0695   -0.0945 
   2017.Jahr |  -0.0019    0.0464   -0.0257    0.1158    0.7699    0.1604   -0.1434    0.3460    0.0026   -0.0591 
   2018.Jahr |  -0.0971   -0.1725   -0.1691   -0.0229    0.6975    0.0290    0.4196    0.4932   -0.0316   -0.1780 
       _cons |  -0.1720   -0.7835   -0.1696   -0.2972   -0.3599    0.0150   -0.2856   -0.2285   -0.3158   -0.2905 

             |               2015.     2016.     2017.     2018.          
        e(V) |     GoSc      Jahr      Jahr      Jahr      Jahr     _cons 
-------------+------------------------------------------------------------
        GoSc |   1.0000                                                   
   2015.Jahr |   0.0141    1.0000                                         
   2016.Jahr |   0.0279    0.6546    1.0000                               
   2017.Jahr |   0.1603    0.7566    0.8155    1.0000                     
   2018.Jahr |  -0.0061    0.5217    0.7630    0.6051    1.0000           
       _cons |   0.0956    0.0539   -0.2202   -0.1299   -0.1174    1.0000

[Carlo Lazzaro]

Lu:
1) https://www.stata.com/support/faqs/s...effects-model/. analitically explains why you should not consider _constant in -xtreg,fe.
2) your regression does not seem to suffer from quasi-extreme multicollinearity issues: good news.

[Lu Westfield]

Lu:
1) The F-test you refer to (the one in the upper right corner of -xtreg,fe- output) is the usual F-test (that is reported by -regress-, too). Basically, it is a test of all your coefficients being jointly zero (which is not your case).
2) That said, my guess is that you refer to another F-test, that appears as a footnote of the -xtreg,fe- outcome table (see -xtreg- entry in Stata .pdf manual for further details). Unoforunately, it is not reported when non-default standard errors are invoked.
3) Your within R-sq = 0.7509 is good. Have you already ruled out potential quasi-extreme multicollinearity issues via -estat vce, corr-?
4) corr(u_i, Xb) = -0.1701 expresses the correlation of the panel-wise effect u_i term of the composite error) with the vector of regressors (a form of weak endogeneity allowed by the -fe- machinery).
5) The _cons in -fe- is basically immaterial: so stop worrying about it and read https://www.stata.com/support/faqs/s...effects-model/.

As most of your questions refer to the building blocks of the (theoretical demanding) panel data regression methods, I would recommend you to take a comprehensive tour of the whole stuff in any decent panel data econometrics textbook. Stata users like https://www.stata.com/bookstore/micr...metrics-stata/ , coupled with Jeff Wooldridge 's https://mitpress.mit.edu/books/econo...second-edition.

Hi Carlo,
i have one more question about the output from Stata regard my regression.
1.) I did some further analysis after my paneldataregression like forward stepwise regression multilevel mediation. How it´s possible that some results are different to the results from the panelregression?
2.) some years are signifikant and some aren´t significant- how it´s possible to interpret this?

1 . xtset Unternehmen Jahr
panel variable: Unternehmen (unbalanced)
time variable: Jahr, 2014 to 2018, but with gaps
delta: 1 year
2 . xtreg CDSSpread Verschuldung nUG GKR ALTMAN Zinsstrukturkurve Marktliquidität Marktentwicklung implVola i.Jahr, f
> vce(robust)
Fixed-effects (within) regression Number of obs = 344
Group variable: Unternehmen Number of groups = 79
R-sq: Obs per group:
within = 0.7422 min = 1
between = 0.3895 avg = 4.4
overall = 0.5404 max = 5
F(12,78) = 34.66
corr(u_i, Xb) = -0.2170 Prob > F = 0.0000
(Std. Err. adjusted for 79 clusters in Unternehmen)
Robust
CDSSpread Coef. Std. Err. t P>|t| [95% Conf. Interval]
Verschuldung .2848077 .1970388 1.45 0.152 -.1074664 .6770817
nUG -3.275013 5.070523 -0.65 0.520 -13.36965 6.819623
GKR -.3970197 .3520745 -1.13 0.263 -1.097946 .3039067
ALTMAN -12.74651 3.10502 -4.11 0.000 -18.92813 -6.564889
Zinsstrukturkurve 1.70377 5.311331 0.32 0.749 -8.870278 12.27782
Marktliquidität 10.22229 .8418369 12.14 0.000 8.546325 11.89826
Marktentwicklung -.0026877 .007624 -0.35 0.725 -.0178658 .0124905
implVola -.1610713 .2465409 -0.65 0.515 -.6518966 .3297539
Jahr
2015 10.80228 2.416352 4.47 0.000 5.991693 15.61287
2016 9.692142 4.951764 1.96 0.054 -.1660623 19.55035
2017 8.934302 5.83122 1.53 0.130 -2.674764 20.54337
2018 17.87215 2.731239 6.54 0.000 12.43467 23.30963
_cons 56.81684 57.05361 1.00 0.322 -56.76818 170.4019
sigma_u 22.166669
sigma_e 12.341649
rho .7633655 (fraction of variance due to u_i)
3

Thank you in advance!