[Luca Toni]

Luca:
1) if you get a coefficient from -i.nationality- under -fe-, some player changed her/his nationality;
2) using -timevar- as -panelid- is simply wrong, no matter the results.

1) This is assuming I run the model with series as -panelid-. If I run it with individualplayer as-panelid-, it indeed will be omitted, which makes sense.
2) I agree with you. I think there is no choice here but to set my panelid as "individualplayer Year". However, when I do it, I get the error of "repeated time values within panel", so I need to group both variables into something like this:

egen player_year = group(individualplayer Year)
xtset player_year

Is it correct?

[Carlo Lazzaro]

Luca:
1) Agreed.
2) Not quite. If you do not plan to use time-series related commands such as lags and leads, you can simply -xtset- your dataset with -panelid- only.

[Luca Toni]

Luca:
1) Agreed.
2) Not quite. If you do not plan to use time-series related commands such as lags and leads, you can simply -xtset- your dataset with -panelid- only.

Hi Carlo,
Sorry for the late response. I was quite busy the past month and now I can focus on my project.
I run the OLS regression with individualplayer as -panelid- along with year fixed effect and series fixed effect (ATP 250, ATP 500, Masters 1000, Grand Slam).
Here is two examples of regressions I run. The first example refers to the effort of each player, while the second example refers to the aggregate effort of both players in the match as independent variable. Note that in the second example, -panelid- is defined as matchplayers and not as individualplayer since it's measuring both players effort.

. encode Tournament, g(tournament)

. encode Nationality, g(nationality)

. encode IndividualPlayer, g(individualplayer)

. encode Series, g(series)

. encode MatchPlayers, g(matchplayers)

. xtset individualplayer

Panel variable: individualplayer (unbalanced)

. xtreg GameswonbyIndividualPlayer IndividualHeterogeneity IndividualPrizeSpread1000 NumOfTourneys SpreadNumOfTourneys Favourite Bestof i.series i.Year, fe vce(cluster individualplayer)

Fixed-effects (within) regression               Number of obs     =     37,060
Group variable: individual~r                    Number of groups  =        654

R-squared:                                      Obs per group:
     Within  = 0.2690                                         min =          1
     Between = 0.3615                                         avg =       56.7
     Overall = 0.2812                                         max =        509

                                                F(17,653)         =     456.81
corr(u_i, Xb) = 0.0687                          Prob > F          =     0.0000

                                  (Std. err. adjusted for 654 clusters in individualplayer)
-------------------------------------------------------------------------------------------
                          |               Robust
GameswonbyIndividualPla~r | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
--------------------------+----------------------------------------------------------------
  IndividualHeterogeneity |  -.0023609   .0003122    -7.56   0.000    -.0029739   -.0017479
IndividualPrizeSpread1000 |   .0027939   .0015879     1.76   0.079    -.0003242     .005912
            NumOfTourneys |   .0184153   .0068828     2.68   0.008     .0049002    .0319303
      SpreadNumOfTourneys |  -.0002235   .0001125    -1.99   0.047    -.0004445   -2.56e-06
                Favourite |   1.314657    .070442    18.66   0.000     1.176337    1.452977
                   Bestof |  -.0445321   .6416177    -0.07   0.945    -1.304415    1.215351
                          |
                   series |
                  ATP500  |  -.3337837   .0735048    -4.54   0.000    -.4781179   -.1894495
              Grand Slam  |   6.214253   1.283044     4.84   0.000     3.694863    8.733643
            Masters 1000  |  -.4011294   .0631825    -6.35   0.000    -.5251948   -.2770639
                          |
                     Year |
                    2014  |  -.0935003   .1096476    -0.85   0.394    -.3088047    .1218042
                    2015  |   .0329302   .1046406     0.31   0.753    -.1725424    .2384029
                    2016  |   -.083932   .1156073    -0.73   0.468    -.3109389    .1430748
                    2017  |  -.0665706   .1155386    -0.58   0.565    -.2934427    .1603015
                    2018  |    .067156   .1194761     0.56   0.574    -.1674476    .3017597
                    2019  |  -.0680303   .1239906    -0.55   0.583    -.3114986     .175438
                    2020  |  -.1585247   .1310829    -1.21   0.227    -.4159196    .0988701
                    2021  |  -.3222647   .1276262    -2.53   0.012    -.5728719   -.0716575
                          |
                    _cons |   10.94864   1.942606     5.64   0.000     7.134134    14.76315
--------------------------+----------------------------------------------------------------
                  sigma_u |  2.6007465
                  sigma_e |  4.5752669
                      rho |  .24421036   (fraction of variance due to u_i)
-------------------------------------------------------------------------------------------

. //second regression
. xtreg GameswonbyIndividualPlayer IndividualHeterogeneity IndividualPrizeSpread1000 Favourite Bestof i.series i.Year, fe vce(cluster individualplayer)

Fixed-effects (within) regression               Number of obs     =     37,060
Group variable: individual~r                    Number of groups  =        654

R-squared:                                      Obs per group:
     Within  = 0.2688                                         min =          1
     Between = 0.3520                                         avg =       56.7
     Overall = 0.2804                                         max =        509

                                                F(15,653)         =     502.67
corr(u_i, Xb) = 0.0686                          Prob > F          =     0.0000

                                  (Std. err. adjusted for 654 clusters in individualplayer)
-------------------------------------------------------------------------------------------
                          |               Robust
GameswonbyIndividualPla~r | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
--------------------------+----------------------------------------------------------------
  IndividualHeterogeneity |  -.0024577   .0003143    -7.82   0.000    -.0030748   -.0018405
IndividualPrizeSpread1000 |   -.000374   .0006148    -0.61   0.543    -.0015813    .0008333
                Favourite |   1.336677   .0706779    18.91   0.000     1.197893     1.47546
                   Bestof |  -.0417947    .641297    -0.07   0.948    -1.301048    1.217458
                          |
                   series |
                  ATP500  |  -.3249413   .0738492    -4.40   0.000    -.4699518   -.1799309
              Grand Slam  |   6.205432   1.283456     4.83   0.000     3.685233    8.725631
            Masters 1000  |  -.3854366   .0619527    -6.22   0.000    -.5070871   -.2637862
                          |
                     Year |
                    2014  |  -.0987801   .1092683    -0.90   0.366    -.3133397    .1157794
                    2015  |   .0354015   .1059005     0.33   0.738     -.172545     .243348
                    2016  |  -.0934448   .1155436    -0.81   0.419    -.3203266    .1334369
                    2017  |  -.0611828   .1166424    -0.52   0.600    -.2902223    .1678567
                    2018  |   .0709728   .1187949     0.60   0.550    -.1622933    .3042389
                    2019  |  -.0558739    .124418    -0.45   0.654    -.3001814    .1884336
                    2020  |  -.2288289   .1252234    -1.83   0.068    -.4747179    .0170602
                    2021  |  -.3277693   .1274498    -2.57   0.010    -.5780302   -.0775084
                          |
                    _cons |   11.20481   1.925714     5.82   0.000     7.423472    14.98615
--------------------------+----------------------------------------------------------------
                  sigma_u |  2.6209374
                  sigma_e |  4.5759297
                      rho |  .24702254   (fraction of variance due to u_i)
-------------------------------------------------------------------------------------------

. table () ( command ) (), command(xtreg GameswonbyIndividualPlayer IndividualHeterogeneity IndividualPrizeSpread1000 NumOfTourneys SpreadNumOfTourneys Favourite i.series i.Year, fe vce(cluster individualplayer)) comman
> d(xtreg GameswonbyIndividualPlayer IndividualHeterogeneity IndividualPrizeSpread1000 Favourite Bestof i.series i.Year, fe vce(cluster individualplayer))

--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
> --------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                 |  xtreg GameswonbyIndividualPlayer IndividualHeterogeneity IndividualPrizeSpread1000 NumOfTourneys SpreadNumOfTourneys Favourite i.series i.Year, fe vce(cluster indiv
> idualplayer)   xtreg GameswonbyIndividualPlayer IndividualHeterogeneity IndividualPrizeSpread1000 Favourite Bestof i.series i.Year, fe vce(cluster individualplayer)
---------------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------
> --------------------------------------------------------------------------------------------------------------------------------------------------------------------
Individual Heterogeneity         |                                                                                                                                                                      
>    -.0023609                                                                                                                                               -.0024577
Individual Prize Spread ($1,000) |                                                                                                                                                                      
>     .0027932                                                                                                                                                -.000374
NumOfTourneys                    |                                                                                                                                                                      
>     .0184167                                                                                                                                                        
Spread*NumOfTourneys             |                                                                                                                                                                      
>    -.0002235                                                                                                                                                        
Favourite                        |                                                                                                                                                                      
>     1.314637                                                                                                                                                1.336677
Series=ATP250                    |                                                                                                                                                                      
>            0                                                                                                                                                       0
Series=ATP500                    |                                                                                                                                                                      
>     -.333793                                                                                                                                               -.3249413
Series=Grand Slam                |                                                                                                                                                                      
>     6.125352                                                                                                                                                6.205432
Series=Masters 1000              |                                                                                                                                                                      
>    -.4011497                                                                                                                                               -.3854366
Year=2013                        |                                                                                                                                                                      
>            0                                                                                                                                                       0
Year=2014                        |                                                                                                                                                                      
>    -.0935085                                                                                                                                               -.0987801
Year=2015                        |                                                                                                                                                                      
>     .0329139                                                                                                                                                .0354015
Year=2016                        |                                                                                                                                                                      
>    -.0839482                                                                                                                                               -.0934448
Year=2017                        |                                                                                                                                                                      
>    -.0665916                                                                                                                                               -.0611828
Year=2018                        |                                                                                                                                                                      
>      .067136                                                                                                                                                .0709728
Year=2019                        |                                                                                                                                                                      
>    -.0680534                                                                                                                                               -.0558739
Year=2020                        |                                                                                                                                                                      
>    -.1585733                                                                                                                                               -.2288289
Year=2021                        |                                                                                                                                                                      
>    -.3222655                                                                                                                                               -.3277693
Best of                          |                                                                                                                                                                      
>                                                                                                                                                            -.0417947
Intercept                        |                                                                                                                                                                      
>     10.81506                                                                                                                                                11.20481
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
> --------------------------------------------------------------------------------------------------------------------------------------------------------------------

. collect label levels command 1 "Model 1" 2 "Model 2", modify

Second example:

. encode Tournament, g(tournament)

. encode Nationality, g(nationality)

. encode IndividualPlayer, g(individualplayer)

. encode Series, g(series)

. encode MatchPlayers, g(matchplayers)

. xtset matchplayers

Panel variable: matchplayers (unbalanced)

. xtreg Totalsumofgameswonpermatch Heterogeneity PrizeSpread1000 Bestof i.series i.Year, fe vce(cluster matchplayers)

Fixed-effects (within) regression               Number of obs     =     18,530
Group variable: matchplayers                    Number of groups  =     13,560

R-squared:                                      Obs per group:
     Within  = 0.3478                                         min =          1
     Between = 0.3387                                         avg =        1.4
     Overall = 0.3351                                         max =         15

                                                F(14,13559)       =     150.14
corr(u_i, Xb) = -0.0068                         Prob > F          =     0.0000

                         (Std. err. adjusted for 13,560 clusters in matchplayers)
---------------------------------------------------------------------------------
                |               Robust
Totalsumofgam~h | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
----------------+----------------------------------------------------------------
  Heterogeneity |  -.0028484   .0018229    -1.56   0.118    -.0064216    .0007247
PrizeSpread1000 |   .0012275   .0013695     0.90   0.370    -.0014569    .0039119
         Bestof |   1.674422   1.186041     1.41   0.158    -.6503836    3.999227
                |
         series |
        ATP500  |  -.0047427   .3155812    -0.02   0.988    -.6233256    .6138403
    Grand Slam  |   9.256325   2.374459     3.90   0.000     4.602056    13.91059
  Masters 1000  |   .0492267   .2740786     0.18   0.857    -.4880054    .5864587
                |
           Year |
          2014  |  -.6096555   .4718764    -1.29   0.196    -1.534599    .3152879
          2015  |  -.6740411   .4421081    -1.52   0.127    -1.540634    .1925523
          2016  |  -1.154098   .4601262    -2.51   0.012    -2.056009   -.2521869
          2017  |  -1.317497   .4610066    -2.86   0.004    -2.221133   -.4138597
          2018  |  -.9895531   .4827993    -2.05   0.040    -1.935907   -.0431994
          2019  |  -.8223668   .5030608    -1.63   0.102    -1.808436    .1637022
          2020  |  -1.443851   .6315866    -2.29   0.022    -2.681849   -.2058537
          2021  |  -1.721374   .6238365    -2.76   0.006     -2.94418   -.4985675
                |
          _cons |   19.04583   3.577602     5.32   0.000     12.03324    26.05843
----------------+----------------------------------------------------------------
        sigma_u |   7.078819
        sigma_e |  7.3292935
            rho |  .48262098   (fraction of variance due to u_i)
---------------------------------------------------------------------------------

. table () ( command ) (), command(xtreg Totalsumofgameswonpermatch Heterogeneity PrizeSpread1000 Bestof i.series i.Year, fe vce(cluster matchplayers))

--------------------------------------------------------------------------------------------------------------------------------------------
                      |  xtreg Totalsumofgameswonpermatch Heterogeneity PrizeSpread1000 Bestof i.series i.Year, fe vce(cluster matchplayers)
----------------------+---------------------------------------------------------------------------------------------------------------------
Heterogeneity         |                                                                                                            -.0028484
Prize Spread ($1,000) |                                                                                                             .0012275
Best of               |                                                                                                             1.674422
Series=ATP250         |                                                                                                                    0
Series=ATP500         |                                                                                                            -.0047427
Series=Grand Slam     |                                                                                                             9.256325
Series=Masters 1000   |                                                                                                             .0492267
Year=2013             |                                                                                                                    0
Year=2014             |                                                                                                            -.6096555
Year=2015             |                                                                                                            -.6740411
Year=2016             |                                                                                                            -1.154098
Year=2017             |                                                                                                            -1.317497
Year=2018             |                                                                                                            -.9895531
Year=2019             |                                                                                                            -.8223668
Year=2020             |                                                                                                            -1.443851
Year=2021             |                                                                                                            -1.721374
Intercept             |                                                                                                             19.04583
--------------------------------------------------------------------------------------------------------------------------------------------

. collect label levels command 1 "Model 1", modify

Two questions:
1) I also want to test in the OLS regression whether there are cultural differences between players, based on the Nationality variable. Note that I don't want to check how a player's country effects his own effort exertion, but generally for all the players from the same country (=nationality). Should I just add Nationality as an explanatory variable to the first example of regression?
2) Besides testing the effort exertion of the players, I want to estimate the probability of either player to win the match with odds ratio (logistic regression). I argue that the aggregate effort levels of both players in the match, along with prize spread and different nationalities (cultural differences) may impact the probabilities of the favourite/underdog. Is it reasonable to use the explained variable from the second example above as an explanatory variable in this regression? Moreover, how can I check the cultual differences in this case? The explained variable in this regression will be: ln(Pr(FavouriteWins)/Pr(UnderdogWins)), where it gets 1 if favourite won the match and 0 if underdog won the match.
Thanks in advance!

[Carlo Lazzaro]

Luca:
the main issue here seems to be that you do not have a panel -wise effect in your regressions.
That said:
1) the fixed effect estimator will wipe out all the time-invariant variables, like players' nationality;
2) I'm not clear with your logistic regression strategy.

[Luca Toni]

Luca:
the main issue here seems to be that you do not have a panel -wise effect in your regressions.
That said:
1) the fixed effect estimator will wipe out all the time-invariant variables, like players' nationality;
2) I'm not clear with your logistic regression strategy.

1) This is assuming I use i.nationality, which is not the case. I'm thinking of using nationality as an explanatory variable in the regression.
2) Basically, my theory is that higher heterogeneity (difference in ATP rankings) between two players will lead to lower total effort in the match. Then I want to check how lower effort from both players will effect the probability that the favourite player will win vs the underdog. This is in addition to prize spread in each match (which I assume that higher prize spread leads to higher effort from both players), and possible cultural differences between the players (nationality).

[Luca Toni]

Luca:
the main issue here seems to be that you do not have a panel -wise effect in your regressions.
That said:
1) the fixed effect estimator will wipe out all the time-invariant variables, like players' nationality;
2) I'm not clear with your logistic regression strategy.

Also, could you please explain what do you mean by that I don't have panel wise effect?

[Carlo Lazzaro]

Luca:
1) I meant exactly what you think that I did not. The -fe- estimator wipes out all time-invariant variables, regardless of their being y or xs. For instance: was Milos Raonic always a Canadian citizen from his very first steps in the ATP tour? If that were the case, the -fe- estimator will give you back no coefficient at all. In addition, if you code -i.nationality-, you clearly mean a predictor. So, I'm unclear with your idea of explanatory variable. That said, why not trying it yourself whenever you think that replies to your questions are off target?
2) the regressand of logistic regression is made of 1 and 0. In addition, I'm still unclear about the way you're going to model the lower effort made by both players;
3) sigma_e>sigma_u. This is apparent in the first regression and likely in the second one.

[Luca Toni]

Luca:
1) I meant exactly what you think that I did not. The -fe- estimator wipes out all time-invariant variables, regardless of their being y or xs. For instance: was Milos Raonic always a Canadian citizen from his very first steps in the ATP tour? If that were the case, the -fe- estimator will give you back no coefficient at all. In addition, if you code -i.nationality-, you clearly mean a predictor. So, I'm unclear with your idea of explanatory variable. That said, why not trying it yourself whenever you think that replies to your questions are off target?
2) the regressand of logistic regression is made of 1 and 0. In addition, I'm still unclear about the way you're going to model the lower effort made by both players;
3) sigma_e>sigma_u. This is apparent in the first regression and likely in the second one.

Thanks.
3) What I can do to deal with this porblem?
1) I agree that i.nationality is a predictor. How can I check cultural differences, though?
2) I want to predict the probability that the Favourite will win, based on both players effort (=total games won in a match), prize spread and cultural differences. What is not clear? I'm very confused.

[Carlo Lazzaro]

Luca:
3) if you do not have a panel-wise effect, you should go pooled OLS ( that is more similar to an -re- estimator);
1) if there's no within-panel variation, the -fe- estimator cannot give you back any coefficient about cultural difference;
2) if the regressand is coded 1=the favourite player wins; 0=otherwise, I'm fine with that. I do not know whether the number of games won in a match can be considered by a skilled reviewer as a good/acceptable/reasonable proxy for the effort made by both players during the match.

[Luca Toni]

Luca:
3) if you do not have a panel-wise effect, you should go pooled OLS ( that is more similar to an -re- estimator);
1) if there's no within-panel variation, the -fe- estimator cannot give you back any coefficient about cultural difference;
2) if the regressand is coded 1=the favourite player wins; 0=otherwise, I'm fine with that. I do not know whether the number of games won in a match can be considered by a skilled reviewer as a good/acceptable/reasonable proxy for the effort made by both players during the match.

Thanks.
3) Okay, so can you give me an example for pooled OLS? I'm not clear with it.
1) I mean, how can I check cultural differences without the -fe- estimator?
2) In some papers I found the rationaliztion behind number of games won in a match being a proxy for effort. But for now I want to specify the model.

[Carlo Lazzaro]

Luca:
3) pooled OLS is a multivariable OLS with clustered standard errors at -panelid- level;
1) you can check them with pooled OLS or -re-;
2) fine with that if reported in the literature.

[Luca Toni]

Luca:
3) pooled OLS is a multivariable OLS with clustered standard errors at -panelid- level;
1) you can check them with pooled OLS or -re-;
2) fine with that if reported in the literature.

Hi Carlo,
I tested which estimation method is preferred. All regressions point for using pooled OLS, right?

. encode Tournament, g(tournament)

. encode Nationality, g(nationality)

. encode IndividualPlayer, g(individualplayer)

. encode Series, g(series)

. encode MatchPlayers, g(matchplayers)

. xtset individualplayer

Panel variable: individualplayer (unbalanced)

. xtreg GameswonbyIndividualPlayer IndividualHeterogeneity IndividualPrizeSpread1000 NumOfTourneys SpreadNumOfTourneys Favourite Bestof i.series i.Year, fe

Fixed-effects (within) regression               Number of obs     =     37,060
Group variable: individual~r                    Number of groups  =        654

R-squared:                                      Obs per group:
     Within  = 0.2690                                         min =          1
     Between = 0.3615                                         avg =       56.7
     Overall = 0.2812                                         max =        509

                                                F(17,36389)       =     787.72
corr(u_i, Xb) = 0.0687                          Prob > F          =     0.0000

-------------------------------------------------------------------------------------------
GameswonbyIndividualPla~r | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
--------------------------+----------------------------------------------------------------
  IndividualHeterogeneity |  -.0023609   .0002631    -8.98   0.000    -.0028765   -.0018453
IndividualPrizeSpread1000 |   .0027939   .0011984     2.33   0.020      .000445    .0051428
            NumOfTourneys |   .0184153   .0064187     2.87   0.004     .0058344    .0309961
      SpreadNumOfTourneys |  -.0002235   .0000803    -2.78   0.005     -.000381   -.0000661
                Favourite |   1.314657   .0620341    21.19   0.000     1.193069    1.436246
                   Bestof |  -.0445321   .5735238    -0.08   0.938    -1.168656    1.079591
                          |
                   series |
                  ATP500  |  -.3337837   .0782178    -4.27   0.000     -.487093   -.1804744
              Grand Slam  |   6.214253   1.146856     5.42   0.000     3.966382    8.462124
            Masters 1000  |  -.4011294   .0663054    -6.05   0.000    -.5310899   -.2711689
                          |
                     Year |
                    2014  |  -.0935003   .1052767    -0.89   0.374    -.2998458    .1128452
                    2015  |   .0329302   .1070078     0.31   0.758    -.1768082    .2426687
                    2016  |   -.083932   .1074253    -0.78   0.435    -.2944888    .1266247
                    2017  |  -.0665706   .1080118    -0.62   0.538    -.2782768    .1451357
                    2018  |    .067156   .1100075     0.61   0.542    -.1484619     .282774
                    2019  |  -.0680303    .112315    -0.61   0.545    -.2881709    .1521103
                    2020  |  -.1585247   .1405395    -1.13   0.259    -.4339862    .1169367
                    2021  |  -.3222647   .1225655    -2.63   0.009    -.5624968   -.0820327
                          |
                    _cons |   10.94864   1.725505     6.35   0.000     7.566601    14.33068
--------------------------+----------------------------------------------------------------
                  sigma_u |  2.6007465
                  sigma_e |  4.5752669
                      rho |  .24421036   (fraction of variance due to u_i)
-------------------------------------------------------------------------------------------
F test that all u_i=0: F(653, 36389) = 2.01                  Prob > F = 0.0000

. estimates store fixed

. xtreg GameswonbyIndividualPlayer IndividualHeterogeneity IndividualPrizeSpread1000 NumOfTourneys SpreadNumOfTourneys Favourite Bestof i.series i.Year, re

Random-effects GLS regression                   Number of obs     =     37,060
Group variable: individual~r                    Number of groups  =        654

R-squared:                                      Obs per group:
     Within  = 0.2675                                         min =          1
     Between = 0.3931                                         avg =       56.7
     Overall = 0.2835                                         max =        509

                                                Wald chi2(17)     =   14655.63
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

-------------------------------------------------------------------------------------------
GameswonbyIndividualPla~r | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
--------------------------+----------------------------------------------------------------
  IndividualHeterogeneity |  -.0025504   .0002383   -10.70   0.000    -.0030174   -.0020833
IndividualPrizeSpread1000 |   .0036111    .001182     3.05   0.002     .0012943    .0059279
            NumOfTourneys |    .027603   .0046801     5.90   0.000     .0184302    .0367759
      SpreadNumOfTourneys |  -.0001945   .0000797    -2.44   0.015    -.0003507   -.0000383
                Favourite |   1.566812   .0574792    27.26   0.000     1.454155    1.679469
                   Bestof |  -.1760476   .5775278    -0.30   0.760    -1.307981     .955886
                          |
                   series |
                  ATP500  |  -.2177268   .0769566    -2.83   0.005     -.368559   -.0668946
              Grand Slam  |   6.587952   1.154729     5.71   0.000     4.324725    8.851179
            Masters 1000  |  -.1322213   .0636915    -2.08   0.038    -.2570543   -.0073883
                          |
                     Year |
                    2014  |   .0132113   .1024043     0.13   0.897    -.1874973      .21392
                    2015  |   .1750611   .1020665     1.72   0.086    -.0249856    .3751078
                    2016  |   .1154712   .1010772     1.14   0.253    -.0826365    .3135789
                    2017  |   .1550005   .1000298     1.55   0.121    -.0410542    .3510553
                    2018  |   .3406011    .099737     3.41   0.001     .1451203     .536082
                    2019  |   .2725252   .0996974     2.73   0.006     .0771218    .4679285
                    2020  |   .3320167   .1213176     2.74   0.006     .0942384    .5697949
                    2021  |   .2220665   .1015366     2.19   0.029     .0230585    .4210746
                          |
                    _cons |   10.68619   1.736184     6.15   0.000     7.283333    14.08905
--------------------------+----------------------------------------------------------------
                  sigma_u |          0
                  sigma_e |  4.5752669
                      rho |          0   (fraction of variance due to u_i)
-------------------------------------------------------------------------------------------

. estimates store random

. hausman fixed random

Note: the rank of the differenced variance matrix (16) does not equal the number of coefficients being tested (17); be sure this is what you expect, or there may be problems computing the test.  Examine the output of
        your estimators for anything unexpected and possibly consider scaling your variables so that the coefficients are on a similar scale.

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |     fixed        random       Difference       Std. err.
-------------+----------------------------------------------------------------
Individual~y |   -.0023609    -.0025504        .0001894        .0001115
Individ~1000 |    .0027939     .0036111       -.0008172        .0001972
NumOfTourn~s |    .0184153      .027603       -.0091878        .0043927
SpreadNumO~s |   -.0002235    -.0001945        -.000029        9.95e-06
   Favourite |    1.314657     1.566812       -.2521548        .0233317
      Bestof |   -.0445321    -.1760476        .1315155               .
      series |
          2  |   -.3337837    -.2177268       -.1160569        .0139897
          3  |    6.214253     6.587952        -.373699               .
          4  |   -.4011294    -.1322213       -.2689081        .0184337
        Year |
       2014  |   -.0935003     .0132113       -.1067116        .0244246
       2015  |    .0329302     .1750611       -.1421308        .0321419
       2016  |    -.083932     .1154712       -.1994033        .0363812
       2017  |   -.0665706     .1550005       -.2215711        .0407504
       2018  |     .067156     .3406011       -.2734451        .0464132
       2019  |   -.0680303     .2725252       -.3405555        .0517211
       2020  |   -.1585247     .3320167       -.4905414        .0709462
       2021  |   -.3222647     .2220665       -.5443312        .0686486
------------------------------------------------------------------------------
                          b = Consistent under H0 and Ha; obtained from xtreg.
           B = Inconsistent under Ha, efficient under H0; obtained from xtreg.

Test of H0: Difference in coefficients not systematic

   chi2(16) = (b-B)'[(V_b-V_B)^(-1)](b-B)
            = 350.08
Prob > chi2 = 0.0000
(V_b-V_B is not positive definite)

. hausman fixed random, sigmamore

Note: the rank of the differenced variance matrix (16) does not equal the number of coefficients being tested (17); be sure this is what you expect, or there may be problems computing the test.  Examine the output of
        your estimators for anything unexpected and possibly consider scaling your variables so that the coefficients are on a similar scale.

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |     fixed        random       Difference       Std. err.
-------------+----------------------------------------------------------------
Individual~y |   -.0023609    -.0025504        .0001894        .0001168
Individ~1000 |    .0027939     .0036111       -.0008172        .0002536
NumOfTourn~s |    .0184153      .027603       -.0091878        .0044751
SpreadNumO~s |   -.0002235    -.0001945        -.000029        .0000146
   Favourite |    1.314657     1.566812       -.2521548        .0247497
      Bestof |   -.0445321    -.1760476        .1315155        .0349149
      series |
          2  |   -.3337837    -.2177268       -.1160569        .0174387
          3  |    6.214253     6.587952        -.373699        .0719913
          4  |   -.4011294    -.1322213       -.2689081        .0204376
        Year |
       2014  |   -.0935003     .0132113       -.1067116         .028159
       2015  |    .0329302     .1750611       -.1421308        .0351565
       2016  |    -.083932     .1154712       -.1994033        .0390904
       2017  |   -.0665706     .1550005       -.2215711        .0432122
       2018  |     .067156     .3406011       -.2734451        .0486683
       2019  |   -.0680303     .2725252       -.3405555        .0538384
       2020  |   -.1585247     .3320167       -.4905414        .0733711
       2021  |   -.3222647     .2220665       -.5443312        .0705606
------------------------------------------------------------------------------
                          b = Consistent under H0 and Ha; obtained from xtreg.
           B = Inconsistent under Ha, efficient under H0; obtained from xtreg.

Test of H0: Difference in coefficients not systematic

   chi2(16) = (b-B)'[(V_b-V_B)^(-1)](b-B)
            = 296.78
Prob > chi2 = 0.0000

. xttest0

Breusch and Pagan Lagrangian multiplier test for random effects

        GameswonbyIndividualPlayer[individualplayer,t] = Xb + u[individualplayer] + e[individualplayer,t]

        Estimated results:
                         |       Var     SD = sqrt(Var)
                ---------+-----------------------------
               Games~yer |    29.7192       5.451532
                       e |   20.93307       4.575267
                       u |          0              0

        Test: Var(u) = 0
                             chibar2(01) =     0.00
                          Prob > chibar2 =   1.0000

. ssc install xttest3
checking xttest3 consistency and verifying not already installed...
all files already exist and are up to date.

. xtreg GameswonbyIndividualPlayer IndividualHeterogeneity IndividualPrizeSpread1000 NumOfTourneys SpreadNumOfTourneys Favourite Bestof i.series i.Year, fe

Fixed-effects (within) regression               Number of obs     =     37,060
Group variable: individual~r                    Number of groups  =        654

R-squared:                                      Obs per group:
     Within  = 0.2690                                         min =          1
     Between = 0.3615                                         avg =       56.7
     Overall = 0.2812                                         max =        509

                                                F(17,36389)       =     787.72
corr(u_i, Xb) = 0.0687                          Prob > F          =     0.0000

-------------------------------------------------------------------------------------------
GameswonbyIndividualPla~r | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
--------------------------+----------------------------------------------------------------
  IndividualHeterogeneity |  -.0023609   .0002631    -8.98   0.000    -.0028765   -.0018453
IndividualPrizeSpread1000 |   .0027939   .0011984     2.33   0.020      .000445    .0051428
            NumOfTourneys |   .0184153   .0064187     2.87   0.004     .0058344    .0309961
      SpreadNumOfTourneys |  -.0002235   .0000803    -2.78   0.005     -.000381   -.0000661
                Favourite |   1.314657   .0620341    21.19   0.000     1.193069    1.436246
                   Bestof |  -.0445321   .5735238    -0.08   0.938    -1.168656    1.079591
                          |
                   series |
                  ATP500  |  -.3337837   .0782178    -4.27   0.000     -.487093   -.1804744
              Grand Slam  |   6.214253   1.146856     5.42   0.000     3.966382    8.462124
            Masters 1000  |  -.4011294   .0663054    -6.05   0.000    -.5310899   -.2711689
                          |
                     Year |
                    2014  |  -.0935003   .1052767    -0.89   0.374    -.2998458    .1128452
                    2015  |   .0329302   .1070078     0.31   0.758    -.1768082    .2426687
                    2016  |   -.083932   .1074253    -0.78   0.435    -.2944888    .1266247
                    2017  |  -.0665706   .1080118    -0.62   0.538    -.2782768    .1451357
                    2018  |    .067156   .1100075     0.61   0.542    -.1484619     .282774
                    2019  |  -.0680303    .112315    -0.61   0.545    -.2881709    .1521103
                    2020  |  -.1585247   .1405395    -1.13   0.259    -.4339862    .1169367
                    2021  |  -.3222647   .1225655    -2.63   0.009    -.5624968   -.0820327
                          |
                    _cons |   10.94864   1.725505     6.35   0.000     7.566601    14.33068
--------------------------+----------------------------------------------------------------
                  sigma_u |  2.6007465
                  sigma_e |  4.5752669
                      rho |  .24421036   (fraction of variance due to u_i)
-------------------------------------------------------------------------------------------
F test that all u_i=0: F(653, 36389) = 2.01                  Prob > F = 0.0000

. xttest3

Modified Wald test for groupwise heteroskedasticity
in fixed effect regression model

H0: sigma(i)^2 = sigma^2 for all i

chi2 (654)  =   6.5e+34
Prob>chi2 =      0.0000

 encode Tournament, g(tournament)

. encode Nationality, g(nationality)

. encode IndividualPlayer, g(individualplayer)

. encode Series, g(series)

. encode MatchPlayers, g(matchplayers)

. xtset matchplayers

Panel variable: matchplayers (unbalanced)

. xtreg Totalsumofgameswonpermatch Heterogeneity PrizeSpread1000 Bestof i.series i.Year, fe

Fixed-effects (within) regression               Number of obs     =     18,530
Group variable: matchplayers                    Number of groups  =     13,560

R-squared:                                      Obs per group:
     Within  = 0.3478                                         min =          1
     Between = 0.3387                                         avg =        1.4
     Overall = 0.3351                                         max =         15

                                                F(14,4956)        =     188.79
corr(u_i, Xb) = -0.0068                         Prob > F          =     0.0000

---------------------------------------------------------------------------------
Totalsumofgam~h | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
----------------+----------------------------------------------------------------
  Heterogeneity |  -.0028484   .0018288    -1.56   0.119    -.0064337    .0007369
PrizeSpread1000 |   .0012275    .001061     1.16   0.247    -.0008525    .0033075
         Bestof |   1.674422   1.914941     0.87   0.382     -2.07971    5.428553
                |
         series |
        ATP500  |  -.0047427   .3388821    -0.01   0.989    -.6691017    .6596163
    Grand Slam  |   9.256325   3.829819     2.42   0.016     1.748185    16.76446
  Masters 1000  |   .0492267   .2919567     0.17   0.866    -.5231377     .621591
                |
           Year |
          2014  |  -.6096555    .461218    -1.32   0.186    -1.513847     .294536
          2015  |  -.6740411   .4579201    -1.47   0.141    -1.571767     .223685
          2016  |  -1.154098   .4687471    -2.46   0.014     -2.07305   -.2351462
          2017  |  -1.317497   .4729697    -2.79   0.005    -2.244727   -.3902666
          2018  |  -.9895531    .498714    -1.98   0.047    -1.967253   -.0118529
          2019  |  -.8223668    .512864    -1.60   0.109    -1.827807    .1830737
          2020  |  -1.443851   .6389287    -2.26   0.024    -2.696434    -.191268
          2021  |  -1.721374   .6231108    -2.76   0.006    -2.942947   -.4998006
                |
          _cons |   19.04583   5.757251     3.31   0.001     7.759072     30.3326
----------------+----------------------------------------------------------------
        sigma_u |   7.078819
        sigma_e |  7.3292935
            rho |  .48262098   (fraction of variance due to u_i)
---------------------------------------------------------------------------------
F test that all u_i=0: F(13559, 4956) = 1.08                 Prob > F = 0.0003

. estimates store fixed

. xtreg Totalsumofgameswonpermatch Heterogeneity PrizeSpread1000 Bestof i.series i.Year, re

Random-effects GLS regression                   Number of obs     =     18,530
Group variable: matchplayers                    Number of groups  =     13,560

R-squared:                                      Obs per group:
     Within  = 0.3450                                         min =          1
     Between = 0.3456                                         avg =        1.4
     Overall = 0.3400                                         max =         15

                                                Wald chi2(14)     =    9578.12
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

---------------------------------------------------------------------------------
Totalsumofgam~h | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
----------------+----------------------------------------------------------------
  Heterogeneity |  -.0029592   .0005384    -5.50   0.000    -.0040144   -.0019041
PrizeSpread1000 |   .0013567   .0008093     1.68   0.094    -.0002296    .0029429
         Bestof |  -.3231794   1.331626    -0.24   0.808    -2.933119    2.286761
                |
         series |
        ATP500  |  -.3779085    .177292    -2.13   0.033    -.7253944   -.0304226
    Grand Slam  |   13.13855   2.662544     4.93   0.000     7.920055    18.35704
  Masters 1000  |  -.2238654   .1468021    -1.52   0.127    -.5115923    .0638615
                |
           Year |
          2014  |   .0180459     .23667     0.08   0.939    -.4458188    .4819106
          2015  |   .3838133   .2358749     1.63   0.104     -.078493    .8461197
          2016  |   .2445954   .2339697     1.05   0.296    -.2139768    .7031676
          2017  |   .3665561   .2313251     1.58   0.113    -.0868329     .819945
          2018  |   .7213323   .2306617     3.13   0.002     .2692437    1.173421
          2019  |    .598253    .229887     2.60   0.009     .1476827    1.048823
          2020  |   .3789206   .2746955     1.38   0.168    -.1594728    .9173139
          2021  |   .4050027   .2353402     1.72   0.085    -.0562556    .8662611
                |
          _cons |    23.8909   3.998841     5.97   0.000     16.05332    31.72849
----------------+----------------------------------------------------------------
        sigma_u |  1.7279101
        sigma_e |  7.3292935
            rho |  .05265346   (fraction of variance due to u_i)
---------------------------------------------------------------------------------

. estimates store random

. hausman fixed random

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |     fixed        random       Difference       Std. err.
-------------+----------------------------------------------------------------
Heterogene~y |   -.0028484    -.0029592        .0001108        .0017478
PrizeSp~1000 |    .0012275     .0013567       -.0001291        .0006861
      Bestof |    1.674422    -.3231794        1.997601        1.376143
      series |
          2  |   -.0047427    -.3779085        .3731658        .2888056
          3  |    9.256325     13.13855       -3.882221        2.752883
          4  |    .0492267    -.2238654        .2730921        .2523645
        Year |
       2014  |   -.6096555     .0180459       -.6277014        .3958653
       2015  |   -.6740411     .3838133       -1.057854        .3924969
       2016  |   -1.154098     .2445954       -1.398694        .4061798
       2017  |   -1.317497     .3665561       -1.684053        .4125397
       2018  |   -.9895531     .7213323       -1.710885        .4421661
       2019  |   -.8223668      .598253        -1.42062        .4584555
       2020  |   -1.443851     .3789206       -1.822772        .5768642
       2021  |   -1.721374     .4050027       -2.126376        .5769593
------------------------------------------------------------------------------
                          b = Consistent under H0 and Ha; obtained from xtreg.
           B = Inconsistent under Ha, efficient under H0; obtained from xtreg.

Test of H0: Difference in coefficients not systematic

   chi2(14) = (b-B)'[(V_b-V_B)^(-1)](b-B)
            =  28.18
Prob > chi2 = 0.0135

. hausman fixed random, sigmamore

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |     fixed        random       Difference       Std. err.
-------------+----------------------------------------------------------------
Heterogene~y |   -.0028484    -.0029592        .0001108        .0017517
PrizeSp~1000 |    .0012275     .0013567       -.0001291        .0006894
      Bestof |    1.674422    -.3231794        1.997601        1.381579
      series |
          2  |   -.0047427    -.3779085        .3731658        .2896172
          3  |    9.256325     13.13855       -3.882221        2.763753
          4  |    .0492267    -.2238654        .2730921         .253054
        Year |
       2014  |   -.6096555     .0180459       -.6277014        .3969622
       2015  |   -.6740411     .3838133       -1.057854        .3935874
       2016  |   -1.154098     .2445954       -1.398694         .407284
       2017  |   -1.317497     .3665561       -1.684053        .4136466
       2018  |   -.9895531     .7213323       -1.710885        .4433143
       2019  |   -.8223668      .598253        -1.42062        .4596267
       2020  |   -1.443851     .3789206       -1.822772        .5783089
       2021  |   -1.721374     .4050027       -2.126376        .5783332
------------------------------------------------------------------------------
                          b = Consistent under H0 and Ha; obtained from xtreg.
           B = Inconsistent under Ha, efficient under H0; obtained from xtreg.

Test of H0: Difference in coefficients not systematic

   chi2(14) = (b-B)'[(V_b-V_B)^(-1)](b-B)
            =  28.03
Prob > chi2 = 0.0141

. xttest0

Breusch and Pagan Lagrangian multiplier test for random effects

        Totalsumofgameswonpermatch[matchplayers,t] = Xb + u[matchplayers] + e[matchplayers,t]

        Estimated results:
                         |       Var     SD = sqrt(Var)
                ---------+-----------------------------
               Totalsu~h |   86.30302       9.289942
                       e |   53.71854       7.329293
                       u |   2.985673        1.72791

        Test: Var(u) = 0
                             chibar2(01) =    60.78
                          Prob > chibar2 =   0.0000

. ssc install xttest3
checking xttest3 consistency and verifying not already installed...
all files already exist and are up to date.

. xtreg Totalsumofgameswonpermatch Heterogeneity PrizeSpread1000 Bestof i.series i.Year, fe

Fixed-effects (within) regression               Number of obs     =     18,530
Group variable: matchplayers                    Number of groups  =     13,560

R-squared:                                      Obs per group:
     Within  = 0.3478                                         min =          1
     Between = 0.3387                                         avg =        1.4
     Overall = 0.3351                                         max =         15

                                                F(14,4956)        =     188.79
corr(u_i, Xb) = -0.0068                         Prob > F          =     0.0000

---------------------------------------------------------------------------------
Totalsumofgam~h | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
----------------+----------------------------------------------------------------
  Heterogeneity |  -.0028484   .0018288    -1.56   0.119    -.0064337    .0007369
PrizeSpread1000 |   .0012275    .001061     1.16   0.247    -.0008525    .0033075
         Bestof |   1.674422   1.914941     0.87   0.382     -2.07971    5.428553
                |
         series |
        ATP500  |  -.0047427   .3388821    -0.01   0.989    -.6691017    .6596163
    Grand Slam  |   9.256325   3.829819     2.42   0.016     1.748185    16.76446
  Masters 1000  |   .0492267   .2919567     0.17   0.866    -.5231377     .621591
                |
           Year |
          2014  |  -.6096555    .461218    -1.32   0.186    -1.513847     .294536
          2015  |  -.6740411   .4579201    -1.47   0.141    -1.571767     .223685
          2016  |  -1.154098   .4687471    -2.46   0.014     -2.07305   -.2351462
          2017  |  -1.317497   .4729697    -2.79   0.005    -2.244727   -.3902666
          2018  |  -.9895531    .498714    -1.98   0.047    -1.967253   -.0118529
          2019  |  -.8223668    .512864    -1.60   0.109    -1.827807    .1830737
          2020  |  -1.443851   .6389287    -2.26   0.024    -2.696434    -.191268
          2021  |  -1.721374   .6231108    -2.76   0.006    -2.942947   -.4998006
                |
          _cons |   19.04583   5.757251     3.31   0.001     7.759072     30.3326
----------------+----------------------------------------------------------------
        sigma_u |   7.078819
        sigma_e |  7.3292935
            rho |  .48262098   (fraction of variance due to u_i)
---------------------------------------------------------------------------------
F test that all u_i=0: F(13559, 4956) = 1.08                 Prob > F = 0.0003

. xttest3

Modified Wald test for groupwise heteroskedasticity
in fixed effect regression model

H0: sigma(i)^2 = sigma^2 for all i

chi2 (13560)  = 1.1e+36
Prob>chi2 =      0.0000

[Luca Toni]

Luca:
3) pooled OLS is a multivariable OLS with clustered standard errors at -panelid- level;
1) you can check them with pooled OLS or -re-;
2) fine with that if reported in the literature.

One more code:

. encode Tournament, g(tournament)

. encode Nationality, g(nationality)

. encode IndividualPlayer, g(individualplayer)

. encode Series, g(series)

. encode MatchPlayers, g(matchplayers)

. xtset individualplayer

Panel variable: individualplayer (unbalanced)

. xtreg DiffIngameswonbyFavandUnd Heterogeneity PrizeSpread1000 Bestof i.series i.Year, fe

Fixed-effects (within) regression               Number of obs     =     18,530
Group variable: individual~r                    Number of groups  =        367

R-squared:                                      Obs per group:
     Within  = 0.0477                                         min =          1
     Between = 0.0004                                         avg =       50.5
     Overall = 0.0339                                         max =        493

                                                F(14,18149)       =      64.98
corr(u_i, Xb) = -0.0969                         Prob > F          =     0.0000

---------------------------------------------------------------------------------
DiffIngameswo~d | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
----------------+----------------------------------------------------------------
  Heterogeneity |   .0067286    .000366    18.38   0.000     .0060112     .007446
PrizeSpread1000 |  -.0044263   .0005463    -8.10   0.000    -.0054971   -.0033554
         Bestof |   1.351407   .8916107     1.52   0.130    -.3962348    3.099048
                |
         series |
        ATP500  |  -.3775258   .1219053    -3.10   0.002    -.6164718   -.1385798
    Grand Slam  |  -.9808101     1.7831    -0.55   0.582    -4.475855    2.514234
  Masters 1000  |  -.3395359   .1031708    -3.29   0.001    -.5417604   -.1373114
                |
           Year |
          2014  |  -.0525744   .1638633    -0.32   0.748    -.3737621    .2686133
          2015  |   .1385333   .1671947     0.83   0.407    -.1891841    .4662508
          2016  |  -.1340997   .1684127    -0.80   0.426    -.4642046    .1960053
          2017  |  -.4425871   .1690888    -2.62   0.009    -.7740171   -.1111572
          2018  |  -.4306342   .1730089    -2.49   0.013    -.7697481   -.0915204
          2019  |  -.7240737   .1765527    -4.10   0.000    -1.070134   -.3780138
          2020  |  -.6243809   .2112932    -2.96   0.003    -1.038536   -.2102262
          2021  |  -.6980748   .1933546    -3.61   0.000    -1.077068   -.3190813
                |
          _cons |  -2.341599    2.67739    -0.87   0.382    -7.589538     2.90634
----------------+----------------------------------------------------------------
        sigma_u |  3.2101967
        sigma_e |  5.0243405
            rho |  .28988884   (fraction of variance due to u_i)
---------------------------------------------------------------------------------
F test that all u_i=0: F(366, 18149) = 5.14                  Prob > F = 0.0000

. estimates store fixed

. xtreg DiffIngameswonbyFavandUnd Heterogeneity PrizeSpread1000 Bestof i.series i.Year, re

Random-effects GLS regression                   Number of obs     =     18,530
Group variable: individual~r                    Number of groups  =        367

R-squared:                                      Obs per group:
     Within  = 0.0476                                         min =          1
     Between = 0.0009                                         avg =       50.5
     Overall = 0.0353                                         max =        493

                                                Wald chi2(14)     =     881.04
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

---------------------------------------------------------------------------------
DiffIngameswo~d | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
----------------+----------------------------------------------------------------
  Heterogeneity |   .0065557   .0003609    18.16   0.000     .0058483    .0072631
PrizeSpread1000 |  -.0041721   .0005455    -7.65   0.000    -.0052412   -.0031029
         Bestof |   1.296934   .8915097     1.45   0.146    -.4503932     3.04426
                |
         series |
        ATP500  |  -.2971972   .1211109    -2.45   0.014    -.5345703   -.0598242
    Grand Slam  |   -.828509   1.782848    -0.46   0.642    -4.322826    2.665808
  Masters 1000  |  -.2362592   .1022965    -2.31   0.021    -.4367565   -.0357618
                |
           Year |
          2014  |  -.0181109   .1615341    -0.11   0.911    -.3347118      .29849
          2015  |   .2027717   .1637222     1.24   0.216     -.118118    .5236613
          2016  |  -.0812475   .1640359    -0.50   0.620     -.402752    .2402569
          2017  |  -.3550785   .1641142    -2.16   0.030    -.6767363   -.0334206
          2018  |   -.347249   .1667316    -2.08   0.037     -.674037   -.0204611
          2019  |  -.6084672    .169118    -3.60   0.000    -.9399324   -.2770021
          2020  |  -.4684134   .2016972    -2.32   0.020    -.8637327    -.073094
          2021  |  -.5058561   .1801663    -2.81   0.005    -.8589756   -.1527367
                |
          _cons |  -3.276753   2.678904    -1.22   0.221    -8.527307    1.973802
----------------+----------------------------------------------------------------
        sigma_u |  1.4537897
        sigma_e |  5.0243405
            rho |  .07725503   (fraction of variance due to u_i)
---------------------------------------------------------------------------------

. estimates store random

. hausman fixed random

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |     fixed        random       Difference       Std. err.
-------------+----------------------------------------------------------------
Heterogene~y |    .0067286     .0065557        .0001729        .0000606
PrizeSp~1000 |   -.0044263    -.0041721       -.0002542        .0000303
      Bestof |    1.351407     1.296934         .054473         .013424
      series |
          2  |   -.3775258    -.2971972       -.0803286        .0138944
          3  |   -.9808101     -.828509       -.1523011         .029979
          4  |   -.3395359    -.2362592       -.1032767        .0134032
        Year |
       2014  |   -.0525744    -.0181109       -.0344635        .0275308
       2015  |    .1385333     .2027717       -.0642383        .0338985
       2016  |   -.1340997    -.0812475       -.0528521        .0381455
       2017  |   -.4425871    -.3550785       -.0875087         .040713
       2018  |   -.4306342     -.347249       -.0833852        .0461808
       2019  |   -.7240737    -.6084672       -.1156065        .0506946
       2020  |   -.6243809    -.4684134       -.1559675        .0629527
       2021  |   -.6980748    -.5058561       -.1922186        .0701864
------------------------------------------------------------------------------
                          b = Consistent under H0 and Ha; obtained from xtreg.
           B = Inconsistent under Ha, efficient under H0; obtained from xtreg.

Test of H0: Difference in coefficients not systematic

   chi2(14) = (b-B)'[(V_b-V_B)^(-1)](b-B)
            = 125.42
Prob > chi2 = 0.0000

. hausman fixed random, sigmamore

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |     fixed        random       Difference       Std. err.
-------------+----------------------------------------------------------------
Heterogene~y |    .0067286     .0065557        .0001729         .000061
PrizeSp~1000 |   -.0044263    -.0041721       -.0002542        .0000321
      Bestof |    1.351407     1.296934         .054473        .0221359
      series |
          2  |   -.3775258    -.2971972       -.0803286        .0141012
          3  |   -.9808101     -.828509       -.1523011        .0462358
          4  |   -.3395359    -.2362592       -.1032767         .013557
        Year |
       2014  |   -.0525744    -.0181109       -.0344635        .0277202
       2015  |    .1385333     .2027717       -.0642383        .0340588
       2016  |   -.1340997    -.0812475       -.0528521        .0382901
       2017  |   -.4425871    -.3550785       -.0875087        .0408496
       2018  |   -.4306342     -.347249       -.0833852        .0463069
       2019  |   -.7240737    -.6084672       -.1156065        .0508143
       2020  |   -.6243809    -.4684134       -.1559675        .0630908
       2021  |   -.6980748    -.5058561       -.1922186        .0702901
------------------------------------------------------------------------------
                          b = Consistent under H0 and Ha; obtained from xtreg.
           B = Inconsistent under Ha, efficient under H0; obtained from xtreg.

Test of H0: Difference in coefficients not systematic

   chi2(14) = (b-B)'[(V_b-V_B)^(-1)](b-B)
            = 118.87
Prob > chi2 = 0.0000

. xttest0

Breusch and Pagan Lagrangian multiplier test for random effects

        DiffIngameswonbyFavandUnd[individualplayer,t] = Xb + u[individualplayer] + e[individualplayer,t]

        Estimated results:
                         |       Var     SD = sqrt(Var)
                ---------+-----------------------------
               DiffIng~d |   28.57526       5.345583
                       e |     25.244        5.02434
                       u |   2.113505        1.45379

        Test: Var(u) = 0
                             chibar2(01) = 11938.58
                          Prob > chibar2 =   0.0000

. ssc install xttest3
checking xttest3 consistency and verifying not already installed...
all files already exist and are up to date.

. xtreg DiffIngameswonbyFavandUnd Heterogeneity PrizeSpread1000 Bestof i.series i.Year, fe

Fixed-effects (within) regression               Number of obs     =     18,530
Group variable: individual~r                    Number of groups  =        367

R-squared:                                      Obs per group:
     Within  = 0.0477                                         min =          1
     Between = 0.0004                                         avg =       50.5
     Overall = 0.0339                                         max =        493

                                                F(14,18149)       =      64.98
corr(u_i, Xb) = -0.0969                         Prob > F          =     0.0000

---------------------------------------------------------------------------------
DiffIngameswo~d | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
----------------+----------------------------------------------------------------
  Heterogeneity |   .0067286    .000366    18.38   0.000     .0060112     .007446
PrizeSpread1000 |  -.0044263   .0005463    -8.10   0.000    -.0054971   -.0033554
         Bestof |   1.351407   .8916107     1.52   0.130    -.3962348    3.099048
                |
         series |
        ATP500  |  -.3775258   .1219053    -3.10   0.002    -.6164718   -.1385798
    Grand Slam  |  -.9808101     1.7831    -0.55   0.582    -4.475855    2.514234
  Masters 1000  |  -.3395359   .1031708    -3.29   0.001    -.5417604   -.1373114
                |
           Year |
          2014  |  -.0525744   .1638633    -0.32   0.748    -.3737621    .2686133
          2015  |   .1385333   .1671947     0.83   0.407    -.1891841    .4662508
          2016  |  -.1340997   .1684127    -0.80   0.426    -.4642046    .1960053
          2017  |  -.4425871   .1690888    -2.62   0.009    -.7740171   -.1111572
          2018  |  -.4306342   .1730089    -2.49   0.013    -.7697481   -.0915204
          2019  |  -.7240737   .1765527    -4.10   0.000    -1.070134   -.3780138
          2020  |  -.6243809   .2112932    -2.96   0.003    -1.038536   -.2102262
          2021  |  -.6980748   .1933546    -3.61   0.000    -1.077068   -.3190813
                |
          _cons |  -2.341599    2.67739    -0.87   0.382    -7.589538     2.90634
----------------+----------------------------------------------------------------
        sigma_u |  3.2101967
        sigma_e |  5.0243405
            rho |  .28988884   (fraction of variance due to u_i)
---------------------------------------------------------------------------------
F test that all u_i=0: F(366, 18149) = 5.14                  Prob > F = 0.0000

. xttest3

Modified Wald test for groupwise heteroskedasticity
in fixed effect regression model

H0: sigma(i)^2 = sigma^2 for all i

chi2 (367)  =   4.2e+34
Prob>chi2 =      0.0000

Pooled OLS should be used, right?

[Carlo Lazzaro]

Luca:
what does make you think that pooled OLS is the way to go?
In addition, generating codes over codes won't take you anywhere far.
Try to focus on a data generating process and expand on it.
An an aside, your staying with default standard errord it too optimistic and probably misleading.

[Luca Toni]

Luca:
what does make you think that pooled OLS is the way to go?
In addition, generating codes over codes won't take you anywhere far.
Try to focus on a data generating process and expand on it.
An an aside, your staying with default standard errord it too optimistic and probably misleading.

sigma e>sigma u
Those codes are different regressions I SHOULD run to research different things in my project.
those codes are testing whether I should use FE or POLS. I might use different std erros as we did before.