Pooled OLS vs Panel Regression

[Roshni Garg]

Hello! this question is more of a modelling problem than a Stata problem.

Here it goes: I am trying to figure out whether foreign investors are superior stock pickers in comparison to domestic investors. Literature says that if foreign investors are superior, then the companies in which foreign investors acquire a higher stake should have better operating performance than the ones in which they acquire a low stake as well as the ones in which domestic investors acquire higher stakes. My sample comprises of data on accounting performance of companies that had their IPOs between 2009-22. I want to examine if companies which had more foreign investor participation in their IPOs outperform the companies which had more domestic investor participation in their IPOs. For this, my dependent variable is return on assets (roa) and my independent variable is domestic participation (domperc) and foreign participation in IPO (forperc). There are also some control variables impacting return on assets such as liquidity (cr), leverage (der) etc. I was wondering if this dataset would qualify for a panel data regression analysis or pooled OLS regression analysis? My confusion stems from the following facts:

1. My sample is not fixed from year to year and therefore does not look like a conventional panel dataset. Some IPOs take place in 2009, some in 2010, others in 2012. For each of these IPOs, I want to examine the return on assets for 3 years after the IPO. Therefore, for companies which had their IPO in 2010, I am looking at return on assets from 2010-2012 and for companies which had their IPO in 2017, I am looking at the return on assets data from 2017-19. This gives the data its time series nature. However, not all companies' return on assets can be analyzed for the same years due to difference in IPO dates. Once I figure out how to do the analysis, I will also be looking at five-year data.
2. My sample has time invariant variables. While return on assets for each IPO differs from one year to other, extent of foreign participation in its IPO remains fixed as it is based the IPO is not taking place every year. Same goes for extent of domestic participation in IPOs.

A snapshot of my data is attached in dataex format for clarity.

* Example generated by -dataex-. To install: ssc install dataex
clear
input long capcode int(ipoyear year) float(roa der cr domperc forperc)
 2038 2021 2020   .02341292   .34   .39 30.65 14.38
 2038 2021 2021         .01   .03   .53 30.65 14.38
 2038 2021 2022   .07635704   .34    .8 30.65 14.38
 2038 2021 2023  .026405483   .04     1 30.65 14.38
 2038 2021 2024           .     .     . 30.65 14.38
 2038 2021 2025           .     .     . 30.65 14.38
 2038 2021 2026           .     .     . 30.65 14.38
 5492 2009 2008  .071361795    .8  1.52  4.94  9.89
 5492 2009 2009        .073   .92  1.87  4.94  9.89
 5492 2009 2010   .04868371   .48  3.89  4.94  9.89
 5492 2009 2011   .04805506   .37  7.85  4.94  9.89
 5492 2009 2012  .031379487   .75  3.93  4.94  9.89
 5492 2009 2013  .026349297   .81  2.77  4.94  9.89
 5492 2009 2014   .04981148   .61  2.85  4.94  9.89
 5525 2019 2018 -.006136978     0     0 20.11 24.87
 5525 2019 2019       -.012     0     0 20.11 24.87
 5525 2019 2020  .000673949     0     0 20.11 24.87
 5525 2019 2021  .009355194     0     0 20.11 24.87
 5525 2019 2022  .018075025     0     0 20.11 24.87
 5525 2019 2023  .018762574     0     0 20.11 24.87
 5525 2019 2024           .     .     . 20.11 24.87
 5982 2016 2015  .007643986     0     0  11.7 18.31
 5982 2016 2016        .007     0     0  11.7 18.31
 5982 2016 2017  .009161258     0     0  11.7 18.31
 5982 2016 2018  .010267073     0     0  11.7 18.31
 5982 2016 2019  .010787705     0     0  11.7 18.31
 5982 2016 2020  .005683104     0     0  11.7 18.31
 5982 2016 2021  .005044976     0     0  11.7 18.31
 7167 2018 2017   .10919832   .49  1.34 18.33 11.68
 7167 2018 2018         .09   .38  1.32 18.33 11.68
 7167 2018 2019   .12829202   .26  1.35 18.33 11.68
 7167 2018 2020   .13074681   .21  1.43 18.33 11.68
 7167 2018 2021   .11410425   .19  1.49 18.33 11.68
 7167 2018 2022   .07120063    .2  1.48 18.33 11.68
 7167 2018 2023   .11487078   .19  1.54 18.33 11.68
12232 2010 2009  -.06802534  2.65   .99  6.43 10.59
12232 2010 2010       -.029   1.8  1.26  6.43 10.59
12232 2010 2011   .03078333   .96  1.29  6.43 10.59
12232 2010 2012   .04446261    .5  1.12  6.43 10.59
12232 2010 2013   .10273594   .24  1.46  6.43 10.59
12232 2010 2014           .     .     .  6.43 10.59
12232 2010 2015   .19456124    .1  1.96  6.43 10.59
12466 2018 2017    .1654821   .65  1.26 27.75 21.62
12466 2018 2018        .192   .81   1.5 27.75 21.62
12466 2018 2019   .10479826    .6  1.41 27.75 21.62
12466 2018 2020   .12146883   .95  1.32 27.75 21.62
12466 2018 2021   .13089329  1.77  1.31 27.75 21.62
12466 2018 2022   .10130566  2.72  1.23 27.75 21.62
12466 2018 2023  .071540095   3.3  1.23 27.75 21.62
12622 2017 2016    .2068735     0  4.24 12.63 17.41
12622 2017 2017          .2     0  4.48 12.63 17.41
12622 2017 2018    .1721754     0  4.87 12.63 17.41
12622 2017 2019   .17432377     0   4.7 12.63 17.41
12622 2017 2020   .14614712     0  2.87 12.63 17.41
12622 2017 2021   .19662575     0  1.88 12.63 17.41
12622 2017 2022    .1945791     0   1.6 12.63 17.41
12854 2021 2020  .013381525  7.29 19.23 20.33  9.67
12854 2021 2021        .012  8.42  3.09 20.33  9.67
12854 2021 2022  .013533573  9.25  2.97 20.33  9.67
12854 2021 2023  .012902478  9.34  3.01 20.33  9.67
12854 2021 2024           .     .     . 20.33  9.67
12854 2021 2025           .     .     . 20.33  9.67
12854 2021 2026           .     .     . 20.33  9.67
13090 2012 2011   .27330908     0   .87  6.86  8.15
13090 2012 2012         .25     0  1.58  6.86  8.15
13090 2012 2013    .2234997     0  1.13  6.86  8.15
13090 2012 2014   .22161175     0   .61  6.86  8.15
13090 2012 2015    .3131947     0   .49  6.86  8.15
13090 2012 2016   .23402266     0   .49  6.86  8.15
13090 2012 2017   .25854164     0   .66  6.86  8.15
13212 2010 2009  .029545464  1.86   1.2  5.99 11.99
13212 2010 2010         .05  1.93  1.52  5.99 11.99
13212 2010 2011   .04901854   .85  1.63  5.99 11.99
13212 2010 2012  .027441267   .52  1.32  5.99 11.99
13212 2010 2013   .04609448   .56  1.15  5.99 11.99
13212 2010 2014   .05006648   .59  1.07  5.99 11.99
13212 2010 2015   .04811945   .61   1.1  5.99 11.99
13369 2016 2015   .13856791   .01   .42 11.89 17.84
13369 2016 2016        .131   .01   .49 11.89 17.84
13369 2016 2017    .1494108     0   .49 11.89 17.84
13369 2016 2018   .15823352     0   .38 11.89 17.84
13369 2016 2019    .1583358     0   .43 11.89 17.84
13369 2016 2020   .19086137   .01   .43 11.89 17.84
13369 2016 2021   .13374029   .02   .48 11.89 17.84
13722 2018 2017   .11474272   .27  1.98 19.36 10.65
13722 2018 2018         .12    .2  2.32 19.36 10.65
13722 2018 2019   .13436812   .15  2.51 19.36 10.65
13722 2018 2020   .08126603   .14  2.19 19.36 10.65
13722 2018 2021    .1381705   .11  2.36 19.36 10.65
13722 2018 2022   .15301538   .03  2.87 19.36 10.65
13722 2018 2023   .13792011   .04  2.69 19.36 10.65
14185 2015 2014  -.05750865  4.91   .33 26.66     0
14185 2015 2015        .014  1.95   .82 26.66     0
14185 2015 2016   .02551326  1.19   .83 26.66     0
14185 2015 2017 -.001394617  1.36   .49 26.66     0
14185 2015 2018  -.20241204  2.77   .26 26.66     0
14185 2015 2019  -.11524013 40.99   .16 26.66     0
14185 2015 2020  -.08636498     0   .14 26.66     0
14546 2020 2019    .1282298     0  3.77 11.22 18.68
14546 2020 2020        .189     0  4.82 11.22 18.68
end

I would be grateful for any guidance regarding this issue. Will be happy to share more information if required. Thank you in advance.

[Carlo Lazzaro]

Roshni:
welcome to this forum.
1) usually, POLS is not the first line choice when dealing with a short panel dataset with a continuous regressand. Therefore, I'd go -xtreg- first;
2) you have a short panel dataset with repeated time values within panel. Therefore, you should -xtset- your data with -panelid- only;
3) the -fe- estimator, that is often the first choice with -xtreg- will wipe out time-invariant predictors. See -hausman- or the community-contributed module -xtoverid- (if you go cluster-robust standard errors) outcome to choose between -fe- and -re- (that said, -re- is based on the unrealistic assumption of no correlation of the u with the vector of regressors);
4) see -egen- function -mean- to calculate ROA, if that is what you mean.

[Roshni Garg]

Hi Carlo. Thank you for the prompt reply. I have understood points (1) to (3). With respect to point (4) I would be grateful if you could clarify further. Considering that I want to track the changes in ROA across 3 years and compare the same for IPOs with higher foreign participation to that of IPOs with higher domestic participation, may I know how would taking the mean of ROA help? Also, if I calculate the mean across the three years, wouldn't my data lose its temporal character? Ideally, I want to be able to answer the following question with my work: in the post-IPO period, do IPOs with higher foreign participation undergo significantly higher improvements in their ROA than IPOs with higher domestic participation?

Thank you again, in advance.

[Carlo Lazzaro]

Roshni:
you might be interested in something along the following lines:

. bysort capcode (year): gen bef_after=0 if year<= ipoyear


. bysort capcode (year): replace bef_after=1 if year>ipoyear


. bysort capcode (year): gen dom_foreign=0 if domperc> forperc


. bysort capcode (year): replace dom_foreign=1 if forperc > domperc


. label define bef_after 0 "Before_IPO" 1 "After_IPO"

. label val bef_after bef_after

. label define dom_foreign 0 "More_domestic" 1 "More_foreign"

. label val dom_foreign dom_foreign

. xtset capcode

. xtreg roa i.bef_after##i.dom_foreign i.year, fe allbase
note: 1.dom_foreign omitted because of collinearity.

Fixed-effects (within) regression               Number of obs     =         92
Group variable: capcode                         Number of groups  =         15

R-squared:                                      Obs per group:
     Within  = 0.2527                                         min =          2
     Between = 0.0202                                         avg =        6.1
     Overall = 0.0632                                         max =          7

                                                F(17, 60)         =       1.19
corr(u_i, Xb) = -0.0164                         Prob > F          =     0.2976

-------------------------------------------------------------------------------------------
                      roa | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
--------------------------+----------------------------------------------------------------
                bef_after |
              Before_IPO  |          0  (base)
               After_IPO  |  -.0065019   .0195319    -0.33   0.740    -.0455715    .0325676
                          |
              dom_foreign |
           More_domestic  |          0  (base)
            More_foreign  |          0  (omitted)
                          |
    bef_after#dom_foreign |
Before_IPO#More_domestic  |          0  (base)
 Before_IPO#More_foreign  |          0  (base)
 After_IPO#More_domestic  |          0  (base)
  After_IPO#More_foreign  |    .029737   .0226376     1.31   0.194    -.0155449    .0750188
                          |
                     year |
                    2008  |          0  (base)
                    2009  |  -.0547782   .0464518    -1.18   0.243    -.1476955    .0381392
                    2010  |   -.050802   .0472023    -1.08   0.286    -.1452206    .0436166
                    2011  |  -.0326942   .0491226    -0.67   0.508    -.1309539    .0655655
                    2012  |  -.0446649   .0491226    -0.91   0.367    -.1429246    .0535949
                    2013  |  -.0391246   .0511854    -0.76   0.448    -.1415106    .0632614
                    2014  |  -.0450031   .0522411    -0.86   0.392    -.1495009    .0594947
                    2015  |   .0142197    .052548     0.27   0.788     -.090892    .1193314
                    2016  |  -.0110717   .0560369    -0.20   0.844    -.1231621    .1010187
                    2017  |  -.0273385   .0596991    -0.46   0.649    -.1467546    .0920776
                    2018  |  -.0583323   .0617491    -0.94   0.349    -.1818488    .0651843
                    2019  |  -.0532898   .0639521    -0.83   0.408    -.1812129    .0746334
                    2020  |  -.0499282   .0647666    -0.77   0.444    -.1794806    .0796242
                    2021  |  -.0483011   .0656935    -0.74   0.465    -.1797076    .0831054
                    2022  |  -.0434338   .0689264    -0.63   0.531    -.1813071    .0944396
                    2023  |  -.0528338   .0696966    -0.76   0.451    -.1922478    .0865802
                          |
                    _cons |   .1164869   .0501924     2.32   0.024      .016087    .2168867
--------------------------+----------------------------------------------------------------
                  sigma_u |  .08287688
                  sigma_e |   .0385966
                      rho |  .82176974   (fraction of variance due to u_i)
-------------------------------------------------------------------------------------------
F test that all u_i=0: F(14, 60) = 27.41                     Prob > F = 0.0000

.

[Roshni Garg]

Many thanks for this Carlo. This was exactly what I was looking for.