Tobit regression in Panel Data and the effect of time

[Fimi Karimi]

Hello everyone,

I am using a country level panel data to study the effect of some variables on the Dividend_ratio. Dividend ratio can be between 0-100%. I read conflicting materials regarding how to include and control the effect of time. Do we have fixed effect year in Tobit? How I can consider the effect of time in my model? Could I ask you to guide me about the correct code for the Tobit regression in panel data with time?


tobit Pay_Ratio Financial CEOgender Governance Reputation, ll(0) ul(100)

input double(Pay_Ratio Financial) byte( CEOgender Governance) double Reputation
. 0 0 0 .
. 0 0 0 .
. 0 0 0 .
. 5 0 0 .
. 22.5 0 0 .
. 22.5 0 0 .
. 22.5 0 0 .
. 22.5 0 0 .
. 17.5 0 0 .
. 17.5 0 0 .
. 17.5 0 0 .
. 17.5 0 0 .
1.100000023841858 22.5 0 0 .
3.0999999046325684 22.5 0 0 .
2.200000047683716 22.5 0 0 .
3.200000047683716 22.5 0 0 .
6.400000095367432 50 0 0 .
4.099999904632568 50 0 0 .
6.300000190734863 50 0 1 .
8.800000190734863 50 0 1 .
. . 0 1 .
. 30.7392996108949 0 0 .
. 33.7254901960784 0 0 .
. 36.1867704280156 0 0 23.49665924276169
. 35.0194552529183 0 0 23.49665924276169
. 40 1 0 23.49665924276169
. 40 1 0 23.49665924276169
. 38.5214007782101 1 0 23.49665924276169
. 38.5214007782101 1 0 22.482197355035606
. 37.3540856031128 1 0 22.482197355035606
. 37.3540856031128 1 0 22.482197355035606
. 36.5758754863813 1 0 22.482197355035606
. 36.5758754863813 1 0 22.482197355035606
. . 0 0 20.459848677517805
. 35.7976653696498 0 0 20.459848677517805
11.100000381469727 38.1322957198444 0 0 18.4375
11.100000381469727 38.9105058365759 0 0 18.4375
6.400000095367432 40.1574803149606 0 0 18.4375
3.200000047683716 40.8560311284047 0 0 18.4375
10 44.7470817120623 0 0 18.4375
. 44.7470817120623 0 0 18.4375
. . 0 0 18.4375
. 25.3333333333333 0 0 .
. 24.6666666666667 0 0 .
. 24.6666666666667 0 0 18.168812589413445
. 24.6666666666667 0 0 18.168812589413445
. 26.6666666666667 0 0 18.168812589413445
. 26.6666666666667 0 0 18.168812589413445
8.399999618530273 27.3333333333333 0 0 18.168812589413445
10.199999809265137 24.6666666666667 1 0 13.45229924502402
13.800000190734863 24.6666666666667 1 0 13.45229924502402
13.900000095367432 24.6666666666667 1 0 13.45229924502402
14 26 0 0 13.45229924502402
15.300000190734863 26 0 0 13.45229924502402
23.100000381469727 26.6666666666667 0 0 11.307155209104188
26 28.6666666666667 0 0 11.307155209104188
28.700000762939453 28.6666666666667 0 0 9.162011173184357
31.5 28.6666666666667 0 0 9.162011173184357
31.200000762939453 30.4635761589404 0 0 9.162011173184357
34 30.4635761589404 0 0 9.162011173184357
34.79999923706055 31.1258278145695 0 0 9.162011173184357
37.20000076293945 38.4105960264901 0 0 9.162011173184357
. . 0 0 9.162011173184357
. 33.879781420765 0 0 .
. 33.879781420765 0 0 .
. 33.879781420765 0 0 .
. 32.2404371584699 0 0 .
. 32.7868852459016 0 0 .
. 27.3224043715847 0 0 .
6.800000190734863 27.8688524590164 0 0 .
7.300000190734863 27.8688524590164 0 0 .
10.800000190734863 27.8688524590164 0 0 .
11.050000190734863 27.8688524590164 0 0 .
11.300000190734863 33.3333333333333 0 0 .
16 32.2404371584699 0 0 .
17.399999618530273 30.6010928961749 0 0 14.520202020202019
20.899999618530273 30.6010928961749 0 0 14.520202020202019
19.200000762939453 34.4262295081967 0 1 14.520202020202019
21.200000762939453 34.4262295081967 0 1 14.520202020202019
31.799999237060547 39.344262295082 1 1 14.520202020202019
34.5 39.344262295082 0 1 14.520202020202019
37.70000076293945 40.4371584699454 0 1 14.520202020202019
42.599998474121094 40.9836065573771 0 1 14.520202020202019
. . 0 1 14.520202020202019
. 35.3333333333333 0 0 .
. 34.6666666666667 0 0 .
. 34.6666666666667 0 0 .
. 34.6666666666667 0 0 .
. 35.3333333333333 0 0 .
. 35.3333333333333 0 0 .
6.900000095367432 38 0 0 .
7.699999809265137 39.3333333333333 0 0 .
9.399999618530273 38 0 0 .
9.299999713897705 38 0 0 .
9.199999809265137 38 0 0 .
16.799999237060547 39.3333333333333 0 0 .
24.299999237060547 39.3333333333333 0 0 .
27.700000762939453 39.3333333333333 0 0 .
30.399999618530273 38 0 0 .
31.100000381469727 38 0 0 .
end
[/CODE]
------------------ copy up to and including the previous line ------------------

Listed 100 out of 1553 observations

[Jeff Wooldridge]

Fimi: Do you really have country-level panel data? I'm surprised you'd see any zeros or 100s if it's aggregate data. And the CEOgender variable appears to be binary rather than a fraction. You haven't listed a time variable, such as year, so I don't know what N (cross section) and T (time series) dimensions are.

If you really have lots of outcomes at zero, I'd recommend fractional logit rather than Tobit. It requires fewer distributional assumptions and the parameters are easier to interpret (and partial effects easier to obtain).

[Fimi Karimi]

Oh, My bad. You are right I sent wrong data. It's data. I include just some part of data as I have lots of variables.

input str52 CountryName long Country int Year double(Pay_Ratio leverage) byte Quota double(Ln_GDP GDP_GR Market_depth)
"United Arab Emirates" 227 2003 . 0 0 25.54633672 8.80054081486432 3.332204510175204
"United Arab Emirates" 227 2004 . 0 0 25.71929072 9.56643663716161 3.4657359027997265
"United Arab Emirates" 227 2005 . 0 0 25.9196472 4.85514119630904 4.007333185232471
"United Arab Emirates" 227 2006 . 5 0 26.12646804 9.83731977348489 4.007333185232471
"United Arab Emirates" 227 2007 . 22.5 0 26.2759003 3.18439017367239 4.0943445622221
"United Arab Emirates" 227 2008 . 22.5 0 26.47734406 3.19183627610384 4.634728988229636
"United Arab Emirates" 227 2009 . 22.5 0 26.25881646 -5.2429219066759 4.6443908991413725
"United Arab Emirates" 227 2010 . 22.5 0 26.39241357 1.60285004831249 4.6443908991413725
"United Arab Emirates" 227 2011 . 17.5 0 26.58310021 6.92850859456967 4.68213122712422
"United Arab Emirates" 227 2012 . 17.5 0 26.675496 4.77662573440196 4.672828834461906
"United Arab Emirates" 227 2013 1.1 17.5 0 26.71527656 5.05555965807968 4.762173934797756
"United Arab Emirates" 227 2014 2.2 17.5 0 26.74938629 4.16569184064921 4.787491742782046
"United Arab Emirates" 227 2015 2.2 22.5 0 26.63751308 6.78677287656617 4.8283137373023015
"United Arab Emirates" 227 2016 3.0999999046325684 22.5 0 26.63475418 5.56149075979932 4.8283137373023015
"United Arab Emirates" 227 2017 4 22.5 0 26.69073684 .735068713941203 4.844187086458591
"United Arab Emirates" 227 2018 3.200000047683716 22.5 0 26.78016561 1.31391388153578 4.867534450455582
"United Arab Emirates" 227 2019 3.649999976158142 50 0 26.75872268 1.10834813453296 4.867534450455582
"United Arab Emirates" 227 2020 4.099999904632568 50 0 26.57969219 -4.95705243303315 4.867534450455582
"United Arab Emirates" 227 2021 6.300000190734863 50 1 26.75159638 3.91629607562494 .
"United Arab Emirates" 227 2022 8.800000190734863 50 1 26.95283136 7.41110320184745 .
"United Arab Emirates" 227 2023 . . 1 . . .
"Argentina" 10 2003 . 30.7392996108949 0 25.57206411 8.83704079576924 4.663439094112067
"Argentina" 10 2004 . 33.7254901960784 0 25.82713601 9.02957330068152 4.634728988229636
"Argentina" 10 2005 . 36.1867704280156 0 26.01524866 8.85165992013436 4.605170185988092
"Argentina" 10 2006 . 35.0194552529183 0 26.17240231 8.04715150043027 4.61512051684126
"Argentina" 10 2007 . 40 0 26.38459481 9.00765087504757 4.663439094112067
"Argentina" 10 2008 . 40 0 26.61368841 4.05723310346405 4.672828834461906
"Argentina" 10 2009 . 38.5214007782101 0 26.53133771 -5.91852507634946 4.61512051684126
"Argentina" 10 2010 . 38.5214007782101 0 26.77212018 10.1253981561002 4.61512051684126
"Argentina" 10 2011 . 37.3540856031128 0 26.99644125 6.00395169280578 4.59511985013459
"Argentina" 10 2012 6.5 37.3540856031128 0 27.02585253 -1.02642045443209 4.61512051684126
"Argentina" 10 2013 7 36.5758754863813 0 27.03685943 2.40532378079436 4.574710978503383
"Argentina" 10 2014 8.2 36.5758754863813 0 26.98917461 -2.51261532081393 4.553876891600541
"Argentina" 10 2015 2.5 . 0 27.11140578 2.73115982828943 4.532599493153256
"Argentina" 10 2016 6.8 35.7976653696498 0 27.04678631 -2.0803278437781 4.532599493153256
"Argentina" 10 2017 7.8 38.1322957198444 0 27.19038737 2.81850297775918 4.564348191467836
"Argentina" 10 2018 9.2 38.9105058365759 0 26.98632099 -2.61739646282038 4.532599493153256
"Argentina" 10 2019 9.4 40.1574803149606 0 26.82751135 -2.00086100285784 4.51085950651685
"Argentina" 10 2020 9.7 40.8560311284047 0 26.67791184 -9.94323513446069 .
"Argentina" 10 2021 13.1 44.7470817120623 0 26.91199623 10.3982494646903 .
"Argentina" 10 2022 13.1 44.7470817120623 0 27.17337329 5.24304449924879 .
"Argentina" 10 2023 . . 0 . . .
"Australia" 13 2003 . 25.3333333333333 0 26.87066083 3.11139820789409 7.247792581767846
"Australia" 13 2004 . 24.6666666666667 0 27.14379216 4.21663327252608 7.322510433997394
"Australia" 13 2005 . 24.6666666666667 0 27.26761644 3.15375271041142 7.404279118037268
"Australia" 13 2006 . 24.6666666666667 0 27.34054505 2.74063570365783 7.467942332285852
"Australia" 13 2007 . 26.6666666666667 0 27.47369721 3.77791678266477 7.556427969440253
"Australia" 13 2008 . 26.6666666666667 0 27.68521201 3.56827003225819 7.562161631225652
"Australia" 13 2009 . 27.3333333333333 0 27.55697597 1.87048696091407 7.540090320145325
"Australia" 13 2010 10.199999809265137 24.6666666666667 0 27.7695384 2.20656631017092 7.556427969440253
"Australia" 13 2011 13.800000190734863 24.6666666666667 0 27.96639 2.3913851323057 7.592366128519796
"Australia" 13 2012 13.900000095367432 24.6666666666667 0 28.06730811 3.90200780631799 7.580189417944541
"Australia" 13 2013 14 26 0 28.08612028 2.57875428825342 7.578145472419466
"Australia" 13 2014 20 26 0 28.01464265 2.57901711177596 7.584264818389059
"Australia" 13 2015 23.100000381469727 26.6666666666667 0 27.93155549 2.15273590593909 7.5953872788539725
"Australia" 13 2016 26 28.6666666666667 0 27.81879686 2.73054799209893 7.585281078639126
"Australia" 13 2017 28.700000762939453 28.6666666666667 0 27.9135405 2.28218364248465 7.607381425639791
"Australia" 13 2018 31.5 28.6666666666667 0 27.9874826 2.88304512347683 7.602900462204755
"Australia" 13 2019 31.200000762939453 30.4635761589404 0 27.96191965 2.1713962244835 7.5766097669730375
"Australia" 13 2020 34 30.4635761589404 0 27.91390014 -.0508853360838941 7.550661243105336
"Australia" 13 2021 34.79999923706055 31.1258278145695 0 28.0710185 2.23621243944461 .
"Australia" 13 2022 37.200000762939


I was asked to run Tobit Regression. my dependent variable is Pay ratio. At first I run fixed effect regression but now I don't know how I CAN consider the effect of time in Tobit regression? Does tobit have fixed effect Year?
Thanks for your guidance.

[Jeff Wooldridge]

In the data you've shown, Pay_Ratio is either missing or strictly between 0 and 100. If you never reach the endpoints of 0 and 100, Tobit is not appropriate. If this is true in your entire data set, use a linear model and use the usual two-way fixed effects estimator.

[Fimi Karimi]

Thank you so much for your help and guidance. I have 0 and 100% in my data for some countries.

[Nick Cox]

Scaling the outcome to lie between 0 and 1 is essential for most defensible approaches, but easy enough.

[Fimi Karimi]

Thanks, Nick. Do you think it's correct to use command " tobit dependent variable indevendent variables i.Year, ll(0) ul (1) " to run a fixed effect year tobit regression?

[Nick Cox]

I don't see the point of tobit here. Nothing is censored. And the linear functional form is to me a poor choice for bounded outcomes.

As Jeff Wooldridge said in #2, something more like fractional logit seems to make much more sense.

What else you need is a matter for economists to discuss.