Fractional Regression (Unbalanced panel)

[Hugo Rocha]

Dear all,

I have an unbalanced panel (dataex below) and I would like to estimate how the level of schooling affects shares of employment across different sectors. Given that my dependent variable is a proportion [0,1], I thought about a fractional response estimator (as in Wooldridge (2010)). The beta regression does not contemplate endpoints. Nevertheless, I do have a few zeros and ones (but not many). I do have a couple of questions since I am kind of unfamiliar with QMLE and fractional regressions:

1- My time periods are on five year intervals from 1965-2015, which possibly means I cannot include year fixed effects?

2- If I include cluster robust at the country level, I do not have to worry about country fixed effects?

3- How can I make sure my mean is correctly specified?

Regarding 3, initially I was trying

 fracreg probit share_tech lhc if tech_intensity==1, vce(cluster country)

Thank you!

dataex country year tech_intensity share_tech lhc lsc lpc yr_sch_pri yr_sch_sec yr_sch_ter

----------------------- copy starting from the next line -----------------------

* Example generated by -dataex-. To install: ssc install dataex
clear
input float country double year float(tech_intensity share_tech lhc lsc lpc yr_sch_pri yr_sch_sec yr_sch_ter)
4 1975 1   .4064895  1.46  .677   .838  .622  .259 .089
4 1980 1   .4117739 1.987 1.052  1.524  .816  .357  .12
4 1985 1   .3964349 2.649 1.485  3.154 1.162  .421 .151
4 1990 1          . 3.172  1.81  5.004  1.44  .448 .177
4 2005 1   .3372534  4.16 6.415  7.616  2.29  .807 .224
4 2010 1   .3316387 4.254 8.638 11.648 2.683 1.022 .228
4 2015 1          . 4.967 9.631 18.218 3.278 1.266 .282
4 1975 1   .4064895  1.46  .677   .838  .622  .259 .089
4 1980 1   .4117739 1.987 1.052  1.524  .816  .357  .12
4 1985 1   .3964349 2.649 1.485  3.154 1.162  .421 .151
4 1990 1          . 3.172  1.81  5.004  1.44  .448 .177
4 2005 1   .3372534  4.16 6.415  7.616  2.29  .807 .224
4 2010 1   .3316387 4.254 8.638 11.648 2.683 1.022 .228
4 2015 1          . 4.967 9.631 18.218 3.278 1.266 .282
4 1975 1   .4064895  1.46  .677   .838  .622  .259 .089
4 1980 1   .4117739 1.987 1.052  1.524  .816  .357  .12
4 1985 1   .3964349 2.649 1.485  3.154 1.162  .421 .151
4 1990 1          . 3.172  1.81  5.004  1.44  .448 .177
4 2005 1   .3372534  4.16 6.415  7.616  2.29  .807 .224
4 2010 1   .3316387 4.254 8.638 11.648 2.683 1.022 .228
4 2015 1          . 4.967 9.631 18.218 3.278 1.266 .282
4 1975 1   .4064895  1.46  .677   .838  .622  .259 .089
4 1980 1   .4117739 1.987 1.052  1.524  .816  .357  .12
4 1985 1   .3964349 2.649 1.485  3.154 1.162  .421 .151
4 1990 1          . 3.172  1.81  5.004  1.44  .448 .177
4 2005 1   .3372534  4.16 6.415  7.616  2.29  .807 .224
4 2010 1   .3316387 4.254 8.638 11.648 2.683 1.022 .228
4 2015 1          . 4.967 9.631 18.218 3.278 1.266 .282
4 1975 1   .4064895  1.46  .677   .838  .622  .259 .089
4 1980 1   .4117739 1.987 1.052  1.524  .816  .357  .12
4 1985 1   .3964349 2.649 1.485  3.154 1.162  .421 .151
4 1990 1          . 3.172  1.81  5.004  1.44  .448 .177
4 2005 1   .3372534  4.16 6.415  7.616  2.29  .807 .224
4 2010 1   .3316387 4.254 8.638 11.648 2.683 1.022 .228
4 2015 1          . 4.967 9.631 18.218 3.278 1.266 .282
4 1975 1   .4064895  1.46  .677   .838  .622  .259 .089
4 1980 1   .4117739 1.987 1.052  1.524  .816  .357  .12
4 1985 1   .3964349 2.649 1.485  3.154 1.162  .421 .151
4 1990 1          . 3.172  1.81  5.004  1.44  .448 .177
4 2005 1   .3372534  4.16 6.415  7.616  2.29  .807 .224
4 2010 1   .3316387 4.254 8.638 11.648 2.683 1.022 .228
4 2015 1          . 4.967 9.631 18.218 3.278 1.266 .282
4 1975 1   .4064895  1.46  .677   .838  .622  .259 .089
4 1980 1   .4117739 1.987 1.052  1.524  .816  .357  .12
4 1985 1   .3964349 2.649 1.485  3.154 1.162  .421 .151
4 1990 1          . 3.172  1.81  5.004  1.44  .448 .177
4 2005 1   .3372534  4.16 6.415  7.616  2.29  .807 .224
4 2010 1   .3316387 4.254 8.638 11.648 2.683 1.022 .228
4 2015 1          . 4.967 9.631 18.218 3.278 1.266 .282
4 1975 1   .4064895  1.46  .677   .838  .622  .259 .089
4 1980 1   .4117739 1.987 1.052  1.524  .816  .357  .12
4 1985 1   .3964349 2.649 1.485  3.154 1.162  .421 .151
4 1990 1          . 3.172  1.81  5.004  1.44  .448 .177
4 2005 1   .3372534  4.16 6.415  7.616  2.29  .807 .224
4 2010 1   .3316387 4.254 8.638 11.648 2.683 1.022 .228
4 2015 1          . 4.967 9.631 18.218 3.278 1.266 .282
4 1975 2 .032477524  1.46  .677   .838  .622  .259 .089
4 1980 2  .03337481 1.987 1.052  1.524  .816  .357  .12
4 1985 2  .02368685 2.649 1.485  3.154 1.162  .421 .151
4 1990 2          . 3.172  1.81  5.004  1.44  .448 .177
4 2005 2  .13477801  4.16 6.415  7.616  2.29  .807 .224
4 2010 2  .13851541 4.254 8.638 11.648 2.683 1.022 .228
4 2015 2          . 4.967 9.631 18.218 3.278 1.266 .282
4 1975 3  .06103301  1.46  .677   .838  .622  .259 .089
4 1980 3  .05485133 1.987 1.052  1.524  .816  .357  .12
4 1985 3  .07987828 2.649 1.485  3.154 1.162  .421 .151
4 1990 3          . 3.172  1.81  5.004  1.44  .448 .177
4 2005 3  .02796864  4.16 6.415  7.616  2.29  .807 .224
4 2010 3  .02984594 4.254 8.638 11.648 2.683 1.022 .228
4 2015 3          . 4.967 9.631 18.218 3.278 1.266 .282
4 1975 2 .032477524  1.46  .677   .838  .622  .259 .089
4 1980 2  .03337481 1.987 1.052  1.524  .816  .357  .12
4 1985 2  .02368685 2.649 1.485  3.154 1.162  .421 .151
4 1990 2          . 3.172  1.81  5.004  1.44  .448 .177
4 2005 2  .13477801  4.16 6.415  7.616  2.29  .807 .224
4 2010 2  .13851541 4.254 8.638 11.648 2.683 1.022 .228
4 2015 2          . 4.967 9.631 18.218 3.278 1.266 .282
4 1975 2 .032477524  1.46  .677   .838  .622  .259 .089
4 1980 2  .03337481 1.987 1.052  1.524  .816  .357  .12
4 1985 2  .02368685 2.649 1.485  3.154 1.162  .421 .151
4 1990 2          . 3.172  1.81  5.004  1.44  .448 .177
4 2005 2  .13477801  4.16 6.415  7.616  2.29  .807 .224
4 2010 2  .13851541 4.254 8.638 11.648 2.683 1.022 .228
4 2015 2          . 4.967 9.631 18.218 3.278 1.266 .282
4 1975 2 .032477524  1.46  .677   .838  .622  .259 .089
4 1980 2  .03337481 1.987 1.052  1.524  .816  .357  .12
4 1985 2  .02368685 2.649 1.485  3.154 1.162  .421 .151
4 1990 2          . 3.172  1.81  5.004  1.44  .448 .177
4 2005 2  .13477801  4.16 6.415  7.616  2.29  .807 .224
4 2010 2  .13851541 4.254 8.638 11.648 2.683 1.022 .228
4 2015 2          . 4.967 9.631 18.218 3.278 1.266 .282
4 1975 2 .032477524  1.46  .677   .838  .622  .259 .089
4 1980 2  .03337481 1.987 1.052  1.524  .816  .357  .12
4 1985 2  .02368685 2.649 1.485  3.154 1.162  .421 .151
4 1990 2          . 3.172  1.81  5.004  1.44  .448 .177
4 2005 2  .13477801  4.16 6.415  7.616  2.29  .807 .224
4 2010 2  .13851541 4.254 8.638 11.648 2.683 1.022 .228
4 2015 2          . 4.967 9.631 18.218 3.278 1.266 .282
4 1975 3  .06103301  1.46  .677   .838  .622  .259 .089
4 1980 3  .05485133 1.987 1.052  1.524  .816  .357  .12
end

[Jeff Wooldridge]

How large is this data set, and how many countries do you have? You should definitely include year effects. If you have lots of observations per country you should probably include country effects, too. Whether you cluster by country is a more difficult question.

[Hugo Rocha]

How large is this data set, and how many countries do you have? You should definitely include year effects. If you have lots of observations per country you should probably include country effects, too. Whether you cluster by country is a more difficult question.

I have 77 countries over the period 1965-2015 in five year intervals. The total number of observations oscillates between 50005 and 10010 in each estimation (depending on which group of industries per country I use. Tech_intensity is a dummy representing a subset of industries) Initially, what I have been doing is the following:

 glm share_tech lhc i.year i.country if tech_intensity==2, fam(bin) link(probit) robust

So, in my draft I've included country and year fixed effects. I am very unsure about the robust. In Chapter 18 of your Econometrics of Cross-Section and Panel Methods, you suggest robust standard errors... so, I kind of went in that way. But I couldn't find a complete explanation as to why (at least, one I could understand).

[Hugo Rocha]

I have 77 countries over the period 1965-2015 in five year intervals. The total number of observations oscillates between 50005 and 10010 in each estimation (depending on which group of industries per country I use. Tech_intensity is a dummy representing a subset of industries) Initially, what I have been doing is the following:

 glm share_tech lhc i.year i.country if tech_intensity==2, fam(bin) link(probit) robust

So, in my draft I've included country and year fixed effects. I am very unsure about the robust. In Chapter 18 of your Econometrics of Cross-Section and Panel Methods, you suggest robust standard errors... so, I kind of went in that way. But I couldn't find a complete explanation as to why (at least, one I could understand).

sorry, it is between 5005 and 10010, I added an extra zero

[Hugo Rocha]

Any hope? XD

[Hugo Rocha]

How large is this data set, and how many countries do you have? You should definitely include year effects. If you have lots of observations per country you should probably include country effects, too. Whether you cluster by country is a more difficult question.

Even if the panel is unbalanced?