Hello,

I am doing a research about the effect of gender diversity on firm performance with panel data.

As a control variable, I added a quota dummies. For instance, the law required 20% of women on boards by 2014 and 40% by 2017. My dataset is going from 2005 to 2019.

So my dummies are:
NoQuota=1 from 2005 to 2013
BoardQuota20=1 if ReportingYear==2014, 2015 and 2016
BoardQuota40=1 if ReportingYear==2017, 2018 and 2019

Now, when I am running xreg i.ReportingYear, I have multiple years being omitted.
2005 is omitted because because Stata use it as a comparison.
It seems that 2016 is omitted because of BoardQuota20 and 2019 is omitted because of NoQuota and BoardQuota40.


I looked on the forum, asked my supervisor, but did not find a solution. How would you proceed to keep a quota dummy but correct this issue?



To create my dummies, I did:

Code:
generate NoQuota=1
replace NoQuota=0 if ReportingYear==2014
replace NoQuota=0 if ReportingYear==2015
replace NoQuota=0 if ReportingYear==2016
replace NoQuota=0 if ReportingYear==2017
replace NoQuota=0 if ReportingYear==2018
replace NoQuota=0 if ReportingYear==2019

generate BoardQuota20=0
replace BoardQuota20=1 if ReportingYear==2014
replace BoardQuota20=1 if ReportingYear==2015
replace BoardQuota20=1 if ReportingYear==2016

generate BoardQuota40=0
replace BoardQuota40=1 if ReportingYear==2017
replace BoardQuota40=1 if ReportingYear==2018
replace BoardQuota40=1 if ReportingYear==2019


Then for the regressions, I did:
Code:
xtset RIC ReportingYear
xtreg ROA BoardGenderDiversity i.ReportingYear
--> Here I had no problem, no variable omitted

Code:
xtreg ROA BoardGenderDiversity NoQuota i.ReportingYear
note: 2019.ReportingYear omitted because of collinearity
Code:
xtreg ROA BoardGenderDiversity BoardQuota20 i.ReportingYear
note: 2016.ReportingYear omitted because of collinearity
Code:
xtreg ROA BoardGenderDiversity BoardQuota40 i.ReportingYear
note: 2019.ReportingYear omitted because of collinearity
Code:
xtreg ROA BoardGenderDiversity NoQuota BoardQuota20 BoardQuota40 i.ReportingYear
note: BoardQuota40 omitted because of collinearity
note: 2016.ReportingYear omitted because of collinearity
note: 2019.ReportingYear omitted because of collinearity


Here is the result from the last one for you to understand:
Code:
. xtreg ROA BoardGenderDiversity NoQuota BoardQuota20 BoardQuota40 i.ReportingYear
note: BoardQuota40 omitted because of collinearity
note: 2016.ReportingYear omitted because of collinearity
note: 2019.ReportingYear omitted because of collinearity

Random-effects GLS regression Number of obs = 1,058
Group variable: RIC Number of groups = 112

R-sq: Obs per group:
within = 0.0457 min = 1
between = 0.0054 avg = 9.4
overall = 0.0104 max = 15

Wald chi2(15) = 45.45
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0001

--------------------------------------------------------------------------------------
ROA | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------------+----------------------------------------------------------------
BoardGenderDiversity | .0069789 .0127523 0.55 0.584 -.0180151 .0319728
NoQuota | .0141971 .0066756 2.13 0.033 .0011132 .0272811
BoardQuota20 | .0009718 .0039353 0.25 0.805 -.0067413 .0086849
BoardQuota40 | 0 (omitted)
|
ReportingYear |
2006 | -.0021102 .0049543 -0.43 0.670 -.0118204 .0076001
2007 | -.0012082 .0048026 -0.25 0.801 -.0106212 .0082047
2008 | -.0042524 .0047132 -0.90 0.367 -.0134902 .0049854
2009 | -.0218363 .0049033 -4.45 0.000 -.0314466 -.012226
2010 | -.0092194 .0047844 -1.93 0.054 -.0185967 .0001579
2011 | -.0097298 .0048925 -1.99 0.047 -.0193189 -.0001407
2012 | -.0138445 .0051586 -2.68 0.007 -.0239552 -.0037338
2013 | -.0139143 .0053079 -2.62 0.009 -.0243175 -.003511
2014 | -.0027877 .0040655 -0.69 0.493 -.0107559 .0051806
2015 | .0010093 .0037689 0.27 0.789 -.0063776 .0083962
2016 | 0 (omitted)
2017 | .0024925 .0038145 0.65 0.513 -.0049837 .0099687
2018 | .0072331 .0039234 1.84 0.065 -.0004567 .0149229
2019 | 0 (omitted)
|
_cons | .0439863 .0087964 5.00 0.000 .0267457 .061227
---------------------+----------------------------------------------------------------
sigma_u | .068035
sigma_e | .02444248
rho | .8856846 (fraction of variance due to u_i)
--------------------------------------------------------------------------------------
Thank you very much for your help,
Best,