Panel data xtreg i.years - multiple years omitted

[Ambroise Lescudier]

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:

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:

xtset RIC ReportingYear
xtreg ROA BoardGenderDiversity i.ReportingYear

--> Here I had no problem, no variable omitted

xtreg ROA BoardGenderDiversity NoQuota i.ReportingYear
note: 2019.ReportingYear omitted because of collinearity

xtreg ROA BoardGenderDiversity BoardQuota20 i.ReportingYear
note: 2016.ReportingYear omitted because of collinearity

xtreg ROA BoardGenderDiversity BoardQuota40 i.ReportingYear
note: 2019.ReportingYear omitted because of collinearity

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:

. 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,

[Phil Bromiley]

You have a logical problem. If you have variables that are identical to the year, then you can't control for both the year and that variable. One alternative would be to move from dummies for year to a continuous variable.

[Ambroise Lescudier]

You have a logical problem. If you have variables that are identical to the year, then you can't control for both the year and that variable. One alternative would be to move from dummies for year to a continuous variable.

Hello,
Thank you very much. However, why are not all years omitted then? (Including BoardGender20 should omit 2014, 2015 and 2016, no? (and not only 2016)

My ultimate goal is to do a difference-in-difference analysis to see the impact of the quotas requirements, but I would need to not have some years omitted in panel data.

I tried the continuous variable:

generate Quota=0
replace Quota=1 if ReportingYear==2014
replace Quota=1 if ReportingYear==2015
replace Quota=1 if ReportingYear==2016
replace Quota=2 if ReportingYear==2017
replace Quota=2 if ReportingYear==2018
replace Quota=2 if ReportingYear==2019

and got the following:

xtset RIC ReportingYear
       panel variable:  RIC (strongly balanced)
        time variable:  ReportingYear, 2005 to 2019
                delta:  1 unit

. 
. xtreg ROA BoardGenderDiversity Quota i.ReportingYear
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
               Quota |  -.0070986   .0033378    -2.13   0.033    -.0136405   -.0005566
                     |
       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  |  -.0089144   .0038665    -2.31   0.021    -.0164926   -.0013362
               2015  |  -.0051174   .0037141    -1.38   0.168    -.0123968     .002162
               2016  |  -.0061268   .0037436    -1.64   0.102    -.0134641    .0012106
               2017  |   .0024925   .0038145     0.65   0.513    -.0049837    .0099687
               2018  |   .0072331   .0039234     1.84   0.065    -.0004567    .0149229
               2019  |          0  (omitted)
                     |
               _cons |   .0581835   .0074573     7.80   0.000     .0435674    .0727996
---------------------+----------------------------------------------------------------
             sigma_u |    .068035
             sigma_e |  .02444248
                 rho |   .8856846   (fraction of variance due to u_i)
--------------------------------------------------------------------------------------

2019 is still dropping out in this case... Do you think of something else?

Thank you very much for your help.
Best,

[Carlo Lazzaro]

Ambroise:
it may well be that -i.2019- is perfectly correlated to another predictor.
But the substantive issue with your model seems to be a very low R-sq between (actually, this is the R-sq to consider under a -re- specification): I would check whether your model is misspecified and whether all the predictors needed to give a true and fair view of the data generating process were actually included.

[Ambroise Lescudier]

Hello Carlo,
Thank you for your response.

it may well be that -i.2019- is perfectly correlated to another predictor.

This is what I concluded.

About the R-sq, I simplified my model for the purpose of my problem. I have more control variables and thus a higher r-sq. I just wanted to resolve the Quota issue. But thank you!