Gender dropping out from fixed effects due to collinearity.

[Chumani Ward]

Hi.

I am currently looking to estimate a fixed effects regression - it looks at how natural disasters affect test scores.
I wish to include child fixed effects (engrade and gender) and household fixed effects headedu and hhsize.

As gender is likely to play a role in influencing the role of child labour, I feel it is important.
However - it drops out due to being time invariant.
Am I able to estimate the model without gender? Or is there a better way to incorporate its influence that won't cause it to drop out?

Also - I don't fully understand the xtset command. When I specify xtset panelid round - does this mean that round is being used as a fixed effect, and as such I could remove engrade from the model as a way of controlling for the role of the child's age in influencing test scores. Or - am I right in thinking i.engrade is necessary,

xtset panelid round
xtreg ppvt disaster worktime juntos disjunt foodsec i.engrade i.gender i.headedu i.hhsize, fe
note: 2.gender omitted because of collinearity

Fixed-effects (within) regression Number of obs = 5,056
Group variable: panelid Number of groups = 1,783

R-sq: Obs per group:
within = 0.7978 min = 1
between = 0.2545 avg = 2.8
overall = 0.5126 max = 3

F(48,3225) = 265.17
corr(u_i, Xb) = 0.0578 Prob > F = 0.0000

--------------------------------------------------------------------------------------------------------------------
ppvt | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------------------------------------------------+----------------------------------------------------------------
disaster | -.3327084 .4389233 -0.76 0.449 -1.193305 .5278886
worktime | .3705333 .1381362 2.68 0.007 .0996897 .6413768
juntos | -.8159844 .7564076 -1.08 0.281 -2.299073 .6671039
disjunt | .5679331 .5821971 0.98 0.329 -.5735806 1.709447
foodsec | -.2515621 .2981846 -0.84 0.399 -.8362126 .3330884
|
engrade |
grade 1 (Primary, Grade 1) | -31.74428 2.255193 -14.08 0.000 -36.16603 -27.32252
grade 2 (Primary, Grade 2) | -25.51156 1.907192 -13.38 0.000 -29.25099 -21.77213
grade 3 (Primary, Grade 3) | -17.99302 1.951363 -9.22 0.000 -21.81906 -14.16699
grade 4 (Primary, Grade 4) | -2.450614 2.149643 -1.14 0.254 -6.665418 1.76419
grade 5 (Primary, Grade 5) | -.0301754 1.966074 -0.02 0.988 -3.885057 3.824706
grade 6 (Primary, Grade 6) | 1.970767 1.893533 1.04 0.298 -1.741883 5.683417
grade 7 (Secondary, Year 1) | 6.933335 1.929764 3.59 0.000 3.149648 10.71702
grade 8 (Secondary, Year 2) | 14.02948 1.974338 7.11 0.000 10.15839 17.90056
grade 9 (Secondary, Year 3) | 13.17903 1.912108 6.89 0.000 9.429958 16.9281
grade 10 (Secondary, Year 4) | 17.18161 1.987756 8.64 0.000 13.28422 21.079
grade 11 (Secondary, Year 5) | 21.95274 4.045356 5.43 0.000 14.02101 29.88447
Incomplete Cent. Tecnico Productivo CETPRO/ Cen.. | 5.923465 12.01991 0.49 0.622 -17.64398 29.49091
|
gender |
female | 0 (omitted)
|
headedu |
Grade 1 | 3.08687 2.422483 1.27 0.203 -1.662892 7.836633
Grade 2 | -.1294352 2.186381 -0.06 0.953 -4.416273 4.157402
Grade 3 | 3.416051 2.012164 1.70 0.090 -.5291995 7.361301
Grade 4 | 2.01608 2.34269 0.86 0.390 -2.577231 6.609392
Grade 5 | .1457518 2.15339 0.07 0.946 -4.0764 4.367903
Grade 6 | 2.59335 1.862947 1.39 0.164 -1.059331 6.246031
Grade 7 | 2.523363 2.353032 1.07 0.284 -2.090226 7.136952
Grade 8 | -.248374 2.310862 -0.11 0.914 -4.77928 4.282532
Grade 9 | -1.218605 2.100773 -0.58 0.562 -5.33759 2.90038
Grade 10 | 3.31664 2.613716 1.27 0.205 -1.808073 8.441354
Grade 11 | .6734153 1.920759 0.35 0.726 -3.092616 4.439447
Technical, pedagogical, CETPRO (incomplete) | .4053503 2.354462 0.17 0.863 -4.211042 5.021743
Technical, pedagogical, CETPRO (complete) | 2.045722 2.214856 0.92 0.356 -2.296945 6.388389
University (incomplete) | 2.068615 2.70868 0.76 0.445 -3.242293 7.379523
University (complete) | -.1819136 2.528003 -0.07 0.943 -5.138568 4.774741
17 | 7.301087 11.99829 0.61 0.543 -16.22396 30.82614
|
hhsize |
3 | -2.372459 1.570443 -1.51 0.131 -5.451626 .7067074
4 | -2.630457 1.584098 -1.66 0.097 -5.736398 .4754845
5 | -2.624139 1.606283 -1.63 0.102 -5.773579 .5253001
6 | -3.593771 1.650597 -2.18 0.030 -6.830096 -.3574468
7 | -3.079095 1.707965 -1.80 0.072 -6.427902 .269713
8 | -1.720169 1.800351 -0.96 0.339 -5.250116 1.809779
9 | -4.19117 1.964325 -2.13 0.033 -8.042621 -.3397188
10 | -1.438381 2.192615 -0.66 0.512 -5.737442 2.86068
11 | -5.012737 2.734015 -1.83 0.067 -10.37332 .3478449
12 | 6.449574 4.191184 1.54 0.124 -1.76808 14.66723
13 | 9.503201 6.221924 1.53 0.127 -2.696125 21.70253
14 | 1.026939 5.661173 0.18 0.856 -10.07292 12.1268
15 | 7.801022 11.92675 0.65 0.513 -15.58375 31.18579
16 | -10.13639 9.08781 -1.12 0.265 -27.95485 7.682083
18 | -6.216919 12.11358 -0.51 0.608 -29.96802 17.53418
|
_cons | 84.05819 3.043993 27.61 0.000 78.08983 90.02655
---------------------------------------------------+----------------------------------------------------------------
sigma_u | 14.773323
sigma_e | 9.5909853
rho | .70349545 (fraction of variance due to u_i)
--------------------------------------------------------------------------------------------------------------------
F test that all u_i=0: F(1782, 3225) = 4.05 Prob > F = 0.0000

[Chumani Ward]

https://www3.nd.edu/~rwilliam/stats2/panel.pdf
"So, the bad news is that the effects of time-invariant variables like black cannot be estimated in a fixed effects model. The good news is that, so long as the effects of the time-invariant variables are also time invariant (e.g. black has the same effect in 1990 as in 1992 as in 1994) those variables are controlled for whether we have measured them or not. (For stable characteristics that are measured, I could include interactions with time if I thought the effects were not time- invariant.)"

Does the above explanation make sense here - that I can proceed with the omitted i.gender as it is being controlled for anyway?

[andrew rich]

I cannot comment on whether engrade is necessary, but my understanding is that xtset lets Stata know what your panel identifier is. Also, since gender is time invariant, it is likely already being controlled for by using a fixed effect regression. If you are interested in assessing its effect then you should consider an alternative approach.

[Richard Williams]

If you want to estimate the effect of age rather than just control for it, consider using a random effects model.

Or, consider the use of hybrid models. See

https://www3.nd.edu/~rwilliam/Taiwan2018/Hybrid.pdf

https://statisticalhorizons.com/problems-with-the-hybrid-method

[Chumani Ward]

I cannot comment on whether engrade is necessary, but my understanding is that xtset lets Stata know what your panel identifier is. Also, since gender is time invariant, it is likely already being controlled for by using a fixed effect regression. If you are interested in assessing its effect then you should consider an alternative approach.

Thank you - this has clarified most of my concerns.

Richard - I will now look into hybrid models which I had not previously considered.

(Both xtset panelid round)
xtreg ppvt disaster worktime engrade juntos disjunt foodsec hhsize headedu, fe
xtreg ppvt disaster worktime i.engrade juntos disjunt foodsec i.hhsize i.headedu, fe

With the above models - could someone clarify the exact theoretical difference. Am I correct in thinking that the first includes only fixed effects based on the panel identifier?

[Richard Williams]

If engrade, hhsize, and headedu are already 0/1 dichotomies, I don't see any differences between the two commands.

You earlier cited https://www3.nd.edu/~rwilliam/stats2/panel.pdf. Read it again, or at least the summary on pp. 9-10.

Very briefly, we can say that FE models control for time-invariant variables with time-invariant effects, e.g. something like gender at birth if the effect of gender is the same at all time periods. If the effect of gender varies across time you need to include interactions of gender with time -- which you can only do, of course, if gender is a variable in the data. There is a good chance gender will be, but other time-invariant variables may not be.