omitted variables and the interpretation of 2SLS

[Yossinee Varakjunkiat]

Hi, I must say that I am a beginner in Stata. My analysis is about the effect of students'scores on decision-making in higher education from 2004-2006 (the independent variable and outcome variable are a dummy: whether pupils got good marks during in high school and the decision whether they decide to study further). I have some questions about omitted variable in 2sls such as parents' ethnicity which is separated into White, Black, Asian and other, employment status: unemployed, employed and other. When I run 2sls, I put only 3 ethnicity- Black, Asian and other but Black and Asian are omitted themselves and the similar case with employment status. However, this problem appear inly in 2005 but no omitted variables in 2004 and 2006.



. ivregress 2sls applyforUni sibs exclude bullied agemum agedad ethnicYP2 ethnicYP3 ethnicYP4 ethnicmum2 ethnicmum3 ethnicmum4 ethnicdad
> 2 ethnicdad3 ethnicdad4 employmum2 employmum3 employdad2 employdad3 HHincome2 HHincome3 qualimum2 qualimum3 qualimum4 qualidad2 qualid
> ad3 qualidad4 ( gotgoodmarks = playtruant ) if year==2005 & sex==1, first
note: ethnicmum4 omitted because of collinearity
note: ethnicdad2 omitted because of collinearity
note: ethnicdad4 omitted because of collinearity
note: employmum3 omitted because of collinearity
note: employdad2 omitted because of collinearity
note: employdad3 omitted because of collinearity
note: qualimum3 omitted because of collinearity

First-stage regressions
-----------------------

Number of obs = 44
F( 20, 23) = 1.23
Prob > F = 0.3161
R-squared = 0.5162
Adj R-squared = 0.0955
Root MSE = 0.3053

------------------------------------------------------------------------------
gotgoodmarks | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
sibs | -.0091035 .066297 -0.14 0.892 -.1462493 .1280424
exclude | -.0111437 .1759313 -0.06 0.950 -.3750852 .3527978
bullied | .3265464 .1645857 1.98 0.059 -.0139251 .6670179
agemum | -.4737876 .1992758 -2.38 0.026 -.8860209 -.0615543
agedad | .1437429 .1429087 1.01 0.325 -.1518863 .4393722
ethnicYP2 | .5870566 .5233486 1.12 0.274 -.4955725 1.669686
ethnicYP3 | .4698338 .616951 0.76 0.454 -.8064267 1.746094
ethnicYP4 | .4136424 .3469893 1.19 0.245 -.3041596 1.131444
ethnicmum2 | -.1475068 .4621708 -0.32 0.752 -1.10358 .8085662
ethnicmum3 | -.0984527 .4056151 -0.24 0.810 -.9375314 .7406259
ethnicmum4 | 0 (omitted)
ethnicdad2 | 0 (omitted)
ethnicdad3 | -.1945947 .4473433 -0.44 0.668 -1.119995 .7308054
ethnicdad4 | 0 (omitted)
employmum2 | .1417959 .2261403 0.63 0.537 -.326011 .6096028
employmum3 | 0 (omitted)
employdad2 | 0 (omitted)
employdad3 | 0 (omitted)
HHincome2 | .2473541 .1405987 1.76 0.092 -.0434964 .5382047
HHincome3 | -.1716411 .2262386 -0.76 0.456 -.6396513 .2963692
qualimum2 | -.0206404 .1629039 -0.13 0.900 -.3576328 .316352
qualimum3 | 0 (omitted)
qualimum4 | -.2244219 .2178899 -1.03 0.314 -.6751615 .2263178
qualidad2 | -.0756771 .1478103 -0.51 0.614 -.3814459 .2300918
qualidad3 | .6226908 .4127443 1.51 0.145 -.2311357 1.476517
qualidad4 | -.3703418 .2299829 -1.61 0.121 -.8460977 .1054141
playtruant | -.3474518 .1854381 -1.87 0.074 -.7310596 .0361561
_cons | 1.093653 .2259099 4.84 0.000 .6263227 1.560983
------------------------------------------------------------------------------


Instrumental variables (2SLS) regression Number of obs = 44
Wald chi2(20) = 29.87
Prob > chi2 = 0.0720
R-squared = 0.2879
Root MSE = .35364

------------------------------------------------------------------------------
applyforUni | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
gotgoodmarks | 1.538012 .6181795 2.49 0.013 .3264025 2.749622
sibs | -.1060722 .07562 -1.40 0.161 -.2542847 .0421404
exclude | .1143196 .2039809 0.56 0.575 -.2854755 .5141148
bullied | -.3708249 .2625466 -1.41 0.158 -.8854068 .1437569
agemum | .6957723 .391867 1.78 0.076 -.072273 1.463818
agedad | -.4051377 .2011253 -2.01 0.044 -.7993361 -.0109393
ethnicYP2 | -.1164035 .7327689 -0.16 0.874 -1.552604 1.319797
ethnicYP3 | .3019239 .7589562 0.40 0.691 -1.185603 1.789451
ethnicYP4 | .1740415 .491461 0.35 0.723 -.7892045 1.137287
ethnicmum2 | .100364 .5462727 0.18 0.854 -.9703107 1.171039
ethnicmum3 | -.0604635 .4733872 -0.13 0.898 -.9882853 .8673583
ethnicmum4 | 0 (omitted)
ethnicdad2 | 0 (omitted)
ethnicdad3 | .0785538 .526641 0.15 0.881 -.9536435 1.110751
ethnicdad4 | 0 (omitted)
employmum2 | .1731726 .2583681 0.67 0.503 -.3332195 .6795647
employmum3 | 0 (omitted)
employdad2 | 0 (omitted)
employdad3 | 0 (omitted)
HHincome2 | -.2208077 .2443773 -0.90 0.366 -.6997785 .258163
HHincome3 | .8420891 .2790908 3.02 0.003 .2950813 1.389097
qualimum2 | -.2004021 .1890051 -1.06 0.289 -.5708453 .170041
qualimum3 | 0 (omitted)
qualimum4 | -.1261699 .2872582 -0.44 0.661 -.6891856 .4368459
qualidad2 | .3184029 .1832555 1.74 0.082 -.0407713 .677577
qualidad3 | .3804777 .451774 0.84 0.400 -.5049831 1.265938
qualidad4 | .6419637 .3791697 1.69 0.090 -.1011952 1.385123
_cons | -.796578 .6927067 -1.15 0.250 -2.154258 .5611023
------------------------------------------------------------------------------
Instrumented: gotgoodmarks
Instruments: sibs exclude bullied agemum agedad ethnicYP2 ethnicYP3
ethnicYP4 ethnicmum2 ethnicmum3 ethnicdad3 employmum2
HHincome2 HHincome3 qualimum2 qualimum4 qualidad2 qualidad3
qualidad4 playtruant





Ps. Sex= 1 if they are male and 0 otherwise





Another question is that when I run 2sls regression, I separate the regression into boys and girls. the coefficient of boys who have got good is 1.538. How can I interpret it as dummy variable. from now, I can only interpret that 'boys who got good marks during in high school will go to a college greater than who did not get good marks around 2 units'. Is it ok to say like this?

[Phil Bromiley]

You'll increase your chances of a helpful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata outpu (fixed spacing fonts help), and sample data using dataex. Also, cut your posting down the the minimum needed to demonstrate the problem.

You should look at factor variable notation in the documentation - you don't need to create these dummies manually.

As for your problems, you have too many parameters for too few observations. While there is no hard and fast rule, two observations per parameter is way too low. 5 or 10 observations per parameter are rules of thumb I've heard. This lack of observations then feeds into colinearity. Do you even have an Asian in that year?

[Phil Bromiley]

Note also that with a dummy dv, logit or probit is more appropriate than regression.