This document analyzes how race, sex, and age affect education levels using survey data from 1993-1994. A linear probability model found that being black or having higher income decreases the probability of having only a high school degree or less. A multinomial logit model estimates the probabilities of different education levels for black versus non-black females of average age, finding black females are more likely to have a high school degree but less likely to have a bachelor's or graduate degree. Testing for independence of irrelevant alternatives shows no systematic difference between coefficients.

1. How race, sex and age affect the level of
education attained?
By
Deepika Gadhella Thulasiram

2. INTRODUCTION
• This study investigates the impact race, sex and age could have on the level of education
attained in the U.S.. This investigation is based on a dataset spanning different levels of
education namely Graduate degree, bachelors, junior college, high school and less than high
school.
• The variables present in the dataset are “female, black, degree, income, age”
variable name type format label variable label
storage display value
size: 36,784
vars: 5 21 Apr 2019 11:12
obs: 4,598 1993 and 1994 General Social Survey
Contains data from C:/Users/deepi/OneDrive/Documents/ammapls/econ/kid.dta
. d
age 4,598 46.12375 17.33162 18 99
income 4,103 34790.7 22387.45 1000 75000
degree 4,584 1.430628 1.165915 0 4
black 4,598 .1233145 .3288336 0 1
female 4,598 .5704654 .4950636 0 1
Variable Obs Mean Std. Dev. Min Max
. su
(1993 and 1994 General Social Survey)
. use C:/Users/deepi/OneDrive/Documents/ammapls/econ/kid.dta,clear
• The summary of these variables are as follows
Sorted by:
age byte %8.0g age age of respondent
income long %8.0g income91 total family income
degree byte %14.0g EDdeg rs highest degree
black byte %9.0g dummy Black
female byte %9.0g dummy Female
variable name type format label variable label
storage display value
size: 36,784
vars: 5 21 Apr 2019 11:12
obs: 4,598 1993 and 1994 General Social Survey
Contains data from C:/Users/deepi/OneDrive/Documents/ammapls/econ/kid.dta
. d
age 4,598 46.12375 17.33162 18 99
income 4,103 34790.7 22387.45 1000 75000
degree 4,584 1.430628 1.165915 0 4
black 4,598 .1233145 .3288336 0 1
female 4,598 .5704654 .4950636 0 1
Variable Obs Mean Std. Dev. Min Max
. su
(1993 and 1994 General Social Survey)
. use C:/Users/deepi/OneDrive/Documents/ammapls/econ/kid.dta,clear
• The description of the dataset is as follows

3. • First we Develop a dummy variable which equals one if the highest level of education is
high school diploma or less and zero otherwise
Total 4,098 100.00
4 306 7.47 100.00
3 684 16.69 92.53
2 256 6.25 75.84
1 2,164 52.81 69.59
0 688 16.79 16.79
degree Freq. Percent Cum.
rs highest
. tab degree,nolabel
. gen hsless = degree < 2
(500 observations deleted)
. drop if income == . |female == . | black == . | degree == . | age == .
Total 1,246 2,852 4,098
graduate 306 0 306
bachelor 684 0 684
junior college 256 0 256
high school 0 2,164 2,164
lt high school 0 688 688
degree 0 1 Total
rs highest hsless
. tab degree hsless

4. • Second we estimate a linear probability model with the dummy from the previous slide as the dependent
variable and female black and income as the explanatory variables
_cons .9359086 .0155062 60.36 0.000 .9055081 .9663092
income -7.23e-06 3.03e-07 -23.84 0.000 -7.83e-06 -6.64e-06
black .0778157 .0210534 3.70 0.000 .0365395 .1190918
female .0048651 .013552 0.36 0.720 -.0217043 .0314344
hsless Coef. Std. Err. t P>|t| [95% Conf. Interval]
Total 867.152757 4,097 .211655542 Root MSE = .42865
Adj R-squared = 0.1319
Residual 752.22846 4,094 .183739243 R-squared = 0.1325
Model 114.924297 3 38.3080991 Prob > F = 0.0000
F(3, 4094) = 208.49
Source SS df MS Number of obs = 4,098
. regress hsless female black income
(option xb assumed; fitted values)
. predict hslesshat

5. • Now let’s examine how many of the predicted probabilities are less than zero and how many are greater
than one
21
. count if hslesshat >1
0
. count if hslesshat<0
• We can say that 21 of the predicted probabilities are greater than one and 0 of the predicted probabilities are
less than zero
• Now let’s see what percent of the predictions are correct?
2,964
. count if (hslesshat>=0.5 & hsless==1)|(hslesshat<0.5 & hsless==0)
• We can say that 64.46% of the predicted probabilities are correct

6. • Now let’s estimate the model using logit
_cons 2.102162 .0900301 23.35 0.000 1.925706 2.278618
income -.0000356 1.68e-06 -21.23 0.000 -.0000389 -.0000323
black .5444023 .133058 4.09 0.000 .2836134 .8051912
female .0434692 .073424 0.59 0.554 -.1004392 .1873777
hsless Coef. Std. Err. z P>|z| [95% Conf. Interval]
Log likelihood = -2240.3181 Pseudo R2 = 0.1100
Prob > chi2 = 0.0000
LR chi2(3) = 553.82
Logistic regression Number of obs = 4,098
Iteration 4: log likelihood = -2240.3181
Iteration 3: log likelihood = -2240.3181
Iteration 2: log likelihood = -2240.338
Iteration 1: log likelihood = -2246.3226
Iteration 0: log likelihood = -2517.2274
. logit hsless female black income
(option pr assumed; Pr(hsless))
. predict hslesshat2
2,961
. count if (hslesshat2>=0.5 & hsless==1)|(hslesshat2<0.5 & hsless==0)
• Here we can say that 64.39% of the predicted probabilities are correct

7. • Now let’s use degree as the dependent variable, estimate a multinomial logit model with black, female and age as
the explanatory variables and less than high school diploma as the base category
_cons -1.850514 .1877946 -9.85 0.000 -2.218585 -1.482443
age .0047408 .0037216 1.27 0.203 -.0025534 .0120349
female -.4659054 .1230449 -3.79 0.000 -.7070689 -.2247418
black -.8616501 .2584425 -3.33 0.001 -1.368188 -.3551121
graduate
_cons -.642916 .1365366 -4.71 0.000 -.9105228 -.3753092
age -.0077586 .0028153 -2.76 0.006 -.0132764 -.0022408
female -.148289 .0887708 -1.67 0.095 -.3222766 .0256986
black -1.102228 .1926358 -5.72 0.000 -1.479787 -.7246684
bachelor
_cons -1.646408 .2075934 -7.93 0.000 -2.053283 -1.239532
age -.0107398 .0043353 -2.48 0.013 -.0192369 -.0022427
female -.0526683 .133773 -0.39 0.694 -.3148585 .209522
black .0205775 .1959399 0.11 0.916 -.3634577 .4046126
junior_college
high_school (base outcome)
_cons -2.617042 .1472928 -17.77 0.000 -2.90573 -2.328353
age .0315539 .0025872 12.20 0.000 .0264831 .0366247
female -.2508275 .0902757 -2.78 0.005 -.4277646 -.0738903
black .5124631 .1230954 4.16 0.000 .2712006 .7537256
lt_high_school
degree Coef. Std. Err. z P>|z| [95% Conf. Interval]
Log likelihood = -5189.569 Pseudo R2 = 0.0278
Prob > chi2 = 0.0000
LR chi2(12) = 296.77
Multinomial logistic regression Number of obs = 4,098
Iteration 4: log likelihood = -5189.569
Iteration 3: log likelihood = -5189.569
Iteration 2: log likelihood = -5189.5827
Iteration 1: log likelihood = -5195.4386
Iteration 0: log likelihood = -5337.9535
. mlogit degree black female age,baseoutcome(1)

8. • Now we compare the estimated probability of attaining each level of education for black females with average
age and compare those to the estimates for non-black females with average age
5 .0309105 .007604 4.07 0.000 .016007 .045814
4 .0627536 .011007 5.70 0.000 .0411802 .0843269
3 .0678055 .0118298 5.73 0.000 .0446196 .0909915
2 .5961567 .0235294 25.34 0.000 .5500399 .6422734
1 .2423737 .0209973 11.54 0.000 .2012198 .2835276
_predict
Margin Std. Err. z P>|z| [95% Conf. Interval]
Delta-method
age = 46.12375
female = 1
at : black = 1
5._predict : Pr(degree==graduate), predict(pr outcome(4))
4._predict : Pr(degree==bachelor), predict(pr outcome(3))
3._predict : Pr(degree==junior_college), predict(pr outcome(2))
2._predict : Pr(degree==high_school), predict(pr outcome(1))
1._predict : Pr(degree==lt_high_school), predict(pr outcome(0))
Model VCE : OIM
Adjusted predictions Number of obs = 4,098
. margins, at(black==1 female==1 age==46.12375)
5 .0683884 .0056331 12.14 0.000 .0573477 .0794291
4 .1766021 .0085631 20.62 0.000 .1598188 .1933854
3 .0620861 .0053321 11.64 0.000 .0516355 .0725368
2 .5572197 .0109954 50.68 0.000 .535669 .5787704
1 .1357037 .0075274 18.03 0.000 .1209502 .1504572
_predict
Margin Std. Err. z P>|z| [95% Conf. Interval]
Delta-method
age = 46.12375
female = 1
at : black = 0
5._predict : Pr(degree==graduate), predict(pr outcome(4))
4._predict : Pr(degree==bachelor), predict(pr outcome(3))
3._predict : Pr(degree==junior_college), predict(pr outcome(2))
2._predict : Pr(degree==high_school), predict(pr outcome(1))
1._predict : Pr(degree==lt_high_school), predict(pr outcome(0))
Model VCE : OIM
Adjusted predictions Number of obs = 4,098
. margins, at(black==0 female==1 age==46.12375)
From the results above we can say that the probability of going to high school, junior college for average aged black female is higher as
compared to average aged non-black females. Whereas it is vice versa for bachelor and graduate degree.
Which means that non-black females of average age tend to pursue higher education (i.e get more bachelor and graduate degrees) when
compared to black females of average age.

9. • Let’s do something more
• Let’s test for IIA by running the model with graduate degrees omitted
.
_cons -.6948802 .1259173 -5.52 0.000 -.9416735 -.4480869
age -.0071197 .0025472 -2.80 0.005 -.0121122 -.0021273
female -.1395937 .0847907 -1.65 0.100 -.3057805 .0265931
black -.9800519 .1718278 -5.70 0.000 -1.316828 -.6432755
bachelor
_cons -1.689483 .1944543 -8.69 0.000 -2.070607 -1.30836
age -.0110785 .0040042 -2.77 0.006 -.0189267 -.0032303
female -.0332206 .1297744 -0.26 0.798 -.2875737 .2211325
black .0306302 .185541 0.17 0.869 -.3330235 .394284
junior_college
high_school (base outcome)
_cons -2.532556 .1349254 -18.77 0.000 -2.797005 -2.268107
age .0294916 .0023253 12.68 0.000 .0249341 .0340491
female -.1875715 .0846324 -2.22 0.027 -.353448 -.0216951
black .5063439 .112897 4.49 0.000 .2850699 .7276179
lt_high_school
degree Coef. Std. Err. z P>|z| [95% Conf. Interval]
Log likelihood = -4603.0895 Pseudo R2 = 0.0304
Prob > chi2 = 0.0000
LR chi2(9) = 288.44
Multinomial logistic regression Number of obs = 4,250
Iteration 4: log likelihood = -4603.0895
Iteration 3: log likelihood = -4603.0895
Iteration 2: log likelihood = -4603.1021
Iteration 1: log likelihood = -4608.3604
Iteration 0: log likelihood = -4747.3085
. mlogit degree black female age if degree != 4

10. .
(V_b-V_B is not positive definite)
Prob>chi2 = 0.8998
= 5.58
chi2(11) = (b-B)'[(V_b-V_B)^(-1)](b-B)
Test: Ho: difference in coefficients not systematic
B = inconsistent under Ha, efficient under Ho; obtained from mlogit
b = consistent under Ho and Ha; obtained from mlogit
_cons -.6531521 -.642916 -.0102361 .
age -.0075033 -.0077586 .0002553 .
female -.1495907 -.148289 -.0013017 .0021962
black -1.103331 -1.102228 -.0011028 .
bachelor
_cons -1.663721 -1.646408 -.0173128 .
age -.0103471 -.0107398 .0003927 .
female -.0517001 -.0526683 .0009682 .0004396
black .0199896 .0205775 -.0005879 .
junior_college
_cons -2.577591 -2.617042 .0394505 .
age .0307199 .0315539 -.000834 .
female -.2506909 -.2508275 .0001366 .0040045
black .5171441 .5124631 .0046811 .0031335
lt_high_school
removedgrad allcats Difference S.E.
(b) (B) (b-B) sqrt(diag(V_b-V_B))
Coefficients
your variables so that the coefficients are on a similar scale.
Examine the output of your estimators for anything unexpected and possibly consider scaling
tested (12); be sure this is what you expect, or there may be problems computing the test.
Note: the rank of the differenced variance matrix (11) does not equal the number of coefficients being
. hausman removedgrad allcats, alleqs constant
• On examining the output from hausman, we see that there is no evidence that the IIA assumption has been
violated