135 J. Arkes Economics of Education Review 18 1999 133–141
interpret the presence of attributes that are unobservable to the firm and correlated with productivity and edu-
cation. In a human capital model, if the researcher cannot measure or does not include some ability-type measure
that is correlated with educational attainment and pro- ductivity, then the estimated returns to education would
be biased, but a sorting model should intentionally omit attributes that are unobservable to the firm and correlated
with education and productivity. The premise is that employers cannot observe abilities in potential and new
employees, but can only infer workers’ skills by observ- ing their credentials. Thus, part of the return to education
is attributable to education signaling the attributes that employers find worthwhile, some of which are unobserv-
able to the employers. To include measures of these attri- butes in a wage regression would result in a downwardly
biased measure of the wage premium for credentials. Therefore, when estimating the wage premiums associa-
ted with credentials, it is important to indicate whether one is assuming that a sorting model or a human capital
model applies in order to properly interpret the estimates.
An important point from the discussion above is that in a sorting framework, controlling for abilities that are
unobservable to employers would result in an estimated wage premium for credentials that is meaningless by
itself since it no longer represents the difference in pro- ductivity between the credentialled and noncredentialled
workers. In fact, if a researcher were to control for the complete set of abilities that the credentials signal, then
the estimated wage premiums for the credentials should be zero. However, the differences in the estimates when
controlling and not controlling for abilities are informa- tive since they identify the portions of perceived pro-
ductivity differences between credentialled and noncre- dentialled workers attributable to credentials signaling
these abilities.
Frazis 1993 controls for ability — observed ability and unobserved ability calculated from an ordered pro-
bit — to determine if selection bias explains the college degree effect. He finds that including ability measures
has little effect on the college degree coefficient estimate. In addition, he interacts the ability measures with years
of college to address a hypothesis of Chiswick 1973, that the degree effect results from the fact that those who
are receiving more benefits from education are more likely to stay in school and receive their degrees. Again,
Frazis finds no evidence supporting this hypothesis.
This analysis advances Frazis’ work in several ways. First, Frazis uses mean values to proxy for measurable
abilities for respondents who have missing ability data, who comprise 27 of the sample. His method could
dampen the explanatory power of these ability measures. In contrast, I exclude these workers since my interest
is in whether credentials signal these abilities. Second, whereas Frazis considers a sample of 25-year olds, many
of whom had not completed their schooling, this analysis uses a sample of workers aged 28–30. Thus, it is more
likely that the respondents in my sample are finished with school. Third, while Frazis only focuses on the
bachelor’s degree, I examine the high school diploma, college attendance, the associate’s degree and the
advanced degree credentials as well. Finally, I consider the initial stage of the sorting model, analyzing what
abilities credentials signal.
3. Data
The sample consists of males drawn from the 1993 wave of the National Longitudinal Survey of Youth. The
NLSY began with 12 686 14- to 22-year old individuals in early 1979, 6403 of whom are males.
Weiss 1995 states that in sorting models, “schooling is correlated with differences among workers that were
present before the schooling choices were made.” If ability were measured during or after one’s education,
then one could not separate the abilities signaled by edu- cation from the productive skills learned in school. For
the NLSY, however, individuals were aged 15–24 when they took the test in July 1980. In light of Weiss’ state-
ment, I restrict the sample to respondents who were aged 15–18 when they took the test in July 1980, and who
had not attended college at the time. Thus, the measure of ability is pre-college.
Additional criteria to be in the sample are that the respondents must have been working at the time of the
interview, had an average hourly wage rate greater than one-half the minimum wage at the time and less than
60, had not been enrolled in school, had not been self- employed, and had taken the ability tests. The respon-
dents in the sample were aged mostly 28–30 in 1993. The final sample size is 1064 individuals. Table 1 shows
the descriptive statistics for the sample.
Of the original sample, 94 took the Armed Services Vocational Aptitude Battery ASVAB. The tests, along
with what they measure, are as follows Bishop, 1992: 1. general science — knowledge of the physical and bio-
logical sciences; 2. arithmetic reasoning — ability to solve arithmetic
word problems; 3. word knowledge — ability to select the correct mean-
ing of words presented in context and to identify the best synonym for a given word;
4. paragraph comprehension — ability to obtain infor- mation from written passages;
5. numerical operations — ability to perform arithmetic computations in a speeded context;
6. coding speed — ability to use a key in assigning code numbers to words in a speeded context;
7. auto and shop information — knowledge of auto- mobiles, tools, and shop terminology and practices;
136 J. Arkes Economics of Education Review 18 1999 133–141
Table 1 Descriptive statistics. Number of observations 5 1064
Mean Standard
deviation Average hourly earnings
11.54 5.72
Age 29.52
0.87 Completed the 8th grade
0.994 0.07
High school years completed 3.57
0.98 College years completed
1.20 1.65
Grad years completed 0.16
0.63 GED
0.07 0.25
High school diploma 0.78
0.41 College attendance
0.52 0.50
Associate’s degree 0.05
0.22 Bachelor’s degree
0.20 0.40
Advanced degree 0.04
0.19 Adjusted AFQT score
0.0 28.85
Experience 10.25
2.47 Experience-squared
115.99 48.41
SMSA 0.79
0.41 Northeast
0.15 0.36
South 0.41
0.49 West
0.19 0.39
White 0.66
0.47
8. mathematics knowledge — knowledge of high school mathematics principles;
9. mechanical comprehension — knowledge of mechan- ical and physical principles and ability to visualize
how illustrated objects work; and 10. electronics information — knowledge of electricity
and electronics. The scores from four of the 10 tests in the ASVAB —
arithmetic reasoning, word knowledge, paragraph com- prehension and numerical operations — constitute the
Armed Forces Qualification Test AFQT score.
3
In this analysis, I consider the AFQT score as a comprehensive
ability measure since it is a commonly used measure of ability and is found to have high correlations — with a
median correlation of 0.38 — with job performance in 23 military occupations Widgor and Green, 1991.
Since age affects competency in these areas, I use age- corrected test scores, which are the residuals from a
regression of the test scores on age dummy variables Neal and Johnson, 1994. The scores are then transfor-
med so that each point represents one percentile in the sample.
The educational data come from self-reported attain- ment. Included as indicators of the productive skills
acquired in school are the number of high school years
3
The AFQT score is the sum of the arithmetic reasoning score, word knowledge score, paragraph comprehension score
and one-half the numerical operations score.
ranging from 0 to 4, college years and post-graduate years completed.
4,5
The educational credentials are a high school diploma, college attendance without neces-
sarily completing a year of college, an associate’s degree, a bachelor’s degree and an advanced degree. If
a person has both an associate’s and a bachelor’s degree, the associate’s degree is disregarded because employers
would probably be more interested in the abilities that a bachelor’s degree signals than in those marked by an
associate’s degree. Also, employers probably would not consider a person with both degrees to be more pro-
ductive than one with only a bachelor’s degree.
Finally, this analysis may suffer from attrition bias. The 1993 interview for the NLSY includes 78 of the
14-, 15- and 16-year olds from the 1979 survey who took the ASVAB exam in July 1980 and who had not entered
college by early 1980. This analysis assumes that attrition is unrelated to the wages respondents earn or
the education they attain. To the extent that this is not true, the results may be biased.
6
4. What pre-college abilities do educational credentials signal?
