298 A. Light Economics of Education Review 18 1999 291–309
to obtain the “academic” score, while the “nonacademic” score is the sum of the raw scores for the numerical oper-
ations, coding speed, auto and shop information, mech- anical comprehension, and electronics information tests.
As Table 3 shows, mean scores on both the academic and nonacademic portions of the ASVAB increase sig-
nificantly as we move from the nonworkers to the stu- dents who average 1–10 h per week, and again as we
move from the 1–10 category to the 11–20 category. The upward trend then levels off, with the two most intensive
employment categories exhibiting mean scores that are statistically indistinguishable.
Among the family background, demographic, and market characteristics considered in Table 3, a number
of interesting contrasts emerge. First, there is a clear, positive relationship between high school employment
intensity and per capita family income: students who do not work in grades 11 and 12 come from families with
an average, annual income of US3210 per capita, while those who average over 20 h per week have an average,
annual, per capita family income of US6480. One explanation for this pattern is that the money earned on
jobs held in high school contributes to family income. A more likely explanation is that students who work tend
to come from families where one or more parents work continuously throughout the year. Students from such
families may learn about employment opportunities from their employed parents or even obtain jobs at their par-
ents’ work places. Second, students’ work efforts are also positively correlated with their mothers’ and,
although it is not reported in Table 3, fathers’ schooling attainment. Parental schooling is positively correlated
with parental employment level and earnings, so this pat- tern is consistent with the preceding one. Third, race and
high school employment are strongly related. Among the 143 males who do not work at all during grades 11 and
12, 40 are nonblack, non-Hispanic henceforth referred to as “white”, 43 are black, and the remaining 17
are Hispanic. Among individuals averaging more than 20 h of work per week, 71 are white and only 17
are black. This pattern is consistent with the well known finding that young, black men are more likely than non-
blacks to be nonemployed. Such patterns are generally attributed in part to the fact that blacks are concentrated
in economically depressed urban areas where jobs are scarce, but Table 3 shows that nonemployed high school
males do not differ significantly from others in their tendency to live in urban areas or in locales with above-
average unemployment rates.
The bottom rows of Table 3 reveal that high school employment intensity is positively related to post-high
11
The ASVAB was administered to virtually all NLSY respondents in the summer and fall of 1980, when the members
of my sample were still in high school or had just graduated.
school employment. The typical male who averages more than 20 h of work per week during high school
works an average of 34 h per week in the following year and 38 h per week in the following 6 years. This is sub-
stantially more work effort than is seen among the “inter- mediate” workers and especially the nonworkers, who
average only 19 h per week in the year after high school. Individuals who work 21 1 h a week in high school
also tend to earn higher wages than their less employed counterparts when a fixed amount of post-graduation
time has elapsed. One year after graduation, for example, their
average wage
is US5.11h,
versus about
US4.50h for the other groups. There are also statisti- cally significant, but smaller, differences in mean wages
among these “types” of students when the amount of actual, post-high school work experience as opposed to
time elapsed, or “potential” work experience is held constant.
3. Wage model
The summary statistics shown in the preceding section demonstrate systematic relationships between hours
worked in high school and subsequent wages, as well as a large number of characteristics that are likely to influ-
ence wages. Because high school employment is corre- lated with so many wage determinants, it is apparent that
one must proceed carefully in identifying the marginal, skill-enhancing effect of high school employment on
subsequent wages. In this section I describe the wage model used to identify the effects of interest, define the
covariates, and describe the IVGLS estimation pro- cedure used to handle the endogeneity issues discussed
in the introduction.
To identify the wage effects of high school employ- ment, I model post-high school wages as follows:
ln W
it
5 b
1
1 b
2
HSX
i
1 b
3
HSA
i
1 b
4
HSQ
i
1 1
b
5
A
i
1 b
6
MKT
it
1 b
7
EXP
it
1 a
i
1 e
it
where W
it
is the average hourly wage earned by individ- ual i at time t during the period after high school gradu-
ation. Eq. 1 assumes post-high school wages depend on high school work experience HSX, high school
achievement HSA, high school quality HSQ and ability A, none of which vary during the post-high
school period. The next term in Eq. 1, MKT, represents market characteristics prevailing at the time the wage is
paid; in practice, MKT can be expanded to include demographic and job-related factors e.g., union status
that also influence wages or skill accumulation. EXP rep- resents post-high school work experience, and also varies
over time. The remaining terms in Eq. 1, a
i
and e
it
, represent time-invariant and time-varying unobserved
factors that influence wages.
299 A. Light Economics of Education Review 18 1999 291–309
Because Eq. 1 represents a twist on conventional human capital earnings functions, it is worth comparing
it to the following, more orthodox model: ln W
it
5 g
1
1 g
2
S
i
1 g
3
A
i
1 g
4
MKT
it
1 g
5
EXP
it
2 1
h
it
Eq. 2 resembles specifications used by Hanoch 1967 and Mincer 1974 in their pioneering empirical studies,
and by legions of subsequent researchers who share their “human capital” approach to analyzing life-cycle wage
paths. As is well known, the rationale for Eq. 2 is that wages are tied to the amount of marketable skill
embodied by worker i at time t. Baseline or innate skill levels are captured by A, or measured ability, although
analysts often omit A for lack of data.
12
Years of school- ing S control for skills obtained during the pre-employ-
ment portion of the life-cycle when individuals devote all their effort to skill acquisition. EXP, which may mea-
sure years since school exit or, ideally, actual work experience gained during that period, controls for skills
obtained via on-the-job training subsequent to school exit. MKT and h represent additional sources of
observed and unobserved heterogeneity.
The covariates A, MKT and EXP play the same roles in my model Eq. 1 as in Eq. 2. I eliminate S in Eq.
1 because my sample is homogeneous with respect to schooling attainment. However, it has long been recog-
nized that a measure of “education”—what is actually learned in school—is desired in models such as Eqs. 1
and 2, and not simply measures of school quantity. Thus, I control for school quality HSQ and student
achievement HSA in Eq. 1 to capture differences in “education” among my sample of terminal high school
graduates.
13
The remaining term in model 1, high school experience HSX, is the key covariate in my
analysis and the most significant departure from the orthodox model 2. Whereas model 2 does not
acknowledge a “transition period” during which individ- uals combine work and school, my model does. By con-
trolling for HSX, I explicitly account for the fact that individuals who have not begun their post-school careers
12
Even when test scores and other ability measures are avail- able, as they are in the NLSY, it is unclear whether they meas-
ure innate ability.
13
Welch 1966 was among the first to examine the link between school quality and subsequent earnings; Betts 1995
is an example of a more recent, NLSY-based study of school quality. Rumberger and Daymont 1984, Altonji 1995 and
Levine and Zimmerman 1995 are among the small number of studies that examine the effect of academic achievement as
measured by course work on subsequent wages.
might possess varying levels of marketable skill as a result of their in-school labor market experiences.
14
The dependent variable ln W used to estimate Eq. 1 is the natural logarithm of the CPI-deflated, average,
hourly wage in 1982 dollars earned on jobs held during the 9 years following high school graduation. The NLSY
reports wages and other job-related characteristics for virtually all employment spells encountered by respon-
dents, with the exception of jobs lasting less than 2 months. Multiple annual wages are reported for jobs
that span adjacent interview dates, while a single wage is reported for shorter jobs. The sample used to estimate
Eq. 1 contains 5689 observations for 685 men, and con- sists of all wages reported during the 9 years following
each respondent’s high school graduation date. Summary statistics for the dependent variable, as well as for the
covariates described below, appear in Table 4.
To construct a measure of high school work experi- ence HSX for inclusion in Eq. 1 I must summarize
the employment data described in Table 1 in a parsi- monious, yet meaningful, way. The variable I use for
much of the analysis measures the cumulative number of hours worked during the junior and senior academic
years. I divide this cumulative measure by 1800 to con- vert it to “one-year” units; an individual who averages
25 h of work per week for two, 36-week long academic years is considered to earn one year of high school work
experience. To allow for nonlinearities in the wage effects of high school work experience, I also use an
alternative measure of HSX consisting of three dummy variables indicating whether the average number of
hours per week worked in grades 11–12 is 1–10, 11–20, or 21 or more; no employment is the omitted group. To
allow the wage effects of high school experience to vary over time, I interact my continuous measure of HSX with
a series of dummy variables indicating the number of years since high school graduation. This unrestricted
spline function allows the relationship between high school experience and log-wages to change over time in
a very flexible manner.
My decision to use work experience accumulated throughout the junior and senior years of high school as
my measure of HSX requires some justification, especially in light of Ruhm’s 1997 conclusion that
senior-year employment affects subsequent career out- comes but earlier work experience does not. I “start the
14
To develop a formal model of optimal, life-cycle human capital accumulation that gives rise to Eq. 1, one would have
to argue that school and in-school employment are distinct skill- generating activities with different labor market pay-offs. A
model of heterogeneous human capital similar to the one pro- posed by Willis 1986 would be appropriate for this purpose,
although the development of such a model is beyond the scope of this paper.
300 A. Light Economics of Education Review 18 1999 291–309
Table 4 Means and standard deviations of variables used in wage models
Mean S.D.
Dependent variable Log of average hourly wage 1982 dollars
1.60 0.43
High school employment Years of work experience in grades 11–12
a,b
0.44 0.41
Years of work experience in grade 12
a,c
0.56 0.53
1 if average hours worked per week in grades 11–12 equals 1–10
a
0.35 11–20
a
0.26 21 1
a
0.20 High school achievement
Number of credits in humanitiessocial studies
a
3.74 1.29
mathematicsnatural science
a
0.87 0.87
vocational subjects
a
3.65 2.20
other subjects
a
1.88 1.42
High school quality Student–teacher ratio
19.07 3.67
Average teacher salary 1000s of 1982 dollars 10.79
0.92 Ability
ASVAB academic test score 68.46
22.80 ASVAB nonacademic test score
102.26 30.64
Family background, demographics 1 if foreign born
0.04 Per capita family income 1000s of 1982 dollars
2.50 1.99
Number of siblings 3.96
2.60 Mother’s highest grade completed
10.70 2.51
1 if child under age 6 0.26
1 if married 0.25
1 if black 0.28
1 if Hispanic 0.12
Market factors Area unemployment rate
8.43 3.29
1 if live in urban area 0.70
1 if live in South 0.40
1 if government job 0.06
1 if union job 0.15
Post-school work experience Years of work experience
a,d
3.58 2.60
Years of work experience squared
a,d
19.60 23.91
Years since high school graduation 4.06
2.29 Instrumental variables
e
Per capita family income in grade 12 4.80
3.49 Area unemployment rate in grade 12
8.32 3.38
1 if live in urban area in grade 12 0.70
1 is school has distributive education program 0.62
Number of observations 5689
Number of individuals 685
a
Endogenous variable.
b
Cumulative hours worked in grades 11–12 divided by 1800.
c
Cumulative hours worked in grade 12 divided by 900.
d
Cumulative hours worked since high school graduation divided by 1800.
e
See text for description of additional instrumental variables.
301 A. Light Economics of Education Review 18 1999 291–309
clock” on workers’ high school employment experiences at the start of the junior year because most students are
legally barred from entering the work force until shortly before that date. My primary reason for using a cumulat-
ive measure of junior- and senior-year experience is that there is no a priori reason to control for one and not the
other. Just as orthodox wage models control for cumulat- ive work experience gained since the start of the career,
my measure of “pre-career” experience treats all years identically. Moreover, I lack compelling statistical evi-
dence that the junior and senior years should be treated differently. Following Ruhm 1997, I estimate a version
of Eq. 1 in which junior- and senior-year work experi- ences are controlled for separately. The estimated coef-
ficient for junior-year employment is about 30 smaller than the one for senior-year employment, but because
both are estimated imprecisely due to a high degree of correlation between the two variables I cannot reject the
null hypothesis that the two coefficients are equal.
15
Although my preferred measure of high school employ- ment is cumulative hours worked in grades 11–12, for
comparability with Ruhm’s analysis I also present results based on a measure of senior-year employment only.
The measures of high school achievement HSA, high school quality HSQ and ability A in Eq. 1 are ident-
ical to variables summarized in the preceding section. I control for high school achievement with four variables
measuring the cumulative number of Carnegie credits accumulated during grades 11 and 12 in four subject
areas: humanities and social studies, mathematics and science, vocational subjects, and other subjects. High
school quality is measured by the student–teacher ratio
15
Ruhm 1997 reports similar findings, but draws con- clusions that differ from mine. For example, he reports coef-
ficients in the bottom panel of column b of his Table 4 that imply roughly 9 and 16 wage premia associated with 10 h
per week of employment in the junior and senior years, respect- ively. The p-values for the junior- and senior-year coefficients
are 0.243 and 0.002, so he opts to omit junior-year employment from the model because the 9 return is not statistically dis-
tinguishable from 0.
It is worth noting that another difference between Ruhm’s analysis and mine is that he uses “reference week” employment
as his primary measure of high school work experience, while my measure comes from the week-by-week employment data
in the work history file. Ruhm also experiments with the work history data but argues that they are likely to be error-ridden
because they require respondents to recall their employment experiences over a roughly one-year retrospective. Research
on retrospective recall in the NLSY and other longitudinal sur- veys e.g., Duncan Hill, 1985; Dugoni et al., 1997 does not
indicate that the NLSY work history data are likely to be unduly error-ridden. In fact, I am concerned that “reference week” data
do not accurately measure employment throughout the aca- demic year for respondents who vary their work effort over
time.
in the respondent’s high school, as well as the average annual salary in thousands of CPI-deflated, 1982
dollars paid to first-year teachers. These values are obtained directly from schools as part of the NLSY high
school survey, but are missing for about 15 of obser- vations. I set missing observations equal to the sample
mean and define two dummy variables indicating miss- ing high school quality data. To control for student
ability, I use respondents’ scores on both the academic and nonacademic portions of the ASVAB see Section
2 for details.
The covariate vector MKT in Eq. 1 includes not only market-related factors, but also family background and
personal characteristics that are likely to influence both in-school and post-school skill acquisition. These vari-
ables, along with the measures of post-school experience EXP are fairly standard in wage models such as 1
and 2. I control for family and personal characteristics with dummy variables indicating the respondent is
foreign born, black, or Hispanic with non-black, non- Hispanic the omitted race group, and with continuous
measures of his number of siblings in 1979 and his mother’s highest grade of school. While these variables
are time-invariant, I also control for three factors meas- ured at time t: per capita, family income net of the
respondent’s annual labor earnings, whether he is mar- ried, and whether his household contains children under
age 6. Because family income and mothers’ schooling levels are unreported for 6 and 7 of all observations,
respectively, I include “missing” dummies for those two variables. To control for market characteristics at time t,
I include the unemployment rate in the respondent’s local labor market, and I also include dummy variables
indicating whether he lives in an urban area or in the South, whether he works in the public sector, and
whether his job is unionized. My measures of post- school work experience include the number of months
since high school graduation divided by 12 “potential” experience and the number of hours worked between
high school graduation and time t divided by 1800 “actual” experience and its square. I control for both
actual and potential experience to contend with the unemployment and nonemployment that characterize the
careers of young men. In a group of individuals with the same amount of post-school work experience, those who
have been out of school the longest have spent the most time nonemployed and are likely to earn less than their
more continuously employed counterparts.
I assume the time-invariant, person-specific compo- nent of the error term in Eq. 1 a
i
and the time-varying component e
it
are distributed with zero means and con- stant variances equal to s
2 a
and s
2 e
, respectively. I assume e
it
is orthogonal to a
i
and each of the covariates in Eq. 1, but a
i
is likely to be correlated with HSX, HSA and actual experience a component of EXP inso-
far as individuals’ work- and study-related time allo-
302 A. Light Economics of Education Review 18 1999 291–309
cation decisions are affected by factors that cannot be observed. By assuming these unobservables are time-
invariant, I am able to formally address the endogeneity issues discussed in the introduction.
16
To contend with the potential correlation between a
i
and HSX, HSA and EXP, I estimate the parameters in Eq. 1 using a variant of the instrumental variables, gen-
eralized least squares IVGLS method proposed by Hausman and Taylor 1981. Following Hausman and
Taylor, the “core” instruments consist of deviations from within-person means of each time-varying regressor,
plus the within-person means of each exogenous regressor. Given my assumptions about the error struc-
ture of Eq. 1, each of these variables is orthogonal to both a
i
and e
it
and is, therefore, a valid instrument. To improve the R
2
in the first-stage regressions for HSX and HSA, I also use four additional instruments: per capita,
family income during the respondent’s senior year of high school, the unemployment rate in his local labor
market during that year, a dummy variable indicating whether he lives in an urban area during that period, and
a dummy indicating whether his high school offers a dis- tributive education program. All four variables which
are summarized in Tables 3 and 4 help explain high school employment decisions, but should be orthogonal
to the error terms in Eq. 1. Because I include among the covariates in Eq. 1 family income, unemployment
rates, and urban status measured at time t, I am relying on intertemporal variation in these variables due partly
to post-high school geographic mobility for identifi- cation. The addition of the four “extra” instrumental vari-
ables increases the R
2
in the first-stage regressions by a nontrivial amount e.g., from 0.26 to 0.32 in a typical
regression, and I reject at a 5 significance level the null hypothesis that these four instruments belong in the
second-stage regression.
4. Findings
