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
The goal of my econometric analysis is to identify the “value added” of high school employment, by which I
mean its effect on subsequent wages net of any corre- lation with other factors that influence wages. Only by
identifying the “value added” can we determine whether high school employment has a direct effect on labor mar-
ket productivity. I believe IVGLS estimation of wage model 1 is an appropriate way to achieve this goal
16
ASVAB scores, union membership and marital status are also likely to be correlated with unobserved, personal character-
istics. However, my estimated coefficients for HSX and HSA are not sensitive to assumptions about the endogeneity of these
covariates, so I treat them as exogenous.
because the model controls for numerous sources of observed heterogeneity and also contends with corre-
lation between high school employment and personal characteristics that remain unobserved. In this section, I
present IVGLS estimates of 1 as well as estimates of alternative specifications that reveal how inferences
about the “value added” of high school employment are affected by the failure to control for observed and unob-
served sources of heterogeneity.
In Table 5, I present estimated coefficients from alter- native specifications of my wage model. Column head-
ings 1 through 12 refer to alternative specifications that vary in terms of the measure of high school work experi-
ence and the inclusion of other covariates HSA and EXP. For each specification I present both IVGLS and
GLS estimates; the latter account for the nonspherical nature of the disturbances due to each respondent con-
tributing multiple wage observations to the sample, but assume the disturbances are unrelated to each covariate.
Table 5 contains estimated coefficients for the high school employment HSX covariates only; estimated
coefficients for the remaining covariates for selected specifications appear in Tables 6 and 7.
17
I begin by discussing the estimates for specifications 1–3, each of which controls for high school work experi-
ence with a single, cumulative measure of the number of hours worked in grades 11 and 12 divided by 1800.
These specifications are quite restrictive in that they con- strain the relationship between hours worked in high
school and log-wages to be linear. Specification 1 omits both HSA and EXP, which means b
3
and b
7
in Eq. 1 are constrained to be zero. Specification 2 includes EXP
among the covariates, and specification 3 controls for both HSA and EXP. I do not show results of experiments
in which A and HSQ are excluded from the model because their presence proves to have an insignificant
effect on the estimated coefficients for high school work experience, although they help explain the variation in
log-wages.
Table 5 reveals that when GLS is used to estimate specification 1—that is, when I assume that the residuals
are orthogonal to all included covariates—the estimated coefficient for high school employment is 0.075, with a
standard error of 0.021. This implies that an individual who averages 25 h per week throughout his junior and
senior years of high school subsequently earns 7.5 higher wages during the entire 9-year observation period
than an individual who was nonemployed in high school. An individual who works only 10 h per week in grades
11 and 12 accumulates 720 h of work experience, or 0.4 years, and receives a 3 wage premium. When I esti-
17
The estimated coefficients for the covariates listed in Tables 6 and 7 change very little across specifications, so I
present them for three versions only.
303 A. Light Economics of Education Review 18 1999 291–309
Table 5 Estimated coefficients for selected covariates in alternative specifications of wage model
GLS IVGLS
1 2
3 1
2 3
Years of work experience in grades 0.075
0.033 0.030
0.146 0.068
0.062 11–12
0.021 0.014
0.014 0.068
0.021 0.021
4 5
6 4
5 6
Years of work experience in grade 12 0.064
0.026 0.024
0.122 0.055
0.051 0.017
0.011 0.011
0.052 0.016
0.016 7
8 9
7 8
9 1 if average hours worked per week in
grades 11–12 equals 1–10
0.004 0.019
0.018 0.003
0.015 0.012
0.023 0.022
0.022 0.081
0.077 0.077
11–20 0.004
0.016 0.021
0.061 0.046
0.046 0.026
0.025 0.025
0.088 0.083
0.085 21 1
0.087 0.053
0.049 0.102
0.071 0.059
0.028 0.026
0.025 0.063
0.057 0.048
10 11
12 10
11 12
Years of work experience in grades 11–12 interacted with dummy variable
indicating years since high school graduation equals
1 0.035
0.035 0.034
0.073 0.033
0.030 0.031
0.031 0.032
0.045 0.046
0.045 2
0.028 0.025
0.023 0.063
0.019 0.020
0.031 0.031
0.030 0.041
0.040 0.040
3 0.094
0.066 0.060
0.094 0.041
0.038 0.030
0.030 0.030
0.040 0.039
0.039 4
0.082 0.062
0.059 0.084
0.042 0.042
0.029 0.028
0.027 0.038
0.041 0.040
5 0.088
0.061 0.058
0.109 0.028
0.038 0.029
0.029 0.028
0.039 0.030
0.030 6
0.164 0.058
0.054 0.173
0.065 0.059
0.029 0.028
0.027 0.042
0.030 0.029
7 0.128
0.044 0.049
0.194 0.050
0.045 0.030
0.031 0.030
0.046 0.033
0.032 8
0.166 2
0.031 2
0.028 0.220
2 0.016
2 0.005
0.041 0.051
0.050 0.050
0.053 0.055
9 0.170
2 0.048
2 0.036
0.226 2
0.017 2
0.001 0.100
0.060 0.060
0.152 0.063
0.059 Control for post-high school work
no yes
yes no
yes yes
experience Control for high school course credits
no no
yes no
no yes
Note: Standard errors are in parentheses. Additional GLS and IVGLS estimates for specifications 3, 9, and 12 appear in Tables 6 and 7.
mate the identical model using the IVGLS procedure described in Section 3 with high school employment as
the sole endogenous variable, the estimated coefficient almost doubles to 0.146. The difference between the
GLS and IVGLS estimates suggests that high school employment intensity is negatively correlated with unob-
served, personal characteristics. Individuals who are rela- tively low wage earners for unobserved reasons accumu-
late the most work experience in high school, and the failure of GLS to control for this correlation causes the
304 A. Light Economics of Education Review 18 1999 291–309
Table 6 Additional GLS estimators for selected wage models summarized in Table 5
Specification 3 Specification 9
Specification 12 Coeff.
S.E. Coeff.
S.E. Coeff.
S.E. Constant
1.052 0.130
1.018 0.130
1.100 0.130
Number of credits in humanitiessocial studies
0.006 0.007
0.008 0.007
0.005 0.006
mathematicsnatural science 2
0.034 0.010
2 0.033
0.010 2
0.033 0.009
vocational subjects 0.007
0.002 0.007
0.002 0.006
0.003 other subjects
2 0.008
0.006 2
0.007 0.006
2 0.008
0.006 Student–teacher ratio
0.005 0.002
0.005 0.002
0.004 0.002
1 if student–teacher ratio missing 0.020
0.029 0.028
0.028 0.018
0.028 Average teacher salary 1000s
0.018 0.009
0.020 0.009
0.018 0.008
1 if average teacher salary missing 2
0.015 0.029
2 0.021
0.028 2
0.013 0.028
ASVAB academic test score 0.001
0.001 0.001
0.001 0.001
0.000 ASVAB nonacademic test score
0.001 0.000
0.001 0.001
0.001 0.000
1 if foreign born 2
0.025 0.042
2 0.018
0.042 2
0.024 0.041
Per capita family income 1000s 0.009
0.003 0.008
0.004 0.008
0.002 1 if family income missing
2 0.044
0.040 2
0.041 0.040
2 0.045
0.040 Number of siblings
2 0.002
0.003 2
0.003 0.003
2 0.002
0.003 Mother’s highest grade completed
0.001 0.004
0.003 0.005
0.003 0.003
1 if mother’s highest grade missing 2
0.021 0.030
2 0.024
0.029 2
0.019 0.029
1 if child under age 6 0.008
0.015 0.010
0.015 0.008
0.015 1 if married
0.044 0.015
0.044 0.015
0.044 0.014
1 if black 0.011
0.024 0.010
0.025 0.011
0.023 1 if Hispanic
0.056 0.030
0.054 0.029
0.057 0.029
Area unemployment rate 2
0.012 0.002
2 0.013
0.002 2
0.012 0.002
1 if live in urban area 0.020
0.015 0.019
0.015 0.019
0.014 1 if live in South
2 0.018
0.016 2
0.018 0.016
2 0.020
0.016 1 if government job
2 0.022
0.023 2
0.020 0.024
2 0.022
0.022 1 if union job
0.231 0.015
0.232 0.015
0.229 0.015
Years of post-HS experience 0.084
0.009 0.084
0.009 0.081
0.008 Years of post-HS experience squared
2 0.004
0.001 2
0.004 0.001
2 0.003
0.000 Years since high school graduation
2 0.010
0.008 2
0.010 0.008
2 0.012
0.002 s
2 a
0.052 0.052
0.051 s
2 e
0.126 0.126
0.125 Root mean squared error
0.328 0.327
0.325 Number of observations
5689 5689
5689 Note: Each specification also includes dummy variables indicating the calendar year 1981–91. s
2 a
and s
2 e
are the estimated variances of the individual and transitory components of the residual.
direct effect of high school employment to be under- stated relative to the preferred IVGLS estimate.
Specification 2 is identical to 1 except it also controls for three measures of post-school work experience: time
elapsed since high school graduation and hours of actual work experience divided by 1800 and its square. Table
5 indicates that the addition of these three variables has a dramatic effect on the estimated coefficient for high
school employment. The GLS estimate falls to 0.033 and the IVGLS estimate falls to 0.068; both are less than
half as large as the corresponding estimates for specifi- cation 1.
18
Because high school employment and post- school employment are strongly, positively correlated as
shown in Table 3, omission of the latter causes the effect of high school work experience to be overstated.
The large estimated effect in specification 1 reflects the direct, skill-enhancing effect of high school employment
on subsequent wages plus the indirect effect of its corre- lation with subsequent work effort. The latter effect is
important, for it suggests that high school employment may foster good work habits, impart job-seeking skills,
and otherwise enhance the post-school work continuity
18
High school employment and actual experience and its square are the endogenous variables in specification 2.
305 A. Light Economics of Education Review 18 1999 291–309
Table 7 Additional IVGLS estimators for selected wage models summarized in Table 5
Specification 3 Specification 9
Specification 12 Coeff.
S.E. Coeff.
S.E. Coeff.
S.E. Constant
1.062 0.130
1.001 0.140
1.158 0.131
Number of credits in humanitiessocial studies
0.006 0.007
0.009 0.007
0.004 0.006
mathematicsnatural science 2
0.033 0.010
2 0.033
0.010 2
0.034 0.009
vocational subjects 0.006
0.004 0.006
0.004 0.007
0.005 other subjects
2 0.007
0.007 2
0.005 0.007
2 0.010
0.006 Student–teacher ratio
0.004 0.002
0.005 0.002
0.004 0.002
1 if student–teacher ratio missing 0.015
0.029 0.032
0.031 0.020
0.028 Average teacher salary 1000s
0.018 0.009
0.021 0.009
0.020 0.008
1 if average teacher salary missing 2
0.014 0.029
2 0.026
0.031 2
0.011 0.028
ASVAB academic test score 0.001
0.001 0.001
0.001 0.000
0.000 ASVAB nonacademic test score
0.001 0.000
0.001 0.000
0.001 0.000
1 if foreign born 2
0.022 0.043
2 0.011
0.044 2
0.023 0.042
Per capita family income 1000s 0.008
0.003 0.008
0.003 0.010
0.002 1 if family income missing
2 0.043
0.041 2
0.039 0.041
2 0.051
0.040 Number of siblings
2 0.003
0.003 2
0.003 0.004
2 0.002
0.003 Mother’s highest grade completed
0.002 0.004
0.000 0.004
0.000 0.003
1 if mother’s highest grade missing 2
0.015 0.030
2 0.025
0.031 2
0.020 0.029
1 if child under age 6 0.006
0.015 0.010
0.016 0.010
0.015 1 if married
0.045 0.015
0.046 0.015
0.041 0.015
1 if black 0.013
0.025 0.007
0.025 0.004
0.024 1 if Hispanic
0.060 0.030
0.055 0.030
0.058 0.029
Area unemployment rate 2
0.013 0.002
2 0.013
0.002 2
0.013 0.002
1 if live in urban area 0.021
0.015 0.019
0.015 0.022
0.015 1 if live in South
2 0.018
0.017 2
0.017 0.016
2 0.019
0.016 1 if government job
2 0.027
0.022 2
0.024 0.023
2 0.026
0.022 1 if union job
0.233 0.015
0.233 0.015
0.232 0.015
Years of post-HS experience 0.040
0.006 0.041
0.007 0.040
0.009 Years of post-HS experience squared
0.000 0.001
0.000 0.001
0.000 0.002
Years since high school graduation 0.002
0.009 0.003
0.009 0.002
0.000 s
2 a
0.052 0.052
0.051 s
2 e
0.126 0.126
0.125 Root mean squared error
0.331 0.330
0.328 Number of observations
5689 5689
5689 Note: Each specification also includes dummy variables indicating the calendar year 1981–91. s
2 a
and s
2 e
are the estimated variances of the individual and transitory components of the residual.
of young men. However, only by netting out this indirect effect can we identify the productivity-enhancing effect
of high school employment among otherwise identical individuals.
Of course, specification 2 fails to control for another potentially important source of heterogeneity: high
school achievement. Specification 3 is identical to 2 except it includes measures of course credits accumu-
lated in four subject areas. Using either GLS or IVGLS estimation, the addition of these measures causes the
estimated effect of high school experience to decrease by about 10. Taken at face value, this suggests a positive
correlation between high school employment and high school achievement—that is, students who work the
most intensively take the “best” courses in terms of their effect on future wages. Thus, failure to control for high
school achievement causes the estimated effect of high school employment to be overstated because it also cap-
tures the wage-enhancing effects of related course work. However, the difference between the specification 2 and
3 estimates is small in economic terms and also statisti- cally insignificant. Using standard significance levels, I
fail to reject the null hypothesis that the specification 2 and 3 coefficients for high school employment are equal.
Because the relationship between high school curricu- lum and subsequent wages is not well understood, it is
worth investigating my findings a bit further. Estimated GLS and IVGLS coefficients for the high school
306 A. Light Economics of Education Review 18 1999 291–309
achievement measures for specification 3 appear in Tables 6 and 7. The GLS estimates indicate that courses
in humanitiessocial studies and vocational subjects have a very small, positive effect on log-wages, courses in
“other” subjects have an equally small, negative effect and mathscience courses have a pronounced, negative
effect. However, only the coefficients for vocational sub- jects and mathscience are statistically distinguishable
from zero at conventional significance levels. The esti- mated GLS coefficient of 0.007 for vocational subjects
implies that a student accumulating four Carnegie credits in grades 11–12 roughly the mean among the more
intensive workers earns 2.8 more after high school than his counterparts who take no vocational courses. A
student earning only one credit in math or science, how- ever, earns 3.4 less than if he were to take no courses
in those subject areas. The corresponding IVGLS esti- mates shown in Table 7 are very similar in magnitude
to the GLS estimates, but the associated standard errors are larger.
Two comments on the estimated wage effects of high school course work are warranted. First, because high
school students who work the most tend to accumulate above average credits in vocational courses which
enhance future wages and below-average credits in math and science which decrease future wages, they do
not appear to face a trade-off in deciding how to allocate their time. Students who focus their efforts on employ-
ment and vocational courses enhance their future wages on both fronts, although the vocational courses have a
very small impact. This conclusion is consistent with the estimates in Table 5, which indicate the effect of high
school employment may be overstated slightly although the difference is statistically insignificant when high
school course work is not controlled for. Second, my finding that vocational courses have a weak, positive
effect on future wages corroborates evidence seen else- where Bishop, 1989; Rumberger Daymont, 1984;
Kang Bishop, 1989 but my finding with respect to math and science courses does not. Other studies
Altonji, 1995; Levine and Zimmerman, 1995 indicate that math and science courses have either no effect on
subsequent wages or a small, positive effect. I believe I find a negative effect because I control for junior- and
senior-year course work only, and terminal high school graduates who study math and science in these 2 years
are likely to be meeting requirements that they failed to satisfy earlier.
19
The remaining rows of Table 5 present GLS and
19
When I reestimate specification 3 with the larger sample that includes college-goers, the estimated GLS coefficient for
math and science courses is 0.002, with a standard error equal to 0.006 and the coefficient for vocational courses is 0.003 with
a standard error of 0.001.
IVGLS estimates for several specifications that use alternative measures of high school employment but are
otherwise identical to 1–3. To follow up on the measure- ment issues discussed in Section 3, specifications 4–6
control for cumulative hours worked in grade 12 only divided by 900. The patterns revealed by specifications
1–3 apply to versions 4–6 as well: the IVGLS estimates are roughly twice as large as the GLS estimates, con-
trolling for post-school experience specification 5 causes a substantial decline in the estimated effect of
high school experience, and the inclusion of high school achievement specification 6 causes the estimated effect
to decline further, but by a small, statistically insignifi- cant amount. However, after taking the rescaling into
account, in specifications 4–6 the estimated effects of senior-year employment are larger than the correspond-
ing coefficients for specifications 1–3. Whereas the IVGLS estimate for specification 3 indicates that a stud-
ent averaging 25 h per week throughout his senior year receives a 3.1 increase in future wages, the IVGLS
estimate for specification 6 implies a 5.1 wage boost. Of course, specification 3 also implies a 3.1 wage
boost from working 25 h per week in grade 11, while specification 6 constrains that effect to be zero. My
interpretation of these results is that employment in the junior year of high school does affect future wages.
Given my inability to identify separate coefficients for junior and senior year employment due to the high cor-
relation between the two I believe controlling for “total” high school employment is the preferred strategy.
Specifications 7–9 relax the restriction that log-wages are linear in high school work experience. I replace the
single measure of cumulative experience with three dummy variables indicating whether the average, weekly
effort in grades 11–12 is 1–10, 11–20, or 21 1 h. The GLS estimates indicate that the “return” to high school
employment is concentrated among individuals who work 21 1 h per week; young men who work less inten-
sively in high school subsequently earn wages that are virtually identical to those of their nonemployed counter-
parts. The IVGLS coefficients for the 1–10 category are also effectively zero. The remaining IVGLS coef-
ficients, while imprecisely estimated, indicate that sub- sequent wage boosts accrue to individuals working 11–
20 h per week in high school as well as those averaging 21 1 h per week. Specification 9 which controls for
high school achievement and post-school experience implies that the most intensive workers receive a 5.9
wage return to their high school work experience. This estimate is comparable to specification 3, which predicts
a 5.2 wage premium for 21 h per week and a 6.2 premium for 25 h per week. Thus, while specifications
7–9 indicate that the wage boosts associated with high school employment are concentrated among the most
intensive workers, these specifications make predictions that are comparable to what we have already seen.
307 A. Light Economics of Education Review 18 1999 291–309
The final specifications summarized in Table 5 allow the estimated wage effect of high school work experi-
ence to vary over time. I use an unrestricted spline func- tion in which the continuous measure of high school
employment from specifications 1–3 is interacted with a set of dummy variables indicating that the wage is earned
in the jth year after high school graduation, where j 5 1, …, 9. Both the GLS and IVGLS estimates for speci-
fication 10, which omits high school achievement and post-school experience, suggest that the return to high
school experience increases steadily over time. The IVGLS estimates which continue to be larger than the
GLS estimates indicate that a year of high school employment raises wages 6–7 in the first year after
graduation, 17 after 6 years, and 22 after 9 years. However, this pattern disappears when heterogeneity in
post-school work experience is held constant in specifi- cations 11–12. The addition of EXP to the set of covari-
ates again causes both the GLS and IVGLS estimates of the high school employment coefficients to decline
dramatically, but the decline is relatively greater at higher levels of potential experience. This is what one
would expect, for young men become increasingly het- erogeneous in their accumulation of actual work experi-
ence as time goes by. Both the GLS and IVGLS esti- mates indicate that with actual experience held constant,
the wage benefits of high school employment peak at the 6-year mark and decline rapidly thereafter. For example,
IVGLS estimates for specification 12 indicate that a year of high school employment is “worth” 5.9 after 6 years
and nothing after 9 years. The large, positive, and long- lived returns implied by specification 10 reflect the fact
that young men who work intensively in high school accumulate more post-school work experience and mar-
ketable skill than their classmates who did not work in high school.
I conclude this discussion by contrasting my findings to those of Ruhm 1997. I view the IVGLS estimates
for specifications 3, 9, and 12 as the preferred estimates because they control for the widest array of observed
covariates, contend with the endogeneity of key covari- ates, and measure high school employment in the most
comprehensive manner possible. The estimated coef- ficient for high school work experience in specification
3 is 0.062, which is roughly equal to the estimated coef- ficient of 0.059 associated with 21 1 h per week in
specification 9 and the estimate of 0.059 associated with 6 years of potential experience in specification 12. Thus,
I view 6 as an “upper bound” of the true, productivity- enhancing effect of high school employment. This esti-
mate implies that an individual who averages 25 hweek of work experience throughout his junior and senior
years of high school receives a 6 wage premium after high school graduation but only after 6 years in specifi-
cation 12, while an individual who works 10 h per week in his senior year and zero hours in his junior year
receives a 1.2 wage boost. Ruhm’s preferred estimate per his Table 10, column c indicates that a male who
averages 10 h per week in his senior year of high school earns wages after 6–9 years that are 3.1 higher than
those of his nonemployed counterparts. Clearly, my esti- mates suggest that high school employment has a smaller
effect on subsequent wages than do Ruhm’s, and that the effect is shorter-lived because it falls to zero within
8 years of high school graduation.
I believe the differences in the magnitudes of my esti- mates and Ruhm’s can be attributed to three factors.
First, my measure of high school work experience is a cumulative measure of experience gained in grades 11
and 12, so I estimate an average return to those 2 years of experience. Ruhm measures senior-year experience only,
and constrains the smaller effect of junior-year experi- ence to be zero. Second, I estimate a fairly conventional,
human capital wage model that controls for heterogen- eity in post-school skill acquisition with a quadratic in
“actual” work experience. Ruhm uses average wages earned 6–9 years after high school graduation as his
dependent variable, but does not include post-school work experience among his regressors. Thus, his esti-
mated “return” to high school employment identifies the direct, productivity-enhancing effect of experience
gained in grade 12 plus the indirect effect of increased future work effort.
20
Third, I eliminate heterogeneity in postsecondary schooling by focusing on terminal high
school graduates, while Ruhm does not. When I add col- lege-goers to my sample and reestimate specification 12,
I obtain smaller estimated coefficients for the first 6 years when respondents are in college and larger coefficients
for years 7–9, presumably because the estimated high school employment effect includes the wage-enhancing
effects of additional schooling.
5. Concluding comments
