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High School Graduation, Performance, and Wages
Author(s): Andrew Weiss
Source: Journal of Political Economy, Vol. 96, No. 4 (Aug., 1988), pp. 785-820
Published by: The University of Chicago Press
Stable URL: http://www.jstor.org/stable/1830474
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High School Graduation, Performance,
and Wages
AndrewWeiss
Boston Universityand National Bureau of EconomicResearch
Using data from the Panel Study of Income Dynamics and a proprietary
sample of semiskilled production workers, this paper investigates
the reasons for the discontinuous increase in wages associated
with graduation from high school. I find a discontinuous decrease in
workers' propensities to quit or be absent. However, I do not find
that high school graduates have a comparative advantage in production
jobs requiring more training, nor in either sample is there a
discontinuous increase in required training associated with the jobs
held by high school graduates. The wage premium associated with
graduation from high school appears to be procyclical: falling during
slumps, periods in which employers are likely to be hoarding
labor and in which quits and absences are least important to firms.
There is also some evidence suggesting that prior quits have a larger
effect on the wages of high school graduates than on the wages of
high school dropouts.
I. Introduction
It has often been noticed that graduation from high school induces a
discontinuous upward shift in the relationship between schooling and
I am grateful to Roger Klein, Richard Spady, James Heckman, an anonymous referee,
and participantsat the seminarsat the Universityof Chicago,StateUniversityof
New York at Stony Brook, the National Bureau of Economic Research, Stanford University,
Cornell University, and Columbia University for valuable comments and suggestions.
Gerald McTigue, Ali Moazami, and Andrea Shepard provided valuable assistance
in processing the data and in computer programming. John Raisian
reconstructed his blue-collar-white-collar classification scheme for my use. The research
was done while I was employed by Bell Communications Research and Columbia
University. While I was at Columbia, the research was supported by the Spencer Foundation.
The views expressed are not necessarily those of Bell Communications Re-
search.
[Journal of Political Economy, 1988, vol. 96, no. 4]
?:)1988 by The University of Chicago. All rights reserved. 0022-3808/88/9604-0010$0 1.50
785
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786 JOURNAL OF POLITICAL ECONOMY
wages. For example, Hashimoto and Raisian (1985) find that completion
of high school increases the earnings of men by between five and
six times as much as does completion of a year of education that was
not associated with completion of high school. This effect held regardless
of whether workers were employed at small, medium, or
large firms.'
Using data from the Panel Study of Income Dynamics (PSID), I
found that even when education squared and education cubed were
included as additional independent variables in a wage equation, the
increase in wages associated with completion of high school was more
than three times as great as the increase in wages associated with
completion of eleventh grade (see table 9 below). Hence the discontinuity
in wages associated with completion of high school does not
appear to be due to nonlinearities in the relationship between education
and wages.
I investigated possible reasons for this discontinuity. Using a proprietary
data set of semiskilled manufacturing workers, I found that
high school graduation was associated with a discontinuous fall in quit
propensity and absenteeism. On the other hand, there is not a discontinuous
increase in output associated with completion of high school,
nor did I find that high school graduates had a comparative advantage
in the more complex jobs in this study (job assignment was ran-
dom).
This evidence suggests that at least part of the relationship between
secondary education and wages may be due to the discontinuous decrease
in quit and absenteeism rates associated with completion of
high school.2
l The following data, from the CurrentPopulation Survey,appear in Hashimoto and
Raisian (1985, p. 730) (t-statistics are in parentheses):
REGRESSION RESULTS OF MALE EARNINGS
U.S. FIRM SIZE
Small Medium Large
Years of schooling .0367 .0362 .0296
(5.6) (4.2) (5.0)
High school graduate .1630 .1735 .1286
(4.9) (3.9) (4.5)
University graduate .0630 .0808 .1590
(1.7) (1.8) (5.6)
2
In two-stage wage equations estimated using the PSID, the predicted probability of
a worker's quitting had a significant negative effect on wages. In particular, when high
school graduation was not included directly in the wage equation, I estimated that
workers with a 10 percent higher predicted probability of quitting received between 7
percent and 10 percent lower wages, depending on the form of the wage equation
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HIGH SCHOOL GRADUATION 787
The PSID data support this view. In the data high school graduates
have lower quit rates than would be expected from a continuous
relationship between quits and education. On the other hand, there is
not a discontinuous increase in required training forjobs held by high
school graduates. Finally, it appears that the wage premium associated
with high school graduation is procyclical: rising during booms,
when quits and absences are most harmful to employers, and falling
during slumps. (This last finding is especially tentative since problems
of collinearity hindered me in separating procyclical effects of high
school graduation on wages from procyclical effects of education on
wages.)
Because there are unlikely to be demographic characteristics that
affect quit propensity (or the propensity to be absent) and do not
directly affect wages, it is difficult to use standard data sets to estimate
the impact of differences in quit propensity on wages. However, Mirvis
and Lawler (1977) directly calculated the cost of quits and absenteeism
for a sample of bank tellers. Their measurements suggest that
a considerable portion of the wage premium associated with graduation
from high school can be explained by the lower propensities to
quit or be absent of high school graduates:
being estimated. Of course, the negative correlation between wages and quit propensity
is due in part to the positive correlation between high school graduation and quit
propensity already mentioned. This problem would be avoided if high school graduation
was included not only indirectly in the wage equation as one of the instrumental
variables predicting quit propensity but also directly as one of the independent variables.
When both predicted quit propensity and high school graduation were included
in a wage equation, both were statistically significant; however, in that case there were
no variables affecting quit propensity that did not directly affect wages. Hence, the
model was identified only by functional form restrictions. Consequently, I did not
pursue this approach further. The reader may obtain copies of the two-stage estimates
by writing directly to the author.
3 Mirvis and Lawler (1977) calculated that the total cost of turnover of bank tellers
was 85 times as large as their daily earnings plus benefits. Hence, if graduation from
high school decreases a worker's probability of quitting during his or her first year on
the job from 20 percent to 10 percent (assuming the average work year was 240 days),
high school graduation would increase earnings of newly hired bank tellers by 4.4
percent. This calculation was made by assuming a constant quit rate and 240 workdays
per year so that a worker with a 10 percent per year probability of quitting has a daily
quit probability of .000439 and a worker with a 20 percent per year quit probability has
a daily quit probability of .000929. Let the wages of the low-quit-rate and high-quit-rate
worker be denoted wo and wl, respectively. Let the cost of a quit be 85w(. Then in
equilibrium
wo + 85 x .000439wo = w1 + 85 x .000929w(,
1.0373wo= w1 + .0790wo,
w(,= 1.044w1.
Mirvis and Lawler also estimated that the total cost of absenteeism for a sample of 160
bank tellers was more than twice the cost in salaries and benefits. Thus if, as estimated
below, high school graduation results in a 14 percent decrease in the percentage of days
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788 JOURNAL OF POLITICAL ECONOMY
I conclude from this research that standard estimates of rates of
return to education are capturing, in part, the higher earnings of
high school graduates associated with their lower quit rates and lower
rates of absenteeism. To the extent that these traits were not learned
in secondary school, the standard models are overestimating rates of
return to secondary schooling. To the extent that these traits were
selectively learned in primary school, standard models are underestimating
the rates of return to primary education.4
These biases obtain in both signaling and human capital theoretic
models of schooling and wages.5 In the signaling model, individuals
choose their length of secondary schooling to signal these traits to
potential employers (see Spence 1974). Schooling is an effective signal
of these traits because of the same attributes that give workers low
quit propensities and low rates of absenteeism are likely to give them
low nonpecuniary costs of schooling. It is unlikely that a low quit
propensity can be directly observed for new entrants into the labor
force. High school transcripts generally do not contain information
on absenteeism or tardiness, and high schools generally either fail to
respond to requests by firms for transcripts or respond too slowly to
affect hiring decisions (see Bishop 1986). Even if low quit and absenteeism
propensities were directly observed by firms but not by the
researcher (as in some human capital models), standard estimates of
rates of return to education would still be biased upward. However,
schooling decisions would not be distorted (see Griliches [1977] and
Hausman and Taylor [1981] for analyses of the role of unobserved
attributes in human capital models).
Alternatively, one could consider a human capital model in which
the same unobserved traits that cause individuals to have low quit and
absenteeism rates increase the efficiency with which they learn in
school-increasing the returns to schooling and making it more likely
that students complete high school. Then the increase in wages associated
with graduation from high school would be due to the superior
absent, then one would expect that at a 6 percent absence rate the negative correlation
between absenteeism and education leads to roughly a 2 percent higher wage for high
school graduates working as bank tellers. (This calculation is made by noting that a
worker with a 6 percent absence rate is paid 12 percent less than a [hypothetical]
worker with zero expected absences, while a worker with a 6.84 percent absence rate is
paid 13.68 percent less. Hence decreasing one's expected absence rate from 6.84 to 6
percent would increase one's earnings by 1.95 percent.)
4 Studies of rates of return to education in countries in which there are many early
school leavers typically estimate very high rates of return to primary schooling; these
estimates are much higher than estimated returns to secondary schooling (see Psacharopoulos
1981).
5 Note that in both the sorting models and some versions of the human capital model
the error term in an estimated earnings equation is correlated with the education
variable, causing the estimated coefficient to be biased.
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HIGH SCHOOL GRADUATION 789
cognitive skills of high school graduates. However, I find this last
explanation unpersuasive and not supported by the data.
II. Overview of the Data
The data for this study come from the PSID and from a proprietary
data set that I assembled consisting of the personnel files of 2,920
newly hired, semiskilled production workers employed by a highwage,
unionized firm at three widely separated geographic locations.
These data sets have different advantages and drawbacks. Consequently,
I am encouraged that the overall story is consistent with the
evidence in both data sets. The PSID data have two major disadvantages.
First, they do not contain a direct measure of output or a good
measure of absenteeism. Second, since education typically affects job
assignments and promotional opportunities, it would be difficult, if
not impossible, using the PSID or other standard data sets to determine
whether lower quit rates of high school graduates are due to the
jobs they have or to attributes of high school graduates.
The main drawback from using data derived from the personnel
files of a single firm is that they may be subject to serious sample
selection biases. That issue is addressed later in this section, where I
argue that the effects of sample selection bias are likely to be small. In
Section VI, I show that, to the extent that sample selection biases are
present, they are likely to lead to underestimates of the negative correlation
between high school graduation and propensities to quit or
be absent.
On the other hand, using data on workers in similar jobs at a single
firm has several important advantages over standard survey data.
First, I was able to obtain detailed records of the physical output of a
large number of workers and expert evaluation of the complexity of
the jobs to which they were assigned. Second, by limiting the sample
to workers on similar jobs at the same firm, I was able to focus on the
effects of individual attributes on output, absenteeism, and quit propensity,
holding constant firm and job effects. Third, since these data
were copied from personnel records, they are likely to be more accurate
than those obtained in surveys. The difference in accuracy is
especially relevant for data on absences and job characteristics. (Mellow
and Sider [1983] found that 42.3 percent of the workers surveyed
reported for themselves a three-digit occupation different from the
one reported by their employer.) Fourth, because this data set contains
direct measures of three aspects of productivity-output per
hour, absenteeism, and quits-it is possible to measure the effects of
education separately for each of those aspects of productivity. Fifth,
because the data include a measure of the complexity of the job to
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790 JOURNAL OF POLITICAL ECONOMY
which the worker was assigned and because job assignment was
(nearly) random, I could estimate whether better-educated workers
have a comparative advantage on more complex jobs.6 Finally, because
in this sample the wage schedule faced by a worker was independent
of his actual or predicted performance or absenteeism and I
was able to partially control for alternative opportunities, I avoided
some of the problems present in standard data basis in which wage
differences bias estimates of the effects of demographic characteristics
on quits, absences, or productivity.
Although all workers at each location in the sample received the
same wage, they obviously did not have the same alternative opportunities.
The effect of differences in alternative opportunities on quits
and absences is discussed in Section III. A detailed description of this
data set is presented in Appendix A.
Before investigating the effect of education, and particularly
graduation from high school, on the performance of workers in the
sample, I first examine the effect of education and other observable
characteristics on previous wages for some of the workers in the
sample.
Job applicants at one of the plants used in constructing the data
base (referred to as plant A) were asked their wage at their most
recent job and whether or not they were currently employed at that
job. Using those data, I estimated the effect of an additional year of
education on the previous pay of workers who were employed when
they applied for their current job.7 Column 2 of table 1 contains
6
In general, studies that rely on productivity measures of experienced workers
within a given job classification are subject to important sample truncation biases.
Landau and Weiss (1985) have shown that, in a model with heterogeneous labor, if all
workers have to meet a given productivity standard before being assigned to a given job
and are promoted if they exceed some higher standard, then even if output Q were
equal to education (or experience) times ability (i), on any given job, productivity could
be uncorrelated or negatively correlated with education (or experience). For example,
if output Q = ix, where x could be experience or education and the normalized density
of unobserved abilityf(i) = ki, then average productivity would be uncorrelated with
the observed characteristic x. If promotion criteria are less stringent for the better
educated, as would appear from table 4 of Medoff and Abraham (1981), a negative
correlation between productivity and education could obtain for a wide range of distributions
of unobserved ability. This problem does not arise in the data here since none
of the workers was promoted, job assignments were (nearly) random, and sample
selection bias was likely to be small.
7 I excluded from the sample workers that were unemployed when hired since the
wage on their previous job, one that they either could not keep or found less desirable
than unemployment, does not seem representative of their expected earnings. Wages
at the previous job were used because at the firm studied wages for experienced workers
are a function solely of seniority and the output of their pay group. Obviously this is
a biased estimate of the effect of education on earnings for workers in the population:
the workers in the sample chose to leave the jobs for which I have recorded their
earnings. In Sec. VI, I analyze the effect of this bias.
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HIGH SCHOOL GRADUATION 791
TABLE I
NATURAL LOG OF HOURLY EARNINGS IN 1979
(CurrentPopulation SurveySample versus Weiss Sample)
Plant A in
CPS* Weiss Samplet
Intercept (1) (2)
Nonwhite --.065 -.051
(-5.14) (-2.11)
Female -.247 -.253
(-35.47) (-13.06)
Nonwhite x female .050 .052
(2.81) (1.43)
Education .018 .166
(2.28) (2.25)
(Education/I 0)2 .098 - .519
(3.61) (-1.86)
Job tenure .013 .034
(7.15) (.9()
(Job tenure/I ()2 - .036 - .184
(-11.61) (-2.64)
Other experience .014 .042
(8.01) (3.57)
(Other experience/ 10)' - .021 - .056
(-11.13) (-4.84)
Education x job tenure .00060 .0015
(5.15) (.50)
Education x other experience - .00033 - .0017
(- 3.29) (-1.99)
Sample size 18,551 1,272
R2
.537 .204
NOTE.-The smaller R2 in col. 2 compared with col. I is due, in part. to the smaller range of the independent
variables among workers at plant A.
*T'Iheother independent variables in the col. I regression were whether the worker belonged to a union, the
percentage ol workers tinionized in the worker's industry, interactions betweeit tnion metbership and firm size.
and plant size.
TIhe data in col. 2 are front the only plant in this study for which wage data on the previottsjob are available. The
dependent variable is the logarithn of the wage at the most recent job divided hy the ntean wage in the economy at
the tine the job was held, or In(most recent previous Iay + average p)ayin the ULnitedStates at that date). On the
present jtmbthe lifetime wages of all the workers are approximately identical.
estimates of the effect of various demographic variables on the
logarithm of the previous hourly wage of workers at that plant. Column
1 reproduces the coefficients estimated by Mellow (1982) for
workers in the 1979 CurrentPopulationSurvey(CPS). When one evaluates
the marginal effect of education at the mean values in each sample
for education, tenure, and experience,' a In wage/aeducation =
.043 for the CPS sample and .037 for this sample.
Table 1 can be used in various ways depending on how ambitious
one wishes to be. First, the estimates of a In wage/aeducation provide a
8
The relevant mean values for the 1979 CPS are mean(education) = 12.64,
mean(tenure) = 6.51, and mean(other experience) = 11.57, where other experience is
measured by age - education - tenure - 6.
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792 JOURNAL OF POLITICAL ECONOMY
measure of the effect of education on earnings (in their previous job)
for the subsample of workers for whom there are data on previous
wages. One can then estimate how much of that effect can be explained
by the partial correlation between education and various
aspects of performance for workers in that limited sample. This
approach does not make any assumptions that the sample is representative
of a larger population but simply seeks to find those factors that
contributed to earnings differences on previous jobs for workers
within this subsample. It does assume that performance on current
jobs is correlated with performance on previous jobs. I shall, however,
also assume that workers for whom usable pay data were available are
representative of workers in the sample, so that a year of education
has approximately a 4 percent effect on the hourly wage on otherjobs
for the workers in the larger sample.9
A second use of the data in table 1 is to provide a partial check of
the importance of sample selection bias for the sample if one wishes to
generalize the results outside the sample. Since the major concern
here is in explaining the relationship between education and wages, it
is useful to check to see if the return to education in the sample is
biased. This is a potentially serious problem because one would expect
that better-educated individuals who apply for these jobs are less
representative of their schooling cohort than less well educated workers.
However, the estimated value of the return on education for
workers for whom there are wage data is roughly the same as returns
estimated using the CPS sample. Thus it does not seem that this
sample differs from the CPS sample in ways that grossly distort the
effect of education on earnings. In addition, the sign of the effect of
race, sex, education, tenure, and experience on the logarithm of the
(previous) wage is the same for this sample as for the randomly selected
CPS sample.
The personnel practices at these plants also provide grounds for
believing that the sample is representative. Only 22 percent of applicants
whose applications were reviewed were rejected. Of those, 85
percent were rejected because of a low score on the Crawford Physical
Dexterity Test.lo The estimation procedures included the worker's
score on the dexterity test as an independent variable, thus eliminat'
I had usable data on previous pay for 77 percent of the workers employed at plant
A (those workers constituted 43 percent of the entire sample).
10 Of course some residual sample selection bias occurs if unobserved attributes that
lead workers to wait in line longer, such as the ability to withstand the cold, are correlated
with performance and with observed attributes studied here. Applications were
reviewed in order of the applicant's place in line with some adjustments to ensure racial
and sexual balance. At the location used for table 1 the individual's place in line is
known. It was uncorrelated with any of the measures of performance. Consequently, I
have assumed that this source of bias is small and have disregarded it.
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HIGH SCHOOL GRADUATION 793
ing that potential source of sample selection bias. In addition, the
average pay increase for workers for whom there were wage data was
103 percent, and workers waited for more than 36 hours in freezing
temperatures to receive job application forms. This evidence indicates
that the firm was paying above-market wages. These high wages are
likely to reduce the sample selection problems derived from more
"able" applicants not applying to the firm, where ability refers to
unobserved worker characteristics that are correlated both with observed
characteristics and with productivity. These high wages and
the concomitant excess supply of job applicants were routine features
at the manufacturing locations of this unionized firm. At another
location of this firm, when recall notices were mailed to former employees,
90 percent of those who had found alternative work quit
their jobs to return to work for the firm.
I was also able to test for possible biases introduced by the job
assignment decisions of the firm. The personnel officers of the firm
maintained that newly hired workers were randomly assigned to
entry-level jobs. I tested whether this policy was followed in practice
by regressing the measure of the complexity of the job to which a
worker was assigned against all the observed demographic characteristics
of the workers, including schooling, previous work experience,
and scores on each part of the physical dexterity test. Those explanatory
variables were neither economically nor statistically significant,
nor were they jointly significant.' Consequently I have assumed that
sample selection and job assignment biases were small and have not
corrected for them.'2
Sections III and IV present evidence linking the wage premium
received by high school graduates to their low propensities to quit or
be absent. In Section V, I present corroborating evidence suggesting
that the wage premium received by high school graduates is unlikely
to be due solely to skills learned in high school. Section VI discusses
the effects of selection bias on the results. Section VII contains some
concluding remarks.
III. Models
Typically an individual's choice of a level of education is a function of
both observable and unobservable traits. The traits that are observI
did find, however, that males were assigned to simpler jobs.
12 Alternatively I could have used the Bloom and Killingsworth (1984) procedure to
correct for sample selection bias. (Because the characteristics of excluded observations
are unknown, the standard Heckit correction cannot be used.) However, their procedure
is extremely sensitive to assumptions about the distribution of the error term in
the selection equation. Indeed, as they point out, the equation being estimated is
identified only if the assumed distribution of the error term of the selection equation
is nonlinear. See Muthten and joreskog (1983) for a discussion of this issue.
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794 JOURNAL OF POLITICAL ECONOMY
able for this sample and that affect the schooling decision include age,
race, sex, and manual dexterity. I grouped together under the rubric
"stick-to-itiveness" all the unobserved attributes that affect an individual's
choice of a level of schooling. Stick-to-itiveness represents the
combined effect on schooling level of characteristics such as selfdiscipline,
desire for variety, and susceptibility to illness or to the urge
to "take a day off." Years of schooling and high school graduation
were used as proxies for the traits referred to as stick-to-itiveness.
In addition to representing these unobserved characteristics, education
also indicates a level of training. One skill that is likely to have
been acquired in school is the ability to learn complex tasks. Of
course, that skill may have been acquired prior to the years of schooling
across which the sample differs (almost the entire sample had at
least 9 years of education) and influenced the individual's choice of a
level of education. I assume that skills such as the ability to learn
complex tasks that affect the productivity of workers and that may
plausibly have been learned in secondary school were learned there.
That is, I intentionally biased the analysis in favor of a learning explanation
for the correlation between education and wages.
The performance equations estimated are whether or not the
worker quit during his first 6 months on the job, absenteeism (both
days absent and occasions of absenteeism), and output per hour during
the first month on the job as a fraction of expected output given
the complexity of the job. (These normalizations are routinely performed
by the industrial engineering staff as part of their efforts to
compute the piece rate for different jobs.) The critical independent
variables for the analysis are years of education, high school graduation,job
complexity, and a measure of the "match"between education
level and job complexity: match [education - mean(education)] X
[job complexity - mean(job complexity)]. If better-educated individuals
have a comparative advantage in more complex production jobs,
the coefficient on the match term in an output equation would be
positive.
Job complexity was defined as the logarithm of the number of
weeks the plant's industrial engineering staff estimates it should take
a new employee to learn the job (achieve the expected productivity
rating for an experienced worker on that job). The main component
in the industrial engineers' calculation is the number of times per
week an experienced worker performs the task (see fig. 1). Mean job
complexity is the average level of job complexity for the subsample of
workers at each location.
Although there is a large literature examining the effect of job
enrichment and job complexity on job satisfaction and performance,
there is considerable controversy in interpreting these results. There
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HIGH SCHOOL GRADUATION 795
25
20 -
U/)
0
L-L 15-
0
23.2
z 21.6
U 10 1
Er
- ~~~~13.2
-10.7 12.0
5
8.2
5.2
3.4 2.8
1-2 3-4 5-6 7-8 9-10 11-12 13-14 15-16 17+
WEEKSREQUIREDTO LEARNTHEJOB
FIG. 1
are both biases in experimental design-often the studies rely on
screened volunteers who are given pay supplements (see Fein 1975)and
biases in the reporting of results: Hackman (1974) points out that
papers describing the results of job enrichment programs are typically
written by the consultants that implemented them. Consultants
are more likely to publicize their successes than their failures.
In general one would expect stick-to-itiveness (those unobservable
traits that lead individuals to complete high school) to have its greatest
effect on quit propensity and to have a lesser effect on other aspects
of behavior such as absenteeism. On the other hand, one direct effect
of education and of high school graduation is to improve alternative
opportunities, increasing the probability of a quit.
A. Quits
Let Si denote worker i's present value of his current job, V, denote i's
present value of his best opportunity elsewhere, and M, denote i's
mobility costs (both real and psychic) of ajob change (housework and
leisure are counted asjobs). Assume that worker i is risk neutral and
quits if and only if
Vi- S1>MI. (1)
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796 JOURNAL OF POLITICAL ECONOMY
Denote the time discount rate of workers by r, worker i's age at the
start of the observation period by a., and the value of an individual's
alternative and present job at time t by Vi(t) and S1(t), respectively.
Then, assuming that male workers anticipate working until they are
65 years old and normalizing t = 0 for the time when the quit decision
is made, we get
- - ~~65 - a + 3oF
Vi - Si= ert[V(t) - SI(t)]dt, (2)
where F is a dummy variable indicating whether a worker is a female,
and Pois an estimated parameter of the problem. If females anticipate
working fewer years, Pois negative. Next, let pi(t) represent the probability
that individual i changes jobs after the observation period and
before period t, and let the value of that new job be a weighted
average of the value of the previous job and some constant term B,.
Assume that the values of the alternative and the present job grow
at an exponential rate so that
Vi(t) = eut{[ - p(t)]V1(0) + p1(t)[-yVJ(0)+ (1 - y)B1(O)]}, (3a)
Sit) = eut{[1 - pi(t)]SJ(O)+ p1(t)[yS7(0)+ (1 - y)Bi(O)]}, (3b)
where 0 < -y< 1. Then, with 8 = (r - u) and xi= 1 - (1 - -y)pi(t),
worker i quits if and only if
r65 -ai + D3oFe
{65|a+ xoFie- t[V7(O) - SI(O)]dt> Mi, (4)
To obtain an estimable quit equation from (4), assume
QV(O)= XP31 (5)
tS(O)= X212 (6)
M = X3X3. (7)
Denoting [e8(65-a?+ oF) - 1]/8 by g(a, 8, 1oF) and substituting (5)-(7)
into (4), we get
- f1 if g(a, 8, J30F)(Xlf3l- X282) - X433 > 0 (8)
0 otherwise.
Clearly, the net gain from changing jobs, the left-hand side of (8), will
be measured with error. Assume that this error term, denoted pLQ,is
distributed N(O, a2). Therefore, the quit equation estimated is
Q t if g(a, 8, 1oF)(Xp131- X2X2) - X43 > P1Q (9)
0 otherwise.
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HIGH SCHOOL GRADUATION 797
The worker characteristics that are measured and that affect alternative
opportunities include education, race, sex, age, geographic location,
dexterity (as measured by scores on the physical dexterity test),
and employment status when hired (a worker who was on a temporary
layoff from a desirable previous job might be likely to quit when
recalled from the layoff). 13The factors affecting alternative opportunities
could also affect job satisfaction. For example, one would expect
workers that were employed at the time of' application to have a
significantly higher level of job satisfaction (one reason they left the
previous job was the anticipation of' increased job satisfaction) and
hence to be less likely to quit. There are also job-related characteristics,
such asjob complexity, that affect job satisfaction but not alternative
opportunities.
Finally, one would expect stick-to-itiveness (as measured by high
school and college graduation) and the worker's marital status to impose
additional mobility costs. 15 Those variables are not multiplied by
g(a, 8, 1OF).They enter directly into the quit equation as elements of
X3. I also included education as an element of'X3. Thus education was
allowed to directly affect quit propensity if students learn not to quit
during their postprimary years of schooling (the years over which
schooling levels differed in the sample). Since education may affect
alternative opportunities and job satisfaction, I also included education
times g(a, 8, P(3F)as a right-hand variable in the estimated quit
equation.
As can be seen in table 2, the major hypothesis is confirmed. High
school graduation has a strong negative effect on a worker's probability
of quitting. Because this effect is independent of the direct effect
of schooling, we can reject the hypothesis that the reason bettereducated
individuals have lower quit propensities is that they learned
not to quit in secondary school.
Equation (9) was estimated by the method of maximum likelihood,
using a pooled sample from plants A and B. Individuals were omitted
if they were laid off before being with the firm for 6 months, and
selection bias was avoided by also omitting workers who would have
been laid off before 6 months had passed had they not already quit.
13 Of course employers are concerned with the total effect of education on the worker's
probability of quitting, taking into account the better alternative opportunities
available to the better-educated workers. However, we are concerned with explaining
wage differences in the market, not at the firm being studied, where there are no wage
differences due to education differences. In the market equilibrium, better-educated
workers have higher wages as well as better alternative opportunities. It is differences
in quit propensities, not of the effect of alternative opportunities on quits, that contribute
to differences in the equilibrium wage at different education levels.
14 Contemporaneous wage was not included as an element of X2 because all workers
had substantively the same expected lifetime wage on their current job.
15 See Mincer (1978) for an analysis of the effect of marital status on worker mobility.
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798 JOURNAL OF POLITICAL ECONOMY
TABLE 2
PROBABILITY OF QUITTING WITHIN FIRST 6 MONTHS ON THE JOB
(Maximum Likelihood Estimation Procedure)
ESTIMATED STANDARD ERRORS
COEFFICIENT
OR Gradient Hessian White's
INDEPENDENT VARIABLE* VALUE Method Method Method
8 .26 2.04 .61 .28
(-.13) (-.42) (-.9 1)
3 (effect of being female on -6.81 42.3 10.6 4.19
anticipated work life) (- .16) (- .63) (- 1.62)
High school graduate -.342 .140 .135 .136
(- 2.44) (-2.54) (-2.61)
College graduate -.242 .367 .397 .444
(-.66) (-.62) (-.59)
Education - .07 .171 .057 .035
(-.44) (-.67) (-.76)
g(a, 8, OF) x education .015 .143 .044 .029
(.11) (.34) (.53)
Married - .091 .078 .077 .077
(-1.16) (-1.18) (-1.17)
g(a, 8, OF) x employed - .098 .774 .231 .107
at application (- .13) (- .43) (- .92)
Number of observations 2,146
Log likelihood - 741.99
NOTE.-t-statistics are in parentheses. Throughout this paper I loosely use the term I"to refer to the estimated
coefficient divided by the standard error.
* Other independent variables included scores on each half of the dexterity test, race-location interactions,
location effects, age. and an intercept term. I used three different methods for calculating the standard errors
because there is rio consensus as to which is the correct technique. It the model is correctly specified, the three
methods give the same asyinptotic estimates. 1he estimates obtained are sufficiently similar to provide some
confidence that the model is rot grossly misspecified. (Computational costs precluded perforining the model
specification test suggested by White (1982).
(All layoffs were made strictly by seniority.) Because the likelihood
function is almost flat with respect to changes in 8, offset by compensating
changes in the vector of variables multiplied by 8, the standard
errors of 8 and of the coefficients of variables multiplied by g(a, 8,
IoF) are high. Although statistically insignificant, they have values
consistent with the model. Individuals such as white males who have
better alternative opportunities are more likely to quit these jobs;
workers who were employed when they applied for these jobs are less
likely to quit. Similar confirmation was provided by the negative value
of r3o(The estimates suggest that females in the sample anticipate
spending 7 fewer years in the labor force than males. This finding is
consistent with unpublished research byJacob Mincer. Using the National
Longitudinal Study sample, he finds that women spend roughly
25 percent less time in the labor force than men. Finally, the similarity
in the standard errors obtained using the gradient, Hessian, and
White (1982) methods suggests that the model is not grossly misspeci-
fied.
To obtain more precise estimates of the coefficients and to make
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HIGH SCHOOL GRADUATION 799
TABLE 3
PROBABILITY OF QUITTING WITHIN FIRST 6 MONTHS
l\ QUIT PROBABILITY
FROM A ONE-UNIT
CHANGE IN THE
VARIABLE EVALUATED AT
QUIT PROBABILITY OF
INDEPENDENT VARIABLE COEFFICIENT t-STATISTIC 10% 20%
Intercept - .922 -1.54 ... ...
High school graduate -.341 -2.54 -.059 -.096
College graduate - .280 -.72 -.049 -.078
Education -.106 -1.32 -.(19 -.030
Married -.097 -1.26 -.017 -.027
h(a, 8, OF) x education .0055 1.45 .00097 .0015
h(a, 8, 'F) x age -.00029 -.32 -.000052 -.000083
h(a, 8, OF) x male .0012 .16 .00022 .00034
h(a, 8, OF) x white .068 4.58 .012 .019
X South
h(a, 8, 'F) x South -.036 -2.34 - .0062 - .0099
h(a, 8, OF) x white .0061 1.00 .0011 .0017
X Midwest
h(a, 8, 'F) x employed - .0023 -4.95 -.0040 -.0064
at application
h(a, 8, wF) x pins section .00020 .34 .000035 .0(00056
of dexterity test
h(a, 8, 'F) x screws section .00094 1.94 .00016 .00026
of dexterity test
Number of observations 2,146
NOTE-.- set equal to - .25. 8 set equal to .05; 0.124 of observations had Q =I; the niean of h(a, 8, yF) is 16.12.
use of' Mincer's findings on the shorter work life of women, we can
reformulate equation (9) as
Q 1 if h(a, 8, -jyF)(XIfI - X2f2) - X3f3l > 11Q (9')
O otherwise,
where h(a, 8, jF) [e- 05(l-.25F)(65-age) - 1]/-.05. That is, we can
impose the restrictions that r - p. = .05 and that the effective work
life of women is 25 percent shorter than that of men.
Equation (9') was estimated using a probit estimation procedure.
The estimated coefficients and the effect of a change in each independent
variable on a worker's probability of quitting are presented in
table 3.16
16
Note that in table 3 job complexity and match were not included as independent
variables. If they are included as independent variables when (9') is estimated, the
sample size falls to 1,532 and the absolute value of all the t-statistics also falls. However,
none of the results in table 3 is significantly affected: high school graduation is estimated
to correspond to a reduction in the worker's probability of quitting of' - .059 at a
10 percent quit probability and - .096 at a 20 percent quit probability. Similarly, if quit
propensity is estimated separately for men and women in the sample, the qualitative
effects in table 3 hold for each subsample.
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8oo JOURNAL OF POLITICAL ECONOMY
High school graduation has a large and statistically significant effect
on a worker's probability of quitting. Evaluated at a 10 percent probability
of quitting, high school graduation decreases a worker's probability
of quitting by almost 6 percent. At a 20 percent probability of
quitting the decrease is 9.6 percent. The continuous effect of education
on quit propensity is also negative, suggesting that workers with
more education have more stick-to-itiveness, while when education is
interacted with the h( ) function its coefficient is positive, as would be
predicted from the better alternative opportunities available to bettereducated
workers.
The other estimated variables in table 3 are also consistent with the
model. Being employed when hired by your current employer has a
negative effect on a worker's probability of quitting. This is consistent
with our model since those workers incurred greater costs in taking
this job and hence were likely to have a higher anticipated level of job
satisfaction. Southern blacks are far less likely to quit than southern
whites, perhaps reflecting differences in their alternative opportunities.
On the other hand, males do not seem more likely to quit than
females, suggesting that sex discrimination by other firms may be of
relatively low magnitude compared with race discrimination in the
South.
These results were not sensitive to the particular specification of the
quit equation. When I estimated either a probit, logit, or linear probability
model with no interactions between the h( ) function and the
explanatory variable, the results were substantially unaffected. The
results from the probit model with no interactions between the h( )
function and the other explanatory variables are presented in table 4.
In this table, high school graduation continues to have a strong negative
relationship with predicted quit propensity, while the continuous
relationship between years of education and quit propensity is weak
and statistically insignificant. Apparently the greater stick-to-itiveness
of better-educated workers is offsetting their superior alternative opportunities,
eliminating any discernible relationship between education
(other than high school graduation) and quits.
To provide a rough check of whether peculiarities in the distribution
of education were generating the results in tables 2, 3, and 4, I
plotted in figure 2 histograms of the proportions of quitters and
nonquitters at each education level. I also checked to see if the
dummy variable for high school graduation was capturing nonlinearities
in the relation between education and quits. When the
dummy variable for high school graduation, in the model estimated
in table 3, was replaced by a dummy variable for completion of eleventh
grade or completion of thirteenth grade, the coefficients of these
latter terms were statistically insignificant. As an alternate means of
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HIGH SCHOOL GRADUATION 801
TABLE 4
PROBABILITY OF QUITTING WITHIN FIRST 6 MONTHS ON THE JOB
(Probit Model with Repressed Interaction Terms)
COEFFICIENT
INDEPENDENT VARIABLE (1) (2)
Intercept -.561 -.664
(-1.00) (-.36)
High school graduate -.329 -.314
(-2.51) (-7.27)
College graduate -.227 ...
(-.59)
Education - .024 .0025
(-.53) (.008)
Education squared ... -..0016
(-.14)
Married - .082 - .083
(-1.1() (-1.11)
Age -.021 -.021
(-3.64) (3-.61)
Male .173 .173
(2.05) (3.61)
White-South .956 .954
(5.09) (5.08)
South -.354 -.352
(-1.77) (-1.76)
White-Midwest .088 .083
(.861) (.822)
Employed when hired -.392 -.392
(-5.20) (-5.18)
Score on pins part of dexterity test .0026 .0026
(.280) (.27)
Score on screws part of dexterity test .018 .018
(2.26) (2.26)
Number of observations 2,236 2,236
Log likelihood - 788.8 - 788.99
NOTE.-t-statistics are in pauerntheses.
capturing nonlinearities, I added education squared and education
cubed to the independent variables listed in table 3. With that cubic
specification, I found that at a 10 percent quit probability the discontinuous
effect on quits from graduation from high school reduces a
worker's probability of quitting by 5.1 percent; at a 20 percent quit
probability the discontinuous effect of graduation from high school
reduces a worker's probability of quitting by 8.1 percent. The tstatistic
on high school graduation given the cubic specification for the
effect of education is - 1.84.17
17This fall in the t-statistic from including higher-order polynomial terms is, of
course, not surprising. There are several reasons why I expected the coefficient on high
school graduation to be sensitive to the addition of (education)' and (education)3 as
independent variables: (1) there were relatively few quits, (2) the sample clustered
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802 JOURNAL OF POLITICAL ECONOMY
0
(0
rig~CO
LLc
C\J
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Yearsof Education
FIG. 2.-Years of education for quitters and nonquitters. Left columns of'pairs refer
to nonquitters, right columns to quitters.
I checked the finding that high school graduation significantly affects
quit propensities using the 1968-82 PSID sample. As in table 4,
I suppressed the interactions between the h( ) function and the other
explanatory variables. The results in table 5 are consistent with those
in tables 2, 3, and 4. Completion of high school is associated with a
reduction in the individual's quit rate of roughly one-third, while
postprimary schooling (aside from completion of twelfth grade) has
an insignificant effect on quit rates. These results are also robust to
changes in the specification of the quit function and of the error term.
around an education level of 12.1 (the standard deviation was 1.2), and (3) with the
cubic specification the independent variables included six different measures of education.
Given these difficulties, I was surprised to find that the discontinuous relationship
between graduation from high school and quit propensity was still observable with the
cubic specification for the continuous effect of education on quit probabilities.
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TABLE 5
MALE PRIVATE-SECTOR EMPLOYEES IN PSID SAMPLE, 1968-82
A. QUITS PER YEAR
Independent Variable Coefficient
High school graduate -.030
(-3.58)
Education - .024
(-2.26)
Education squared .0030
(2.53)
Education cubed -.00011
(-2.76)
ln(mean experience while in sample) -.025
(-3.67)
New entrant .014
(1.62)
Nonwhite - .030
(-5.05)
Age - .0023
(-5.30)
Mean city unemployment rate minus mean -.003
national unemployment rate (-1.79)
Number of observations 3,781
R2 .16
Mean quits per year .092
B. ANNUAL PROBABILITY OF QUITTING (Logistic Model)
Independent Variable* coefficient Standard Error
Intercept 1.48 .590
Education - .59 .180
Education squared .072 .020
Education cubed -.0025 .00065
Work experience -.111 .0118
Work experience squared .0012 .00033
Disabled .172 .119
Nonwhite - .429 .087
Married - .408 .083
Union member -.744 .086
High school graduate -.338 .132
Part-time worker .263 .094
National unemployment rate -.084 .027
County unemployment rate .016 .062
County unemployment rate squared -.0033 .004
NOTE.-Each observation was weighted by the square root of the number of years the individual was in the
sample. t-statistics are in parentheses in pt. A. I did not include wages as an independent variable in these regressions
since I was concerned with the indirect effect of various demographic characteristics on wages through their effect
on quit propensities.
* Eight location dummies were also included.
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804 JOURNAL OF POLITICAL ECONOMY
B. Absenteeism
In Appendix B I show why differences in expected absenteeism rates
can significantly affect the wages of workers. In this subsection, I
estimate the discontinuities in expected absenteeism rates associated
with high school graduation for workers in the sample.
In estimating the determinants of absenteeism I assume that a
worker is more likely to be absent the higher is his level of job dissatisfaction
and the lower his stick-to-itiveness. As in the quit equation, job
satisfaction is measured by the elements of X2. Education and high
school graduation are used as proxies for persistence: an individual
who had insufficient persistence to complete high school is likely to
have poorer than expected attendance habits. I assume that both days
and occasions of absenteeism as percentages of possible days worked
are linear functions of X2, the proxies for stick-to-itiveness, and normally
distributed error terms (consecutive days absent are referred to
as a single occasion).
In the quit equation we can separate the effect of education on job
satisfaction from its effect on stick-to-itiveness by arguing that job
satisfaction has a greater effect on the quit rates of workers with
longer expected future work lives. (The education x g(a, 8, f(3F)term
captured the effect of education on quits that was caused by its effect
on either alternative opportunities or job satisfaction.) This option is
not available in the absenteeism equations: workers are trading off
one-period gains and losses from absences. Consequently, the estimated
coefficients on education and high school graduation reported
in tables 6 and 7 could be estimating the effect of lower (or higher)
levels of job satisfaction of better-educated workers on their absence
rates rather than the effect of stick-to-itiveness on absenteeism. However,
the results from the previously estimated quit equations suggest
that this is not happening.
Percentage of days absent was estimated using a Tobit procedure. 18
I calculated the percentage of days workers were absent during their
first 6 months on the job. However, because not all the workers in the
sample completed 6 months of work, those observations were
weighted by the square root of the number of days for which they
were observed. I also used occasions of absenteeism as a dependent
variable. In those calculations I restricted the sample to individuals
who worked for 6 months. I assumed that occasions of absenteeism
18 The Tobit procedure implicitly assumes that discrete absenteeism data can be
approximated by a continuous distribution and that the error term in the estimation
equation is normally distributed but truncated, so that absenteeism rates that the model
predicts would be negative are recorded as zeros. Of course, theoretically absences are
also truncated from above: no one can be absent more than 100 percent of the time. In
this sample the problem did not arise.
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HIGH SCHOOL GRADUATION 805
TABLE 6
DAYS ABSENT AS A PERCENTAGE OF DAYS WORKED
(Tobit Estimation Procedures)
Independent Variable Coefficient
Intercept 7.38
(2.54)
Male .398
(- .95)
Age - .143
(-5.89)
Education .133
(.58)
High school graduate -2.35
(-4.04)
College graduate - 1.34
(- .69)
Married - .046
(-.13)
Job complexity -.12
(- .45)
Match - .21
(- 1.10)
Employed at application - 1.23
(-3.56)
Number of observations 1,890
Log likelihood -4,781.2
NOTE.-The data for tables 6-8 come from three locations of
the firm, rather than only the two included in the quit equations.
Each observation was weighted by the square root of the number of
days worked. t-statistics are in parentheses.
are generated from a Poisson arrival process and that the Aparameter
that describes the Poisson process has a gamma distribution across the
population. The resulting distribution is negative binomial.919 computed
maximum likelihood estimates for that distribution. (Estimation
using Tobit is inappropriate for this problem because the continuity
assumption of the Tobit procedure is grossly violated when
computing occasions of absences.)
Whether days or occasions are used as a measure of absenteeism,
we find that high school graduation has a negative effect on absenteeism.
This effect is statistically significant regardless of the estimation
procedure used and holds even when we attempt to capture
nonlinearities in the relationship between education and absenteeism
by allowing for a cubic specification. The continuous effect of secondary
education on absenteeism is small relative to the discontinuous
effect of graduation from high school. It seems unlikely that high
school graduates learned in secondary school the traits that gave them
19This result comes from Greenwood and Yule (1920). A derivation appears in
Johnson and Kotz (1969, p. 124).
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8o6 JOURNAL OF POLITICAL ECONOMY
TABLE 7
OCCASIONS ABSENT DURING THE FIRST 6 MONTHS
ON THE JOB
(Negative Binomial Model)
Independent Variable* Coefficient
Intercept 4.46
(1.03)
Male -.113
(- 2.33)
Age -.031
(- 8.03)
Education - .945
(-.786)
High school graduate -.362
(-2.94)
College graduate .389
(.998)
Married .0344
(.716)
Match -.00736
(-.238)
Job complexity .00819
(1.52)
Employed at application - .181
(-3.84)
Number of observations 1,740
Log likelihood 1,533.78
NOTE.-Standard errors were calculated using the Hessian
method. t-statistics are in parentheses.
* Other independent variables were location, score on the screws
section of the dexterity test, and race-location interactions for the
two plants at which race data were available.
low rates of absenteeism. Instead, the same unobserved characteristics
that lead to successful completion of high school seem to lead to low
rates of absenteeism.
C. Outputper Hour
The final indicator of performance explored was the logarithm of
normalized output per hour during the worker's first month at the
manufacturing facilities studied (see table 8). As previously noted, job
assignments of newly hired workers were independent of their education,
scores on either part of the physical dexterity test, and prior
work experience. They are paid piece rate during that month. I assume
that output per hour is a linear function of observed characteristics,
including the match term described above. The distribution of
jobs was described in figure 1.
Assigning high school graduates to more complex jobs has neither
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HIGH SCHOOL GRADUATION 807
TABLE 8
NORMALIZED FIRST-MONTH OUTPUT ESTIMATED BY ORDINARY LEAST SQUARES
COEFFICIENT
INDEPENDENT VARIABLE* (1) (2) (3)
Intercept 67.36 69.05 71.63
(5.80) (6.24) (7.14)
Male 8.91 8.87 8.87
(5.81) (5.80) (5.80)
Age -.11 -.11 -.11
(-1.15) (-1.16) (-1.16)
Education 1.36 1.34 1.33
(1.63) (1.61) (1.59)
High school graduate 4.44 2.54 -.21
(.64) (.45) (-.08)
Match .49 ... .03
(.48) (.04)
Job complexity x high school graduate - 2.64 - 1.55 ...
(-.73) (-.55)
College graduate - 12.96 - 13.12 - 13.03
(-2.09) (-2.11) (-2.10)
Married 4.01 4.02 4.01
(2.98) (2.98) (2.98)
Score on dexterity test .22 .22 .21
(1.52) (1.53) (1.53)
Job complexityt 7.82 6.98 5.63
(2.45) (2.60) (5.26)
Employed at application 1.48 1.45 1.48
(1.08) (1.06) (1.08)
Number of observations 1,859 1,859 1,859
Multiple R2 .382 .382 .382
NOTE.-t-statistics are in parentheses.
* Other independent variables were location dumnmies.
t I he statistically significant coefficients for job complexity suggest that the industrial engineers overestimate the
difficulty of performing complex jobs.
a statistically nor economically significant effect on output, nor does
matching better-educated workers with the more complex jobs
significantly affect output. These findings suggest that the pecuniary
reward to education for the workers in the sample is not due to skills
learned in school that help those workers learn complex production
tasks.
The direct effect of education on output is marginally significant
but does not seem large enough to explain the correlation between
education and wages. In table 1 I computed the effect of education on
the logarithm of their real wages on their previous job for workers in
plant A. The best estimate was that each year of secondary education
had roughly a 3.7 percent effect on the previous wage of the workers
in that plant. On the other hand, I find that each year of secondary
education has roughly a 1.3 percent effect on the output of workers in
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8o8 JOURNAL OF POLITICAL ECONOMY
that plant. (This estimated effect is not statistically different from
zero. The mean value of job complexity for this subsample was 1.76.
Consequently, for the average job, high school graduation does not
affect output.)
IV. Effects on Wages
Although one should be cautious about generalizing the results in
Section II beyond the sample of semiskilled production workers, the
PSID provides evidence that the wage premium received by high
school graduates is due, at least in part, to their low quit propensity.
There are both theoretical and empirical grounds for believing that
during business slumps firms hoard workers: pay wages above the
value of the product of the workers. (Fay and Medoff [1985] estimate
excessive staffing levels of 4 percent for a typical manufacturing plant
duringits mostrecenttroughquarter.)Consequently,duringbusiness
slumps one would expect firms to benefit from (or be hurt less
by) quits and absences. To obtain quantitative estimates of the effect
of the low quit propensity and low absenteeism of high school graduates
on their wages, I interacted county unemployment rates with
high school graduation while estimating a wage equation for privately
employed males in the PSID data set between 1976 and 1982.20 I
included education, education squared, and education cubed as independent
variables to reduce the possible role of high school graduation
in approximating a precluded degree of curvature in the relationship
between wages and education.
As a further check on possible nonlinearities generating these results,
I replaced the dummy variable for high school graduation first
with a dummy variable for completion of eleventh grade and then
with a dummy variable for completion of the thirteenth year of
schooling. Neither of these dummy variables was statistically significant.
Thus the results do not seem due to the dummy variable for
completion of high school capturing additional nonlinearities in the
relationship between education and wages.
In table 9, I estimate that at the mean county unemployment rate of
20
Complete wage data are not available in the PSID data set for years prior to 1976.
For those years it is possible to construct wages using reported earnings and hours
worked. Duncan and Hill (1985, pp. 519-20) verified reported earnings calculated in
this way with employer records and found that "errors in interview reports of average
hourly earnings (defined as the ratio of interview reports of annual earnings to annual
hours) were enormous." Consequently, I used only years in which wages were directly
reported. Because wages reported were truncated for 1976 and 1977 (no one could
report a wage above $9.99), I inferred wages for workers that reported a wage of $9.99
by extrapolating back from their reported wage in 1978. I assumed that their percentage
wage increase was equal to the average in the sample, except that if the extrapolated
wage was less than $9.99 I assumed that it was equal to $9.99.
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TABLE 9
NATURAL LOG OF REAL WAGES OF MALE PRIVATE-SECTOR EMPLOYEES
IN PSID SAMPLE, 1976-81
ESTIMATED
COEFFICIENT
INDEPENDENT VARIABLE* (1) (2)
Intercept .051 .054
(5.62) (5.93)
Education .078 .077
(2.87) (2.84)
Education squared -.0062 -.0062
(-2.16) (-2.16)
Education cubed .00029 .00029
(3.22) (3.23)
Reported experience .028 .028
(13.71) (13.52)
Reported experience squared -.00040 -.00039
(-12.09) (-11.86)
Age - .0031 - .003
(-2.14) (-2.34)
Disabled -.087 -.085
(-6.44) (-6.35)
Married .084 .082
(8.25) (8.11)
Part-time work ... -.081
(-6.75)
Nonwhite -.156 -.159
(-17.79) (-18.02)
High school graduate .133 .140
(5.03) (5.12)
High school graduate x county employment rate - .010 - .010
(- 3.03) (- 2.99)
New hire (less than 1 year of tenure) - .110 - .099
(-11.88) (-9.48)
Union member .169 .167
(21.08) (20.77)
County unemployment rate .0015 .0014
(.51) (.51)
Average quits per year in the sample ... - .126
(- 2.28)
(Average quits per year in the sample)2 ... .118
(1.96)
High school graduate X average quits ... - .070
(- 1.63)
Number of degrees of freedom 9,517 9,514
NOTE.-t-statistics are in parentheses.
* Other independent variables were eight location dummy variables, 5-year dummy variable for each year, and an
intercept term. This model was also estimated with tenure and tenure squared as independent variables. The
coefficients on high school graduate and high school times unemployment were unchanged to two decimal places.
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81o JOURNAL OF POLITICAL ECONOMY
6 percent, going from 11 to 12 years of schooling has three times the
effect on wages as going from 10 to 11 years. At a zero unemployment
rate, completion of twelfth grade has more than four times as
large an effect on wages as completion of eleventh grade.2' At a 15
percent unemployment rate, completion of twelfth grade has the
same effect on wages as completion of eleventh grade.
The procyclical behavior of the wage premium for completion of
high school is especially surprising given the occupational distributions
of high school dropouts and high school graduates. High school
dropouts are overrepresented among blue-collar workers: 54 percent
of the blue-collar workers in the PSID sample were high school dropouts,
while only 10 percent of the white-collar workers were high
school dropouts. Raisian (1983) finds that the wages of blue-collar
workers relative to those of white-collar workers are procyclical.22
Hence the different occupations chosen by high school graduates and
high school dropouts would lead the wage premium for high school
graduation to behave countercyclically.23
Of course the procyclical behavior of the wage premium associated
with graduation from high school may be due to a procyclical effect of
education on wages. Unfortunately the data were inadequate to obtain
meaningful estimates of the cyclical effects of both high school
graduation and education on wages.
Table 9 also shows that average quits per year that a worker was in
the sample, when evaluated at the mean average quit rate of 0.11, has
a negative effect on wages. This effect appears stronger for high
school graduates than for high school dropouts. However, the statistical
significance is weak. The estimate obtained of the effect of the
interaction between high school graduation and previous quits on real
wages was sensitive to the particular independent variables included
and the number of observations. When the model was estimated including
constructed wage data from 1968 to 1976, the estimated
coefficient (which as argued in n. 20 is likely to be subject to serious
measurement error) was - 0.080 with a t-statistic of - 2.60 (the number
of observations was 13,604). On the other hand, when average
21 The effect of high school graduation on wages includes the effect calculated from
the continuous education variables for completion of twelfth grade as well as the
coefficient on the dummy variable for high school graduates.
22 Used the same classification scheme as Raisian (1983) in determining which twodigit
occupations were blue-collar and which were white-collar.
23 Note that the formulation I have chosen has the form In W, = X4,3 + qi,, where
nit1 N(O, cr2). Coleman (1984) has argued against assuming that nit is distributed independently
and identically if'one wishes to study cyclical effects. He argues persuasively
that a more reasonable model is In Wi, = X',r + nt + E,. Consequently, the t-statistics
for the ordinary least squares estimates of the cyclical variables should be viewed with
caution. (However, most of the variance in county unemployment rates is due to crosssectional
rather than cyclical effects.)
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HIGH SCHOOL GRADUATION 81 1
quits was replaced by ln(average quits + 1), the coefficient on high
school graduates times ln(average quits + 1) fell to - 0.072 with a tstatistic
of - 1.31 while the coefficient of ln(average quits + 1) was
-0.081 with a t-statistic of - 1.63.
V. Corroborative Evidence
The PSID provides some evidence suggesting that the discontinuous
increase in earnings associated with graduation from high school is
not due to a discontinuous increase in the cognitive skills of high
school graduates associated with their superior learning ability. This
would be an implication of human capital models in which choices of
levels of education are determined by the efficiency with which individuals
learn.
In 1976 and 1978 respondents to the PSID were asked the training
required for an average worker to learn their job. Better-educated
individuals reported having jobs requiring more training. However,
after correcting for the continuous effect of education, I did not find
that high school graduates had jobs requiring more training. Since I
had previously found a large negative effect of high school graduation
on quit propensities and quit rates (see tables 2-5), I would have
expected that, if high school graduates and dropouts derive the same
benefit from training, the former would have jobs requiring more
training. The data in table 10 suggest that while employers may believe
that better-educated workers have a comparative advantage in
acquiring job training, they do not believe that there are special skills
in assimilating training associated with high school graduation.24
One problem with this interpretation of the data in table 10 is that
individuals were asked how long it would take the average worker to
become fully trained on their job. It is not clear how the respondents
interpreted the phrase "average person." They might interpret the
average worker as someone like themselves. In that case high school
graduates could be assigned to more complex jobs, but if they learn
those jobs more rapidly, the two effects could cancel one another.
In table 11, I took a different approach to this question. I estimated
the effect on wages of the interaction between high school graduation
and on-the-job training. In column 1 the effect was estimated for all
workers, while in columns 2 and 3 I considered only workers who had
24
An alternative explanation for the data in table 10 is that skills learned in high
school by high school graduates are substitutes for skills taught on the job. However,
that explanation seems inconsistent with better-educated workers' being assigned to
jobs requiring more training unless it is only the skills associated with high school
graduation that are substitutes for training, while the other traits learned in school
complement the skills learned on jobs.
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812 JOURNAL OF POLITICAL ECONOMY
TABLE 10
YEARS OF TRAINING REQUIRED FOR JOB
IN 1976-78
(PSID Sample, Ordinary Least Squares
Estimation)
Independent Variable* Coefficient
Intercept -2.46
(-5.36)
Education .310
(2.13)
Education squared -.24
(- 1.46)
Education cubed .00119
(2.10)
Work experience .058
(4.63)
Work experience squared -.0010
(-5.05)
Age .033
(3.80)
Race = nonwhite -.87
(-16.29)
High school graduate -.02
(- .23)
College graduate -.37
(-.197)
Married .12
(1.69)
Disabled .012
(.88)
R2 .1638
Number of observations 9,941
NOTE.-t-statistics are in parentheses.
* The other independent variables were eight dummy variables
for different areas of the country.
completed the training needed to fully learn their job. When I estimated
the coefficients listed in columns 1 and 2, I obtained the surprising
(astonishing?) result that the continuous effect of education
on the impact of on-the-job training on wages has the opposite sign as
the effect of graduation from high school. (When I omitted the interaction
between education and completed training, I estimated a
negative coefficient for the effect of the interaction between high
school graduation and completed training on wages.)
On the other hand, the estimated coefficients in column 3 suggest
that these results may be due to nonlinearities in the interaction between
education and returns to on-the-job training. In column 3 I
allowed for a cubic specification of the interaction between education
and on-the-job training and found that, for relevant levels of education,
differences in education levels do not affect the impact of onThis
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HIGH SCHOOL GRADUATION 813
TABLE 11
EFFECT OF TRAINING ON LN WAGES OF MALE PRIVATE-SECTOR EMPLOYEES IN PSID
SAMPLE, 1976-81
COEFFICIENT
INDEPENDENT VARIABLE* (1) (2) (3)
Education .073 .059 .057
(2.78) (2.09) (20.83)
Education squared -.0064 -.0056 ...
(-2.33) (-1.87)
Education cubed .00030 .00030 ...
(3.48) (3.12)
Required training for job cur- .025 ...
rently held (8.00)
Attained training (includes .056 ... ...
workers still in training) (5.57)
High school graduate X attained .013 ... ...
training (2.07)
Education x attained training -.0036
(- 3.98)
High school graduate .116 .105 .057
(4.43) (3.49) (2.01)
High school graduate x county - .0093 - .010 - .0087
unemployment (-2.86) (-2.82) (-2.36)
Years of completed training ... .099 .527
(10.01) (7.49)
High school graduate x years of ... .017 .0045
completed training (2.53) (.48)
Education x years of completed ... - .0049 - .121
training (-5.08) (-6.15)
Education squared x years of ... ... .00975
completed training (5.39)
Education cubed x years of ... ... - .00026
completed training (-.487)
Number of degrees of freedom 9,510 6,526 6,526
R2 .522 .548 .543
NOTE.-t-statistics are in parentheses.
* The other independent variables were the same as those in col. 2 of table 9, except the interaction between high
school graduation and previous quits was omitted. In col. 3 education squared and cubed were also omitted. The
sample size falls in cols. 2 and 3 because 1 included only workers who had completed their training.
the-job training on wages, nor does there appear to be a discontinuous
change in the impact of on-the-job training on wages associated
with graduation from high school.
Note that the coefficient of required training in column 1 is 0.025
with a t-statistic of 8.00. This coefficient is consistent with the evidence
presented in Weiss (1984) that workers on more complex semiskilled
production jobs have higher quit rates, suggesting that workers dislike
those jobs and hence need to be rewarded with a compensating
wage differential. It is also consistent with efficiency wage models that
predict that firms pay higher wages in jobs for which the returns to
effort or to ability are highest.
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814 JOURNAL OF POLITICAL ECONOMY
There are several reasons why the estimated coefficients obtained
in all three columns of table 11 should be viewed with particular
caution. First, the range of realized education levels is fairly small,
and education is allowed to affect wages in a wide variety of ways
leading to serious problems of multicollinearity. Second, the process
by which workers choose or are assigned to jobs is not known. The
resulting simultaneous equation bias could be seriously affecting the
estimated coefficients. Third, as noted in the discussion of the results
in table 10, it is not clear what the training requirements reported by
workers are actually measuring. These problems are added to the
usual problems of model misspecification, misreporting of wages, and
omission of fringe benefits in measures of reported wages that are
likely to affect the estimated coefficients in table 11.
VI. Sample Selection Bias25
As discussed above, there are persuasive reasons for believing that
sample selection bias is not a serious problem for the analysis. However,
to the extent sample selection bias is a problem, the results
obtained above are stronger than would be indicated from the estimated
coefficients and t-statistics.
Since only a trivial number of applicants were rejected for reasons
other than low scores on the dexterity test, I shall restrict the discussion
in this section to the biases introduced from the application decision
of workers. Thus we shall consider a model in which the sorting
effect of wages differs across different groups of workers (see Weiss
1980).
Consider an unobserved application equation. A worker applies for
a job with this firm if and only if
X(yo > E1, (10)
where X0 includes all observable characteristics of the worker and El
includes unobserved characteristics of a worker as well as random
noise. Having applied and been accepted for this job, the worker
subsequently quits if and only if
Xoyl > E21(Xo()o > E1) (11)
and is absent if and only if
XO,^Y2> E31(XoY()> El). (12)
Because better-educated workers had higher wages on their previous
jobs and generally have higher reservation wages when unem-
25 The material in this section is a direct application of the seminal treatment of these
issues in Heckman (1976).
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HIGH SCHOOL GRADUATION 815
ployed, we would expect the coefficients on education and high
school graduation in (10) to be negative. Since (10) is not estimated,
within the sample we would expect E1 and education to be negatively
correlated. It seems reasonable to expect that, at least for employed
applicants, E is positively correlated with E2 and E3: A worker who was
easily induced to leave his previous job is likely to be easily induced to
leave his current job, and a low level of job commitment might also be
expected to lead to a higher than expected probability of being absent.
Therefore, we expect E2 and E3 to be negatively correlated with
education in equations (1 1) and (12).
Hence, for this sample there is positive bias on the estimated
coefficients on education and high school graduation in the quit and
absenteeism equations, resulting in an underestimate of the magnitude
of the negative correlation between high school graduation
and the propensity to be absent or to quit. (In the market equilibrium
it is the unbiased correlation between high school graduation and quit
or absenteeism propensity that is relevant for explaining the positive
correlation between high school graduation and wages.)
VII. Review of Results
Recent large-sample studies have shown returns to education in the
region of 4-5 percent. There is a not dissimilar rate of return for the
pay on their previous job for workers in the proprietary sample I
assembled. A large component of this rate of return is the discontinuous
increase in wages associated with high school graduation.
Presumably the higher earnings of high school graduates are due to
their better performance relative to high school dropouts. I investigated
four components of performance: output per hour, comparative
advantage in more complex jobs, propensity to quit, and propensity
to be absent.
For the sample of semiskilled production workers, high school
graduation appears to be uncorrelated with output per hour, and
high school graduates did not appear to have a comparative advantage
in more complex production jobs. On the other hand, high
school graduates were significantly less likely to quit or to be absent.
The wage premium received by high school graduates in the PSID
sample appears to be procyclical. Consequently, if a low quit propensity
and a low rate of absenteeism are more valuable during booms
than slumps, these data suggest that a considerable fraction of the
estimated return to high school graduation is due to unobserved traits
that are associated with that credential.
Finally, I found that high school graduates in the PSID do not have
jobs requiring more training than would be expected from a continuous
relationship between education and required training.
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8i6 JOURNAL OF POLITICAL ECONOMY
Appendix A
A Description of the Proprietary Data Set
Each of the workers in this sample was initially paid according to the same
nonlinear piece rate. The form of this pay schedule was such that for newly
hired workers wages were a convex function of output. When a worker
achieved 83 percent of expected output for 1 month, he or she was assigned
to a pay group. All the members of a pay group received the same pay. Pay
was proportional to the output of the group-the average group size was 126
members-and promotion opportunities were insignificant. Thus there was
little financial incentive for group members to achieve high levels of output.
Consequently, I used the output of workers only during their first month on
the job in this study. (Among experienced workers, the range in output from
the bottom to top deciles was less than 20 percent of the mean.)
Almost all workers were assigned to a pay group within their first 3 months
on the job. Therefore, expected lifetime earnings differences among the
newly hired workers at each location were trivial.
For each worker data were available on sex, age, marital status, education,
employment status when he applied for work, an estimate of the time required
for an average employee to learn the worker'sjob as well as his output
per hour (measured in physical units and normalized by the industrial engineering
force to be equivalent acrossjobs), number of days absent, number
of occasions absent (consecutive days absent are a single occasion), whether or
not the worker quit, and the date a quit occurred. The workers did not know
that they were going to be subjects of an empirical study. All the data were
routinely collected either by the personnel office, industrial engineers, or
foremen at the three locations. Although the total sample contained 2,920
individuals, complete data were not available for all workers. In some cases
workers were assigned jobs for which there were no measures ofjob complexity;
in other cases the worker failed to answer all the questions on the application
form. Also at each location different information was available in the
personnel records. In location C, race data were not available and only the
screws half of the Crawford Physical Dexterity Test was administered; in
the other two locations both the pins and screws sections of the dexterity test
were administered before a worker was hired. The scores on this test were
used by the firm in deciding whether to hire the worker but were not used in
assigning workers to jobs. Job assignments were random.
An additional problem arose at location C: the plant was divided into two
halves, with significantly different promotional opportunities. Unfortunately
the data did not reveal to which half of the plant particular workers were
assigned, that initial assignment may not have been random. At that plant,
workers assigned to more complex jobs had better promotional opportunities.
Because of these unobserved differences in promotion opportunities, the
relatively small sample size at that location, and the missing data on race,
prior experience, employment status when they applied for this job, and
scores on the pins section of the dexterity test, I did not use data from that
location in estimating quit equations.
Table Al presents some summary statistics that provide a context within
which to evaluate the data.
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HIGH SCHOOL GRADUATION 817
TABLE Al
MEAN VALUES OF THE RELEVANT VARIABLES
Plant A Plant B Plant C
Percentage white .72 .76 NA
Percentage black .24 .20 NA
Age 24.6 25.3 26.7
(7.52) (7.07) (8.23)
Education 12.1 12.2 11.9
(1.20) (1.26) (.98)
Percentage employed at time of application .64 .29 .38
(1 if employed, 0 otherwise)
Percentage male .57 .19 .41
Percentage married .43 .48 .42
Tenure on previous job (in years) 1.56 NA NA
(2.04)
Previous work experience (in years) 3.54 NA NA
(7.74)
Weeks to learn job 7.5 5.1 11.7
(4.9) (2.4) (4.4)
Score on screws test 22.6 21.3 24.0
(5.08) (4.20) (4.02)
Score on pins test 22.4 23.5 NA
(4.10) (3.64)
First-month output 111 63 105
(19.7) (22.2) (29.2)
Percentage days absent 2.96 2.3 3.0
(6.53) (4.23) (4.38)
Percentage occasions absent 1.2 1.1 1.12
(4.5) (1.4) (1.1)
Quit rate in first 6 months 9.8 18.2 12.3
on job (%)
NOTE.-Standard errors are in parentheses below the relevant variables. NA nteans data were not available. For
the subsample used to estimate the output equation, 56 percent were il lolalstA, 34 percent in plant B, and 10
percent in plant C.
Appendix B
To evaluate the cost of absenteeism to firms, the nature of the production
process is critical. Traditional economic analyses of absenteeism assume that a
worker's marginal product is equal to his wage and the cost of absenteeism is
the wage of the worker. In this Appendix, we will consider the case in which
the production process used by all firms requires k workers to operate. If
more than k workers are present, the extra workers are redundant; they do
not increase output. If fewer than k workers appear, output is zero.
To simplify the notation, assume output is linear in the number of workers
and normalize the value of output to be equal to k. The number of workers
hired is denoted by n, the wage of each worker by w, the probability that a
worker appears for work by p, and the expected profit of a firm employing n
workers by Trr(n).Let P(S, ? k) denote the probability that at least k workers
are present when n workers are hired. Finally, assume that the absenteeism
rate of each worker is common knowledge and that workers are not paid if
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8i8 JOURNAL OF POLITICAL ECONOMY
TABLE BI
RELATIONSHIP BETWEEN ABSENTEEISM AND WAGES
Probability Profit-maximizing
of Number of Equilibrium
Being Absent Employees Daily Wage
.20 30 197.66
.19 30 198.42
.18 29 199.51
.17 29 200.43
.16 28 201.46
.15 28 202.64
.14 27 203.47
.13 27 205.07
.12 27 205.56
.11 26 207.70
.10 26 208.60
.09 25 210.53
.08 25 212.05
.07 24 213.59
.06 24 216.02
.05 23 217.02
.04 23 220.87
.03 23 222.08
.02 22 227.61
.01 21 231.60
.00 20 250.00
they are absent (this assumption is made so that we can focus on the indirect
costs of absenteeism rather than the direct cost of paying for an absent
worker): w(n) = kP(S, ? k) - np. The expected marginal product of the n +
1 worker is k[P(S, + 1 kk) - P(S?,? k)]. The net expected value of the marginal
worker is
w(n + 1) - w(n) = kP(Sn+1I k) - (n + O)po - kP(S,, ? k) + np/o
= pkP(S, ? k - 1) + (1 - p)kP(S,, ? k)
- kP(S, ? k) - po (B1)
= pk[P(S, ? k - 1) -P(S,, ? k)] -pw
= p[kP(S,, = k - 1) - ].
The expected value of the marginal worker is the probability that the worker
is decisive (enables the plant to operate) times the value of the production
process, minus that worker's expected cost to the firm.
A firm increases the number of workers it employs as long as (B 1) is positive;
it chooses the smallest n such that
pk- n pJ(1 -p)"' -j po K 0, (B2)
(n - j)
where j = k - 1.
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HIGH SCHOOL GRADUATION 819
If we consider the case in which workers are paid even if they are absent,
the usual policy in U.S. firms for routine levels of absenteeism, (B1) is rewritten
as pkP(Sn = k - 1) - w and (B2) as
pa n njl p~-i-(t<
(n -1)1
To illustrate the effect of absenteeism on the equilibrium value of a worker
to the firm, let us consider a production process that requires 20 workers to
operate, generates $10,000 of income per day if it operates, and has a fixed
cost of $5,000 per day whether it operates or not. We shall assume that
workers are not paid if they are absent. In equilibrium, if the probability of a
worker's being absent is known by all employers, firms compete for workers
so that wages are bid up to the level at which each production process earns
zero profits, and all the workers at a given plant have the same absenteeism
rate, the relationship between absenteeism and wages shown in table B 1 follows.
These calculations suggest that, even if employees are not paid when
they are absent, in competitive markets employers might pay significantly
higher wages to workers with lower probabilities of being absent.
References
Allen, Steven G. "An Empirical Model of Work Attendance." Rev. Econ. and
Statis. 63 (February 1981): 77-87.
Bishop, John. "The Recognition and Reward of Employee Performance."
Manuscript. Ithaca, N.Y.: Cornell Univ., 1987.
Bloom, David, and Killingsworth, Mark. "Correcting for Truncation Bias
Caused by a Latent Truncation Variable." Technical Working Paper no.
38. Cambridge, Mass.: NBER, 1984.
Coleman, Thomas. "Cyclical Variations in Individual Wages and Employment."
Manuscript. Chicago: Univ. Chicago, 1984.
Duncan, Greg J., and Hill, Daniel H. "An Investigation of the Extent and
Consequences of Measurement Error in Labor-Economic Survey Data."J.
LaborEcon. 3 (October 1985): 508-32.
Fay, Jon A., and Medoff, James L. "Labor and Output over the Business
Cycle: Some Direct Evidence." A.E.R. 75 (September 1985): 638-55.
Fein, Mitchell. "Job Enrichment Does Not Work." Atlanta Econ. Rev. 55
(November-December 1975): 45-54.
Greenwood, Major, and Yule, G. Udny. "An Inquiry into the Nature of
Frequency Distributions of Multiple Happenings." J. Royal Statis. Soc., ser.
A, 83 (March 1920): 255-79.
Griliches, Zvi. "Estimating the Returns to Schooling: Some Econometric Problems."
Econometrica45 (January 1977): 1-22.
Hackman, Richard. "On the Coming Demise of Job Enrichment." Technical
Report no. 9. New Haven, Conn.: Yale Univ., Dept. Admin. Sci., December
1974.
Hashimoto, Masanori, and Raisian, John. "Employment Tenure and Earnings
Profiles in Japan and the United States." A.E.R. 75 (September 1985):
721-35.
Hausman, Jerry A., and Taylor, William E. "Panel Data and Unobservable
Individual Effects." Econometrica49 (November 1981): 1377-98.
This content downloaded from 147.251.189.14 on Wed, 26 Aug 2015 14:16:57 UTC
All use subject to JSTOR Terms and Conditions
820 JOURNAL OF POLITICAL ECONOMY
Heckman, James J. "The Common Structure of Statistical Models of Truncation,
Sample Selection and Limited Dependent Variables and a Simple
Estimator for Such Models." Ann. Econ. and Soc.Measurement5 (Fall 1976):
475-92.
Johnson, Norman L., and Kotz, Samuel. Discrete Distributions. New York:
Wiley, 1969.
Landau, Henry, and Weiss, Andrew. "On the Negative Correlation between
Performance, Experience, and Education." Working Paper no. 1613. Cambridge,
Mass.: NBER, April 1985.
Medoff, James L., and Abraham, Katharine G. "Are Those Paid More Really
More Productive? The Case of Experience."J. Human Resources16 (Spring
1981): 186-216.
Mellow, Wesley. "Employer Size and Wages." Rev. Econ. and Statis.64 (August
1982): 495-501.
Mellow, Wesley, and Sider, Hal. "Accuracy of Response in Labor Market
Surveys: Evidence and Implications."J. LaborEcon. 1 (October 1983): 331-
34.
Mincer, Jacob A. "Family Migration Decisions." J.P.E. 86 (October 1978):
749-73.
Mirvis, Philip H., and Lawler, Edward E., III. "Measuring the Financial Impact
of Employee Attitudes."J. Apple.Psychology62 (February 1977): 1-8.
Muthen, B., and Joreskog, K. G. "Selectivity Problems in Quasi-experimental
Data." Manuscript. 1983.
Psacharopoulos, George. "Returns to Education: An Updated International
Comparison." ComparativeEducation 17 (October 1981): 321-41.
Raisian, John. "Contracts, Job Experience, and Cyclical Labor Market Adjustments."
J. LaborEcon. 1 (April 1983): 152-70.
Spence, A. Michael. MarketSignaling: InformationalTransferin Hiring and RelatedScreeningProcesses.Cambridge,
Mass.: Harvard Univ. Press, 1974.
Weiss, Andrew. "Job Queues and Layoffs in Labor Markets with Flexible
Wages."J.P.E. 88 (June 1980): 526-38.
"Determinants of Quit Behavior."]. LaborEcon. 2 (July 1984): 371-
87.
White, Halbert. "Maximum Likelihood Estimation of Misspecified Models."
Econometrica50 (January 1982): 1-25.
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