Discussion Paper No.

530

HUMAN CAPITAL ACCUMULATION
OF SALARIED AND
SELF-EMPLOYED WORKERS
Daiji Kawaguchi

The Third ISER-Moriguchi Prize (2001) Awarded Paper

March 2001

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Human capital accumulation of salaried andself-employed workers
Daiji Kawaguchi1 2
October 6, 2000

1 Daiji Kawaguchi: Economics Department, 101 Marshall Hall, Michigan State

University, East Lansing, MI 48823 USA. Tel: 517-353-9935 Fax: 517-432-1068
E-Mail:kawaguc2@msu.edu
2 I would like to thank David Neumark, Gerhard Glomm, Jeff Biddle, Linda Bailey, Facundo Sepulveda for helpful comments. I also would like to thank Catherine
Fleck for advice on English. All remaining errors are of course mine.

Abstract
Both human capital accumulation and Lazear contracts can explain the raising wage of salary/wage worker through job experience or tenure. To distinguish between these two effects, Lazear and Moore (1984) used self-employedworkers’ wage growth to partial out the effect of human capital accumulationfrom salary/wage workers’ wage growth. When the human capital accumulation behavior is identical across two kinds of jobs, the difference in wage
growth between salary/wage workers and self-employed workers are due toLazear contract since self-employed workers’ wage are determined by theirproductivity. However, in the model developed in this paper, when selfemployed workers face more wage variation but enjoy a higher return forhuman capital, human capital accumulation for those two kinds of jobs areshown to be different. The model predicts that workers with higher humancapital select to be self-employed. Under general assumptions on humancapital production technology, workers with high human capital have flatterwage-experience profile as a result of optimal human capital accumulation.
Thus the heterogeneity of salary/wage and self-employed workers that induces a different pattern of human capital accumulation can explain theobserved lower wage growth of self-employed workers inLazear and Moore(1984).

1

Introduction

Worker’s wage growth with work experience is one of the most robust empirical findings in economics. Lazear (1979) and Lazear (1981) explained wage
growth among salary/wage workers based on principal-agent theory. In his
model, worker’s behavior is not perfectly observed and worker’s shirking is
detected only by chance. In Lazear model, it is optimal for an employer topay his employee less than the worker’s marginal product when the worker
is young and more than the worker’s marginal product when the worker isold. The employer takes the difference between marginal product and wage
when worker is young and returns it to the worker when the worker is old.
This payment system discourages workers from shirking since the worker isfired when the shirking is detected and thus cannot take his money back.
A difficulty of testing this theory is that the human capital theory also predicts wage growth with work experience because of worker’s skill formation.
Since Lazear theory and human capital theory are not mutually exclusive, it
is very difficult to attribute the observed wage growth to the specific theory.
As an indirect test of Lazear theory, Lazear and Moore (1984) comparedwage growth of salary/wage workers and self-employed workers. Since selfemployed workers do not have an incentive to shirk, the wage growth ofself-employed workers can be attributed to the human capital accumulation.
Assuming identical human capital accumulation between salary/wage (SW)
workers and self-employed (SE) workers, the difference of wage growth be-

1tween SW workers and SE workers can be attributed to Lazear theory. In fact
Lazear and Moore (1984) found the steeper wage-experience profile among
SW workers than SE workers and used the finding as a supporting evidenceof Lazear theory.
The purpose of this paper is to propose the model that predicts the flatterwage-experience profile among SE workers only based on the human capital theory. To develop the model, two crucial aspects of self-employmentthat differentiate self-employment from salary/wage job are considered. As
mentioned in many studies (Kihlstrom and Laffont (1979), Kanbur (1982),
Carrington et al. (1996), and Cressy (2000)), one important aspect of selfemployment is the larger variation in income compared with SW workers. On
the other hand, there is a premium for self-employment as shown in the empirical study in this paper. Only the entrepreneur with high human capitalcan enjoy this premium for long period, though. Bates (1990) found the highhuman capital of entrepreneurs as a critical factor of small business longevity.
In addition, Borjas and Bronars (1989) and Fairlie and Meyer (1996) reporthigher return to education among SE workers than SW workers using Census
data. We interpret these findings as evidence of the higher return for humancapital among SE workers. To summarize, we assume that higher risk andhigher return for human capital characterize SE workers.
Modeling these two characteristics of the wage determination with workers’ risk aversion, workers’ optimal human capital investment decision produces a steeper wage profile among SW workers, as Lazear and Moore (1984)2

observed. Due to the different characteristics of SE jobs and SW jobs, SE
workers are not necessarily a good ‘control group’ for the SW workers.
In the model, the workers choose to be SW or SE workers when they finish
their schooling. Since to be SE is risky, the worker with high human capital
selects SE since for these people the higher return for human capital compensates the risk. Using a standard human capital accumulation technology
as in Lucas (1988), we can show that the optimal human capital investment
is a function of current human capital level. Current human capital has apositive effect on human capital investment since a worker with high humancapital is more efficient in additional human capital production. On theother hand, the opportunity cost of human capital investment is higher for aworker with high human capital. Under the convexity assumption of humancapital production, we can show that the latter effect dominates the former
effect. As a result, a worker with high human capital invests less in his human capital. Thus SE workers, who have higher human capital as a result of
self-selection, tend to have a flatter wage profile compared with SW workers
because of the different human capital investment behavior. We also showthat the SW workers who will select SE in later periods tend to invest morein their human capital than the SW workers who plan to stay in SW jobs.
In sum, SE workers invest less in their human capital on average because of
two characteristics of self-employment, which are high-income risk and highreturn for their human capital.
The structure of the rest of this paper is as follows. Since the wage risk3

of self- employment is a crucial assumption for our main conclusion, thenext section examines the wage risk for self-employed workers. The model ofhuman capital accumulation under the income risk is introduced in the third
section. The fourth section provides evidences consistent with our model.
The conclusion follows.

2

Replication of Lazear and Moore (1984)’s
result and wage risk of self- employed workers

2.1

The model and estimation

In this section, we replicate the result obtained in Lazear and Moore (1984)
using a different data set; we then test to see if the wages of SE workers
are more volatile than the wage of SW workers. Since we are interested in
the wage variation faced by an individual, residuals from fixed-effect wage
regression are used to create a measure of wage variation.
Data for the years 1985 to 1998 were taken from NLSY79. The sample isrestricted to white male and is used to estimate the model:
ln wit = Xit β1 + sit Xit β2 + ci + uit ,(1)

where wit is hourly wage rate and Xit is a vector of standard control variables in Mincer type wage equation1 , sit is a dummy variable which takes
one if the worker is self-employed and ci is individual heterogeneity. The
1

The variables included in the regression appear in Table 1. The variable names are
self-explanatory.

4

interaction with the self-employed dummy is included to replicate Lazear
and Moore (1984)’s findings and to avoid systematic correlation of uit with
self-employment status. The model is estimated by both pooled OLS and
fixed effect2 . The estimation results appear in the first and second column intable 1. The results of the fixed effect regression, which appear in the second
column of table 1, shows that SE workers earn 23.5% more ceteris paribus.
The return to experience among SE workers (about 7% for the first year) isalmost half of SW workers’ (about 12% for the first year). In addition, there
is almost no return to tenure among SE workers while SW workers enjoy areturn of 3.2% for the first year of tenure. These results almost match with
the Lazear and Moore (1984)’s findings. This might be because of the Lazear
contract or less on-the-job human capital investment among SE workers. In
sum, SE workers earn higher wages and experience less wage growth, ceterisparibus.
Then using the residual of the previous fixed effect estimation,uˆ2it = Xit γ1 + sit Xit γ2 + ai + vit ,(2)is estimated using both OLS and fixed effect estimation3 . We are interested
in the null hypothesis:
H0 : γ2 = 0.
The results of the multiple regression, along with the simple regression, appear in table 1. By using the results of the simple regression, we can say that
2
3

The assumption E[uit |Xi., si. , ci ] = 0 is posed here.
Essentially this is Breush-Pagan’s test for heteroscedasticity.

5the conditional wage variance among SE workers is twice or three times larger
than that of the salaried workers. To avoid the possibility that the result isderived from the correlation of self-employment status with the other factorsthat affect wage volatility, a multiple regression is also estimated. The null
hypothesis of no difference in the coefficients is rejected through F-test. Also
the results are essentially the same for both OLS and fixed-effect. From theseevidences, we can conclude that being self-employed is more risky than beinga SW worker.

2.2

The issues of measurement error

There is a possible flaw with the previous analysis due to measurement error
in the wage of self-employed workers. Smaller return to experience and tenure
among SE workers may be due to measurement error in the wage of SE thatis systematically correlated with experience or tenure. It is also likely thatlarger conditional variance of wage among SE workers is due to measurement error. Joulfaian and Rider (1998) report that SE workers underreporttheir income by 18% on average using the data from Tax Payer Compliance
Measurement Program data collected by the IRS. Although respondents do
not have an incentive to avoid taxation by underreporting their income inthe case of NLSY, the underreporting is still possible since the respondents
may refer to their 1040 form to report their income to NLSY. Thus it isworth discussing the issues of measurement error explicitly. The model with6

measurement error is assumed to be following.
ln wit∗ = Xit β1 + sit Xit β2 + ci + eit ,(3)ln wit = ln wit∗ + di + bi selfit + uit ,(4)

where di is an individual specific tendency of misreport regardless of employment status and bi is an individual specific tendency of misreport of wage
when the respondent is self-employed. The assumptions that these individual
tendencies are time-invariant are crucial in the following discussion. Thesetendencies (bi , di , ) and errors in equations (eit , uit ) are assumed not to becorrelated. The assumptions on error terms are following:E[eit |bi , ci , di , Xi , selfi ] = 0,E[uit |bi , ci , di , Xi , selfi ] = 0andE[e2it |bi , ci , di , Xi , selfi ] = (1 + φselfit )σe2 .
To test if self-employed worker faces the larger risk, we are interested in if
φ = 0. The model that is actually estimated isln wit = Xit β1 + sit Xit β2 + ci + eit + di + bi selfit + uit .

(5)

Applying fixed effect transformation, we obtain¯ it ) (6)wit − w̄i = (Xit − X̄i )β1 + (sit Xit − si Xi )β2 + eit + uit + bi (selfit − self
In this situation, fixed effect estimator is not consistent estimator sinceˆ = βself + b, where b = E(bi ).Thus fixed effect estimator of βself
plim βself
7

estimates the lower bound of βself given b < 0. In this case, the SE premium
found in the regression should be understood as the lower bound estimate.
Another possible measurement error arises from the differential concept
on the income between SW workers and SE workers. SE workers may report
return for physical capital of their own business as their wage; also they may
subtract the cost of physical investment in their own business from their own
wage. It is likely that SE workers invest in physical capital when they start
their business and collect the return later. Then the wages of short tenured
SE workers are understated and the wages of long tenured SE workers areoverstated. Thus the error term of the measurement errorE(uit |bi , ci , di , Xi. , selfi. ) = bi selfit + ai selfit tenureit ,(7)

where bi ≤ 0, ai ≥ 0, becomes a possible case. As a result the probability
limit of fixed effect estimators areˆ = βself + b, plim βselfˆtenure = βself tenure + a,
plim βself(8)ˆ is likely to be a lower bound estimator ofwhere a = Eai . Therefore βself
βself and βselfˆtenure is likely to be an upper bound estimator of βself tenure .
Therefore neither of these inconsistencies weakens our discussion. We stillconclude that SE workers earn higher wage and SE workers experience lesswage growth.
The conditional variance of measurement error may also depend on the
self-employment status since the measurement error depends more on individuals among SE workers compared with SW workers thorough the effect8¯ it ). Thenof bi . Define vit = eit + uit + bi (selfit − self
¯ i )2 ].
E[v 2 |Xit , i] = (1 + φselfit )σe2 + σu2 + E[b2i (selfit − self

(9)

The last term tells us that the job status changer tends to have a larger
variance. However, the last term of this expression is constant for eachindividual, so when we regress the squared residual of fixed effect estimationof wage equation (1) on self employment status using the fixed effect, we
obtain the consistent estimator of φ. Thus the coefficient of self-employment
status found in column 5 of table 1 (0.189 with s.e. of 0.038) is understoodas an estimate of φ. Therefore, we still conclude that the self-employment is
twice as risky as being a wage-salary worker under the assumption that thetendency to misreport is constant within individual and job status.

3

The model

Suppose each worker lives for two periods. Each worker is endowed with
one unit of time for each period. Each worker knows his ability at the first
period. Each worker has the following preference with constant absolute risk
aversion.
Ûi = − exp[−γi (wi1 + wi2 )]

9

(10)

where γi is the degree of absolute risk aversion of worker i and wit is the wage
offer for worker i at time t4 . The wage offer depends on job choice, whether
the worker is the self-employed or salaried worker. The wage offer for eachjob is2
witSE = bSE (1 − nit )hit + eitSE , eitSE ∼ N (0, σSE
),

(11)

2
witSW = bSW (1 − nit )hit + eitSW , eitSW ∼ N (0, σSW
),

(12)

and

where hit is the human capital of worker i at period t, nit ∈ [0, 1] is the portionof time devoted to the human capital accumulation by the worker i at time t.
The initial human capital hi1 is given as an endowment for each worker. Thisinitial level of human capital includes human capital accumulated througheducation and innate ability. Although we recognize the endogeneity of theeducational decision, we treat this as given since the main interest of ouranalysis here is on-the-job human capital accumulation. The human capitalfor both periods is assumed to be general across the jobs. The parameter bj ,which is exogenously given by the labor market for the workers, is the unit
price of human capital in job j. The random variable eitj is a shock to thewage. We assume eitj is independently distributed across individual, time
4

Although the utility function is not defined over consumption, this ‘indirect’ utility
function is the solution of a problem such as
max − exp[−γ(c1 ,c2α −α β −β α β) () c1 c2 ],α+βα+βsubject to
c1 + c2 = w1 + w2 .
The crucial assumption is that the workers do not face the liquidity constraint.

10and two jobs. By taking expectation of the life-time utility, we obtainˆ it =
EU

Z Z

= −
·

Z

Z

− exp[−γi (wi1 + wi2 )]dF (ei1j )dG(ei2j )exp[γi (bj hi1 (1 − ni1 ) + eij1 )]dF (eij1 )exp[γi (bj hi2 (1 − ni2 ) + eij2 )]dG(eij2 )= − exp[−γi (bj (1 − ni1 )hi1 − (γi /2)σj2+bj hi2 − (γi /2)σj2 )].

(13)

The independence of error terms across periods derives the second line andthe property of log normal distribution induces the third line5 . Using theordinal property of utility function,
EU = bj (1 − ni1 )hi1 − (γi /2)σj2 + bj (1 − ni2 )hi2 − (γi /2)σj2 ,(14)

is a equivalent expression of (13). Each worker has access to the following
human capital accumulation technology.
hi2 = hi1 + δ(ni1 hi1 )α , α ∈ (0, 1),(15)

where δ is efficiency of human capital investment on human capital accumulation6 . The parameter α represents a worker’s learning ability whichis assumed to be identical for all the workers. This technology shows thatthe worker with higher human capital is more efficient in the production of
additional human capital, but the effect diminishes since α ∈ (0, 1).
5

When ln x ∼ N (m, s2 ), it is known that Ex = exp(m + (1/2)s2 ). In our case, e =ln x ∼ N (m, s2 ) thus E exp(e) = Ex = exp(m + (1/2)s2 ).
6This functional form of human capital accumulation is standard in the literature ofmacroeconomics. See Lucas (1988).

11Each worker maximizes his lifetime expected utility by choosing ni1 anda career path ({j}2t=1 ) under constraint of human capital accumulation technology7 .
Now we are going to make two assumptions that distinguish SW and SE
workers.
2
2
Assumption 1 σSE> σSW.

i.e. the wages for SE workers are more volatile than those of SW workers’.
The empirical evidence supports this assumption as seen in the previous
section.
Assumption 2 bSE > bSW .
i.e. the return for human capital is higher for self-employed workers.
This assumption is justified by the robust finding of the premium for the
self-employment found in table 1 and this premium can be enjoyed giventhat the worker can remain self-employed. Whereas the failure rate of selfemployment is very high (Bates (1990), Schiller and Crewson (1997)) andBates (1990) found high human capital of entrepreneur as a critical determinant of small business longevity. Thus the worker with high human capital
exclusively enjoys the SE premium. In other word, we assume that the returnfor human capital is higher for SE workers. Also empirical studies which use
census data report higher return to education among SE workers than SW
7

As a result of optimization, ni2 = 0 is trivially chosen.

12workers (Borjas and Bronars (1989) and Fairlie and Meyer (1996)).
Under these assumptions, we will solve the worker’s maximization problem for each possible career path and calculate the corresponding indirect
utility function. Each worker chooses a career path that yields the highest
lifetime utility. Since we can rule out the possible career path of SE - SW8 ,we should consider three possible career paths of SE - SE, SW - SW, andSW - SE.
Each worker solves
max{{jt }2t=1 ,ni1 }EU = bj (1 − ni1 )hi1 − (γi /2)σj2 + bj hi2 − (γi /2)σj2 ,(16)

subject to
hi2 = hi1 + δ(ni1 hi1 )α , α ∈ (0, 1),(17)given hi1 .
The optimal human capital investment time, ni1 , is1 (δα) 1−αh−1 ,ni1 = i1
1
1
−1
SE 1−α( bbSW) (δα) 1−α hi1,

for job stayers.
for job changers.

(18)

These solutions show the human capital investment time is decreasing in
the initial human capital. There are two factors that relate the initial humancapital level and human capital investment. First, from (17) the worker withhigher human capital is more productive in human capital accumulation.
This effect is diminishing because the term (ni1 hi1 ) is exponentiated by α ∈(0, 1). Second, the worker with higher human capital pays more opportunity
8

This career path is always dominated by the SW - SE from the assumption 2.

13

cost of human capital investment, which is bj ni1 hi1 . Therefore marginal
benefit of investment diminishes in hi1 but marginal cost is constant in hi1 ,thus the worker with high hi1 chooses lower ni1 . The assumption of theconvexity of human capital production, α ∈ (0, 1) is the crucial assumption
to derive this result, after all. To summarize, under the assumption of convex
human capital production technology, the worker with higher initial humancapital devotes less time in his human capital investment.
By substituting the optimal ni1 in the objective function of each career
path, we obtain the following indirect utility functions for each career pathfor each individual i.
1

α

1

2
+ bSE δ 1−α (α 1−α − α 1−α )vSE−SE (hi1 , γi ) = 2bSE hi1 − γi σSE
1

α

(19)

1

2
+ bSW δ 1−α (α 1−α − α 1−α ) (20)vSW −SW (hi1 , γi ) = 2bSW hi1 − γi σSW22vSW −SE (hi1 , γi ) = (bSW + bSE )hi1 − (γi /2)(σSW
+ σSE
)
−α

1

1

α

1

1−α 1−α 1−α+bSWbSE δ (α 1−α − α 1−α )(21)These expressions tell us that the choice of career path depends on eachworker’s first period human capital and the degree of risk aversion. From
the first two expressions, we can clearly see that the worker with high hi1
is likely to be the SE worker. Those less risk adverse workers (the workers
with low γi ) are likely to choose self-employment. The relationship between
lifetime utility for each career path and initial human capital is graphed infigure 1 given the degree of risk aversion. This graph shows the lifetime
utility of being a SE worker is higher than being a SW worker for the high14

human capital worker. In addition, the graph shows that the worker withthe ‘medium’ level of human capital switches the job in the middle of his
career. The increasing risk aversion (γ) increases the distance of intercepts
and makes the choice of self-employment less likely.
The worker with higher initial human capital selects self-employment.
How does this selection affect the wage growth of SE and SW workers? The‘average’ wage growth for each career path is9 ,
Ew2SE
Ew1SE
Ew2SW
gSW −SW =
Ew1SW
Ew2SE
gSW −SE =Ew1SW
gSE−SE =hi1 + δ 1/(1−α) αα/(1−α),(22)
hi1 − δ 1/(1−α) α1/(1−α)
hi1 + δ 1/(1−α) αα/(1−α)=,(23)
hi1 − δ 1/(1−α) α1/(1−α)
bSE hi1 + δ 1/(1−α) ((bSE /bSW )α)α/(1−α). (24)=bSW hi1 − δ 1/(1−α) ((bSE /bSW )α)1/(1−α)=

Interestingly, if the initial human capital is given, the wage profile of the
SE and the SW workers are identical since gSE−SE = gSW −SW . This growthrate decreases and converges to one as hi1 increases. This is because the time
devoted to human capital accumulation, ni1 , is decreasing in initial humancapital, hi1 . However what we observe is gSE−SE < gSW −SW because theSE worker’s initial human capital, hi1 , is higher than SW worker’s. Thus
the observed difference of the wage profile is the result of heterogeneity ofworkers in the initial human capital. The wage growth of the job changer ishigher than the stayers’ wage growth. The opportunity cost of human capital
investment is low while being a SW worker but the return of the accumulated
9
Although expected value of a ratio is not a ratio of expected values, this measure gives
us a rough idea.

15human capital is higher since he becomes a SE worker in the second period.
The low opportunity cost of the human capital investment and the highreturn for the accumulated human capital encourages the investment. Thus,
among SW workers, prospective job changers invest more in their humancapital compared with prospective job stayers.
Now, we continue our analysis using a numerical example. From the empirical findings in the previous section, we assume the variance of the wages ofself-employed workers is three times as large as the salaried workers’. The return for the human capital among self-employed workers is three times larger
than the salaried workers’ according to assumption 2. The learning parameteris chosen such that convexity of human capital production is satisfied. Since
we know little about the degree of risk aversion, the parameter of risk aversion
was chosen such that a plausible result can be obtained. The parameters are22
assumed to be α = 0.3, γ = 15, bSE = 3, bSW = 1, σSE= 3, σSW= 1, δ = 0.9.

The simulation result appears in figure 2 to 4. It is worth noting that theabsolute value of the indirect utility does not mean anything. Only the ordermatters. From figure 2, we see that the worker with low human capital in
the first period selects the career path of SW - SW. The worker with highhuman capital chooses the career path of SE - SE. The worker with medium
level of the initial human capital chooses the career path of SW - SE.
In figure 3 the wage growth of the job stayer is drawn. As discussed before,
although the wage growth of SE workers and SW workers are the same foreach level of human capital, what we observe is the high wage growth for SW
16

workers and the low wage growth for SE workers. However this observation
is simply because of the worker’s heterogeneity of the initial human capital.
In figure 4 the wage growth of career changer is drawn. We can confirm thewage growth of the career changer is higher than the stayer’s.

4

Supporting evidence of the model

4.1

SE workers have higher human capital

The theory discussed in the previous section predicts that the worker withhigher human capital selects self-employment. With respect to the observable characteristics, several studies observe that the worker with high education is more likely to be self-employed (Borjas and Bronars (1989), Evansand Leighton (1989)). Also Bates (1990) reports that the high educational
attainment of an entrepreneur is the critical determinant of small businesslongevity.
Borjas and Bronars (1989) observed the positive selection into SE amongwhite males based on unobservable heterogeneity when they estimated wage
equation with Heckman style selection correction assuming bivariate normal
error term. The reduction of the SE premium in the fixed effect estimation
relative to the SE premium in the OLS estimation in our empirical analysis
also suggests positive correlation of (unobserved) individual heterogeneity
and self-employment status.
It is a stylized fact that the worker who has a self-employed father is more17

likely to be a SE worker even after controlling for the inheritance10 (Lindh
and Ohlsson (1996) Blanchflower and Oswald (1998), Hout and Rosen (1999)
and Dunn and Holtz-Eakin (2000)).
Among the studies, Dunn and Holtz-Eakin (2000) emphasize the importance of the intergenerational transmission of human capital rather than the
mitigated liquidity constraint to explain this finding, since they found verylarge effect of the parent’s self-employment status on the son’s selection into
self-employment even after controlling the amount of parent’s asset. They
also found that the son of a successful self-employed worker is likely to be
self-employed. From this finding, they conclude that the transmission of human capital is the important channel to explain intergenerational correlationof self-employment status. In addition, they did not find a stronger intergenerational correlation of occupation among self-employed workers. Thus, theyspeculate, the human capital that is transferred from the parents to theirson is non-occupational specific human capital. Although their findings may
imply the transmission of human capital that is specific to the SE, the theoretical discussion made in this paper still holds since the worker with ‘anykind of’ higher human capital experience lower wage growth. These results
support the prediction of our model; the self-employed workers experiencelower wage growth because of higher initial human capital.
The model also predicts that some of the workers plan to be self-employed10

By controlling inheritance, the researchers try to partial out the effect of liquidity
constraint.

18

in the middle of their career. Several studies show that probability to be selfemployed is an increasing function of age (Borjas and Bronars (1989), Evansand Leighton (1989), and Schiller and Crewson (1997)). This finding is a very
robust finding that is observed in any empirics to explain SE status. The
workers who plan to be SE in the future prepares for the time by acquiring
skill through OJT in the firm, thus when the worker become SE the worker
is already well prepared and does not have strong incentive to acquire moreskill due to high opportunity cost resulting from high human capital.
As a bottom line, several empirical studies support the prediction of themodel; the worker with the higher human capital is more likely to be selfemployed.
Also the model predicts that the planned job changers accumulate morehuman capital while they are a salaried worker compare with the othersalaried workers who plan to stay11 . Lazear’s model does not predict thissince the wage profile of salaried worker is identical regardless of future
plan12 . We can test this prediction and use the result of this test as supporting evidence for the model. The prediction is tested using the following
econometric model.
ln wit = Xit β0 + β1 f selfit + β2 expit f selfit + β3 exp2it f selfit
11

Remember, (18) shows the planned job changer devotes more time in human capital
accumulation relative to the stayers. Also the planned job changer has higher humancapital compared with the planned job stayer.
12
If the employer predicts the worker’s quit in the near future, the employer may offera steeper profile to extract the worker’s effort. However this explanation is rather tricky,
since the employer who notices the worker’s plan to quit can fire the worker immediately
to prevent him from shirking before he quits.

19

+β4 tenit f selfit + β5 tenit2 f selfit + ci + uit ,(25)

where the dummy variable f selfit is an indicator which takes one if theworker will be self-employed in the future at time t13 . This model is estimated by OLS and fixed effect using the sample of salaried workers under
the assumption
E[uit |ci , Xi. , expi. , f selfi. , selfi. = 0] = 0.
The null hypothesis that we are interested in is
H0 : β2 = 0,
againstH1 : β2 > 0.
If the null is rejected, it imply that the prospective job changer accumulate
more human capital through OJT.
The regression results are in Table 2. For both OLS and fixed effect,
the return to experience is 20%-50%higher for the prospective self-employedworker. The return to tenure is the same for the prospective self-employedworkers and stayers. If we interpret the return to experience as the returnfor general human capital, this result is consistent with the prediction of
the model. The workers who plan to be SE in the future try to accumulate
general human capital before embarking upon a dangerous undertaking.
13

Here we assume the perfect foresight as in the theoretical model. If we assume therational expectation model, the estimated coefficient is subject to the attenuation bias. In
this case we are estimating the lower bound of the effect.

20

4.2

Both winner and loser select SE?

The model predicts a very simple selection rule; the worker with high humancapital selects SE. A sensible criticism for this prediction is that there are
two kinds of SE workers. The first kind is an eligible entrepreneur and thesecond kind is the SE worker who is not qualified to work for the firm andforced to work by himself. If this story describes the real world, it is not
surprising that the latter group experience less wage growth since the lesseligible worker has less learning ability and experiences less wage growth.
Could we observe this kind of ‘two tail selection rule’ among SE workers?
To examine this possibility, we study the distribution of ability among
self-employed and wage-salary workers. If there are ‘two tail selection rule’among SE workers, we should find bimodal distribution of ability among SE
workers that have two peaks at high and low ability. As a proxy for the ability
we use AFQT89 (Armed Force Qualifying Test) score that is contained in
NLSY 79. The result of kernel density estimation of the distribution of testscore for the SE and SW workers appears in figure 5. Comparing two panels,
we find bimodal distribution among SW workers rather than SE workers.
The workers with high scores and low scores select SW. The distribution ofability among SE workers is rather unimodal. Although it is not clear why
the distribution of ability among SW workers is bimodal, this evidence showsthat ‘two tail selection rule’ among SE workers are unlikely.

21

5Conclusion

In this paper the human capital accumulation by self-employed (SE) andsalaried and wage (SW) workers was analyzed. Under the assumptions thatthe wages of SE workers are more volatile than salaried workers’ and thewages of SE workers more sharply reflect their human capital, SE workers
invest less in their human capital because of their higher initial human capital. This difference in human capital investment behavior results in the
flatter wage profile for SE than SW workers. This theory was indirectly
supported by the empirical facts about self-employed workers.
The model shows that the self-employed workers are not necessarily agood ‘control’ group to test the Lazear contract, since not only the incentive
effect of the Lazear contract produces the steeper wage profile of salaried
workers, the difference of human capital investment does as well. This conclusion does not deny the existence of the Lazear contract, nor the result of
Lazear and Moore (1984). However simply attributing the difference of wage
profiles to the incentive effect of the Lazear contract may overestimate theimportance of the Lazear contract.
A more direct test of this theory, such as the estimation of human capital
investment function, is left for future research.

22

References
Bates, Timothy, 1990. Entrepreneur human capital inputs and small businesslongevity. Review of Economics and Statistics, Vol. 72(4), pp. 551–559.
Blanchflower, David G. and Oswald, Andrew J., 1998. What makes an entrepreneur? Journal of Labor Economics, Vol. 16(1), pp. 26–60.
Borjas, George J. and Bronars, Stephen G., 1989. Consumer discriminationand self-employment. Journal of Political Economy, Vol. 97(3), pp. 581–
605.
Carrington, William J., McCue, Kristin, and Pierce, Brooks, 1996. The roleof employer/employee interactions in labor market cycles: Evidence fromthe self-employed. Journal of Labor Economics, Vol. 14(4), pp. 571–602.
Cressy, Robert, 2000. Credit rationing or entrepreneurial risk aversion? analternative explanation for the Evans and Jovanovic finding. Economics
Letters, Vol. 66, pp. 235–240.
Dunn, Thamas and Holtz-Eakin, Douglas, 2000. Financial capital, humancapital, and the transition to self-employment: Evidence from intergenerational links. Journal of Labor Economics, Vol. 18(2), pp. 282–305.
Evans, David S. and Leighton, Linda S., 1989. Some empirical aspects ofentrepreneurship. American Economic Review, Vol. 79(3), pp. 519–535.

23

Fairlie, Robert W. and Meyer, Bruce D., 1996.

Ethnic and racial self-

employment differences and possible explanations. Journal of Human Resources, Vol. 31(4), pp. 757–793.
Hout, Michael and Rosen, Harvey S. Self-employment, family background,and race. Working paper 7433, NBER, 1999.
Joulfaian, David and Rider, Mark, 1998. Differential taxation and tax evasion
by small business. National Tax Journal, Vol. 51(4), pp. 675–687.
Kanbur, S. M. Ravi, 1982. Entrepreneurial risk taking, inequality, and public
policy: An application of inequality decomposition analysis to the generalequilibrium effects of progressive taxation. Journal of Political Economy,
Vol. 90(1), pp. 1–21.
Kihlstrom, Richard E. and Laffont, Jean-Jacques, 1979. A general equilibrium entrepreneurial theory of firm formation besed on risk aversion.
Journal of Political Economy, Vol. 84(4), pp. 719–748.
Lazear, Edward P., 1979. Why is there mandatory retirement? Journal of
Political Economy, Vol. 87(6), pp. 1261–1284.
Lazear, Edward P., 1981. Agency, earning profiles, productivity, and hour
restrictions. American Economic Review, Vol. 71(4), pp. 606–620.
Lazear, Edward P. and Moore, Robert L., 1984. Incentives, productivity, andlabor contracts. Quarterly Journal of Economics, Vol. 99, pp. 275–295.
24

Lindh, Thomas and Ohlsson, Henry, 1996. Self-employment and windfall
gains: Evidence from the swedish lottery. Economic Journal, Vol. 106,
pp. 1515–1526.
Lucas, Robert E., 1988. On the mechanics of economic development. Journalof Monetary Economics, Vol. 22(1), pp. 3–42.
Schiller, Bradley R. and Crewson, Philip E., 1997. Entrepreneurial origins:
A longitudinal inquiry. Economic Inquiry, Vol. 35, pp. 523–531.

25

Table 1 The replication of the Lazear and Moore (1984)’s finding andthe risk of self-employed workers.

Method ofestimation
Dependent variableeducation
experience
experience2
tenuretenure2
self-employed
self*educself*exper
self*exper2
self*tenure
self*tenure2
Constant
Observations
Number of ID
R2
F statistics(p-value)
Note:
1.
2.
3.
4.

(1)
OLS
ln wage
0.070(0.003)0.063(0.005)-0.001(0.000)0.052(0.004)-0.002(0.000)0.438(0.173)-0.007(0.011)-0.043(0.020)0.002(0.001)-0.054(0.016)0.002(0.001)
5.566(0.058)
23887
0.31

(2)
Fixed
Effectln wage
0.092(0.007)0.116(0.008)-0.002(0.000)0.032(0.003)-0.002(0.000)0.235(0.092)0.011(0.006)-0.047(0.012)0.002(0.000)-0.031(0.009)0.002(0.001)
23887
2715
-

(3)
OLS

(4)
OLS

residual2of (2)

residual2of (2)
0.015(0.005)0.002(0.008)0.000(0.000)-0.026(0.006)0.001(0.000)0.058(0.214)0.004(0.013)0.018(0.021)-0.001(0.001)0.019(0.019)0.000(0.001)0.014(0.088)23887
22.35(0.000)0.237(0.041)0.147(0.009)
23887
-

(5)
Fixed
Effectresidual2of (2)

0.189(0.038)

23887
2715
-

(6)
Fixed
Effectresidual2of (2)
0.000(0.018)-0.023(0.021)0.000(0.001)-0.010(0.007)0.001(0.001)-0.095(0.242)0.022(0.015)0.001(0.030)0.000(0.001)-0.008(0.023)0.000(0.002)
23887
2715
10.13
(0.000)Standard errors are in parenthesis for coefficient estimates, the p-value is in parenthesis for the Fstatistics. For OLS estimates, standard errors and F statistics are corrected for the panel clustering.
Dependent variable in the each regression (3) – (6) is the squared idiosyncratic residual of
regression (2).
F statistics are for the null hypothesis that the idiosyncratic variance of wage of self-employedworkers is same as salaried workers’.
Time dummies are included but coefficients not reported.

Table 2 Wage determination of salaried worker and future self-employment.

education
experience
experience2
tenuretenure2
future self
fself*educfself*exp
fself*exp2
fself*tenfself*ten2
Constant
Observations
Number of ID
R-squared(1)
ln wageOLS
0.070(0.003)0.063(0.006)-0.001(0.000)0.054(0.005)-0.003(0.000)0.143(0.090)-0.019(0.006)0.033(0.013)-0.002(0.001)0.000(0.012)0.000(0.001)
5.497(0.057)
20301
0.32

(2)
ln wage
Fixed-Effect
0.102(0.007)0.116(0.009)-0.002(0.000)0.032(0.003)-0.002(0.000)0.032(0.071)-0.008(0.005)0.021(0.010)-0.001(0.001)0.001(0.009)0.000(0.001)
20301
2648
-

Note:
1. Standard errors are in parenthesis.
2. All the samples are salaried or wage workers.
3. future self (fself) =1 if the worker is self-employed in the future. Mean of thisvariable is 0.162.
4. Time dummies are included but coefficients not reported.

Figure 1
Life time utility of each career path and initial human capitalLife time utility

SE - SE (Vss)SW - SE (Ves)
SW - SW (Vee)

Initial human capital(Weak risk aversion, low gamma)

Life time utility
SE - SE (Vss)SW - SE (Ves)
SW - SW (Vee)
Initial human capital(Strong risk aversion, high gamma)

Note:
SE: Self-Employed workers.
SW: Salary and Wage workers.

Figure 2
Life time utility of each career path and initial human capital(Numerical Example)v

Vss

Initial humancapital andcareer path

Ves

20

15

Vee

10

5

h_1
6

7

8

9

Figure 3
Wage growth of job stayers and initial human capital(Numerical example)gWage growthof jobstayer

1.35
1.3
1.25
1.2
1.15

Gee=Gss

1.1
1.05
h_1

Figure 4
Wage growth of job changer and initial human capital(Numericalexample)
6

g

7

8

9

Wage growthof job changer

2.5

2.4

2.3

2.2

2.1

h_1
6

7

8

9

Ges

Figure 5 Distribution of test scores among SW workers

Density.011115.001984-5percentile of test score

105

Note: AFQT89 is used as a test score. Bandwidth = 6 and Epanechnikov kernel was used to estimate thekernel density. The distribution of percentile ranges from –5 to 105 because of the bandwidth = 6, actual
distribution of test score ranges from 1 to 99.

Figure 6 Distribution of test scores among SE workers

Density.011556.001942-5

Note: Same note applies as figure 5.

percentile of test score105