Earnings And The Value Of A Canadian
University Degree
James McIntosh
Economics Department
Concordia University
1455 De Maisonneuve Blvd. W.
Montreal Quebec, H3G 1M8, Canada.
Danish National Institute of Social Research
Herluf Trolles Gade 11
DK-1052 Copenhagen K, Denmark
February 16, 2009
E-mail Addresses and Telephone Numbers: jamesm@vax2.concordia.ca.
514 848 2424 3910.
Keywords: Canada, Earnings functions, Mincer equations, Ability, and Unobservable Heterogeneity.
JEL Classification Numbers: J24, J30.
Abstract
Using methods which deal with unobserved worker characteristics I am able
to identify three distinct earnings groups of fully employed Canadian males who
were included in the 1973 and 1997 Survey of Consumer Finances. While mean
real earnings exhibit an increase of 5.4% over this period my results show that
the two survey years are rather different in terms of the composition of ability
or skill groups. In 1997 the high earners, the superstars who had earned much
more than the other two types in 1973, had disappeared and were replaced by
a low income group. In 1997 this group, which made up 22.3% of the sample,
was earning 22.8% less than average. The present value of earnings over the
ages 25-60 also declined for all three groups so that in terms of remuneration
the value of a university degree is less in 1997 than it was in 1973. Employment
rates have also fallen for this group of elite workers so the value of a Canadian
university degree has unambiguously declined over this period.
1
Introduction
The university system in Canada has expanded dramatically in the last half
of the twentieth century. More specifically, data from the Survey of Consumer
Finances shows that in 1973 12.6% of males aged 25-34 had a university degree.
By 1997 this figure had increased to 17.7%. Results from the 2002 Survey of
Approaches to Educational Planning described in Shipley et al (2003, p. 8)
1
indicate that this trend will continue since a majority of parents, 61%, with
children in secondary school wanted them to go to university. While most
Canadians are enthusiastic about the success of Canadian higher education and
appreciate the increased access to universities, a comprehensive and objective
assessment of the real contributions of the expansion of university system has
yet to be made. To contribute to our understanding of this issue I examine
an aspect of university graduates’ labour market performance. The question
that this research addresses is how the earnings of male university graduates
have evolved as the number of university degree holders has increased over this
twenty-four year period1 .
Knowing what a university degree is worth is essential for both rational individual decision making and government policy making. For Canada much of the
research on earnings has been comparative and has concentrated on earnings
differentials across educational categories so this topic has not been fully investigated. There are some results, however, on how real earnings have changed
over the last twenty-five years. For the period 1980-2000 Chung (2006) reports
a slight increase in average real weekly earnings for degree holders in the 25-54
age group working full time but a 5% reduction in their full-time paid employment. It would, therefore, appear that recent male graduates have not suffered
any decline in real earnings. However, as will be seen, this apparent absence of a
significant downward trend in average real earnings over all employees masks a
serious reduction in the earnings of many degree holders. Using methods which
deal with unobserved worker characteristics I am able to identify three distinct
groups of individuals who were included in the Survey of Consumer Finances
for 1973 and 1997. These groups appear in different proportions in the two
surveys with the emergence of a low income group in the 1997 survey. Comparisons across the two surveys reveal lower discounted present values for all three
groups in 1997. Employment rates have also fallen for university graduates over
this period. Thus, some of the problems that researchers in the economics and
sociology of education have noted may be having an impact on the earnings of
university graduates.2 .
1 This study only deals with males. Preliminary investigations suggested that females
needed to be treated separately. For example, females experienced increases in both real
weekly earnings and employmnet rates over this period!
It also concentrates on the top end of the labour market, those workes who earn more than
the minimum wage and have full time jobs.
2 Côté and Allahar (2007) in their monograph on Canadian universities write on page 54
“Being able to play the system to make your way through university may be good training for
some jobs that do not require integrity, but it is not beneficial for jobs that require the ability
to manage one’s time and motivate oneself to complete tasks honestly and responsibly. The
attendance and effort of many university students would get them fired if they were in the
labour force; in many universities sporadic attendance and minimal effort often have little or
no consequences in grades. ..... At the same time we all know that many students are slipping
through our courses with minimal learning and skills mastery, ....The wrong signals are being
sent to employers about the quality of some of our university graduates, and policy makers are
misled about the value added by the surplus of university credentials. Put another way, we
may not be producing the level and quality of human capital that employers and governments
think we are.”
2
In this study earnings functions are estimated using data from the two surveys mentioned above. The dependent variable is the natural logarithm of total
annual income from all sources. Only those males earning more than ten thousand real (2002) dollars per year and worked a full year were included in each
sample. The explanatory variables included were an age variable, type of residential area, province, and mother tongue. The data is described in section 4.
The rest of the paper is organized in the following way. Section 2 reviews the
relevant economic theory and Canadian empirical work. The data is described
in section 3. Section 4 outlines the statistical models employed in the analysis
and the paper ends with a discussion of the results.
2
A Brief Review of the Theoretical and Canadian Empirical Literature
How one views earnings functions depends on the assumptions made about
educational decision making. There are several issues in this area that need to
be examined. In earnings functions, like Mincer equations for example, are the
schooling and experience variables endogenous or exogenous?
The simplest way to examine these issues is to formulate a reasonable model
of individual educational decision making. Here reasonableness means that the
model be forward looking and sequential, taking into account the fact that
current decisions have future consequences which are uncertain.
To be specific, some notation and assumptions are required. Let St be the
number of years of school that an individual has acquired by the beginning of
year t, and dt be a decision variable that takes the value 1 if the individual decides to do an additional year of schooling and 0 otherwise. The cost of staying
in school in year t is h(St , a). Following in the tradition of Spence (1973), education costs vary inversely with ability, a and I assume that costs increase with
the amount of schooling. Individuals in school earn no income and are assumed
to make education decisions which maximize the present value of discounted
expected earnings. They have an economic life span of T (t), T 0 < 0, years.
In this highly stylized model anyone who decides not to continue in school in
year t immediately starts working and earns y(St , 0, a, ut ) in year t and works
full time until t + T (t) − St and is never unemployed. The zero in y() refers
to the initial level of experience. ut is a random and is known before the year
t decision is taken. In keeping with the Spence view, those with more ability
will earn more so that y() is increasing in ability. To keep the model relatively
simple it is assumed that only complete years are considered, everyone starts
school at age zero, those who leave school can never return, and all additions to
human capital after the cessation of school are determined exogenously.
Letting Ωt be the information set at the beginning of year t the value function
3
for the Bellman equation given by
V (St , ut ) =
M ax [dt {−h(St , a) + δE[V (St + dt , ut+1 )|Ωt , dt = 1]}
dt ∈{0,1}
T (t)−St
+ (1 − dt ){
Σ
j=0
δ j E[y(St , j, a, ut+j )|Ωt , dt = 0]}]
(1)
where δ = 1/(1 + r) and r is the individual’s discount rate.
The first term in the value function is the value of continuing one more year
in school and the second term gives the present expected discounted value of
earnings if the individual ceases school and enters the work force at the beginning
of year t. The decision to continue in school in year t will be determined by
comparing the two parts of V (St , ut ). If the first part is larger than the second
then the individual will continue in school leaving the decision the leave school
to year t + 1, otherwise he or she will leave school and start working. Clearly
St+1 = St + dt
dt = {0, 1}
(2)
and completed schooling is
t∗
St∗ = Σ dt
t=0
(3)
and t∗ is the year in which the individual decided to finish school and start
working.
This model is quite well known. It is a version of the Mare (1980) grade
transition model whose properties are discussed in great detail by Cameron and
Heckman (1998) and Heckman et al (2006, p. 342-358). Dynamic models of
earnings and together with various forms of human capital formation, educational, and occupational choice have also been estimated by a number of authors.
A review of this literature may be found in Belzil (2006).
The model has a number of features which inform researchers about the way
earnings functions should be estimated. First, St∗ depends on {(us , Ωs ) s ≤ t∗ },
the potential earnings profiles, and, of course, ability. Hence, it is determined in
a way which is much more complex than that suggested by static models, like
those reviewed in Card (1999), for example, that are commonly employed to
explain earnings. Secondly, it is clear from the structure of the model that the
estimation of the parameters in the earnings function that St∗ and the amount of
experience that the individual has accumulated should be treated as exogenous
variables. They are determined prior to the time that earnings are observed3 .
This feature of the model will allow earnings functions to estimated for separate educational categories, such as determined by the number completed years
of schooling, without generating any selection problems. It is only when researchers are interested in the impact of the level education or the number of
3 Belzil (2006, p.7) makes this point in his 5th footnote where he says ‘Technically speaking,
the term ”endogeneity” used in the empirical literature abuses the true meaning of endogeneity.
In cross-section data wages are usually measured much beyond the time when schooling is
completed. Because returning to school is rarely observed, schooling may be therefore be
viewed as predetermined. It is only the correlation between schooling and unobserved skills
that is problematic’
4
completed years of schooling on earnings that the traditional unobserved ability
bias problem needs to be addressed.
With these theoretical perspectives in mind I now turn to a brief summary of
the literature that examines the earnings of Canadians. Most of the Canadian
research focuses on the size of the ‘wage premium’ paid to university graduates.
This issue is examined in by Bar-Or et al (1995), Burbidge et al (2002), Morissette et al (2004) and Boothby and Drewes (2006). For the period 1971-1991
the first authors find a ‘U ’ shaped university premium for males which has a
larger value at the beginning of the period. For females no clear results are obtained. These results are largely based on the data using graphical procedures
although some of their results are obtained by regression methods. The next two
papers fit Mincer type earnings functions and find a more or less constant wage
premium over the period 1980-2000. Both of these papers consider various subpopulations like age groups, gender, or field or occupational category. None of
these papers consider the problems that can arise when there are unobservable
characteristics that affect earnings.
In an important paper Green and Riddell (2003) fit Mincer equations augmented with some family background variables and a literacy test score for the
respondent. They find, that as a measure of cognitive skills, it has a significant
effect on earnings and this confirms the results that Osberg (2000) found. It also
demonstrates the importance of using procedures which deal with unobserved
ability. Unfortunately, as was shown in McIntosh and Munk (2007) including
test scores may not be sufficient to solve all of the problems that arise from the
presence of unobservable factors.
3
Data
The data used in this paper comes from the Survey of Consumer finances for the
years 1973 and 1997. 1997 was the last year that Statistics Canada administered
this survey. It was started in 1971 and was initially run every two years after
1980 it was run every year. 1973 was the first survey that had large enough
sample sizes for the analysis carried out here. Unfortunately, the surveys that
replaced the Survey of Consumer Finances, The Survey of Labour Income Dynamics and The General Social Survey, do not collect the data in the same way
making it problematic to make comparisons between the 1973 results and for
years later than 1997.4
The earnings measure is total income from all sources before taxes. Real
income was obtained by dividing this by the consumer price index (2002 = 100).
For the sample only males earning ten thousand 1997 dollars are included. Some
sample selection is required since some earnings are negative but the number
here is small being less than 1%. To analyze the most productive part of the
4 There is data from the SLID for 1997 but it gives mean real earnings which are 25% higher
than the SCF earnings data for the same year. It is, therefore, difficult to distinguish changes
that arise as consequences of labour market behaviour from those that are due to differences
in survey design.
5
labour force I chose only those who were employed all year and had significant
earnings. The lower limit of ten thousand dollars was chosen since this is a good
approximation of the earnings of an individual who earns the minimum wage.
The selection problems that arise because of the lower bound on income are
dealt with by using truncated distributions.
Real earnings by age and year are displayed in Table 1 by 5 year intervals.
The surveys also contain information on province of residence, size of the urban
community in which the respondent resided and mother tongue. These variables
are represented by sets of dummy variables and are used as regressors in all of
the models. The employment rate is also shown. This is sometimes equal to 1
because of the small sample sizes in the 1973 survey. This is the proportion of
university graduates who in full time employment. Mean earnings for each educational category are displayed in Table 1 as are the shares of each educational
category. Only males aged 25-60 are included in the sample and the averages
are taken over these ages.
4
Statistical Models
Real earnings for individual i depend on his educational qualifications as well as
his ability which is represented by the variable ai . A model that is much more
general than the established Mincer equation is described by the equation
ln(yi ) = Xi γ + α0 (ai ) + α1 (ai )zi + α2 (ai )zi2 +
(4)
where the variable zi is (Agei − 24) and the functions α0 (ai ), α1 (ai ), and
α2 (ai )depend on the level of educational attainment. This variable, zi , plays
the role of experience in the model. While there was no data on actual work
experience or the age when the agent started full time work, all the agents that
are being examined here have a university degree and reported as having worked
for at least 48 weeks in the year prior to the interview. Consequently, zi will be
highly correlated with actual work experience. The idea here is that ability and
education interact differently at each level of educational attainment so that
there is a version of equation (4) with its own specific set of {aj (ai ), j = 0, 1, 2}
for each level of education. Furthermore, ability has an age or experience specific
effect on real earnings.
Turning now to the question of how the parameters in equation (4) should be
estimated, the first point to note is that since the focus of interest is on the value
of a university degree only the earnings equation for university graduates will
be estimated. As was pointed out in section 2 it is possible to estimate earnings
functions for university graduates as a separate group without encountering any
biases due to this selection process because, with respect earnings, the level of
education is exogenous.
The question that remains to be answered is how to deal with the unobservable ability variable, ai . One procedure that can be used to deal with its effects
is to follow Heckman and Singer (1984) and assume that ai takes on a finite
number of values {ai = a1 , a2 , ....aL } where Pr{ai = a , = 1, 2...L} = p and
6
P
p = 1. This means that there are a finite number of ability types and their
earnings functions have means
µi = Xi γ + α0 + α1 zi + α2 zi2
(5)
if individual i is of type . This leads to a model which is a generalization of the
Heckman-Singer (1984) procedure and belongs the latent class models discussed
by Wedel et al (1993) and Deb and Trivedi (1997).
This means that a type worker has a specific response to his educational
attainment and age which depends on his individual characteristics. Those with
more ability can be expected get more out of their educational qualifications and
experience. The term Xi γ represents other characteristics of the individual:
province, mother tongue, and urbanization dummies.
While it is not possible to assign a type to each individual the procedure
assumes that individual i will be of type with probability p .These probabilities
can then be estimated along with the type parameters by maximizing the sample
likelihood function whose natural logarithm is
ln(L) =
N
P
i=1
ln[
L
P
p{
=1
φ(ln(yi ), µi , σ )
_
}]
1 − Φ(ln( y), µi , σ )
(6)
where L and N are the number of types and the sample
size, respectively and
_
density
functions,
Φ(ln(
y),
µ
,
φ(ln(yi ), µi , σ ) are normal
i σ ) is the cumulative
_
normal distribution, and y is 10,000.
The choice of the number of mixtures to apply is an empirical issue to be
determined by criteria involving the value of the maximized likelihood together
with the number of parameters. The appropriate model to be selected is determined by the data in Table 4. The first line contains the value of the maximized
likelihood function using a single truncated distribution with no covariates except a constant term and a variance parameter. This serves as a baseline which
can be used to compare other models and to construct a pseudo-R2 for each
model. Additional mixtures were added until there was no significant increase
in the penalized likelihood function or until one of the probabilities converged
to zero. For both surveys 3 mixtures were all that could be estimated.
5
Results and Discussion
Maximum likelihood estimates for the parameters of interest for two surveys
are displayed in Tables 2 and 3 for each mixture distribution. Age profiles are
significantly concave for all types in each survey and the parameters associated
with z and z 2 are highly significant for all types in each survey. Types differ
significantly by at least one estimated coefficient and there are significant differences in the estimates of the standard deviations across the three types in each
survey. The estimates for the parameters associated with the province or the
size of the locality in which the individual lived, the respondent’s mother tongue
are not included since they are of no particular interest and their inclusion would
make the tables reasons already mentioned.
7
In each survey there are three distinct ability types. It is clear from Table 4
that the increases in the ln-likelihood function justify the increase in the number
of mixing distributions5 . For the data the process stopped at three for each
survey because the probability of the fourth mixture converged to zero when a
four mixture model was estimated or the procedure would not converge when
four mixture models were being estimated. The reason for this is that the four
mixture latent class model appears not to be identified. There may, in fact, be
more than three ability types but the data is not rich enough to identify them.
The ln-likelihood values in Table 4 also generate the psuedo-R2 statistics. The
model explains much more of the variation in the data in 1973 than in 1997 but
given the type of data that is being examined here the models do an acceptable
job of explaining it.
In Table 5 predicted average earnings profiles for all three types are displayed
for university graduates for each of the two surveys. Because of the truncation
in the distributions these are computed as
_
yb = exp[µ + σ {
φ(ln( y), µ )
_
}]
1 − Φ(ln( y), µ )
(7)
Looking first at the 1973 data, of the three types, type 2 and type 3 are very
similar. For this survey the increase in the ln-likelihood function that results
when the third type is added is significant but quite small. Type 1, on the
other hand, earns much more than the other two. It is for this reason that the
individuals in this category are referred to as superstars and by age sixty earn
two and a half times what the other groups earn. Superstars make up 6.8% of
the sample.
For the 1997 there are two groups which earn a little more than average
earnings. There there are no earnings superstars; instead a low income group
has emerged. They are much more numerous than the 1973 superstars and earn
22.8% less than average earnings. They make up 22.3% of the sample.
This is a significant decline but it represents at best a lower bound on the
extent of the devaluation of university education. The situation could actually
be worse. This study focuses on only those who were lucky enough to have
found employment for the full year. Some university graduates are either not
employed for fifty-two weeks or make less than ten thousand dollars per year.
In 1997 the 19.1% of all males aged 25-60 in the survey were excluded because
they did not meet either the employment or the income constraint. This is a
substantial increase over the corresponding rate of 10.1% for the 1973 data.
Finally, a caveat is in order. The discussion about types has focused on a
rather abstract notion which I have referred to as ability or skill. In reality
this is a euphemism for a much broader set of excluded characteristics, some of
which are more observable and concrete than others. One important individual
characteristic in earnings determination is the specific type of university degree
5 Likelihood ratio tests confirm this. It should be noted that this procedure is legitimate
contrary to the clain of Deb and Trivedi (1997), since the null hypothesis does not involve the
boundary of the parameter space.
8
that the individual has obtained. Science, engineering and business degrees are
now more likely to produce higher earnings profiles than those for historians
or sociologists. Hence one of the reasons why earnings could have deteriorated
is because these differentials are of recent origin or because the expansion of
the educational system has favoured these social science and humanities programmes over more technical subjects. Of course, as many economists believe,
the choice of degree programme is not unrelated to ability in its more abstract
sense so that the deterioration in the quality of those pursuing a university degree which Côté and Allahar (2007) mention may also be related to the recent
degree choices that have been made.
When larger proportions of high school graduates attend universities it is
very reasonable to expect that the upper tail of the ability distribution from
which this population has been drawn has increased and that the average ability
of university graduates has declined. While the plausibility of this conjecture
is not in question further and more detailed research is needed to confirm this.
The large number of components in the error terms suggests that there are many
other potential contributors to individual earnings and to put most of the blame
on the university system is perhaps premature.
References
[1] Bar-Or, Yuval, John Burbidge, Lonnie Magee, and A. Leslie Robb (1995),
“The Wage Premium to a University Education in Canada.” Journal of
Labor Economics, 13, 762-794.
[2] Belzil, Christian (2006). “ The Return to Schooling in Structural Dynamic
models”. IZA Working Paper #2370.
[3] –––––– (2007) “Testing the Specification of the Mincer Equation”.
IZA Working Paper #2650. To appear in The European Economic Review.
[4] Belzil, Christian and Jörgen Hansen (2005). “A Structural Analysis of
the Correlated Random Coefficient Wage Regression”. IZA Working Paper #1585. To appear in The Journal of Econometrics.
[5] Boothby, Daniel and Torben Drewes (2006). “Post-Secondary Education in
Canada: Returns to University, College, and Trades Education.” Canadian
Public Policy, XXXII, 1-21.
[6] Burbidge, John, Lonnie Magee, and A. Leslie Robb (2002). “The Education
Premium in Canada and the United States”. Canadian Public Policy, 28,
203-217.
[7] Cameron, Stephen and James J. Heckman (1998). “Life Cycle Schooling
and Dynamic Selection Bias: Models and Evidence for Five Cohorts of
American Males” Journal of Political Economy 106, 262-333.
9
[8] Card, David (1999). “The Causal Effects of Education on Earnings.” Chapter 30 in Handbook of Labor Economics, Volume 3, Edited by Orley Ashenfelter and David Card. Elsevier Science.
[9] Chung, Lucy (2006). “Education and Earnings.” Perspectives on Labour
and Income, Statistics Canada, Autumn, 28-36.
[10] Côté James E., and Anton L. Allahar (2007). Ivory Tower Blues: A University System in Crisis. University of Toronto Press, Toronto.
[11] Deb, Partha and Trivedi, Pravin K. (1997). Demand for Medical Case by
the Elderly: a Finite Mixture Approach. Journal of Applied Econometrics
12: 313-336.
[12] Green, David A. and W. Craig Riddell (2003). “Literacy and Earnings:
An Investigation of the Interaction of cognitive and Unobserved Skills in
Earnings Generation.” Labour Economics, 10, 165-184.
[13] Heckman, James J., Lance J. Lochner, and Petra Todd (2006). “Earnings
Functions, Rates of Return, and Treatment Effects.” Chapter 7 in Handbook
of the Economics of Education, Volume I. Edited by Eric A. Hanushek and
Finis Welch. Elsevier Science.
[14] Heckman, James J. and Singer, B. (1984). A Method for Minimizing the
Impact of Distributional Assumptions in Econometric Models for Duration
Data. Econometrica 52: 271-320
[15] Mare, R. D. 1980. Social Background and School Continuation Decisions.
Journal of the American Statistical Association 75: 295-305
[16] Mas-Colell, Andreu, Michael D. Whinston, and Jerry R. Green (1995).
Microeconomic Theory. Oxford University Press, Oxford, U.K.
[17] McIntosh, James and Munk, Martin D. (2007). Scholastic Ability vs. Family
Background in Educational Success: Evidence form Danish Sample Survey
Data, Journal of Population Economics. 20 (1).
[18] Morissette, René, Yuri Ostrovski, and Garnett Picot (2004). “Relative
Wage Patterns Among the Highly Educated in a Knowledge-based Economy.” Paper 11F0019MIE No. 232 Business and Labour Market Analysis
Division, Statistics Canada.
[19] Sibley, Lisa, Sylvie Oullette, and Fernando Cartwright (2003). “Planning and Preparation: First Results from the Survey of Approaches
to Educational Planning (SAEP) 2002”. Paper 81-595-MIE2003010. Culture, Tourism, and the Centre for Education Statistics Division, Statistics
Canada.
[20] Spence, A Michael (1973). “Job Market Signalling” Quarterly Journal of
Economics, 87, 355-74
10
[21] Wedel, M., Desarbo, W.S., Bult, J.R. and Ramaswamy, V. (1993). “A
Latent Class Poisson Regression Model for Heterogeneous Count Data”
Journal of Applied Econometrics 8: 397-411.
11
Tables
Table 1
Real Earnings Profiles And Employment Rates For
University Graduates By Age.
Real
Employment
Real
Earnings
Rate
Earnings
Age
1973
Employment
Rate
1997
25
34479
0.623
39961
0.667
30
46225
0.941
43909
0.766
35
56208
0.930
62633
0.832
40
68539
1.000
72057
0.908
45
75487
0.929
68555
0.934
50
68367
0.913
61265
0.896
55
70398
0.944
84667
0.836
60
68765
0.857
57917
0.650
Average
60636
0.915
63952
0.821
Present Value
1239848
1128752
Sample Size
1133
2725
Table 2
Maximum Likelihood Parameter Estimates, 1973
Typ e
Typ e 1
Typ e 2
Typ e 3
Unmixed
α0 (a )
α1 (a )
α2 (a )
σ
10.247** (0.088)
10.452** (0.045)
10.163** (0.151)
10.326** (0.049)
0.090** (0.016)
0.056** (0.006)
0.080** (0.020)
0.063** (0.005)
-0.013** (0.005)
-0.012**(0.002)
-0.017** (0.006)
-0.013** (0.001)
0.121** (0.002)
0.256** (0.015)
0.664** (0.047)
0.400** (0.008)
p
0.068** (0.024)
0.676** (0.041)
0.256** (0.039)
1.0
Variable
Symb ol
Intercept
z
z
2
Notes: For this table and table 3
†, ∗, and ∗∗ indicate
significant at the 10, 5,
and 1 p ercent levels, resp ectively. Standard errors are in round brackets.
Table 3
Maximum Likelihood Parameter Estimates, 1997
Typ e
Typ e 1
Typ e 2
Typ e 3
Unmixed
10.615** (0.034)
10.414** (0.052)
9.471** (0.378)
10.361** (0.050)
0.051** (0.016)
0.048** (0.006)
0.142** (0.037)
0.057** (0.005)
Variable
Symbol
Intercept
z
z
2
α0 (a )
α1 (a )
α2 (a )
σ
p
-0.009** (0.001)
-0.007**(0.002)
-0.035** (0.010)
-0.012** (0.001)
0.051** (0.007)
0.395** (0.023)
0.907** (0.085)
0.518** (0.007)
0.110** (0.014)
0.666** (0.050)
0.224** (0.052)
1.0
12
Table 4
Model Selection Criteria
Number of
Distributions
Number of
Parameters
ln(L)
ln(L)
1
2
-739.501
-2215.966
1
18
-568.025
-2060.693
2
23
-528.132
-1902.445
3
28
-522.805
-1855.439
0.293
0.163
Psuedo- R
2
1973
1997
Table 5
Real Earnings Profiles For University Graduates
By Age, Type, and Year
Typ e 1
Age
Typ e 2
Typ e 3
Type 1
1973
Typ e 2
Typ e 3
1997
25
33478
39753
37281
44656
37266
23592
30
49645
49872
46334
54798
47041
36500
35
67411
57496
55473
66809
58816
49954
40
93035
67610
67416
75327
67903
59550
45
117814
73209
74796
74839
68672
58183
50
132210
70497
72604
78983
72938
53868
55
146372
67211
68207
78865
73422
43618
60
151303
61801
61306
72132
68419
30437
Share
0.068
0.676
0.256
0.110
0.666
0.223
Average Earnings
82921
59369
58158
70301
67150
49419
Present Value
1554000
1232000
1192000
1262394
1185738
894770
of Earnings
13