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Unformatted text preview: Human Capital II
Lecture 3, January 24, 2012 Announcements
• Sketch of the next several Friday classes:
– January 27: Review of Regression Analysis
• “Leftover” time available for Q&A r.e. term paper – February 3: Term Paper Session
• Andrea Williams, Lecturer in Writing Instruction – February 10: Term Paper Session
• Me: Miscellaneous (e.g., Peer Scholar, Q&A, etc.) – February 17: Term Paper Session
• Eveline Houtman, Coordinator of Library Instruction • Term Paper: First draft due Friday March 2, 10:00am.
– 5.5 weeks… 1 Review: Human Capital Earnings Function
• Last day we finished with the human capital earnings function, a simplified
version of which is given by: ln Wi = α + rSi + β1 x1i + β 2 x2 i + ... + β k xki + ε i
• Si is the number of years of schooling, a particular measure of human
capital, and r is the rate of return to a year of schooling (education).
• The xi are controls for other observable factors that may affect earnings
(e.g., age), while εi captures unobserved determinants of earnings.
• We can also specify richer models for various types of education and
human capital, as well as more flexible responses of earnings to education
(e.g., quadratics in Si).
• The return to education, r, is determined in the market for skilled workers,
and is a compensating differential, supported by higher productivity to
2 Review: The market return to human capital
• NB: Education must increase productivity.
Wage – Education Locus U2 I3 U1
3 Review: Investment in human capital
• Assume that an individual at age 18 is deciding between two options:
– Finish high school, then work from age 18 until retirement, earning income
– Finish high school, then attend university for four years (at a cost “d” per year),
then work from age 22 to retirement at age T, earning income stream “B.” • Further assumptions:
– The individual receives no direct utility or disutility from attending university;
Hours of work over the lifecycle are fixed;
The income streams associated with each choice are known with certainty;
Individuals can borrow and lend at the real interest rate, r. • Individual will choose the option that yields the highest Present Value
(PV): Costs and benefits may occur in different time periods. 4 A graphical Illustration
Earnings Income Stream B
Benefits Income Stream A
18 d 22 T Age
5 Review: The University Decision
• What is the PV of working after high school?
PV ( H ) = ∑
, τ = t − 18
(1 + r )τ t =22 (1 + r )τ
21 • And the PV of attending university:
PV (U ) = ∑
t =18 (1 + r )
t = 22 (1 + r )
21 • Choose whichever stream has the highest present value. 6 Review: Infinite horizon approximation
• For simplicity, assume that the income streams associated with higher and
lower levels of education are given by:
– No more education: Y
– One more year of education: Y + ΔY
• The marginal cost of one more year of education of education is therefore
• The marginal benefit is given by the higher earnings paid over one’s
lifetime, the PV of which we can approximate by:
Y + ΔY Y ΔY
• The optimal amount of education will satisfy MB = MC: ΔY
7 Review: infinite horizon approximation
• We also saw that this decision could be expressed in terms of setting the
internal rate of return of the investment in one more year of education, i,
equal to the opportunity cost of funds, r. ΔY
• This also gives us another way to see where the log earnings function
• If the direct costs of school are approximately negligible: r= ΔY
= d ln Y ,
Y d ln Y
d ln S ln Y = α + rS
8 Review: Signaling and Screening
• Education may serve a role as a signal, so that high ability (more
productive) workers can signal their otherwise unobservable productivity to
• Basic idea: Education conveys information about worker ability.
– As long as it is more costly for low ability workers to acquire education, then
education will be a useful signal to employers. • In a pooling equilibrium, all workers (irrespective of ability) are paid the
• In a separating equilibrium, only high ability workers acquire education,
and employers can distinguish between high and low ability workers
(paying them accordingly) 9 Outline for today
• How much does education increase earnings?
– Age-earnings profiles as a summary
Ability bias in OLS estimation of the returns to education
Addressing the problem of ability bias:
• Wald Estimator and “Natural Experiments” • The Rising Returns to Education (and skill)
• Boys versus girls
– Theoretical models: who pays for training?
– Government-sponsored training programs
• Program Evaluation 10 the returns to schooling, and attempting to evaluate the neoclassical human capital model.
Figure 9.4 shows age-earnings profiles for four educational categories of Canadian males: (a)
some elementary and high school but no high school diploma, (b) high school diploma (11 to
13 years of elementary and secondary schooling, depending on the province) but no further Age-Earnings Profiles2005
Earnings by Age and Education, Canadian Males, F IGURE 9.4 This graph shows the average earnings by age group
for different levels of education. For example, the lowest
line shows the relationship
between age and earnings
for those men who have not
completed their high school
education. Their earnings
generally increase with
age, as they accumulate
on-the-job experience. The
age-earnings profiles are
higher on average for those
men with more education,
being highest for university
graduates. 120,000 Annual earnings ($) 100,000
0 20–24 25–29 30–34 35–39 40–44 45–49 50–54 55–59 60–64
Less than high school
Some post secondary High school diploma
University Earnings by age and education, FYFT Canadian males, 2005 NOTES: 1. Earnings are average wage and salary income of full-year (49 plus weeks), mostly full-time (30 hours per week or more)
2. Education categories are defined as (1) less than high school—elementary school or high school, but no high school
diploma; (2) high school diploma—holds a high school diploma (11 to 13 years of high school, depending on the province) but no further schooling; (3) some post secondary—some post-secondary education, but not a university degree;
(4) university—at least a bachelor’s degree.
SOURCE: Data from Statistics Canada, Individual Public Use Microdata Files, 2006 Census of Population. 11 Regression-based estimates
• The return to education is typically estimated from a cross-section
regression of log earnings on years of schooling.
• In the absence of covariates, ln Yi = α + rSi + ε i
• The basic idea of the the procedure is illustrated graphically in the
– A sample of 35 year old women, drawn from the Canadian Census, 2005. 12 from this sample. While the regression function fits quite well, yielding a rate of return to
schooling of 11 percent per year, there is still considerable dispersion around this function.
On average, earnings rise with education, but there are plenty of examples of low-educated
women earning more than the higher-educated ones. These women may be the “anecdotes”
used by high school dropouts to justify their decisions, but it is clear that such women are
the minority. OLS Regression (Earnings Function)
This scatter plot shows
the relationship between
education and earnings for
a sample of 35- to 39-yearold women in 2005. Each
point represents a particular
woman, with her level of
education and annual
earnings. Also shown is
the estimated regression
line, which shows the level
of predicted earnings for
women with a given number
of years of schooling. While
most observations lie close
to the regression line, there
are obviously some women
whose earnings are higher
than predicted, and some
whose earnings are lower
than predicted. Log Earnings by Years of Schooling, Women aged 35 to 39 Years, 2005
Ln Y = 8.94 + 0.110S
10 Ln Y F IGURE 9.5 9
5 8 10 12 14 16 18 20 22 Years of Schooling
NOTES: This figure shows the log annual earnings-schooling pairs and the predicted log earnings from a regression of log earnings on the years of schooling. SOURCE: Data from Statistics Canada, Individual Public Use Microdata Files, 2006 Census of Population. 13 More conventionally
• Recognizing the accumulation of human capital over one’s lifetime through
work experience, the earnings function is augmented: ln Yi = α + rSi + β1EXPi + β 2 EXPi 2 + ε i
• Where EXP is a proxy for work experience, approximated by “Potential
Experience,” defined as: EXPi = Agei − Si − 5
• Results of this specification are shown in the following table, based on
(updated) data from the 2006 Census.
– The OLS estimated return to education for women is approximately 11% per
– The corresponding estimated return for men is about 8% per year. 14 Confirmi OLS Estimates of the returns to HC
CHAPTER 9: Human Capital Theory: Applications to Education and Training TABLE 9.2 Estimated Returns to Schooling and Experience, 2005
(dependent variable: log annual earnings)
Men Women Intercept 8.966 (734.91) 8.355 (628.57) Years of schooling 0.081 (114.46) 0.114 (145.33) Experience 0.054 (79.18) 0.043 (64.88) 2 0.0008 (59.85) 2 0.0006 (46.15) Experience squared
Sample size 0.148 0.210 126,725 98,115 NOTES: The regressions are estimated over the full samples of full-year (49 or more weeks worked in 2005), mostly full- time men and women, respectively. Absolute t-values are indicated in parentheses, with t-values greater than 2 generally
regarded as indicating that the relationship is statistically significant, and unlikely due to chance. SOURCE: Data from Statistics Canada, Individual Public Use Microdata Files, 2006 Census of Population. In summary, the most conventional approach to estimating the returns to schooling is
to estimate the human capital earnings function. The simplest, most common specification
replaces age with a quadratic function of potential experience: lnY 5 a 1 rS 1 b1 EXP 1 b2 EXP2 1 ε. But OLS may be biased
• In the empirical strategy adopted above, we imagine that individuals with
less schooling are otherwise identical to those with more schooling.
• In this way, people with different levels of education serve as
“counterfactuals”: what would happen (on average) if an individual had a
different level of education?
• The problem is, counterfactuals are not ever observed.
• And individuals choose the level of education that is best for them.
• As a result, people with different levels of education may not serve as
– “Selection Bias” • What happens if the chosen level of education depends on unobserved
– Ability bias
• While not exactly OLS, we can see the potential for ability bias with an
estimator that uses the same assumptions.
• An estimator of the regression slope is given by: β= Δ ln Y Δy
ΔS ˆ = yH − yL
SH − SL
• The true levels of earnings are given by: yHi = α + β SHi + ε Hi
yLi = α + β SLi + ε Li 17 Ability Bias
• We can express the estimator in terms of the true model, obtaining: yH − yL = Δy = β ( SH − SL ) + ( ε H − ε L )
ˆ = Δy = β ( SH − SL ) + ( ε H − ε L ) = β + ( ε H − ε L )
( SH − SL )
( SH − SL )
• The estimator will be unbiased if E [ ε H ] = E [ ε L ]
• But if this does not hold, the estimator will be biased:
E [ε H ] > E [ε L ] → E ⎡β ⎤ > β
E [ε H ] < E [ε L ] → E ⎡β ⎤ < β
18 Using Twins to Address Ability Bias
• By examining differences in outcomes between identical twins, we have a
(potential) way of accounting for genetic ability, as well as family
background in estimating the return to schooling.
• Label the twins 1, 2 and denote the true model as: y1i = α + β S1i + ε1i
y2 i = α + β S2 i + ε 2 i
• Now assume that we have a model for the unobservables: ε1i = λ F + v1i
ε 2 i = λ F + v2 i 19 Twin “Fixed-Effects”
• Now consider the difference in their education and earnings: y1i − y2 i = (α − α ) + β (S1i − S2 i ) + (ε1i − ε 2 i )
= β (S1i − S2 i ) − (λ F + v1i − λ F − v2 i )
= β (S1i − S2 i ) − (v1i − v2 i )
• The new error term has been purged of the “genetic ability” component.
• If that was the only problem, then we could use these within-twin
differences, and estimate the model by OLS.
– But errors of measurement are amplified;
– And why do twins get different levels of education? • Ashenfelter and Rouse (1998)
– Twinsburg, Ohio 20 The Wald Estimator
• A different set of strategies is based on “Instrumental Variables”, or its
simplified version, the “Wald Estimator.”
• Basic idea: exploit “natural experiments” and the resulting variation in
levels of education (or whatever “treatment” we are interested in).
• The Wald Estimator is based on partitioning the sample into two groups
(e.g., “1” and “2”).
• Consider the estimator:
βW = 1 2
S1 − S2
• Assume that the true model is given by: y1i = α + β S1i + ε1i
y2 i = α + β S2 i + ε 2 i
21 Conditions for the Wald Estimator
• The numerator of the estimator is given by: y1 − y2 = Δy = β (S1 − S2 ) + (ε1 − ε 2 )
• And: βW = Δy
ΔS ε1 − ε 2
=β+ 1 2
ΔS • This estimator will be unbiased if two conditions hold:
• 1) E ⎡ ΔS ⎤ ≠ 0 , so that the grouping is correlated with the level of
• 2) E [ ε1 ] = E [ ε 2 ] , so that the unobservables are the same (on average) in
the two groups.
22 Natural Experiments
• Of course, the groups are not constructed randomly.
• Typically, studies exploit “natural experiments” that generate a “treated”
group and a “control” group.
– Quarter of birth and compulsory schooling laws;
– Distance to nearest college/university;
– “GI Bill” in Canada, post-WWII. • The bottom line from most of these studies is that the OLS isn’t too far off,
and there is little evidence of ability bias.
• But there is clear evidence of heterogeneous returns (i.e, the returns to
education vary across individuals and groups). 23 Rising returns to education
• As we saw in the first lecture, the returns to education also vary over time.
• Consider again the figure from Goldin and Katz (2007), showing wage
dispersion and the college-high school wage premium for the U.S.
• The patterns are similar for Canada, though not as pronounced. 24 141 Claudia Goldin and Lawrence F. Katz
Figure 2. Selected Measures of Weekly and Hourly Wage Inequality
Log wage ratio Log wage ratio
March CPS Full-Time Weekly Wages, 1963–2005 1.7 0.65 1.6 0.60 1.5
1.3 Overall 90-10 ratio,a
males only (left scale) 0.55
0.50 1.2 Residual 90-10 ratio,b
males only (left scale) 0.45 1.1
1.0 College–high school
wage differential,c both
sexes (right scale) 0.9
1965 1970 1975 1980 1985 1990 0.40 1995 2000 CPS MORG Hourly Wages, 1973–2006d
Source: Goldin and Katz, Brookings Papers on Economic Activity, 2007.
1.6 0.65 Increasing Returns to Skill
• In the U.S. (shown in the previous slide), and elsewhere (including
Canada), the return to education (notably a university degree) has been
• Overall wage inequality is rising more generally, suggesting increasing
returns to all dimensions of skill.
• Most explanations fit within the simple supply and demand model sketched
• Excellent example, Claudia Goldin and Larry Katz, The Race Between
Education and Technology, 2008.
– They describe the 20th Century as the “Human Capital Century.”
– Until recently, educational attainment kept up with technological change
– “Skill-Biased Technological Change” 26 Skill-Biased Technological Change
W US D S′
D DS U DU ′
Unskilled Skilled Claudia Goldin, Lawrence F. Katz, and Ilyana Kuziemko 135 Which brings us to boys…
College Graduation Rates (by 35 years) for Men and Women: Cohorts Born from
1876 to 1975
0.4 Fraction graduated 0.3
0.2 Females 0.1 0.0
1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 Birth year
Sources: 1940 to 2000 Census of Population Integrated Public Use Micro-data Samples (IPUMS).
Notes: The ﬁgure plots separately by sex the fraction of each birth cohort who had completed at least four
years of college by age 35 for the U.S. born. When the IPUMS data allows us to look directly at
thirty-ﬁve-year-olds in a given year, we use that data. Since educational attainment data was ﬁrst collected
in the U.S. population censuses in 1940, we need to infer completed schooling at age 35 for cohorts born
prior to 1905 based on their educational attainment at older ages. We also don’t observe all post-1905
birth cohorts at exactly age 35. We use a regression approach to adjust observed college graduation rates
for age based on the typical proportional life-cycle evolution of educational attainment of a cohort. The
age-adjustment regressions are run on birth-cohort year cells pooled across the 1940 to 2000 IPUMS with What are they thinking?! Source: Goldin, Katz, and Kuziemko
28 29 The problems start in high school (or earlier)
The Homecoming of American College Women: The Reversal of the College Gender Gap 141 Figure 5
Male-to-Female Ratio of High School Courses in Math and Science, 1957 to 2000 Ratio of Male to Female semesters or units 1.4
Chemistry 1.3 1.2 1.1 1 0.9
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 Sources: 1957 Wisconsin Longitudinal Survey; 1972 National Longitudinal Survey; 1992 National
Educational Longitudinal Survey; and 1982 and 1992 are from U.S. Department of Education (2004,
Notes: The ﬁgure plots the ratio of the mean number of high school courses taken by male graduating
seniors to that of female graduating seniors in each reported subject area for the high school graduating
classes of 1957, 1972, 1982, 1992, and 2000. Courses are measured in semesters for 1957 and 1972 and
are measured in Carnegie units for 1982, 1992, and 2000. Source: Goldin, Katz, and Kuziemko striking in the harder math courses and in chemistry and physics; for example the
average boy took 1.01 semesters of physics, and the average girl took just 0.30 of a 30 And extend to Ontario (and the OECD) While the focus of this report is on university attendance, it is important to note that the gap in
the fractions of women and men with either a college or university credential is similarly
widening. This increase is shown in Figure 1b, where we plot the fractions of Canadian-born
Ontario residents with either a college or university credential by birth cohort and gender.
Among men and women born in the late 1940s, roughly equal fractions had a postsecondary
credential. Among the most recent cohorts there is a 16 percentage point gap, with women
substantially ahead of men in both university and college completion. Source: Card, Payne, and Sechel, 2011 31 Why are girls doing better than boys?
• CANNOT be factors that are common to boys and girls (e.g.,
socioeconomic status, tuition, etc.).
• Common across a wide variety of cultures and countries, so it is difficult to
blame any particular model of universities or education systems.
– Note: Trend is generally positive for both sexes. • A variety of candidates (see Goldin, Katz, and Kuziemko):
– Human capital investment (women have higher returns to education);
– Changing expectations, social norms, and age at first marriage (“The Pill”)
• Also, rising divorce rates, changes in the marriage market – “Feminization” of education at the elementary and high school levels.
• Card, Payne, and Sechel confirm that the Ontario gap also originates in high school
(e.g., streaming). – Boys have more behavior problems in school. 32 Training
• Training is essentially the same as education.
– The only difference is that we do not think of it as formal schooling. • Consider the provision of human capital (training) that occurs on the job, or
• Becker (1964) distinguishes between general and specific human capital:
– General Human Capital: increases worker productivity at all firms;
– Specific Human Capital: increases worker productivity only at a specific firm. • Questions?
– Who pays for general human capital (worker or firm)?
– Who pays for specific human capital (worker or firm)?
– Will the optimal amount of training be provided? 33 Stylized Training and Productivity
VMP VMP* (with training)
Benefits of training
Wa=VMPa (no training)
VMPt (while training) t* Time
34 General Human Capital
• Assume that training is worthwhile, so that the costs exceed benefits.
• Perhaps the firm can invest into the worker’s human capital:
– Pay the worker Wa during and after training, so that the worker is no worse off
than working elsewhere at the outset.
– While only receiving VMPt during training, the employee will produce VMP*
after training. • The problem for the firm is that the worker is now worth VMP* to ALL
firms, who have an incentive to poach the worker, and pay her up to
– The firm would lose its investment.
– Unless there is some kind of bonding. • Predict that workers will pay for general training (i.e., work for the training
wage equal to VMPt.
35 Specific Human Capital
• For specific human capital, poaching is not a problem, as the training is not
useful to other firms.
• In this case, if it is worthwhile to do so, the firm will pay for firm-specific
investments in human capital.
– Pay the worker Wa during and after training, so that the worker is no worse off
than working elsewhere at the outset. • But this also may not be a great idea: what if the worker quits?
• To reduce the probability of turnover, the firm and worker may share the
investment in human capital:
– Pay the worker Wt > VMPt during the training period, so that the worker pays
for some of the training;
– Pay the worker W*, such that W* > Wa, and W* < VMP* so that the benefits of
higher productivity are shared. • The gap between W and VMP may also affect responses to demand shocks. 36 Sharing investment in specific training
VMP VMP* (with training)
Employer’s benefits W*
Employee’s benefits Wa=VMPa (no training)
Employee’s costs Wt Employer’s costs VMPt
and Employee’s benefits Wt
VMPt Wa = VMPa Employee’s
costs And a “smoother” version
period t* Time (c) Earnings growth with gradual training
Employee’s costs Wt W*
Wa = VMPa Employer’s costs VMPo
0 Time and after training. However, because the employee can earn W* elsewhere, the firm’s strategy
won’t work. Thus, in the absence of bonding arrangements (as are used for limited periods in
the armed forces for certain types of general training, such as pilot training), general training
will be financed by employees. Training Programs
• Question: Should the government provide job training?
• Why might governments provide training?
– Imperfect capital markets, especially for general training;
– Speed labor market adjustment
• Displaced workers
• Also, to compensate “losers from policy changes (e.g., trade) – Distributional: Help the most disadvantaged.
• Disadvantaged workers
• Maybe cheaper than welfare (workfare)
• May also be more politically palatable • Question: Does it pay anyway? 39 Program Evaluation
• In the absence of experimental evidence, it is difficult to evaluate the
impact of government training programs.
• One measure of the benefit of training would be the improvement of
earnings experienced by the trainee: Yi , AFTER − Yi , BEFORE
• The problem (as always) is that we do not observe the counterfactual
– Earnings prior to training may have been especially low;
– Earnings might have risen anyway;
– Trained workers may be the most motivated (selection, either by the worker, or
the trainers) 40 Program Evaluatoin
• The ideal solution is to conduct an experiment:
– Assign treated workers to training program;
– Assign control workers to “no training”
– Follow-up • Then we can calculate: (YAFTER − YBEFORE )TRAINED − (YAFTER − YBEFORE )NOT TRAINED
• Experimental evidence suggests that the returns to training programs are
modest at best.
– But note the size of the potential returns.
– A year’s tuition at Harvard is close to $50K, and 7% is $3500.
• Training programs aren’t quite Harvard… 41 Next week
• Selected problems from Chapter 9
– They are all useful!
– Add to last week’s list: Problems #4 and #7 • Start Immigration (Chapter 11) 42 ...
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