III. Wage Determination and Labour Market...

Fortin/Lemieux – Econ 561 Lecture 3D

III. Wage Determination and Labour Market Discrimination

9. Returns to Education

1. Problems in the Estimation of the Returns to Education a. Ability Bias b. Card’s Modeling of Individual Heterogeneity c. Measurement Error

2. Heterogenous Returns and Interpretation of Estimates

3. Instrumental Variables Estimates using the Institutional Environment a. Compulsory Schooling Laws (CAL)


9.1 Problems in the Estimation of the Returns to Education

• The maximization problem where individuals view schooling and other forms of training as production processes for human capital leads the Mincer wage equation

log(y) = a + bS + cX + dX2 + e

• This model implies that there are increasing returns to S. This only makes sense if the costs of S, both direct and in terms of income forgone, rise at least as fast as the return from it.

• If forgone income is only the cost of an additional year of schooling, and if the

increment in log income due to this additional schooling rate is constant forever then b = (∂Y / ∂S) /Y has the interpretation of the “rate of return to the investment in schooling”.

• In this basic model, all individuals are identical, but then why should individuals choose different amounts of education? No reason!!


• Therefore the model was extended to allow for differences across individuals in tastes and access to funds (Becker, Card). o This may help to explain why we observe a distribution of schooling

choices.

• But this generates some problems in the interpretation of the coefficient on schooling o Ability bias: Upward “bias” o Heterogeneity in effects: ??? o Measurement Error: Downward “bias”

a. Ability Bias

• One of the first potential econometric problems to be addressed in the estimation of the returns to schooling was the one posed by the “ability bias” (Griliches, 1977): it is a classic example of the omitted variable bias.


• Suppose one wanted to estimate iii Sy εβα ++=)ln( (1) • But that the “true model” was:

iiii ASy εγβα +++=)ln( , where iA denotes ability and is not observed by the econometrician,

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• Thus, if ability has an independent positive effect on earnings ( 0>γ ) and if

schooling and ability are correlated ( ),( ii ASCov >0), there will be an upward bias in β̂ .

Source: Angrist and Krueger (1999)

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• Note that this is only one of a number of ways in which heterogeneity could be modeled and Card’s results depend on this particular way.

• Using simple linear approximations to MB and MC, heterogeneity is captured in terms of

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• Individuals do not necessarily know the parameters of their earnings functions when

they make their schooling choices.

• interpretation: individual's best estimate of his/her earnings gain per year of education, as of early adulthood.

o One might expect this estimate to vary less across individuals than their realized values of schooling

o the distribution of may change over time with shifts in labor market conditions, technology, etc.

• Note that condition (5), which yields a differential equation

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where iγ is a person-specific constant of integration. • That is, potential heterogeneity affects both the intercept iγ and the slope ib of the

earnings equation.


• Equation (7) together with condition (6) describe a two-equation system for

schooling and earnings in terms of the underlying random variables ,, ii ba and ir . • Assuming that (7) is the correct model, it can be written in terms of deviation from

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where 0aa ii −≡ γ has mean 0. • Suppose that (8) is the true earnings regression and that we are using OLS to

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• Equation (11) can be seen as a generalization of the “ability bias” formula.

• Considering the two cases:

1) Homogeneous returns (identical market ability), bbi = , and if log earnings are linear in schooling, 01 =k , we are back to equation (2):

,lim 0λβ +=olsbp (2’)

o The bias comes from the correlation of ability to the marginal cost of schooling. If the marginal costs ( ir ) are lower for children from more privileged backgrounds, and if these children would also tend to earn more at

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2) Heterogenous schooling ib ,lim 00 Sbp ols ψλβ ++=

we get the additional bias terms in due to the self-selection of years of schooling.


• The size of this bias depends on the importance of the variation in ib in determining the overall variance of schooling outcomes. o The bigger the contribution of variation in ib to the overall variance of

schooling, the larger the 0ψ and the more convex is the observed relationship between log earnings and schooling.

• Why then do we observe that in many cases, the wage equation is linear in

schooling? o The linear model appears to fit so well because there is a bias introduced by

heterogeneity which is convex and independent of the concavity of the opportunity curve.

o More simply put, the concavity from quadratic term in (8) is offset by the convexity from 0ψ giving an approximately linear relationship.

• If 10 2k≈ψ in (10), the relationship will be linear. Conversely, the bigger the

contribution of ib to the overall variance of schooling, 0ψ is bigger and the more the convexity.


c. Measurement Error

• Measurement error is another potential source of bias in the returns to schooling.

• In the case of classic measurement error (that is uncorrelated with S ), this lead to a downward bias in the estimates of the returns to schooling, possibly offsetting somewhat the “ability” bias.

• But to the extent that there is top-coding in schooling, the assumption of classical

measurement error may not hold. o Because individuals with high levels of schooling cannot report positive errors

in schooling whereas individuals with very low levels of schooling cannot report negative errors in schooling.

• The error is likely correlated with level of schooling, the measurement error may

actually exacerbates the attenuation bias.


9.2 Heterogenous Returns and Interpretation of Estimates • Card (1999) classifies the estimation methods that attempt to address those

problems into 4 categories and give the assumptions needed to reduce the biases (Table 3)

1) Instrumental variables 2) Control functions 3) Family background models 4) Sibling/Twin models

• The main implications of the impact of the methods on the potential biases are:

1) The OLS estimator has two biases relative to the average marginal return to

education ( β ): ,lim 00 Sbp ols ψλβ ++= one attributable to the correlation )( 0λ between schooling and the intercepts of the earnings function ( ia ), another attributable to the correlation ( 0ψ ) between schooling and the slope of the earnings function ( ib ).


2) The necessary conditions for IV or control functions estimators to yield a

consistent estimate of β in the presence of heterogeneity in the returns to education are fairly strict.

The requirements are that we have individual specific heterogeneity components that are mean independent of the instrument. The second moment of the return to education is also independent of the instrument. The conditional expectation of the unobserved component of optimal school choice is linear in b. IV will likely recover a weighted average of the marginal returns for the affected subgroups.

3) If the OLS estimator is upward-biased by unobserved ability, one would expect an

IV estimator based on family background to be even more upward-biased. linear projections of unobserved ability components on individual schooling now includes a measure of family background (Fi):

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4) If twins or siblings have identical abilities (and the distributions of abilities among twins are the same as those in the population as a whole) then a within-family estimator will recover an asymptotically unbiased estimate of the average marginal return to education, otherwise it will be biased.

With twins, we may be able to impose the symmetry conditions so that λ1=λ2=λ, ψ1=ψ2=ψ and With these assumptions and the pure family effects specification, all biases from ability and schooling are sucked up by the family average schooling component which differences out.

5) Measurement error biases are potentially important in interpreting the estimates from different procedures. • OLS estimates are probably downward biased by about 10% • OLS estimates that control for family background may be downward biased by

about 15% or more • within-family differenced estimates may be downward-biased by 20-30% with

the upper range more likely for identical twins.

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Ch. 30: Causal Effect of Education on Earnings 1843

Table 5 Estimates of the return to education with and without controlling for family background, and IV estimates using family background ~

Author Seanple and family background variable(s) OLS coefficients IV coefficient

No Control control

1. Card (1995b) NLS Young Men (see Table 4). Family 0.073 0.069 0.084 background variables are both parents' (0.006) (0.006) (0.009) education (main effects and interactions) plus family structure u

2. This chapter General Social Survey of adult household Men 0.073 0.067 0.106 heads age 24-61, 1974-1996 data. Annual (N = 7860) (0.003) (0.003) (0.007) earnings (imputed from categorical data). Controls include cubic in age, race, Women 0.112 survey year and region. Family back- (N = 7500) (0.004) ground variable is mother's education

0.113 0./10 (0.004) (0.01 l)

3. Conneely and Finnish male veterans (see Table 4). 0.085 0.082 0.114 Uusitalo Farnily background variable is parent's (0.001) (0.001) (0.006) (1997) education

4. Ashenfetter NLS Young Men (1966 Cohort) merged Brother 1, 0.059 0.052 0.080 and with NLS Older Men. Family background using other (0.014) (0.015) (0.027) Zimmerman variables are brother's or father's brother's (1997) education. Controls include quadratic education

in age Sons, using 0.057 0.049 0.109 father's (0.009) (0.009) (0.025) education

5. Miller et al. Australian Twins Register (male and No allowance 0.064 0.048 (1995) female identical twins). Income imputed for measure- (0.002) (0.003)

from occupation. F~unily background ment error variable is twin's education. Controls include quadratic in age and marital status

IV using 0.073 0.078 twin's reporff (0.003) (0.009)

6. Ashenl)lter 1991-1993 Princeton Twins Survey (men No allowance 0.102 0.092 and Rouse and women). Identical twins. Family for measure- (0.010) - (1998) background variable is twin's education, ment error

Controls include gender, race, and quadratic in age IV using 0.112 0.108

twin's report ~ -

Table 2: OLS and IV Estimates of the Return to Education with Instruments Based on Features of the School System

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Schooling Coefficients �� Author Sample and Instrument OLS IV ��

1. Angrist and 1970 and 1980 Census Data, Men. 1920-29 cohort in 1970 0.070 0.101 Krueger (1991) Instruments are quarter of birth (0.000) (0.033) interacted with year of birth. Controls include quadratic in 1930-39 cohort in 1980 0.063 0.060 age and indicators for race, (0.000) (0.030) marital status, urban residence. 1940-49 cohort in 1980 0.052 0.078 (0.000) (0.030)

2. Staiger and 1980 Census, Men. Instruments are 1930-39 cohort in 1980 0.063 0.098 Stock (1997) quarter of birth interacted with (0.000) (0.015) state and year of birth. Controls are same as in Angrist and Krueger, 1940-49 cohort in 1980 0.052 0.088 plus indicators for state of birth. (0.000) (0.018) LIML estimates.

3. Kane and NLS Class of 1972, Women. Models without test 0.080 0.091 Rouse (1993) Instruments are tuition at 2 and score or parental (0.005) (0.033) 4-year state colleges and distance education to nearest college. Controls include race, part-time status, Models with test scores 0.063 0.094 experience. and parental education (0.005) (0.042) Note: Schooling measured in units of college credit equivalents.

4. Card (1995b) NLS Young Men (1966 Cohort) Models that use college 0.073 0.132 Instrument is an indicator for proximity as instrument (0.004) (0.049) a nearby 4-year college in 1966, (1976 earnings) or the interaction of this with parental education. Controls Models that use college -- 0.097 include race, experience (treated proximity × family back- (0.048) as endogenous), region, and ground as instrument parental education.

5. Conneely and Finnish men who served in the Models that exclude 0.085 0.110 Uusitalo army in 1982, and were working parental education (0.001) (0.024) (1997) full time in civilian jobs in and earnings 1994. Administrative earnings and education data. Instrument Models that include 0.083 0.098 is living in university town in parental education (0.001) (0.035) 1980. Controls include quadratic and earnings in experience and parental education and earnings.

6. Harmon and British Family Expenditure Survey 0.061 0.153 Walker (1995) 1978-86 (men). Instruments are (0.001) (0.015) indicators for changes in the minimum school leaving age in 1947 and 1973. Controls include quadratic in age, survey year, and region.

7. Ichino and Austria: 1983 Census, men born Austrian Men 0.518 0.947 Winter-Ebmer before 1946. Germany: 1986 GSEP (0.015) (0.343) (1998) for adult men. Instrument is indicator for 1930-35 cohort. (Second German IV also uses dummy German Men 0.289 0.590 / 0.708 for father’s veteran status). (0.031) (0.844) (0.279) Controls include age, unemployment rate at age 14, and father’s education (Germany only). Education measure is dummy for high school or more.

��

Notes: see text for sources and more information on individual studies. Table continues.

Source: Card (2000)

Table 2: OLS and IV Estimates of the Return to Education with Instruments Based on Features of the School System, Continued

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Schooling Coefficients �� Author Sample and Instrument OLS IV ��

8. Lemieux and Canadian Census, 1971 and 1981: 1971 Census: 0.070 0.164 Card (1998) French-speaking men in Quebec (0.002) (0.053) and English-speaking in Ontario. Instrument is dummy for Ontario men age 19-22 in 1946. 1981 Census: 0.062 0.076 Controls include full set of (0.001) (0.022) experience dummies and Quebec- specific cubic experience profile.

9. Meghir and Swedish Level of Living Survey SLLS Data 0.028 0.036 Palme (1999) (SLLS) data for men born 1945-55, (Years of education) (0.007) (0.021) with earnings in 1991, and Individual Statistics (IS) sample of IS Data 0.222 0.245 men born in 1948 and 1953, with (Dummy for 1-2 years (0.020) (0.082) earnings in 1993. Instrument is of college relative dummy for attending “reformed” to minimum schooling) school system at age 13. Other controls include cohort, father’s education, and county dummies. Models for IS data also include test scores at age 13.

10. Maluccio (1997) Bicol Multipurpose Survey (rural Models that do not 0.073 0.145 Philippines): male and female wage control for selection (0.011) (0.041) earners age 20-44 in 1994, whose of employment status families were interviewed in 1978. or location Instruments are distance to nearest high school and indicator for local Models with selection 0.063 0.113 private high school. Controls correction for (0.006) (0.033) include quadratic in age and location and employment indicators for gender and residence status in a rural community.

11. Duflo (1999) 1995 Intercensal Survey of Indo- Model for hourly wage 0.078 0.064 / 0.091 nesia: men born 1950-72. Instru- (0.001) (0.025) (0.023) ments are interactions of birth year and targeted level of school building activity in region of birth. Other Model for monthly wage 0.057 0.064 / 0.049 controls are dummies for year and with imputation for (0.003) (0.017) (0.013) region of birth and interactions self-employed. of year of birth and child population in region of birth. Second IV adds controls for year of birth interacted with regional enrollment rate and presence of water and sanitation programs in region.

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Notes: see text for sources and more information on individual studies.

Source: Card (2000)

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• Let’s focus on the local average treatment effect (LATE) likely estimated by IV. Recall that IV estimate can be written as a Wald estimator when the instrument is a binary variable,

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• Which of the above effects is estimated essentially depends on what the instrument is though to affect.

• For example, if an IV transformation could eliminates the heterogeneity in the intercept, but not in the slope of the returns to education, we would get TTiv ββ =ˆ . o The differences-in-differences estimator is an example of this type of

comparison. It is more likely in case where there is a before and after comparison (e.g. GED) than in the case of formal schooling.


• If we compare two groups that have a similar distribution of abilities, but who, for some exogeneous reform, experience the different schooling outcomes, the IV estimate will recover the LATE effect. The estimates comparing adjacent cohorts subject to different minimum school leaving age is an example of that.

• More formally, let iS1 and iS0 be the schooling i would get if 1=iZ and 0=iZ , respectively. We can write

( ) iiiiiiii ZZSSSS νκκ ++=−+= 10010 , where in the random-coefficients notation, the causal effect of iZ on iS is iii SS 011 −≡κ .

• Angrist et al. (1996) call the individuals with 11 =iS and 00 =iS , the compliers. They are the individuals who we allow us to identify the effect of the treatment. Those whose behaviour is not affected by the treatment ( 101 == ii SS or 001 == ii SS ) are not troublesome, but the non-compliers, 01 =iS and 10 =iS , have to be excluded, this is done via the monotonicity assumption ( ii SS 01 ≥ ).


• For example, the case where the instrument is proximity to a college, non-compliers would be those individuals who choose not to go to college if there is one nearby and go if the college is far away (perhaps they simply want to get out of the parental home).

• Under the independence assumption{ } ZSSSg iiii C01 ,),( and the monotonicity

assumption, ii SS 01 ≥ , together with the first-stage assumptions, the IV estimator reduces to

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• If the instrument was the school leaving law, then the IV estimate recovers the average returns among those induces to achieve 11 =iS by the school age reform. o These could be a group with very low returns, if those who now achieve 11 =iS

were those who had little to gain and the local average would be very low. o On the other hand, if these individuals were those who previously left school

because of a lack of information or family resources, the local average return could be very high.

• The types of instruments that are now thought to generate the more reliable

estimates of returns to education are based on changes in the institutional environment o School Entry Laws o School Leaving Laws (e.g. Angrist and Krueger, 1991; Oreopoulos, ) o Differential Tuitions (e.g. Kane and Rouse, 1995) o Distance to College/University (Card, 1991)

ideal when random construction of schools, (e.g. Duflo, 2001)


Example of Policy Interventions used in recent NBER working papers


• Note that IV based studies generate returns to education estimates that are about 30% higher than OLS, the LATE interpretation of IV in combination with underlying heterogeneity is the most likely reason for it.

o Bound and Jaeger further argue that IV estimate are more upward biased than the corresponding OLS estimates by unobserved differences between the characteristics of treatment and comparison groups implicit in the IV scheme.

• Other reasons: o There may also be a publication bias: only papers with large and significant

point estimates can be published and IV has generally larger standard errors.

o Ashenfelter and Harmon cite a positive correlation across studies between IV-OLS gap in estimated returns and the sampling error of the IV estimates.


9.3 Instrumental Variables Estimates using Features of the Institutional Environment

a. Using Compulsory Schooling Laws (CAL)

• First study estimating the returns to education based on compulsory schooling laws was by Angrist and Krueger (1991)

• Angrist and Krueger (AK) use quarter of birth as an instrument for education to determine the impact of education on earnings.

• In the presence of school entry and compulsory schooling laws, quarter of birth will impact education attainment

Children born earlier in the years will reach legal school leaving age earlier without completing the school year when school entry laws require that children be six years of age by January 1 of the academic year in which they enter school.

• At the time, this source of schooling variation was thought to be uncorrelated

with other factors influencing earnings, but these ideas have recently been challenged

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Bob enters at age 6, Ron enters at age 5

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4th quarter kid has 1 more year of schooling than 1st quarter kid

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Vietman War Draft Effect

984 QUARTERLY JOURNAL OF ECONOMICS

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Year of Birth

FIGURE III

Years of Education and Season of Birth 1980 Census

Note. Quarter of birth is listed below each observation.

year of birth, based on the sample of men in the 1980 Census, 5 percent Public Use Sample. (The data set used in the figures is described in greater detail in Appendix 1.) The graphs show a generally increasing trend in average education for cohorts born in the 1930s and 1940s. For men born in the late 1950s, average education is trending down, in part because by 1980 the younger men in the cohort had not completed all of their schooling, and in part because college attendance fell in the aftermath of the Vietnam War.

A close examination of the plots indicates that there is a small but persistent pattern in the average number of years of completed education by quarter of birth. Average education is generally higher for individuals born near the end of the year than for individuals born early in the year. Furthermore, men born in the fourth quarter of the year tend to have even more education than men born in the beginning of the following year. The third quarter births also often have a higher average number of years of education than the following year's first quarter births. Moreover,


On the one hand, children born earlier being bigger in their classes may have greater self-confidence, a non-cognitive skill that influences earnings

On the other hand, Buckles and Hungerman (2009) show that children born in the winter are disproportionally born to women who are more likely to be teenagers and less likely to be married or have a high school degree.

• First stage: Does quarter of birth affect education attainment? See Figure I, II and

III.

• Regress de-trended education outcomes on quarter of birth dummy variables:

where education outcome E of individual I in cohort c and birth quarter j, , birth quarter Q

• This shows that Q does impact education outcomes such as total years of education

and high school graduation. But is this due to compulsory schooling laws?

ijccjicj QQQEE εβββα ++++=− 332211)(


• Indirect evidence: o Examine impact of birth quarter on post-secondary outcomes that are not

expected to be affected by compulsory schooling laws. o No birth quarter impact on post-secondary outcomes is consistent with a theory

that compulsory schooling laws are behind the birth quarter-education relationship for secondary education.

• Direct evidence: Construct a difference-in-difference measure of schooling law

impact between high age requirement states and low age requirement states:

where %Eage 16, high is the fraction of 16 year olds enrolled in high school in states where attendance in mandatory up to age 17 or 18)

• Counterpoints:

o Bound and Jaeger (1995) find that for cohorts of men born during the first half of the 20th century, the association between quarter of birth and both educational attainment and earnings would appear to be too strong to be explained solely by compulsory school attendance laws.

)]%(%)%[(%Law ofImpact ,15,15,16,16 lowagehighagelowagehighage EEEE −−−=

THE EFFECTS OF COMPULSORY SCHOOL ATTENDANCE 987

TABLE I THE EFFECT OF QUARTER OF BIRTH ON VARIOUS EDUCATIONAL

OUTCOME VARIABLES

Quarter-of-birth effeCta Birth F-testb

Outcome variable cohort Mean I II III [P-value]

Total years of 1930-1939 12.79 -0.124 -0.086 -0.015 24.9 education (0.017) (0.017) (0.016) [0.0001]

1940-1949 13.56 -0.085 -0.035 -0.017 18.6 (0.012) (0.012) (0.011) [0.0001]

High school graduate 1930-1939 0.77 -0.019 -0.020 -0.004 46.4 (0.002) (0.002) (0.002) [0.0001]

1940-1949 0.86 -0.015 -0.012 -0.002 54.4 (0.001) (0.001) (0.001) [0.0001]

Years of educ. for high 1930-1939 13.99 -0.004 0.051 0.012 5.9 school graduates (0.014) (0.014) (0.014) [0.0006]

1940-1949 14.28 0.005 0.043 -0.003 7.8 (0.011) (0.011) (0.010) [0.0017]

College graduate 1930-1939 0.24 -0.005 0.003 0.002 5.0 (0.002) (0.002) (0.002) [0.0021]

1940-1949 0.30 -0.003 0.004 0.000 5.0 (0.002) (0.002) (0.002) [0.00181

Completed master's 1930-1939 0.09 -0.001 0.002 -0.001 1.7 degree (0.001) (0.001) (0.001) [0.1599]

1940-1949 0.11 0.000 0.004 0.001 3.9 (0.001) (0.001) (0.001) [0.0091]

Completed doctoral 1930-1939 0.03 0.002 0.003 0.000 2.9 degree (0.001) (0.001) (0.001) [0.0332]

1940-1949 0.04 -0.002 0.001 -0.001 4.3 (0.001) (0.001) (0.001) [0.0050]

a. Standard errors are in parentheses. An MA(+2, -2) trend term was subtracted from each dependent variable. The data set contains men from the 1980 Census, 5 percent Public Use Sample. Sample size is 312,718 for 1930-1939 cohort and is 457,181 for 1940-1949 cohort.

b. F-statistic is for a test of the hypothesis that the quarter-of-birth dummies jointly have no effect.

variable indicating whether person i was born in the jth quarter of the year. Because the dependent variable in these regressions is purged of MA(+2,-2) effects, it is necessary to delete observations born in the first two quarters and last two quarters of the sample.

Table I reports estimates of each quarter of birth (main) effect %) relative to the fourth quarter, for men in the 1980 Census who were born in the 1930s and 1940s.6 The F-tests reported in the last

6. We focus on men born in the 1930s and 1940s because many individuals in the 1950s birth cohorts had not yet completed their education by 1980.


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TABLE II PERCENTAGE OF AGE GROUP ENROLLED IN SCHOOL BY BIRTHDAY AND LEGAL

DROPOUT AGEa

Type of state lawb

School-leaving School-leaving age: 16 age: 17 or 18 Column

Date of birth (1) (2) (1) - (2)

Percent enrolled April 1, 1960

1. Jan 1-Mar 31, 1944 87.6 91.0 -3.4 (age 16) (0.6) (0.9) (1.1)

2. Apr 1-Dec31, 1944 92.1 91.6 0.5 (age 15) (0.3) (0.5) (0.6)

3. Within-state diff. -4.5 -0.6 -4.0 (row 1 - row 2) (0.7) (1.0) (1.2)


4. Jan 1-Mar 31, 1954 94.2 95.8 -1.6 (age 16) (0.3) (0.5) (0.6)

5. Apr 1-Dec31, 1954 96.1 95.7 0.4 (age 15) (0.1) (0.3) (0-3)

6. Within-state diff. -1.9 0.1 -2.0 (row 1 - row 2) (0.3) (0.6) (0.6)


7. Jan 1-Mar 31, 1964 95.0 96.2 -1.2 (age 16) (0.1) (0.2) (0.2)

8. Apr 1-Dec 31, 1964 97.0 97.7 -0.7 (age 15) (0.1) (0.1) (0.1)

9. Within-state diff. -2.0 -1.5 0.5 (row 1 - row 2) (0.1) (0.2) (0.3)

a. Standard errors are in parentheses. b. Data set used to compute rows 1-3 is the 1960 Census, 1 percent Public Use Sample; data set used to

compute rows 4-6 is 1970 Census, 1 percent State Public Use Sample (15 percent form); data set used to compute rows 7-9 is the 1980 Census, 5 percent Public Use Sample. Each sample contains both boys and girls. Sample sizes are 4,153 for row 1; 12,512 for row 2; 7,758 for row 4; 24,636 for row 5; 42,740 for row 7; and 131,020 for row 8.

attend school until their seventeenth or eighteenth birthday.9 A summary of the compulsory schooling requirement in effect in each state in 1960, 1970, and 1980 is provided in Appendix 2.

The first three rows of Table II focus on individuals who were

9. There are three exceptions: Mississippi and South Carolina eliminated their compulsory schooling laws in response to Brown v. Board of Education in 1954. South Carolina reenacted compulsory schooling in 1967, and Mississippi in 1983. In 1960 Maine had an age fifteen compulsory schooling law. Ehrenberg and Marcus [1982] and Edwards [1978] also provide evidence on the impact of compulsory schooling legislation on school enrollment.


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o Moreover, they find an association between quarter of birth and labor market outcomes in cohorts whose education predates the existence of effective compulsory attendance laws.

• Impact on earnings: 1. Wald estimate compares the overall difference in education and earnings between Q1 and Q2-4 individuals

• Consistency requires that the grouping variable (Q) is correlated with education (Educ), but uncorrelated with wage determinants other than education. o For instance, this assumes that ability is distributed uniformly throughout the

year. 2. Two-Stage Least Squares (2SLS) uses two equations model:

o First stage: o Second stage:

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TABLE III PANEL A: WALD ESTIMATES FOR 1970 CENSUS-MEN BORN 1920-1929a

(1) (2) (3) Born in Born in 2nd, Difference

1st quarter 3rd, or 4th (std. error) of year quarter of year (1) - (2)

in (wkly. wage) 5.1484 5.1574 -0.00898 (0.00301)

Education 11.3996 11.5252 -0.1256 (0.0155)

Wald est. of return to education 0.0715 (0.0219)

OLS return to education' 0.0801 (0.0004)

Panel B: Wald Estimates for 1980 Census-Men Born 1930-1939

(1) (2) (3) Born in Born in 2nd, Difference

1st quarter 3rd, or 4th (std. error) of year quarter of year (1) - (2)

in (wkly. wage) 5.8916 5.9027 -0.01110 (0.00274)

Education 12.6881 12.7969 -0.1088 (0.0132)

Wald est. of return to education 0.1020 (0.0239)

OLS return to education 0.0709 (0.0003)

a. The sample size is 247,199 in Panel A, and 327,509 in Panel B. Each sample consists of males born in the United States who had positive earnings in the year preceding the survey. The 1980 Census sample is drawn from the 5 percent sample, and the 1970 Census sample is from the State, County, and Neighborhoods 1 percent samples.

b. The OLS return to education was estimated from a bivariate regression of log weekly earnings on years of education.

estimate in this case because unobserved earnings determinants (e.g., ability) are likely to be uniformly distributed across people born on different dates of the year.15

The last row of each panel in Table III provides the OLS

15. We note that our procedure will slightly understate the return to education because first-quarter births, whose birthdays occur midterm, are more likely to attend some schooling beyond their last year completed. Consequently, the difference in years of school attended between first and later quarters of birth is less than the difference in years of school completed. Since the difference in completed education rather than the difference in years of school attended appears in the denominator of the Wald estimator, our estimate is biased downward. In practice, however, this is a small bias because the difference in completion rates is small.


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• Identification: The excluded instruments in the wage equation for the TSLS

estimates are three quarter-of-birth dummies (quarter 1, 2 and 3, base is 4) interacted with nine year-of-birth dummies. o Because year-of-birth dummies are also included in the wage equation, the

effect of education is identified by variation across quarters of birth within a birth year.

o Because there are many birth years in each Census regression, the models are overidentified and pass the overdid test for 1970 and 1980 Censuses separately, but not quite for the combined Censuses.

o Because school entry age vary by state, Angrist and Krueger also use as instruments dummies interacted with fifty state-of-birth dummies, in addition to three quarter-of-birth dummies interacted with nine year-of-birth dummies. The estimates also include fifty state-of-birth dummies in the wage equation, so the variability in education used to identify the returns to education in the TSLS estimates is due to differences by season of birth, which are allowed to vary by state and birth year.


• In summary, Angrist and Kruger (1991) opened up a new breed of instruments based on features of the institutional environment o This had lead to many papers on the topic o Between 10 to 33% of potential drop outs are kept in school due to

compulsory attendance laws. o Returns to an additional year of schooling are remarkably similar to those

estimated with OLS, approximately 7.5% depending on the specification.

• A notable successor is the paper by Phil Oreopoulos (2006) who can use a RD (regression discontinuity design) of the direct change in compulsory schooling because of a very large change in enrollment following changes in school leaving age in the UK, first considered by Harmon and Walker (1995).

• It provides a great example of a RD estimate as an IV-Wald estimator

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Fortin – Econ 560 Lecture 2C

VOL. 96 NO. 1 OREOPOULOS: ESTIMATING ATE AND LATE WITH COMPULSORY SCHOOLING LAWS 169

TABLE 4--OLS, IV-DD, AND IV-RD ESTIMATES OF THE RETURNS TO (COMPULSORY) SCHOOLING FOR THE UNITED STATES, CANADA, AND THE UNITED KINGDOM

(4) (1) (2) (3) IV with

OLS IV with IV with regional trends and full sample regional controls regional trends regional controls

Dependent variable United States [1901-1961 birth cohorts aged 25-64 in the 1950-2000 censuses] Log weekly earnings (all workers) 0.078 0.142 0.175 0.405

[0.0005]*** [0.0119]*** [0.0426]*** [0.7380] Log weekly earnings (males) 0.070 0.127 0.074 0.235

[0.0004]*** [0.0145]*** [0.0384]* [0.1730] Log weekly earnings (black males) 0.074 0.172 0.119 0.264

[0.0004]*** [0.0137]*** [0.0306]*** [0.1295]** Canada [1911-1961 birth cohorts aged 25-64 in the 1971-2001 censuses]

Log annual earnings (all workers) 0.099 0.096 0.095 0.142 [0.0007]*** [0.0254]*** [0.1201] [0.0652]**

Log annual earnings (males) 0.087 0.124 -0.383 0.115 [0.0008]*** [0.0284]*** [1.1679] [0.0602]*

United Kingdom [1921-1951 birth cohorts aged 32-64 in the 1983-1998 GHHS]

Log annual earnings (all workers) 0.079 0.158 0.195 NA [0.0024]*** [0.0491]*** [0.0446]***

Log annual earnings (males) 0.055 0.094 0.066 NA [0.0017]*** [0.0568] [0.0561]

Britain [1921-1951 birth cohorts aged 32-64 in the 1983-1998 GHHS] OLS RD

Log annual earnings (all workers) 0.078 0.147 NA NA [0.002]*** [0.061]**

Log annual earnings (males) 0.055 0.150 NA NA [0.0017]*** [0.130]

Note: Regressions in the top three panels include fixed effects for birth year, region (state, province, Britain/N. Ireland), survey year, sex, and a quartic in age. The U.S. results also include a dummy variable for race, and state controls for fractions living in urban areas, black, in the labor force, in the manufacturing sector, female, and average age based on when a birth cohort was age 14. Provincial controls for Canada include fraction in urban areas, in the manufacturing sector, and controls for per capita public and school expenditures. Data are grouped into means by birth year, nation, sex, race (for the U.S.) and survey year and weighted by cell population size. Huber-White standard errors are shown from clustering by region and birth cohort. Single, double, and triple asterisks indicate significant coefficients at the 10-percent, 5-percent, and 1-percent levels, respectively. The omitted variable indicates ability to drop out at age 13 or lower for the U.S. and Canada, and 14 or less for the U.K. Samples include all adults aged 25 to 64. The last panel repeats regression discontinuity results from Table 2 using the British sample only and a quartic birth cohort polynomial instead of cohort fixed effects. See text for more data specifics.

sample, though the associated standard errors are high. Overall, there is no evidence that the U.S. or Canadian effects are higher than the British ones, except perhaps for U.S. black males.

The detailed IV estimates for the returns to compulsory schooling are shown in Table 4. Column 2 includes the IV results corresponding to the first and second stages in columns 1 and 2 of Table 3. All regressions in the first three panels include a quartic in age and fixed effects for birth cohort, region, survey year, and gender. The U.S. results also include a dummy variable for race; a number of state controls (fraction of state that lives in urban areas, is

black, is in the labor force, works in the manufacturing sector, is female); and a variable for average age based on when the birth cohort was age 14. Province controls were used for Canada, including the fraction of the province that lives in urban areas and works in the manufacturing sector, as well per capita public and school expenditures. Data are grouped into means by birth year, region, gender, race (for the United States), and survey year. Huber-White standard errors are shown from clustering by region and birth cohort. The IV-RD results for Britain are repeated in the fourth panel of Table 4 and include a quartic cohort control and age fixed effects.

VOL. 96 NO. 1 OREOPOULOS: ESTIMATING ATE AND LATE WITH COMPULSORY SCHOOLING LAWS 171

TABLE 5-OLS AND IV ESTIMATES FOR EFFECTS OF (COMPULSORY) SCHOOLING ON SOCIALECONOMIC OUTCOMES

(1) (3) Mean (2) IV

< HS sample OLS full sample

Country (schooling variable) Health outcomes (ages 25-84)

United States (total years of schooling) Physical or mental health disability that limits personal care 0.092 -0.014 -0.025

[0.0003]*** [0.0058]*** Disability that limits mobility 0.128 -0.020 -0.043

[0.0004]*** [0.0070]*** United Kingdom (age left full-time education)

Self reported poor health 0.150 -0.037 -0.032 [0.0016]*** [0.0113]***

Self reported good health 0.564 0.065 0.060 [0.0021]*** [0.0155]***

Other socialeconomic outcomes (ages 25-64) United States (schooling variable: total years of schooling)

Unemployed 0.064 -0.004 -0.005 [0.0002]*** [0.0040]

Receiving welfare 0.067 -0.013 -0.011 [0.0002]*** [0.0024]***

Below poverty line 0.220 -0.023 -0.064 [0.0002]*** [0.0085]***

Canada (total years of schooling) Unemployed: looking for work 0.062 -0.038 -0.010

[0.0044]*** [0.003]*** Below low-income cutoff 0.227 -0.038 -0.026

[0.0004]*** [0.0038]*** United Kingdom (age left full-time education)

In labor force: looking for work 0.110 -0.030 -0.032 [0.0044]*** [0.0150]**

Receiving income support 0.066 -0.025 -0.059 [0.0024]*** [0.0259]**

Note: All regressions include fixed effects for birth year, region (state, province, Britain/N. Ireland), survey year, sex, and a quartic in age. The U.S. results also include a dummy variable for race, and state controls for fractions living in urban areas, black, in the labor force, in the manufacturing sector, female, and average age based on when a birth cohort was age 14. Provincial controls for Canada include fraction in urban areas, in the manufacturing sector, and controls for per capital public and school expenditures. Data are grouped into means by birth year, nation, sex, race (for the U.S.) and survey year and weighted by cell population size. Huber-White standard errors are shown from clustering by region and birth cohort. Single, double, and triple asterisks indicate significant coefficients at the 10-percent, 5-percent, and 1-percent levels, respectively. See text for more data specifics.

eral population. I find, instead, that the gains from compulsory schooling are very large-- between 10 and 14 percent-whether these laws affect a majority or minority of those exposed.

This finding of high returns to compulsory schooling raises the question of why dropouts drop out in the first place. Why did so many leave school in the United Kingdom if staying on would have led to substantial gains, on average, to labor market and health outcomes?

One possibility, sometimes used to explain why IV returns to schooling estimates exceed

OLS, is that individuals dropping out are credit- constrained. Considering the similarity of IV results across countries, this explanation could apply only if students from the United Kingdom tend to face greater financial constraints from staying on than students from the United States and Canada. As I discuss in Section II, however, while about half of secondary students in Brit- ain paid some fees to attend school, the removal of these fees in 1944 did not affect attainment beyond age 15. Furthermore, many early school leavers do not work. Among 15- and 16-year-


Take-Away

1. Consistent with summary of the literature from the 1960s and 1970s by Griliches, the average return to education in a given population is not much below the estimate that emerges from a simple cross-sectional regression of earnings on education.

2. Estimate of the return to schooling based on comparisons of brother or fraternal

twins contain some positive ability bias less than the corresponding OLS ability differences appear to exert relatively less influence on within-family schooling difference

3. IV estimates of the return to education based on family background are

systematically higher than corresponding OLS estimates and may contain a bigger upward bias

4. IV estimates of the return to education based on interventions in the school system

tend to be 20% or more above the corresponding OLS estimates.


There is some evidence that this is due to the higher than average marginal returns of the individuals targeted by these programs.


10.1 Social Returns to Schooling

• There is not much empirical evidence of education externalities in productivity.

• Acemoglu and Angrist (1999) show (Table 7) that the social return to schooling (in terms of wages) is small and statistically insignificant in the US.

• They regress wages on schooling and average schooling in state of residence. They instrument individual schooling with quarter of birth and average schooling with compulsory schooling laws.

• Moretti (2002) argues that there are spillovers in education at the city. However, it is not clear that these spillovers are not being priced out in the market.

• Moretti uses a panel of individuals and examines how an individuals’ wage changes when the human capital of individuals around him also change. He controls for individual and individual-city fixed effects and only uses individuals who do not migrate to identify the externality.

• However, education has effects on many other outcomes besides productivity.


• For example, education has important effects on health, criminal behavior, citizenship, and others.

• These may or may not be taken into account by an individual at the time of the

schooling decision is being made.

• But even if they are, these behaviours by themselves may involve important externalities (ex: crime).

• Lochner and Moretti (2004) show the effects of education on the probability of

imprisonment in the US, especially for blacks. They use quarter of birth as their instrument.

• Therefore there may be important externalities of education through its effect

on many types of non-monetary outcomes.


Basic readings: Card, D. “The Causal Effect of Education on Earnings,” in Ashenfelter, O.C. and D. Card,

editors, Handbook of Labor Economics, North-Holland, Vol. III A,1999. Card, D. “Estimating the Return to Schooling: Progress on Some Persistent Econometric

Problems,” NBER Working Paper No. 7769, June 2000. *Carneiro, P., Heckman, J.J. and E. Vytlacil, “Understanding What Instrumental Variables

Estimate: Estimating Marginal and Average Returns to Education”, mimeo, July 2003.

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