Ability, Schooling Inputs and Earnings: Evidence from the NELS

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Ability, Schooling Inputs and Earnings: Evidence from the NELS
Ozkan Eren
Department of Economics
University of Nevada, Las Vegas
Abstract
Utilizing the National Educational Longitudinal Study data, this paper examines the role of pre-market
cognitive and noncognitive abilities, as well as schooling inputs, on young men’s earnings. In addition to
the conditional mean, we estimate the impacts over the earnings distribution using recently developed
(instrumental) quantile regression techniques. Our results show that noncognitive ability is an important
determinant of earnings, but the e¤ects are not uniform across the distribution. We …nd noncognitive
ability to be most e¤ective for lower quantiles. Cognitive ability, on the other hand, shows a reversed
pattern with more pronounced e¤ects at the upper tail of the earnings distribution. We also …nd that,
on average, pupil-teacher ratio is a signi…cant determinant of earnings. However, similar to ability, the
e¤ects are not homogeneous.
JEL: C20, C21, J24, I21, I28
Keywords: Cognitive Ability, Instrumental Quantile Regression, Measurement Error, Noncognitive
Ability, Pupil-Teacher Ratio
The author thanks to the participants at the Canadian Economic Association Meetings at University of British Columbia
(June, 2008), the Summer Econometric Society Meetings at Carnegie Mellon University (June, 2008) and the Winter
Econometric Society Meetings (January, 2009) for helpful comments, which led to an improved version of this paper.
Corresponding address: Ozkan Eren, Department of Economics, University of Nevada, Las Vegas, 89154-6005, Tel: (702)
895-3653 Fax: (702) 895-1354. E-mail: [email protected]
1
Introduction
Earnings dispersion among individuals for a given age, education level, gender and race has increased
substantially in the United States over the past few decades (see, for example, Autor et al. 2008,
Katz and Murphy 1992). Many economists attribute the increase in within-group as well as acrossgroup inequality to a growing importance of productive skills in the labor market (Juhn et al. 1993).
Researchers have traditionally focused on cognitive skills, measured by knowledge and aptitude tests, as
the primary example of productive skills. However, viewing cognitive traits as the sole or main aspect of
productive skills may be misleading because there is prominent otherwise evidence. For instance, Green et
al. (1998) report the survey results from the British Employers’Manpower and Skills Practices in which
roughly one-third of the establishments respond positively to the skill shortage inquiry and identify the
recruitment problem arising mainly from poor personality, motivation and attitude rather than the lack
of cognitive skills. Similarly, in a 1998 survey conducted by the U.S. Census Bureau in collaboration with
the Department of Education, employers, when considering the hiring process, rank noncognitive skills
as far more important than the years of schooling or academic performance. Moreover, the sociology and
psychology literature have given the noncognitive skills an equally predictive power for many labor market
and social outcomes as they do to cognitive skills (see, for example, Barrick and Mount 1991, Hogan and
Holland 2003). Given this evidence, it is surprising how little work has been devoted to understanding
the role of noncognitive skills on economic success.
To date, there have been only a limited number of studies pertaining to the impact of noncognitive
traits. Using the National Longitudinal Survey of Youth (NLSY), Goldsmith et al. (1997) …nd positive
and signi…cant e¤ects of self-esteem on earnings. Bowles et al. (2001) with di¤erent data sets discuss
the e¤ects of personal traits such as self-esteem, optimism and aggression on earnings and schooling.
Coleman and DeLeire (2003), using the National Educational Longitudinal Study (NELS) data, obtain
a signi…cant impact of locus of control on the expected earnings at age 30. Heckman et al. (2006)
with the NLSY data demonstrate that noncognitive ability as measured by locus of control and self1
esteem scales are important in explaining various aspects of social and economic life. Segal (2006) with
the NELS data …nds a negative and signi…cant association between early adolescence misbehaving and
schooling/earnings. Finally, Fortin (2008) using the NELS data examines the role of several noncognitive
traits (for example, self-esteem and locus of control) in explaining the gender wage gap and …nds a modest
but signi…cant role of these traits in accounting for the gender wage gap.
While the aforementioned studies provide careful and important evidence on the e¤ectiveness of
noncognitive as well as cognitive ability, there are numerous gaps remaining. Recent studies either
…nding large or small e¤ects of ability on, say, earnings have primarily used OLS estimation and therefore,
focused on a single measure of central tendency, the conditional mean. Even though the mean impact is
an interesting and important measure, it is uninformative about ability at various points of the earnings
distribution when the e¤ect is heterogeneous. The heterogeneity may arise due to di¤erential valuation
of ability in the labor market. For instance, the e¤ect of noncognitive ability can be larger for a manager
than for a construction worker. If this is the case, it is not possible to capture these kinds of potentially
important variations with the single central tendency focus. Moreover, researchers analyzing the role
of noncognitive skills, with the exception of Heckman et al. (2006), overlook the self-rated (subjective)
structure of these measures. However, this structure may lead to substantial measurement error and
contaminate the estimates of noncognitive ability and related variables on any outcome. As indicated in
a survey by Borghans et al. (2008), accounting for measurement error is empirically important in using
noncognitive measures in applied work.
The analysis in this paper is based on the NELS data, which is an excellent source of data providing
detailed longitudinal information not only on demographics, family and schooling characteristics, but also
on a variety of pre-market measures of ability. Speci…cally, the NELS includes subject test scores as well
as the self-esteem and locus of control scales, which constitute our measure of noncognitive ability. In
addition to the conditional mean, we estimate the e¤ects of pre-market cognitive and noncognitive ability
over the earnings distribution controlling for the measurement error inherent in the latter.
2
Our distributional approach is based on quantile regression, which was initially introduced by Koenker
and Bassett (1978) for use when the assumption of normality of the error term is not strictly satis…ed.1
Among many others, Buchinsky (1994, 1998) and Powell (1986) extend the use of quantile regression
to get information about the e¤ects of exogenous explanatory variables on the dependent variable at
di¤erent parts of the distribution. Most recently, Chernozhukov and Hansen (2006, 2008) formulate the
instrumental quantile regression model from which the conditional quantiles of the distribution can be
recovered through the use of instruments under a set of assumptions.
Apart from the ability focus of the paper, the availability of the schooling inputs in the NELS data
also allows us to provide additional evidence regarding the controversy over whether particular aspects
of school quality have signi…cant e¤ects on earnings. The controversy in the school quality literature
stems from the fact that there is no consensus on the role of schooling inputs on earnings.2 While some
studies …nd signi…cant impacts, others …nd none. For instance, Card and Krueger (1992), focusing on a
cohort of individuals aged 30 to 60 in 1980 and using state-level inputs, obtain signi…cant e¤ects, whereas
Betts (1995), for individuals aged 32 and younger in 1989 with the individual-level data, concludes no
association between schooling inputs and earnings. One promising explanation for the di¤erent …ndings
is that the e¤ect of school quality has been declining over time and/or is less important for young
cohorts than it is for older cohorts. Another explanation pertains to the extent of aggregation involved
in measuring school inputs.3 The latest follow-up survey in the NELS was administered in 2000, when
almost all individuals were 26-27 years old. The nature of the NELS may shed additional light on the
controversy in the literature. To our knowledge, this is the …rst study that examines the relation between
school quality and earnings using the NELS data. Speci…cally, we look at the e¤ects of pupil-teacher ratio
1
There are several other distributional approaches (for example, stochastic dominance analysis, counterfactual distribution
estimation) to examine the data. Among many others, see Maasoumi and Millimet (2005) and Machado and Mata (2005)
for di¤erent empirical applications.
2
Parallel work examining the relation between schooling inputs and student achievement is equally indecisive (see, for
example, Hanushek 2003, Krueger 2003).
3
Due to aggregation, using the state-level measures of school quality may mitigate the problem of measurement error,
however, at the same time the state measures may capture some aspects of the state other than the quality of the actual
school.
3
and type of school. For completeness, the paper also reports the e¤ects of ability and schooling inputs
on educational attainment.
Utilizing the NELS data, we reach to the following striking empirical …ndings. Eighth grade noncognitive ability is an important determinant of earnings. However, the e¤ects are not homogeneous; those
at the lower quantiles bene…t the most from higher values of noncognitive ability. Moreover, the results
indicate substantial measurement error in noncognitive ability that correcting for it via instruments more
than doubles the mean and distributional estimates. Cognitive ability measured by eighth grade math
test scores, on the other hand, yields signi…cant e¤ects for those at the upper quantiles of the earning
distribution and the attenuation bias in noncognitive ability coe¢ cients seem to lead to upward biases for
cognitive ability estimates. Furthermore, almost in all speci…cations, the coe¢ cient estimates of noncognitive ability are larger in magnitude than the cognitive ability, which may be evidence for the higher
valuation of the former in the labor market. Using an attractive feature of the median regression, we also
show that our ability estimates are not a by-product of a selective sample. In addition, the results reveal
that, on average, eighth grade pupil-teacher ratio of the school has a negative and signi…cant e¤ect on
earnings. However, the distributional …ndings suggest that the mean e¤ect is driven predominantly by
quantiles around the median. Finally, we obtain signi…cant e¤ects of ability, pupil-teacher ratio and the
school type variables on educational attainment.
The remainder of the paper proceeds as follows. Next section contains a description of the empirical
methodology. Section 3 describes the data and evaluates the instruments used in the paper. Section 4
examines the results. Section 5 concludes and discusses the important policy implications of our analysis.
4
2
Empirical Methodology
2.1
Mean Approach
To initially examine the data, we utilize standard regression approach and thereby focus on the conditional
mean. Speci…cally, we estimate a linear regression model of the form
w = NC + C +
0
+"
(1)
where w is the (log) weekly earnings, N C and C are noncognitive (measured with error) and cognitive
abilities, respectively. The
is a lengthy vector of individual, family and schooling characteristics and "
is the error term. We estimate equation (1) by ordinary least squares (OLS) and instrumental variables
(IV), where the latter is employed to take into account the potential attenuation bias in the e¤ect of
noncognitive ability.
2.2
2.2.1
Distributional Approach
Standard Quantile Regression
Focusing on the mean may mask meaningful and policy relevant heterogeneity across the distribution.
To examine such heterogeneity, we utilize the quantile regression (QR) approach. The basic quantile
regression model speci…es the conditional quantile as a linear function of explanatory variables and is
given by
w = X0 +
Q (w j X = x) = x0 ( ) and 0 <
5
<1
(2)
where X is the vector of all explanatory variables including the cognitive and noncognitive abilities ,
the error term and Q (w j X = x) denotes the
of the error term
th
quantile of w conditional on X = x: The distribution
is left unspeci…ed and by equation (2), it is only assumed that
restriction Q ( j X = x) = 0: The
th
is
satis…es the quantile
regression quantile estimate, ^ ( ); is the solution to the following
minimization problem
M in
2<
X
w X0
jw
X0 j +
X
(1
X0 j
)jw
w<X 0
where the left (right) term is a sum of positive (negative) residuals weighted by the factor : Repeating
the estimation for di¤erent values of
between 0 and 1, we can trace the distribution of w conditional
on X and therefore, obtain a much more complete view of the e¤ects of explanatory variables.
2.2.2
Instrumental Quantile Regression
The standard QR model, similar to OLS, relies on the assumption that the explanatory variables are
measured accurately. However, if, say, noncognitive ability is measured with error, then the use of
conventional quantile regression to infer about it over the distribution of w will yield biased results.
Chernozhukov and Hansen (2006, 2008) propose an instrumental quantile regression (IQR) model that
takes into account this potential attenuation bias (or any other endogeneity).
Consider the following structural equation de…ned as
w = N C + X1
1
+U
where N C is the noncognitive ability measured with error, X1 is the vector of explanatory variables
including the cognitive ability and U is the error term. Rewriting the correspondence of equation (2) in
the IQR model, we have
Q (w j N C; X1 ) = ( )N C + X10
6
1(
)
Chernozhukov and Hansen (2006, 2008) derive an estimation equation of the form
P [w
( )N C + X10
1(
)jX1 ; Z] =
(3)
under the following set of assumptions:
( )N C + X10
1.
2. U
1(
) is strictly increasing in :
U (0; 1):
3. Conditional on X1 ; fU g is independent of Z; where Z represents the instrument(s).
4. Z is not independent of N C:
Equation (3) provides a moment restriction, which can be used to obtain the IQR estimates
1(
): Speci…cally, for a given value of
; we run the conventional QR of w
( ) and
( )N C on X1 and Z to
estimate ^ 1 ( ; ) and ^ ( ; ) where ^ ( ; ) are the estimated coe¢ cients on the instruments. The moment
equation in (3) is equivalent to the statement that zero is the quantile solution of w
conditional on (X1 ; Z): Hence to …nd an estimate for
( ); we will search for a value
( )N C
X10
1(
)
that makes the
coe¢ cients on the instrumental variables ^ ( ; ) as close to zero as possible. Formally,
^ )[^ ( ; )]
^ ( ) = arg inf [Wn ( )]; Wn ( ) = n[^ ( ; )0 ]A(
[email protected]
where @ is the parameter space for
and, as indicated in Chernezhukov and Hansen (2006, 2008),
^ ) is set to be the inverse asymptotic covariance matrix of pn(^ ( ; )
A(
( ; )) in which case Wn ( )
turns out to be the Wald statistics for testing ( ; ) = 0: The parameter estimates are then given by
(^ ( ); ^ 1 ( )) = (^ ( ); ^ 1 (^ ( ); )):
In practice, the estimation strategy for a given
works as follows:
(i) Run a series of traditional quantile regressions of w
^ (
1
j;
) and ^ (
j;
) where
j
is a grid over :
7
j(
)N C on X1 and Z to obtain coe¢ cients
(ii) Use the inverse of the covariance matrix of ^ (
the
j(
) that minimizes the Wn (
j)
j;
as the estimate of
) to obtain the Wald statistics Wn (
( ): Estimates of
1(
j ):
Take
) are the corresponding
coe¢ cients on X1 :
3
Data and Evaluation of the Instrument
3.1
Data
The data is obtained from the National Educational Longitudinal Study (NELS) of 1988, a large longitudinal study of eighth grade students conducted by the National Center for Education Statistics (NCES).
The NELS is a strati…ed sample, which was chosen in two stages. In the …rst stage, a total of 1032
schools on the basis of school size were selected from a universe of approximately 40,000 schools. In the
second stage, up to 26 students were selected from each of the sample schools based on race and gender.
For subsample of respondents, follow-up surveys were administered in 1990 (…rst-follow up, tenth grade),
1992 (second-follow up, twelfth grade), 1994 (third-follow up) and 2000 (fourth-follow up).
The respondents were administered cognitive tests in reading, social sciences, mathematics and science
during the spring of the base year, …rst and second follow-ups to measure academic achievement. Each of
the four grade speci…c tests contain material appropriate for each grade, but included su¢ cient overlap
from previous grades to permit evaluation of the academic growth. We use the eighth grade standardized
(mean of zero and standard deviation of one) math test score as our measure of cognitive ability.
With respect to the noncognitive trait, we utilize the eighth grade Rosenberg Self-Esteem and Rotter
Locus of Control Scales. The Rosenberg Scale refers to the perceptions of self-esteem (Rosenberg 1965).
The Rotter Scale, on the other hand, refers to the extent to which individuals believe that they can
control outcomes that a¤ect them (Rotter 1966). Individuals who believe that outcomes result primarily
from their own behavior and actions have an “internal”locus of control, while those who believe that fate,
chance or intervention of others determine their outcomes have an “external” locus of control. Similar
8
to cognitive tests, respondents were asked to complete a series of questionnaire items pertaining to each
trait in the base year, …rst and second follow-ups. The items were measured on a four point Likert
scale ranging from “strongly agree” (1) to “strongly disagree” (4) and the NELS constructed composite
measures, which constitute the Rosenberg Self-Esteem and the Rotter Locus of Control scales.4 Higher
values of the composite scales imply more self-esteem and an internal locus of control. These measures
have been commonly used in previous studies analyzing the role of noncognitive skills on labor market
outcomes (see, for example, Coleman and DeLeire 2003 and Heckman et al. 2006). Hence our measure of
noncognitive ability is the standardized average of the respondents’scores on the Rosenberg and Rotter
scales.
The dependent variable used throughout the paper is the log weekly earnings obtained by dividing
annual earnings by weeks worked in 1999. We restrict our analysis solely to young men who were not
enrolled in school at the time of the interview, who reported working at least 25 weeks in 1999 and were
not self-employed. Moreover, we exclude individuals whose weekly earnings are below $168 and above
4
Items that make up the self-esteem include responses to the following questions: How do you feel about the following
statements?
1. I feel good about myself;
2. I feel I am a person of worth, the equal of other;
3. I am able to do things as well as most other people;
4. On the whole, I am satis…ed with myself;
5. I feel useless at times;
6. At times I think I am no good at all;
7. I feel I do not have much to be proud of.
The …rst, second, third and fourth questionnaires are reverse scoring items and therefore, the values were reversed before
the Rosenberg Self-Esteem Scale was created.
Items that make up the locus of control include responses to the following questions: How do you feel about the following
statements?
1. I do not have enough control over the direction my life is taking;
2. In my life, good luck is more important than hard work for success;
3. Every time I try to go ahead, something or somebody stops me;
4. My plans hardly ever work out, so planning makes me unhappy;
5. When I make plans, I am almost certain I can make them work;
6. Chance and luck are very important for what happens in my life.
The …fth questionnaire is a reverse scoring item and therefore, the values were reversed before the Rotter Locus of Control
Scale was created.
9
$1,760. This corresponds to the 1st and 99th percentile of the weekly earnings distribution.
Since researchers interested in the impact of ability measures are typically (and correctly) concerned
about the potential endogeneity of these variables, we utilize a lengthy vector of individual, family and
school characteristics. Including schooling inputs in the regressions not only enable us to mitigate any
potential endogeneity problem, but also provide further evidence on their e¤ectiveness on earnings with
a novel data set. Speci…cally, our estimations control for the following variables:
Individual: race, region, educational attainment;
Family: father’s education, mother’s education, parents’marital status, socioeconomic status
of the family, family size, family income, indicators for home reading materials (books and
daily newspaper), indicator for a home computer;5
School: indicators for school type (public, Catholic, other religious and non-religious private),
pupil-teacher ratio, percentage of students from single parent homes, percentage of minority
students, percentage of students receiving free lunch, urban/rural status and region.
Information on family and schooling variables come from the base year survey questionnaires and
data pertaining to individual characteristics are obtained from the fourth-follow up survey. The e¤ective
sample excludes observations with missing data on weekly earnings, on the cognitive and noncognitive
ability measures, as well as on schooling inputs. Dummy variables are used to control for missing values
of the remaining variables. The …nal sample contains 2767 individuals. The detailed summary statistics
are provided in Table A1 in the appendix.
Prior to continuing, several comments are warranted related to the estimation strategy. First, our
use of pre-labor market measures of cognitive and noncognitive abilities allows us to avoid the reverse
causality problem (for example, the possibility that earnings develop self-esteem). Second, it is well
5
Socioeconomic status of the family ranges from -2.97 to 2.56 and was created by the administrators of the NELS using
the following parental questionnaires: (i) father’s education, (ii) mother’s education, (iii) father’s occupation, (iv) mother’s
occupation, and (v) family income.
10
known that cohort e¤ects contaminate estimates of ability measures (see, for example, Hansen et al.
2004, Neal and Johnson 1996). The problem mainly arises due to di¤erences in years of schooling and
age. For instance, the AFQT in the NLSY data were administered when the respondents were between
15 to 23 years old. That is, some respondents had already entered the labor force as full-time workers or
completed their postsecondary education. Since job experience and education enhances human capital,
the AFQT scores in the NLSY, particularly for older youths, do not solely re‡ect the cognitive ability
and require adjustment. These kinds of contaminations, however, are ruled out by the very nature of
the NELS data. Third, when isolating the e¤ects of schooling inputs on any outcome, endogeneity issues
may arise due to omission of input variables that a¤ect both the outcome variable and the respective
schooling inputs. For instance, parents with greater interest in child’s academic achievement may use
the pupil-teacher ratio of the school as a factor in determining the residential choice. Since an active
interest in the child’s achievement may lead to higher earnings, such self-selection may generate biased
estimates of the pupil-teacher ratio.6 To overcome (or at least to substantially reduce) the potential
biases of schooling inputs, we follow Dearden et al. (2002) and Dustmann et al. (2003) and utilized
a lengthy vector of family background and schooling characteristics. Finally, the self-rated structure of
the questionnaire items that form the noncognitive ability raises the question of reliability. As discussed
below, we attempt to correct for any measurement error by instrumental variable estimations.
3.2
Evaluation of the Instrument
Economists are usually reluctant to use self-rated composite measures such as Rosenberg or Rotter scales
in the analysis. The problem stems from the fact that these variables may su¤er from serious measurement
error. As widely recognized, the most common solution to this kind of problem is the use of instrumental
variable estimation, which depends on the existence of an appropriate instrument or multiple indicators
6
We choose to use the pupil-teacher ratio of the school rather than the actual class size. Aggregation to school level
avoids the endogeneity due to nonrandom assignment of the students to di¤erent classes (for example, assigning students
with learning di¢ culties to smaller classes).
11
of the variable measured with error. The latter can be applied to a situation where the same variable
is observed more than once and the later measure can be used to provide information about the earlier
estimates. The “repeated measurement” speci…cation is a common practice in the literature (see, for
example, Hausman et al. 1995 and Bound et al. 2001). In this paper, we use this approach to address
the measurement error in noncognitive ability. Speci…cally, the panel structure of the NELS data allows
us to observe the noncognitive ability measures at multiple points of time. We use the standardized tenth
grade Rosenberg and Rotter scales as instruments for the eighth grade noncognitive ability (standardized
average of Rosenberg and Rotter scales).
If the tenth grade scales are valid instruments, then (i) they must be correlated with the eighth grade
noncognitive ability, but (ii) they must not be correlated with the error term in the earnings equation.
To check the …rst condition, we run a regression, controlling for all the other covariates, of eighth grade
noncognitive ability on tenth grade Rosenberg and Rotter scales, which yields a partial R2 and F statistics as 0.202 and 275.83, respectively. The Cragg and Donald (1993) test statistic also supports the
instruments relevance (p-value=0.00). Therefore, weak identi…cation should not be a problem. Since we
have multiple instruments, we can also apply the overidenti…cation test to see whether the instruments
are correlated with the error term in the earning equation. Doing so with the Hansen’s J-statistics yields
a p-value=0.30, which indicates that our instruments satisfy the second condition as well.
Even though the usual IV conditions seem to be satis…ed, assuming independence over time across the
errors of noncognitive measures (classical measurement error assumption) may not be utterly convincing.
In their seminal survey, Bound et al. (2001) claim that the errors of two reports taken from the same
individual at di¤erent points of time is likely to be positively correlated. Under this circumstance, the
IV estimation will not produce an unbiased estimate of the true parameter, but the good news is that
correcting for the measurement error will tighten the bounds on the true parameter (
7
To see this, consider a general measurement error framework such as w =
suppose there are two error ridden indicators of N C given by N C1 = N C +
12
^
IV
^
7
OLS ).
N C + " where N C is unobserved and
1
and N C2 = N C +
2:
Using N C1 as a
In this respect, we believe that there is value added in reporting the instrumental variable estimations
even in the presence of positive correlation between the measurement errors.
4
Empirical Results
4.1
4.1.1
Mean Results
Ordinary Least Square Estimations
Table 1 presents our baseline OLS estimates. Robust standard errors are given in parentheses beneath
each coe¢ cient. Column 1 shows the simple regression between noncognitive ability and log weekly
earnings. In the absence of any controls, a one-standard deviation increase in noncognitive ability is
associated with a signi…cant 6% increase in weekly earnings. Column 2 adds the eighth grade math
test scores, which also yields a statistically signi…cant and positive coe¢ cient. A one-standard deviation
increase in test scores raises weekly earnings by 7.1%. Comparing the second column to the …rst one, we
observe that controlling for cognitive ability decreases the coe¢ cient estimate of noncognitive ability by
1.6% points. However, noncognitive ability continues to be an important determinant of earnings. This
…nding may provide some evidence on the multidimensionality of ability.8
Even though the simple regressions indicate non-negligible e¤ects of cognitive and noncognitive ability,
these speci…cations may be misleading because they do not take into account many observable variables
that are known to a¤ect earnings. Therefore, we …rst include the individual characteristics in the third
column of Table 1. The ability variable estimates are similar in magnitude. The fourth column of Table
proxy for N C and N C2 as an instrument for N C1 ; Bound et al. (2001) derive the following instrumental variable estimate
IV
=
[
2
NC
[ 2N C + N C
+ NC ; 2 ] +
; 2]
+
NC ; 1
2 ;"
+
1; 2
where IV = if
= x ; 1 = 1 ; 2 = 0: In other words, if the classical measurement error assumptions hold, the
2 ;"
instrumental variable estimate will yield an unbiased estimate of the true parameter. However, as indicated in Bound
et al. (2001), if N C1 and N C2 represent two reports on N C taken from the same individual but at di¤erent points of
time, it seems likely that two reports will be positively correlated (i.e.,
> 0). Even if this is the case, as long as
1; 2
= x ; 1 = 0 holds, correcting for measurement error via IV estimation still tightens the bound on the true parameter
2 ;"
8
2
NC
).
+ 21
The simple correlation between cognitive and noncognitive ability is 0.23.
estimate (
IV
OLS
=
2
NC
13
1 augments the family background variables. The coe¢ cient on noncognitive ability is barely a¤ected,
while there is a large decrease in the eighth grade math test score coe¢ cient from 0.061 to 0.036. However,
note that cognitive ability still remains signi…cant.
Another concern regarding the impact of ability measures is that schooling environment has a role
in the formation of ability and it is conceivable that schools a¤ect the earnings. Moreover, controlling
for school characteristics may itself be interesting since they shed additional light on the impact of
schooling inputs on earnings. The …fth column of Table 1 presents the results. Even though including
the eighth grade school measures do little change in the coe¢ cient estimates of the ability variables,
we …nd that the pupil-teacher ratio yields a negative and signi…cant e¤ect on earnings. Speci…cally,
a one-standard deviation increase in the pupil-teacher ratio decreases the weekly earnings by 1.8% (0.0041*4.492). Utilizing UK data, Dustmann et al. (2003) obtain a statistically signi…cant negative e¤ect
of 0.33% at age 33 and 0.30% at age 42 on hourly wages from a unit increase in the pupil-teacher ratio.
Our coe¢ cient estimate of -0.0041 (-0.41%) is consonant with these …ndings. The school type variables,
on the other hand, are imprecisely estimated.
In order to understand to what extent the association between ability and earnings is attributable to
educational attainment, we incorporate the educational controls in the last column of Table 1. Conditioning on educational attainment also gives the schooling input coe¢ cients a direct e¤ect interpretation
(excluding the e¤ect that works through the educational attainment). Doing so leaves the coe¢ cient
estimates of noncognitive ability and pupil-teacher ratio similar, while the math test score coe¢ cient falls
from 0.035 to 0.020. This suggests that more than 40% of the impact of cognitive ability on earnings
works through the educational channels. The school type variables continue to be statistically insignificant in the last column of Table 1. As an alternative to this speci…cation, we add eighth grade school
…xed e¤ects to the regression. The school dummies are jointly signi…cant (p-value=0.00) and the ability
estimates are similar to that of column 6.
We also examine the e¤ects of ability and schooling inputs on educational attainment. The Table A2
14
in the appendix presents the ordered probit estimation results where the highest educational attainment
is given the highest rank and thus a positive coe¢ cient implies an increase in the chances of a higher
attainment. The marginal e¤ects, evaluated at the sample means of those who have a college degree or
higher, are reported in square brackets. Cognitive and noncognitive ability estimates, in all speci…cations,
are positive and statistically signi…cant. Considering the most extensive speci…cation (column 5), a onestandard deviation increase in noncognitive ability (math test scores) increases the chances of a college
degree or higher by 3.6% (15.3%). Moreover, the eighth grade pupil teacher ratio and attending a Catholic
(or a non-religious private) secondary school are statistically signi…cant determinants of educational
attainment. Speci…cally, a one-standard deviation increase in the pupil-teacher ratio decreases the chances
of obtaining a college degree or higher by 1.7% points (-0.0037*4.613) and switching from a public to a
Catholic secondary school increases the same chances by 19.5%.9
4.1.2
Instrumental Variable Estimations
The measurement error corrected estimates for noncognitive ability, using the tenth grade Rosenberg
and Rotter scales as instruments, are reported in Table 2. The …rst column gives the results without
conditioning on educational attainment. The disattenuated coe¢ cient estimate for noncognitive ability
is much larger (more than twice) than the corresponding least square estimate. A one-standard deviation
increase in noncognitive ability is associated with a 9.2% increase in weekly earnings. Our noncognitive
ability estimate is similar to that of Heckman et al. (2006), who use the same measure with the NLSY
data. The OLS coe¢ cient on noncognitive ability for log hourly wages more than triples (from 0.043 to
0.135) when the authors correct for measurement error by a factor model with simulated sample from the
NLSY. Comparing our IV and OLS (column 5 of Table 1) estimates, we observe a reduction of roughly
30% in the math test score coe¢ cient, but the impact continues to be statistically signi…cant. This
decrease implies an upward bias in the math test score coe¢ cient due to measurement error inherent in
9
The educational attainment sample standard deviation for the pupil-teacher ratio is 4.613.
15
noncognitive ability estimate.10 The coe¢ cient for the pupil-teacher ratio, on the other hand, is similar
in magnitude and signi…cant. Including the educational attainment controls to the regression (column 2)
does not alter the …ndings with respect to noncognitive ability and pupil-teacher ratio, but the coe¢ cient
estimate for cognitive ability falls short of statistical signi…cance.11
So far, we have assumed that cognitive ability is measured accurately. However, it is plausible that the
estimate of this variable is also attenuated towards zero. To check this, we utilize the “error-in-variable”
regression and adjust for the potential attenuation bias of test score impact by imposing a reliability
ratio, known as Cronbach’s alpha. The ratio that we use in the estimations comes from Murnane et al.
(1995).12 The authors report the estimated reliability ratios for math test scores segregated by gender
for the National Longitudinal Study of the High School Class of 1972 and High School and Beyond data.
We use the lowest reported reliability value among these two data sets, which is 0.86, for males. In other
words, we impose the ratio of 0.86 to disattenuate the potential bias in the math test score coe¢ cient.
Table A3 in the appendix presents the “error-in-variable”regression results. Comparing the measurement
error corrected cognitive ability estimates with the OLS coe¢ cients from Columns 5 and 6 of Table 1,
we only observe slight changes. Therefore, attenuation bias does not seem to be a severe problem for
the test score. We also calculate the reliability ratio among the questionnaire items that constitute the
noncognitive ability measure in the NELS data. The estimated value is 0.73. Table A4 in the appendix
reports the error-in-variable regression results, which adjusts for the measurement error in noncognitive
ability by imposing the ratio of 0.73. The …ndings from the Table provide additional evidence for the
10
To see this, consider a general measurement error framework: w = N C + C + " where N C is unobserved, but C is
observed. Suppose there is an error ridden indicator of N C such that N C = N C + and using N C as a proxy for N C
leads to the well known attenuation bias for . However, this is not the only estimate that is going to be biased. In this
simple setup, the OLS estimate for is
^= +
V ar( )
Cov(C; N C )
where =
and =
: Since cognitive and noncognitve abilities are posV ar( ) + V ar(N C )
V ar(C)(1 Corr(C; N C )2 )
tively correlated (see, footnote 8), then > 0 and the e¤ect of on w is upward biased.
11
As an alternative to our present IV speci…cations, we replace eighth grade noncognitive ability measure with the tenth
grade and use eighth grade Rosenberg and Rotter scales as instruments. The IV estimates of noncognitive ability are almost
identical to those presented in Table 2.
12
The NELS data does not report the questionnaire items that form the eighth grade math and reading scores and
therefore, it is not possible to estimate the reliability ratio.
16
downward bias in noncognitive ability.
Taken altogether, our conditional mean estimates provide three key insights. First, eighth grade
cognitive and noncognitive abilities are two important determinants of earnings, as well as educational
attainment, for young men. Taken at the face value and considering the most extensive speci…cation
(column 6 of Table 1), a one-standard deviation increase in noncognitive (cognitive) ability is associated
with an increase of 3.7% (2%) in weekly earnings. This …nding is further supported by the instrumental
variable estimations, which indicate that correcting for measurement error more than doubles the coe¢ cient estimates on noncognitive ability. Although the attenuation bias is not a serious problem for test
scores, the measurement error inherent in noncognitive ability leads to a non-negligible upward bias in
the estimate of cognitive ability. Moreover, a large extent of the relation between cognitive ability and
earnings seem to work through the educational channels and that controlling for attainment reduces the
coe¢ cient on math test score for both OLS and IV estimations. Second, the stability of noncognitive
measure coe¢ cient in the earnings equation to the inclusion of math test score (column 2 of Table 1) provides additional evidence to a growing body of research, which emphasizes that a unidimensional vision of
ability is a faulty one (see, for example, Borghans 2008, Carneiro and Heckman 2003). Third, on average,
we …nd a negative and signi…cant impact of pupil-teacher ratio and no evidence on the e¤ectiveness of
the school type variables on young men’s earnings. However, it is important to note that the school type
variables turn out to be important predictors when we switch the focus to educational attainment.
Comparing the mean …ndings of this paper with studies (Segal 2006, Fortin 2008) that use the same
data and similar measures of ability, our results di¤er in the following aspects. Segal (2006) construct a
teacher-rated standardized eighth grade student misbehavior index and use this index with eighth grade
composite (math and reading) test score as measures of noncognitive and cognitive ability, respectively.
The author’s most extensive speci…cation, which controls for individual characteristics, school …xed e¤ects
and educational attainment, reveals a negative e¤ect for misbehave index of around 3.5% and a positive
but insigni…cant impact of eighth grade composite test score on earnings for young men. In the absence
17
of measurement error correction, our OLS estimate of noncognitive ability (column 6 of Table 1) is similar
in magnitude to that of Segal (2006). However, as indicated above, measurement error correction leads
to substantial increment in the noncognitive ability estimates and there is no apriori reasoning to believe
that teacher-rated (subjective) index is free from measurement error bias. Fortin (2008), on the other
hand, uses twelfth grade self-esteem, locus of control and math test score measures for noncognitive
and cognitive ability and obtains signi…cant e¤ects of twelfth grade self-esteem and math test score on
earnings. However, using the twelfth grade test battery results in a very selected sample because only 80%
of school in participants and 40% of the dropouts actually took the test battery. In contrast, eighth grade
test battery has a take up rate of about 95% for school in participants and eighth grade, by construction,
has no dropouts. Moreover, twelfth grade measures of noncognitive ability are also likely to su¤er from
the measurement error problem and this may lead to an understatement of the true e¤ect.13
4.2
4.2.1
Distributional Results
Standard Quantile Regression Estimation
Turning to the distributional results, in Figure 1 we report the e¤ects of noncognitive (left column) and
cognitive (right column) ability obtained from the standard quantile regression. The top panel of Figure
1 contains QR estimates without controlling for educational attainment, while the bottom panel presents
the estimates with educational controls. The shaded region in the panels represents the 95% con…dence
interval. Finally, Table 3 reports the coe¢ cient estimates of ability measures and schooling inputs for
the selected quantiles.14
In the absence of educational controls, Figure 1 (top left panel) reveals that the noncognitive ability
coe¢ cients are positive and statistically signi…cant for (almost) all quantiles across the distribution and
the e¤ects are more pronounced at the lower tail. For instance, a one standard deviation increase in
13
Fortin (2008) reports the regression estimates for the pooled sample of males and females and therefore, it is not possible
to observe the isolated e¤ect of noncognitive ability measures on males.
14
Standard errors are computed using a Gaussian kernel and Silverman’s (1986) rule of thumb bandwidth. See Buchinsky
(1998) for further discussion of the alternative estimators of the covariance matrix of the quantile regression estimates.
18
noncognitive ability is associated with an increase of 4.9% on earnings at the 10th quantile and a 2%
increase at the 90th quantile. The e¤ects of cognitive ability, on the other hand, show a reversed pattern
(top right panel). We do not observe any impact at the lower end of the earnings distribution, while it
turns out to be more e¤ective and signi…cant as we move along the quantile index. With respect to the
schooling inputs (Table 3, Panel A), our QR …ndings indicate a statistically signi…cant impact for only
those at the 60th quantile of the earnings distribution. Similarly, we observe a weak evidence of gain from
attending a Catholic school on earnings at the same quantile.
Controlling for education (bottom left panel) does not largely alter our …ndings regarding to noncognitive ability estimates. Figure 1 indicates that the impact of noncognitive ability keeps roughly ranging
from 5% to 2% and, similar to the top panel, the e¤ects are not di¤erent from zero at the very upper
quantiles. More pronounced reductions are observed in the impact of cognitive ability and it falls short
of statistical signi…cance below roughly the 70th quantile . As with schooling inputs, conditioning on
educational attainment (Table 3, Panel B) shifts the statistically signi…cant impact of pupil teacher ratio
to those at the median, whereas the gain from attending a Catholic school at the 60th quantile disappears.
4.2.2
Instrumental Quantile Regression Estimation
The next set of results pertains to IQR estimates. The e¤ects of noncognitive and cognitive ability are
plotted in Figure 2 and Table 4 contains the coe¢ cient estimates of ability measures and schooling inputs
for the selected quantiles. The computation of the IQR estimates is conducted over the parameter space
@ = [ 0:5; 0:5] using a step size of
j
= 0:01:15
Similar to the mean …ndings, correcting for measurement error more than doubles the noncognitive
ability coe¢ cients across the entire distribution (top right panel, Figure 2). The IQR estimates roughly
range from 15% to 6% and show a decreasing pattern in the quantile index. Moreover, the impact of
15
Standard errors are computed using a Gaussian kernel and Silverman’s (1986) rule of thumb bandwidth. See Chernozhukov and Hansen (2006, 2008) for further discussion of the estimator of the covariance matrix of the instrumental
quantile regression estimates.
19
noncognitive ability is only weakly signi…cant for the very upper quantiles, which further supports our
…nding that the e¤ects are more pronounced for lower quantiles. The e¤ects of eighth grade math test
score reveal similarity to that of QR estimates; statistically meaningful e¤ects exist for quantiles above
the median of the distribution. However, the magnitude of the coe¢ cients are smaller than the QR,
which may once again suggest evidence for the upward bias in the estimates of cognitive ability due
to attenuation bias in noncognitive ability estimates. It is also important to note that the in‡uence of
noncognitive ability on earnings is considerably larger in magnitude than the cognitive ability throughout
the distribution. When we turn to the schooling inputs in the IQR model (Table 4, Panel A), the most
notable di¤erence relative to Panel A of Table 3 is that the pupil teacher ratio is more precisely estimated
at the median rather than the 60th quantile. A one standard deviation increase in pupil-teacher ratio is
associated with a 2.4% (-0.0054*4.492) decrease in median weekly earnings. Including the educational
attainment controls do not largely overturn the results for noncognitive ability and pupil-teacher ratio
estimates, however, the impact of cognitive ability now falls short of statistical signi…cance everywhere
below roughly the 80th quantile (bottom panel, Figure 2 and Table 4, Panel B).
In sum, neither the ability nor the pupil-teacher ratio estimates show a uniform e¤ect across the
quantiles and this heterogeneity casts doubt on the validity of a single statistic, such as the conditional
mean, to provide a clear overall picture.
4.3
Sample Selection Issue
Even though the NELS data o¤ers some bene…ts such as providing multiple measures of ability during
adolescent and no need for cohort di¤erences adjustment, it does not refer to “prime earning” ages.
That is, some of the respondents are still enrolled in a postsecondary institution, which may lead to a
selective sample and thereby may contaminate the returns to cognitive and noncognitive abilities. The
raw examination of the data reveals that 14% of the e¤ective sample are still enrolled in school. To see
the e¤ect of this on our results, we follow the strategy described in Johnson et al. (2000) and undertake
20
a sensitivity analysis using the attractive feature of the median regression. Speci…cally, the 50th quantile
coe¢ cient estimate is only a¤ected by the position of earnings with respect to the median rather than
the speci…c values. If missing earning observations for those enrolled in school are imputed on the correct
side of the median, the 50th quantile may provide valuable information pertaining to sample selection
issue. In other words, assigning a very large or a very low value does not change the median estimate
as long as the imputation is on the correct side of the median. The earnings of those enrolled in a
postsecondary institution will most likely fall above the median so that we assign some arbitrarily large
earning value above the median. In the absence of educational controls, the QR (IQR) estimates for the
50th quantile are 2.9% (2.2%) and 3.4% (7%) for cognitive and noncognitive abilities, respectively and
are all statistically signi…cant. Comparing these coe¢ cients to the corresponding 50th quantile estimates
from Panel A of Table 3 and 4, there is only slight di¤erence in the math test score coe¢ cients for the
IQR, while larger di¤erences are observed for the QR and if anything, there is evidence for upward bias
of cognitive ability impact. The coe¢ cients for noncognitive ability are almost identical and continue to
be larger in magnitude than the cognitive ability estimates.
Furthermore, intuitive appeal implies that those enrolled in postsecondary institutions are more prone
to earn at the upper tail of the conditional earnings distribution and our policy proposal, which is more
relevant to lower quantiles, is unlikely to be a¤ected by this potential sample selection contamination.
5
Discussion and Conclusion
Utilizing the NELS data, this paper investigates the role of pre-labor market cognitive and noncognitive
ability, as well as schooling inputs, on young men’s earnings. In addition to the conditional mean, we
estimate the impact of ability and schooling inputs over the earnings distribution by recently developed
(instrumental) quantile regression techniques. Viewing the complete set of results, we have …ve striking
conclusions.
First, our …ndings show that cognitive and noncognitive abilities are two important determinants
21
of earnings. However, the e¤ects are not uniform across the distribution. We …nd noncognitive ability
to be most e¤ective for lower quantiles of the earnings distribution. Moreover, we observe substantial
measurement error inherent in noncognitive ability coe¢ cients that correcting for it more than doubles
the estimates. Cognitive ability as measured by eighth grade math test scores, on the other hand, shows a
reversed pattern with the e¤ects being more pronounced at the upper tail of the earnings distribution. The
reductions observed in the cognitive ability estimates to the inclusion of the educational controls imply
that a signi…cant extent of the association between cognitive ability and earnings works through the
educational channels. Furthermore, in almost all speci…cations, the coe¢ cient estimates on noncognitive
ability is larger in magnitude than the cognitive ability, which may be evidence for the higher valuation
of noncognitive ability in the labor market. Third, although there is some correlation between cognitive
and noncognitive ability, the …ndings in the paper support the argument that a unidimensional vision of
ability is a faulty one. Fourth, on average, our results indicate a negative and signi…cant impact of pupilteacher ratio on earnings and controlling for education does not overturn the pupil-teacher ratio estimate.
However, analogous to noncognitive ability, we observe heterogeneity in the coe¢ cient estimates of the
pupil-teacher ratio. Speci…cally, we obtain a meaningful impact of pupil-teacher ratio around the median
and the 60th quantile. The school type variables, on the other hand, do not yield any signi…cant e¤ects on
earnings. The noncognitive ability accompanied with the pupil-teacher ratio estimates suggest that the
conditional mean obscures some important information. Finally, even though it is not the main focus of
the paper, we …nd that ability (cognitive and noncognitive), pupil-teacher ratio and school types matter
for educational attainment.
In recent years, a body of empirical research documenting the importance of noncognitive ability for
earnings, schooling and a variety of behavioral outcomes has emerged. These …ndings in conjunction with
our results have important policy implications. It is widely recognized that cognitive ability is fairly set
by age eight, while there is strong evidence for the malleability of noncognitive ability at later ages (see,
for example, Carneiro and Heckman 2003, Cunha et al. 2006). Given this nature and the quantitative
22
importance of noncognitive ability, the educational/social policy interventions during early childhood or
adolescence aiming to alter noncognitive rather than the cognitive ability may be more e¤ective to combat
adverse labor market and educational outcomes. Indeed, early intervention programs such as the Perry
Preschool, which emphasized participants’intellectual and social development, was much more successful
in changing the noncognitive ability compared to the cognitive ability.
Moreover, taken at the face value, our mean …ndings suggest that a one-standard deviation increase
in noncognitive ability has a much larger impact on earnings and educational attainment than the same
unit of increase in the pupil-teacher ratio. Furthermore, when we extend the focus to a distributional
framework, we observe that all individuals bene…t from higher values of noncognitive ability, whereas
the pupil-teacher ratio reduction, in terms of earnings, is only bene…cial around the median and the 60th
quantile. In the absence of a detailed cost-bene…t analysis, it may be premature to draw a …rm policy
conclusion. However, for economic success and to reduce earnings inequality, focusing on the ways to
boost noncognitive ability may be a more e¤ective tool than simply pouring more funds into schools to
lower the pupil-teacher ratio.
23
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28
Table 1: OLS Estimations
Specification
(1)
8th Grade Noncognitive Ability
8th Grade Cognitive Ability
0.060***
(0.007)
… ..
(2)
0.044***
(0.008)
0.071***
(0.008)
… ..
(3)
(4)
(5)
(6)
0.046***
(0.008)
0.061***
(0.008)
… ..
0.041***
(0.008)
0.036***
(0.008)
… ..
0.040***
(0.008)
0.035***
(0.008)
-0.0041**
(0.0021)
0.042
(0.035)
0.001
(0.059)
-0.024
(0.048)
0.037***
(0.008)
0.020**
(0.009)
-0.0037*
(0.0020)
0.025
(0.034)
-0.009
(0.059)
-0.033
(0.048)
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
Pupil-Teacher Ratio
… ..
Catholic School
… ..
… ..
… ..
… ..
Other Religious School
… ..
… ..
… ..
… ..
Non-Religious Private School
… ..
… ..
… ..
… ..
Other Controls:
Individual
Family
Schooling Inputs
Educational Attainment
No
No
No
No
No
No
No
No
Yes
No
No
No
Yes
Yes
No
No
NOTES: Robust standard errors are presented in parentheses. See text for definition of the variables.
* significant at 10%, ** significant at 5%, *** significant at 1%.
Table 2: IV Estimations
Specification
8th Grade Noncognitive Ability
8th Grade Cognitive Ability
Pupil-Teacher Ratio
Catholic School
Other Religious School
Non-Religious Private School
Other Controls:
Individual
Family
Schooling Inputs
Educational Attainment
(1)
(2)
0.092***
(0.017)
0.024***
(0.009)
-0.0045**
(0.0020)
0.035
(0.035)
-0.012
(0.058)
-0.028
(0.048)
0.083***
(0.017)
0.012
(0.009)
-0.0040**
(0.0020)
0.021
(0.035)
-0.021
(0.058)
-0.036
(0.048)
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
NOTES: Robust standard errors are presented in parentheses. See text for definition
of the variables.
* significant at 10%, ** significant at 5%, *** significant at 1%.
Table 3: Standard Quantile Regression Estimations
Panel A
8th Grade Noncognitive Ability
8th Grade Cognitive Ability
Pupil-Teacher Ratio
Catholic School
Other Religious School
Non-Religious Private School
Other Controls:
Individual
Family
Schooling Inputs
Educational Attainment
θ=0.10
θ=0.40
0.049***
(0.014)
0.035*
(0.020)
-0.0032
(0.0046)
-0.013
(0.079)
-0.116
(0.143)
-0.043
(0.090)
0.040***
(0.010)
0.031***
(0.011)
-0.0033
(0.0028)
0.012
(0.050)
0.058
(0.078)
-0.043
(0.060)
θ=0.50
0.030***
(0.010)
0.046***
(0.011)
-0.0035
(0.0024)
0.048
(0.044)
0.094
(0.063)
-0.008
(0.053)
θ=0.60
0.034***
(0.010)
0.034***
(0.010)
-0.0054**
(0.0026)
0.075*
(0.042)
0.061
(0.066)
-0.028
(0.057)
θ=0.90
0.020*
(0.012)
0.036***
(0.013)
-0.0028
(0.0031)
0.098
(0.062)
0.038
(0.073)
0.048
(0.085)
Yes
Yes
Yes
No
Yes
Yes
Yes
No
Yes
Yes
Yes
No
Yes
Yes
Yes
No
Yes
Yes
Yes
No
θ=0.10
θ=0.40
θ=0.50
θ=0.60
θ=0.90
0.052***
(0.015)
0.021
(0.021)
-0.0022
(0.0046)
-0.060
(0.092)
-0.170
(0.164)
-0.085
(0.092)
0.038***
(0.010)
0.011
(0.011)
-0.0032
(0.0026)
-0.012
(0.044)
0.028
(0.084)
-0.039
(0.063)
0.033***
(0.009)
0.018
(0.010)
-0.0054**
(0.0023)
0.046
(0.043)
0.074
(0.065)
-0.011
(0.057)
0.034***
(0.009)
0.012
(0.010)
-0.0042
(0.0026)
0.059
(0.042)
0.099
(0.063)
0.009
(0.055)
0.023*
(0.013)
0.027*
(0.014)
-0.0008
(0.0032)
0.049
(0.062)
0.040
(0.075)
0.041
(0.091)
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Panel B
8th Grade Noncognitive Ability
8th Grade Cognitive Ability
Pupil-Teacher Ratio
Catholic School
Other Religious School
Non-Religious Private School
Other Controls:
Individual
Family
Schooling Inputs
Education Attainment
Yes
Yes
Yes
Yes
NOTES: Robust standard errors are presented in parentheses. See text for definition of the variables.
* significant at 10%, ** significant at 5%, *** significant at 1%.
Table 4: Instrumental Quantile Regression Estimations
Panel A
θ=0.10
8th Grade Noncognitive Ability
8th Grade Cognitive Ability
Pupil-Teacher Ratio
Catholic School
Other Religious School
Non-Religious Private School
Other Controls:
Individual
Family
Schooling Inputs
Educational Attainment
0.150***
(0.040)
0.016
(0.021)
-0.0024
(0.0045)
-0.037
(0.091)
-0.127
(0.158)
-0.105
(0.095)
θ=0.40
0.110***
(0.023)
0.026**
(0.012)
-0.0030
(0.0029)
0.023
(0.053)
0.026
(0.081)
-0.054
(0.071)
θ=0.50
0.080***
(0.024)
0.030**
(0.012)
-0.0054**
(0.0026)
0.057
(0.047)
0.062
(0.071)
0.002
(0.058)
θ=0.60
θ=0.90
0.080***
(0.021)
0.022**
(0.011)
-0.0039
(0.0025)
0.073*
(0.041)
0.079
(0.064)
0.003
(0.056)
0.060*
(0.035)
0.033**
(0.015)
-0.0023
(0.0033)
0.094
(0.062)
0.009
(0.077)
-0.004
(0.084)
Yes
Yes
Yes
No
Yes
Yes
Yes
No
Yes
Yes
Yes
No
Yes
Yes
Yes
No
Yes
Yes
Yes
No
θ=0.10
θ=0.40
θ=0.50
θ=0.60
θ=0.90
0.100***
(0.023)
0.005
(0.012)
-0.0035
(0.0027)
-0.024
(0.046)
0.007
(0.080)
-0.093
(0.066)
0.080***
(0.021)
0.011
(0.011)
-0.0041
(0.0026)
0.025
(0.046)
0.059
(0.071)
0.012
(0.061)
0.070***
(0.020)
0.006
(0.011)
-0.0051**
(0.0025)
0.051
(0.042)
0.087
(0.061)
-0.007
(0.056)
0.070*
(0.039)
0.029*
(0.016)
-0.0017
(0.0035)
0.082
(0.064)
0.024
(0.080)
0.005
(0.086)
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Panel B
8th Grade Noncognitive Ability
8th Grade Cognitive Ability
Pupil-Teacher Ratio
Catholic School
Other Religious School
Non-Religious Private School
Other Controls:
Individual
Family
Schooling Inputs
Educational Attainment
0.140***
(0.041)
0.010
(0.021)
-0.0037
(0.0043)
0.002
(0.008)
-0.172
(0.197)
-0.144
(0.095)
Yes
Yes
Yes
Yes
NOTES: Robust standard errors are presented in parentheses. See text for definition of the variables.
* significant at 10%, ** significant at 5%, *** significant at 1%.
Figure 1: Standard Quantile Regression Estimates
Standard Quantile Regression
Standard Quantile Regression
0.09
0.08
0.08
0.07
0.06
Cognitive Ability Effects
Noncognitive Ability Effects
0.06
0.05
0.04
0.03
0.04
0.02
0.02
0
0.01
0
-0.02
-0.01
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.1
0.2
0.3
0.4
0.5
0.6
Quantile
Quantile
Standard Quantile Regression
Standard Quantile Regression
0.7
0.8
0.9
0.7
0.8
0.9
0.08
0.06
0.07
0.04
Cognitive Ability Effects
Noncognitive Ability Effects
0.06
0.05
0.04
0.03
0.02
0
0.02
0.01
-0.02
0
-0.01
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
-0.04
0.1
Quantile
0.2
0.3
0.4
0.5
0.6
Quantile
NOTES: The top left (right) panel contains standard quantile regression estimates for noncognitive (cognitive) ability
without educational attainment controls, while the bottom left (right) panel contains standard quantile regression estimates
for noncognitive (cognitive) ability with educational attainment controls. The shaded region is the 95% con…dence band
using heteroskedasticity-robust standard errors. Estimates are reported for
2 [0.1,0.9] at 0.01 unit intervals.
Figure 2: Instrumental Quantile Regression Estimates
Instrumental Quantile Regression
Instrumental Quantile Regression
0.25
0.06
0.2
Cognititve Ability Effects
Noncognitive Ability Effects
0.04
0.15
0.1
0.02
0
0.05
-0.02
0
-0.04
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.1
0.2
0.3
0.4
0.5
0.6
Quantile
Quantile
Instrumental Quantile Regression
Instrumental Quantile Regression
0.7
0.8
0.9
0.7
0.8
0.9
0.06
0.2
0.04
Cognitive Ability Effects
Noncognitive Ability Effects
0.15
0.1
0.02
0
0.05
-0.02
0
-0.04
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.1
0.2
Quantile
0.3
0.4
0.5
0.6
Quantile
NOTES: The top left (right) panel contains instrumental quantile regression estimates for noncognitive (cognitive) ability
without educational attainment controls, while the bottom left (right) panel contains instrumental quantile regression estimates for noncognitive (cognitive) ability with educational attainment controls. The shaded region is the 95% con…dence
band using heteroskedasticity-robust standard errors. Estimates are reported for
2 [0.1,0.9] at 0.01 unit intervals.
Appendix:
Table A1: Summary Statistics
Education
Less Than High School
High School
Some College
College/Advanced Degree
Race
White
Black
Others
Mother's Education
Less Than High School
High School
Some College
College/Advanced Degree
Family Income
0-$9,999
$10,000-$34,999
$35,000-$74,999
$75,000 or more
Intact Family (1=Yes)
Family Size
Socioeconomic Status of the Family
Pupil-Teacher Ratio
School Type
Public School
Catholic School
Other Religious School
Non-Religious Private School
Sample Size
Mean
SD
0.049
0.228
0.425
0.290
0.216
0.419
0.494
0.454
0.845
0.116
0.034
0.361
0.320
0.183
0.115
0.378
0.109
0.292
0.319
0.485
0.311
0.455
0.089
0.434
0.357
0.064
0.751
4.524
-0.051
17.580
0.285
0.495
0.479
0.246
0.432
1.384
0.722
4.492
0.883
0.072
0.025
0.017
0.320
0.259
0.158
0.131
2767
NOTES: NELS sampling weights utilized. The variables are only a subset of those used in the
analysis. The remainder are excluded in the interest of brevity. The full set of sample statistics
are available upon request.
Table A2: Ordered Probit Estimations of Educational Attainment
Specification
(1)
8th Grade Noncognitive Ability
8th Grade Cognitive Ability
0.235***
(0.015)
[0.084]
… ..
(2)
0.124***
(0.016)
[0.043]
0.647***
(0.018)
[0.224]
… ..
(3)
0.123***
(0.016)
[0.042]
0.640***
(0.018)
[0.221]
… ..
(4)
0.111***
(0.017)
[0.037]
0.462***
(0.020)
[0.154]
… ..
Pupil-Teacher Ratio
… ..
Catholic School
… ..
… ..
… ..
… ..
Other Religious School
… ..
… ..
… ..
… ..
Non-Religious Private School
… ..
… ..
… ..
… ..
Other Controls:
Individual
Family
Schooling Inputs
No
No
No
No
No
No
Yes
No
No
Yes
Yes
No
(5)
0.109***
(0.017)
[0.036]
0.463***
(0.021)
[0.153]
-0.0113**
(0.0044)
[-0.0037]
0.533***
(0.078)
[0.195]
0.157
(0.123)
[0.054]
0.284**
(0.115)
[0.100]
NOTES: Asymptotic standard errors are presented in parentheses, marginal effects, evaluated at the sample means of those
who have a college degree or higher, are shown in square brackets. Sample size is 4931. See text for definition of the variables.
* significant at 10%, ** significant at 5%, *** significant at 1%.
Yes
Yes
Yes
Table A3: Error-in-Variable Regression Estimations
Specification
8th Grade Noncognitive Ability
8th Grade Cognitive Ability
Pupil-Teacher Ratio
Catholic School
Other Religious School
Non-Religious Private School
Other Controls:
Individual
Family
Schooling Inputs
Educational Attainment
(1)
(2)
0.039***
(0.007)
0.043***
(0.010)
-0.0041**
(0.0020)
0.041
(0.034)
0.001
(0.056)
-0.026
(0.048)
0.036***
(0.007)
0.026**
(0.011)
-0.0036*
(0.0020)
0.025
(0.034)
-0.010
(0.056)
-0.034
(0.048)
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
NOTES: Asymptotic standard errors are presented in parentheses. The reliability
ratio imposed for cognitive ability is 0.86 and comes from Murnane et al. (1995).
See text for definition of the variables.
* significant at 10%, ** significant at 5%, *** significant at 1%.
Table A4: Error-in-Variable Regression Estimations
Specification
8th Grade Noncognitive Ability
8th Grade Cognitive Ability
Pupil-Teacher Ratio
Catholic School
Other Religious School
Non-Religious Private School
Other Controls:
Individual
Family
Schooling Inputs
Educational Attainment
(1)
(2)
0.057***
(0.011)
0.031***
(0.008)
-0.0042**
(0.0020)
0.039
(0.034)
-0.003
(0.056)
-0.026
(0.048)
0.053***
(0.011)
0.017*
(0.009)
-0.0038*
(0.0020)
0.023
(0.034)
-0.013
(0.056)
-0.034
(0.048)
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
NOTES: Asymptotic standard errors are presented in parentheses. The reliability
ratio imposed for noncognitive ability is 0.73. See text for definition of the variables.
* significant at 10%, ** significant at 5%, *** significant at 1%.
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