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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. 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(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%.