Education, Ability and Earnings, 1980s vs. 2000s

Transcription

1 Education, Ability and Earnings, 1980s vs. 2000s Gonzalo Castex and Evgenia Dechter y February 2011 Abstract This study examines changes in returns to formal education and cognitive ability over time using data from the 1979 and 1997 National Longitudinal Study of Youth cohorts. We show that cognitive skills had a larger impact on wages of young men and women in the 1980s than in the 2000s, while returns to formal education were higher for the later cohort. We apply a propensity score weighting procedure and show that changes in distributions of workers observable characteristics cannot explain the changing returns to skills. We examine our ndings within human capital accumulation theory and asymmetric employer-learning framework. We argue that a more rapid technological change in 1980s vs. 2000s can explain much of the decrease in returns to cognitive ability. Keywords: returns to education; returns to ability; ability bias. JEL classi cation: J21; J24; J31. 1 Introduction Families and policy makers implement various strategies to enhance an individual s capacity to succeed in the labor market. Investment in an individual s human capital is one of the most important tools to achieve this goal. A large literature documents that workers with higher educational attainment have higher earnings and that this wage di erential has been increasing over time. The standard estimates obtained using the least-squares method show that between the 1980s and 2000s there was an increase in returns to education in the range of 20% - 50% (see, for example, Goldin and Katz 2007, among others). Many studies argue that this growth We would like to thank Mark Bils, Denise Doiron, Ronni Pavan and seminar participants at University of New South Wales and 2010 Stockman Conference (University of Rochester) for valuable comments. y Gonzalo Castex, Central Bank of Chile. gcastex@bcentral.cl. Evgenia Dechter, School of Economics, University of New South Wales. e.dechter@unsw.edu.au. 1

2 was more rapid in the rst half of the 1980s. There is an extensive debate about whether more educated workers earn higher wages due to formal education or due to their unobservable characteristics, for example, due to higher cognitive ability. There is also some debate about the interpretation of the rising return to schooling and whether it is due to an increase in return to formal education or a rising return to cognitive ability. In this work we add to this literature by examining the changing roles of formal education and cognitive ability in wage determination between 1980s and 2000s. 1 We show that returns to formal education grew substantially during the entire period and did not slow down in the nineties. On the other hand, returns to cognitive ability decreased over time. The standard view is that both formal education and cognitive ability increase labor market productivity. Presence of a positive correlation between education and ability generates an upward bias in the estimated economic return to education when unable to account for ability. This is the classic ability-bias model discussed in Willis and Rosen (1979) and many following studies. This upward bias is greater in periods when the return to ability is greater (see, for example, Rubinstein and Tsiddon 1999), even if there is no change in the correlation between education and ability. On the other hand, the correlation between ability and schooling may vary over time, for example, due to introduction of more merit-oriented policies in educational enrollment, even if the return to ability remains constant (Herrnstein and Murray 1994). Then, without knowing how ability bias is evolving over time, it is impossible to derive conclusions about changes in returns to education. Another common assumption (and a nding in a limited empirical research) often used in the relevant literature, is that the price of cognitive ability has been rising in the market for skills. For example, Juhn, Murphy and Pierce (1993) argue that the increase in within-group wage inequality re ects a rising price for some unobserved skills. A number of studies have examined the trend in the return to cognitive ability as measured by scores on standardized tests. The results vary substantially across these studies. Blackburn and Neumark (1993) report that the rise in the return to education is concentrated among those with both high education and high ability, but they argue that there is no trend in the return to ability. 2 They estimate the model using NLSY79, gathering information for the period, for a single experience group, using only entry wages. Grogger and Eide (1995) employ 1 Years 1979 to 1991 are de ned as 1980s, and 1999 to 2008 are de ned as 2000s. Section 2 describes data selection in detail. 2 In this study cognitive ability is measured by three subsets average of the Armed Services Vocational Aptitude Battery (ASVAB) test scores. 2

3 two longitudinal surveys that follow the same individuals: National Longitudinal Study of the High School Class of 1972 (NLS72) and the High School and Beyond (HSB), using late 1970s and mid 1980s data. 3 They assume linear experience e ects and no age e ects and nd that standardized test scores and high school grades had no e ect on the change in the college wage premium for men, but returns to math ability rose considerably for women. They also nd that the rise in the economic return to education is concentrated among the most able. Bishop (1991) uses NLSY79 for the period, and assumes linear time and age e ects. He nds that the time trend of ability is not statistically signi cant for either men or women. These studies attempt to decompose the increasing return to schooling using data that follow the same people or using repeated cross-section samples of the same cohorts over time. When following the same people or cohort over time, the identi cation of age, cohort and time or period e ects, is merely possible, largely because we do not observe two individuals of similar age who were born in di erent periods. Therefore, it is di cult to infer whether the rise in return to education or ability is due to changes in the value of cognitive skills, or it is because with workers aging ability, it becomes more valuable for the labor market. Studies that include ageability interactions typically nd no statistically signi cant evidence of a rise in return to ability over time. On the other hand, studies that do not include age-ability interaction cannot resolve the inference problem without making strong parametric assumptions (see Cawley, Heckman, Lochner and Vytlacil 1998, for further discussion). Murnane, Willett and Levy (1995) implement an alternative approach and identify time and age e ects. They use the NLS72 and the HSB datasets to compare wages in 1978 with wages in In their last year in high school, participants in the NLS72 and HSB samples were administered several academic tests. Murnane et al. use the mathematics score as a measure of cognitive skill. They employ nonparametric speci cations for time and work experience, and estimate the contribution of ability to the rise in the return to education measured at one age in two di erent years. They conclude that 38% of the rise in the return to education for 24 year-old males during the period can be attributed to a rise in the return to ability. Cawley, Heckman and Vytlacil (2001) re-estimate the Murnane et al. model, conditioned on years of work experience instead of age. They nd that the increase in the return to education is generally statistically signi cant, and falls when controlling for cognitive ability. 3 Ability is measured by standardized test scores and high school grades. They use a math test, a vocabulary test, and a "mosaic" test that measures perceptual speed and accuracy. 3

4 Several studies evaluate returns to unobservable skills by examining the changing patterns of wage distribution. During the recent decades there were two important changes in the wage distribution: an increase in the college/high school wage gap, and a substantial rise in the variance of wage residuals. The second change is typically attributed to an increase in the demand for unobserved skill. Chay and Lee (2000) and Taber (2001) examine these changing distributional patterns to evaluate returns to schooling and ability while they also acknowledge that this same increase in demand for unobserved skill could drive the evolution of the measured college premium. Chay and Lee nd evidence of an increase in the return to skill, but argue that it cannot be large enough to account for the full increase in the return to schooling. Their results are in contrast to Taber ndings, that suggest that an increase in the demand for unobserved ability could play a major role in the growing college premium. This work provides new evidence for the relationships between formal education, ability and wages. We evaluate to what extent cognitive skills measured by the Armed Forces Quali cation Test (AFQT) scores a ect wages of young adults. 4 The time period under study is di erent from those used in previous research that mainly focused on developments in the 1980s; we examine the determinants of wages in 1980s and 2000s using NLSY79 and NLSY97. We use waves in NLSY79 and waves in NLSY97, and analyze the age group in both datasets to facilitate comparison. 5 By examining how the AFQT score-wage relationship di ers between the two cohorts, we evaluate the changing role of cognitive skills in determining wages. We nd that cognitive skills, measured by the AFQT score, were substantially more important in the 1980s than in the 2000s. Using the standard Mincer (1974) model we show that returns to cognitive ability decreased by more than 50% between 1980s and 2000s for men and by 40% for women. We also show that the slowing down in the increase of returns to education during this period was less pronounced when controlling for ability. When performing the estimations we control for various personal characteristics and macroeconomic conditions and nd that results are robust under all speci cations. We also evaluate the e ects of changes in population characteristics and survey methodology in NLSY79 and NLSY97 on estimates. First, we address changing distributions of skills and assess how the returns to education and cognitive ability would have changed if the observable population characteristics remained constant between the 1980s and 2000s. One of the 4 AFQT scores are widely used in the literature as a measure of cognitive achievement, aptitude and intelligence. 5 The oldest participant in the most recent wave of NLSY97 was interviewed in 2008 and is 28 years old. 4

5 di erences between the two samples is in age distributions of the respondents. Although the age range is chosen to be similar in both datasets, NLSY97 respondents are younger on average than NLSY79 respondents. Another di erence is in the family background measures: the respondents of 1997 cohort have more educated parents and are more likely to live in single-parented households. We also consider other changing characteristics. To test whether these di erences can explain the estimation results we adjust both samples following the density reweighting procedure described in DiNardo, Fortin and Lemieux (1996). We re-estimate wage equations for both periods applying population weights that x personal characteristics densities across samples. We conclude that changing distributions of various characteristics cannot explain the decrease in returns to cognitive ability. Second, we examine whether changing labor market structure can explain the decreasing return to cognitive skills. We perform a similar reweighting procedure to adjust the distributions of occupations and industries across surveys, and show that these adjustments do not change the results. Third, we assess whether changes in test-taking conditions and incentives could a ect the outcomes through a measurement error in test scores. We do not nd this to be a plausible explanation for the decreasing AFQT coe cient in the log-wage regression. To explain the ndings we employ a wage equation that allows for variation in education and ability di erentials by work experience. There are several possible mechanisms behind these dynamics. First, the human capital accumulation hypothesis suggests that ability may a ect post-schooling investments in human capital, and that formal education may become obsolete over time. If this theory is correct, then adding dynamics to the model should capture e ects of technological changes over time on human capital accumulation mechanism. The alternative framework that uses a similar empirical speci cation is asymmetric employer-learning theory (see, for example, Altonji and Pierret 2001). If this theory is correct, then estimating the dynamic equation will capture changes in signaling and monitoring mechanisms between the 1980s and 2000s. We analyze our ndings with respect to each theory. Within the human capital accumulation framework we show that a more rapid technological change in 1980s vs. 2000s can explain much of the decrease in returns to cognitive ability via two channels: higher depreciation rate of formal education and higher need for on-the-job training to adopt new technologies in the 1980s relative to the 2000s. Using the asymmetric employerlearning theory, the results suggest that there were advances in signaling about ability between 1980s and 2000s. Employer s learning about worker s ability plays a less important role in wage 5

6 dynamics for the later cohort. This paper proceeds as follows. Section 2 describes the NLSY79 and NLSY97 data in detail. Our main empirical results are reported in Section 3. In this section, we examine the changing roles of cognitive skills and formal education in the wage function. Here we also perform a sensitivity analysis to evaluate whether di erences in skills distributions and changing testtaking conditions can explain the outcomes. Section 4 explores the dynamics of wages. Here we discuss alternative explanations for our main ndings. Conclusions are o ered in Section 5. 2 Data This section describes the samples and variables used in the analysis. We use data from the National Longitudinal Survey of Youth 1979 and 1997 cohorts. The former provides a nationally representative sample of young men and women who were ages at the beginning of 1979, and the latter samples youth who were ages at the beginning of We pool observations for years for the NLSY79, and for the NLSY97. We employ both the crosssectional samples and the supplemental samples (excluding the military supplement) in the NLSY79 and NLSY97, to maximize the number of observations used in the analysis. Individuals enrolled in school and military service are excluded. Only full-time workers with at least 20 hours per week and real wages within the range of 3 to 100 dollars (in 2007 prices) are considered. We exclude individuals who are missing information on key variables. Since the oldest individual in the NLSY97 turned 28 in the most recent 2008 wave of data, we limit our analysis to the age group. 6 The nal samples contain observations for men in the 1979 cohort and in the 1997 cohort. The number of individuals in each cohort is 4635 and 3030, respectively. For women we use observations in NLSY79 and observations in NLSY97, pooling information on 4438 and 2943 respondents. In all estimations we use weights provided by the Bureau of Labor Statistics to achieve representativeness of the population. 7 The data contain detailed information on individuals, including measures of cognitive ability, education, labor market activity and other family and personal characteristics. Many of these variables are compatible across 1979 and 1997 cohorts, but some require further adjustments to facilitate comparison across samples. Altonji, Bharadwaj and Lange (2008) provide a detailed analysis of 6 A very small number of respondents were age 29 at the time of the 2008 wave of the NLSY97. 7 For some estimations we construct alternative sets of weights to evaluate e ects of changing distributions of skills on labor market outcomes. 6

7 each dataset and suggest methods to achieve compatibility. We follow their methodology where available. 8 Table 1 summarizes the variables used from NLSY97 and NLSY79. We use hourly real wages in 2007 prices for both cohorts. Statistics in Table 1 show a lower mean wage in 1997 than in This result is due to di erences in age (and work experience) distributions across samples. Later in this study we describe our methodology to reweight the sample to obtain similar age distributions. We report adjusted summary statistics in Tables 7 and 8, for men and women respectively. Adjusting the samples by age distributions results in increasing real wage over time for men, although female mean wage remains fairly constant over time. Both data sources contain comparable measures of ability - Armed Forces Quali cation Test (AFQT) scores, widely used in the literature as a measure of cognitive achievement, aptitude and intelligence. The AFQT score is a composite measure derived from the Armed Services Vocational Aptitude Battery (ASVAB) and created by adding the outcomes of four of the ASVAB subtests (word knowledge, paragraph comprehension, arithmetic reasoning, and mathematics knowledge). There are two main reasons to question the compatibility of the test scores in NLSY79 and NLSY97. First, participants in the NLSY79 took the ASVAB exam in the summer of 1980 when they were years old. For the NLSY97 cohort, the test was administered when individuals were between 12 to 16 years old. Second, the NLSY79 cohort was administered a pencil and paper (P&P) version of the ASVAB while the NLSY97 took a computer assisted test (CAT) format. We follow the methodology developed in Altonji et al. (2008) to achieve compatibility. We use comparable age-adjusted AFQT scores provided by Altonji et al. which are based on a mapping between the P&P and the CAT test formats provided by Segall (1997). 9 Figure 1 shows the distributions of AFQT scores for each cohort after adjustments. Table 1 provides mean and standard deviations of the AFQT measure in both samples. The statistics do not reveal much di erence in ability measures between the two cohorts. We also perform various robustness tests to evaluate whether the di erences in test-taking conditions can a ect our outcomes. The tests and results are described in Section 3.1. In our main estimations we use binary variables of educational attainment. Population 8 Some studies have raised a concern regarding the representativeness of NLSY97. These issues are discussed in detail by Altonji et al. (2008), and we adopt their assumption that by using the survey weights, the available data are representative of the 1997 and 1979 populations. Attrition patterns are also discussed by Altonji et al., who suggest that it does not present a major obstacle for the analysis. 9 We thank Joseph Altonji, Prashant Bharadwaj and Fabian Lange for help with the AFQT data. 7

8 proportions by level of educations are reported in Table 1. These do not di er much across samples. However, when reweighting the samples to obtain comparable age distributions for each dataset these proportions change. As reported in Tables 7 and 8, for male workers, the proportion of individuals with a bachelor s degree is 15% and signi cantly higher in NLSY97 than in NLSY79, where only 8% of individuals completed a college degree. For women, the di erences across cohorts are less pronounced, and do not change as much after reweighting. Years of schooling are not used in main estimations since, on average, it takes longer for the later cohort to complete their degrees. For example, a 25 year-old individual (male or female) with a bachelor s degree has 15.9 years of schooling on average in NLSY79, but 16.5 years in NLSY97. The main ndings of this study are robust to alternative choices of the schooling. We also estimate the earnings model using the years-of-schooling variable. In the NLSY79 sample the mean value of the years of schooling is for males and for females. Limiting the observations to 25 year-old individuals we obtain 12.6 and 13.1 years of education for males and females, respectively. In the 1997 sample, the average years of education for the entire sample is for males and 12.1 for females. In the 25 year-old subsample of NLSY97 data, these numbers are 13.1 and 13.9 respectively. Another alternative speci cation assumes that a respondent has completed high school if he or she has more than 12 years of schooling. Individuals are considered to have attended college if they acquired at least 13 years of education. 10 Following this de nition, the 1979 sample of year-old full time male employees who are not enrolled in school has 29.5% college attendees and 86.4% high school graduates; for female employees these proportions are 36.6% and 93.5%. These ratios in 1997 sample are as follows: male college graduates are 36.3% of the entire sample and high school graduates are 87.8%; these ratios are 48% and 90% for women. It should be noted that the samples have di erent age distributions and the 1997 cohort sample is younger than that of the 1979 cohort. For instance, considering only 25 year-olds in both cohorts gives the following proportions for male workers: in NLSY79 there are 33.2% college attendees and 88.1% high school graduates; in NLSY97 these ratios are 47.2% and 90.6%, respectively. To construct work experience we count the number of years after completing the most recent degree. There are signi cant di erences across cohorts, but these are smaller after reweighting the samples by age. One of the reasons for these di erences is the longer time spent on each 10 This de ntion was used by Belley and Lochner (2007). 8

9 degree. Hours of work are decreasing over time for men and women. Macroeconomic conditions are summarized by the unemployment rate, and these are not very di erent, on average, across samples. Finally, the proportions of black workers are not similar across cohorts, unless reweighting the samples by age, evident from comparison of Table 1 with Tables 7 and 8. This is due to a higher attrition of black workers in the earlier waves of the survey. This issue is discussed further by Altonji et al. (2008). In Table 1 we summarize the main variables used in estimations. Some estimations also include information on family background, and the main variables are given in Table 2. Both NLSY79 and NLSY97 contain measures of family income reported in early survey years. The NLSY79 contains measures of family income reported in early survey years, while the NLSY97 contains measures of both family income and net wealth in For the 1979 cohort, we use average family income when youth are ages 16-17, excluding those not living with their parents at these ages. This limits the sample to the younger cohorts of the NLSY79 born between The NLSY97 analysis is based on family income and family net wealth in 1997, dropping individuals not living with their parents that year. We denominate the family income measure in 2007 dollars, using the consumer price index. Mean family income remained fairly constant over time but its dispersion increased. Family structure information is provided by an indicator variable for whether both parents were living with the child when he/she was 14 years old in the NLSY79, and in 1997 (i.e., ages 13-17) in the NLSY97. There are more single-parent households in the later cohort. Finally, Table 2 shows statistics on parental years of schooling which increased signi cantly over time. 3 Estimation Our analysis centers on estimating wage functions using NLSY79 and NLSY97, treating men and women separately. To evaluate the changes in e ects of schooling and cognitive ability on earnings, we employ identical estimation speci cations for both NLSY79 and NLSY97 cohorts. For simplicity of interpretation and to facilitate comparison with other studies, we use the standard Mincer framework: ln wage it = T 1 EDUC it + T 2 AF QT it + T 2 EXP it + T 2 EXP 2 it + X it T 3 + " it ; (1) 11 When income is available only for age 16 or age 17 and not both, we use the available measure. 9

10 wage it is real hourly wage rate paid to an individual i at time t, EDUC it corresponds to the level of education, AF QT it is the AFQT score to proxy for an individual s cognitive ability, EXP it corresponds to labor market experience, upper scripts on the coe cients denote the cohort used in estimation, T 2 fnlsy 79; NLSY 97g, and X is a vector of personal characteristics and family background variables. We present our results including and excluding various controls. Because we employ full samples we also control for race. The samples for both years are pooled observations for year-old full-time workers. Therefore, the coe cients of education and ability may re ect not only prices of these skills, but also the e ects of human capital depreciation and on-the-job training. We discuss the interpretation of the coe cients in later sections, and also propose a more dynamic model to estimate returns to formal schooling and ability. The results for men are presented in Table 3, and the results for women are in Table 4. First, we analyze the e ects of education on subsequent wages without controlling for cognitive ability, shown in columns 1 and 5 of Tables 3 and 4. Most coe cients display modest changes between the two time periods. There is a small increase in returns to education for both men and women, con rming patterns described in other studies. Returns to experience are lower for the NLSY97 cohort than for the NLSY79 cohort. The wage gap between black and white workers is smaller in the 2000s, and statistically signi cant only for male workers, again con rming ndings in other studies. Unemployment rate (measured by a 3-years moving average) is negatively associated with wages and the e ect is larger in the 2000s, for men and women. The remaining columns of Tables 3 and 4 display estimation results that include the AFQT measure to proxy for cognitive ability. The basic results are given in columns 2 and 6. The most striking outcome is the signi cant drop in the AFQT coe cient in the 2000s. For male workers, an increase in the AFQT score by 10 points is associated with a 2.7% increase in hourly wage for the 1979 cohort, but only with a 1.1% increase for the 1997 cohort. For female workers, the e ect of a 10 point increase in AFQT score on real wage rate drops from 3.6% to 2.2%. When controlling for ability, the increase in returns to education is more pronounced at all levels for both men and women. For instance, the returns to bachelor s degree in the 1980s are 5.6% for men and 6.5% for women in the speci cation that excludes the ability measure, (column 1 in Tables 3 and 4). In a similar speci cation, these returns are 6% and 6.9% in the 2000s, (column 5 in Tables 3 and 4). Estimates obtained from the model that includes the ability measure gives 4.1% and 4.9% for men and women in the 1980s, and 5.5% and 6% in the 2000s. 10

11 These outcomes imply that the returns to education are signi cantly higher in the 2000s and the ability bias is larger when estimating the wage equation for the 1980s. In both periods, returns to experience do not change signi cantly when controlling for AFQT scores. The gap between black and white workers drops more substantially in the 1980s than in the 2000s for men, and remains statistically insigni cant for women. Tables 3 and 4 also report estimation results of the wage equation controlling for other personal characteristics, family background and occupations and industries. AFQT coe cients are lower when additional controls are included. However, the di erences in returns to cognitive skills between the 1980s and 2000s remain signi cant under all speci cations, for men and women. Less can be said about returns to education and work experience since some industry-occupation cells have a low variation in education levels which does not allow a simple interpretation of the results. Equation (1) is also estimated using the alternative speci cations of the education variable. Columns 1, 2 and 5, 6 in Tables 11 and 12 report estimation results using years of education (highest grade completed) for men and women. The drop in returns to cognitive ability is substantial in these speci cations as well. Columns 1 and 5 report the results using the basic speci cation and show that between 1980s and 2000s the return to ability decreases. The AFQT coe cient drops from 2.3% for a 10-points increase in test score to 0.6% for men, and from 3.1% to 1.9% for women. Including other controls in the regressions does not a ect change signi cantly this outcome. Finally, if we consider high school completion for any individual with 12 years of school, and college attendance for any individual with at least 13 years of school, we nd a very similar outcome. Using this speci cation and including the standard controls in the regression of log wages, we nd that the return to cognitive ability decreases from 3% for 10 points to 1.3% for men, and drops from 4% to 2.8% for women between 1980s and 2000s. 12 One possible explanation for the estimation results is that a change in selection of individuals into the labor force and distributions of workers characteristics, might be di erent for each cohort. In both samples we use only individuals who are not in military service or enrolled in school, work 20 or more hours per week and have real wages within the range of 3 and 100 dollars (in 2007 prices). Summary statistics of the key variables are reported in Tables 1 and 2 and are very similar across cohorts. Nevertheless, the ratio of the 18 to 28 year-old population 12 These regression results are not reported here and are available from the authors upon request. 11

12 that satis es these criteria is increasing over time. For men, this ratio is 43% in NLSY79 and 56% in NLSY97. For women, the ratios are 34% and 48%, respectively. To limit the e ects of possible selection into the labor force participation as de ned above, we estimate the model for more homogeneous samples, grouping individuals by education level and age. In NLSY79 around 68% of male high school graduates at age of 25 are working according to our de nition; this proportion is 70% in NLSY97. For males with 16 years of schooling or more between 25 and 28 years old, these proportions are 56% and 66%. 13 For females, 55% and 62% of high school graduates are working in NLSY79 and NLSY97, respectively. For higher educated females these proportions are 55% and 66%, respectively. We estimate equation (1) for these subgroups and report the results in Table 5. For the high school group we observe a drop in the return to cognitive ability (measured by the increase in the wage rate following a 10-point increase in AFQT score), from 2.7% to 1.9% for men, and a decrease from 3.3% to 2.6% for women. For the higher education group the return changes from 3.3% to 2.4%, and from 4.6% to 2.4% for women. From these results we conclude that change in selection into labor force participation could contribute to the changing returns to cognitive ability, although it cannot explain the entire change. We evaluate alternative explanations for our ndings. In the next subsection we discuss in detail how changing observable characteristics of the samples used in the estimations could a ect the outcomes. We perform propensity score matching to minimize the possible selection bias. We nd that changing densities of various skills and personal attributes cannot explain the main ndings, although we cannot control for changing distributions of unobservable variables. 3.1 Robustness/ Sensitivity Analysis The results reported in Tables 3 and 4 are robust in various speci cations, and the main ndings do not change much when including additional control variables. Here we perform a few more tests to evaluate whether changes in test-taking incentives or changes in the distributions of individual characteristics can explain the main ndings. First, we check whether changes in test-taking conditions and incentives a ected the outcomes. To do so, we use reporting about the reason to take the ASVAB test. We split the NLSY97 sample into more- and less-motivated test-takers. Returns to cognitive ability and 13 We do not use a single age group for the higher educated group due to a smaller number of observations. There are 1862 and 838 working male respondents who are 25 years old and have high school diploma in 1979 and 1997 data, respectively. There are 748 and 382 males in the higher educated group who are between 26 and 28 years old, in 1979 and 1997 samples, respectively. The observations for the higher education groups are pooled across ages, and standard errors of the coe cients are adjusted accordingly. 12

13 returns to education do vary across these groups, and increase with test-taking motivation, probably re ecting measurement error in test scores. However, the results show that even for the most motivated test-takers the returns to AFQT are still below those of the NLSY79 cohort, suggesting that measurement error in the ability measure cannot explain the main ndings in Table 4. Second, we reexamine the samples used in estimations. Although both surveys were conducted by the same agency, for the same purpose and contain similar sets of variables, there are di erences in a few dimensions. First, although the age range in both NLSY samples is similar, the age distributions di er across samples. Individuals in NLSY97 are substantially younger than those in NLSY79. Therefore, we estimate the basic wage equation (1) using reweighted samples. We construct a new set of weights that preserve population representativeness and also generate similar age densities of the data in both periods. The respondents in the two surveys also di er in other dimensions. We perform another test where we also take the distributions of family background variables into account. In addition, we examine whether the changing labor market structure can explain the decrease in returns to cognitive ability, and show that changing distributions of occupations and industries cannot explain the decrease in returns to cognitive ability. Changes in test-taking conditions Earlier we mentioned that to achieve compatibility in AFQT scores, we had to adjust for the younger age of test-takers in NLSY97 and also for the test format (P&P vs. CAT). 14 Additional di erence in test-taking methodologies between the two samples is in the amount of monetary award for participating in ASVAB, which was lower for the later cohort and could a ect performance in the test. Our concern is that NLSY97 provided a lower monetary reward to participate in ASVAB tests, which could a ect the motivation and the outcome of the test. The respondents in the NLSY97 survey were asked about the reason they took the ASVAB test, and there were 7 alternative responses: (1) Because it s an important study; (2) To see what it s like to take a test on a computer; (3) To see how well I could do on the test; (4) To learn more about my interests; (5) Family member wanted me to take it; (6) To get the money; or (7) I had nothing else to do today. We split the 2000s sample into two groups, 14 In Section 2 we described our procedure to obtain comparable AFQT score distributions across samples. We also performed our tests for the group of individuals who took the ASVAB test when they were 16 years old, which is the only overlapping age to take the test across the NLSY cohorts. Results obtained from these estimations are not di erent from the ones reported in Tables 3 and 4, suggesting that this aspect of the changing survey methodology cannot explain the main ndings in the paper. These estimation results are available from the authors upon request. 13

14 "motivated" - with responses from (1) to (4), and "non-motivated" - for responses (5) to (7). 15 The estimations results for men, for both subgroups, are reported in Table 6. Individuals who are assumed to have higher motivation to take the test also have a higher AFQT coe cient than the less-motivated respondents. We consider a higher measurement error behind this outcome. We expect the AFQT scores to be less informative about the true cognitive ability of respondents who put lower e ort into the test. This result may also suggest correlations of unobservable personal characteristics that a ect wages and the reason to take the test, but we do not nd any correlation between the reason to take ASVAB and wages. 16 Results for women are not reported but suggest similar conclusions. Splitting the sample by reason to take the test has no e ect on estimated coe cients of AFQT scores in the wage regression for female workers. The return to cognitive ability estimated for the 1980s is signi cantly higher than the return estimated using the NLSY97 subsample with the lowest measurement error. This nding supports our conclusion that returns to ability decreased over time. Estimation of Propensity Scores and Reweighting We reweight both samples to generate similar distributions of observable skills. To construct the sets of alternative weights we pool data from NLSY79 and NLSY97 and estimate the propensity score to be in NLSY79, using skill measures observed in both samples. These probability estimations are performed using sampling weights provided by the NLSY79 and NLSY97 to achieve population representative samples. Using the obtained propensity scores, we generate the weights and apply them to both samples. 17 The reweighted data are then used to calculate summary statistics and to estimate equation (1). To construct the weight-generating function, we follow a variation of speci cation proposed by DiNardo et al.(1996), and use two years of data, estimate the probability that an observation is in the rst year or the second, then we reweight the observations by an inverse propensity score so that the distributions of skills are nearly equal across the two years. Changes in means or distributions in the reweighted data are then interpreted as estimates of change, had the means of the observable characteristics used in the propensity scores estimations not changed over time. Guo and Fraser (2010) and Nichols (2007) suggest a variation for the weight function 15 The results are not very sensitive to the division of individuals into subgroups. For example, estimating equation (1) using only individuals who chose answer (4) vs. those who chose (7), provides very similar estimates. 16 These results are not reported and are available upon request. 17 We do not report the distributions of propensity weights for di erent models, these are available from the authors upon request. 14

15 which we implement here, (X) = d1979 P (d1979jx) + 1 d P (d1979jx). Where d [0; 1] is an indicator that a given observation is taken from NLSY79, and P (d1979jx) is the conditional probability of appearing in NLSY79, conditional on observable characteristics X. When estimating the propensity scores we consider various characteristics to include in X. The weight function (X) is used to reweight both NLSY79 and NLSY97. We provide estimation results reweighted by age, family background, occupations and industries. Age For our analysis we use 18 to 28 year-old individuals in both samples. Although the age range is similar, age distributions are very di erent between the two cohorts. The NLSY97 sample is much younger than the NLSY79 sample. We use a probit model to estimate individual propensity of being in the 1979 cohort, and we use the propensity scores generated from the model to construct weights to statistically adjust the samples. First, we pool data from NLSY79 and NLSY97, and estimate the propensity score P (d1979jage; age 2 ), where d [0; 1] using sampling weights provided by NLSY79 and NLSY97. We then generate the weights, (age; age 2 ) = d1979 P (d1979jage;age 2 ) + 1 d1979. These weights are used to reweight the 1 P (d1979jage;age 2 ) NLSY79 and NLSY97 data. The age distributions before and after reweighting are shown in Figures 2a and 2b. Data-summary statistics using the age-adjusted data are reported in Tables 7 and 8. There are signi cant changes in means of the reweighted data. Mean wage rate, AFQT score and educational attainment are higher in 2000s. These results are similar to those in other studies. For example, Altonji et al. (2009) also nd increasing AFQT scores and education levels for NLSY97 respondents, although they report statistics comparing 22 year-old individuals in both samples. The reweighting has a much smaller e ect on estimates of women. Estimation results using the age-adjusted reweighted data are on the left panel of Table 9. The changes in estimates, including the AFQT coe cient, are only slightly a ected by using alternative weights. The AFQT coe cient increases slightly in both samples and it is still signi cantly higher in the 1980s. Family Background In Table 2, we showed that there were several changes in the distributions of family background variables. Parental education level and proportion of single-parented families increased in the 2000s. We construct a new set of weights adding to the age and age 2, mother s and father s education, family income and an indicator for presence of both families in the household. Summary statistics of the variables used in the probit model to estimate the 15

16 propensity scores are in Table 2. These variables are predetermined and in uence skill development and economic decision-making. Estimation results of equation (1) using the reweighted data are reported in the right panel of Table The estimates of AFQT coe cients change for both cohorts, but still show a signi cant decrease over time for men and women. Finally, we use a full set of personal characteristics and family background variables to estimate the propensity scores of being in the NLSY79 sample. The full set includes AFQT score, education level, experience, hours worked, race, unemployment rate as well as age, age 2, and family background characteristics. Estimation results of equation (1) using weights constructed employing the full set propensity scores do not change signi cantly. 19 Occupational and Industrial Shift We also examine whether the change in return to cognitive ability can be attributed to changes in the market structure. Many studies have documented and examined the e ects of the structural change in the labor market. For example, Acemoglu (2002) argues that technical change over the past sixty years has been skill-biased. We test how the returns to cognitive ability and schooling would have changed if there were no shift in the distributions of industries and occupations over time. We use age, age 2, occupations and industries indicators to construct another set of weights. Estimations results based on samples with similar densities of occupations and industries (and age) are reported in Table 10. The e ect of structural change on the estimates is relatively small for both men and women. Therefore, we conclude that occupational and industrial shift cannot explain the decreasing return to cognitive ability. 4 Explaining the Decrease in Returns to Cognitive Ability Estimation results in the preceding section provide new evidence on changes in wage structure over time. Returns to formal education increased between the 1980s and 2000s while returns to cognitive ability dropped substantially. These results were obtained using the standard Mincer equation given by (1). Here we explore a more dynamic speci cation for the wage equation to allow for variation in education and ability di erentials by work experience. This speci cation is in line with two important (although not mutually exclusive) theories. First, the human capital accumulation hypothesis suggests that ability may a ect post-schooling investments in human 18 Sample sizes are smaller since some variables, especially family income, are not available for all respondents. 19 Available from the authors upon request. 16

17 capital, and that formal education may become obsolete over time. If this theory is correct, then adding dynamics to the model should capture e ects of technological changes over time on the human capital accumulation process. The alternative framework that uses a similar empirical speci cation is the asymmetric employer-learning theory. For example, Altonji and Pierret (2001) use a similar empirical implementation in their study. If this theory is correct, then estimating the dynamic equation will capture changes in signaling and monitoring mechanisms between the 1980s and 2000s. We analyze our ndings with respect to each theory. First we consider the human capital accumulation theory. We show that incorporating technological change into the standard model suggests plausible explanations for our ndings. We conclude that a more rapid technological change in 1980s vs. 2000s can explain much of the decrease in returns to cognitive ability via two channels: higher depreciation rate of formal education and higher need for on-the-job training to adopt new technologies in the 1980s but less in the 2000s. The dynamic analysis stems from the standard Ben-Porath (1967) framework and distinguishes between formal schooling and on-the-job training. In the conventional model of optimal investment in human capital, individuals allocate their time between work and on-the-job training. The stock of human capital increases potential earnings. The objective of the individual is to maximize the present value of his/her life-time earnings, while retirement age is given and leisure is not valued. We adopt several standard assumptions about the roles of cognitive ability and technological change in the human capital accumulation process. We rely on earlier ndings by Veum (1993) and assume that cognitive ability makes workers more trainable and more able workers receive more training. 20 Additionally, we assume that technological change may a ect investments in training. This assumption also relies on ndings in previous research. Bartel and Sicherman (1998) use the NLSY79 data from 1987 through 1992 and nd that production workers in manufacturing industries with higher rates of technological change are more likely to receive formal company training than those working in industries with lower rates of technological change, controlling for a set of worker, job and industry characteristics. Gashi, Pugh and Adnett (2008) reach a similar conclusion using an administrative German dataset. They nd that establishments operating with new technologies, or those with greater investment volume in previous years, are more likely to provide training. Then, technological change is likely to a ect several parameters in the Ben-Porath framework that determine the human capital accu- 20 Veum (1993) uses NLSY79 and proxies cognitive ability with AFQT scores. 17

18 mulation mechanism. First, a more rapid technological change may increase the depreciation rate of previously acquired human capital. Second, technological change can a ect the returns to human capital. Skill-biased technological change can raise the price of human capital but also the opportunity cost of on-the-job training. Third, technological change may a ect the costs of production of human capital. The e ects of technological change and the return to on-the-job training may di er by education, ability level and other personal characteristics. At any period t, the stock of human capital is given by the remaining formal human capital, acquired prior entering the job market, and investments made after completion of the formal schooling. The law of motion of human capital accumulation can be described as follows: H t = Q t + (1 )H t 1, where H t is the stock of human capital in period t, Q t is the human capital produced in the current period t (investment), and is the depreciation rate of human capital. Human capital stock at t = 0, the year the individual enters the labor market, is H 0, which denotes the level of formal schooling. A higher depreciation rate implies a faster depletion of formal and acquired on-the-job human capital. Total stock of human capital, H t, may increase or decrease, depending on the investments made over the life cycle. Human capital produced in current period, Q t, is assumed to depend on the personal ability level, current stock of human capital and technology. Individuals with higher cognitive skills produce higher Q t s due to lower costs and higher skill prices. At any given period, individual wage is a function of human capital, cognitive ability and other personal characteristics. Equation (1) can be rewritten as follows: ln wage it = T 1 H it + T 2 ability it + X T it 3 + it : (2) All equations are estimated for both cohorts and T 2 fnlsy 79; NLSY 97g. Other controls are summarized by X it and include personal characteristics, occupation, industry and macroeconomic conditions. Finally, it is the error term. This equation can be reformulated further to incorporate human capital accumulation technology which may vary over the life cycle: ln wage it = T 1 H i0 + T 2 ability it + T 3 EXP it H i0 + T 4 EXP it ability + X it T 5 +! it ; (3) where EXP it is labor market experience of an individual i in period t, measured by years since completing formal schooling. In this speci cation the depreciation rate of human capital is re ected in the coe cient of interaction of formal education and experience, 3 T. Human capital 18