Estimating returns to schooling: when does the career begin?

Economics of Education Review, Vol. 17, No. 1, pp. 31–45, 1998  1998 Elsevier Science Ltd All rights reserved. Printed in Great Britain 0272-7757/98 $19.00+0.00

Pergamon

PII: S0272-7757(97)00011-3

Estimating Returns to Schooling: When Does the Career Begin? Audrey Light Department of Economics, Ohio State University, 1945 North High Street, Columbus, OH 43210-1172, U.S.A.

Abstract — Because the life cycle is not neatly divided into a period of full-time schooling followed by a period of full-time employment, it is unclear where analysts should “start the clock” on the career for purposes of estimating the returns to schooling. This study uses data from the National Longitudinal Survey of Youth to determine how estimated returns to schooling are influenced by the choice of career starting date. Schooling and experience measures are defined for four alternative starting dates and then used to estimate a standard wage model for samples of white and non-white men. Estimated returns to schooling increase dramatically as an increasingly later starting date is used because increasingly large amounts of unmeasured, “pre-career” work experience bias the schooling effects. A specification that controls more accurately for the accumulation of schooling and work experience is suggested as an alternative to the orthodox model. [JEL I2, J3]  1998 Elsevier Science Ltd. All rights reserved

1. INTRODUCTION

because sample members gain work experience while still in school—estimated returns to schooling are likely to reflect the wage benefits of (unmeasured) “pre-career” work experience as well as the schooling itself. If individuals gain additional schooling after the chosen career starting date and analysts ignore this “post-career” schooling, estimated returns to schooling will again be distorted. To illustrate these problems, I use data for a sample of male respondents in the National Longitudinal Survey of Youth (NLSY) to estimate a standard, Mincerstyle wage model with controls for schooling acquired prior to labor market entry and work experience gained subsequent to that date. I consider four alternative career starting dates: the 16th birthday, the first exit from school, the last observed exit from school, and the first “permanent” labor market entrance, defined as the beginning of a three-year (or longer) spell in which the individual works at least 26 weeks per year and averages at least 30 hours of work per week. I demonstrate that the choice of career starting date systematically alters sample size, the measurement of schooling and work experience and, as one would expect, inferences about early career returns to schooling and labor market experience. In some ways my entire analysis is a “straw man,” for data have improved dramatically since Mincer performed his pioneering work. We now have the ability to control for more than cumulative schooling gained prior to labor market entry and cumulative

Panel data have revealed that relatively few young people make a clean transition from full-time school to full-time, long-term employment. Instead, they often accumulate a substantial amount of work experience before leaving school or, at the other extreme, endure long spells of non-employment prior to gaining any appreciable amount of post-school work experience. Furthermore, many young people cycle back and forth between school enrollment and non-enrollment. As a result of these phenomena, it is not clear where analysts using panel data should “start the clock” on the career for purposes of analyzing labor market outomes. In this paper, I ask whether the choice of career starting date affects estimates of the returns to schooling for a sample of young men. It has become standard practice to assess the returns to schooling with a log-linear earnings function similar to the one pioneered by Mincer (1974), in which measures of schooling attainment and work experience proxy skills gained before and after labor market entry. Panel data users often measure actual work experience rather than approximating it, as Mincer did, with “age minus schooling minus six (or some other constant),” but regardless of how experience is measured the standard earnings model requires analysts to arbitrarily carve the life cycle into a school phase and a subsequent work phase.1 If analysts choose a career starting date that succeeds actual labor market entry for a significant number of sample members—perhaps

[Manuscript received 2 August 1996; revision accepted for publication 26 March 1997]

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work experience gained post-entry; instead, we can now control for complicated patterns of schooling and work effort that are observed in the data. The complete development of such a model is beyond the scope of this paper, but I conclude the analysis by examining the schooling effects implied by a model that controls separately for in-school (“pre-career”) work experience gained prior to the completion of school, as well as both part-time and full-time labor market experience gained after schooling is ostensibly completed. The primary purpose of this paper, however, is simply to caution that the orthodox approach to measuring schooling and work experience is no longer optimal or necessary, given recent advances in data availability. Whether one looks at the “returns to schooling” literature or the broader literature on life cycle earnings paths, studies that explicitly consider how (and whether) to define the start of the career are in short supply. The discussion of the subject by Ornstein (1976) is the lengthiest I have encountered, although his empirical analysis is based on a single, arbitrarily chosen definition. (He considers the career to begin when an individual leaves full-time schooling for a period of labor force participation that lasts at least 16 months.) Hanoch (1967) uses census data to estimate school exit ages, and provides evidence that S + 6 is generally too early a career starting age, particularly among college graduates. Garvey and Reimers (1980) compare “age minus schooling minus six” with a measure of predicted experience. In estimating predicting equations they ease the assumption that S + 6 is the career starting date, but maintain the assumption that work experience acquired while in school is irrelevant. While few studies focus on the choice of career starting date, evidence suggesting that we should worry about this issue has been produced in abundance. The importance of in-school work experience is documented in Griliches (1980), Stephenson (1981), Coleman (1984), D’Amico (1984), Meyer and Wise (1984), Michael and Tuma (1984), Ehrenberg and Sherman (1987), Lillydahl (1990), Steel (1991), Ruhm (1995) and Light (1996c). Evidence that many young people undergo multiple transitions between school and work (or, more accurately, school and non-school) is presented in Griliches (1980), Coleman (1984), Marcus (1984, 1986), Meyer and Wise (1984), and Light (1995, 1996a). The alarming tendency among many youth, particularly non-whites, to accumulate far more non-employment than employment experience during the initial post-school years has been widely analyzed; Freeman and Wise (1982) compile several studies that focus on this aspect of the early career. Taken as a whole, this body of research indicates that the transition from school to work is an ongoing and muddled process and that wage models should be respecified to capture heterogeneous patterns in the acquisition of schooling and work experience.

The paper is organized as follows. In the next section, I discuss the data and define the four career starting dates that are used throughout the analysis. I also examine the schooling distribution that corresponds to each alternative starting date and the accumulation of experience between various pairs of starting dates. This descriptive analysis indicates why the choice of career starting date has such a large effect on wage model estimates. In section 3, I define the covariates used in the wage model and describe the estimation procedure. Section 4 presents the estimates, and section 5 contains concluding remarks. 2. SAMPLE CHARACTERISTICS The data are from the National Longitudinal Survey of Youth (NLSY), which began in 1979 with a sample of 12,686 men and women born in 1957– 1964. Respondents were interviewed from 1979 to 1994 and in 1996, with the next interview scheduled for 1998. I use data for survey years 1979–1991, and I reduce the sample to 1896 male respondents by imposing a number of selection rules. First, I eliminate the 6283 female respondents in the original NLSY sample. This selection rule is imposed to streamline the presentation of results, for I find that the restrictions implied by pooling males and females are rejected by the data, yet my inferences about the returns to schooling are qualitatively similar for both genders. Second, I eliminate all 824 male respondents from the military subsample. These respondents were serving in the military as of September 30, 1978 and, as a result, are likely to have very different school-towork transitions than the typical civilian respondent. Next, I eliminate 3318 respondents whose 16th birthdays occurred before January 1, 1978—that is, I eliminate five of the eight birth cohorts represented in the NLSY. The NLSY contains detailed event history data on all jobs held since January 1, 1978, including a week-by-week indicator of labor market status. Eliminating older respondents allows me to track each remaining sample member’s work effort from his 16th birthday onward, thereby avoiding difficulties associated with left-censored careers. I also eliminate 175 individuals for whom school exit dates and/or school attainment cannot be accurately determined. The NLSY contains a great deal of information on school attainment and dates of school enrollment, including a month-by-month accounting of enrollment status from January 1980 onward. However, the schooling information reported by some respondents contains inconsistencies that cannot be easily resolved. To ensure that career starting dates based on reported schooling information are extremely accurate, I eliminate the respondents with particularly “dirty” data. I also eliminate 127 individuals who claim to leave school prior to their 16th birthday to further reduce the risk of obtaining errorridden starting dates and, more importantly, to avoid left-censored careers. Finally, I discard 63 individuals

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Estimating Returns to Schooling who fail to leave school for the first time prior to their last interview.2 These selection rules produce a sample of 1896 male respondents. Throughout the analysis, I segment the sample into subgroups of 826 blacks and Hispanics, and 1070 non-black, non-Hispanic men. For brevity, I refer to members of the two samples as “nonwhite” and “white.” Table 1 summarizes the four career starting dates that I consider. For each sample member, the earliest starting date used is the 16th birthday. It is unlikely that an analyst would “draw the line” between school and work at such an early point in the life cycle, but I use this starting date for illustrative purposes because little, if any, “pre-career” work experience goes unmeasured. The first row of Table 1 indicates that this starting date (referred to throughout the discussion as SD16) is observed (and, therefore, defined) for all 1896 respondents—i.e. it occurs between January 1, 1978 and the last interview. In fact, my sample selection rules ensure that the 16th birthday occurs during calendar year 1978, 1979, or 1980 for all 1896 individuals in the sample. The second career starting date corresponds to the first time the respondent leaves school. Clearly, all students “leave” school for summer and other school vacations, but I avoid starting the career at these dates by defining a school exit as the beginning of any nonenrollment spell that lasts at least four months.3 The sample selection criteria described above ensure that this starting date (which I refer to as SD1) is observed for all 1896 individuals in the sample, meaning the date falls between January 1, 1978 and the individual’s last interview. The first school exit is a starting date analysts frequently choose, but it correctly partitions the life cycle into the school and work phases only for individuals who leave school without ever having held a job and do not subsequently reenroll in school.

The third career starting date corresponds to the last observed exit from school and is referred to throughout the paper as SDL. SDL is defined similarly to SD1 as the beginning of the last observed non-enrollment spell that survives at least four months. I consider this starting date because, as noted in the introduction and detailed elsewhere (Light, (1995, 1996a)), a non-trivial number of NLSY respondents return to school after a period of nonenrollment. Table 1 shows that SDL is a later date than SD1 for about 26% of the entire sample, meaning these individuals are observed leaving school and subsequently reenrolling. For the remaining 74% of the sample I set SDL equal to SD1; thus, it is defined for the entire sample. It may seem that the distinction between SD1 and SDL is uninteresting, given that they are equal for almost three out of every four individuals, but individuals for whom they diverge frequently accumulate years of full-time work experience between their first and last exit from school, and their schooling completion levels typically increment by about a year. As a result, the choice of career starting date for this group of individuals is likely to exert considerable influence. The fourth career starting date is the point at which the individual makes his first permanent entry into the labor market. To define this date, I divide the period from age 16 (SD16) to the last interview into 52-week intervals. Within each 52-week interval, I count the number of weeks worked and the average number of hours worked per week. The beginning of the first of three consecutive intervals in which the individual works at least 26 weeks and averages at least 30 hrs per week is defined as the start of the “permanent” career (referred to a SDP).4 Permanent labor market entry can be defined a number of different ways, but my definition of SDP is patterned after the career starting date described by Farber (1994). Row 4 of Table 1 reveals that this starting date is defined for

Table 1. Description of alternative career starting dates Row 1 2 3 4 Percent of row 1 for whom

Percent of row 4 for whom

Starting date SD16 (16th birthday) SD1 (first exit from school) SDL (last observed exit from school) SDP (permanent labor market entry)* [Percent of row 1]

Number of whites

Number of non-whites

1070 1070 1070 900 [84.1]

826 826 826 634 [76.8]

SD1 ⬍ SDL SD1 = SDL

26.8 73.2 100.0

26.0 74.0 100.0

SD16 ⬍ = SDP ⬍ SD1 SD1 ⬍ = SDP ⬍ SDL SDL ⬍ = SDP

41.6 54.4 4.0 100.0

33.8 60.7 5.5 100.0

*Permanent labor market entry occurs at the beginning of a spell in which the individual works at least 26 weeks/year and averages at least 30 hours/week for three consecutive years.

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84% of white men and 77% of non-white men; for the remaining respondents, a three-year stretch of full-time, year-round employment is not observed. The fact that SDP is defined for a larger proportion of whites than non-whites is consistent with the wellknown differences in work continuity between these groups. While it is necessarily the case that the 16th birthday is no later than the first school exit and the first school exit is no later than the last school exit for all respondents (SD16 ⱕ SD1 ⱕ SDL), permanent labor market entry (SDP) can occur at any point from the 16th birthday onward. The bottom section of Table 1 reveals that permanent labor market entry precedes the first exit from school for 41.6% of whites and 33.8% of non-whites; as one would expect, the majority of respondents for whom SDP precedes SD1 begin their “permanent” careers while attending college. The more common pattern, however, is to leave school before beginning full-time, year-round work; 58.4% of whites and 66.2% of non-whites fall into this category. As the bottom line of Table 1 reveals, only 4–5% of respondents leave school, subsequently reenroll, and complete their reenrollment prior to permanent labor market entry. Table 2 shows the distribution of highest grade attended at each career starting date except the 16th birthday (SD16) for both race groups. I begin the discussion of Table 2 by considering the difference between the schooling distributions that prevail at the first and last school exits (SD1 vs SDL). The difference between the two distributions is due strictly to the 26% of the sample for whom the first and last exits from school are distinct. Hence, I report the schooling distribution at the last school exit for the entire sample (column 3), and also for the subset of individuals who cause the two distributions to diverge (column 4).

As column 4 of Table 2 reveals, individuals who leave school and subsequently reenroll are a very highly schooled group when they are last observed leaving school. More than 75% of white men have gone beyond high school at that date, and two-thirds of the non-white men have done so.5 The “returners” constitute only 26% of the sample, but their schooling increments are sufficiently large for the rightward shift in the cumulative schooling distributions (column 3 relative to column 1) to be statistically significant for both race groups at a 5% significance level.6 While the cumulative schooling distribution associated with the last exit from school necessarily lies to the right of the distribution associated with the first school exit, the difference between the distributions at SD1 and SDP is less clear-cut. These two distributions would be identical if permanent labor market entry coincided with the first school exit for everyone. Instead, the sample consists of three “types” of individuals: (1) those who permanently enter the labor market before their first school exit (SDP ⬍ SD1), in which case the schooling level at SDP is less than that at SD1, (2) those who permanently enter the labor market after the first school exit (SDP ⬎ SD1), in which case schooling is no less at SDP than at SD1, and (3) individuals who do not permanently enter the labor market (SDP is undefined). Individuals in the first group tend to be highly schooled, while individuals in the latter two groups tend to come from the bottom of the schooling distribution. The net effect is that the schooling distribution at permanent entry lies slightly to the right of the distribution at first school exit, although the distributional shift is not statistically significant for either race group.7 Table 3 summarizes the amount of work experience accumulated between various pairs of career starting dates. Specifically, I measure the number of

Table 2. Distribution of highest grade attended at alternative career starting dates

SD1 (1) Highest grade attended

Career starting date SDP (2) SDL* (3)

SDL† (4)

Number of individuals [percent of column total]

Whites

8–11 12 13–15 16 + 8–16 +

190 [17.8] 481 [45.0] 192 [17.9] 207 [19.3] 1,070 [100.0]

167 [18.6] 362 [40.2] 183 [20.3] 188 [20.9] 900 [100.0]

163 [15.2] 410 [38.3] 241 [22.5] 256 [23.9] 1,070 [100.0]

23 [8.0] 44 [15.3] 126 [43.9] 94 [32.8] 287 [100.0]

Non-whites

8–11 12 13–15 16 + 8–16 +

192 [23.2] 398 [48.2] 152 [18.4] 84 [10.2] 826 [100.0]

137 [21.8] 293 [46.2] 139 [21.9] 64 [10.1] 634 [100.0]

171 [20.7] 355 [43.0] 202 [24.5] 98 [11.9] 826 [100.0]

24 [11.2] 48 [22.3] 107 [49.8] 36 [16.7] 215 [100.0]

Notes: SD1 and SDL are the dates of first and last exit from school; SDP is the date of “permanent” labor market entry. *Includes entire sample; †includes only individuals who reenroll in school, meaning the first school exit precedes the last (SD1 ⬍ SDL).

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Table 3. Mean number of full-time work weeks accumulated between alternative career starting dates (standard deviations in parentheses) Highest grade attended at 2nd starting date

SD16–SD1

SD16–SDP

SD16–SDL

SD1–SDL

Whites

8–11 12 13–15 16 + 8–16 +

26.3 40.8 95.6 131.1 65.5

(40.8) (32.9) (65.5) (75.8) (64.8)

47.8 57.4 83.5 119.8 75.0

(39.7) (46.3) (52.6) (57.5) (44.8)

44.4 58.6 166.2 172.2 107.9

(86.0) (77.9) (139.6) (107.5) (117.8)

123.0 167.8 173.7 142.4 158.5

(154.0) (136.2) (138.2) (88.7) (125.8)

Non-whites

8–11 12 13–15 16 + 8–16 +

18.2 31.4 81.5 123.3 46.9

(22.8) (28.3) (60.7) (87.4) (55.4)

51.0 52.4 75.7 103.3 62.7

(51.5) (46.8) (47.0) (61.4) (52.1)

27.4 45.3 135.8 165.7 78.0

(49.8) (65.2) (127.2) (117.2) (103.0)

64.2 104.2 131.7 144.5 120.2

(92.0) (113.5) (130.3) (96.0) (119.3)

Notes: SD1 and SDL are the dates of first and last exit from school; SD16 is the 16th birthday; SDP is the date of “permanent” labor market entry; full-time work weeks are cumulative hours worked divided by 40. Means are computed for individuals for whom the two starting dates are defined and unequal.

hours worked between pairs of starting dates, convert cumulative hours to cumulative full-time work weeks by dividing by 40, and report the means by race and schooling attainment.8 In measuring work experience between pairs of starting dates, I consider only those individuals for whom both starting dates are defined and unequal. I use each individual’s schooling attainment at the later of the two starting dates to place him into a schooling category. Table 3 reveals that young men typically accumulate a substantial amount of work experience prior to the date that might be chosen as the starting point of their careers. If the first school exit (SD1) is used as the starting date, the typical white male begins his career having already accumulated 65 weeks of fulltime work experience since his 16th birthday. If permanent labor market entry or the last school exit is chosen as the starting date, the amount of pre-career work experience held by the typical white male increases to 75 and 108 weeks, respectively. It is important to bear in mind that these experience measures are denominated in units of 40 hours and represent a significant amount of work effort. When I replace the number of 40-hour work weeks with the number of weeks in which an individual works at all (not shown), I find that white men average 100 weeks of work between age 16 and SD1 and 142 weeks between age 16 and SDL. Reading down each column of Table 3, it is apparent that highly schooled individuals tend to accumulate more work experience between age 16 and subsequent starting dates than their less schooled counterparts. For example, white men who first leave school after 12 years have worked an average of 41 weeks since age 16, while those who complete college have accumulated 131 weeks of full-time experience since age 16. This pattern is to be expected, for elapsed time between SD16 and SD1 or SDL necessarily increases with schooling attainment. The only

exception to this pattern is seen in the last column, which reveals that college graduates accumulate less work experience between SD1 and SDL than do individuals in lower schooling categories. College graduates spend as much as 70% of the weeks between SD1 and SDL working, but they accumulate relatively little experience because the two dates tend to be close together. Given the finite observation period, SDL is only observed when individuals complete relatively little schooling and/or return to school relatively quickly. Table 3 also highlights important racial differences in the accumulation of early career work experience. Between the 16th birthday and either SD1, SDP, or SDL, whites typically accumulate more work experience than non-whites. Among high school graduates at the first school exit, for example, the average number of full-time weeks worked since age 16 is 41 for white men and only 31 for non-white men. These differences stem in part from differences in work intensity: white high school graduates work 31% of the weeks between their 16th birthday and their first exit from school, on average, while the typical non-white works 22% of the weeks. These patterns point to the fact that in-school work experience is much more prominent for whites than for non-whites, as Stephenson (1981), D’Amico (1984), and Michael and Tuma (1984) have found. They also indicate that if “precareer” work experience is ignored in a wage model—that is, if experience is measured from (first or last) school exit or “permanent” labor market entry—the resulting biases in the estimated returns to schooling will be more severe for whites than for nonwhites and for college educated individuals than for their less schooled counterparts. 3. MODEL SPECIFICATION The preceding discussion suggests that inferences about the wage effects of schooling are likely to be

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sensitive to the choice of a career starting date because the starting date will influence (a) which wage observations are included in the sample, (b) the schooling and experience levels associated with each reported wage, and (c) the amount of pre-career work experience that is ignored. Clearly, the same issues arise in estimating models of labor supply, job mobility, and unemployment duration, but nowhere are the effects likely to be larger than when the objective is to identify the separate wage effects of schooling and labor market experience. To investigate this sensitivity, I estimate a standard wage model with samples based on each of the four career starting dates defined in section 2. I estimate each model separately for whites and non-whites in order to learn whether the choice of starting date is particularly influential in analyses that focus on race differences in wages. In the remainder of this section, I explain how the samples are created, define the covariates included in the wage models, and describe the estimation procedure. The sample based on starting date SD16 consists of every wage reported by the 1896 respondents in reference to jobs initiated from their 16th birthdays onward. Samples based on the other three starting dates are created in a similar fashion. During each annual interview, respondents report the current wage and other characteristics associated with their current employers and the “usual” wage and characteristics associated with every employer encountered since the last interview. As a result, virtually every job held after the given career starting date contributes an observation to the given sample, and jobs that survive from one interview year to the next contribute multiple wage observations. The bottom rows of Tables 6 and 7 in the Appendix report sample sizes for the eight subsamples (two race groups × four starting dates). The 1070 white men in the sample report 14,265 wages for jobs held between the 16th birthday and the last interview. Starting the career at the first school exit (SD1) leads to approximately 25% of these observations being discarded; the resulting sample contains only 10,705 observations. Extending the starting date to the last school exit (SDL) reduces the sample to 9179 and using permanent labor market entry (SDP) as the starting date results in a sample size of 9280. The choice of starting date has a similar effect on sample sizes for nonwhite men, although now there is only a 21% sample size reduction when moving from SD16 to SD1, and SDP (rather than SDL) yields the smallest sample of the four. Tables 6 and 7 also show that fewer than 1070 whites and 826 non-whites contribute to these wage samples. The discrepancy is due to individuals who fail to report a wage between the relevant career starting date and the end of the observation period. Tables 6 and 7 report means and standard deviations for the dependent variable and the regressors included in each wage model. The dependent variable is the natural logarithm of the CPI deflated average

hourly wage in 1981 dollars. In estimating the wage models, I control for three dummy variables that indicate whether the amount of school attended is less than 12 years, 12 years, or 16 or more years, with 13–15 years as the omitted group. In all samples except the one based on SDL these dummy variables can change values across observations when individuals return to school. The variables are time-invariant in the SDL sample because no school attendance is observed beyond the last observed school exit. The next regressors listed in Tables 6 and 7 are years of work experience (X), years of job tenure (T), and the squared and cubed values of both variables. To define work experience, I count the number of weeks worked from the career starting date to the date at which the corresponding wage is reported to be earned. I then divide this value by 2080 (52 × 40) in order to express it as years of full-time employment. I define job tenure by subtracting from X all work experience accumulated between the career starting date and the reported starting date for the job. As a result, both X and T are much more accurate measures of accumulated work experience than are more commonly used variables based on the number of weeks, months, or years in which the individual gained any amount of work experience. The wage models also include a fairly standard set of controls for personal, job and market characteristics. Among these controls are dummy variables indicating marital and divorce status, whether a child under the age of six is present in the household, government jobs, whether the job is part-time (less than 30 hours per week), union status, whether the respondent resides in a city or in the South, and calendar year. Union status is missing for about 3% of observations so, rather than discard the observations, I set union status to zero and define an additional dummy variable indicating it is missing. To control further for economy-wide influences on wages I also include the quarterly, seasonally adjusted national unemployment rate for 20–24 year old males. In estimating the wage model, I assume the residual can be specified as ␣i + ⑀it, where ␣i is a time-invariant, person-specific random variable and ⑀it is a time-varying random variable. Both random variables are assumed to be mean zero and have constant variances ␴2␣ and ␴2⑀ , respectively. I estimate the wage model by generalized least squares (GLS) after imposing the additional assumption that both components of the error term are uncorrelated with each of the regressors. In most applications, it is inappropriate to assume that ␣i is uncorrelated with the regressors. School enrollment decisions and, therefore, observed schooling levels are widely acknowledged to be affected by unobserved, time-invariant, personal characteristics such as innate ability (see, for example, Griliches, 1977). In addition, employment decisions that affect observed levels of work experience and tenure, marriage and fertility decisions, and selection into union

Estimating Returns to Schooling jobs are likely to be related to unobserved factors summarized by ␣i. Furthermore, the assumption that ⑀it is independent of the regressors is violated by the fact that, in practice, this term subsumes job-related, environmental, and time-varying, personal characteristics that may be systematically related to the observables. As is always the case, the inability to control perfectly for all sources of heterogeneity is likely to result in biased estimates of most parameters, including the coefficients for key variables such as schooling and work experience. I choose to ignore such biases for two reasons. First, I am primarily interested in comparing parameter estimates across samples based on the four alternative career starting dates. Although all the estimated parameters may be biased, it is not clear that the bias is different when age 16 is chosen as the starting date than when, for example, the last school exit is chosen. Second, there is no easy solution to the problem. I could obtain fixed-effect estimators that are unbiased by the assumed correlation between the regressors and ␣i, but I would be unable to identify coefficients for the schooling variables.9 Alternative estimation techniques exist that utilize cross-person sample variation while correcting for the correlation between ␣i and the regressors. For instance, the method proposed by Hausman and Taylor (1981) uses deviations from person-specific means of the time-varying covariates as instruments for those covariates that are correlated with ␣i. However, the instruments and, therefore, the parameter estimates are affected by the amount of within-person variation in the sample. I was unable to find alternative instrumental variables that perform satisfactorily, and the addition of ability proxies (family background measures and test scores) proved to have little influence on the estimated schooling coefficients.10 4. ESTIMATES I estimate the wage model described in the preceding section using the four different samples based on alternative starting dates for both whites and nonwhites. The eight sets of GLS estimates are presented in Tables 8 and 9. In discussing the results I focus on Table 4, which summarizes the predicted schooling and experience effects implied by the GLS estimates. Specifically, I use the coefficients for the schooling dummy variables to compute the predicted effect on the log-wage of advancing from less than 12 years of school to 12 years, and the effect of advancing from 12 years to 16 or more years. In addition, I report the estimated wage growth associated with one, three, and five years of continuous, fulltime employment (X). For brevity, I refer to these estimated wage gaps as “returns” to schooling and experience. The top section of Table 4 reveals that, among white men, the wage boost associated with completing high school increases as the career starting date

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moves from SD16 to SD1 to SDP to SDL. The standard errors associated with these predicted wage effects are very large; thus, using conventional significance levels, I cannot reject the null hypothesis for any of the four samples that white high school dropouts and high school graduates begin their careers earning identical wages. Underlying these statistics, however, is the finding (seen in Table 8) that the estimated wage gap between high school dropouts/graduates and individuals with 13–15 years of schooling increases dramatically as the starting date moves from SD16 to SD1 to SDP to SDL. Table 4 also shows that college graduates earn significantly more than high school graduates, and that the estimated return to college is highly sensitive to which career starting date is used. When the 16th birthday (SD16) is used as the career starting date, the estimated schooling parameters imply that the return to a college education is 27%. When either the first exit from school (SD1) or the date of permanent labor market entry (SDP) is used, the estimated return to college is about 35%, and when the last school exit (SDL) is used the estimated return increases to 41%. The pattern is clear: the later in the life cycle is the career starting date, the larger is the estimated return to a college education. At the same time, the estimated return to labor market experience is seen to decrease as the career starting date is delayed. When SD16 is used as the starting date, the estimated return to five years of post-entry experience is 22%. This estimate falls to 19% when SD1 or SDP is used, and to 14% when SDL is used. The systematic relationship between the career starting date and the estimated returns to both schooling and work experience can be attributed to the work experience that is ignored by models based on later starting dates. The discrepancy between the SD16 sample and either the SD1, SDP or SDL sample is caused primarily by discarding early career observations contained in the SD16 sample and rescaling experience for the remaining observations. Thus, a portion of the work effort that contributes to wages observed in the SD1, SDP, and SDL is ignored because the model does not allow for “pre-career” experience. This causes the intercept of the wage path fitted for the later starting dates to shift upward and the path to flatten relative to the path fitted for the earlier date. The rotation of the wage path is more dramatic among college graduates because they gain relatively more work experience between age 16 and each subsequent career starting date, as seen in Table 3. I cannot claim that any of the four samples yields a “true” estimate of the early career wage premium associated with attending college, in part because of the potential biases described in section 3. However, it appears that the use of a “late” career starting date causes an upward bias in the estimated return to schooling because predicted starting wages reflect the positive effect on wages of pre-career experience as

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Economics of Education Review Table 4. Estimated returns to schooling using alternative career starting dates

Whites

Non-whites

Effect on ln(wage) of S = 12 vs S ⬍ 12 S ⬎ = 16 vs S = 12 Effect on ln(wage) of 1 yr of X 3 yrs of X 5 yrs of X Effect on ln(wage) of S = 12 vs S ⬍ 12 S ⬎ = 16 vs S = 12 Effect on ln(wage) of 1 yr of X 3 yrs of X 5 yrs of X

SD16

SD1

SDP

SDL

0.001 (0.013) 0.271 (0.015)

0.019 (0.023) 0.350 (0.023)

0.020 (0.028) 0.341 (0.026)

0.030 (0.028) 0.409 (0.028)

0.043 (0.008) 0.134 (0.018) 0.223 (0.023)

0.043 (0.010) 0.123 (0.021) 0.190 (0.026)

0.044 (0.009) 0.122 (0.021) 0.185 (0.027)

0.030 (0.010) 0.089 (0.021) 0.143 (0.026)

0.019 (0.015) 0.229 (0.022)

0.064 (0.023) 0.311 (0.031)

0.038 (0.029) 0.296 (0.037)

0.058 (0.026) 0.366 (0.036)

0.029 (0.011) 0.110 (0.023) 0.207 (0.027)

0.053 (0.013) 0.153 (0.026) 0.243 (0.031)

0.057 (0.013) 0.154 (0.026) 0.232 (0.032)

0.047 (0.013) 0.139 (0.026) 0.223 (0.031)

Notes: SD1 and SDL are the dates of first and last exit from school; SD16 is the 16th birthday; SDP is the date of “permanent” labor market entry; computations are based on the GLS estimates reported in Tables 8 and 9; see Tables 6 and 7 for variable definitions. Standard errors of predictions are in parentheses.

well as schooling, and this upward bias is relatively more severe for more highly schooled individuals.11 The bottom section of Table 4 reveals that for nonwhites, as for whites, the estimated return to a college education is large, statistically significant, and increasing as the career starting date is delayed. College graduates are predicted to earn a 23% wage premium over high school graduates when SD16 is used, a 30% premium when SD1 or SDP is used, and a 37% premium when SDL is used. This is the most striking finding revealed by my comparison of alternative starting dates, and it holds uniformly for whites and non-whites. The remaining estimates for non-whites differ from those of whites in two respects. First, the point estimates for the high school graduation premium are neither zero across the board, nor monotonically increasing as the career starting date is delayed. Using standard, 5% significance levels, I reject the null hypothesis that high school graduates and dropouts earn identical wages when SD1 and SDL are used as starting dates. Moreover, I obtain the highest estimated return (6.4%) when using SD1 as the career starting date, which is generally not the latest starting date considered. Second, although the estimated return to work experience falls (slightly) as I move from SD1 to SDP to SDL, the smallest returns to experience are found for the SD16 sample. In interpreting the differences between whites and non-whites, I begin by once again noting how the four samples based on alternative starting dates differ. Moving the starting date from SD16 to SD1 to SDP to SDL amounts to discarding an increasingly large number of low experience observations and rescaling experience among the observations that remain.12 I can abstract from the former source of change by reestimating the wage models after restricting each sample to the observations that are common to the four samples. With the difference across samples

reduced to a rescaling of experience, the contrast in the GLS estimates (which I do not report) is quite predictable: moving from the SD16 sample to SD1 to SDP to SDL results in a progressive upward shift in the estimated schooling effects and a progressive decrease in the estimated return to work experience. Apparently, the slight deviations from this pattern seen for non-whites in Table 4 reflect the fact that the early career observations that are not common to each sample are particularly influential in determining experience and “high school graduation” effects. I have shown that estimates of the wage premium earned by college graduates are highly sensitive to the choice of career starting date, as are estimates of the returns to labor market experience. The solution to this problem, in my view, is not to find the “correct” career starting date, for any wage model that assumes a clear-cut career starting date is fundamentally at odds with the patterns of skill acquisition seen in panel data. Instead, we need to specify wage models that control for the different patterns of school enrollment and work effort undertaken by young people. I conclude my analysis with a brief discussion of my preliminary efforts to develop such a model. Rather than assume workers accumulate a single “type” of work experience from an arbitrary career starting date onward, I allow for different types of work experience. I control separately for in-school work experience accumulated between the 16th birthday and the first exit from school, and both full-time and part-time work experience accumulated subsequent to that date.13 To define in-school work experience, I count the number of weeks worked from the 16th birthday (SD16) to the first school exit (SD1) and divide the cumulative measure by 2080 (52 × 40). I define both part-time and full-time experience from SD1 to the week each reported wage is earned. Fulltime experience is the number of cumulative hours worked during weeks when at least 30 hours are

39

Estimating Returns to Schooling worked, and part-time experience is the number of hours worked during the remaining, part-time work weeks. I divide full-time experience by 2080 and parttime experience by 1040. I estimate a wage model using all wages earned after the first school exit, so in-school experience (ISX) is a time-invariant regressor while both parttime experience (PTX) and full-time experience (FTX) vary over time for each person. I control for the linear, squared and cubed values of each of the three experience measures, as well as interactions between ISX and FTX and PTX. The model also includes three schooling dummy variables and interactions between each schooling variable and ISX. All other regressors listed in Tables 6–9 are in the model as well. In Table 5, I report the means and standard deviations for the experience—and schooling-related regressors for both whites and non-whites.

Table 5 also reports GLS estimates for the wage model and, in the bottom section, estimates of the implied returns to schooling and work experience for individuals who gain no in-school work experience (ISX = 0). These estimates indicate that among white men who do not work prior to their first school exit, college graduates earn 31% more than than high school graduates. Among non-whites, the corresponding estimate is 22%. The return to high school graduation is zero among whites and 6% for non-whites. Interactions between in-school experience (ISX) and the schooling variables are negative in most cases, but statistically significant at a 5% level only for white college graduates. This indicates that whites who work intensively while in college receive slightly smaller returns to their schooling than their nonemployed counterparts, although their in-school work experience may have a separate, positive impact on wages.

Table 5. GLS estimates of wage model with heterogeneous work experience Whites Variable Constant 1 if yrs of school ⬍ 12 (S11) = 12 (S12) = 16 + (S16) Yrs of in-school experience (ISX)* ISX2/10 ISX3/100 Yrs of full-time experience (FTX)† FTX2/10 FTX3/100 Yrs of part-time experience (PTX)‡ PTX2/10 PTX3/100 ISX*S11 ISX*S12 ISX*S16 ISX*FTX ISX*PTX Root mean squared error Number of observations Number of individuals Effect on ln(wage) of: S = 12 vs S ⬍ 12 S ⬎ = 16 vs S = 12 Effect on ln(wage) of: 1 yr of FTX 3 yrs of FTX 5 yrs of FTX

Mean

S.D.

Non-Whites

Coeff.

S.E.

1.343

0.086

Mean

S.D.

Coeff.

S.E.

1.398

0.106

0.19 0.43 0.16

.39 .50 .37

⫺0.005 ⫺0.021 0.286

0.033 0.029 0.036

0.23 0.47 0.08

0.42 0.50 0.27

⫺0.107 ⫺0.047 0.174

0.039 0.034 0.052

1.10 2.38 7.53

1.08 5.06 29.64

0.179 ⫺0.376 0.330

0.037 0.134 0.130

0.82 1.52 4.59

0.92 4.12 24.49

0.026 0.141 ⫺0.145

0.050 0.192 0.187

3.74 22.95 176.69

3.00 32.31 368.56

0.050 ⫺0.036 0.009

0.010 0.017 0.009

3.41 18.98 130.17

2.71 25.58 248.79

0.066 ⫺0.041 0.017

0.014 0.028 0.017

0.92 3.30 17.99 4.16 0.81 0.09 0.34 0.36

1.56 10.89 105.79 5.58 1.88 .31 .56 .98

⫺0.063 0.123 ⫺0.062 ⫺0.041 ⫺0.033 ⫺0.055 0.001 0.010

0.014 0.034 0.022 0.031 0.024 0.017 0.002 0.004

0.91 3.18 17.36 0.09 0.29 0.17 2.81 0.61

1.53 10.82 112.43 0.27 0.48 0.73 4.10 1.57

⫺0.047 0.056 0.000 0.001 ⫺0.017 ⫺0.011 ⫺0.000 0.023

0.014 0.032 0.018 0.050 0.033 0.025 0.002 0.006 0.355

10,705 1053

0.343 10,705 1053

7894

7894

793

793

⫺0.016 (0.030) 0.308 (0.040)

0.060 (0.031) 0.221 (0.056)

0.046 (0.009) 0.120 (0.020) 0.170 (0.027)

0.062 (0.012) 0.165 (0.025) 0.248 (0.031)

*Weeks worked from age 16 to the first school exit, divided by 2080; †weeks worked during full-time ( ⱖ = 30) work weeks since the first school exit, divided by 2080; ‡weeks worked during part-time ( ⬍ 30) work weeks since the first school exit, divided by 1040. Note: Each model also includes the additional regressors listed in Tables 6–9.

40

Economics of Education Review

The returns to college graduation implied by this model are considerably smaller than what is found with an orthodox model that uses the first school exit (SD1) as the career starting date, as seen in Table 4. However, the college graduation effects implied by the “heterogeneous work experience” model are virtually identical to what is seen in Table 4 for the model using the 16th birthday (SD16) as the career starting date. Based on this comparison, I infer that it is important to control for all work experience— not simply experience gained after leaving school— to avoid overstating the effects of a college education. The difference between the “SD16 model” and the model summarized in Table 5 is that the former constrains all work experience gained since age 16 to have the same effect on wages, while the latter allows for different types of experience.14 This distinction does not affect inferences about the wage benefits associated with college graduation, but it does affect inferences about the returns to work experience. The SD16 model indicates that five years of full-time, year-round experience raises whites’ and non-whites’ wages by about 21%. When different types of work experience are allowed to have different effects on wages, five years of full-time work experience is seen to raise whites’ wages by 17% and non-whites’ wages by 25%. Without exploring the notion of heterogenous work experience in more detail, I cannot determine the reasons for these small, but statistically significant differences. It is important to note, however, that the data resoundingly reject restrictions that force ISX, PTX, and FTX to have identical wage effects. 5. CONCLUSIONS The career starting date is not a well defined concept because the life cycle is not neatly divided into full-time learning (formal schooling) and full-time employment. Instead, young people frequently combine school and work, spend considerable periods of time neither working nor attending school, and return to school after having entered the labor market. Before estimating models that rely on measures of schooling and work experience to control for pre- and post-career skill accumulation, we should ask ourselves when the “work” portion of the life cycle begins. With these issues in mind, I use data for 1896 male

respondents in the 1979–1991 NLSY to construct four alternative samples containing data on wages, work experience, job tenure, and other variables that commonly appear in wage models. The four samples are based on alternative career starting dates: age 16 (SD16), the first exit from school (SD1), the last observed exit from school (SDL), and the first “permanent” entry into the labor market (SDP). Each sample is then used to estimate a standard wage model for both white men and non-white men. As I have demonstrated, the estimates prove to be quite sensitive to the choice of career starting date. For both whites and non-whites, switching from a relatively early starting date to a relatively late one leads to an increase in the estimated returns to college graduation. For white men, this increase in the return to college is accompanied by a pronounced decrease in the estimated return to work experience—that is, the estimated wage path shifts upward and flattens. The sensitivity I have identified appears to be due to the presence of unmeasured, “pre-career” work experience. The later in the life cycle the career is deemed to begin, the more “pre-career” work experience is ignored, particularly among highly schooled individuals. The failure to account for work experience gained prior to the career starting date causes systematic distortions in the estimated returns to schooling. In summary, this paper demonstrates that the choice of career starting date does matter. The analysis leaves unanswered the question of which starting date is “correct” because, in my opinion, that question cannot be answered. After all, the reason such large contrasts are found as I switch from one starting date to another is that there is tremendous heterogeneity, both across people and over time for a given person, in the rate at which work experience is accumulated and schooling is attained. The lesson to be learned from my experiments is that it is impossible to draw a clean line between the school and work phases of the life cycle and, as a result, it is inappropriate to measure experience (and, for that matter, schooling) cumulatively from an arbitrarily chosen point in the life cycle. Instead, we should generalize the ideas about skill accumulation and the specification of wage models originally posed by Becker (1965), BenPorath (1967), Mincer (1974), and others to account for the extremely heterogeneous school and work patterns that characterize the early career.

NOTES 1. Analysts using “age minus schooling minus six” as a measure of potential experience implicitly assume individuals begin school at age six, complete S grade levels in exactly S years and, therefore, begin their careers at age S + 6. This type of proxy for labor market experience has been widely used by analysts working with the Current Population Survey, the decennial census, and other surveys that do not collect information on actual labor market experience. It is important to note that when data on actual experience are available, the date at which to begin tracking experience must still be chosen by the analyst; this may be a “constrained” choice, for surveys typically elicit information on work experience from a given age (e.g. 18) onward. 2. Because of sample attrition, the last interview may occur before 1991. The 63 individuals who are not observed leaving school tend to be early attriters rather than “permanent” students.

Estimating Returns to Schooling 3. I observe a handful of nonenrollment spells of four months’ duration that occur from May to September. These are likely to correspond to summer vacations, so I stretch the four-month cutoff to five months in these cases. 4. I use the week-by-week status and hours arrays from the work history file for these computations. See Center for Human Resource Research (1995) for details on these data. 5. The most common type of reenrollment spell involves attending, but not completing, college, so these individuals also tend to be more highly schooled than “non-returners” prior to their reenrollment(s). 6. Inferences about the statistical significance of distributional shifts are based on Kolmogorov-Smirnov two-sample tests applied to the corresponding cumulative distributions. 7. If I were to start the career when individuals were out of school and working full-time, year-round, the rightward shift would be statistically significant—i.e. I would assign a large number of respondents a higher schooling level at SDP than they attained at their first school exit. 8. The NLSY provides sampling weights, but I use unweighted data throughout the analysis. 9. Schooling coefficients would be statistically unidentified for the sample based on SDL because schooling is time-invariant in that sample. For the other three samples, the coefficients would be identified from the within-person variation in schooling among individuals who reenroll. However, as I demonstrate in Light (1995), the wage increases associated with discontinuous schooling are not representative of the overall returns to schooling. 10. The most promising proxy is percentile scores for the Armed Forces Qualifying Test (AFQT). These scores are constructed from scores for the Armed Services Vocational Aptitude Battery (ASVAB), which was administered to 94% of NLSY respondents in 1980. AFQT scores are positively associated with wages and schooling, but their inclusion in the model does not change my inferences about the returns to schooling. 11. Evidence of “omitted in-school experience bias” is also found in Light (1996b). 12. Although the date of permanent labor market entry (SDP) can occur prior to the first school exit (SD1) or after the last school exit (SDL), it falls between SD1 and SDL for the modal respondent. 13. Clearly, I could define even more types of experience. For example, I could divide in-school work experience into full-time and part-time, and I could control separately for in-school work experience acquired after the first school exit. Such an extension—and, more importantly, an investigation of why different types of experience have differential wage effects—is left for future work. 14. Also, the SD16 model includes wages earned prior to school exit, while the heterogeneous experience model excludes them.

REFERENCES Becker, G. (1965) Human Capital. Columbia University Press, New York. Ben-Porath, Y. (1967) The production of human capital and the life cycle of earnings. Journal of Political Economy 75, 352–365. Center for Human Resource Research (1995) NLS Users’ Guide 1995. Ohio State University, Columbus, OH. Coleman, J. S. (1984) The transition from school to work. In Research in Social Stratification and Mobility, Vol. 3, eds D. J. Treiman and R. V. Robinson. JAI Press, Greenwich, CT. D’Amico, R. (1984) Does employment during high school impair academic progress? Sociology of Education 57, 152–164. Ehrenberg, R. G. and Sherman, D. R. (1987) Employment while in college, academic achievement, and postcollege outcomes. Journal of Human Resources 22, 1–23. Farber, H. S. (1994) The analysis of interfirm worker mobility. Journal of Labor Economics 12, 554–593. Freeman, R. B. and Wise, D. A. (1982) The Youth Employment Problem: Its Nature, Causes, and Consequences. University of Chicago Press, Chicago. Garvey, N. and Reimers, C. (1980) Predicted vs. potential work experience in an earnings function for young women. In Research in Labor Economics Vol. 3, ed. R. Ehrenberg, pp. 99–127. JAI Press, Greenwich, CT. Griliches, Z. (1977) Estimating the returns to schooling: some econometric problems. Econometrica 45, 1–22. Griliches, Z. (1980) Schooling interruptions, work while in school and the returns from schooling. Scandinavian Journal of Economics 82, 291–303. Hanoch, G. (1967) An economic analysis of earnings and schooling. Journal of Human Resources 2, 310–329. Hausman, J. A. and Taylor, W. E. (1981) Panel data and unobservable individual effects. Econometrica 49, 1377–1398. Light, A. (1995) The effects of interrupted schooling on wages. Journal of Human Resources 30, 472–502. Light, A. (1996a) Hazard model estimates of the decision to reenroll in school. Labour Economics 2, 381–406. Light, A. (1996b) In-school Work Experience and the Returns to Schooling. Ohio State University Working Paper No. 91-27, Ohio State University, Columbus, OH. Light, A. (1996c) High School Employment, High School Curriculum, and Post-school Wages. Ohio State University Working Paper 96-28, Ohio State University, Columbus, OH. Lillydahl, J. H. (1990) Academic achievement and part-time employment of high school students. Journal of Economic Education 21, 307–316. Marcus, R. D. (1984) Measuring the rate of return to interrupted schooling. Journal of Educational Statistics 9, 295–310. Marcus, R. D. (1986) Earnings and the decision to return to school. Economics of Education Review 5, 309–317.

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Economics of Education Review Meyer, R. H. and Wise, D. A. (1984) The transition from school to work: the experiences of blacks and whites. Research in Labor Economics 6, 123–176. Michael, R. T. and Tuma, N. B. (1984) Youth employment: does life begin at 16? Journal of Labor Economics 2, 464–476. Mincer, J. (1974) Schooling, Experience, and Earnings. Columbia University Press, New York. Ornstein, M. D. (1976) Entry into the American Labor Force. Academic Press, New York. Ruhm, C. (1995) The extent and consequences of high school employment. Journal of Labor Research 16, 293–303. Steel, L. (1991) Early work experience among white and non-white youths: implications for subsequent enrollment and employment. Youth and Society 22, 419–447. Stephenson, S. P. (1981) In-school labour force status and post-school wage rates of young men. Applied Economics 13, 279–302.

APPENDIX

Table 6. Means and standard deviations for samples based on alternative career starting dates (Whites)

Variable ln(average hourly wage) 1 if yrs of school ⬍ 12 = 12 = 16 + Yrs of work experience (X) 2 X X3 Yrs of job tenure (T) T2 T3 1 if married 1 if divorced 1 if child under age 6 present 1 if government job 0.07 1 if average hrs week ⬍ 30 1 if union member 1 if union status missing Unemployment rate 1 if reside in city 1 if reside in South 1 if 1980 1981 1982 1983 1984 1986 1987 1988 1989 1990 1991 Number of observations Number of individuals

Mean

SD16 S.D.

1.64 0.17 0.44 0.20 3.98 25.92 209.29 1.40 5.29 31.46 0.24 0.05 0.15 0.07 0.30 0.10 0.03 11.45 0.70 0.29 0.05 0.07 0.08 0.08 0.08 0.08 0.09 0.10 0.10 0.09 0.07 14,265 1061

Mean 0.49

3.17 35.30 401.12 1.83 14.54 142.29

2.53

SD1 S.D.

1.72 0.21 0.49 0.12 3.84 23.02 169.63 1.62 6.26 36.78 0.31 0.06 0.20 0.05 0.18 0.11 0.03 10.98 0.69 0.30 0.01 0.03 0.05 0.07 0.08 0.09 0.11 0.13 0.13 0.12 0.09 10,705 1053

Mean 0.50

2.87 29.83 314.03 1.91 15.31 147.89

2.35

SDP S.D.

1.76 0.22 0.43 0.14 4.22 26.97 211.21 1.84 7.45 44.56 0.33 0.06 0.20 0.05 0.16 0.11 0.03 10.82 0.70 0.31 0.01 0.02 0.04 0.05 0.08 0.09 0.12 0.13 0.14 0.13 0.09 9280 898

Mean 0.49

3.03 33.93 382.30 2.02 16.72 163.78

2.22

SDL S.D.

1.74 0.20 0.46 0.15 3.68 21.51 156.56 1.63 6.25 36.40 0.33 0.07 0.22 0.05 0.17 0.11 0.03 10.82 0.68 0.30 0.00 0.02 0.04 0.06 0.07 0.10 0.11 0.14 0.14 0.14 0.10

0.50

2.83 28.97 303.79 1.90 15.21 148.23

2.270

9179 1043

Notes: SD1 and SDL are the dates of first and last exit from school; SD16 is the 16th birthday; SDP is the date of “permanent” labor market entry.

43

Estimating Returns to Schooling Table 7. Means and standard deviations for samples based on alternative career starting dates (Nonwhites)

Variable ln(average hourly wage) 1 if yrs of school ⬍ 12 = 12 = 16 + Yrs of work experience (X) X2 X3 Yrs of job tenure (T) T2 T3 1 if married 1 if divorced 1 if child under age 6 present 1 if government job 1 if average hrs week ⬍ 30 1 if union member 1 if union status missing Unemployment rate 1 if reside in city 1 if reside in South 1 if 1980 1981 1982 1983 1984 1986 1987 1988 1989 1990 1991 Number of observations Number of individuals

Mean

SD16 S.D.

1.56 0.22 0.48 0.11 3.65 21.67 158.34 1.26 4.25 22.34 0.20 0.04 0.26 0.08 0.29 0.14 0.01 11.30 0.83 0.44 0.04 0.07 0.07 0.07 0.08 0.08 0.10 0.11 0.10 0.10 0.08 9983 811

0.47

2.89 28.94 294.89 1.64 11.36 94.37

2.47

Mean

SD1 S.D.

1.62 0.25 0.51 0.07 3.56 19.63 132.27 1.41 4.86 25.09 0.25 0.05 0.32 0.07 0.19 0.15 0.03 10.90 0.84 0.46 0.00 0.02 0.04 0.06 0.08 0.09 0.12 0.13 0.13 0.12 0.10 7894 793

0.48

2.64 24.92 236.91 1.69 11.74 95.90

2.29

Mean

SDP S.D.

1.66 0.24 0.48 0.07 3.95 23.13 164.19 1.67 6.09 31.94 0.28 0.04 0.33 0.08 0.15 0.16 0.03 10.69 0.84 0.47 0.00 0.02 0.03 0.05 0.07 0.09 0.12 0.15 0.14 0.13 0.10 6381 630

0.47

2.75 27.93 282.21 1.82 12.94 103.49

2.16

Mean

SDL S.D.

1.63 0.25 0.49 07 3.45 18.71 125.08 1.42 4.79 24.24 0.26 0.05 0.34 0.08 0.17 0.16 0.04 10.79 0.84 0.47 0.00 0.02 0.04 0.05 0.07 0.09 0.12 0.13 0.13 0.14 0.11

0.49

2.61 24.46 231.53 1.67 11.38 90.87

2.22

6991 781

Notes: SD1 and SDL are the dates of first and last exit from school; SD16 is the 16th birthday; SDP is the date of “permanent” labor market entry.

44

Economics of Education Review Table 8. GLS estimates of wage model using samples based on alternative career starting dates (Whites)

Variable

Coeff.

Constant 1 if yrs of school ⬍ 12 = 12 = 16 + Yrs of work experience (X) X2/10 X3/100 Yrs of job tenure (T) T2/10 T3/100 1 if married 1 if divorced 1 if child under age 6 present 1 if government job 1 if average hrs week ⬍ 30 1 if union member 1 if union status missing Unemployment rate 1 if reside in city 1 if reside in South 1 if 1980 1981 1982 1983 1984 1986 1987 1988 1989 1990 1991

1.397 ⫺0.062 ⫺0.061 0.210 0.042 0.015 ⫺0.019 0.064 ⫺0.087 0.035 0.062 ⫺0.005 ⫺0.013 ⫺0.028 ⫺0.093 0.202 0.067 ⫺0.005 0.072 0.007 ⫺0.015 ⫺0.003 0.033 0.006 ⫺0.013 0.007 0.065 0.074 0.071 0.078 0.085

␴2␣ ␴2⑀ Root mean squared error Number of observations

SD16 S.E. 0.052 0.015 0.012 0.014 0.010 0.016 0.008 0.009 0.023 0.015 0.011 0.019 0.013 0.015 0.008 0.012 0.020 0.005 0.010 0.012 0.021 0.020 0.028 0.029 0.015 0.015 0.017 0.020 0.021 0.023 0.022

Coeff. 1.474 ⫺0.120 ⫺0.101 0.249 0.044 ⫺0.009 ⫺0.007 0.072 ⫺0.099 0.043 0.062 0.015 0.005 ⫺0.014 ⫺0.060 0.209 0.059 ⫺0.003 0.077 ⫺0.011 ⫺0.075 0.021 0.015 ⫺0.005 ⫺0.031 0.007 0.053 0.062 0.058 0.067 0.062

SD1 S.E. 0.082 0.024 0.018 0.021 0.011 0.021 0.012 0.010 0.026 0.017 0.014 0.021 0.012 0.019 0.010 0.014 0.021 0.007 0.012 0.015 0.056 0.030 0.037 0.038 0.018 0.017 0.020 0.026 0.027 0.028 0.026

Coeff. 1.520 ⫺0.137 ⫺0.116 0.224 0.045 ⫺0.014 ⫺0.004 0.060 ⫺0.076 0.029 0.052 ⫺0.001 0.001 ⫺0.022 ⫺0.063 0.218 0.074 ⫺0.001 0.067 ⫺0.016 0.025 ⫺0.056 ⫺0.022 ⫺0.047 ⫺0.034 0.008 0.057 0.067 0.056 0.058 0.066

SDP S.E. 0.097 0.029 0.021 0.024 0.011 0.021 0.012 0.010 0.031 0.017 0.013 0.022 0.013 0.022 0.012 0.015 0.021 0.008 0.014 0.017 0.092 0.040 0.044 0.046 0.019 0.018 0.022 0.030 0.031 0.033 0.030

Coeff. 1.554 ⫺0.210 ⫺0.179 0.230 0.030 0.001 ⫺0.009 0.070 ⫺0.094 0.036 0.054 0.005 0.013 ⫺0.002 ⫺0.041 0.224 0.049 ⫺0.001 0.073 ⫺0.010 ⫺0.120 ⫺0.015 ⫺0.023 ⫺0.056 ⫺0.053 0.020 0.071 0.081 0.073 0.084 0.069

0.038 0.129

0.064 0.123

0.066 0.130

0.073 0.120

0.362 14,281

0.353 10,705

0.341 9280

0.349 9184

SDL S.E. 0.092 0.031 0.025 0.027 0.012 0.022 0.013 0.011 0.028 0.019 0.014 0.022 0.013 0.022 0.011 0.015 0.022 0.008 0.013 0.017 0.064 0.034 0.041 0.043 0.020 0.019 0.021 0.029 0.029 0.030 0.027

Notes: SD1 and SDL are the dates of first and last exit from school; SD16 is the 16th birthday; SDP is the date of “permanent” labor market entry.

45

Estimating Returns to Schooling Table 9. GLS estimates of wage model using samples based on alternative career starting dates (Nonwhites)

Variable

SD16 Coeff.

S.E.

SD1 Coeff.

S.E.

SDP Coeff.

S.E.

SDL Coeff.

S.E.

Constant 1 if yrs of school ⬍ 12 = 12 = 16 + Yrs of work experience (X) X2/10 X3/100 Yrs of job tenure (T) T2/10 T3/100 1 if married 1 if divorced 1 if child under age 6 present 1 if government job 1 if average hrs week ⬍ 30 1 if union member 1 if union status missing Unemployment rate 1 if reside in city 1 if reside in South 1 if 1980 1981 1982 1983 1984 1986 1987 1988 1989 1990 1991

1.499 ⫺0.061 ⫺0.042 0.187 0.025 0.050 ⫺0.033 0.074 ⫺0.122 0.049 0.083 ⫺0.038 ⫺0.010 0.023 ⫺0.012 0.137 0.038 ⫺0.014 0.056 ⫺0.059 ⫺0.014 ⫺0.021 0.020 0.027 ⫺0.017 0.018 0.006 ⫺0.005 ⫺0.023 ⫺0.034 ⫺0.015

0.066 0.018 0.015 0.021 0.013 0.025 0.014 0.012 0.034 0.026 0.014 0.026 0.011 0.016 0.010 0.013 0.035 0.006 0.015 0.014 0.027 0.025 0.036 0.036 0.019 0.018 0.020 0.025 0.026 0.027 0.025

1.462 ⫺0.156 ⫺0.092 0.219 0.054 ⫺0.012 0.000 0.094 ⫺0.168 0.078 0.083 ⫺0.016 ⫺0.010 0.050 0.011 0.151 0.112 ⫺0.005 0.046 ⫺0.089 ⫺0.122 ⫺0.001 ⫺0.004 ⫺0.006 ⫺0.007 0.022 0.009 0.001 ⫺0.019 ⫺0.033 ⫺0.047

0.101 0.026 0.021 0.031 0.015 0.031 0.020 0.013 0.039 0.030 0.015 0.028 0.012 0.019 0.012 0.015 0.027 0.008 0.017 0.016 0.078 0.036 0.047 0.046 0.021 0.020 0.023 0.031 0.032 0.032 0.029

1.335 ⫺0.106 ⫺0.068 0.228 0.060 ⫺0.033 0.011 0.093 ⫺0.173 0.085 0.089 ⫺0.021 ⫺0.022 0.061 0.006 0.169 0.126 0.007 0.053 ⫺0.072 ⫺0.126 ⫺0.065 ⫺0.054 ⫺0.094 ⫺0.025 0.016 0.018 0.024 0.005 0.006 ⫺0.053

0.128 0.032 0.025 0.037 0.015 0.033 0.021 0.014 0.041 0.031 0.017 0.032 0.013 0.022 0.015 0.016 0.029 0.011 0.020 0.018 0.188 0.055 0.058 0.060 0.025 0.023 0.028 0.039 0.039 0.040 0.035

1.461 ⫺0.198 ⫺0.140 0.226 0.048 ⫺0.003 ⫺0.007 0.101 ⫺0.197 0.108 0.086 ⫺0.014 ⫺0.008 0.049 0.025 0.173 0.090 ⫺0.002 0.066 ⫺0.093 ⫺0.143 0.001 ⫺0.023 ⫺0.025 ⫺0.008 0.021 0.022 0.025 ⫺0.002 ⫺0.009 ⫺0.034

0.110 0.031 0.026 0.037 0.016 0.033 0.021 0.014 0.042 0.033 0.016 0.030 0.012 0.020 0.013 0.015 0.026 0.009 0.019 0.017 0.089 0.041 0.052 0.050 0.023 0.022 0.025 0.034 0.034 0.034 0.029

␴2␣ ␴2⑀ Root mean squared error Number of observations

0.037 0.135

0.051 0.132

0.054 0.118

0.056 0.131

0.370 9280

0.365 7894

0.346 6381

0.364 6991

Notes: SD1 and SDL are the dates of first and last exit from school; SD16 is the 16th birthday; SDP is the date of “permanent” labor market entry.