Dynamic Models

• Sample and Measures
• Baseline Model
• Educational Pathways
• Industry and Occupation
• High School Curriculum
• College Field of Study
• Inequality Revisited

        To this point, we have seen descriptive evidence that the past thirty years have brought strong shifts in the American labor market. Wage growth during the key stage of career development--a measure of upward mobility--has stagnated and become more unequal, with less educated workers faring the worst. Youth are taking longer to complete their education, are working more while in school, and are interrupting their schooling more frequently. This volatility has been especially pronounced among those without a four-year college degree. The new pathways into the labor market apparently also have stronger effects on wage growth: in some cases beneficial; in other cases detrimental. Of particular concern are several negative effects on young adults who for various reasons cannot attain a four-year college degree, but who nevertheless make an effort to return to college for skills upgrading.

        In order to confirm and expand these conclusions, we shift to a modeling framework in which we explore the pathway effects dynamically, using multiple regression. In doing so, one of our goals is to explore other factors that might play a role and that might interact with the educational pathways. An obvious question, for example, is the extent to which college field of study might influence some of the patterns described above, especially the increased variability in wage outcomes. Similar questions might be asked about high school curriculum track, and the industries and occupations in which these young workers find jobs and in which the returns to educational decisions are ultimately realized. We will explore the impact of these variables--educational pathway, high school track, field of study, and industry/occupation--in the models discussed in this section.

        Because of selection bias, we must consider the effects of the different pathways as descriptive rather than as causative. Individuals may be on a particular pathway for many reasons, ranging from financial constraint to personal preference. Nevertheless, our goal is to describe how the mechanisms leading to wage growth in the labor market have changed. Because educational pathways have changed so dramatically, variation in their impact on wage growth will provide us with a sense of what matters most in the new economy.

        Unfortunately, the data for the original cohort do not offer sufficient information on these dimensions. We therefore limit the remainder of our analysis to the recent cohort only. The logic is simple. We have used the cross-cohort descriptive comparison to gain a general sense of what has changed over the past thirty years but now focus on the recent cohort in order to more systematically identify the factors that make for success (or lack of it) in the new labor market of the 1980s and 1990s. Specifically, in the models discussed here we are trying to answer questions of the form, "If a worker's educational pathways and early labor market experience contain a specific feature, does this positively or negatively influence long-term wage growth?" We do not construct a complete model capturing all of the determinants of wage growth simultaneously, but we will try to isolate some key factors and determine whether they persist in the presence of other controls. A more complex model might explain a larger portion of the variance, but may obscure important substantive effects, since many of the explanatory covariates are bound to be correlated with each other.

Sample and Measures

        In addition to previous sample restrictions, we require observations from at least three years in which an individual is working, so that our outcome variable, permanent wage growth from ages 16 to 36, is based on a sufficient number of data points. The net effect of these restrictions is to reduce the sample size of recent cohort respondents from 2,063 to 1,947. While the different age groups are still well-represented in this sample, the distribution of final education differs from that of the sample used in previous sections, with a slightly smaller portion of respondents attaining a high school degree or less. We do not adjust sample weights for this situation; rather, we control for final education in all of our regression analyses.

        Recall that our initial analyses were based on a strictly matched sample that excluded four years from the recent cohort to conform to the original cohort's survey years. Since we are now focusing only on the recent cohort, we recomputed our measures to include all available years. We have also expanded our pathway measures, so that we now use (1) the proportion of time an individual was enrolled in school and working and (2) a count of the actual number of interruptions to schooling. We should note that in the first part of the paper, we defined these two pathway measures to be mutually exclusive; here they are not, in order to more flexibly capture the different pathway effects in our models.

        We construct the high school curriculum variable by taking the latest reported value. Three categories were identified: (1) vocational/commercial, (2) general, and (3) academic. (The distributions of this and all other variables are given in Table 3.) In practice, general and vocational education students behave similarly in our models, so they were combined in all analyses. The college field of study measure is based on an extensive typology, grouped into more than twenty broad categories such as "biological sciences" or "health professions." For those with some college, we take the most recent value of this variable. For those with degrees, we identified the last field of study observed as that degree was completed.[8]

Baseline Model

        We begin with a very simple model that regresses permanent wage growth on education, with high school graduates as the reference group. The results, given in the first column of Table 4, confirm the descriptive findings in the first half of the paper (see Figure 2). The premium for college degrees is more than twice that of some college experience and associate's degrees. Not completing a high school degree has a negative effect, but this is not strongly significant. We do not add controls for work experience at this point; such controls will be discussed shortly. This model explains a substantial 18% of the variance in wage growth and will serve as a baseline against which to judge the additional impact of pathway-based covariates.[9]

Educational Pathways

        In the second column of Table 4, we add our measures of educational pathways to the model and find that they have a strong impact on long-term wage growth. Interruptions to education are presented as a series of dummy variables, with no interruptions (a single, clean spell) serving as the reference group. First note that the coefficients for final education remain comparable to their baseline values; however, the manner in which that education is attained matters a great deal. A single interruption reduces wage gains significantly by -0.117 units and more than one interruption reduces growth by -0.207 units--this loss is of the same magnitude as the gains from some college and associate's degrees, so high levels of volatility can, in effect, nullify the value of obtaining college experience. We should note that we are probably underestimating the true negative impact of interrupted schooling because we are only capturing its direct effect.[10] There is also an indirect effect. Some of the youth who interrupt their schooling may never go back to school, and thus end up with less education and therefore lower wage growth. Absent data on respondents' educational intentions at different time points, there is empirically no way to isolate this effect. The reader should keep in mind, however, that the negative impact of interruptions is very likely stronger than we estimate here.

        Working while enrolled also has a strong impact, but in the opposite direction, yielding positive gains in long-term wage growth. In fact, under this relatively simple model, the benefit to working while in school is sufficient to compensate for the negative effect of interrupting schooling. It is possible that the positive effect of working while in school results from the fact that we haven't yet controlled for work experience--the variable may simply be capturing respondents who have been in the labor market longer. Therefore, in the third column of Table 4, we add years of experience (at the last time the individual is observed) and its square.[11] The effect of experience is not statistically significant in the model, and the coefficients on the education variables remain approximately the same; however, the positive effect of working while in school is in fact reduced. This variable is therefore clearly correlated with experience; unfortunately, we cannot disaggregate the two effects, since most individuals in our sample work at some point while they are in school. The negative impact of interruptions remains untouched--in fact, we will find that this effect persists with several different controls in place. Workers on interrupted pathways face losing many of the gains they were trying to achieve.

Industry and Occupation

        We now examine the effect that industry and occupation may have on long-term wage growth. In order to keep the analysis manageable, we have defined the following collapsed groupings. For industries, the categories are (1) construction, mining, agriculture; (2) manufacturing, transportation, and communication; (3) wholesale and retail trade, business services; (4) finance, insurance, and real estate (FIRE); (5) professional services; and (6) public administration. For occupations, the categories are (1) professional, managerial, technical ("white collar"); (2) clerical, sales, private household, service ("pink collar"); and (3) crafts, operatives, farm, other laborers ("blue collar"). We use the finalindustry and occupation observed for our respondents.

        The results of adding industry and occupation to the analysis are provided in Table 5 (the reference group for industry is the manufacturing group; for occupation it is the blue collar group). Note first that the coefficients for the education variables change somewhat as these covariates are added. The premia for all types of college experience are dampened, which makes sense since postsecondary education is a credential for entering different occupations and industries. Not surprisingly, wage growth in wholesale and retail trade is lower than in manufacturing and construction, since the latter are traditionally unionized industries. This is a strong effect, -0.222, which is enough to offset the premium for some college and associate's degrees. We also find that the pink-collar occupations, in aggregate, are not significantly different than the blue-collar ones. On the other hand, jobs in white-collar occupations and in FIRE industries yield strong, positive wage growth, as one might expect. With the many combinations of education, industry, and occupation that are possible, we find that nearly 23% of the inequality of wage gains can be explained. Thus, an important characteristic of workers' pathways into the labor market is the destination industry and occupation.

        In the second column of the table, we include our two measures of educational pathways. The industry and occupation effects are very similar to those of column one, and the pathway effects are comparable to what was observed in the simpler model of Table 4. In other words, interruptions remain highly detrimental and working while enrolled is generally beneficial to wage growth, even after controlling for education, industry, and occupation effects. We do not display results that include the experience variables, but their inclusion has the same effect as in previous models. We were unable to detect any significant interactions between educational pathways and industry/occupation.

High School Curriculum

        High school curriculum turns out to be an important feature of a worker's educational pathway. When contrasting vocational/general track against academic track, we find that the former has a strong negative effect on wage growth, as summarized in the first column of Table 6. In the second column, we interact high school track with each education group. The main education effects are now only for those pursuing an academic track, and the main dummy for vocational/general track refers to high school graduates. We find that the wage growth of high school graduates is largely unaffected by curriculum, but the wage growth of dropouts is affected. While the pattern is not statistically significant, there is mild evidence that vocational curricula offer some value to those who do not complete high school degrees. We witness the opposite pattern for those with some college experience; an academic curriculum has a strong positive payoff for wage growth, while a vocational track does not. Notably, there is no such bifurcation for those with associate's degrees. The value of this degree in the labor market is not mediated by the curriculum taken in high school, so it apparently offers a "fresh start" even to those with vocational education backgrounds. Bachelor's degrees behave similarly--if one completes a four-year degree, then it is not important what one studied in high school. This is not the case for master's degrees, which are severely penalized (0.450 units) for those studying vocational curricula in high school. This effect could be driven by selection, in that a vocational student who pursues a master's degree may end up in a program offering lower "value" as a credential.

        In Table 7, we explore whether the effect of high school track varies by industry and occupation. In the second column, the main effects again refer to those who pursued an academic high school curriculum. The interactions are positive for all industries, indicating that it generally pays to pursue a vocational curriculum. However, none of these interactions is statistically significant, so this finding is only suggestive. The interactions are, however, significant for the occupational groups, with both white- and pink-collar workers faring substantially better when they pursue an academic high school track. Again, this makes sense because these occupations are traditionally more reliant on "cognitive skills" than blue-collar occupations. Finally, note that with these controls in the model, the negative effect of dropping out of high school in an academic track has become significant--the converse is that vocational training pays off for dropouts.

College Field of Study

        The field of study pursued in college serves to differentiate individuals further as they gain specific skills that may prepare them for an industry or for graduate study. When we look at fields of study in groupings such as science, arts, humanities, and social science, we can detect differences in returns to these different choices. But such categories, when combined with pathways, do not provide much insight because they are too specific. For example, what conclusion should we draw if social science majors who work while in school experience small wage gains? We therefore collapsed the field of study into two substantive categories: (1) applied and (2) theoretical. Architecture, business, communications, computer and information science, engineering, health professions, law, military science, and public affairs share a practitioner orientation, so we categorized them as "applied." Examples of "theoretical" fields include biological sciences, foreign languages, letters, mathematics, physical sciences, and social sciences as these tend to emphasize theory rather than practice. Using these categories, we find that the percent of individuals pursuing applied majors is between 65% and 80%, depending on the level of education. While this is a large proportion, the percent pursuing theoretical majors is of nontrivial size and is substantively different.

        We interact the field of study with each of the four postsecondary levels of education and display the results in the first column of Table 8.[12] Fields of study clearly matter a great deal. To wit, applied majors show strong positive effects on the wage growth of respondents with bachelor's degrees and higher. What is surprising is that applied fields do not appear to pay off significantly for workers with associate's degrees or only some college experience--one might expect that practical, usable skills would be even more important in the absence of high educational credentials. We should note, however, that the sample size for associate degree holders is quite small and that Grubb (1997) found a significant wage pay-off for applied field of study for this group.

        Finally, we add the educational pathways to the model in the second column of the table. Very little changes, and the effects of the pathways themselves remain unchanged--strongly negative for interruptions to education, and positive for working while in school. This is important, because it means that interruptions remain detrimental in all of the models that we have considered--the negative impact is strong enough to offset other choices that these young workers make (e.g., about how much education to get, which major to study, which industry to enter).

Inequality Revisited

        We now return to the original motivation for this research, which is to understand the inequality in wage growth that persists within each education group and that has risen so dramatically over the past several decades. To this end, we have built several models of wage growth and documented the outcomes associated with different pathway features. We can explain 27% of the variation in long-run wage growth by combining into one model the following variables: education, educational pathway, the interaction of high school track with education, industry and occupation, the interaction of high school track with industry and occupation, and the interaction of field of study with education. We call this the full model and compute a set of residuals from the fit. We then compare the residuals from the baseline model (which has only the direct education effects) to the residuals from the full model and summarize their variation by education level in Table 9. The baseline variances are measures of within education group inequality and are comparable to those given in Figure 3. We find that the full model does a good job of explaining inequality for those with some college experience and above. The decrease in residual variation within education group ranges from 11% to 18%. For those with only a high school degree or less, however, decisions about pathways into the labor market have little effect. Even when we ran models for high school dropouts and graduates separately, we found it difficult to explain much of the observed inequality. Nevertheless, overall, the full model explains 50% more of the variance than the baseline model, which is quite substantial.

[8] We recognize that the interim fields of study contain pertinent information, and we did explore several analyses in which they where included, but we were unable to detect their influence adequately

[9] Small differences in the number of nonmissing observations in the larger models will yield minor differences in the baseline regression coefficients because each analysis includes different explanatory covariates.

[10] We thank Norton Grubb for this point.

[11] Testing for the impact of work experience is also advisable for technical reasons. Because individuals are observed at different stages of their career, the permanent wage gains across the standardized span of ages 16 to 36 may be biased downward for those with less experience. These workers are necessarily observed before some of their larger wage gains will occur, and our predictions from the random effects model may not be able to correct for this completely. See the Appendix for further discussion.

[12] The interactions are only defined for those respondents with college experience, since we are focusing on college field of study.