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SKILL OBSOLESCENCE AND WAGE INEQUALITY WITHIN EDUCATION GROUPS Eric D. Gould, Omer Moav and Bruce A. Weinberg ABSTRACT Technological progress renders various skills obsolete, however, the rate of skill obsolescence will vary according to the worker’s human capital investments. Workers heavily invested in general skills, such as education, will not suffer high rates of obsolescence, while less-educated workers who invest more in “technology-specific” skills will suffer more when the technology is changed. Consistent with this framework, this chapter demonstrates that increasing randomness is the primary source of inequality growth within uneducated workers, whereas inequality growth within educated workers is determined more by predictable factors. Furthermore, this chapter shows that increasing randomness generates a “precautionary ” demand for education.

1. INTRODUCTION In many advanced countries, wage inequality has increased during the last few decades. This trend is largely characterized by increasing inequality within demographic, occupational, industrial, and education groups. In addition, rising

The Economics of Skills Obsolescence, Volume 21, pages 215–234. Copyright © 2002 by Elsevier Science Ltd. All rights of reproduction in any form reserved. ISBN: 0-7623-0960-1

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wage inequality has occurred simultaneously with rising job insecurity, unemployment, and non-employment (for male workers). All of these trends are found to be related to the collapse in the relative demand for workers with lower ability or skill.1 The consensus in the literature is that changes in technology over the past few decades are responsible for the dramatic changes in the structure of wages and employment. The empirical literature suggests that these trends are caused by the increasing importance of cognitive skills in the wage function.2 The theoretical literature has also mostly relied on changes in the return to ability to generate increasing wage variance “within” demographic groups.3 In contrast, this chapter follows up on Gould, Moav and Weinberg (2001) by focusing on how technological progress generates two different sources of inequality growth: increasing returns to ability and increasing rates of skill obsolescence. This chapter contains two empirical sections. Firstly, we present new evidence that inequality is increasing for different reasons within the different education groups. That is, the empirical results show that inequality growth within educated workers has occurred along predictable dimensions, such as the increasing return to a person’s unobserved ability, while inequality growth within less educated workers is driven more by increasing randomness, which we argue is due to increasing rates of skill obsolescence. Our second empirical analysis shows that workers actually consider these two sources of inequality when making their education investment decisions. The results suggest that workers have responded by investing more in formal education, not only because of the increasing return to education, but also to avoid the increasing randomness associated with the higher rates of skill obsolescence within less educated workers. The next section summarizes the basic theoretical background developed in Gould, Moav, and Weinberg (2001) which motivates the empirical analyses. Section III uses data from the Panel Study of Income Dynamics to show that the sources of inequality growth in the United States are different within education groups. Section IV demonstrates that workers make their education investment decisions mindful of both the return to being educated, and the higher risk of skill obsolescence associated with being a less educated worker. Section V concludes the discussion.

2. THEORETICAL BACKGROUND By summarizing the model in Gould, Moav and Weinberg (2001), this section presents a theoretical basis for thinking about how technological change affects inequality within education groups by having a disparate effect on the rates of

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skill obsolescence within these groups. On a very basic level, a worker’s human capital can be categorized into two components: “technology-specific” skills and “general” skills. Technology-specific skills are those that are tied to a specific machine or production process. When that machine or process is replaced as a result of technological improvements, the human capital tied to that process is rendered worthless in the labor market. As pointed out in the review by de Grip and Van Loo (2001), this type of “economic obsolescence” imposes a heavy cost on the worker, whose wages either fall over time with the loss of productivity, or the worker needs to invest in costly re-training in order to acquire the skills necessary to use the new technology. If the changes in technology are drastic enough, the obsolescence of technology-specific skills can easily lead to the displacement of workers from firms, or even lead to the disappearance of certain specialized firms, industries, and occupations over time. In contrast to “technology-specific” skills, “general” skills are useful with any kind of technology. Rather than being rendered obsolete by technological changes, general skills are used to implement the new machine or production process, and therefore, are likely to be in high demand in periods of rapid technological progress. For example, certain cognitive skills are useful with any type of technology, and are likely to be augmented with improvements in technology.4 Therefore, the skill set of a worker can be broken down into two components: the “technology-specific” component and the “general” component. Although these components are not separable from the worker’s perspective, each worker is relatively invested in each of these components to a certain degree. It is important to note that this distinction is not the same as commonly used terms such as “firm-specific” or “occupation-specific.” Although these are valid ways of categorizing skills for other purposes, they are not always related to the notion of “technology-specific” skills. For example, an opthomologist is very heavily invested in “occupation-specific” skills concerning all matters regarding the eye. However, if a new laser technique is developed to perform eye surgery, this may replace the old technique, but not the doctor’s knowledge of how the eye works, how problems are diagnosed, and how the eye needs to be fixed. Most likely, the new technique will only augment the eye doctor’s knowledge by making him more productive and efficient. After all, the only workers with enough knowledge to implement the new laser technology are the existing eye doctors themselves. In contrast, a factory worker may have spent many years learning how to use certain equipment and tools, and although his skills are very tied to the occupation or even the firm, they are also very “technologyspecific.” That is, if the equipment is changed radically due to technological improvements, or if that part of the production process is automated completely, 217

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this worker will lose all of his human capital since it was entirely tied to the specific machine. In both of these cases, both types of workers have high degrees of “occupation-specific” skills, and perhaps the eye doctor has, on the absolute level, even more “occupation-specific” skills. However, the difference is that the factory worker’s skill set is more “technology-specific,” while the eye doctor has more general skills that allow him to adapt and benefit from new technologies. Consciously or subconsciously, workers choose the degree to which they invest their human capital in general skills vs. technology-specific skills. Workers can invest in general skills by acquiring higher education, or they can forego formal education and acquire technology-specific skills through on the job training. When technology changes, it erodes the skills of less-educated workers more than educated workers, since less-educated workers are relatively more invested in “technology-specific” skills.5 Therefore, technological progress increases the wage gap between educated and less-educated workers, thus increasing the return to education, and consequently, the demand for education. Furthermore, it is reasonable to assume that technological progress occurs at different rates across various types of jobs, occupations, and industries. That is, there is an average rate of technological progress in the economy and there is also a variance in the rate of progress across sectors. In other words, there is an average depreciation rate of technology-specific skills, and there is a variance in the depreciation rate of technology-specific skills across sectors. Ex-ante, workers know the mean and the variance of the rate of skill obsolescence across sectors, but they do not know which specific sectors will, ex-post, depreciate their technology-specific skills more and which sectors will preserve them longer.6 This uncertainty makes investing in technology-specific skills a risky endeavor, and since workers are risk averse, acquiring education is a way of protecting yourself from this risk.7 As a result, technological progress increases the demand for education not only because of the increasing return to education (increasing the average rate of skill obsolescence), but also because of the increasing risk of being a less-educated worker (the variance in the rate of skill obsolescence across sectors). This latter effect is called the “precautionary demand for education” in Gould, Moav and Weinberg (2001): the incentive to invest in general education in order to avoid the risk of not being educated and left to the mercy of random spurts of technological progress which may render your entire human capital worthless in the labor market. Some workers choose to get educated even though their expected wage is lower as an educated worker than as an uneducated worker: the only reason they are investing in education is to avoid the risk of having their human capital wiped out in an unpredictable way.8

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Within this framework, technological progress produces different sources of inequality growth within education groups: increasing randomness is the primary source within uneducated workers, while inequality growth within educated workers is determined more by the changes in the composition and return to ability.9 To see this, suppose there is sudden technological innovation, which increases the average rate of technological progress in the economy. This innovation shock increases the average depreciation rate of technology-specific skills of less-educated workers, thus increasing the wage gap between educated and less-educated workers, and consequently, the demand for education. Now, workers of lower ability will choose to get educated, increasing the variance of ability within educated workers, and therefore, increasing the wage variance within the educated group.10 If the new technological innovation raises the return to ability as well, the wage variance within the educated sector will increase even further.11 The new innovation shock is likely to increase the variance in the rate of progress across sectors in addition to the mean rate of progress. This follows from the idea that the new technology, no matter how revolutionary, is not implemented uniformly across sectors since its usefulness and implementation costs will vary. The innovation is likely to have a huge impact on some sectors and very little on others – so that the variance of the rate of progress across sectors is increasing in the mean rate of progress. Under this assumption, the new innovation will increase inequality within less educated workers due to the increasing variance in the depreciation rate of technology-specific skills of less-educated workers across sectors. That is, uneducated workers will be increasingly knocked around (rendered obsolete) in random ways due to the varying degrees of technological progress. Consequently, the risk of remaining uneducated increases, and as a result, more workers choose to get an education as a way of protecting themselves.12 The theory has two main testable implications. The first is that the sources of inequality growth are different within education groups: increasing randomness is responsible for inequality growth within less-educated workers, while inequality within educated workers is increasing along more predictable dimensions such as the composition and return to ability. Second, increasing inequality increases the risk of not being educated, and consequently, workers will invest more in education as a way of insuring themselves against this risk. The following empirical sections seek to test these implications of the theory.

3. DIFFERENT SOURCES OF INEQUALITY GROWTH This section empirically demonstrates one of the main theoretical implications of the model summarized in Section II: increasing randomness (skill 219

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obsolescence risk) is a major source of inequality growth for less educated workers, and that returns to ability are largely responsible for the inequality trend for more educated workers. The empirical strategy is designed to decompose the inequality growth within education groups into two main components: (1) increases in the return and variation of skills; and (2) increasing randomness due to technological shocks. To see how this is done, let the wage of a worker be represented by: wit = xit t + eit

(1)

where xit is a vector of observable characteristics (education, age, occupation, family background, etc.) for person i and t is the return to those characteristics. The parameter eit represents the value of the unobservables for individual i up to year t. These unobservables represent the value of either unobservable ability or random shocks that have accumulated up to year t. With a panel sample of workers in years t and t + k, we can then isolate the size of random shocks between those years in the following two-stage procedure. In the first stage, the unobservables eit are estimated in year t from a simple OLS regression of wages wit on the observables xit. • Stage 1: Regression in year t wit = xit t + eit • Stage 2: Regression in year t + k with the same sample in Stage 1 wit + k = xit + k t + k + t + k bit + vit + k The estimated residual bit for each person from Stage 1 (standardized by the MSE in the first stage) is then used as an explanatory variable in Stage 2. This is essentially inserting an unobserved fixed-effect from the first stage into the second stage model.13 Because the residual from the first stage already captures the unobserved ability of the individual and the accumulated random shocks of the individual up to year t, the residuals vit + k in the second stage represent the effect of randomness within the past k years. Therefore, the mean squared error (MSE) from the second stage measures the contribution of recent randomness to the

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overall level of inequality. The strategy will be to compare the increase in the size of the MSE from Stage 2 over time relative to the increase in the overall level of inequality. Furthermore, we can do this procedure separately for different education groups to see whether randomness is behaving differently across groups. The procedure is estimated using the Panel Study of Income Dynamics (PSID), which is the largest nationally representative panel study of labor market outcomes in the United States that covers the last few decades. The sample is restricted to white male workers who worked at least 30 weeks and at least 30 hours per week in both years t and t + k. The age ranges are 20 to 55 in year t and 25 to 60 in year t + k, so that we are using residuals from five years earlier (k = 5) in our second stage regressions in year t + k. In order to keep the age ranges constant, we will discuss the increases in inequality for our t + k samples. Our control variables involve levels of education, experience, religion, mother and father’s education, occupation, location of residence, and economic background while growing up. The second stage regression results are presented in Table 1 for three main education groups. The third column presents the familiar trends of increasing wage inequality within all three education groups: high school dropouts, high school graduates, and college graduates. The fifth column shows the familiar trend of increasing residual wage variance, represented by the mean squared error of the regression in year t + k performed without including the residual from year t as a regressor. However, Table 1 shows that “residual inequality” increased mostly in the 1970s for the less educated groups, while increasing for the most educated group only in the 1980s. These differing patterns already suggest that the sources of inequality growth are not equivalent within education groups.14 Column 6 presents the MSE of the regression in year t + k after including the residual in year t. This estimates the size of random shocks that have occurred to these people within the last five years, since the residual from year t is capturing the unobservables as of five years ago. The results indicate that most of the increase in residual inequality (Column 5) is captured by recent randomness (Column 6) for the least educated group. From 1975 to 1990, increasing randomness in the previous five years explains 82% (0.063 of 0.077) of the increase in residual inequality for those with less than 12 years of education. The comparable numbers are 58% (0.060 of 0.103) for those with a high school degree but less than a college degree, and 32% (0.017 of 0.054) for those with a college degree. Clearly, the importance of randomness is inversely related to the level of education. Almost all of the residual variance of the least educated workers is due to random factors which occurred during the previous five years and which 221

1975 1980 1985 1990

1975 1980 1985 1990

1975 1980 1985 1990

S < 12

12 < = S < 16

S > = 16

0.543 0.516 0.602 0.632

0.409 0.488 0.502 0.509

0.401 0.479 0.502 0.495

(3)

Std Dev. Of Log Wages

201 363 391 484

474 683 736 858

205 225 173 187

(4)

Sample Size

0.526 0.486 0.559 0.580

0.375 0.462 0.489 0.478

0.388 0.459 0.466 0.465

(5)

0.443 0.394 0.454 0.460

0.308 0.407 0.417 0.368

0.312 0.343 0.378 0.375

(6)

0.384 0.443 0.453 0.488

0.451 0.320 0.326 0.487

0.442 0.523 0.481 0.473

(7)

0.286 0.286 0.330 0.359

0.216 0.221 0.257 0.306

0.234 0.307 0.283 0.282

(8)

MSE without MSE with R-square with Coefficient on the Residual from year t Residual from year t Residual from year t Residual from year t

The analysis uses data from the PSID. Included in all regressions are dummy variables for the four main education groups (as long as they are identified, they are high school dropouts, high school graduates, college dropouts, and college graduates), experience, experience squared, experience interacted with years of schooling, religion dummy variables (Protestant, Catholic, Jewish, and other), dummy variables for the parents’ education (father is a high school dropout and mother is a high school dropout), and occupational dummy variables (professional, clerical or sales, craftsmen, operatives), a dummy for living in the South, a dummy for living in a SMSA, and a dummy variable if the respondent grew up “poor.”

(2)

Year t + 5

222

(1)

Years of Schooling

The Decomposition of Inequality Within Education Groups.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Table 1.

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is uncorrelated to their ability or luck prior to those five years. In contrast, the increasing residual variance within those most educated is largely explained by observables or the return to prior unobservables. Random luck plays only a small role in the relatively smaller increase in inequality for college graduates. And keeping with the pattern, 58% of the middle education group is explained by recent shocks and 42% by observables or prior unobservables – which lies in between the least and most educated groups for both numbers. These results shed light on those by Juhn, Murphy and Pierce (1993). Since they were using cross-sectional data, they were unable to control for fixed unobservable effects of the individual in their analysis. As a result, they interpreted the increasing residual variance as increases in the return to unobserved ability. With panel data, we are able to show that this is mostly true for the educated group, but not so true for the less educated groups. Inequality within the educated group is occurring in predictable ways. That is, if person i knows he has more ability than person j, then person i knows he will always earn more than person j, and that it is just a matter of how much more he will earn. However, if i and j are uneducated, the future is not so predictable for them. They are getting pushed around in random ways more and more over time. These results reinforce the already considerable amount of evidence that the sources of inequality growth are different between education groups. In particular, the magnitudes are known to be different: from 1970–1978 to 1979–1989, Gottschalk and Moffitt (1994) show that the variance of annual earnings rose by 71% for high school dropouts, 40% for those with at least 12 years of education, and only 18% for those with at least a college education.15 Gottschalk and Moffitt (1994) also decompose the wage variance for each education group into a “permanent” and “transitory” components. Consistent with our findings, Gottschalk and Moffitt (1994) find that the “transitory” variance is much higher in all periods for workers with less education. In addition, the “transitory” component increased much faster for less educated workers from the 1970s to the 1980s: increasing by 96% for high school dropouts, 52% for those with at least 12 years of education, and 43% for those with at least a college education. Using matched CPS files, Gittleman and Joyce (1996) find similar results.16 Again, these results clearly show that inequality is not created the same way within each education group. Further evidence is provided by Davis and Haltiwanger (1991) who decompose the inequality trends in the manufacturing sector into changes in inequality “between” plants and “within” plants. They show that most of the inequality within production workers (which is a good proxy for less educated workers) is accounted for by inequality “between” plants, while most inequality within non-production workers (a proxy for more educated workers) is 223

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accounted for by inequality “within” plants. Further, they show that 90% of the increase in inequality within production workers is accounted for by higher inequality “between” plants. In contrast, they show that increasing inequality “within” plants explains most of the inequality trends for non-production workers (more educated workers). That is, inequality within less educated workers is increasing almost entirely due to exogenous forces which are affecting their place of work. Conversely, inequality within educated workers is not very dependent on their place of work, which implies that personal characteristics determine the distribution of income within this group. Along with these inequality trends, the last few decades have also witnessed increasing unemployment rates and decreasing labor force participation for predominantly less-educated male workers in the U.S.17 These trends seem to be related to the skill obsolescence of less-educated workers, after all, losing one’s job is the ultimate form of skill obsolescence faced by a worker. In addition, less-educated male workers also seem to be suffering from increasing job instability.18 In Europe, inequality did not start increasing until the 1980s, but unemployment rose dramatically in the 1970s and was heavily concentrated within less educated workers.19 All of these trends can be interpreted within the context of the model framework in Section 2: the increasing rates of technological progress in the last few decades disproportionately affected less educated workers since they are the ones most heavily invested in “technologyspecific” skills vs. “general” skills. Consequently, as the average and the variance in the rate of technological progress increases, the human capital of less-educated workers is rendered obsolete at higher average rates, and also at increasingly variable rates across sectors and jobs. Consequently, this results in some combination of rising inequality, rising unemployment, and decreased labor force participation for less-educated workers – as seen in the United States and Europe since the early 1970s.

4. DOES RISK AFFECT SCHOOLING DECISIONS? The previous section demonstrated that less-educated workers are increasingly at the mercy of random shocks, while inequality within educated workers increased along more predictable dimensions. These results indicate that the risk of not being educated has increased over time, and the model in Section 2 predicts that individuals will now choose to invest in education not only because of the increasing return to education, but also to avoid the increased risk of remaining uneducated. In this section, we empirically examine whether individuals consider both the risk and the return when making their investment decisions.

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We examine this issue with United States Census data by explaining the state mean education level of 25 to 27 year old men in year t with measures of the risk and the return to schooling in their state.20 The risk of each education group is proxied by the unemployment rate for that group, which represents the extreme downside risk of being in that group. In addition, as pointed out in Section III, the increasing unemployment rate of less-educated men is considered to be related to the risk of skill obsolescence. The expected return is proxied by the “expected” mean wages (adjusted for the probability of being unemployed and the age composition within the state) for each group. Table 2 presents results explaining the cross-sections of educational attainments in 1980 and 1990, as well as the changes in educational attainments within states from 1980 to 1990. That is, we exploit the panel nature of the data by differencing out any unobserved state heterogeneity which might create a spurious correlation in the cross-section between schooling and unemployment or wages. Therefore, the empirical strategy is to control for state fixed-effects and exploit exogenous variation across states in the perceived riskiness and return to education in order to identify how these factors affect the decision to invest in education. Table 2 presents results for two dependent variables: (1) the mean education of white men at ages 25–27 within the state; and (2) the fraction of 25–27 year old white men who have obtained at least one year of higher education. Both of these dependent variables were chosen since they are likely to represent individuals who are near completion of their schooling decisions, and yet still responsive to the wages and unemployment rates in their state in the last decade. The results are robust to various ways of choosing the relevant age group. However, the ten year differences are exploiting long-term trends within each state, so pin-pointing the exact timing for a precise cohort is not crucial. Although the cross-section results are presented in Table 2, we concentrate our discussion on the fixed-effects results in the middle columns, since unobserved state heterogeneity is likely to bias the cross-section estimates. Overall, the results show that our proxies for the risk associated with each education group are significant and consistent with the predictions of the model. Increases in the unemployment rate of white men with 12 years or less of education increase educational attainments. Increases in the unemployment rate of those with more than 12 years of schooling decrease attainments. These results suggest that students are actively trying to avoid unemployment by choosing their level of schooling. However, only the coefficient for the less-educated group is significant, so it seems that avoiding unemployment is more of a factor regarding less-educated workers. Results concerning the wage measures are mixed and not very significant. Overall, these results confirm the findings of Gould, Moav and Weinberg (2001) and suggest that students do consider the perceived risk 225

**

0.787** (0.328) 1.180 (0.901)

0.235** 0.279** (0.113) (0.107) 0.224 0.236 (0.142) (0.145)

3.328** (1.41) 3.535 (3.865)

1.377** 1.595** (0.528) (0.506) 1.325* 1.334** (0.660) (0.669)

State Mean School Log Expected < = 12 Wages for New School Entrants 10 > 12 years Earlier

(4)

School < = 12 School > 12

1.014 (0.466) 1.979 (1.446)

(3)

State NonEmployment Rate for New Entrants 10 years Earlier

4.759 (1.935) 8.277 (6.294)

(2)

School < = 12 School > 12

**

State Unemployment Rate for New Entrants 10 years Earlier

(1) **

3.374** (1.237) 0.501 (1.946)

(6)

1.212** 1.399 (0.505) (0.520) 0.420 0.701 (0.509) (0.498)

3.014 (1.399) 0.009 (3.094)

(5)

Change in Mean Education at Ages 25–27

0.0004 (0.080) 0.159 (0.089)

0.301 (0.215) 0.034 (0.481)

(7)

0.042 (0.084) 0.109 (0.089)

0.364* (0.035) 0.035 (0.303)

(8)

Change in Fraction of 25–27 Year Olds with Some College

Change in Educational Attainment between 1980 and 1990

0.907 (0.585) 0.182 (0.723)

2.154 (2.446) 3.389 (5.855)

(9)

0.974* (0.557) 0.047 (0.077)

0.928 (1.815) 1.089 (3.582)

(10)

0.188 (0.324) 0.142 (0.625)

(12)

0.190 0.202* (0.104) (0.101) 0.44 0.070 (0.129) (0.127)

0.502 (0.449) 0.755 (1.064)

(11)

Mean Education Fraction of at Ages 25–27 25–27 Year Olds with Some College

Educational Attainment in 1980

226

Mean Education Fraction of at Ages 25–27 25–27 Year Olds With Some College

Educational Attainment in 1990

Determinants of State Changes in Education Attainment (Census Analysis).

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Table 2.

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227 51

51

51

51

51

0.218 51

0.241

0.444** 0.424** (0.147) (0.144)

51

0.181 51

0.207

–0.137 –0.120 (0.129) (0.127)

51

0.727

51

0.726

0.594 0.568 (0.068) (0.069)

51

0.709

51

0.707

0.871** 0.828 (0.096) (0.094)

** indicates significance at the 5% level. * indicates significance at the 10% level. Standard errors in parentheses. Independent variables in columns 5–8 are change in variable between 1970 and 1980. Educational attainment for non-Hispanic white men ages 25–27 (and adults, 30–65) estimated from the 1980 and 1990 censuses. Data for state level labor market conditions estimated from the 1970 and 1980 censuses for non-Hispanic men over 18 with 10 of fewer years of potential experience. See Appendix for sample construction. Labor market conditions measured in the respondent’s state of birth in the previous census. Expected wages adjust for the probability of having a job (measured by unemployment probability in oddnumbered columns; and nonemployment probability in even-numbered columns).

Sample Size

0.613

0.616

0.645

R-Squared

0.657

0.699** 0.672** (0.110) (0.102)

Fraction of Adults with Some College

0.529** 0.497** (0.073) (0.068)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Mean Adult Schooling

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when making their education decisions, thus choosing the level of schooling at which the trade-off between the risk and return is optimal.21

5. CONCLUSION Following-up on the model in Gould, Moav, and Weinberg (2001), this paper is motivated by the disproportionate effects of technological changes on the skill obsolescence of general vs. technology-specific skills, and the resulting precautionary factor in the demand for education which guards against the risk of obsolescence. The underlying model assumes that individuals choose to invest in general skills through education or technology-specific skills through on-thejob training. However, changes in technology render technology-specific skills obsolete and worthless in the labor market. Consequently, the more a worker is invested in specific skills, the more his human capital will depreciate due to technological improvements. Therefore, an increase in the rate of technological progress increases the depreciation rate of technology-specific skills of less educated workers, and thus increases the education premium. The model further assumes that technological progress is absorbed into various sectors at different rates. Thus, there exists an average rate of technological progress and a variance of the rate of progress across sectors. This is a major source of ex-post variability of wages within less educated workers – since they are relatively more invested in technology-specific skills and there is a variance of the depreciation rate of these specific skills across sectors. Furthermore, workers do not know in advance how each sector will be affected. That is, they must choose their sector and level of education solely on the basis of knowing the distribution of the rate of progress across sectors, not the expost realizations within each sector. This creates an element of risk in the model – workers do not know in which sector their specific skills will depreciate more. In this sense, there exists a “precautionary” element in the demand for education as workers consider both the risk and the return in their decision to invest in general education vs. technology-specific skills. The model predicts that the sources of inequality growth within education groups will differ in periods of increased technological progress. Within the less educated group, increasing inequality is mainly determined by the increasing variance of technological implementation across industries which erodes their skills at different rates. In the educated group, the increasing “within” variance is mainly determined by changes in the composition and return to ability within this group. Our empirical results support these predictions. Increasing random shocks explain the bulk of the increasing residual inequality with less educated groups, while increasing returns to ability explain most of the increase for more

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educated groups. Therefore, our analysis shows that increasing inequality has occurred in a largely predictable way for educated workers, while uneducated workers are increasingly at the mercy of exogenous shocks which render their human capital obsolete. Along with the increasing unemployment rates which were largely concentrated within less educated workers, these results illustrate how the relative risk of not becoming educated has increased during the past few decades. Consequently, the model predicts that workers should respond to this increased risk by investing more in general education. Our empirical results support this prediction as well. Using Census data to explain the within-state changes in educational obtainment (controlling for state fixed-effects), we find the students do invest more in education when the unemployment situation of less-educated workers deteriorates. Therefore, workers consider not only the return to investing in education, but also the risk of not being educated and having their technology-specific skills rendered obsolete in the labor market.

NOTES 1. See Juhn, Murphy, and Topel (1991), Juhn (1992), Welch (1997), and Murphy and Topel (1997). 2. Juhn, Murphy, and Pierce (1993) shows that residual inequality has increased since the early 1970s. Murnane, Willet, and Levy (1995) show more directly that certain types of cognitive skills are becoming more important in the determination of wages. Gould (2002) shows more directly that certain cognitive skills are growing in importance within broad occupational categories, so that role of comparative advantage in reducing the level of inequality from a random assignment economy is decreasing. 3. See Galor and Moav (2000) and Rubinstein and Tsiddon (1998). Aghion, Howitt, and Violante (1998) and Violante (2002) use a different mechanism to generate increasing “within-group” inequality, but do not examine inequality within and between education groups. 4. This idea dates back to Schultz (1964). 5. Although educated workers may have more technology-specific skills than less educated workers, we argue that educated workers have less technology-specific skills as a percentage of their total human capital. This idea is consistent with the idea that education enables a worker to cope with technological progress (see Schultz, 1964; and more recently, Galor & Moav, 2000). This view is not contradicted by the idea that human capital derived by education itself may suffer vintage effects over the working life of the individual (see Neuman & Weiss, 1995). 6. Consistent with our model, Neuman and Weiss (1995) show that depreciation rates of human capital are higher in industries with higher rates of technological progress. 7. In reality, workers may know that the average depreciation rate of technologyspecific skills is higher in certain, perhaps high-tech, sectors than others. However, workers will still react to increasing variation in the rates of depreciation by obtaining general education as a way to insure themselves. 229

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8. Theoretically, if workers were not credit constrained, an insurance market could arise to protect workers against this risk. However, investing in general education appears to be a more practical option. 9. The crucial assumptions are: (1) a worker’s wage is more sensitive to his ability if he chooses to get educated than if he remains uneducated (i.e. the return to ability is higher as an educated worker); (2) less-educated workers are relatively more invested in technology-specific vs. general skills than educated workers (i.e. education is a general skill); and (3) the variance in the rate of technological progress is increasing in the average rate of progress (because the usefulness and implementation costs of the new technology vary across sectors). 10. This “composition effect,” which increases the variance of ability, also decreases the mean ability level of those who choose to get educated, which decreases the wage gap between educated and less-educated workers. That is, this effect counteracts the increasing average depreciation rate of technology-specific skills of less-educated workers, which increases the wage gap between the education groups. However, Gould, Moav and Weinberg (2001) show that for any reasonable set of parameters, the latter effect dominates the former so that increases in technology lead to increasing returns to education, even when the supply of educated workers is increasing and the mean ability level of educated workers is falling. 11. See Galor and Moav (2000) for a model focusing on the increasing return to ability during times of increased technological progress. 12. This will further increase the supply of educated workers, as lower ability workers will now decide to get educated. As described in a footnote above, this “composition effect” increases the variance of ability within educated workers, thus increasing the variance of wages within the educated group. It will also decrease the average ability level of educated workers, but as described above, this effect will probably not be large enough to lead to a decrease in the return to education. 13. We are assuming that all serial correlation in the unobservables occurs due to changes in the return to inherent ability or through changes in the return to prior shocks (those accumulated up until year t). Empirically, it is impossible to distinguish between an increase in the return to prior luck and serially correlated luck. Therefore, we make the normalizing assumption that all serial correlation occurs through the return to prior luck and that all new draws from the luck distribution from years t to t + k are exogenous to what happened prior to year t. Conceptually, this is what we want to estimate since we want to estimate the unanticipated variance of new shocks due to exogenous technological changes. 14. The timing of these trends within education groups is a prediction of the model. See Gould, Moav and Weinberg (2001). 15. Gottschalk and Moffitt (1994) also show that the trends are different within education groups for the “permanent” component of annual earnings inequality growth between the two periods: increasing 55% for high school dropouts, 34% for those with at least 12 years of schooling, and 9% for those with at least a college education. Using matched samples across adjacent years of the March CPS files, Gittleman and Joyce (1996) find similar results: for male full-time full-year workers, “long run” inequality increased by 20% for high school dropouts, 16% for high school graduates, 12% for those with some college, and only 10% for college graduates. Gittleman and Joyce (1996) also find that the differences in these trends are even more pronounced with their sample of workers who worked for any length of time. In addition, they show that the

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timing of inequality growth differs between education groups: “long-run” inequality did not increase for male college graduates until the 1980s, while the trend started in the 1970s for males with lower education. 16. They find that earnings “instability” is inversely related to levels of education. However, they find no major trend in instability over time for any particular demographic groups, implying that the transitory component did not increase more for less educated workers in relative terms, but did increase more in absolute terms. 17. See Juhn, Murphy and Topel (1991), Juhn (1992), Welch (1997), and Murphy and Topel (1997). 18. See Table 1 in Gottschalk and Moffitt (1998) for an extensive summary of the vast literature on job instability. The results of this literature are not unambiguous, but do point to increased job instability for less educated workers from the 1970s to the 1980s. However, studies of this problem are complicated by how instability is defined, how job separation is defined (voluntary or involuntary), how unemployed workers are handled, how the consequences of job loss are defined, and how changes in the questionaires over time in various data sets make it difficult to create consistent definitions of these variables. 19. See Nickell and Bell (1996). 20. The sample is restricted to white males. 21. Gould, Moav and Weinberg (2001) used NLSY data to explain the educational investments of individuals at the age of 25 with state measures for the risk and return to each education group.

ACKNOWLEDGMENTS For helpful comments, we wish to thank Lex Borghans, Oded Galor, Peter Howitt, Bas ter Weel, Finis Welch, and seminar participants at the “Understanding Skills Obsolescence Conference 2001” in Maastricht. We are also grateful to the Maurice Falk Institute for financial support and to Vadim Marmer for research assistance.

REFERENCES Aghion, P., Howitt, P., & Violante, G. (1998). Technology, Knowledge, and Inequality. Working Paper. David, S. J., & Haltiwanger, J. (1991). Wage Dispersion Between and Within U.S. Manufacturing Plants: 1963–1986. Brookings Papers on Economic Activity: Microeconomics, 115–180. de Grip, A., & van Loo, J. (2001). The Economics of Skills Obsolescence: A Review. Working Paper. Research Centre for Education and the Labor Market (ROA), Maastricht University. Galor, O., & Moav, O. (2000). Ability Biased Technological Transition, Wage Inequality and Growth. Quarterly Journal of Economics, 115(2), 469–497. Gittleman, M., & Joyce, M. (1996). Earnings Mobility and Long-Run Inequality: An Analysis Using Matched CPS Data. Industrial Relations, 35(2), 180–196. Gottschalk, P., & Moffitt, R. (1994). The Growth in Earnings Instability in the U.S. Labor Market. Brookings Papers on Economic Activity, 2, 217–254.

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Gottschalk, P., & Moffitt, R. (1998). Job Instability and Insecurity for Males and Females in the 1980s and 1990s. Working Paper, Boston College. Gould, E. D. (2002). Rising Wage Inequality, Comparative Advantage, and the Increasing Importance of General Skills in the United States. Journal of Labor Economics, 20(1), 105–147. Gould, E. D., Moav, O., & Weinberg, B. A. (2001). Precautionary Demand for Education, Inequality, and Technological Progress. Journal of Economic Growth, 6, 285–315. Juhn, C. (1992). Decline of Male Labor Market Participation: The Role of Declining Market Opportunities. Quarterly Journal of Economics, 107, 79–121. Juhn, C., Murphy, K. M., & Pierce, B. (1993). Wage Inequality and the Rise in Returns to Skill. Journal of Political Economy, 101, 410–442. Juhn, C., Murphy, K. M., & Topel, R. H. (1991). Why Has the Natural Rate of Unemployment Increased Over Time? Brookings Papers on Economic Activity, 2, 75–142. Maoz, Y., & Moav, O. (1999). Intergenerational Mobility and the Process of Development. The Economic Journal, 109, 677–697. Murnane, R., Willet, J. B., & Levy, F. (1995). The Growing Importance of Cognitive Skills in the Wage Determination. Review of Economics and Statistics, 2, 251–266. Murphy, K. M., & Topel, R. (1997). Unemployment and Non-Employment. American Economic Association Papers and Proceedings, 295–300. Neuman, S., & Weiss A. (1995). On the Effects of Schooling Vintage on Experience Earnings Profiles: Theory and Evidence. European Economic Review, 39(5), 943–955. Nickell, S., & Bell, B. (1996). Changes in the Distribution of Wages and Unemployment in OECD Countries. American Economic Association Papers and Proceedings, 86, 302–308. Rubinstein, Y., & Tsiddon, D. (1998). Coping with Technological Progress: The Role of Ability in Making Inequality so Persistent. Tel-Aviv University. Schultz, T. W. (1964). Transforming Traditional Agriculture. New Haven: Yale University Press. Violante, G. (2002). Technological Acceleration, Skill Transferability and the Rise in Residual Inequality. Quarterly Journal of Economics, 117(1), 297–338. Weinberg, B. A. (2001). Long-Term Wage Fluctuations with Industry-Specific Skills. Journal of Labor Economics, 19(1), 231–264. Welch, F. (1997). Wages and Participation. Journal of Labor Economics, 15 (Part 2), S77–S103.

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APPENDIX DATA CONSTRUCTION PSID The PSID (Panel Study of Income Dynamics) sample used Table 1 is restricted to white, non-Hispanic males between the ages of 20 and 55 in year t (25–60 in year t + k). The sample includes only non-farm workers who have strong attachments to the labor force (those who worked at least 30 weeks and 30 hours per week in the year prior to each survey). In order to maximize the sample size for each pair of years, t and t + k, the samples for each pair were created separately and exclude all respondents with missing variables in year t or year t + k for any of the variables included in the regression: annual earnings (adjusted to real 1982–1984 dollars using the CPI-U), weeks worked, hours per week, education, age, religion, mother’s education, father’s education, occupation, region, urban residence, and family economic status while growing up. Census Data Table 2 uses data from the United States Census in 1970, 1980, and 1990 to construct state measures for educational attainment, as well as wages and employment rates by education level. To focus on individuals at the outset of their careers (“new entrants”), all samples were restricted to persons over age 18, not currently enrolled in school, with 10 or fewer years of potential experience. The samples were restricted to non-Hispanic white men. Census Wage Sample To obtain the most accurate estimate of labor market conditions, wages were estimated for workers with relatively high labor force attachment. The wage samples were restricted to individuals who worked 20 or more weeks and usually worked 35 or more hours per week. The earnings of those at the top-code were multiplied by 1.45. In the 1990 census, the mean earnings among the top-coded workers in each state, which were assigned to individuals with top-coded earnings, were used. Individuals with imputed responses for any of the variables used in the sample construction or analysis were deleted from the sample. Regressions were used to control for differences in characteristics across states. Let wtsei denote the log wage of respondent i in education group e  {HS, College} in state s in survey year t, and let Xtsei denote his observable characteristics (marital status, dummy variables for years of potential experience, and dummy variables for educational attainment within the education groups). A separate regression was run for each survey and for each education group of the form, 233

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wtsei = te Xtsei + tsei. The wage in state s at time t in education group e, Wtse, was estimated using the mean residual for the workers in that group in state s. This residual was then multiplied by the unemployment rate (or non-employment rate) to obtain the expected wage. Census Labor Force Status Sample Unemployment and employment rates by education for each state were also estimated from each Census. A separate sample was used to estimate employment status which includes all individuals meeting the main criteria (described above) except those with imputed employment status or with imputations for any of the other sample selection variables. Individuals who were unemployed or out of the labor force were classified as non-employed. When estimating unemployment rates, individuals who were out of the labor force were dropped so the sample included only those who were employed or unemployed. The procedure described for wages above was used to adjust employment status for individual characteristics. Census Educational Attainment Sample For Table 2, educational attainment for 25–27 year olds and for the adult population (ages 30 to 65) born in each state were estimated from the 1980 and 1990 Censuses. The samples include all non-Hispanic white men born in the U.S. without imputed values for educational attainment or the other variables used in the sample construction. The procedure described for wages above was used to adjust education attainments for age using dummy variables for individual ages.