2.1. A brief overview of data sources

To summarize the basic changes in the US wage structure over the last five decades, we draw on four large and representative household data sources: the March Current Population Survey (March CPS), the combined Current Population Survey May and Outgoing Rotation Group samples (May/ORG CPS), the Census of Populations (Census), and the American Community Survey (ACS).⁷ We describe these sources briefly here and provide additional details on the construction of samples in the Data Appendix. The March Annual Demographic Files of the Current Population Survey offer the longest high-frequency data series enumerating labor force participation and earnings in the US economy. These data provide reasonably comparable measures of the prior year’s annual earnings, weeks worked, and hours worked per week for more than four decades. We use the March files from 1964 to 2009 (covering earnings from 1963 to 2008) to form a sample of real weekly earnings for workers aged 16 to 64 who participate in the labor force on a full-time, full-year (FTFY) basis, defined as working 35-plus hours per week and 40-plus weeks per year.

We complement the March FTFY series with data on hourly wages of all current labor force participants using May CPS samples for 1973 through 1978 and CPS Outgoing Rotation Group samples for 1979 through 2009 (CPS May/ORG). From these sources, we construct hourly wage data for all wage and salary workers employed during the CPS sample survey reference week. Unlike the retrospective annual earnings data in the March CPS, the May/ORG data provide point-in-time measures of usual hourly or weekly earnings. We use CPS sampling weights for all calculations.⁸

As detailed in Autor et al. (2005) and Lemieux (2006b), both the March and May/ORG CPS surveys have limitations that reduce their consistency over the fifty year period studied. The March CPS data are not ideal for analyzing the hourly wage distribution since they lack a point-in-time wage measure and thus hourly wages must be computed by dividing annual earnings by the product of weeks worked last year and usual weekly hours last year. Estimates of hours worked last year from the March CPS appear to be noisy, and moreover, data on usual weekly hours last year are not available prior to the 1976 March CPS. The May/ORG samples provide more accurate measures of the hourly wage distribution (particularly for hourly workers) but cover a shorter time period than the March CPS. Both the March and May/ORG CPS samples have undergone various changes in processing procedures over several decades that affect the top-coding of high earnings, the flagging of earning imputations, and the algorithms used for allocating earnings to individuals who do not answer earnings questions in the survey. These changes create challenges in producing consistent data series over time, and we have tried to account for them to the greatest extent possible.⁹

To analyze levels and changes in occupational structure within and across detailed demographic groups, we exploit the 1960, 1970, 1980, 1990 and 2000 Census of Populations and the 2008 American Community Survey (ACS). Because these data sources provide substantially larger samples than either the March or May/ORG surveys, they are better suited for a fine-grained analysis of changing occupational employment patterns within detailed demographic groups.¹⁰ The earnings and employment questions in the Census and ACS files are similar to those in the March CPS and similarly offer retrospective measures of annual earnings and labor force participation that we use to calculate implied weekly or hourly earnings.

2.2. The college/high school wage premium

Motivated by the canonical relative supply-demand framework discussed in the Introduction and developed further in Section 3, a natural starting point for our discussion is to consider the evolution of the wage premium paid to “skills” in the labor market. A useful, though coarse, approximation is to consider a labor market consisting of two types of workers, “skilled” and “unskilled,” and identify the first group with college graduates and the second with high school graduates. Under these assumptions, the college premium—that is, the relative wage of college versus high school educated workers—can be viewed as a summary measure of the market’s valuation of skills.

Figure 1 plots the composition-adjusted log college/high school weekly wage premium in the US labor market for years 1963 through 2008 for full-time, full-year workers. This composition adjustment holds constant the relative employment shares of demographic group, as defined by gender, education, and potential experience, across all years of the sample. In particular, we first compute mean (predicted) log real weekly wages in each year for 40 sex-education-experience groups. Mean wages for broader groups shown in the figures are then calculated as fixed-weighted averages of the relevant sub-group means (using the average share of total hours worked for each group over 1963 to 2008 as weights). This adjustment ensures that the estimated college premium is not mechanically affected by shifts in the experience, gender composition, or average level of completed schooling within the broader categories of college and high school graduates.¹¹

Three features of Fig. 1 merit attention. First, following three decades of increase, the college premium stood at 68 points in 2008, a high water mark for the full sample period. A college premium of 68 log points implies that earnings of the average college graduate in 2008 exceeded those of the average high school graduate by 97 percent (i.e., exp (0.68) – 1 0.974). Taking a longer perspective, Goldin and Katz (2008) show that the college premium in 2005 was at its highest level since 1915, the earliest year for which representative data are available—and as Fig. 1 makes clear, the premium rose further thereafter. Second, the past three decades notwithstanding, the college premium has not always trended upward. Figure 1 shows a notable decline in the college premium between 1971 and 1978. Goldin and Margo (1992) and Goldin and Katz (2008) also document a substantial compression of the college premium during the decade of the 1940s. A third fact highlighted by the figure is that the college premium hit an inflection point at the end of the 1970s. This premium trended downward throughout the 1970s, before reversing course at the end of the decade. This reversal of the trend in the college premium is critical to our understanding of the operation of supply and demand in the determination of between-group wage inequality.

The college premium, as a summary measure of the market price of skills, is affected by, among other things, the relative supply of skills. Figure 2 depicts the evolution of the relative supply of college versus non-college educated workers. We use a standard measure of college/non-college relative supply calculated in “efficiency units” to adjust for changes in labor force composition.¹² From the end of World War II to the late 1970s, the relative supply of college workers rose robustly and steadily, with each cohort of workers entering the labor market boasting a proportionately higher rate of college education than the cohorts immediately preceding. Moreover, the increasing relative supply of college workers accelerated in the late 1960s and early 1970s. Reversing this acceleration, the rate of growth of college workers declined after 1982. The first panel of Fig. 3 shows that this slowdown is due to a sharp deceleration in the relative supply of young college graduate males—reflecting the decline in their rate of college completion—commencing in 1975, followed by a milder decline among women in the 1980s. The second panel of Fig. 3 confirms this observation by documenting that the relative supply of experienced college graduate males and females (i.e., those with 20 to 29 years of potential experience) does not show a similar decline until two decades later.

What accounts for the deceleration of college relative supply in the 1980s? As discussed by Card and Lemieux (2001b), four factors seem particularly relevant. First, the Vietnam War artificially boosted college attendance during the late 1960s and early 1970s because males could in many cases defer military service by enrolling in post-secondary schooling. This deferral motive likely contributed to the acceleration of the relative supply of skills during the 1960s seen in Fig. 2. When the Vietnam War ended in the early 1970s, college enrollment rates dropped sharply, particularly among males, leading to a decline in college completion rates halfa decade later.

Second, the college premium declined sharply during the 1970s, as shown in Fig. 1. This downturn in relative college earnings likely discouraged high school graduates from enrolling in college. Indeed, Richard Freeman famously argued in his 1976 book, The Overeducated American, that the supply of college-educated workers in the United States had so far outstripped demand in the 1970s that the net social return to sending more high school graduates to college was negative.¹³

Third, the large baby boom cohorts that entered the labor market in the 1960s and 1970s were both more educated and more numerous than exiting cohorts, leading to a rapid increase in the average educational stock of the labor force. Cohorts born after 1964 were significantly smaller, and thus their impact on the overall educational stock of the labor force was also smaller. Had these cohorts continued the earlier trend in college-going behavior, their entry would still not have raised the college share of the workforce as rapidly as did earlier cohorts (see, e.g. Ellwood, 2002).

Finally, and most importantly, while the female college completion rate rebounded from its post-Vietnam era after 1980, the male college completion rate has never returned to its pre-1975 trajectory, as shown earlier in Fig. 3. While the data in that figure only cover the period from 1963 forward, the slow growth of college attainment is even more striking when placed against a longer historical backdrop. Between 1940 and 1980, the fraction of young adults aged 25 to 34 who had completed a four-year college degree at the start of each decade increased three-fold among both sexes, from 5 percent and 7 percent among females and males, respectively, in 1940 to 20 percent and 27 percent, respectively, in 1980. After 1980, however, this trajectory shifted differentially by sex. College completion among young adult females slowed in the 1980s but then rebounded in the subsequent two decades. Male college attainment, by contrast, peaked with the cohort that was age 25–34 in 1980. Even in 2008, it remained below its 1980 level. Cumulatively, these trends inverted the male to female gap in college completion among young adults. This gap stood at positive 7 percentage points in 1980 and negative 7 percentage points in 2008.

2.3. Real wage levels by skill group

A limitation of the college/high school wage premium as a measure of the market value of skill is that it necessarily omits information on real wage levels. Stated differently, a rising college wage premium is consistent with a rising real college wage, a falling real high school wage, or both. Movements in real as well as relative wages will prove crucial to our interpretation of the data. As shown formally in Section 3, canonical models used to analyze the college premium robustly predict that demand shifts favoring skilled workers will both raise the skill premium and boost the real earnings of all skill groups (e.g., college and high school workers). This prediction appears strikingly at odds with the data, as first reported by Katz and Murphy (1992), and shown in the two panels of Fig. 4. This figure plots the evolution of real log earnings by gender and education level for the same samples of full-time, full-year workers used above. Each series is normalized at zero in the starting year of 1963, with subsequent values corresponding to the log change in earnings for each group relative to its 1963 level. All values are deflated using the Personal Consumption Expenditure Deflator, produced by the US Bureau of Economic Analysis.

In the first decade of the sample period, years 1963 through 1973, real wages rose steeply and relatively uniformly for both genders and all education groups. Log wage growth in this ten year period averaged approximately 20 percent. Following the first oil shock in 1973, wage levels fell sharply initially, and then stagnated for the remainder of the decade. Notably, this stagnation was also relatively uniform among genders and education groups. In 1980, wage stagnation gave way to three decades of rising inequality between education groups, accompanied by low overall rates of earnings growth—particularly among males. Real wages rose for highly educated workers, particularly workers with a post-college education, and fell steeply for less educated workers, particularly less educated males. Tables 1a and 1b provide many additional details on the evolution of real wage levels by sex, education, and experience groups during this period.

Alongside these overall trends, Fig. 4 reveals three key facts about the evolution of earnings by education groups that are not evident from the earlier plots of the college/high school wage premium. First, a sizable share of the increase in college relative to non-college wages in 1980 forward is explained by the rising wages of post-college workers, i.e., those with post-baccalaureate degrees. Real earnings for this group increased steeply and nearly continuously from at least the early 1980s to present. By contrast, earnings growth among those with exactly a four-year degree was much more modest. For example, real wages of males with exactly a four-year degree rose 13 log points between 1979 and 2008, substantially less than they rose in only the first decade of the sample.

A second fact highlighted by Fig. 4 is that a major proximate cause of the growing college/high school earnings gap is not steeply rising college wages, but rapidly declining wages for the less educated–especially less educated males. Real earnings of males with less than a four year college degree fell steeply between 1979 and 1992, by 12 log points for high school and some-college males, and by 20 log points for high school dropouts. Low skill male wages modestly rebounded between 1993 and 2003, but never reached their 1980 levels. For females, the picture is qualitatively similar, but the slopes are more favorable. While wages for low skill males were falling in the 1980s, wages for low skill females were largely stagnant; when low skill males wages increased modestly in the 1990s, low skill female wages rose approximately twice as fast.

A potential concern with the interpretation of these results is that the measured real wage declines of less educated workers mask an increase in their total compensation after accounting for the rising value of employer provided non-wage benefits such as healthcare, vacation and sick time. Careful analysis of representative, wage and fringe benefits data by Pierce (2001, forthcoming) casts doubt on this notion, however. Monetizing the value of these benefits does not substantially alter the conclusion that real compensation for low skilled workers fell in the 1980s. Further, Pierce shows that total compensation—that is, the sum of wages and in-kind benefits—for high skilled workers rose by more than their wages, both in absolute terms and relative to compensation for low skilled workers.¹⁴ A complementary analysis of the distribution of non-wage benefits—including safe working conditions and daytime versus night and weekend hours—by Hamermesh (1999) also reaches similar conclusions. Hamermesh demonstrates that trends in the inequality of wages understate the growth in full earnings inequality (i.e., absent compensating differentials) and, moreover, that accounting for changes in the distribution of non-wage amenities augments rather than offsets changes in the inequality of wages. It is therefore unlikely that consideration of non-wage benefits changes the conclusion that low skill workers experienced significant declines in their real earnings levels during the 1980s and early 1990s.¹⁵

The third key fact evident from Fig. 4 is that while the earnings gaps between some-college, high school graduate, and high school dropout workers expanded sharply in the 1980s, these gaps stabilized thereafter. In particular, the wages of high school dropouts, high school graduates, and those with some college moved largely in parallel from the early 1990s forward.

The net effect of these three trends—rising college and post-college wages, stagnant and falling real wages for those without a four-year college degree, and the stabilization of the wage gaps among some-college, high school graduates, and high school dropout workers—is that the wage returns to schooling have become increasingly convex in years of education, particularly for males, as emphasized by Lemieux (2006b). Figure 5 shows this “convexification” by plotting the estimated gradient relating years of educational attainment to log hourly wages in three representative years of our sample: 1973, 1989, and 2009. To construct this figure, we regress log hourly earnings in each year on a quadratic in years of completed schooling and a quartic in potential experience. Models that pool males and females also include a female main effect and an interaction between the female dummy and a quartic in (potential) experience.¹⁶ In each figure, the predicted log earnings of a worker with seven years of completed schooling and 25 years of potential experience in 1973 is normalized to zero. The slope of the 1973 locus then traces out the implied log earnings gain for each additional year of schooling in 1973, up to 18 years. The loci for 1989 and 2009 are constructed similarly, and they are also normalized relative to the intercept in 1973. This implies that upward or downward shifts in the intercepts of these loci correspond to real changes in log hourly earnings, whereas rotations of the loci indicate changes in the education-wage gradient.¹⁷

The first panel of Fig. 5 shows that the education-wage gradient for males was roughly log linear in years of schooling in 1973, with a slope approximately equal to 0.07 (that is, 7 log points of hourly earnings per year of schooling). Between 1973 and 1989, the slope steepened while the intercept fell by a sizable 10 log points. The crossing point of the two series at 16 years of schooling implies that earnings for workers with less than a four-year college degree fell between 1973 and 1989, consistent with the real wage plots in Fig. 4. The third locus, corresponding to 2009, suggests two further changes in wage structure in the intervening two decades: earnings rose modestly for low education workers, seen in the higher 2009 intercept (though still below the 1973 level); and the locus relating education to earnings became strikingly convex. Whereas the 1989 and 2009 loci are roughly parallel for educational levels below 12, the 2009 locus is substantially steeper above this level. Indeed at 18 years of schooling, it lies 16 log points above the 1989 locus. Thus, the return to schooling first steepened and then “convexified” between 1973 and 2009.

Panel B of Fig. 5 repeats this estimation for females. The convexification of the return to education is equally apparent for females, but the downward shift in the intercept is minimal. These differences by gender are, of course, consistent with the differential evolution of wages by education group and gender shown in Fig. 4.

As a check to ensure that these patterns are not driven by the choice of functional form, Fig. 6 repeats the estimation, in this case replacing the education quartic with a full set of education dummies. While the fitted values from this model are naturally less smooth than in the quadratic specification, the qualitative story is quite similar: between 1973 and 1989, the education-wage locus intercept falls while the slope steepens. The 1989 curve crosses the 1973 curve at 18 years of schooling. Two decades later, the education-wage curve lies atop the 1989 curve at low years of schooling, while it is both steeper and more convex for completed schooling beyond the 12th year.

2.4. Overall wage inequality

Our discussion so far summarizes the evolution of real and relative wages by education, gender and experience groups. It does not convey the full set of changes in the wage distribution, however, since there remains substantial wage dispersion within as well as between skill groups. To fill in this picture, we summarize changes throughout the entire earnings distribution. In particular, we show the trends in real wages by earnings percentile, focusing on the 5th through 95th percentiles of the wage distribution. We impose this range restriction because the CPS and Census samples are unlikely to provide accurate measures of earnings at the highest and lowest percentiles. High percentiles are unreliable both because high earnings values are truncated in public use samples and, more importantly, because non-response and under-reporting are particularly severe among high income households.¹⁸ Conversely, wage earnings in the lower percentiles imply levels of consumption that lie substantially below observed levels (Meyer and Sullivan, 2008). This disparity reflects a combination of measurement error, underreporting, and transfer income among low wage individuals.

Figure 7 plots the evolution of real log weekly wages of full-time, full-year workers at the 10th, 50th and 90th percentiles of the earnings distribution from 1963 through 2008. In each panel, the value of the 90th, 50th and 10th percentiles are normalized to zero in the start year of 1963, with subsequent data points measuring log changes from this initial level. Many features of Fig. 7 closely correspond to the education by gender real wages series depicted in Fig. 4. For both genders, the 10th, 50th and 90th percentiles of the distribution rise rapidly and relatively evenly between 1963 and 1973. After 1973, the 10th and 50th percentiles continue to stagnate relatively uniformly for the remainder of the decade. The 90th percentile of the distribution pulls away modestly from the median throughout the decade of the 1970s, echoing the rise in earnings among post-college workers in that decade.¹⁹

Reflecting the uneven distribution of wage gains by education group, growth in real earnings among males occurs among high earners, but is not broadly shared. This is most evident by comparing the male 90th percentile with the median. The 90th percentile rose steeply and almost monotonically between 1979 and 2007. By contrast, the male median was essentially flat from 1980 to 1994. Simultaneously, the male 10th percentile fell steeply (paralleling the trajectory of high school dropout wages). When the male median began to rise during the mid 1990s (a period of rapid productivity and earnings growth in the US economy), the male 10th percentile rose concurrently and slightly more rapidly. This partly reversed the substantial expansion of lower-tail inequality that unfolded during the 1980s.

The wage picture for females is qualitatively similar, but the steeper slopes again show that the females have fared better than males during this period. As with males, the growth of wage inequality is asymmetric above and below the median. The female 90/50 rises nearly continuously from the late 1970s forward. By contrast, the female 50/10 expands rapidly during the 1980s, plateaus through the mid-1990s, and then compresses modestly thereafter.

Because Fig. 7 depicts wage trends for full-time, full-year workers, it tends to obscure wage developments lower in the earnings distribution, where a larger share of workers are part-time or part-year. To capture these developments, we apply the May/ORG CPS log hourly wage samples for years 1973 through 2009 (i.e., all available years) to plot in Fig. 8 the corresponding trends in real indexed hourly wages of all employed workers at the 10th, 50th, and 90th percentiles. Due to the relatively small size of the May sample, we pool three years of data at each point to increase precision (e.g., plotted year 1974 uses data from 1973, 1974 and 1975).

The additional fact revealed by Fig. 8 is that downward movements at the 10th percentile are far more pronounced in the hourly wage distribution than in the full-time weekly data. For example, the weekly data show no decline in the female 10th percentile between 1979 and 1986, whereas the hourly wage data show a fall of 10 log points in this period.²⁰ Similarly, the modest closing of the 50/10 earnings gap after 1995 seen in the full-time, full-year sample is revealed as a sharp reversal of the 1980s expansion of 50/10 wage inequality in the full hourly distribution. Thus, the monotone expansion in the 1980s of wage inequality in the top and bottom halves of the distribution became notably non-monotone during the subsequent two decades.²¹

The contrast between these two periods of wage structure changes—one monotone, the other non-monotone—is shown in stark relief in Fig. 9, which plots the change at each percentile of the hourly wage distribution relative to the corresponding median during two distinct eras, 1974–1988 and 1988–2008. The monotonicity of wage structure changes during the first period, 1974–1988, is immediately evident for both genders.²² Equally apparent is the U-shaped (or “polarized”) growth of wages by percentile in the 1988–2008 period, which is particularly evident for males. The steep gradient of wage changes above the median is nearly parallel, however, for these two time intervals. Thus, the key difference between the two periods lies in the evolution of the lower-tail, which is falling steeply in the 1980s and rising disproportionately at lower percentiles thereafter.²³

Though the decade of the 2000s is not separately plotted in Fig. 9, it bears note that the U-shaped growth of hourly wages is most pronounced during the period of 1988 through 1999. For the 1999 through 2007 interval, the May/ORG data show a pattern of wage growth that is roughly flat across the first seven deciles of the distribution, and then upwardly sloped in the three highest deciles, though the slope is shallower than in either of the prior two decades.

These divergent trends in upper-tail, median and lower-tail earnings are of substantial significance for our discussion, and we consider their causes carefully below. Most notable is the “polarization” of wage growth—by which we mean the simultaneous growth of high and low wages relative to the middle—which is not readily interpretable in the canonical two factor model. This polarization is made more noteworthy by the fact that the return to skill, measured by the college/high school wage premium, rose monotonically throughout this period, as did inequality above the median of the wage distribution. These discrepancies between the monotone rise of skill prices and the nonmonotone evolution of inequality again underscore the potential utility of a richer model of wage determination.

Substantial changes in wage inequality over the last several decades are not unique to the US, though neither is the US a representative case. Summarizing the literature circa ten years ago, Katz and Autor (1999) report that most industrialized economies experienced a compression of skill differentials and wage inequality during the 1970s, and a modest to large rise in differentials in the 1980s, with the greatest increase seen in the US and UK. Drawing on more recent and consistent data for 19 OECD countries, Atkinson reports that there was at least a five percent increase in either upper-tail or lower-tail inequality between 1980 and 2005 in 16 countries, and a rise of at least 5 percent in both tails in seven countries. More generally, Atkinson notes that substantial rises in upper-tail inequality are widespread across OECD countries, whereas movements in the lower-tail vary more in sign, magnitude, and timing.²⁴

2.5. Job polarization

Accompanying the wage polarization depicted in Fig. 7 through 9 is a marked pattern of job polarization in the United States and across the European Union—by which we mean the simultaneous growth of the share of employment in high skill, high wage occupations and low skill, low wage occupations. We begin by depicting this broad pattern (first noted in Acemoglu, 1999) using aggregate US data. We then link the polarization of employment to the “routinization” hypothesis proposed by Autor et al., (2003“ALM” hereafter), and we explore detailed changes in occupational structure across the US and OECD in light of that framework.

3.1. The simple theory of the canonical model

The canonical model has two skills, high and low. It draws no distinction between skills and occupations (tasks), so that high skill workers effectively work in separate occupations (perform different tasks) from low skill workers. In many empirical applications of the canonical model, it is natural to identify high skill workers with college graduates (or in different eras, with other high education groups), and low skill workers with high school graduates (or again in different eras, with those with less than high school). We will use education and skills interchangeably, but as we discuss below, the canonical model becomes more flexible if one allows heterogeneity in skills within education groups.

Critical to the two-factor model is that high and low skill workers are imperfect substitutes in production. The elasticity of substitution between these two skill types is central to understanding how changes in relative supplies affect skill premia.

Suppose that the total supply of low skill labor is L and the total supply of high skill labor is H. Naturally not all low (or high) skill workers are alike in terms of their marketable skills. As a simple way of introducing this into the canonical model, suppose that each worker is endowed with either high or low skill, but there is a distribution across workers in terms of efficiency units of these skill types. In particular, let denote the set of low skill workers and denote the set of high skill workers. Each low skill worker i ∈ has l_i efficiency units of low skill labor and each high skill worker i ∈ has h_i units of high skill labor. All workers supply their efficiency units inelastically. Thus the total supply of high skill and low skill labor in the economy can be written as:

The production function for the aggregate economy takes the following constant elasticity of substitution form

(2)

where σ e [0, ∞) is the elasticity of substitution between high skill and low skill labor, and Al and Ah are factor-augmenting technology terms.⁵⁴

The elasticity of substitution between high and low skill workers plays a pivotal role in interpreting the effects of different types of technological changes in this canonical model. We refer to high and low skill workers as gross substitutes when the elasticity of substitution σ > 1, and gross complements when σ < 1. Three focal cases are: (i) σ – 0, when high skill and low skill workers will be Leontief, and output can be produced only by using high skill and low skill workers in fixed portions; (ii) σ → ∞ to when high skill and low skill workers are perfect substitutes (and thus there is only one skill, which H and L workers possess in different quantities), and (iii) σ → 1, when the production function tends to the Cobb-Douglas case.

In this framework, technologies are factor-augmenting, meaning that technological change serves to either increase the productivity of high or low skill workers (or both). This implies that there are no explicitly skill replacing technologies. Depending on the value of the elasticity of substitution, however, an increase in A_H or A_L can act either to complement or (effectively) substitute for high or low skill workers (see below). The lack of directly skill replacing technologies in the canonical model is an important reason why it does not necessarily provide an entirely satisfactory framework for understanding changes in the earnings and employment distributions over the last four decades.

The production function (2) admits three different interpretations.

Since labor markets are competitive, the low skill unit wage is simply given by the value of marginal product of low skill labor, which is obtained by differentiating (2) as

(3)

Given this unit wage, the earnings of worker i ∈ L is simply

There are two important implications of Eq. (3):

We again have similar comparative statics. First, ∂w_H/∂H/L < 0, so that when high skill workers become more abundant, their wages should fall. Second, ∂w_H/∂A_L > 0 and ∂w_H/∂A_H > 0, so that technological progress of any kind increases high skill (as well as low skill) wages. Also similarly, the earnings of worker i ∈ H is simply

W_i = w_Lh_i.

It can also be verified that an increase in either A_L or A_H (and also an increase in H/L) will raise average wages in this model (see Acemoglu, 2002a).

Combining (3) and (4), the skill premium—the unit high skill wage divided by the unit low skill wage—is

(5)

Equation (5) can be rewritten in a more convenient form by taking logs,

(6)

The log skill premium, ln ω, is important in part because it is a key market outcome, reflecting the price of skills in the labor market, and it has been a central object of study in the empirical literature on the changes in the earnings distribution. Equation (6) shows that there is a simple log linear relationship between the skill premium and the relative supply of skills as measured by E/ L. Equivalently, Eq. (6) implies:

(7)

This relationship corresponds to the second of the two forces in Tinbergen’s race (the first being technology, the second being the supply of skills): for a given skill bias of technology, captured here by A_H/ A_L, an increase in the relative supply of skills reduces the skill premium with an elasticity of 1/σ. Intuitively, an increase in H/L creates two different types of substitution. First, if high and low skill workers are producing different goods, the increase in high skill workers will raise output of the high skill intensive good, leading to a substitution towards the high skill good in consumption. This substitution hurts the relative earnings of high skill workers since it reduces the relative marginal utility of consumption, and hence the real price, of the high skill good. Second, when high and low skill workers are producing the same good but performing different functions, an increase in the number of high skill workers will necessitate a substitution of high skill workers for the functions previously performed by low skill workers.⁵⁵ The downward sloping relationship between relative supply and the skill premium implies that if technology, in particular A_H/ A_L, had remained roughly constant over recent decades, the remarkable increase in the supply of skills shown in Fig. 1 would have led to a significant decline in the skill premium. The lack of such a decline is a key reason why economists believe that the first force in Tinbergen’s race—changes in technology increasing the demand for skills—must have also been important throughout the 20th century (cf. Goldin and Katz (2008)).

More formally, differentiating (6) with respect to A_H/A_L yields:

(8)

Equation (8) implies that if σ > 1 , then relative improvements in the high skill augmenting technology (i.e., in A_H/A_L) increase the skill premium. This can be seen as a shift out of the relative demand curve for skills. The converse is obtained when σ < 1 : that is, when σ < 1, an improvement in the productivity of high skill workers, A_H, relative to the productivity of low skill workers, A_L, shifts the relative demand curve inward and reduces the skill premium. This case appears paradoxical at first, but is in fact quite intuitive. Consider, for example, how factor-augmenting technology change affects the wages of the augmented factor when the production function is Leontief (fixed proportions). In this case, as A_H increases, high skill workers become more productive, and hence the demand for low skill workers increases by more than the demand for high skill workers. Effectively, the increase in A_H creates “excess supply” of high skill workers given the number of low skill workers, which depresses the high skill relative wage. This observation raises an important caveat. It is tempting to interpret improvements in technologies used by high skill workers, A_H, as “skill biased”. However, when the elasticity of substitution is less than 1 , it will be advances in technologies used with low skill workers, A_L, that increase the relative productivity and wages of high skill workers, and an increase in A_H relative to A_L will be “skill replacing”. Nevertheless, the conventional wisdom is that the skill premium increases when high skill workers become relatively more—not relatively less—productive, which is consistent with σ > 1.⁵⁶

While the case of σ < 1 is interesting (and potentially relevant when we think of different factors of production), in the context of the substitution between college and non-college workers, a relatively high elasticity of substitution is both plausible and consistent with several studies. Most estimates put σ in this context to be somewhere between 1.4 and 2 (Johnson, 1970; Freeman, 1986; Heckman et al., 1998). In this light, in what follows we assume that σ > 1.

3.2. Bringing tinbergen’s education race to the data

The key equation of the canonical model, (6), links the skill premium to the relative supply of skills, H/L, and to the relative technology term, A_H / A_L. This last term is not directly observed. Nevertheless, we can make considerable empirical progress by taking a specific form of Tinbergen’s hypothesis, and assuming that there is a log linear increase in the demand for skills over time coming from technology, captured in the following equation:

(9)

where t is calendar time and variables written with t subscript refer to these variables at time t. Substituting this equation into (6), we obtain:

(10)

Equation (10) implies that “technological developments” take place at a constant rate, while the supply of skilled workers may grow at varying rates at different points in time. Therefore, changes in the skill premium will occur when the growth rate of the supply of skills differs from the pace of technological progress. In particular, when H/L grows faster than the rate of skill biased technical change, (σ − 1) γ1, the skill premium will fall. And when the supply growth falls short of this rate, the skill premium will increase. In the next subsection, we will see that this simple equation provides considerable explanatory power for the evolution of the skill premium. At the same time, the limitations of the model become evident when it is confronted with a richer array of facts.

3.3. Changes in the US earnings distribution through the lens of the canonical model

We begin by replicating the seminal work of Katz and Murphy (1992), who demonstrated the power of the approach outlined above by fitting equation (10) to aggregate time-series data on college/high school relative wages and college/high school relative supplies for the years 1963 through 1987. Following their methods as closely as possible, the first column of Table 8 presents an OLS regression of the composition-adjusted college/high school log weekly wage premium (Fig. 1) on a linear time trend and our measure of college/high school log relative supply (Fig. 2) for years 1963–1987. We obtain the estimate:

As shown in Fig. 19, this simple specification performs relatively well in capturing the broad features of the evolving college premium between 1963 and 1987, most notably, the sharp reversal of the trajectory of the college premium coinciding with the deceleration in the growth of college relative supply in the late 1970s. The power of the model is underscored in Fig. 20, which plots the college premium and college relative supply measures by year, each purged of a linear time trend. The robust inverse relationship between these two series demonstrates the key role played by the decelerating supply of college workers in driving the college premium upward in recent decades.

More formally, these estimates suggest that the evolution of the college premium during the period 1963 through 1987 can be characterized by an elasticity of substitution between college graduate workers and non-college workers of about , and an annual increase of about 2.7 percent in the relative demand for college labor.⁵⁷

Column 2 of Table 8 includes 21 additional years of data beyond 1987 to extend the Katz-Murphy estimate to 2008. When fit to this longer time period, the model yields a substantially higher estimate of the elasticity of substitution, , and a slower trend rate of demand growth (1.6 percent annually).⁵⁸ The proximate cause of this change in the model’s estimated parameters can be seen in Fig. 19, which, following Autor et al. (2008), plots the out-of-sample fit of the Katz-Murphy model for the years 1987–2008. The fit of the model remains quite good through the year 1992, five years out of sample. But the model systematically deviates from the data thereafter, predicting a sharper rise in the college premium than actually occurs. While the observed college premium rose by 12 points between 1992 and 2008, the model predicts a rise of 25 log points. Without further refinements to the model, this discrepancy suggests that either the trend in relative demand decelerated after 1992 or the elasticity of substitution rose.

Subsequent columns of Table 8 explore this possibility by freeing up the linear time trend with somewhat richer specifications: a linear spline, allowing the time trend to deviate from its initial trajectory after 1992; a quadratic time trend; and a cubic time trend. When fit to the data, all three of these variants suggest a significant deceleration in trend relative demand takes place sometime during the 1990s. Conditional on the more flexible time trend, the elasticity of substitution in these estimates returns to the range of 1.6 to 1.8. Thus, taken at face value, this model suggests that relative demand for college workers decelerated in the 1990s, which does not accord with common intuitions regarding the nature or pace of technological changes occurring in this era. We return to this point below.

One can gain additional identification and explanatory power with this model by considering a slightly richer set of facts. As shown in Tables 1a and 1b, changes in the college/high school wage gap have differed substantially by age/experience groups over recent decades. This pattern may be seen through a comparison of the college premium for younger workers (those with 0–9 years of potential experience) and older workers (those with 20–29 years of potential experience). Figure 21 shows that the rapid rise in the college/high school gap during the 1980s was concentrated among less experienced workers. Conversely, from the mid-1990s forward, the rise in the college/high school premium was greater among experienced workers.

These facts may better accord with a simple extension to the canonical model. To the extent that workers with similar education but different ages or experience levels are imperfect substitutes in production, one would expect age-group or cohort-specific relative skill supplies—as well as aggregate relative skill supplies—to affect the evolution of the college/high school premium by age or experience, as emphasized by Card and Lemieux (2001b). Consistent with this view, Fig. 3 (presented in Section 2) shows a rapid deceleration in relative college supply among younger workers in the mid to late 1970s, several years after the end of the Vietnam war reduced male college enrollment. Two decades later (circa 1995), this kink in the relative supply schedule generates a sharp deceleration in the availability of experienced college workers. Notably, the differential rises in the college premium for young and (later) for experienced workers roughly coincide with the differential slowdown in college supply among these experience groups (though these slowdowns are 20 years apart). This pattern offers a prima facie case that the college premium for an experience group depends on its own-group relative supply as well as the overall supply of college relative to high school graduates.

We take fuller account of these differing trends by experience group in Table 9 by estimating regression models for the college wage by experience group. These extend the basic specification in Eq. (10) to include own experience group relative skill supplies. The first column of Table 10 presents a regression pooled across 4 potential experience groups (those with 0–9, 10–19, 20–29, and 30–39 years of experience), allowing for group-specific intercepts but constraining the other coefficients to be the same for all experience groups. Specifically, we estimate:

where j indexes experience groups, δ_j is a set of experience group main effects, and we include a quadratic time trend. This specification arises from an aggregate constant elasticity of substitution production function in which college and high school equivalents from the aggregate inputs, similar to Eq. (2) above, where these aggregate inputs are themselves constant elasticity of substitution sub-aggregates of college and high school labor by experience group (Card and Lemieux, 2001b). Under these assumptions, 1 /β₁ provides an estimate of σ₂, the aggregate elasticity of substitution, and 1 /β provides an estimate of σ_j, the partial elasticity of substitution between different experience groups within the same education group.

The estimates in the first column of Table 9 indicate a substantial effect of both own-group and aggregate supplies on the evolution of the college wage premium by experience group. While the implied estimate of the aggregate elasticity of substitution in this model is similar to the aggregate models in Table 8, the implied value of the partial elasticity of substitution between experience groups is around 3.7 (which is somewhat smaller than the estimates in Card and Lemieux (2001b)). This model indicates that differences in own-group relative college supply go some distance towards explaining variation across experience groups in the evolution of the college wage premium in recent decades.

The final four columns of Table 9 present regression models of the college wage premium estimated separately by experience group. These estimates show that trend demand changes and relative skill supplies play a large role in changes in educational differentials for younger and prime age workers. The college wage premium for workers with under 20 years of experience is quite responsive to both own group and aggregate relative skill supplies. However, aggregate supplies appear equally important for workers with 20-plus years of experience, while own-group supplies are not found to exert an independent effect.

3.4. Overall inequality in the canonical model

Our brief overview of the salient empirical patterns in the previous section highlights that there have been rich and complex changes in the overall earning distribution over the last four decades. While changes in the college premium (or more generally in the returns to different levels of schooling) have contributed to these changes in the earnings distribution, there have also been significant changes in inequality among workers with the same education—i.e., within groups as well as between groups.

The canonical model introduced above can also provide a first set of insights for thinking about within-group inequality and thus provides a framework for interpreting changes in the overall wage distribution. In particular, the model generates not only differing wages for high and low skill workers, but also wage variation among workers with a given level of observed skill. This follows from our assumption that the efficiency units of labor supplies vary across workers of each skill group.

Nevertheless, this type of within group inequality (i.e., due to cross-worker, within skill group heterogeneity in efficiency units) is invariant to skill prices and thus changes in overall inequality in this model will closely mimic changes in the skill premium. In particular, recall that all workers in the set L (respectively in the set H) always face the same skill price. Therefore changes in the skill premium should have no direct effect on within group inequality. Mathematically, in this model the relative earnings of two workers in the same group, say L, is given by

In this simple form, the canonical model can exhibit significant within group wage inequality, but inequality will be independent of the skill premium.⁵⁹

Naturally, this feature can be changed by positing that there are increasing returns to efficiency units of skill, so when the relative demand for high skill labor increases, this increases the demand for “more skilled” college graduates by relatively more than for “less skilled” college graduates. One way to incorporate this idea is to extend the canonical model by drawing a distinction between observable groups (such as college vs. non-college) and skills. For example, we can remain fairly close to the spirit of the canonical model and continue to assume that there are only two skills, but now suppose that these skills are only imperfectly approximated by education (or experience).

Specifically, we can assume that the two observable groups are college and non-college, and a fraction φ_c of college graduates are high skill, while a fraction ϕ_n < ϕ_c of non-college graduates are high skill (the remaining fractions in both groups being low skill as usual). Let us again denote the skill premium by ω = w_H/w_L. This is no longer the college premium, i.e., the ratio of average college to non-college wages, however, since not all college workers have high skill and not all non-college workers have low skill. Given our assumption, we can compute the college premium simply as the ratio of (average) college wages, w_C, to (average) non-college wages, w_N, that is,

It is straightforward to verify that, because ϕ_n < ϕ_c, this college premium is increasing in ω, so that when the true price of skill increases, the observed college premium will also rise. In addition, we can define within group inequality in this context as the ratio of the earnings of high wage college graduates (or non-college graduates) to that of low wage college graduates (or non-college graduates). Given our assumptions, we also have ω^within = ω (since high wage workers in both groups earn w_H, while low wage workers earn w_L). As long as ϕ_c and ϕ_n remain constant, ω^c and ω^within will move together. Therefore in this extended version of the canonical model, an increase in the returns to observed skills—such as education—will also be associated with an increase in the returns to unobserved skills. Moreover, we can also think of large changes in relative supplies being associated with compositional changes, affecting ϕ_c and ϕ_η, so within group inequality can change differently than the skill premium, and thus overall inequality can exhibit more complex changes as supplies and technology evolve.⁶⁰

This model thus provides a useful starting point for thinking about changes in within group inequality and the overall earnings distribution, and linking them both to the market price of skills. In light of this model, the increase in the overall earnings inequality starting in the late 1970s or early 1980s is intimately linked to the increase in the demand for skills, also reflected in the increase in the college premium. While this parsimonious framework is valuable for analyzing the evolution of distribution of earnings, it does not provide sufficient nuance for understanding why different parts of the earnings distribution move differently and, moreover, do so markedly during different time periods.

3.5. Endogenous changes in technology

The canonical model is most powerful as an empirical framework when skill biased technical change can be approximated by a steady process, such as the (log) linear trend posited in (9). However, the discussion in Autor et al. (1998) suggests that the pace of skill biased technical change was likely more rapid between 1970 and 1990 than between 1940 and 1970. The evidence discussed above, on the other hand, suggests that the pace of skill biased technical change slowed during the 1990s, at least viewed through the lens of the canonical model. As also discussed in Acemoglu (2002a), a relatively steady process of skill biased technical change is likely to be a particularly poor approximation when we consider the last 200 years instead of just the postwar period. For example, the available evidence suggests that the most important innovations of the nineteenth century may have replaced—rather than complemented—skilled workers (in particular artisans). The artisanal shop was replaced by the factory and later by interchangeable parts and the assembly line, and products previously manufactured by skilled artisans were subsequently produced in factories by workers with relatively few skills (see, e.g., Mokyr, 1992; James and Skinner, 1985; Goldin and Katz, 2008; Hounshell, 1985; Acemoglu, 2002a).

But once we recognize that skill biased technical change is not a steady process, it becomes more important to understand when we should expect it to be more rapid (and when we should expect it not to take place at all). The canonical model is silent on this question. Acemoglu (1998, 2002a) suggests that modeling the endogenous response of the skill bias of technology might generate richer insights. In particular, as we discuss further in Section 4.8, under relatively general conditions, models of endogenous (directed) technical change imply that technology should become more skill biased following increases in the supply of high skill workers (and conversely, less skill biased following increases in the supply of low skill workers). According to this perspective, steady skill biased technical change might be partly a response to the steady increase in the supply of skills during the past century (thus uniting the two parts of Tinbergen’s race); the skill replacing technologies of the nineteenth century might be partly a response to the large increase in the supply of low skill workers in the cities; the acceleration in skill bias in the 1980s might, in part, be a response to the more rapid increase in the supply of college skills in the late 1960s and early 1970s noted in Section 2; and the deceleration of demand shifts favoring skilled workers in the 1990s might in part be a response to the deceleration in the supply of college skills during the 1980s (see again Section 2).

As we discussed above, computer technology is particularly well suited for automating routine tasks. This creates a natural tendency for the type of skill bias described by Autor et al. (2003). It does not, however, imply that the path of technical change and its bias are entirely exogenous. Exactly how computer technology is developed and how it is applied in the production process has much flexibility, and it is plausible that this will respond to profit opportunities created by different types of applications and uses.