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There are few concentrated studies on wage inequality across local labor markets at the city or metropolitan level. This paper studies the changes in wage inequality among 170 metropolitan areas by using micro-level data from the U.S. Census and American Community Survey from 1980 to 2019. We propose that shifts in the relative demand for “college-educated” or “college equivalent” workers have been persistent in both temporal and spatial dimensions; and that this persistence has contributed to the increase in wage inequality along with the rise in managerial employ- ment. Using fixed-effects models, we find that on average, changes in managerial intensity between 1980 and 2019 accounts for 6.9% of the change in wage inequality across U.S. labor markets. Keywords: Wage inequality, Labor markets, Labor demand JEL Classification: B59, C33, J23, J31 for labor and redistribute resources. Widening disparities 1 Introduction across and within places in the U.S., revealed in debates A voluminous literature on wage inequality (dispersion) around wages, housing affordability, have motivated poli - documents the substantial widening of the U.S. wage cymakers and researchers to give increased attention to structure that emerged during the 1980s, and which has the local dimensions of inequality. ceaselessly grown in following decades in both the United Nevertheless, aside from the large urban economics States and globally (see Autor and Katz 1999; Acemoglu literature on the urban wage premium (see for instance, 2002b; and Piketty and Saez 2006). The surge in wage Gould 2007; Heuermann et al. 2010), there has been lit- inequality is illustrated in Fig. 1 (plot a), which depicts a tle concentrated study on the rise of wage or income monotonic spreading out of the entire wage distribution inequality across local labor markets within the met- for both men and women. The literature on wage inequal - ropolitan or city level. Most studies on wage inequal- ity has explored how much of the growth in inequality ity, in fact, have been either at the national or state level can be explained by the erosion of labor institutions such (for example, Katz and Murphy 1992; Ciccone and Peri as unions and the declining value of the minimum wage 2005). This may be due in part to the recognized fact that (for instance, Card 2001; Koeniger et al. 2007), with shifts “within” or “between” group decompositions of the urban in the relative demand for “skilled” labor in the form wage premium has been within, rather than among spa- of college educated workers. Research has historically tial units such as standard metropolitan statistical areas framed income inequality as a national issue, one best (MSAs). Baum-Snow and Pavan (2012), for instance, addressed through national policies that raise demand find that experience and wage-level effects are the most *Correspondence: firstname.lastname@example.org Anthony Eisenbarth and Zhuo Fu Chen contributed equally to this work Department of Economics, University of Utah, 260 South Central Campus Drive, Gardner Commons Suite 4100, Salt Lake City, UT 84102, USA Full list of author information is available at the end of the article © The Author(s) 2022. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/. 2 Page 2 of 25 A. Eisenbarth , Z. F. Chen Fig. 1 Wage dispersion, stylized facts: 1964–2019. Lines in plots a, c, and d, are smoothed regression lines fit by a generalized additive model. The effective minimum wage rate in b is simply the average of the real value of state minimum wages. Inequality measures are standardized. All amounts expressed in 2019 dollars Source: Census 5 Percent Samples for 1980, 1990, and 2000. American Community Survey 2005–2019. Bureau of Economic Analysis, National Income and Product Accounts Tables 6.4A:6.4D. U.S. Department of Labor, State Minimum Wage Laws. Current Population Survey, Merged Outgoing Rotation Groups, 1979–2019 important “mechanisms” contributing to the urban wage 1980s. At the same time, the decline in manufactur- premium. ing employment increased its descent into the 1980s. Considerable attention has been given to fundamen- Lastly, the widely used measures of wage inequality tal changes in the institutions of the labor market, such the log p(50)–p(10) or “lower tail,” log p(95)–p(50) or as the decline in union membership and the falling “upper tail,” and log p(95)–p(10) (the “overall” meas- value of the federal minimum wage (see for instance, ure) ratios all increased dramatically in this period. Lee 1999; Autor et al. 2016; and Farber et al. 2020). But while the p(95)–p(50) and p(95)–p(10) measures Such trends are plotted in Fig. 1 (plots b and c). These have continued to increase, lower tail inequality has figures show that the real value of the minimum wage, remained fairly constant since the end of the 1990s, and both at the federal and at the ’effective’ level (the aver - even recently, is beginning to decline. age of the state minimum rates) fell precipitously in the Changes in trade terms through globalization also changed the composition of firms within the U.S. Manufacturing employment, for instance, has declined Baum-Snow and Pavan (2012) find that these mechanisms are important for both high school and college graduates throughout the city size distribution. considerably over the past several decades, even as Differences in wage intercepts across location categories are more important manufacturing output grew strongly. What had been a for generating wage gaps between medium and small cities, while differences slow decline in employment accelerated after the turn in returns to experience are more important for generating large-to-small city wage differentials. The evolution of wage inequality within local U.S. labor markets Page 3 of 25 2 of the century and especially during the Great Reces- On the other hand, managerial and supervisory sion. Manufacturing employment bottomed in 2010, employment, as well as compensation, have grown and overall employment in manufacturing is at its steadily since the 1980s. Data from the Bureau of Labor lowest levels since the U.S. entered the Second World Statistics’ Occupational Employment and Wage Statis- War. The decline in manufacturing employment and tics (OEWS) survey, which collects data on wage and union density coincided with the rising importance of salary workers in non-farm establishments provides the services industry, which grew from roughly 25% information on compensation for managerial and non- of national employment in the U.S. at the start of the managerial positions. In 1996, the average hourly wage 1960s to approximately half of total employment by for managerial and supervisory employees was $30.13. 2010. By 2019, the average hourly wage for managerial and These trends overlapped with the advent of the “Com - supervisory employees increased by 50%. In compari- puter Revolution.” The vast improvements in informa - son, the real average hourly earnings of production and tion technology (IT) seemingly gave rise to a demand non-supervisory employees increased 30%, increasing for a relatively more educated workforce with new and from $19.67 to $23.51. Cumulatively from 1980, manage- advanced technical skills. Growth in the college wage rial compensation increased 48.1%, while regular workers premium during the 1980s have been attributed to this experienced a 25.5% increase. The fact that managerial correlation between the rise of IT and the growth in the pay has grown far faster than the pay of regular workers relative wage for college educated workers. And hence, indicates that managerial compensation growth does not the effects derived from the computer and IT revolu - simply reflect the increased value of highly paid profes - tion have emerged as the leading hypothesis for explain- sionals in a competitive race for skills. ing the growth in the relative demand for skills through In light of these stylized facts, we propose that while the Skill Biased Technical Change (SBTC) argument. The education attainment in the U.S. has increased relative SBTC contention, however, has its limitations. Perhaps gains for some in the labor force, domestic and global the main difficulty, as both Card and DiNardo (2001) and forces have led to an increase in wage inequality through Lemieux (2006), have argued, is that the relative demand the weakening of workers’ bargaining power and labor for this “unobservable skill” of college educated work- disciplining effect of firms leveraging more manage - ers should have been experienced in both the 1980s and rial and supervisory employees. Changes in the relative 1990s; the fact that this occurred mostly in the 1980s is a supply and demand for college educated workers can- stumbling block to the SBTC argument. In contrast, the not alone account for such broad sweeping changes in college premium, the wage of college educated workers the wage structure. We note two trends: first, managerial relative to high school workers, declined during the so- employment has grown steadily throughout the past sev- called “Roaring Nineties” rather than steadily increase eral decades, and secondly, managerial compensation has as predicted by the core SBTC model developed by Katz grown in real terms, whereas real compensation for regu- and Murphy (1992). lar (non-supervisory and non-managerial) workers have An under-looked phenomenon in comparison, have stagnated. This can be seen clearly in the rise of manage - been the fundamental changes in the relations between rial and supervisory employees share of total compensa- capital and labor during the 1980s, and perhaps more tion for the private sector, which rose despite the growth importantly in the workplace itself. On the one hand, in managerial and supervisory employees. new business practices and technologies have led many We use U.S. Census and American Community Survey workers to supply their labor outside of the traditional (ACS) data from 1980 to 2019, to explore and study the employment relationship. An estimated 15 million Amer- nature of changes in the education-specific employment ican workers have “alternative arrangements” for their shares and college wage premiums across 170 metropoli- primary employment—a measure that includes inde- tan areas. The principal approach follows the constant- pendent contractors, on-call workers, temporary help elasticity-of-substitution (CES) methodology of Katz agency workers, and workers provided by contract firms and Murphy (1992). The use of the CES method allows (Katz and Krueger 2019). The OEWS data provides wage estimates for roughly 800 occupations and 415 industries. Prior to 1996, the OEWS program collected only occupational employment data for selected industries in each year of the three-year survey 2 cycle and produced only industry-specific estimates of occupational employ - The Bureau of Economic Analysis industry groupings generally follow the ment. The 1996 survey round was the first year that the OEWS program North American Industry Classification System, better known as NAICS. The began collecting occupational employment and wage data in every state. services industry is a general grouping of occupations and services for dispa- rate industries such as hotel and lodging, legal services, and health care. Such an attempt is similar in nature to Black et al. (2009), Moretti (2013), and Lindley and Machin (2014). 2 Page 4 of 25 A. Eisenbarth , Z. F. Chen us to estimate the elasticity of substitution between Section 3, we review the pertinent literature. Section 4 workers with diverse levels of education; in our case, describes our empirical approach to estimating residual the estimated slope of demand for more educated work- wage inequality and discusses the data. Section 5 gives ers relative to less educated workers across metropolitan our primary ordinary least squares (OLS) and two-stage areas. The estimate can then be used to assess the extent least squares 2SLS estimates utilizing the Katz-Murphy to which changes in the college wage premium are due to model that we use to interpret relative wage data and a shift in relative demand. evaluates the ability of simple demand shift stories to Our instrumental variables analysis finds that the explain the observed patterns of changes in relative fac- elasticity of substitution between college graduates and tor prices and supplies at the metropolitan level. Sec- high school workers ranges from 2.11 for a pooled sam- tion 6 incorporates the elasticity estimates derived from ple (both men and women), 1.65 for men, and 2.87 for the 2SLS estimation as well as estimated wage percen- women. These estimates are within the range obtained tiles, to study the impact that the increase in demand for at the aggregate national level by Autor et al. (2008). skilled labor have on the wage structure in metropolitan For full-time, full-year (FTFY) workers, the estimates areas. And finally, Section 7 provides a conclusion of our are 2.12, 1.60, and 3.26 for a pooled sample, men, and findings. women respectively. We find that the implied elasticity of substitution is negatively related to metropolitan size, 2 Differences across metropolitan areas with smaller metropolitan areas having larger elasticities. Specifically, metropolitan areas are defined by the U.S. With our estimates of implied demand, we document Office of Management and Budget (OMB) as an urban - that demand for college graduates is negatively related ized area with at least a minimum population of 50,000 to manufacturing employment as might be predicted by inhabitants within one or more counties. Through the a model that is developed by Autor et al. (2003), lending use of these large areas, we are provided with large popu- some credence to the labor market “polarization” hypoth- lations to draw upon to mitigate measurement issues that esis. But we also show that implied demand for college arise with the use of observational data, specifically in graduates is strongly correlated with what Gordon (1990, our case coverage error. 1994, 1996) referred to as “managerial intensity” or the Table 1 reports the characteristics of metropolitan ratio of managerial and supervisory employees to pro- areas with the highest concentration of college graduates duction employees. in the 25-to-65-year-old workforce and compares them With our elasticity estimates we construct a labor against those with the lowest proportion of college grad- demand index for college graduates to explore how much uates. In 1980, the start of our considered time period, the increase in the demand for skilled labor have led to an the MSA with the highest college population in its work- increase in wage inequality across metropolitan areas in the force was Ann Arbor, Michigan, which had a college pop- United States. Our results confirm at the metropolitan level ulation of 38.3%. Ann Abor, Michigan is approximately Gordon’s thesis regarding the growth in managerial employ- three times larger than the MSA with the lowest college ment and its relation to wage inequality. We find that met - population, Ocala, Florida, which had a college popula- ropolitan areas with higher densities of managerial intensity tion share of 9.9%. experienced differential increases in wage inequality. On A standard variance decomposition is a common average, changes in managerial intensity between 1980 and approach to assessing the quantitative contributions 2019 account for 6.9% of the change in wage inequality as of observable and unobservable components of wage measured by the residual variance. Furthermore, managerial dispersion to changes in overall wage inequality. This intensity is strongly correlated with implied demand shifts approach starts with a standard wage equation, suggesting that a phenomenon of “reskilling” among mana- W = X β + ϕ , it it t it (1) gerial and supervisory employees with managerial employ- ees earning college degrees. We offer an interpretation of where W is the log wage of individual i in year t, X is a it it our results that combines the empirical findings of the labor vector of observed individual characteristics (e.g., experi- market polarization literature with the theoretical concep- ence and education), β is the vector of estimated returns tions of labor process theory and Gordon’s labor control to observable characteristics in t, and ϕ is the log wage it thesis. Our paper contributes to the growing literature that residual (which depends on the prices and quantities of casts doubt on the contribution of technology to both the unobserved skills, measurement error, and estimation polarization process and increase in wage inequality (Bea- error). The orthogonality of the predicted values and the udry et al. 2016; Salvatori 2018). We begin in Section 2 by outlining the conceptual These estimates are for full-time, full-year workers, not currently enrolled in framework that motivates our empirical analysis. In school, between the ages of 25 and 65 years old. The evolution of wage inequality within local U.S. labor markets Page 5 of 25 2 Table 1 MSAs with the largest and smallest shares of college graduates. Source: Census 5 Percent Samples for 1980, 1990, and 2000. American Community Survey 2005–2019 Level in 1980 Change from 1980 to 2019 College College Wage Change Change Change population premium inequality in college in college in wage population premium inequality MSAs with the largest college population in 1980 Ann Arbor, MI 38.3 28.6 36.1 15.5 24.8 14.6 Washington D.C. 35.3 49.4 40.4 15.4 17.2 14.6 Champaign-Urbana-Rantoul, IL 31.6 28.9 36.2 14 16.5 6.6 Austin, TX 30.8 44.3 36.4 10.9 34.2 16.2 Gainesville, FL 30.3 44.1 35.8 12.3 12.8 11.6 Fort Collins-Loveland, CO 29.8 35.0 37.9 15.4 22.5 8.8 Raleigh-Durham, NC 28.5 42.7 33.5 15.4 19.1 17.9 Denver-Boulder, CO 28.2 41.7 38.9 13.9 17.7 11.2 San Jose, CA 28.2 47.9 38.6 21.3 31 25 San Francisco-Oakland-Vallejo, CA 27.5 36.7 40.2 18.1 10 18.6 MSAs with the smallest college population in 1980 Ocala, FL 9.9 38.1 38.6 7 46.3 3.2 Brownsville-Harlingen-San Benito, TX 10.4 44.3 38.3 6.8 24.8 8.2 Visalia-Tulare-Porterville, CA 10.9 48.4 41.2 2.9 20.8 4.5 Saginaw-Bay City-Midland, MI 11.1 28.8 35.7 10.8 28.5 4.3 Scranton-Wilkes-Barre, PA 11.3 40.3 30.8 15.5 25.5 5.3 Youngstown-Warren, OH 11.4 27.8 36.6 10.6 21.4 0.9 Joplin, MO 11.4 39.7 33.6 10.3 29.3 4.7 McAllen-Edinburg-Pharr-Mission, TX 11.8 46.3 42.1 6.1 24.8 3.0 Yakima, WA 12.2 30.4 41.5 2.7 42.8 – 2.0 Lakeland-Winterhaven, FL 12.6 44.9 37.7 3.8 43.2 – 0.2 The college population share is defined as the share of the total working population not enrolled in school between the ages of 25 and 65 years old, who have a college degree or more. The change in the college population is the change in the working population share of college graduates between 1980 and 2019. The change in wage inequality is the change in wage inequality between 1980 and 2019 measured as the variance of log real weekly earnings of all workers 18 to 65 years old. All rates are multiplied by 100 residuals in an Ordinary Least Squares (OLS) regression Metropolitan areas in the top panel (those with high implies the variance of can be written as, shares of college graduates) of Table 1, tended to have it larger increases in wage dispersion than those in the bot- Var(W ) = Var(X β ) + Var(ϕ ) it it t it (2) tom panel. This assessment is summarized in Fig. 2 (plot a) where the college employment share in 1980 is on The variance of log wages can be decomposed into two the x-axis and the change in the residual variance from components: a component measuring the contribution 1980 and 2019 is plotted on the y-axis. Likewise, plot b of observable prices and quantities and the residual vari- of Fig. 2 depicts an increasing concentration of college ance (a component measuring the effect of unobserva - graduates in metropolitan areas with prior higher shares bles). The first component Var(X β ) , is often referred it t of college graduates. In the plots, the size of the bubbles to between-group inequality, and the second, Var(ϕ ) the it reflects the metropolitan area’s population in 1980, which residual variance, is referred to as within-group inequal- further shows (plot b of Fig. 2) that college graduates ity. We extend this approach to the metropolitan areas in tend to locate themselves in larger metropolitan areas. our sample, focusing on the residual variance. These spatial patterns have been noted by Moretti (2013), A shortcoming of a reliance only on this approach is that the variance may among others. not be the only inequality measure of interest especially given the sensitivity of the variance to changes in the tails of the distribution. For this reason, other Summarized estimates for the variance and residual measures such as the standard deviation and the log p(90)–p(10) wage differ - variance of log hourly wages are reported in Table 2, ential are sometimes used. A disadvantage of moving away from the variance which also provides summary statistics on the aver and examining other measures of inequality, such as quantile measures like the log p(90)–p(10) differential, is that these alternative measures typically do age employment share of college educated workers as not uniquely decompose into between and within components. 2 Page 6 of 25 A. Eisenbarth , Z. F. Chen Fig. 2 Patterns of spatial persistence: 1980–2019. Bubble size reflects population size in 1980. Fitted regression lines are fit by ordinary least squares Source: Census 5 Percent Samples for 1980, 1990, and 2000. American Community Survey 2005–2019 goes hand in hand with the increasing concentration of Table 2 Wage dispersion, Summary statistics. Source: Census college graduates within larger metropolitan areas, as 5 Percent Samples for 1980, 1990, and 2000. American Community Survey 2005–2019 seen in Table 1. Although all MSAs experienced increases in the college College Managerial Employment Variance Residual wage premium, some MSAs experienced considerably premium intensity share variance less growth in the college wage premium and change in 1980 41.2 17.6 22.0 39.1 21.9 hour shares of college graduates. Among these Augusta, (8.0) (1.45) (4.65) (3.81) (3.27) Daytona, El Paso, Elkhart, Gulfport, Hartford, Lafayette, 1990 56.1 19.4 26.0 39.1 20.6 and Monroe experienced growth in the college wage pre- (7.0) (1.65) (5.83) (3.21) (2.18) mium below 5% from 1980 to 2019; this was well below 2000 62.3 20.0 29.0 42.3 24.7 (9.00) (1.91) (7.19) (4.67) (2.92) the average increase of 20% (Table 1). Figures 2 and 3 2010 62.1 20.1 32.0 50.3 27.0 reveal both a high degree of persistence and an increase (8.0) (1.88) (7.51) (5.72) (3.48) in the relative demand for college educated workers. 2019 63.2 20.8 34.0 55.3 29.7 And yet these patterns vary across metropolitan areas (10.0) (2.09) (8.76) (7.06) (3.85) as evidenced by the increase in the standard deviations This table shows summary statistics for the MSAs in our sample regarding (Table 2). The same holds for the college wage premium. college educated employment. The employment share of college educated workers is similarly defined for employment: it is the ratio of all 18 to 65 years Black et al. (2009) note that, at a point in time, there are old college educated workers to all currently employed persons between 18 substantial spatial differences in the college wage pre - and 65 years old. Managerial intensity is the ratio of managerial and supervisory mium: in their specific case, cross-sections of 1980, 1990, employees to non-supervisory employees for the private, non-farm sector. The delineation of managerial and supervisory employees were established through and 2000 census years. We find similar results. Census occupation codes. Lastly, the college premium is the relative real hourly Different forces may be responsible for the increase in wage of college educated workers to non-college educated workers. Standard deviations reported below in parentheses. All rates are multiplied by 100 relative demand of skilled workers, especially the trans- formation of the economy brought on by the computer revolution of the 1980s (Krueger 1993). Another possible a share of total employment for all workers within the explanation for the increase in the relative demand for sampled MSAs. It also provides information on the aver- skilled workers is a positive shock to the product demand age employment of college graduates within the sampled MSAs. The increasing trend in the college wage premium The evolution of wage inequality within local U.S. labor markets Page 7 of 25 2 Fig. 3 College Wage Premiums: 1980, 1990, 2000, 2010, 2019. Bubble size reflects population size in 1980. Fitted regression lines are fit by ordinary least squares Source: Census 5 Percent Samples for 1980, 1990, and 2000. American Community Survey 2005–2019 faced by industries that employ relatively more skilled in the United States and beyond. But the development workers and are agglomerated in certain cities. For exam- has not been steady. From the end of World War II to ple, the demand for financial services have increased sig - the late 1970s, the relative supply of college workers rose nificantly within the last several decades (Beaudry et al. robustly and steadily, with each cohort of workers enter- 2010). By the same token, it is more than reasonable to ing the labor market boasting a proportionately higher infer that wage inequality has increased in cities where rate of college education than the cohorts immediately specific industries no longer have the presence they once preceding (Goldin and Katz 2007). did: several studies have explored this aspect, for exam- Reversing this pattern, the rate of growth of college ple, Leonardi (2015) and Baum-Snow et al. (2018). workers declined in the early 1980s, with the falling rela- Skilled workers, alternatively, may move to certain cit- tive supply of college graduates (skill workers) and the ies because the relative supply of skilled labor increases in adoption and development of new technologies; the those cities, as skilled workers are enticed by local ameni- conditions were favorable for returns to skill (the college ties. One can assume that amenities are fixed, but the premium) to increase (Acemoglu and Autor 2011). The taste for those amenities may increase (Diamond 2016), core of the argument is traced to Tinbergen (1974) idea or both amenities and tastes can be fixed. Amenities, that new technologies require more skilled workers and however, are considered normal goods, so that college hence, the introduction of new technology leads to a con- graduates are more likely to consume more of it relative tinual demand for more skills. to high school graduates (Gyourko et al. 2013). Moreover, college-educated laborers often seek out One of the most prevalent narratives in the academic employment that is clerical, administrative, or techni- literature posits that in the past 40 years, technological cal, hoping to employ the skills they have acquired from advancement and the increase in educational attainment their university training. Globalization has been an ongo- brought about changes in the relative demand and supply ing process for the past two decades. As manufacturing 2 Page 8 of 25 A. Eisenbarth , Z. F. Chen jobs are off-shored to developing countries with relaxed growth in the demand for occupations involving “cog- labor laws, manufacturing employment in formerly nitive” tasks and a reduction in the demand for more vibrant industrial metropolitan areas is in decline. The middle-wage routine occupations. The Routine Biased inter-competition between U.S. laborers with foreign Technological Change (RBTC) hypothesis claims that laborers has allowed the global firms to create disincen - growth in employment in both the highest-skilled (pro- tives to organize and form labor unions (Bivens 2013). As fessional and managerial) and lowest-skilled (personal labor unions become scarce in the U.S., the influence of services) occupations, with declining employment in the unions as a political vehicle for collective bargaining has middle of the distribution (manufacturing and routine deteriorated due to the competitive dynamics of global office jobs), make a process of what Goos and Manning capitalism. (2007) call “polarization.” The central idea of the RBTC is that technological 2.1 Theoretical context improvements, whether through the adoption of machine An extensive literature contends that the pronounced learning, robotics, automation, have made it possible to rise in wage inequality in the United States and other replace workers performing routine tasks by machines. advanced nations commencing in the 1980s results from The substitution or displacement of workers is driven by Skill Biased Technological Change (SBTC). The theoreti - the declining price of computer capital. Importantly, the cal cornerstone of this literature is what Acemoglu and labor-capital substitution in favor of computer or tech- Autor (2011) refer to as the “canonical model,” which nological capital reduces the relative demand of labor in features two distinct skill groups—most often, college middle-wage occupations due to the increasing ability and high school workers—performing two distinct and of machines to perform routine tasks, which character- imperfectly substitutable occupations or producing two ize these occupations (Acemoglu 2002a; Autor and Dorn imperfectly substitutable goods. Conceptually simple, 2013). the canonical model has been the workhorse model for Technology, of course, is only one factor that can affect many empirical studies and assumes that technology is the demand for college workers; others include interna- factor-augmenting, complementing either high or low- tional trade, outsourcing, and consumer demand pat- skill workers. terns. The notion that technology is a relentless force Following studies brought forward limitations to the creating demand for higher skills is contradicted by SBTC contention. Autor et al. (2008) looked at changes research in other fields. A dominant view of technol - in the distribution of wages and concluded that increas- ogy, in sociology, for instance, is that technology is often ing employment in higher-skill jobs and decreasing designed precisely to reduce skill requirements rather employment in lower-skill jobs in the 1980s explain than the reverse. The technology associated with scien - rising wages in the former and falling wages in the lat- tific management, such as assembly lines, reduces aver - ter. But in the 1990s, employment in low-skill jobs also age skill requirements, increases the supply of labor that increased. Acemoglu and Autor (2011) updated these could perform most jobs, and lowers wages in the pro- analyses to the present and found that the college wage cess. Technological adoption also reduced the control premium remained relatively steady in the 2000s despite and discretionary effort that workers could exercise in a slowdown in the relative supply of college graduates those jobs (Braverman 1974). Additional studies have compared to high school graduates. They infer that the also strongly suggested that employer choices determine increase in the relative demand for college graduates whether skill requirements rise or fall for different work - therefore also slowed down. ers (Zicklin 1987). Several of the studies stressing the limitations of the Indeed, a growing body of literature has come to cast SBTC narrative proposed a new hypothesis, blending doubt on the extent of technology as the primary driver together the results of Autor et al. (2003), Goos and Man- of labor polarization. Beaudry et al. (2014) argue that the ning (2007), and Autor et al. (2008), which contends that demand for higher-skill jobs that require college degrees the years following the 1980s have witnessed a substantial is actually declining and that college graduates are forced to look to jobs that require less skill. Subsequently, they displace applicants without a college degree, who then fare worse than before. In an extension of their work, Influential studies papers by Bound and Johnson (1992), Katz and Murphy (1992), and Juhn et al. (1993) argued that the surge of inequality in the 1980s Beaudry et al. (2016) contend that the IT revolution and reflected an ongoing, secular rise in the demand for skill that accelerated dur - its “de-skilling” process can be seen as a “General Pur- ing the 1980s with the introduction of personal computers and advances in pose Technology,” which will eventually reach maturity if information technology (Krueger 1993). The model proposed by Katz and Murphy (1992) is held by Acemoglu and Autor (2011) to be the canonical it has not already. They propose that this maturation pro - model. See Autor and Katz (1999) for an exhaustive review of the early litera- cess has been coming into effect since 2000. In a similar ture and Acemoglu and Autor (2011) for a more recent evaluation. The evolution of wage inequality within local U.S. labor markets Page 9 of 25 2 vein, Salvatori (2018) finds that the increase in the educa - While a full recapitulation is unnecessary, a review of tional attainment of the workforce is likely to have con- the Bowles–Gintis model’s main elements is fruitful to tributed significantly to the most prominent feature of elucidate this argument. In the Bowles–Gintis model, the polarization process in the U.K. supervisory inputs are necessary to monitor both the While technological change and its effects on the skill intensity of labor services provided by production work- requirements has been much explored in the literature, ers and the effectiveness of monitoring activities by a relatively unexplored dimension has been capital-labor their immediate supervisor. Wage incentives elicit labor relations. Monumental changes occurred in the 1980s, effort only if complemented by supervision; if workers with firms more intensely discouraging organized labor are not observed in their work, given conflicts of inter - and collective bargain agreements (see for instance, Free- est between employers and production employees, they man and Kleiner 1990; Bronfenbrenner 2000). Subse- would have no incentive to increase their labor effort quently, labor unions have become less influential in even in return for a higher wage. In its simplest formula- the collective bargaining process in the U.S (Farber et al. tions, labor effort e is a function of an efficiency wage w 2020). The 1980s also saw a revolution in corporate gov - (the cost of job loss) and some level of supervision s, ernance and management ideology popularly termed the ∂ι ∂ι “Shareholder Revolution.” While popular business views e = ι(w , s), > 0, > 0 (3) ∂w ∂s espoused downsizing, rather than reducing total labor costs as a share of business income (i.e., redirecting cor- By assumption the only input into supervision is super- porate income from workers and managers to sharehold- visory labor, and hence cost minimization (profit maxi - ers), the primary effect of prototypical shareholder value mization) by the ideal firm involves choosing the wage w strategies was to transfer labor income from production and level of supervision s that minimize the cost of a unit workers to managers (Goldstein 2012). of labor input l. The firm chooses the optimal intensity Working within the context of the so-called labor dis- of supervision which satisfies the first-order conditions ∗ ∗ cipline or Bowles-Gintis model of the efficiency wage ι /ι = ξ , where ξ is the hourly cost of a supervisory s w model, Gordon (1990, 1994, 1996) first proposed that input or the supervisory wage (see Bowles 1985 for the patterns in wage inequality could be explained through full derivation). the combination of factors relating to the regulation of The extraction of work effort is considered to be sep - worker effort in the United States. Referencing the great arable from the rest of the production process. In this institutional changes in the labor market that took place case, firms set wages to minimize the ratio of hourly in the 1980s, Gordon (1996) suggests that theories such labor costs to hourly work effort. The equilibrium wage as the skills mismatch, SBTC, and labor market polari- generated by effort-regulation models will generally zation theories for rising wage inequality in the U.S. are exceed the market-clearing wage; equilibrium will there- unpersuasive. fore be characterized by persistent, involuntary unem- Gordon highlights two trends that occurred in the ployment, which serves as an additional regulating device 1980s: (1) the stagnant growth in real wages and (2) for workers. an increasing number of managerial and supervisory A functional expression for the determinants of super- employees who experienced increases in their earnings. visory intensity is Gordon (1996) suggests the two are related, arguing that s = s(w , ξ , Z), (4) stagnant real wages create a need for more intensive managerial supervision to ensure that workers are prop- where Z is a vector of other factors affecting the labor erly monitored and carry out assigned tasks. These man - effort function. It is easy to see that in the event of a fall agers and supervisors are then deferentially compensated in the cost of job loss, corporations and firms hire more based on their seniority, relative position in the pro- managerial and supervisory employees to compensate for duction process, and complexity of the labor tasks they the decline in the cost of job loss. oversee. Other factors, however, may play an important factor in determining the level of effort workers provide and The “shirking” model of the efficiency wage paradigm most often refers to empirical studies have utilized union density, job finding the model presented by Shapiro and Stiglitz (1984) and is often referred to as the Shapiro–Stiglitz model whereas the “labor discipline” or “labor extrac- tion” model is that presented by Bowles (1985). It is perhaps more accurate to refer to the model developed by Bowles as the Bowles–Gintis model, for many The relationship between the worker and the firm is conceptualized as of the precepts of Bowles’ model are developed by Gintis (1976) and further a classic principle-agent problem. Employers and workers have a conflict of refined by Bowles and Gintis (1977). For a detailed review of the efficiency interest in the production process in the specific sense that the employer’s wage literature consult Katz (1986) or Akerlof and Yellen (1987). interests (as measured by profits) are enhanced by being able to compel the worker to act in the interest of the employer. 2 Page 10 of 25 A. Eisenbarth , Z. F. Chen probability, the unemployment rate, quit rate, and occu- terms “cognitive” or “abstract” occupations who consist pational complexity as mitigating factors (see for exam- mainly of managers, professionals, and technical workers ple, Rebitzer 1987; Gordon 1990; Green and Weisskopf and are seen as complementary to information technol- 1990; Green and McIntosh 1998; Fallick et al. 2006). ogy (IT) capital and the organizational forms that go with it; (2) middle-skill or “routine” task occupations, which 3 Literature are mainly done by production and clerical workers, who Several influential papers by Bound and Johnson (1992), are seen as easily replaced by the new technology; and (3) Katz and Murphy (1992), and Juhn et al. (1993) argued low-skill or “manual” task occupations, which are laborer that the surge of inequality in the 1980s reflected an and service type occupations, which, although they do ongoing, secular rise in the demand for skill that com- require low-skill, are not easily substituted for with IT menced decades earlier and accelerated during the capital (Acemoglu and Autor 2011). 1980s with the introduction of personal computers and While the RBTC hypothesis, introduced by Autor et al. advances in information technology (see Krueger 1993; (2003), has replaced SBTC as the most conventional Beaudry et al. 2010). When this secular demand shift met approach to explain changes in the labor market struc- with an abrupt slowdown in the growth of the relative ture induced by technological change, unresolved issues supply of college-equivalent workers during the 1980s— persist. Empirical work, particularly, has been limited in itself a consequence of slowing educational attainment its ability to dissect the distinction between skills in its for cohorts born after 1949 and of smaller entering classification methodology. For example, what consti - labor force cohorts—wage differentials expanded rapidly tutes a “cognitive” or “abstract” task is neither clearly nor (see Autor et al. 1998; Card and DiNardo 2001; Goldin consistently defined. The definition of “routine” tasks is and Katz 2007). The relative supply of college gradu - also problematic. Driving an automobile is widely consid- ates then continued to rise without the college premium ered a non-routine task. Although it involves repetition declining as a result; this was taken as evidence of a shift of core elements and might be considered monotonous in technology biasing demand toward more skilled or (routine from the worker’s perspective), it also requires educated workers. Together, these papers encapsulate the use of skills that human beings have a comparative the core of the Skill Biased Technological Change (SBTC) advantage when compared with technology. argument established early in the literature. Perhaps the major drawback of the RBTC approach is Autor et al. (2003), Goos and Manning (2007), Autor the lack of a unified scheme for data analysis, which has et al. (2008), and Autor and Dorn (2013) contend that the authors using different data sources and classifying tasks years following the 1980s have witnessed a substantial based on the information available in the survey they growth in the demand for occupations involving “cog- use. This creates additional difficulties when interpreting nitive” tasks and a reduction in the demand for more and comparing the results across studies. For example, middle-wage routine occupations. The Routine Biased “managerial tasks” are included in the abstract or cogni- Technological Change (RBTC) hypothesis claims that tive category. While it seems reasonable to assume that growth in employment in both the highest-skilled (pro- cognitive effort is required to perform managerial tasks, fessional and managerial) and lowest-skilled (personal the precise identification of what are managerial tasks in services) occupations, with declining employment in each time and place depends on the social organization the middle of the distribution (manufacturing and rou- of work. The same can be said about “quality control” as tine office jobs), entail a process of “polarization” into an indicator of routine work and tasks. Quality control which the labor force is bifurcated into low and high-skill might be routine and repetitive in traditional production occupations. line jobs that involve mostly manual work and basic tasks From the five set of tasks originally set forth by Autor with machines, but not necessarily in other activities. et al. (2003), the RBTC hypothesis divides workers into Autor (2013) suggests that future research can benefit three categories; (1) high-skill or what the literature from using a task-based approach to further investigate the job polarization trends in industrialized economies Technology is neither specified nor measured directly in typical SBTC stud - ies, rather it is assumed to be an attribute of the economy that is ever increas- ing and often proxied by a simple time trend. Computer use or adoption is a A conventional approach is to “merge” job task requirements from the favorite illustration of such technology (see for instance, Krueger 1993; Autor Fourth Edition of the US Department of Labor’s Dictionary of Occupational et al. 1998). Autor et al. (2003) look directly at the effect of computer use on Titles (DOT) first published in 1977 and its 1991 Revised Edition to existing skill requirements and found that it increased higher-skill, non-routine tasks Census occupation classifications to measure routine, abstract, and manual while reducing lower-skill, routine tasks, also consistent with a SBTC view. task content by occupation. The reliance on the 1977 DOT job requirements is questionable especially given the 50 year span since its publication. The evolution of wage inequality within local U.S. labor markets Page 11 of 25 2 and how to resolve measurement errors. Expanding on in labor market wage inequality in the United States. Autor’s task-based approach, Salvatori (2018) finds that Moretti finds that changes in real wage inequality the sizable increase in university graduates in the U.K. between college-educated workers and non-college edu- is the main contributing factor in the “polarization” over cated workers have grown less in real terms than it has the last three decades rather than technology, a finding in nominal terms; but more importantly, Moretti finds consistent with Beaudry et al. (2016). that increased housing costs for college-educated work- Several studies have addressed the question as to ers relative to less skilled offsets gains in utility from the whether skill requirements at the workplace have been increase college wage premium between 1980 and 2000. increasing and if these changes are associated with tech- Lindley and Machin, studying both MSAs and states nological change (for instance, Howell and Wolff 1992; between 1980 and 2010, find that MSAs and states that Autor et al. 2003; and Autor and Dorn 2013). The litera - experienced greater growth in computer use and research ture recognizes that there are a variety of measures to cat- and development (R&D) intensity–measured as the share egorize skill levels across different industries as opposed of state gross domestic product–also experienced greater to the single measure based on education attainment for increases in the relative demand for college-educated workers. Howell and Wolff (1991) and Howell and Wolff workers. (1992) contend increases in skill requirements appears to In the second part of the regression analysis, we study be inversely related to the growing rate of investment in how changes in the industry mix of metropolitan areas information technologies; they find their results linked to affect the local wage structure via the increase in the the deskilling of production workers and to the growing log variance of real hourly wages. The most common shares of managerial and supervisory employees. Autor approach in the literature is to include variables measur- and Dorn (2013) offer a unified analysis of growth in low- ing overall employment or unemployment rates and the skill service occupations between 1980 and 2005 using share of employment in various industries, particularly Census data. Their results are generally supportive of the manufacturing (durable and non-durable goods sepa- “routinization” hypothesis (put forward by Autor et al. rately), in an equation exploring the determinants of area (2003)), which suggests that the effect of technological wage or income inequality. This is the approach done progress is to replace “routine” labor of clerical and craft by Karoly and Klerman (1994), who examine wage ine- jobs in the middle of the wage distribution. quality in groups of states between 1973 and 1988. They A relatively unaddressed question has been the role of find that the variance of log wages was lower in states heterogeneity for both firms and workers across spatial with a larger fraction of employment in manufactur- dimensions. Moretti (2013) and Lindley and Machin ing, although the result was not robust for the inclusion (2014) are among the few studies on spatial differences of state fixed-effects. Cloutier (1997) adopts a similar approach in examining family income inequality in met- ropolitan areas in 1979 and 1989; she finds evidence of lower levels of inequality in areas with higher shares of The task based approach suggests using three feasible methods to address manufacturing employment. the measurement problem: (1) “use occupations as proxies for job tasks” by aggregating many exhaustive occupations into a few broad categories, such Black et al. (2014) provide a detailed evaluation of wage as production or managerial, as most occupation schemes are hierarchical by inequality across 21 metropolitan areas in the U.S. for col- design; (2) employing a “task categorization step” to reduce the role of sub- lege graduates relative to high school graduates of similar jectivity with descriptors obtained in the DOT and Occupational Information Network (O*NET); and (3) directly “collect job task information directly from age groups. Their results, however, are confined to a nar - survey respondents alongside other demographic, employment, and wage row range (21) of MSAs and a sample of workers (white- data” (Autor 2013) 13 non-Hispanic males). Diamond (2016) uses a static discrete Salvatori (2018) uses datasets from the U.K. Data Archive (NESPD) con- sisting of the Labour Force Survey (LFS), New Earnings Survey (NES, 1979– choice model allowing for workers to have heterogeneous 2002), Annual Survey of Hours and Earnings (ASHE) to investigate the preferences for cities. She provides empirical evidence that U.K. labor composition changes for the 1979-2012 period. Salvatori (2018) college and high school graduates between 1980–2000 updates Goos and Manning (2007) with a longer period and incorporates Autor’s task-based approach to account for measurement problems. increasingly choose to live in different cities because of Howell and Wolff (1991) use direct measures of job-skill requirements endogenous amenities within high-skilled cities. Changes from the U.S. Department of Labor’s Dictionary of Occupational Titles in rent, wages, and local amenities further exacerbate wage (DOT) to examine the effects of changing occupational and industry differences between college graduates versus high school employment patterns on the skill composition. While they find an increase in the demand for cognitive skills, they also find a substantial slowdown in the rates of growth of those skills. Howell and Wolff (1992) suggest that structural differences in production during the 1960s–1980s resulted in firms increasing their demand for cognitive skills during this transition The role of heterogeneity has also been explored by Card et al. (2013) who period. But more importantly, they also find that the growth in the skill find that changes in occupation content from 1985 to 2009 in West Germany measures do not appear to be continuous; there is little correlation between and increasing heterogeneity between workers generated a rise in wage ine- skill growth in the 1960s and skill growth since 1970. quality. 2 Page 12 of 25 A. Eisenbarth , Z. F. Chen graduates in cities spanning three decades. Like Diamond, aggregating the samples of men and women together. Farrokhi and Jinkins (2019) use a discrete choice model to These data are then sorted into sex-education-experi - put forward evidence that there is a relationship between ence groups of two sexes, five education categories (high city size and wage inequality across U.S. cities. They show school dropout, high school graduates, some college, col- that 16.5% of the observed variation in skill wage premium lege graduates, and advanced degree), and eight potential is a result of the cities’ geographic location, although their experience categories (0–5, 5–10, 10–15, 15–20, 20–25, estimates are confined to the 2000 Census year. 25–30, 30–35, and 35–40 years). Log hourly wages of Hershbein and Kahn (2018) adopt the RBTC approach to full-time, full-year workers are regressed in each year a panel of 381 metropolitan areas from 2005 to 2015 to test separately by sex on dummy variables for five education whether skill requirements increased in the aftermath of categories, a quartic in experience, three region dum- the Great Recession. Using online job posting data collected mies, black and other race dummies, and interactions of by Burning Glass Technologies, they adopt the methodol- the experience quartic with three broad education cat- ogy of Acemoglu and Autor (2011) to distinguish “routine- egories (high school graduates, some college, and col- cognitive” occupations from “routine-manual.” They find lege plus). The (composition-adjusted) mean log wage for that the skill requirements of jobs via job ads increased in each of the forty groups in a given year is the predicted MSAs that suffered larger employment shocks in the Great log wage from these regressions. Mean log wages in each Recession, relative to the same areas before the shock and year represent weighted averages of the relevant (compo- other areas that experienced smaller shocks. The upskill - sition-adjusted) cell means using a fixed set of weights, ing of these occupations make them more palatable to equal to the mean share of total hours worked by each higher-skilled workers. They argue that their results clarify group over the period of 1980–2019. the results of Beaudry et al. (2016) and indicate that “cogni- We use a standard measure of college/non-college rela- tive workers” are being drawn into (formerly) routine-task tive supply calculated in “efficiency units” to adjust for occupations as the skill content of occupations evolve. changes in labor force composition. In common with most approaches on the subject, we broaden the col- 4 Data lege category to include college graduates and those To study changes in local labor market inequality, we use with advanced degrees. Specifically, the labor supply for data from the decennial U.S. Census for the years 1980, college/high school groups by experience level is calcu- 1990, and 2000 drawn from the 5 Percent amples; and for lated using efficiency units, equal to mean labor supply 2005 to 2019, we make use of data from the American for broad college (including college graduates and greater Community Survey (ACS). These data are downloaded than college) and high school (including high school from the Integrated Public Use Microdata Series (IPUMS) dropouts and high school graduates) categories, weighted website directed by the University of Minnesota (Rug- by fixed relative average wage weights for each cell. The gles et al. 2021). The spatial unit of observation is standard labor supply of the “some college” category is allocated metropolitan statistical areas (MSAs), which are regions equally between the broad college and high school cat- consisting of a large urban core together with surround- egories. The fixed set of wage weights for 1980–2019 are ing communities that have a high degree of economic and constructed using the average wage in each of the groups social integration with the urban core. (six overall samples, four education groups, and eight For all of our samples, we consider only the non-farm, experience groups) over this period. private sector. We draw a sample of full-time, full-year We instrument relative supply with the log ratio of sup- (FTFY) workers, here defined, in common with Autor plements to wages and salaries (benefits) and the Fred - et al. (2008), as those who worked 35 h or more in a week, die Mac House Price Index (FMHPI). Data for benefits and worked for at least 40 weeks, and were between the come from the BEA regional accounts (Table CAINC30), age of 25 and 50 years old. We draw samples for both which includes actual employer contributions and actu- men and women separately as well as a pooled sample, arially imputed employer contributions to reflect ben - efits accrued by defined benefit pension plan participants through service to employers in the current period and employer contributions to government social insurance. The FMHPI provides a measure of typical price inflation Since 1950, the Bureau of the Budget (later renamed the Office of Manage - ment and Budget, or OMB), has produced and continually updated standard delineations of metropolitan areas for the U.S., defining each area as a county or a set of contiguous counties, or, for New England prior to 2003, as a set of cities or towns. These delineations were consistent for most of the following census years until the significant revision of metropolitan delineations in 2013 This provides us with six total samples: an aggregated broad sample, a by the OMB. broad sample of men and women and similarly for FTFY workers. The evolution of wage inequality within local U.S. labor markets Page 13 of 25 2 for houses within the U.S. from the national level to state mathematical”) occupations. We focus on these two and metropolitan level. occupations, in particular, to complement our estimates We focus on four inequality concepts: changes in over- for the demand of skilled labor (college graduates). For all wage inequality, summarized by the log p(95)-p(10) institutional data, we use data from Hirsch and Macpher- wage differential and the log variance of composition- son (2003), which provides time-consistent national and adjusted wages; changes in inequality in the upper and state-level estimates of union density for the years 1964 lower halves of the wage distribution, summarized by the through 2018. We combine these with state minimum log p(95)-p(50) and log p(50)-p(10) wage gaps (“upper” wage laws to build a data set with relevant institutional and “lower” tail inequality), and between-group wage dif- factors taken into consideration. ferentials, illustrated using the college/high school wage premium. We gather data from the Bureau of Economic 5 Skilled labor demand estimates Analysis’ (BEA) Regional Accounts tables to generate In this section, we draw upon the canonical Katz and employment share by industry. Specifically, we use data Murphy model (Katz and Murphy 1992) supply and from the Economic Profile, Table CAINC30 and Total demand to see if there are differential relative demand Full-Time and Part-Time Employment by Industry, Table shifts by MSA. The canonical model posits two skill CAEMP25. These two tables provide us with data on the groups high and low. It draws no distinction between employment level of an MSA, its income, its population, skills and occupations (tasks), so that high-skill work- among other relevant information. ers effectively work in separate occupations (perform We use the May data from the Bureau of Labor Sta- different tasks) from low-skill workers. In most empiri - tistics (BLS) Occupational and Employment Statistics cal applications of the canonical model, it is convenient (OES) or Occupational Employment and Wage Statistics to identify high-skill workers with college graduates H (OEWS) program, which is a semiannual survey designed and low-skill workers with high school graduates L. A to produce estimates of employment and wages for spe- crucial element to the two-factor model is that high and cific occupations, for the years 2000 and 2005 to 2019. low-skill workers are imperfect substitutes in production. When these data are not available, we turn to our Cen- The total supplies of aggregate low and high-skill inputs sus sample and use the occupational codes provided to production are, for each MSA i in time t, respectively: by IPUMS to produce estimates for occupations. Combining the two sources, we obtain estimates for L = l n d it j j j (5) j ∈ ϕ employment in finance and technology (“computer and and H = h n d , it j j j (6) j ∈ ζ where l or h reflect the efficiency units (or human capi - Freddie Mac publishes the monthly index values of the Freddie Mac House j j Price Index (FMHPI) each quarter. Index values are available for the nation, tal) supplied each hour by low and high-skill labor. Spe- the 50 states, the District of Columbia, and the more than 380 metropolitan cifically, each low-skill worker j ∈ ϕ has l efficiency units statistical areas (MSAs) in the United States. The primary differences between of low-skill labor and each high-skill worker j ∈ ζ has h the FMHPI and other indices are the inclusion of some appraisal values used j for refinance transactions, the choice of geographic weights, the method for units of high-skill labor. identifying outliers, and the use of statistical smoothing to estimate indices more efficiently at finer geographic levels. The OEWS program collects data on wage and salary workers in non- farm establishments to produce employment and wage estimates for about 800 occupations. Data from self-employed persons are not collected and The IPUMS occupation code (OCC2010) is a harmonized occupation cod - are not included in the estimates. The OES program surveys approximately ing scheme based on the Census Bureau’s 2010 ACS occupation classification 180,000 to 200,000 establishments per panel (every 6 months), taking 3 scheme. The 2010 occupation coding scheme for OCC has 493 categories. years to fully collect the sample of 1.1 million establishments. In the interest of harmonization, however, the scheme has been modified to These data are not available at the MSA level prior to 1997. Prior to that achieve the most consistent categories across time. We match these categories year, the OEWS program collected only occupational employment data for to the 480 occupational categories in the OEWS data. selected industries in each year of its three-year survey cycle, and produced Two sources of data are combined to produce these estimates, the only industry-specific estimates of occupational employment. The 1996 Current Population Survey (CPS) and the discontinued Bureau of Labor survey round was the first year that the OEWS program began collecting Statistics publication, the Directory of National Unions and Employee Asso- occupational employment and wage data in every state. In addition, the pro- ciations, which is drawn on data reported by labor unions to the govern- gram’s three-year survey cycle was modified to collect data from all covered ment. industries each year. 1997 is the earliest year available for which the OEWS program produced estimates of cross-industry as well as industry-specific As the Katz-Murphy model is a fairly well known model, we derive only occupational employment and wages. Hence, for the 1990 and 1980 Census, the essential formulations of the model, conforming to the metropolitan we use the IPUMS occupation codes OCC2010. level. 2 Page 14 of 25 A. Eisenbarth , Z. F. Chen The starting point is a CES production function, where spatial level, so that we can construct a measure of output Y is produced by the two skill groups implied relative demand at the spatial level. We can rear- range the previous equation and reintroduce subscripts σ−1 σ−1 σ−1 σ to reach, σ σ (7) Y = φL + ψH , it it it H w it H it D = ln + σ ln , it (12) with parameters φ and ψ reflecting technology constants L w it L it that determine the productivity of low and high-skill where spatial relative demand is the relative supply plus labor inputs. σ ∈[0, ∞] is the elasticity of substitution the product of the elasticity of substitution and the rela- between the two education groups. tive wage. Factor-augmenting technical change is captured by We employ a Two Stage Least Squares (2SLS) estimation changes over time in φ and ψ . Assuming that each MSA approach where we instrument relative supply. Ciccone and has a perfectly competitive labor market, equation (7) Peri (2005) use data from Acemoglu and Angrist (2000) on can be solved for the ratio of the marginal of the two school-attendance and child-labor laws to create instruments kinds of labor, yielding the relationship between rela- for the relative supply of educated workers. In a similar way, tive wages in year t. Ignoring subscripts i and t, com- Lindley and Machin (2014) use state female college enroll- bining the derivatives, and taking the natural log yields ment and state 18-year-old population size as instruments. σ − 1 ψ 1 H We instrument relative supply with the log ratio of supple- ln ω = ln − ln (8) σ φ σ L ments to wages and salaries (benefits) and the Freddie Mac House Price Index (FMHPI). Data for benefits come from This equation shows that there is a simple log linear rela - the BEA Regional Data, Economic Profile CAINC30) table, tionship between the skill premium ω and the relative which includes actual employer contributions and actuarially supply of skills as measured by , specifically that, L imputed employer contributions to reflect benefits accrued by defined benefit pension plan participants through service ∂ ln ω 1 = − < 0 to employers in the current period and employer contribu- (9) ∂ ln σ tions to government social insurance. The FMHPI provides a measure of typical price inflation for houses within the U.S. An increase in the relative supply of skills reduces the 1 from the national level to state and metropolitan level. skill premium with an elasticity of . Intuitively, when We hypothesize that both the level of benefits and the high and low-skill workers are producing the same good state of the local housing market are strong motivating but performing different functions, an increase in the forces for the area that college graduates decide to reside number of high-skill workers will necessitate a substitu- upon graduating. To the discerning worker, the log ratio of tion of high-skill workers for the functions previously the benefits level to housing prices (the FMHPI) signals the performed by low-skill workers. affordability of an area, and hence, is generally indicative of Rearranging (8) allows us to obtain the relative an area’s standard of living. Firms, likewise, take into con- demand function: sideration whether to increase or scale down labor demand H ψ w college graduates due to the associated costs incurred ln = (σ − 1) ln − σ ln (10) through additional wages supplements. Since supplements L φ w to wages and salaries are primarily driven by national which can be further simplified to reach, changes in tax policies and group health insurance poli- cies in the U.S., they should be unrelated to changes in local w 1 H ln = D − ln , productivity. Workers, furthermore, are heterogeneous in (11) w σ L how much they desire the various non-market amenities ψ offered across metropolitan areas (Diamond 2016). These where D = ln indexes relative demand shifts favor- local non-market amenities may include, for example, the ing college educated workers, measured in log units. The MSA’s proximity to a coastline, climate, and so forth, which impact of changes in relative skill supplies on relative are exogenous factors that makes the metropolitan area dif- wages depends inversely upon the magnitude of the elas- ferent. These local non-market amenities can also include ticity of substitution between skilled and unskilled work- how generous are the social insurance programs in the ers; the greater the value of σ , the smaller are the impacts metropolitan area, the quality of the MSA’s public infra- of relative supply shifts on relative wages, and, conse- structure, crime rates, pollution, and so on. quently the greater must be changes in relative demand. For our purposes, we would like an estimate of σ at the The evolution of wage inequality within local U.S. labor markets Page 15 of 25 2 Table 3 First stage regressions, elasticity estimates, 1980–2019, pooled years Source: Census 5 Percent Samples for 1980, 1990, and 2000. American Community Survey 2005–2019. Freddie Mac, Freddie Mac Housing Price Index (FMHPI). Bureau of economic analysis, regional data, economic profile (CAINC30) (1) (2) (3) (4) (5) (6) ∗∗ ∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ log(benefits/FMHPI) 0.173 0.131 0.247 0.155 0.109 0.259 (0.045) (0.036) (0.064) (0.036) (0.028) (0.060) 0.29 0.25 0.29 0.29 0.24 0.29 Adjusted R ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ F-test 14.84 13.18 14.83 18.26 14.83 18.46 ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ AR Wald test 15.51 15.81 15.02 17.19 19.62 17.14 The dependent variable of columns (1)–(6) is the relative supply of college graduates in efficiency units. All models include time and MSA fixed-effects. Clustered robust standard errors reported in parentheses. F-test denotes the Stock–Yogo F statistic. Asterisks (*), (**), and (***) denote statistical significance at the 10, 5, and 1% levels respectively. Each regression utilizes a sample size of 3060 observations across 170 MSAs in 18 time periods To be able to estimate the second stage of equation the error process, and they are sufficiently correlated (12), we need to specify the demand term in some way. with the included endogenous variables. Our choice of To do this, let Y be our dependent variable (the college instruments appear to be strong instruments as indicated it premium) and let A be a function of α , an MSA fixed- by the first stage regressions represented in Table 3. it i effect, a year effect , and an error term specific to each The Staiger and Stock rule of thumb test is not robust MSA v . The estimating equation then becomes: to weak instruments. To further check against this poten- it tial dilemma, we rely on the Anderson-Rubin (AR) test Y = A + X β + ǫ , it it it it (13) robust inference for testing the significance of the endog - enous regressors in the structural equation being esti- where ǫ = u + ν . it i it mated (Anderson and Rubin 1949). The null hypothesis tested is that the coefficients of the endogenous regres - The year effects are specified in a general manner, sors in the structural equation are jointly equal to zero, using a set of year dummy variables, so that the estimat- and, in addition, that the overidentifying restrictions are ing equation expresses the relative wage of skilled work- valid. The test is robust to the presence of weak instru - ers as a function of time, the MSA effect, and relative ments and is equivalent to estimating the reduced form supply X for each MSA. of the equation (with the full set of instruments as regres- The first stage regression is then, sors) and testing that the coefficients of the excluded X = α + + Z γ + u instruments are jointly equal to zero. In all cases, we (14) it i t it it reject the null hypothesis and conclude the instrument is The specification of an instrumental variables model not weak. asserts that the excluded instruments affect the depend - Column 1 of Table 4 shows estimates for the pooled ent variable only indirectly through their correlations sample of men and women, column 2 shows those esti- with the included endogenous variables. If an excluded mates for men only, and finally, column 3 display esti - instrument exerts both direct and indirect influences on 24 mates for women. The estimates indicate that the the dependent variable, the exclusion restriction should elasticity of substitution for the pooled sample (both men be rejected. With one endogenous variable, the F-statis- and women) is 2.11 , 1.65 for men, and 2.87 for 0.475 tic in the first stage regression, which Staiger and Stock women. These estimates are within the range of those (1997) suggest should be greater than 10: from our first obtained at the aggregate national level by Autor et al. stage results, we see that they appear to muster this (2008). For FTFY workers, the estimate are 2.12, 1.60, test. Furthermore, in an exactly identified model, as in and 3.26 for the pooled sample, men, and women respec- the present case, we cannot test the hypothesis that the tively. The elasticity estimates of Lindley and Machin instrument is valid, i.e. that the exclusion restriction is a (2014) differ from the estimates obtained here, which valid one. may have to do with their larger sample size and selection (in terms of number of metropolitan areas per year) as 5.1 Elasticity estimates well as with the composition adjustment they make to Estimates from 2SLS models (reported in Table 4) are wages sampled in their study. Our estimates are closer to weighted by the employment share of college graduates and estimated with clustered standard errors. Instru- mental variables methods rely on two assumptions: the excluded instruments are distributed independently of 24 Columns in the first stage regressions map to the same. 2 Page 16 of 25 A. Eisenbarth , Z. F. Chen Table 4 FE-2SLS elasticity estimates, 1980–2019, pooled years Source: Census 5 Percent Samples for 1980, 1990, and 2000. American Community Survey 2005–2019 Pooled FTFY FTFY Men FTFY Women Full Pooled Full Men Full Women (1) (2) (3) (4) (5) (6) ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ Relative supply − − − − − − 0.471 0.626 0.307 0.475 0.605 0.349 (0.024) (0.050) (0.013) (0.022) (0.042) (0.013) Adjusted R 0.76 0.60 0.74 0.78 0.64 0.74 Dependent variable is the log of the composition adjusted college–high school wage differential. The log ratio of supplements to wages and salaries and the Freddie Mac Housing Price Index (FMHPI) is used as an instrument for relative supply. All models estimated with MSA and year fixed-effects. Estimates are weighted by inverse sampling variance. Standard errors are in parentheses. Asterisks (*), (**), and (***) denote statistical significance at the 10, 5, and 1% levels respectively those obtained by Fortin (2006), who estimated σ to ∇D gives the average change in relative demand for col- it range from 4.39 and 5.68 for a state level sample of work- lege workers across all MSAs for the given time periods. ers between the ages of 26 and 35 from 1979 to 2002. This can be estimated with the regression equation: As noted by Autor et al. (2008), the Katz-Murphy model D = a + ζ D + η , it i, t−1 it (16) does an excellent job forecasting the growth of the col- lege wage premium, but the continued slow growth of which is a general OLS equation with a as the intercept, relative supply after 1990 leads it to slightly over-predict ζ the parameter of interest, η an error term. D is the it i, t−1 the growth in the college wage premium in the 2000s. lagged demand index ( t − 1 ) of equation (15) for MSA i. We estimate this equation for each period t following 5.2 L ocal area labor demand 1980; thus, we estimate for the period 1980–1990, 1990– We are now able to combine the spatial changes in the col- 2000, 2000–2010, and lastly for the period 2010–2019. lege wage premium and relative supply into an implied rel- Table 5 reports these estimates and compares the aver- ative demand index using the estimates of σ . Recall earlier age of our estimates of σ with those obtained by Fortin that A was specified to be some function of α , an MSA it i (2006) and Autor et al. (2008). These estimates show that fixed-effect, a year effect , and an error term specific to the results are comparable with varying estimates of σ . each MSA v . it Furthermore, given that our estimates of relative demand This can be written as: depend on our elasticities of substitution, which in turn depend on the validity of our instruments, these compar- D = φ + σθ it isons check for the robustness of our results. where φ is the relative supply of college educated work- Compared with the 1980s the relative demand for college ers to high school educated workers and θ is the relative graduates has increased across all time periods although wage (wage premium) of college educated workers. Com- these changes get smaller over time. The first row in Table 5 puting this index reveals substantial differences in relative shows these for our estimated σ values and reveals that put- demand for college educated workers across metropolitan ting together the relative supply and relative wage measures areas but also reveals persistence in relative demand for to compute this demand index in this way produces a pat- college educated workers in certain metropolitan areas. tern of highly persistent relative demand shifts at the spatial Table 5 compares the estimates for different values of σ level. The persistence is especially strong in the 1990–2000 from regressions on the relative demand shifts for the time and 2010–2019 periods, where the estimate is greater than 1. periods 1980–1990, 1990–2000, 2000–2010, and 2010– 2019. To further see how the relative demand for college workers changed within each decade, we may write: 5.3 Shifts in demand and supply Combining our estimates of σ with the data, we present how relative demand and supply varied by gender in the ∇D = (D − D ) it it it−1 (15) considered time period. These estimates are presented in i=1 Table 6. The tabulated statistics show that, among FTFY workers, men fared better in terms of relative wage growth during the early part of the considered period (1980 to Empirical studies adopting Katz and Murphy’s model have found similar estimates of the elasticity of substitution: Ciccone and Peri (2005) 1.5 using 2000). Table 6 also shows that demand for skilled labor has a sample of white men between 40 and 50 years of age, Autor et al. (2008) cooled since the early part of the period: across all major obtain 1.57 for full-time-full-year workers, and Lindley and Machin (2014) groups, relative demand was notably smaller in magnitude 2.94 for MSAs. The evolution of wage inequality within local U.S. labor markets Page 17 of 25 2 Table 5 Spatial–temporal dependence in relative demand Source: Census 5 Percent Samples for 1980, 1990, and 2000. American Community Survey 2005–2019 Estimates of ζ from D = a + ζ D + η it i, t−1 it 1990–1980 2000–1990 2010–2000 2019–2010 Eisenbarth-Chen estimates, σˆ = 4.15 0.843*** 1.108*** 0.869*** 1.103*** (0.021) (0.033) (0.027) (0.027) Autor et al. (2008), σˆ = 2.40 0.841*** 1.109*** 0.870*** 1.102*** (0.021) (0.033) (0.027) (0.027) Fortin (2006), σˆ = 5.68 0.842*** 1.113*** 0.869*** 1.109*** (0.020) (0.033) (0.027) (0.026) The dependent variable is the implied relative demand shift log and the explanatory variable is the implied relative demand shift in the previous decade t − 1 . Presented author estimates an average of estimates of the elasticity of substitution as described in text. Standard errors are reported in parentheses beneath the estimates. Asterisks (*, **, ***) denote statistical significance at the 10, 5, and 1% levels after 2010 as compared with earlier. This may be due in Table 6 Changes in relative demand, supply, and earnings part to the sluggish recovery following the Great Reces- Source: Census 5 Percent Samples for 1980, 1990, and 2000. sion. In particular, the shift in the Beveridge curve and the American Community Survey 2005–2019 shock to the hiring rate undoubtedly factors in largely. Bar- 1980–1990 1990–2000 2000–2010 2010–2019 nichon et al. (2012) find that the Beveridge curve did shift for the United States after the Great Recession in 2009 and Pooled that the shift was caused by a decline in hires per vacancy Demand 8.5 8.4 13.5 0.1 expected at the relevant level of unemployment. Relative wage 17.9 8.2 10.7 0.8 To see more clearly the differences in relative demand Supply 2.7 5.7 10.0 0.4 for college workers, we present figures to show the spa - Men tial distribution of the demand shift measure: these Demand 8.1 9.8 12.6 0.4 show that the relative demand shift has strongly favored Relative wage 18.9 10.2 7.9 5.0 college workers, but also, these shifts tend to favor larger Supply 0.2 5.5 9.3 2.5 MSAs (see Fig. 4). The plots display remarkable spatial Women persistence in relative demand for college graduates Demand 5.6 5.2 11.3 0.5 in larger metropolitan areas. In particular, MSAs that Relative wage 16.5 5.5 14.4 4.4 have high and persistent demand for college educated Supply 1.9 4.0 8.1 1.5 workers are MSAs such as San Jose, Boston, San Fran- Tabulated numbers are changes in the (composition-adjusted) mean log wage cisco, Washington D.C., and New York (see Table 1). for each group, using data on full-time, full-year workers ages 18 to 18 covering 1980 to 2019. These data are sorted into sex-education-experience groups These areas are well known for exhibiting agglomeration of two sexes, four education categories (high school dropout, high school effects through the clustering of certain industries: soft - graduate, some college, college graduate, and post-college), and eight potential ware and computer technology, for example, in San Jose. experience year groups (0–5, 5–10, 10–15, 15–20, 20–25, 25–30, 30–35, and 35–40 all measured in potential years of experience). Log hourly wages of full- In contrast, MSAs that experienced lower shifts in time, full-year workers are regressed in each year separately by sex on dummy demand for skilled labor tended to have higher manu- variables for four education categories, a quadratic in experience, three region dummies, black and other race dummies, and interactions of the experience facturing employment in 1980 (the start of our sample). quadratic with three broad education categories (high school graduate, some Elkhart-Goshen, Indiana; Mansfield, Ohio; Hickory, college, and college plus) North Carolina; and Lancaster, Reading, and York-Hano- ver of Pennsylvania are MSAs that were heavily concen- demand shifts for college graduates. These areas are nota - trated in manufacturing and tended to experience lower bly in the Rust Belt region of the U.S., the plight of which following de-industrialization has been widely docu- 26 27 Davis et al. (2012) also find fewer hires than expected in the period since mented, both in academic literature and popular media. recovery from the Great Recession officially began. They also find evidence of Other areas such as Brownsville-Harlingen, Texas, considerable variation across employers in their ability, or inclination rather, Visalia-Porterville, California, and Yakima, Washington to fill vacancies. These results suggest that something about the manner in which firms are recruiting and selecting candidates may explain why vacan - also experienced lower demand shifts. cies last longer. This is related to the findings of Molloy et al. (2016) who sug - gest that the U.S. has experienced a decline in labor market “fluidity”—an index they compile from transitions into and out of employment and job-to- job transitions, job creation and job destruction rates, and interstate migra- Since the term “Rust Belt” is used to refer to a set of economic and social tion—which has decreased by 10% to 15%, by their estimates, since the 1980s. conditions rather than to an overall geographical region of the United States, the Rust Belt has no precise boundaries. 2 Page 18 of 25 A. Eisenbarth , Z. F. Chen Fig. 4 Implied demand shifts, 1980, 1990, 2000, 2010, 2019. Bubble size reflects population size in 1980. Fitted regression lines are fit by ordinary least squares Source: Census 5 Percent Samples for 1980, 1990, and 2000. American Community Survey 2005–2019 5.4 S killed labor demand correlates specialization. With respect to manufacturing employment, We can further relate our estimates of implied demand to labor demand for college graduates appears to have a mark- variables that may influence the demand of college gradu - edly negative linear relationship as seen in Fig. 5d. ates, these include the proportion of workers covered by col- In the approximate forty-year period we study, increases lective bargaining agreements (union density), the minimum in relative demand were faster in MSAs with higher degrees wage, manufacturing employment, and managerial intensity of managerial intensity and where employment in techni- or the proportion of the workforce employed in managerial cal occupations is more intensive. At the same time, MSAs and supervisory positions. We also check the relationship where manufacturing has fallen by more have also seen between implied demand and employment in finance and slower demand shifts in favor of more educated workers. technical occupations. From the standpoint of the simple Such patterns appear to be akin to the predictions of the Katz-Murphy model, skilled labor demand should be highly model presented by Autor and Dorn (2013). Union density correlated with increases in these two occupational catego- and the minimum wage appear to have little effect on the ries. We plot these relationships (Fig. 5a–f) allowing us to demand of skilled workers: the smoothed line is nearly hori- visually inspect how institutional and labor market forces zontal when considering union coverage and only has a slight are related to changes in relative demand for college gradu- upward bent when considering the minimum wage. These ates. Implied demand estimates are strongly associated with managerial intensity, technology, and financial occupation Their model predicts that labor markets historically specialized in routine task-intensive industries should: (1) differentially adopt computer technology We obtain estimates for these occupations using a combination of the and displace workers from routine task-intensive occupations; (2) undergo IPUMS OCC2010 occupation code and the OEWS occupation codes. The employment polarization as low-skill labor is reallocated to low-task-intensive OEWS codes are adopted from the Standard Occupational Classification in-person services; (3) exhibit larger wage growth at both ends of the occu- (SOC) system. Technical occupations are defined by the detailed OEWS codes pational skill distribution (wage polarization); and (4) experience larger net in the range of 15–1000 to 15–2098. We similarly defined finance occupations inflows of workers with both high and low educational levels driven by rising as being in the range of 13–2000 to 13–2098 for “Financial Specialists.” demand for both. The evolution of wage inequality within local U.S. labor markets Page 19 of 25 2 Fig. 5 Correlates of skilled labor demand: 1980–2019, Pooled. Bubble size reflects population size in 1980. Fitted regression lines are fit by ordinary least squares. All rates are long-term rates of change (averages) Source: Census 5 Percent Samples for 1980, 1990, and 2000. American Community Survey 2005–2019 patterns appear to suggest that institutional factors have little and let A be a measure of unobserved components, we it influence on the demand for skilled workers. have a standard fixed-effects model, Y = D + γ + ζM + X β + u , (17) it i t it it it 6 Local area wage inequality Using the IPUMS data, we calculate measures of wage where u is assumed to be iid over i and t, and ζ is the it inequality and various measures of labor force composi- effect of interest. tion for each of the local areas that are included in our The parameter D captures unobserved heterogene- sample for the 1980–2019 period. In particular, we are ity among the metropolitan areas and γ a vector of time interested in the effect of managerial intensity M on wage dummies; the unobserved individual effects are coef - inequality. Our causal assumption regarding managerial ficients on dummies for each individual MSA while the intensity is related fundamentally to the efficiency wage year effects are coefficients on time dummies. Through model discussed earlier. More specifically, our causal this treatment, we can estimate the causal effect of mana - assumptions align more with the Bowles–Gintis version gerial intensity on residual wage inequality. of the efficiency wage model (see for example, Rebitzer The model assumes that Y is a function of exogenous it 1987; Green and Weisskopf 1990) rather than the Shap- factors, X , while the conventional analysis of variance it iro–Stiglitz interpretation. In which case, an increase in (ANOVA) model stipulates that the expected value of Y it managerial intensity should lead to an increase in wage dispersion. It is perhaps more appropriate to call models of this sort an Unobserved To address this question, let Y be the observed value it Effects Model (UEM) in line with Wooldridge (2002) since the treatment of for wage inequality for MSA i in time t. Suppose that the whether the effects are “fixed” or “random” lies more in how the researcher effects of managerial intensity are additive and constant views how the unobserved components affect Y (Angrist and Pischke 2009). it 2 Page 20 of 25 A. Eisenbarth , Z. F. Chen depends only on the MSA (or “group”), i, to which the obser- MSA level from the Hirsch and Machperson database. vation considered belongs and that the value of the meas- From our demand index construction, we include the ured quantity, Y , assumes the relation that Y = α + ǫ , estimated demand shifts for each MSA. And lastly, we it it i it where the effects of all other characteristics, ǫ , are random use publicly available state minimum wage laws to con- it and are in no way dependent on the individual-specific struct a variable (the ratio of the state minimum wage to effects, α . But if Y is also affected by other variables that we the estimated average hourly wage at the MSA level) to i it are not able to control and standardize within-groups, the capture the effect of the minimum wage. within-group sum of squares will be an overestimate of the stochastic component in Y . Consequently, the differences 6.1 Results it between-group means will reflect not only any group effect Our estimates are reported in Table 7. Column 1 reports but also the effects of any differences in the values assumed the baseline OLS estimates, Columns 2 and 3 reports fixed- by the uncontrolled variables in different groups (Hsiao effects estimates. Our preferred estimates are the fixed- 2014). effects estimates in the third column. We reduce the model We fit specifications to this general form using the log by culling independent variables that are not statistically sig- residual variance of composition-adjusted hourly wages as nificant within acceptable confidence intervals; this provides the dependent variable Y . Our baseline model is a pooled a reduced model of 5 independent variables. it OLS model, where we regress wage inequality against union The effect of the main variable of interest, managerial density, manufacturing employment, managerial intensity, intensity, is both positive and statistically significant at the and estimated labor demand for college graduates. Addition- 5% level in all model specifications. Similarly, the estimates ally, we include dummy variables for regional specialization for technology occupations (computer and mathematical), in finance and technology occupations, and a dummy varia - are positive and statistically significant in all specifications. ble for any MSA where the immigrant labor share is equal or Along these estimates, it is interesting to note the statistically greater than 20%. To account for heterogeneity, we estimate insignificant effect of the skilled labor demand index and models using clustered robust standard errors. Failure to the specialization of finance occupations. On the whole, this control for within-cluster error correlation can lead to mis- seems to support the predictions of Gordon ’s extension of leadingly small standard errors, and consequently misleading the Bowles–Gintis model. confidence intervals, large t -statistics and low p-values. The effect of manufacturing employment is estimated to To account for agglomeration effects through regional be negative and statistically significant, suggesting that wage clustering of the finance and technology industries, we esti - inequality tends to be lower in areas with denser manufac- mate the location quotient (LQ) for our sample of MSAs for turing intensity. The estimate for the immigrant share is pos - these occupations. We limit our estimation of location LQs itive and statistically significant. A plausible reason for the for regional specialization to technology and finance. We positive coefficient for the immigrant share of employment construct dummy variables based upon the LQ coefficient’s is that immigrants to the U.S. typically possess much lower value where the dummy is equal to 1 if the LQ coefficient is educational attainment levels than native-born citizens. greater than 1 and 0 otherwise; this provides a categorical And furthermore, they are more likely to work in low-wage, variable where “1” indicates regional specialization. low-skill occupations than native-born citizens. Although We include the share of total employment in durable the presence of immigrants may put downward pressure on goods manufacturing and in non-durable goods manu- low-skilled citizens wages, we caution against this interpreta- facturing, expecting to find that larger shares of both tion given that the effects of immigration are mixed (see for types of manufacturing are associated with lower ine- instance, LaLonde and Topel 1991; Ottaviano and Peri 2012). quality. Managerial intensity is the ratio of managerial We can calculate how much a one standard deviation and supervisory employees to non-supervisory employ- increase in our independent variables of the reduced model ees for the private, non-farm sector for each MSA. The can account for using clustered robust standard errors. The β σ(X ) i i delineation of managerial and supervisory employees equation used for this is , wher e x is understood to be σ(Y ) were established through Census occupation codes in the ˆ the independent variable i, and β the estimated coefficient, line of Gordon (1994). We expect to find a positive rela - and Y the residual wage dispersion measured by the log vari- tionship between managerial intensity and inequality. We ance of the composition adjusted wages. The ranges of mag - include the union coverage rate at first at the MSA level nitudes within a 95% confidence interval that emerge from and the state level where this data is not available at the the reduced model are: managerial intensity, 0.35% to 10.5%; The Hirsch–Machpherson estimates are not available at the metropolitan e E 31 ij j The location quotient is \ where e is total employment in industry or level before 1986. Furthermore, estimates are not consistently available for all ij e E occupation j in region i, e total employment in region i, and E and E, their metropolitan areas. Further details are available at the Union Membe rship i ij equivalents at the national level.and Cover age Datab ase (Union stats. com). The evolution of wage inequality within local U.S. labor markets Page 21 of 25 2 Table 7 Determinants of wage dispersion, pooled years Source: six potential factors connected to inequality. Present- Census 5 Percent Samples for 1980, 1990, and 2000. American ing the empirical associations in this form enables us to Community Survey 2005–2019. Union Membership and see which MSAs are the most and least correlated with Coverage Database, State and Metropolitan Estimates 1980– these factors. Of the metropolitan areas we consider, the 2019. Occupational Employment and Wage Statistics 2000–2019. Bridgeport-Stamford-Norwalk metropolitan area has U.S. Department of Labor, State Minimum Wage Laws, Historical the largest long-run increase in residual wage inequal- Tables. Bureau of Economic Analysis, Regional Data, Total Full- ity, followed closely by New-York-Newark-Jersey City, Time and Part-Time Employment by Industry (CAEMP25), Santa-Cruz-Watsonville, San-Jose-Sunnyvale, and San- Economic Profile (CAINC30) Francisco-Oakland. Conversely, Sheboygan, Wausau, and Pooled OLS Fixed-effects Fixed effects Eau-Claire (all of Wisconsin), Mansfield, Ohio and John - (reduced stown, Pennsylvania had the lowest long-run increase in model) wage inequality. (1) (2) (3) The areas which saw the largest increases in wage ine - ∗∗∗ ∗∗∗ ∗∗∗ Manufacturing − − − 0.071 0.082 0.089 quality tend to have: (1) deeper managerial intensity ratios (0.042) (0.028) (0.027) (Fig. 6c); (2) a higher long-run shift in demand for college ∗∗∗ ∗∗ ∗∗∗ Managerial intensity 0.212 0.099 0.102 graduates (the proxy for skilled-labor) as shown in Fig. 6f; (3) (0.110) (0.030) (0.030) a larger long-run increase in technical occupations (Fig. 6e); Finance 0.002 0.036 and (4), tended to have lower levels of manufacturing (0.545) (0.134) employment (Fig. 6a). The long-run decline in union cover - ∗∗∗ ∗∗∗ ∗∗∗ Immigrant share 0.226 0.155 0.150 age appears to have little relationship with wage inequality; (0.031) (0.019) (0.027) the fitted line in Fig. 6b is approximately horizontal and this ∗∗∗ ∗∗ ∗∗∗ Technology is confirmed by our estimates in Table 7. This pattern is dif - 0.334 0.195 0.222 ficult to interpret but may be motivated by profound recent (0.086) (0.102) (0.097) ∗∗∗ changes in the composition of the unionized workforce as Union coverage − 0.018 0.050 reported by Card et al. (2018), who find that the impact of (0.027) (0.014) ∗∗∗ ∗ ∗∗ unions on wage inequality has declined due to the shifting Minimum wage − − − 0.175 0.016 0.131 composition of union jobs toward the public sector. Histori- (0.030) (0.010) (0.010) cally, union jobs were concentrated among low-skilled men ∗∗∗ Demand 0.010 0.071 in private sector industries, half of unionized workers are (0.008) (0.006) now in the public sector, the majority of which are women. ∗∗∗ Constant 0.292 Since our sample only considers the private sector, the pro- (0.029) found changes in the composition of union jobs is perhaps 0.59 0.61 0.60 Adjusted R the best explanation. And lastly, the minimum wage (Fig. 6d) F-Statistic 108.09 16.49 21.82 appears to possess the expected negative relationship with A total of n = 170 metropolitan statistical areas over t = 18 time periods. wage inequality as documented by Lee (1999) and Autor Samples include persons between the ages of 18 and 65 years old, currently et al. (2016), although this is not borne out by the results in employed and worked in the prior year. Wage inequality is measured as the log residual variance of real weekly earnings of all non-self-employed workers. Table 7. Clustered robust standard errors are reported beneath in parentheses. Critical F values depend on df(9; 170), df(8; 169), and df(8; 169) respectively. Asterisks (*, **, ***) denote statistical significance at the 10, 5, and 1% levels6.2 Alternative measures We extend these specifications (Table 8) to study the manufacturing employment, – 24.85% to – 6.13%; technol- impact of these factors on “lower” tail inequality meas- ogy occupations, 1.55% to 20.65%; immigrant workforce ured by the log p(50)–p(10) ratio, upper tail inequal- share 24% to 51%; and the minimum wage ratio – 6.15% to ity measured by the log p(95)–p(50) ratio, and overall 0.01%. inequality measured by the log p(95)–p(10) ratio. Addi- Figure 6 shows the spatial aspects of these empiri- tionally, we also consider the impact on between log cal connections between the MSA level wage inequal- ity measure and the variables we consider, by plotting Card et al. (2018) find striking differences between the private and pub - long-run 1980–2019 spatial wage inequality against lic sectors in the effects of unionization on male and female wage inequal - ity. These differences have become more pronounced over time as private The effect of the magnitudes are derived from the 95% confidence interval and private sector unionization have diverged. They estimate that the overall of the estimated slope coefficient for the variable of interest, constructed by effects of unions on the economy-wide wage structure are modest in size– using the clustered robust standard errors. The interval estimation for the reductions in male wage inequality of 3.5% in the U.S. and female inequality ˆ ˆ ˆ ˆ estimated slope is then β ± t(β ) · s(β ) , where s(β ) is the clustered robust of 3.4%. Furthermore, disaggregating by sector of employment yields striking i i i i standard error of the estimated coefficient, and t(β ) the critical t-statistic. differences: reductions in male wage inequality in the private sector of 1.7% in the U.S. and female wage inequality by 0.6%. 2 Page 22 of 25 A. Eisenbarth , Z. F. Chen Fig. 6 Residual wage dispersion, key factors: 1980–2019, pooled. Bubble size reflects population size in 1980. Fitted regression lines are fit by ordinary least squares. All rates are long-term rates of change (averages) Source: Census 5 Percent Samples for 1980, 1990, and 2000. American Community Survey 2005–2019 ratio of the 95th and 90th percentile log p(95)–p(90). wage, similarly, is found to be statistically significant for We constrain our model specifications to “two-way” only the lower tail of the wage distribution and overall fixed-effects, with dummy variables for time and metro - distribution. Intuitively, this result is sensible due to the politan area. The slope estimates are broadly consistent fact that those at the upper percentiles are unlikely to be with those in the residual variance specifications. Labor adversely affected by the changes in the minimum wage. demand for college graduates is found to be statistically significant in all specifications at standard levels of confi -6.3 Limitations dence, except for the upper end (between the 95 and 90th The aim of fixed-effects is to mitigate the effects of unob - percentiles). servable attributes, particularly endogeneity caused by Based on these estimates and the actual changes in time. However, omitted variables such as the macro- managerial employment over the period 1980-2019, on economic conditions of the region could still potentially average, changes in managerial intensity account for 5% inflict omitted variable bias on our models. Additional and 9% of the changes in upper tail inequality (measured sources of confounding factors could stem from public by the log p(95)–p(50) and log p(95)–p(95)), 5.7% for the policy constraints prohibiting the building up of infra- lower tail, and 5.1% for the overall measure in local areas structure or cultural and social practices specific to the over this period. Comparing the results across the wage local labor market. For example, the Ivy League universi- distributions, we see that the effect of managerial inten - ties of the Northeast and the social networks associated sity is more pronounced at the upper end of the distri- with these elite institutions could influence hiring prac - bution. More importantly, the estimated coefficient for tices through network effects (Zimmerman 2019). the demand for skills is not statistically significant for Although they control for a certain type of omitted the gap between the log p(95)–p(90) ratios. It is interest- variable, fixed-effects estimates are notoriously suscepti - ing to note that union coverage is not statistically signifi - ble to attenuation bias from measurement error. On one cant in these specifications. The effect of the minimum hand, variables like managerial status tend to be persis- tent (a worker who is a manager this year is most likely The evolution of wage inequality within local U.S. labor markets Page 23 of 25 2 Table 8 Determinants of wage dispersion (percentiles), discrimination lawsuits, formed the basis of numerous pooled years Source: Census 5 Percent Samples for 1980, 1990, government reports, and made the term “glass ceiling” a and 2000. American Community Survey 2005–2019. Union popular term. But this has limitations, as most managers Membership and Coverage Database, State and Metropolitan tend to be non-Hispanic white males, a historical pattern Estimates 1980–2019. Occupational Employment and Wage that strongly persists and which may, in fact, stem from Statistics 2000–2019. U.S. Department of Labor, State Minimum the longstanding, biased hiring decisions of firms within Wage Laws, Historical Tables. Bureau of Economic Analysis, the United States (see Stainback and Tomaskovic-Devey Regional Data, Total Full-Time and Part-Time Employment by 2009; Giuliano et al. 2009). Managerial employment, Industry (CAEMP25), Economic Profile (CAINC30) moreover, could potentially stem from an additional ln 50–10 ln 95–50 ln 95–10 ln 95–90 non-random process, as managers and supervisors are (1) (2) (3) (4) selected non-randomly from the population of workers. ∗∗∗ ∗∗∗ ∗∗∗ Individual choices made by workers, such as choice of Manufacturing 0.014 − − − 0.212 0.175 0.051 collegiate degree, can also affect the future employment (0.023) (0.047) (0.061) (0.022) prospects and access to supervisory roles. ∗∗ ∗∗ ∗∗ Managerial intensity 0.112* 0.201 0.336 0.194 Lastly, we are unable to interpret our estimates as (0.083) (0.100) (0.100) (0.070) strictly causal estimates of treatment effects. The aim of ∗∗∗ ∗∗∗ ∗∗∗ Immigrant share 0.002 0.029 0.035 0.081 standard statistical analysis, typified by regression, esti - (0.003) (0.004) (0.020) (0.002) mation, and hypothesis testing techniques, is to assess ∗∗ ∗∗ Finance 0.001 0.002 0.028 0.006 parameters of a distribution from samples drawn of that (0.006) (0.002) (0.003) (0.001) distribution. With the help of such parameters, one can ∗∗∗ ∗∗ Technology 0.001 − − 0.003 0.010 0.008 infer associations among variables, estimate beliefs or (0.003) (0.003) (0.004) (0.002) probabilities of past and future events, as well as update − − − Union coverage 0.013 0.013 0.000 0.018 those probabilities considering new evidence or new (0.027) (0.032) (0.040) (0.019) measurements. These tasks are managed well by stand - ∗∗∗ ∗∗∗ Minimum wage − 0.040 − 0.055 0.429 0.511 ard statistical analysis so long as experimental conditions (0.040) (0.020) (0.060) (0.025) remain the same. ∗∗∗ ∗∗ ∗ Demand 0.011 0.048 0.028 0.045 (0.011) (0.011) (0.014) (0.007) 7 Conclusion 0.43 0.79 0.87 0.43 Adjusted R Wage inequality has risen considerably since the 1980s, but ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ F Statistic (8; 170) there are also significant disparities with which it has grown 8.97 2.77 7.05 3.13 between local areas. Using data from the U.S. Census and A total of n = 170 metropolitan statistical areas over t = 18 time periods. Samples include persons between the ages of 18 and 65 years old, currently America Community Survey, we study several factors sur- employed and worked in the prior year. Clustered robust standard errors rounding local labor market inequality in 170 Metropoli- are reported beneath in parentheses. Asterisks (*, **, ***) denote statistical tan Statistical Areas (MSAs) between 1980 and 2019. One significance at the 10, 5, and 1% levels contribution has been to provide estimates of the elasticity of substitution between skilled and unskilled workers at the a manager next year). On the other hand, measurement metropolitan level. Our instrumental variables analysis finds error often changes from year-to-year (managerial status that the substitution of elasticity between college gradu- may be misreported or miscoded this year but not next ates and high school workers ranges from 2.11 for a pooled year). Therefore, while managerial and supervisory status sample (both men and women), 1.65 for men, and 2.87 for may be misreported or miscoded for only a few workers women. These estimates are comparable to those obtained at in any single year, the observed year-to-year changes may the aggregate national level by Autor et al. (2008). For full- be mostly noise. time, full-year (FTFY) workers, the estimates are 2.12, 1.60, A further element to consider is the potential endoge- and 3.26 for a pooled sample, men, and women respectively. neity of our factor of interest. Managerial intensity might Using fixed-effects models, we confirm David Gordon’s very well be increasing due to the increased integration thesis regarding wage inequality and managerial employ- of the workforce in terms of gender and race. Indeed, dif- ment. On average, changes in managerial intensity ferential access to managerial jobs is one of inequality’s linchpins, as these positions secure higher average wages A distribution function cannot tell us how that distribution would differ if external conditions were to change because the laws of probability theory do and other rewards for their incumbents than do other not dictate how one property of a distribution ought to change when another jobs. Besides spawning expansive literature, the ques- property is modified. This information must be provided by causal assump - tion of access to managerial jobs for protected groups tions which identify relationships that remain invariant when external con- ditions change: behind every causal conclusion there must lie some causal has also been the focus of countless gender and race assumption that is not testable in observational studies. 2 Page 24 of 25 A. Eisenbarth , Z. F. Chen References between 1980 and 2019 account for 6.9% of the change in Acemoglu, D.: Directed technical change. Rev. Econ. Stud. 69(4), 781–809 (2002) wage inequality as measured by the residual variance; this Acemoglu, D.: Technical change, inequality, and the labor market. J. Econ. Lit. effect is robust to alternative measures of wage inequality. 40(1), 7–72 (2002) Acemoglu, D., Angrist, J.: How large are human-capital externalities? 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Journal for Labour Market Research – Springer Journals
Published: Dec 1, 2022
Keywords: Wage inequality; Labor markets; Labor demand; B59; C33; J23; J31
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