Wage inequality, tasks and occupations

Transcription

1 Wage inequality, tasks and occupations Carol A. Scotese August 2012 Virginia Commonwealth University Abstract This paper shows that wage changes within occupations are quantitatively important for explaining changes in overall wage inequality and that an occupation's task content is related to within occupation wage changes. Physical tasks are associated with occupation wage declines predominantly in the middle/upper portion of the occupation wage distribution while cognitive or interpersonal tasks are associated with wage increases throughout the occupation wage distribution in the 1980s and in the upper portion of the distribution in the 1990s. These patterns help to explain overall wage inequality changes and suggest modications for existing task-based models of wage inequality. JEL classication: J31, E24, J24 Key words: Wage inequality, computerization, skill, tasks. Virginia Commonwealth University, Department of Economics, Richmond, VA

2 1 Introduction This paper will present evidence showing that within occupation wage changes are quantitatively important for explaining the increase in overall wage inequality between 1980 and 2000 and that occupation task content is a signicantly related to within occupation wage changes. Moreover, dierent occupational tasks (for example, physical tasks versus cognitive tasks) are associated with changes in dierent portions of the occupation wage distributions in a manner that helps to explain the change in overall wage inequality during the 1980s and 1990s. The results suggest that trends in the lower portion of the overall wage distribution are driven by changes in the wage structure of occupations intensive in physical tasks and may not be well explained by the dominant task-based (computerization) model of wage inequality. Also, given the importance of within occupation wage changes, the results also suggest that task-based models of wage inequality should aim to explain this feature of the data as well as explaining between occupation wage changes. Beginning with Autor, Levy, and Murnane (2003), studies have documented signicant shifts in occupational employment and task usage. According to their computerization hypothesis, demand for some routine tasks that are easily replaced by computerization decreased while demand for other non-routine cognitive and manual tasks that are not as easily replicated by computerization rose. 1 Since nonroutine manual tasks tend to be associated with occupations in the lower portion of the wage distribution while non-routine cognitive tasks tend to be linked to occupations in the upper portion of the wage distribution, the computerization hypothesis has been seminal for understanding and documenting the polarization of employment growth. However, the research relating occupational task content to wage inequality is relatively new and scarce. 2 Acemoglu and Autor (2011) show that in a typical 1 Routine tasks are those that are reproducible by computer coding. 2 There is an extensive literature that attempts to understand the increase in U.S. wage inequality in the last 30 years. The current emphasis on changing task demand arising from computerization and/or o-shoring has its origin in the skill-biased technological change hypothesis (see the surveys Acemoglu (2002), Hornstein, Krussel and Violante (2005) and Acemoglu and Autor (2011) and the 1

3 wage regression the explanatory power of occupation task measures is as large as the explanatory power of occupation dummies (using 10 occupation groups) and the power has doubled over the last three decades. However, with the exception of Firpo, Fortin and Lemieux (2011) (hereafter, FFL), there is very little empirical research that directly links occupation taskcontent to changes in the wage distribution. 3 FFL show that occupation task measures linked to computerization are associated with wage changes both between and within occupations during the 1990s. 4 Their data include 40 occupations at the 2- digit occupation code level. However, they do not address the question of whether within occupation wage changes have had a quantitative signicance for changes to the overall wage distribution. One major contribution of this study is to show that the quantitative importance of within occupation wage changes is equal to or larger than that of between occupation wage changes. Using decennial census data rather than CPS data, the larger sample size allows the analysis to be conducted at the 3-digit occupation code level encompassing 264 occupations for males and 183 occupations for females. At the 2-digit occupation level used in FFL, within occupation wage shifts could be generated by employment shifts between 3-digit occupations. Moreover, the results in this paper adjust for variations in the education and age composition of the workforce between periods and indicate that the polarization of employment growth alone cannot explain wage inequality changes. Establishing the quantitative importance of within occupation wage changes implies that if within occupation wage distribution shifts are related to occupation tasks, then task measures are an important element for understanding the rise in wage inequality. It also implies that models that seek to explain changes in the references therein). 3 Most evidence documents employment shifts linked to changing task demand, but does not directly link employment shifts to wage structure changes. Work documenting the polarization of employment growth includes Autor, Katz and Kearny (2006, 2008), Acemoglu and Autor (2011), Goos and Manning (2007) and Goos, Manning and Salomans (2009, 2011). 4 FFL also construct three additional task measures to measure the o-shorability of an occupation. Also see, e.g. Blinder (2007), Grossman and Rossi-Hansberg (2008) and Crino (2010) for studies relating task measures to trade or o-shoring. 2

4 wage distribution should account for both the within and between occupation wage patterns. 5 Therefore, a second major contribution of the paper is to detail the relationship between task measures and within occupation wage changes. First, a broad set of task measures is constructed using principal components analysis (PCA) on four subsets of the O*NET data. 6 The PCA produces task measures by grouping together occupation attributes to explain the maximum variance of the attributes across occupations. Two of this paper's task measures are similar to FFL's computerization-related task measures (routine/automated tasks and information content attributes). Other measures roughly divide into brains or brawn type tasks. The brains tasks can be sub-divided into those using more complex cognitive skills and those that require more moderate cognitive tasks. The brawn type measures span dierent types of physical tasks, including a subset of tasks related to working with equipment. Therefore, one can assess the importance of tasks that are directly aected by computerization (such as the ones used in FFL) relative to tasks that may be indirectly aected or relatively unaected by computerization. Importantly, the analysis is able to ascertain whether task measures are associated with wage changes throughout the occupation wage distribution or only with changes in the upper or lower portions of distribution. This latter point is important because, for example, if an occupation wage distribution compresses, it could driven by either wages in the upper portion of the distribution falling or by wages in the lower portion rising. These would suggest two very dierent wage dynamics and potentially different labor reallocation resulting from technological change. Therefore, this paper directly estimates the relationship between task measures and wages changes at the top, bottom and middle of the occupation wage distribution. 5 The existing task-based models such as Acemoglu and Autor (2011), Autor and Dorn (2012) and Goos, Manning and Salomons (2011) oer models of labor re-allocation across tasks. However, all of the models are silent on wage variance within occupations. 6 The Occupation Information Network (O*NET) is the more comprehensive successor to the Dictionary of Occupational Titles (DOT) classication. O*NET measures hundreds of occupation attributes relating to job requirements, tasks, and work environment. 3

5 The results show that occupations intensive in complex cognitive tasks experienced wage increases throughout the occupation wage distribution during the 1980s but wages increased only at the middle/top of the occupation wage distributions during the 1990s. On the other hand, occupations whose tasks are predominantly physical or associated with machinery and equipment work experienced wage declines in the middle and top of the occupation distribution during the 1980s while during the 1990s wages either stabilized or decreased at the very top of the occupation wage distribution. That is, there is a clear distinction in the wage dynamics between brains vs brawn intensive occupations. There is also a clear dierence in the relationship between task content and wage changes in the 1980s relative to the 1990s. Interestingly, the results show that wages in occupations that are highly automated and/or routine decreased throughout the occupation wage distribution during the 1980s, but then stabilized during the 1990s. While some results support the computerization hypothesis, several ndings raise questions not well answered by current versions of the computerization hypothesis. For example, according to the computerization hypothesis many types of physical work (e.g. installing equipment, construction, driving vehicles) are not easily replaceable by computers. Yet wages and in these occupations have fallen. Therefore, it is not clear that trends in the lower portion of the wage distribution are signicantly aected by computerization. More generally, the ndings have important insights for the impact of changing task demand for overall wage inequality. For occupations characterized by physical tasks and/or work with equipment, the upper portion of the occupation wage distribution was in the middle of the overall occupation distribution in Occupations intensive in cognitive tasks have wage distributions whose lower portions were also in the middle of the overall wage distribution in Therefore, the dierential pattern of within occupation wage inequality exhibited by these two occupation types would tend to spread out the entire wage distribution during the 4

6 1980s. During the 1990s most of the within occupation wage changes occur in the upper end of the occupation distributions, regardless of task content. Occupations intensive in cognitive tasks were associated with wage increases at the top of the occupation wage distribution and this contributed to the widening in upper portion of the overall wage distribution. Meanwhile the returns to physical work declined for those at the top of their occupation wage distribution (the middle of the overall wage distribution), also contributing to the increased spread at the top of the overall wage distribution and the compression of the lower portion of the overall wage distribution. That is, changes in the within occupation wage distribution related to task measures are consistent with the increased dispersion of the overall wage distribution in the 1980s, the increased inequality in the upper portion of the wage distribution and the compression in the lower portion of the wage distribution during the 1990s. In the remainder of the paper, section 2 discusses the data and details the construction of the task measures; section 3 documents the relative importance of within and between occupation wage changes for overall wage inequality; section 4 relates occupation wage structure changes and employment share changes to the occupation task measures; section 5 discusses the implications for the computerization hypothesis; section 6 concludes. 2 Data The wage and other individual level data come from the decennial census for the years 1980, 1990 and The sample selection criteria is consistent with other work on wage inequality and culls workers with more than a marginal labor force attachment. 7 Annual wage and salary data were divided by the product of usual hours worked per week and number of weeks worked to calculate an hourly wage rate. The census collects data on occupational aliation and I employ the codes 7 For example, FFL, Lemieux (2006) and Autor, Katz and Kearney (2008). See the data appendix for details on selection and data cleaning. 5

7 developed by Meyer and Osborne (2005) that recast each decennial year's occupation census code into their 1990 equivalents. For example, the information collected about the respondent's occupation in 1980 is used to determine which occupation the respondent would have been placed in under the 1990 rubric. To quantify the task intensity for each occupation I use four subsets of the O*NET data: (1) skill attributes from the work requirements section of the O*NET data, (2) ability attributes from the abilities sub-section of the worker characteristics section, (3) task attributes from the general work activities sub-section of the occupational requirements section and (4) work context attributes from the work context sub-section of the occupational requirements section. These are the relevant subsets of the data that measure the skills, actions, and tasks used in each occupation. Because each subset measures dozens of occupation attributes, using the data to parsimoniously quantify occupation characteristics can be cumbersome and/or subjective. 8 Some studies have used just a few attributes to measure a specic occupation characteristic. For example, FFL select ve attributes to measure routine manual tasks. Acemoglu and Autor (2011) select three attributes (2 are the same as FFL) and Autor, Levy and Murnane (2003) and Autor and Dorn (2012), use one attribute. 9 On the other hand, Goos, Manning and Salomons (2011) utilize 96 of the O*NET attributes and condense them into three task measures. In this paper, I use a strategy similar to that of Goos, Manning and Salomons (2011) and employ principal components analysis (PCA), but do so separately on the four O*NET data subsets. One advantage of PCA is that statistical methods guide the grouping of tasks by occupations. 10 Another advantage is that when it 8 The four subsets contain 35, 52, 41 and 56 individual attributes, respectively. The Data Appendix lists all of the attributes. For more detailed information see the online description of the O*NET data at 9 Autor, Levy and Murnane (2003) used data from the Dictionary of Occupational Titles (DOT). Acemoglu and Autor (2011) construct measures from both DOT and O*NET data. FFL use O*NET data. 10 Autor, Levy and Murnane (2003) (in one specication) and Crino (2010) also use principal components analysis to construct occupation measures from the DOT and O*NET, respectively. In both cases, principal components analysis was used to produce one measure from a few attributes 6

8 is applied separately to the four subsets, a ner mesh of task measures is produced. Specically, 18 task measures are estimated. Because the PCA analysis is conducted on each subset of the O*NET data separately, the measures produced from one subset will be uncorrelated with each other. A few of the measures between subsets have signicant correlation. 11 But even among those correlated measures, each captures dierent task content. For example, one measure each from the abilities, skills, and work activities subsets measures a form of cognitive tasks and these are correlated. The former best reects reasoning tasks, the second captures interpersonal tasks while the latter is associated with analyzing data. Since the occupation data are at the 3-digit occupation code level (with 264 occupations in the male sample) while all other studies are conducted at the 2-digit occupation level (with 40 occupations in FFL and 21 occupations in Goos, Manning and Salomons (2011)), there will be more variation in task content across occupations and this opens up the possibility of estimating the relationship between wages and tasks for a wider range of tasks. Before conducting the PCA, the O*NET data must be matched to the census occupation codes in a two-step process. First, the SOC codes used in the O*NET are matched to 2000 census occupation codes and then the 2000 census occupation codes are matched to 1990 census occupation codes. 12 In addition, the O*NET data quantify the attributes in the skills, abilities and work activities subsets in both the importance and level for each occupation. I follow FFL and Blinder (2007) and use a Cobb-Douglas specication to combine these two measures with the importance measure assigned an exponent of two-thirds and the level measure that had been preselected to measure a particular taxonomy (e.g. routine manual work). That is, PCA was used to combine the preselected elements rather than simply summing the values of each individual element as in FFL and Acemoglu and Autor (2011). In this paper, PCA is used as a data reduction tool. The methodology is consistent with understanding that occupations are a bundle of attributes as in Yamaguchi (2012). 11 That is, correlation coecients ranging from.61 to Matching the SOC codes to the 2000 codes was relatively straight forward. For some occupations, the 2000 census category encompassed two or more SOC categories. In these circumstances, the occupation attributes were averaged across SOC categories. When matching the 2000 census categories to the 1990 codes, the cases where multiple 2000 codes matched to one 1990 code, the attributes were combined using a weighted average based on the census cross-walk. 7

9 assigned an exponent of one-third. When choosing the number of factors to estimate from the PCA, I eliminated the components that added less than 3% to explaining the cumulative variance. 13 This produced three factors from the skills subset, four factors from the abilities subset, ve factors from the work activities subset and six factors from the work context subset. 14 Each factor estimated from the PCA has heavy factor loadings on attributes that tend to group together within an occupation. 15 Therefore, each factor a particular task grouping. I denote these task categories as attribute-bundles. Table 1 summarizes the tasks captured in each attribute bundle and lists the occupations that use each task measure most intensively. 16 Because the dierent subsets of the O*NET data quantify dierent types of occupation attributes, forming the attribute-bundles on each subset individually, rather than pooling the attributes, produces attribute-bundles that capture dierent types of cognitive and physical tasks. Broadly speaking, the attribute-bundles can be divided in brains and brawn task types. Within the brains group, the bundles cognitive: interpersonal, cognitive: reasoning, information analysis, programming/systems, and decision-making represent more complex cognitive skills. Denote this group of attribute bundles as Cognitive I. The bundles coordinate, oversee, advise, working with the public, interpersonal: conictual and coordinate teams measure cognitive or interpersonal tasks at more moderate levels of cognitive ability. Denote this second group of attribute bundles as Cognitive II. None of these eight brains bundles encompass tasks that would be easily replaced by computerization. 13 When there was ambiguity, I choose the greatest number of factors and then eliminated the last one if there were no factor loadings on any individual attribute that exceeded The cumulative variance explained by the selected factors was 73%, 78%, 78% and 70% for the skills, ability, work activities and work context subsets, respectively. The Data Appendix shows the factor loadings for each attribute. 15 I dene heavy as a factor loading that is approximately.60 or larger. The factor loadings can be thought of as coecients on each attribute, so attributes with heavy loadings are given more weight in the construction of the factor. 16 A complete ranking of occupations for each attribute-bundle is given in the Data Appendix. 8

10 Table 1: Attribute Bundles and Related Occupations Skill bundles Cognitive-interpersonal: Communication, complex interpersonal skills, problem solving, judgment Teachers, lawyers, judges, physicians, veterinarians, dentists, sales engineers, counselors Equipment 1: selection, installation, reparation, monitoring, control and maintenance of equipment Machine repairers, installers and maintenance workers. Programming/systems operation: programming, systems analysis and evaluation Operations/computer systems, engineers, scientists, accountants, airplane pilots some managers. Ability bundles Cognitive reasoning : comprehension, expression, and reasoning abilities Air trac control, medical professionals, engineers, physicists/astronomers, lawyers, judges Physical coordination and strength: manual dexterity, coordination, exibility, strength Fireghters, baggage porters, nurses, millwrights, masons, roofers, carpenters, veterinarians, waiters Visual and spatial: spatial orientation, vision abilities, reaction time, sound localization Drivers, pilots, miners, police detectives, some equipment operators Fine motor skills: nger dexterity, wrist-nger speed, control precision Precision instrument makers, medical technicians, textile workers, tailors, upholsterers, packers Task bundles Information analysis: getting, processing, analyzing, documenting info., interacting with computers Scientists, engineers, clinical and biological technicians, air trac controllers, computer operators Coordinate, oversee, advise: coordinates work activities, builds teams, trains, guides, coaches, stas Managers and supervisors Equipment 2: : inspects, repairs, and operates equipment; physical, handles objects Equipment installers & repairers, boilermakers, power plant operators, millwrights Working with the public: works with public, communicates with persons outside of the organization Barbers, hairdressers, repairer of household appliances, some sales jobs, art makers, pest control Assisting others: assists or cares for others Nursing professions, police and other law enforcement, guards, social workers. Work-context bundles Uncomfortable or hazardous conditions : outdoors, uncomfortable temperatures or body positions Structural metal workers, heavy equipment operation or repair, paving, ship crews, oil well drillers Physical & exposed to contaminants: climbing, bending, walking, stooping, using hands, contaminants Nursing aides, radiological technicians, hairdressers, housekeepers, veterinarians, dentists, miners Interpersonal - conictual: deal with external customers or unpleasant people, frequent conict Law enforcement, parking lot attendants, baggage porters, telephone operators, hotel clerks, cashiers Decision-making: freedom to make decisions, unstructured work, decisions impact co-workers/company Dentists, veterinarians, physicians, hairdressers, pest control, elevator installers, chemists, taxi drivers Coordinate teams: Coordinate or lead, work with group or team, responsible for outcomes Production supervisors, postmasters, power plant operators, chemists, ship crews, high school teachers Routine/automated: repetitive motions automatized, accuracy, pace set by equipment, time pressure Telephone operators, air trac controllers, some machine operators, type-setters, computer operators, dispatchers, insurance adjusters, data entry, bookkeepers, drafters 9

11 The bundles physical: coordination and strength, and physical and exposed to contaminants belong to the brawn group and are self-explanatory. The sampling of occupations that have high scores in these areas give a good illustration of the types of tasks reected in these bundles. The bundle uncomfortable or hazardous conditions measures attributes that are associated with physical work within a more hazardous context. Denote those three attribute bundles as Physical I. A second category of physical work reects tasks that are associated with working with machinery or equipment. There are two such equipment attribute-bundles. Both include equipment repair and maintenance tasks, but they dier in that the equipment 1 attribute bundle also includes selection and monitoring while the equipment 2 includes operation and hands on physicality. Similar to the cognitive tasks bundles, the tasks captured by the equipment bundles would not be easily replaced with computerization. A third category of physical work measures more specialized physical abilities and is represented by two attribute bundles: visual and spatial skills and ne motor skills. The former bundle represents tasks that are primarily associated with driving or operating moving equipment. The latter attribute bundle emphasizes the use of hand and nger dexterity and other ne motor skills that have been used to describe an occupation's vulnerability for automation. 17 There are two remaining attribute bundles: routine/automated and assisting others. Interestingly, the routine/automated bundle heavily weights attributes subjectively chosen by others (FFL and Acemoglu and Autor (2011)) to quantify the degree to which an occupation's tasks can be replaced by computerization. The latter attribute bundle gives high scores to nursing occupations, police and other law enforcement and social workers. Presumably, computers would be less apt to replace these tasks. In summary, the attribute bundles capture a broad array of cognitive and physical tasks. The tasks that are most vulnerable to replacement by computerization are 17 See, for example, Autor, Levy and Murnane (2003). 10

12 measured with the routine/automated bundle and the ne motor skills bundle. Other bundles measure dierent types of cognitive and physical non-routine tasks. Section 4 relates these bundles to within and between occupation changes. But rst, the next section documents the relevance of within occupation changes for overall wage inequality changes. 3 Within and between occupation changes The results presented below show that (1) within-occupation wage changes are quantitatively as important or more important than between occupation wage changes between 1980 and 2000 and that (2) shifts in occupational composition (holding constant wage structure) are relatively unimportant for explaining overall wage inequality trends. The conclusions are drawn from two experiments. The rst is a decomposition of the wage variance. During the 1980s male wage distribution changes were nearly symmetric about the median and the variance decomposition oers a reasonable characterization of changes in the overall wage distribution. However, between 1990 and 2000 the upper portion of the male wage distribution expanded while the lower portion compressed. Similarly, changes in the female wage distribution are asymmetric about the mean or median, particularly so during the 1990s. Figure 1 documents these trends in the decennial census data. Therefore, in addition to the variance decomposition, two additional counterfactual wage distributions are calculated. In one counterfactual exercise the within occupation wage distribution is held constant between periods but occupation median wages are permitted to change as observed in the data. The wage distribution statistics calculated from this counterfactual distribution simulate the impact of changes in median occupation wages on the overall wage distribution. In the other counterfactual construction median occupation wages are held constant between periods while the occupation wage distribution takes on its observed structure each period. The wage statistics calculated from this counter- 11

13 Figure 1: Wage Gaps Wage Gap Year Male Female Wage Gap Year Male Female factual distribution simulate the impact of within-occupation wage changes to the overall wage distribution. Decomposing the variance for the rst experiment begins with the following expression that details the dierence between the variance for the entire sample (σ 2 ) and the sum of the variances by occupation weighted by occupation employment ( Kk=1 share θ k σk) 2 K K σ 2 θ k σk 2 = w 2 θ k w 2 k 2 N k=1 k=1 K n k ( w w k ) w ik (1) k=1 i=1 where σ 2 k is the variance in occupation k, θ k is the employment share in occupation k, w is the mean overall wage, w k is the mean wage in occupation k, w ik is the wage of individual i in occupation k, and n k is the number of workers in occupation k. 12

14 As equation (1) indicates, the weighted variance measure deviates from the overall variance because of dierences in occupation mean wages from the overall mean wage. The portion of the overall variance not explained by changes to the weighted variance can be attributed to changes in the dispersion of mean wages across occupations. Both within occupation variance changes and changes in the distribution of employment across occupations contribute to changes in the weighted variance. To separate the contribution of occupational employment shifts from within occupation wage dispersion, a counterfactual weighted variance is constructed for 1990 using 1980 employment shares and for 2000 using 1990 employment shares. The dierence between the change in the actual and counterfactual weighted variance gives the portion of variance change due to within occupation wage changes. In the second set of experiments, the entire distribution of wages is recreated under the two counterfactual scenarios. The within occupation wage distribution is approximated by measuring the wage distance between the median wage in occupation k time t (wkt 50) and the wage at any percentile (wp kt ) in the same occupation and time period: d kt (p) = w p kt w50 kt. (2) So, for any individual, i, at a given wage percentile, his wage can be written as: 18 w p,i kt = w50 kt + d kt (p) (3) In one counterfactual construction, each individual, i, who is at the p th wage percentile in their occupation, is assigned a counterfactual wage, ŵ p,i kt that represents the wage they would have earned at that wage percentile in that occupation if the occupation wage distribution was the same as in the previous period: 18 The distance is calculated for each unit wage percentile Wages falling within those units are assigned a linearly interpolated distance between the two integer percentiles containing that wage observation. 13

15 ŵ p,i kt = w50 kt + d k,t 1 (p) (4) In the other counterfactual, each individual, i, who is at the p th wage percentile in their occupation, is assigned a counterfactual wage, w p,i kt that represents the wage they would have earned at that wage percentile in that occupation in the previous period if the occupation's median wage was the same as in the previous period: w p,i kt = w50 k,t 1 + d kt (p) (5) The advantage of the above methodology is that it allows the construction of the entire wage distribution under the two counterfactual scenarios and allows one to consider the impact of occupational wage structure on dierent parts of the overall wage distribution. a decomposition. The major disadvantage of the methodology is that it is not That is, for any given distributional statistic, the sum of the contributions of the between and within occupation changes will not necessarily equal the total change. 3.1 Results Table 2 shows the calculated contribution of between and within occupation wage changes to the change in the variance of male and female wages during the 1980s and the 1990s. During the 1980s changes to within occupation variance account for 54% of the total change in the male variance and 78% of the total change in female variance. 19 Table 3 presents changes to the gaps between the 90 th and 50 th wage percentiles (the gap) and the 50 th and the 10 th wage percentiles (the gap) that 19 While all of the top-coded wage values are above the 90 th percentile of the overall wage distribution, there are a few occupations where the extent of top-coding may bias mean and variance estimates. All of the results that rely on occupation means or variances, are calculated from means and variances that are adjusted to account for truncation of the distribution. (See the Data Appendix for details.) 14

16 Table 2: Variance Decomposition Male Female Total change in variance Due to within occupation Due to between occupation Due to occupation shifts Table 3: Changes in the and Wage Gaps Male Total change Due to wage dispersion within occupations Due to wage changes between occupations Female Total change Due to wage dispersion within occupations Due to wage changes between occupations would have occurred under the two counterfactual wage scenarios. For example, the second row of column 1 shows that the male wage gap increased by.0778 when comparing the actual 1980 values to the 1990 values from the counterfactual wage distribution that keeps occupation median wages xed. Similarly, the second row of the third column shows that the male wage gap increased by.0342 when comparing values from the actual 1990 distribution to the counterfactual 2000 distribution that keeps the occupation median wage xed. In nearly all instances, within occupation wage changes contribute more to the total change than do between occupation wage changes. The only instance when between occupation wage changes dominate is in the upper portion of the female wage distribution during the 1980s. However, it is shown below that once composition eects are accounted for the importance of between occupation wage changes is diminished. Table 4 recalculates the counterfactual wage distributions by re-weighting the 15

17 counterfactual wages to replicate the composition of the sample in the previous period. The re-weighting uses the methodology in DiNardo, Fortin and Lemieux (1996) where a logistic regression estimates the probability of an observation belonging to one of two time periods (e.g., 1990 versus 1980) as a function education, experience and occupation. 20 The second row of Table 4 shows the change in the wage gaps calculated from the re-weighted distributions that holds constant the education, age and occupational composition of the workforce. The third row of Table 4 shows how much of the wage gaps arises from changes to within occupation wage changes in the composition-constant wage distribution. Within occupation wage changes remain quantitatively more important than between occupation wage changes. The only exception is the female wage gap during the 1990s where within and between occupation wage changes contribute approximately the same amount to the composition adjusted overall change in the gap. Comparing actual total changes to composition adjusted total changes for the male distribution indicates that composition played a minor role in changing the wage structure. The largest impact of composition occurs in the lower portion of the distribution during the 1980s where composition changes account for about 20% of the increase in the gap. Female distributions tend to have been more in- uenced by composition changes. Adjusting for composition changes diminishes the importance of between occupation wage changes in the upper portion of the female distribution during the 1980s and is responsible for all of the relatively small increase in inequality in the lower portion of the female distribution during the 1990s. Without the change in composition, female lower tail inequality would have decreased during the 1990s as did its male counterpart. Composition changes also diminished 20 More specically, the regression includes dummy variables for eight education categories and ten age categories, each education dummy is interacted with a quartic in age, and a full set of occupation dummies. Therefore, the re-weighted 1990 wage distribution mimics the composition of the 1980 sample in terms of age, education and occupational aliation. The 2000 wage distribution is re-weighted to mimic the composition of the 1990 sample. The analysis is then conducted looking at changes, so the the change in distributional statistic between 1990 and 2000 compares the actual 1990 values to the 2000 counterfactual values. 16

18 Table 4: Changes in the and Wage Gaps Male Total change Total: composition constant Due to wage dispersion within occupation Due to wage changes between occupations Female Total change Total: composition constant Due to wage dispersion within occupation Due to wage changes between occupations the increase in upper tail inequality during the 1990s. Without composition changes the wage gap would have increased 30% more than the observed change. This time period saw a large increase in educational attainment, particular at the collegiate level, as well as shifts of female employment into traditionally non-female jobs. Therefore, it seems reasonable that composition changes might play a larger role in the female wage structure. The results from both the variance decomposition and the counterfactual distributions indicate that changing occupational structure contributes little to the overall male wage inequality patterns between 1980 and 2000 and modestly to some portions of the change in the female wage distribution. While certainly there have been significant changes in occupational composition, it is shifting wage structure, not shifting employment, that explains the vast majority of wage dispersion. And to reiterate, within occupation wage changes are at least as important as between occupation wage changes for understanding the determinants of overall wage inequality. 17

19 4 Occupation attributes, wages and employment shifts 4.1 Wages The above section established the quantitative signicance of within occupation changes for overall wage inequality changes. In this section, I estimate the relationship between within occupation wage changes and the occupation attribute bundles described in Section 2. Specically, I estimate the following regression equation for each gender and for two time periods: and w p kt = βs,p N S 0t + i=1 β AS,p it A S ik + γ t U tk + ε t (6) where w p kt denotes the change in the wage at the pth percentile in occupation k between time t and the previous decennial census, S denotes the O*NET subsets (skills, abilities, tasks and work contexts), A S i denotes the i th attribute-bundle in subset S, N S is the number of attribute-bundles in subset S, and U tk denotes the change in union coverage for occupation k at time t. 21 Because much of the literature has focused on the wage gap and the wage gap, the above wage equation is estimated for the 90 th, 50 th, 10 th percentiles of the occupation-specic wage distributions. 22 If the estimated coecient β AS,50 it positive, then occupations with greater intensity in task measure A S i is are associated with rising median wages. Similarly, an estimated positive coecient for β AS,90 it indicates that occupations with greater intensity in task measure A S i are associated with rising wages in the upper portion of the occupation wage distribution. If β AS,90 it is greater than β AS,50 it then task measure A S i is associated with more inequality in the 21 Consider union coverage as an additional occupation characteristic. See, Card (1996, 2001), Freeman (1993), DiNardo, Fortin and Lemieux (1996) and FFL for evidence that unionization inuences the wage structure. The union data are described in Hirsch and MacPherson (2003) and are located at The variable used is the percentage of employees in the occupation covered by a collective bargaining agreement. 22 Each attribute bundle, by construction of the factor scores, has a mean of zero and a standard deviation equal to one. 18

20 upper portion of the occupation wage distribution. The estimated coecients on the occupation attribute-bundles have three major determinants: the change in the market return to that attribute-bundle, the change in the skill set of the workers within the occupation and changes in the relative labor supply into the occupation. It is likely that occupations with increasing returns will also experience an inow of workers and employers will select the most highly qualied of those workers. The additional inow of workers will dampen the wage increase while the selection of higher quality workers will enhance the wage increase. To diminish the impact of worker and skill ows, I estimate equation (6) using a counterfactual wage that has been adjusted for the education, age and occupational composition of the workforce. That is, again using the DiNardo, Fortin and Lemieux (1996) method, the actual 1990 and 2000 wage distributions are re-weighted to reect the composition in 1980 and 1990, respectively and the occupation specic wage percentiles are calculated from the counterfactual distributions. The estimates from the counterfactual wage regressions should produce less biased estimates of the impact on wages arising from the change in the returns to the attribute-bundles. Tables 5 and 6 present the regression results for males and females, respectively. The wage implications for brains versus brawn stand out quite clearly. The 1980s yield the following observations: (1) All of the statistically signicant positive coecients, in both male and female samples, are associated with cognitive task bundles. (2) In the male sample, all of the physical attribute bundles are associated with wage declines at the 90 th percentile of the occupation wage distribution. Two of the physical bundles also are also associated with wage declines at the 50 th wage percentile. Therefore, all of the physical attribute bundles are related to compression of the within occupation male wage distribution and that compression occurs from declining wages in the upper portion of the wage distribution. (3) In the female sample, two of the physical attribute bundles (visual and spatial and equipment 19

21 Table 5: Impact of tasks on wages within and between occupations: male th 50 th 90 th 10 th 50 th 90 th Skill bundles Cognitive: interpersonal 0.021*** 0.034*** 0.034*** ** (0.006) (0.005) (0.005) (0.005) (0.005) (0.005) Equipment * ** (0.006) (0.005) (0.005) (0.006) (0.005) (0.005) Programming/systems ** 0.012** *** (0.006) (0.005) (0.005) (0.005) (0.005) (0.005) Ability bundles Cognitive: reasoning 0.028*** 0.038*** 0.038*** (0.006) (0.006) (0.005) (0.006) (0.005) (0.006) Physical ** *** (0.006) (0.006) (0.005) (0.006) (0.005) (0.005) Visual & spatial ** (0.006) (0.005) (0.004) (0.006) (0.005) (0.005) Fine motor * ** (0.007) (0.007) (0.006) (0.007) (0.006) (0.006) Task bundles Information analysis 0.018*** 0.028*** 0.028*** * 0.033*** (0.006) (0.006) (0.005) (0.006) (0.005) (0.005) Coordinate, oversee, advise 0.012* 0.015** 0.013*** *** *** (0.005) (0.005) (0.004) (0.005) (0.004) (0.004) Equipment *** *** (0.007) (0.007) (0.006) (0.006) (0.005) (0.005) Working with public *** 0.013*** (0.006) (0.006) (0.005) (0.006) (0.005) (0.005) Not assisting others * (0.006) (0.006) (0.005) (0.006) (0.005) (0.005) Work context bundles Uncomfortable/hazardous * *** * (0.006) (0.006) (0.005) (0.006) (0.005) (0.005) Physical *** *** *** (0.006) (0.006) (0.005) (0.006) (0.005) (0.005) Interpersonal: conictual * ** (0.006) (0.006) (0.005) (0.007) (0.005) (0.006) Decision-making 0.024*** 0.030*** 0.026*** ** 0.019** (0.007) (0.006) (0.005) (0.006) (0.005) (0.005) Coordinate teams *** 0.012*** *** *** (0.005) (0.005) (0.004) (0.006) (0.005) (0.005) Routine/automated *** *** *** (0.006) (0.006) (0.005) (0.007) (0.006) (0.006) Adjusted R-squared Skill attributes equation Ability attributes equation Task attributes equation Work context equation Notes: Dependent variable - change in log of hourly wage at the 10 th, 50 th, 90 th percentile by occupation. A separate equation is estimated for each attribute bundle. *** Signicant at the.1% level or better, ** at the 1% level, and * at the 5% level. 20

22 Table 6: Impact of tasks on wages within and between occupations: female th 50 th 90 th 10 th 50 th 90 th Skill bundles Cognitive: interpersonal 0.012* 0.032*** 0.044*** 0.021*** 0.020** 0.033*** (0.005) (0.005) (0.006) (0.005) (0.007) (0.007) Equipment *** *** (0.007) (0.007) (0.009) (0.007) (0.010) (0.010) Programming/systems 0.021*** 0.033*** 0.028*** * (0.007) (0.006) (0.008) (0.006) (0.008) (0.008) Ability bundles Cognitive: reasoning 0.017*** 0.040*** 0.041*** *** (0.006) (0.006) (0.007) (0.006) (0.008) (0.008) Physical * *** * *** *** (0.006) (0.006) (0.007) (0.005) (0.007) (0.007) Visual & spatial (0.008) (0.009) (0.010) (0.008) (0.010) (0.010) Fine motor (0.006) (0.006) (0.008) (0.006) (0.008) (0.008) Task bundles Information analysis 0.022*** 0.044*** 0.047*** ** 0.035*** (0.006) (0.006) (0.007) (0.006) (0.007) (0.007) Coordinate, oversee, advise ** 0.020*** 0.016** (0.005) (0.005) (0.006) (0.005) (0.006) (0.006) Equipment (0.008) (0.008) (0.010) (0.008) (0.009) (0.009) Working with public ** *** 0.025** (0.006) (0.006) (0.007) (0.006) (0.007) (0.007) Not assisting others *** 0.048*** (0.007) (0.006) (0.007) (0.006) (0.007) (0.007) Work context bundles Uncomfortable/hazardous * (0.012) (0.011) (0.013) (0.012) (0.014) (0.014) Physical * *** *** ** (0.006) (0.005) (0.006) (0.006) (0.007) (0.007) Interpersonal: conictual * (0.007) (0.006) (0.007) (0.007) (0.009) (0.009) Decision-making 0.023** 0.036*** 0.054*** *** 0.044*** (0.007) (0.007) (0.008) (0.007) (0.009) (0.009) Coordinate teams *** 0.041*** (0.007) (0.007) (0.007) (0.007) (0.009) (0.009) Routine/automated (0.006) (0.006) (0.007) (0.007) (0.008) (0.008) Adjusted R-squared Skill attributes equation Ability attributes equation Task attributes equation Work context equation Notes: Dependent variable - change in log of hourly wage at the 10 th, 50 th, 90 th percentile by occupation. A separate equation is estimated for each attribute bundle. *** Signicant at the.1% level or better, ** at the 1% level, and * at the 5% level. 21

23 2) are not statistically signicantly related to any wage changes. 23 However, both the physical:strength/coordination and physical/contaminants bundles are associated with wage declines throughout the within occupation wage distribution, with the declines for the high wage workers exceeding the declines for the lower wage workers. Thus, there is both compression and shifting of the within occupation wage distributions related to physical tasks in the female sample. (4) For the Cognitive I group of tasks, wages tended to increase throughout the wage distribution with the interpersonal, reasoning and information analysis bundles showing higher wages gains in the upper portion of the wage distribution relative to the bottom portion. This is true for both males and females. (5) For the Cognitive II group of tasks, the wage increases were concentrated in the upper portion of the occupation wage distribution, again for both males and females, and the coecient estimates tend to be smaller. Thus, there is an expansion of the within occupation wage distribution, particularly in the upper portion of the distribution associated with both Cognitive I and II groups. (6) For males, the routine/automated bundle was associated with lower wages throughout the occupation wage distribution while ne motor skill bundle was associated with wage declines at the top of the occupation distribution. So, tasks that are most vulnerable to computerization were associated with male wage declines. However this is not true for the female sample where there is no statistically signicant link between routine tasks and occupation wage declines. During the 1990s the contribution of tasks to wage changes becomes less pronounced. In the male sample, the Cognitive I attribute bundles are associated with wage increases only at the top of the occupation wage distribution, if at all; while the Cognitive II bundles are now associated with wage declines at the top of the occupation wage distribution. The physical attribute bundles continue to be associated with wage declines, but only a the very top of the occupation wage distribution. And perhaps most notable, routine tasks have no statistically signicant impact on wages. 23 The occupations that rank high in these task measures are typically male-dominated, so the insignicance in the female sample is not surprising. 22