Complex-Task Biased Technological Change and the Labor Market

K.7 Complex-Task Biased Technological Change and the Labor Market Caines, Colin, Florian Hoffman, and Gueorgui Kambourov Please cite paper as: Caines, Colin, Florian Hoffman, and Gueorgui Kambourov (2017). Complex-Task Biased Technological Change and the Labor Market. International Finance Discussion Papers 1192. https://doi.org/10.17016/IFDP.2017.1192 International Finance Discussion Papers Board of Governors of the Federal Reserve System Number 1192 February 2017

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 1192 February 2017 Complex-Task Biased Technological Change and the Labor Market Colin Caines, Florian Ho(cid:11)mann, and Gueorgui Kambourov NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussionandcriticalcomment. ReferencestoInternationalFinanceDiscussionPapers(otherthan an acknowledgment that the writer has had access to unpublished material) should be cleared with theauthororauthors. RecentIFDPsareavailableontheWebatwww.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from Social Science Research Network electronic library at www.ssrn.com.

Complex-Task Biased Technological Change and the Labor Market Colin Caines(cid:3), Florian Ho(cid:11)manny, and Gueorgui Kambourovx { Abstract: In this paper we study the relationship between task complexity and the occupational wage- and employment structure. Complex tasks are de(cid:12)ned as those requiring higher-order skills, such as the ability to abstract, solve problems, make decisions, or communicate e(cid:11)ectively. We measure the task complexity of an occupation by performing Principal Component Analysis on a broad set of occupational descriptors in the Occupational Information Network (O*NET) data. We establish four main empirical facts for the U.S. over the 1980-2005 time period that are robust to the inclusion of a detailed set of controls, subsamples, and levels of aggregation: (1) There is a positive relationship across occupations between task complexity and wages and wage growth; (2) Conditional on task complexity, routine-intensity of an occupation is not a signi(cid:12)cant predictor of wage growth and wage levels; (3) Labor has reallocated from less complex to more complex occupations over time; (4) Within groups of occupations with similar task complexity labor has reallocated to non-routine occupations over time. We then formulate a model of Complex-Task Biased Technological Change with heterogeneous skills and show analytically that it can rationalize these facts. We conclude that workers in non-routine occupations with low ability of solving complex tasks are not shielded from the labor market e(cid:11)ects of automatization. Keywords: Occupational Task Content; Complex Tasks; Wage Polarization; Skills JEL classi(cid:12)cations: E24, J21, J23, J24, J31 (cid:3) Theauthorisasta(cid:11)economistintheDivisionofInternationalFinance,BoardofGovernorsoftheFederal Reserve System, Washington, D.C. 20551 U.S.A. The views in this paper are solely the responsibility of the authorandshouldnotbeinterpretedasre(cid:13)ectingtheviewsoftheBoardofGovernorsoftheFederalReserve System or of any other person associated with the Federal Reserve System. The email address of the author is colin.c.caines@frb.gov. y The author is Assistant Professor in the Department of Economics, University of British Columbia, 6000 IonaDrive,Vancouver,BC,V6T1Z4,Canada. TheemailaddressoftheauthorisFlorian.Ho(cid:11)mann@ubc.ca. x The author is Associate Professor in the Department of Economics, University of Toronto, 150 St. George St., Toronto, Ontario M5S 3G7, Canada. The email address of the author is g.kambourov@utoronto.ca. { We thank Lance Lochner, Jaromir Nosal, an anonymous referee, and participants at the \Human Capital and Inequality Conference" at the University of Chicago for their comments and suggestions. Kambourov hasreceivedfundingfromtheSocialSciencesandHumanitiesResearchCouncilofCanadagrant#435-2014- 0815andfromtheEuropeanResearchCouncilundertheEuropeanUnion’sSeventhFrameworkProgramme (FP7/2007-2013)/ERC grant agreement n. 324085.

1 Introduction A recent literature on wage and earnings inequality emphasizes the role of occupations for understanding trends in the aggregate wage- and employment structure. A common motivation for this emphasis is the well-established (cid:12)nding that skill-biased technological change (SBTC) cannot account for important changes in the relationship between skills and labor market outcomes. Particularly noteworthy is recent evidence that occupations which formerly o(cid:11)ered middle-class and middle-skill jobs have lost ground in terms of wage and employment relative to both low- and high wage jobs. A popular explanation for this (cid:12)nding, quickly replacing the SBTC hypothesis as the primary theoretical economic framework for studying trends in wage inequality, is routine-biased technological change (RBTC). According to this view occupations are de(cid:12)ned by bundles of tasks, and middle-skill occupations have been under pressure of automatization over the last few decades because they are intensive in routine tasks. This view can be justi(cid:12)ed theoretically from what Autor and Acemoglu (2011) call Ricardian models of the labor market in which it is the comparative advantage of workers in non-routine jobs that determines their labor market outcomes rather than a unidimensional measure of skills, such as education. For routine jobs to lose relative to former low-wage jobs one needs to assume a skill structure that segments labor markets according to whether workers can be replaced by machines or not. Figure 1: Distribution of Hourly Wage Growth for Routine and Non-Routine Occupations noitcarF 51. 1. 50. 0 Routine Occupations −.5 0 .5 1 change in log hourly wage, 1980−2005 noitcarF 51. 1. 50. 0 Non−Routine Occupations −.5 0 .5 1 change in log hourly wage, 1980−2005 Notes: Data taken from the 1980 5% Sample of the US Census and the 2005 American Community Survey (ACS). Hourly wagesconstructedfromtotalwageandsalarydata(adjustedusingPCEde(cid:13)ator),numberofweeksworkedperyear,andusual numberofhoursworkedperyear. Dataisde(cid:12)nedonthe3-digitoccupationlevel. Routineoccupationsde(cid:12)nedasinAutorand Dorn(2013),allotheroccupationsde(cid:12)nedasnon-routine. 1

The view that routine task intensity of occupations is the central predictor of wage and employment growth is not uncontroversial however. For example, Katz (2014) highlights the growing importance of artisanal work that combines creativity with crafting skills to customize and re- (cid:12)ne consumption goods. Indeed, many crafts occupations that are commonly classi(cid:12)ed as manual routine have fared quite well in terms of labor market performance over the last three decades. More generally, the relationship between routine task-intensity and wage growth is far from perfect. Inspecting the distribution of real wage growth between 1980 and 2005 split by routine and non-routine occupations, computed from US Census data and the American Community Survey (ACS) and shown in Figure 1, reveals that both routine and non-routine occupations feature a signi(cid:12)cant share of low- and high wage growth occupations.1 It is therefore natural to ask whether labor markets for routine task intense occupations can be viewed as segmented from the rest of the economy, or whether some routine and non-routine occupations are subject to the same aggregate forces determining wages and employment. For example, machine operators, the quintessential example of routine occupations, may compete in the same labor markets as the non-routine occupation truck drivers, so that their labor market performance may be more tightly related than predicted by common formulations of RBTC. In fact, wage growth in these two occupations line up quite closely. In this paper we thus o(cid:11)er an alternative view of the mechanism behind recent changes in the occupational wage- and employment structure. We hypothesize that it is task complexity (cid:0) that is whether a task involves higher-order skills such as the ability to abstract, solve problems, making decisions, or communicate e(cid:11)ectively (cid:0) rather than routine-intensity that is a prime determinant of wages as well as both wage- and employment growth on the occupational level. According to this view, non-routine and routine occupations that are similar with respect to task complexity will compete in the same labor market, and they are predicted to perform similarly in terms of wages and wage growth. This view is motivated as follows. Occupations with the lowest level of task complexity, which we refer to as simple occupations, involve tasks that involve raw physical, cognitive and interactive skills and abilities only, that is those that carry us through every-day life. Prominent examples are carrying, driving, archiving, cleaning or over-the-counter interaction. 1Similarly, Dustmann et al. (2009), Green and Sand (2014), and Goos et al. (2014) (cid:12)nd that the changes in the occupational employment structure is at best weakly re(cid:13)ected in the changes of the occupational wage structure. 2

Labor supply that can solve such tasks, whether they are in competition with machines or not, can therefore be viewed as abundant. In contrast, complex tasks involve higher-order skills, either innate or acquired via post-secondary education or other forms of human capital investments, and are therefore relatively scarce. If technological progress is complementary with task complexity, then we should observe a strong relationship between complex-task intensity and wage- and employment growth at the occupational level. Hence, an important distinction to existing theories of the occupational wage- and employment structure is that once one conditions on task complexity, then wages, as well as wage growth, are unrelated with routine task intensity or whether an occupation involves the production of goods or services. Consistent with this hypothesis, or with the discussion in Katz (2014) about the growing importance of artisanal work, we (cid:12)nd that many crafts occupations are complex and have performed quite well over the last few decades. To measure task complexity at the occupational level we closely follow the methodology of Yamaguchi (2012), however we apply this to data from the Occupational Information Network (O*NET) instead of the Dictionary of Occupational Titles (DOT). In a (cid:12)rst step we select a large list of occupational descriptors that very clearly relate to our notion of task complexity, such as (cid:13)uency of ideas, complex problem solving, or analyzing data and information. In a second step we aggregate this list of descriptors together with their documented intensity to a single measure using Principal Component Analysis (PCA) and merge it with occupation-level data on wage- and employment growth between 1980 and 2005 from the US Census and ACS.2 Wethendocumentfourstylizedfacts. First,conditionalonourmeasureoftaskcomplexitythere were no signi(cid:12)cant wage di(cid:11)erences between routine and non-routine jobs at either the beginning or the end of our sample period. Second, occupations with a high measure of task complexity had substantially higher wages and larger wage- and employment growth than simple occupations. Third, wagesandwagegrowthinsimpleroutine-andnon-routineoccupationswerenotstatistically di(cid:11)erent, and their employment growth was negative. At the same time, the percent decline in employment in simple non-routine occupations was smaller than in the simple routine occupations. Finally, the wage growth di(cid:11)erences are substantially larger than employment growth di(cid:11)erences. The main part of our empirical analysis tests whether the stylized facts about complex-task biasedtechnologicalchangecontinuetoholdwhencontrollingmore(cid:13)exiblyforvariousoccupational 2Caines et al. (2016) use an alternative procedure to identify complex occupations in German data. 3

characteristics. To this end we estimate various regression models of wage levels in 1980 and 2005 and of 1980-2005 wage- and employment growth at the occupational level as a function of taskcomplexity and routine-task intensity. We (cid:12)nd that wages and wage growth are indeed strongly positively related with task complexity, no matter if we use a continuous or a discrete measure, but unrelated to routine task intensity once one conditions on this measure. The relationship between employment growth and task complexity is also positive, but weaker. At the same time there is a weak, though robust, negative relationship between routine task intensity and employment growth. These results are robust to inclusion of various other occupational characteristics, such as average wages in 1980 and controls for education, age, race, gender, and social-skill intensity. Furthermore, they hold throughout the occupational wage distribution in 1980 and persist if we use data disaggregated further to groups de(cid:12)ned by demographic characteristics. To formalize our interpretation of these facts we formulate a simple stylized static general equilibrium model of Complex-Task Biased Technological Change. Loosely speaking, the model can be viewed as a hybrid of a Ricardian model with labor-replacing technological change in some occupations,asinAutorandAcemoglu(2011)andAutorandDorn(2013),andthecanonicalmodel of SBTC, but with skill requirements measured by task complexity rather than education. More precisely,ourmodelfeaturesthreemaincomponents. First,weconsiderthreeproductionprocesses, called occupations, that di(cid:11)er with respect to their technologies and that aggregate into a single (cid:12)nal output good. Simple routine and non-routine occupations draw from the same pool of labor supply, but the former is characterized by relative capital-skill substitutability while the latter, akin to low-skill services in Autor and Dorn (2013), only involve labor inputs. In contrast, labor in complex occupations is relatively complementary with capital. Second, workers are heterogeneous in terms of their ability to perform complex tasks and sort accordingly across simple and complex occupations. In equilibrium, worker behavior will be characterized by a threshold level of skills in solvingcomplextasksthatallocatesworkersacrosssimpleandcomplexoccupations.3 Weshowthat under a simple and intuitive assumption on the complementarity of the three intermediate inputs in the production of the (cid:12)nal good, the model can rationalize our empirical (cid:12)ndings about the evolutionoftheoccupationalwage-andemploymentstructure. Aplausibleexogenousforcethatcan 3More generally, one can think of our model as one with two-dimensional skills, one for performing simple tasks andoneforperformingcomplextasks,butwiththemarginaldistributionoversimpleskillsassumedtobedegenerate. 4

generate these changes is a relative increase in the factor productivity for the complex production process. We call this \Complex-Task Biased Technological Change." The economic mechanism underlying this result is similar also to the capital-skill complementarity channel emphasized in Krusell et al. (2000). They (cid:12)nd that growth in the stock of equipment capital, such as computers and machines, combined with capital-skill complementarity is consistent with the increase in both theskillpremiumandthesupplyofhighlyskilledworkersasobservedinUSdata. Ourframeworkis di(cid:11)erent along two important dimensions. First, we measure skill requirements by task complexity on the occupational level rather than educational attainment. Second, we introduce a distinction between routine and non-routine tasks and emphasize that they are not direct measures of inherent skills but rather di(cid:11)erent sets of tasks that may be performed by the same skill group. It is insightful to brie(cid:13)y contrast our notion of technological change with alternative views put forward in the existing literature. First, compared with SBTC we take into account the possibility of labor-replacing technological progress whereby some workers are shifted from simple occupations in which labor is relatively substitutable with capital to simple occupations in which labor is the only input. At the same time, labor in complex occupations is subject to economic forces that are isomorphic to SBTC, but with skill requirements related to task complexity rather than the level of education. Second, in contrast to research that emphasizes the importance of routine task intensity, workers in non-routine occupations with a low level of complex-task intensity are not shielded from labor-replacing technological change. Rather, they compete in the same labor markets like workers in simple routine occupations and absorb any labor replaced by technological progress that does not have a su(cid:14)ciently high level of skills for solving complex tasks. In practice, our approach identi(cid:12)es numerous occupations in the goods sector, especially those in the crafts, as complex occupations even though they are routine task intensive. Other examples are many middle-skill middle-rank occupations in (cid:12)nance and insurance. They are classi(cid:12)ed as routine since they are often embedded within a strict hierarchical (cid:12)rm structure and thus o(cid:11)er limited freedom to make independent decisions while our approach identi(cid:12)es them as complex.4 Third, recent work by Deming (2015) (cid:12)nds that the relevance of social skills in occupations is strongly related to occupation-level labor market outcomes. We view our approach as complementary with this 4ThisischaracterizedbyahighintensityoftheDOT-variable\adaptabilitytoworkrequiringsetlimits,tolerances, or standards," used in Autor et al. (2003) for measuring the routineness of an occupation. 5

work since most tasks involving social skills, such as managing or consulting, are also complex. However, they are not the same. Again, an important di(cid:11)erence is that we predict that manualor cognitive task intensive occupations that do not involve a lot of social interaction can perform quite well, as long as they are complex. Examples are some craftsmen and mechanics on the one hand and mathematicians and statisticians on the other hand. Fourth, a number of studies, among them Beaudry et al. (2016), study the relationship between cognitive skill intensity and wage- and employment growth. Cognitive skill intensity is positively related to task complexity, but so are numerous manual tasks, distinguishing our approach from this line of research. Finally, this paper is related to the literature, e.g., Kambourov and Manovskii (2008, 2009a,b), that has emphasized theimportanceofoccupation-speci(cid:12)chumancapitalinunderstandingwagesandwagegrowthfrom the late 1960s to the mid-1990s in the United States. 2 Task Complexity of Occupations A central challenge of the task-based approach to occupations is measurement. In this section we discuss in detail how we construct our measure of task complexity at the 3-digit occupational level anddocumentsomeaggregatetrendsmotivatingourde(cid:12)nitionofcomplex-taskbiasedtechnological change. Since this involves matching our occupation-level task measures to labor market data we start with describing the sample we use to construct aggregate trends in wages and employment. 2.1 Wage and Employment Data We compute data on the occupational wage and employment structure over time from the 1980 CensusIntegratedPublicUseMicrodataandthe2005AmericanCommunitySurvey(ACS),imposing similar sample restrictions to Autor and Dorn (2013). Our working sample consists of non-farm workers in the mainland United States between the ages of 16 and 64 (inclusive). The main part of our empirical analysis focuses on males.5 We also omit from our sample individuals who are institutionalized. Wage data refers to hourly wages, constructed from the census data for total wage and salary income (adjusted using the PCE de(cid:13)ator), number of weeks worked per year, and usual number of hours worked per week. The employment share of an occupation is given by the 5Results for females are documented in Section 3.3.2 6

total number of hours worked in an occupation in a year as a fraction of the total number of hours worked in the economy. 2.2 Classifying Occupations by Complexity Two sources of data are commonly used for quantifying the task content of occupations, the Dictionary of Occupational Titles (DOT) and its successor the Occupational Information Network (O*NET) production database.6 The O*NET has the advantage of o(cid:11)ering a much broader set of occupational descriptors, which allows for a more precise measurement of task complexity. Furthermore, task measures are derived from a survey of incumbent workers rather than occupational analysts, as is the case for the DOT. We therefore rely on O*NET data in this paper (O*NET 20.1, October 2015).7 The O*NET is a publicly available dataset sponsored by the US Department of Labor. It compiles information on standardized measurable characteristics of occupations, referred to as descriptors. In total it contains 277 occupational descriptors sorted into 6 broad categories. These include the activities/tasks involved in working in an occupation, the requirements and quali(cid:12)cations needed to work in an occupation, as well as the knowledge/interests of the typical worker in an occupation.8 In selecting the relevant descriptors and mapping them into a unidimensional measure of task complexity using a principal components analysis we closely follow Yamaguchi (2012), although our selection of descriptors is much broader.9 To be more precise we (cid:12)rst identify 35 O*NET descriptors that relate to our de(cid:12)nition of task complexity. These descriptors are drawn from three subsections of the O*NET: \Abilities" (contained in \Worker Characteristics"), \Skills" (contained in \Worker Requirements"), and \Generalized Work Activities" (contained in \Occupational Requirements"). Examples are \originality" and \inductive reasoning" from the abilities module, \complex problem solving" and \critical thinking" from the skills module, and \analyzing dataorinformation"and\thinkingcreatively"fromtheactivitiesmodule. Theselecteddescriptors areevaluatedwithaconsistent0-7scalethatindicatesthedegreetowhichtheyarerequiredtoper- 6See Autor and Dorn (2013), Autor et al. (2003), Autor et al. (2008), Firpo et al. (2011), Goos et al. (2009), and Ross (2015). 7However, we have also carried out our analysis using the DOT, with similar results. They are available upon request. 8The categories are \Worker Characteristics," \Worker Requirements," \Experience Requirements," \Occupational Requirements," \Labor Market Characteristics," and \Occupation-Speci(cid:12)c Information." 9See also Bacolod and Blum (2010). 7

form in a given occupation. In our view each of these is positively correlated with task complexity. As a second step we map the information contained in our selected occupational descriptors into a single dimension complexity score, converted to percentile rankings, via principal components analysis (PCA).10 A detailed description of this procedure is provided in Appendix A, and in appendix Table A.1 we also provide the full list of descriptors and their factor loadings. In Appendix D11, we list the complexity index for each of our 3-digit occupations.12 The top 10 percent of occupations rated in the complexity ranking largely comprise professional, scienti(cid:12)c/medical, and senior management occupations. Conversely, the 10 percent of occupations at the bottom of the complexity distribution predominantly consist of service occupations, such as various cleaning occupations, as well as some manual occupations, primarily those involving machine operation. In the middle of the complexity distribution we (cid:12)nd a wide range of both service and goods-producing occupations. The latter tend to consist of mechanics, technicians, and craftsmen. In Section 3 we use the continuous complexity index to provide a detailed analysis of the e(cid:11)ect of an occupation’s complexity on its wage level, as well as on its wage- and employment growth. As a preview of our main message, we classify all occupations into either simple or complex,13 and Table 1 provides a preliminary look at the main result in the paper: complex occupations have higher mean wages (in both 1980 and 2005) and have experienced higher wage and employment growththansimpleoccupationsoverthe1980-2005timeperiod. Inparticular,complexoccupations experienced a wage growth of 36 percent over the period compared to a 11 percent wage growth in simple occupations. Furthermore, the employment share of complex occupations increased at the expense of simple occupations. 2.3 Routine Intensity and its Relation to Task Complexity Our de(cid:12)nition of complexity correlates with several aspects of occupational task content considered elsewhere in the literature. To make our de(cid:12)nition of occupational complexity clear it is useful 10See Bacolod and Blum (2010) and Yamaguchi (2012). 11Appendices D-F are in the Appendix. 12The O*NET provides information for 997 di(cid:11)erent occupations coded using the O*NET-SOC taxonomy. In the empirical work that follows we use a time-consistent modi(cid:12)cation to the 1990 US Census occupational codes as the level of our analysis. O*NET-SOC codes are mapped into these occupation codes, and the descriptor values are imputed using Census employment shares to compute weighted averages where necessary. 13Occupationsareclassi(cid:12)edassimpleiftheyarebelowthe66thpercentileofourcomplexityindexandascomplex if they are above it. The facts are quantitatively robust to the choice of this cuto(cid:11). 8

Table 1: Wages and Employment Employment % Employment log(wage ) log(wage ) (cid:1)log(wage) Share Change 1980 2005 1980 2005 simple 1.949 2.062 0.113 0.654 0.595 -0.090 complex 2.304 2.663 0.357 0.346 0.405 0.170 Notes: Wageandemploymentdatatakenfrom19805%sampleoftheUSCensusandthe2005ACS.Samplerestricted tonon-institutionalizedmalesaged16-64inthemainlandUnitedStates. Complexoccupationsde(cid:12)nedasthosewhose complexity index is above the 66th percentile in the occupation-level complexity distribution. All other occupations are de(cid:12)ned as simple. Also note that the table shows the percentage change in the employment shares of simple and complexoccupations,notthechangeintheemploymentshare. Thelattersumtozero. to discuss how it di(cid:11)ers from these concepts. The \routineness" of occupations has been intensively studied by the literature. This has typically denoted the extent to which an occupation is automatable or codi(cid:12)able. The seminal study of the substitutability between processing technology and routine-intensive labor inputs is Autor et al. (2003) (ALM). Their approach of measuring routineness from the DOT has been widely replicated. More recent studies by Autor et al. (2006) (AKK) and Autor and Dorn (2013) (AD) have classi(cid:12)ed the routineness of occupations from three dimensions that they measured in the DOT: abstract task intensity, manual task intensity, and routine task intensity. We compute the routine task intensity index developed in Autor and Dorn (2013) as follows Routine Task Intensity = ln(Routine )(cid:0)ln(Manual )(cid:0)ln(Abstract ) (1) o o o o Asshouldbeexpected,theroutinetaskintensity(RTI)isnegativelycorrelatedwithourcomplexity index (the correlation coe(cid:14)cient between the complexity and RTI percentile is -0.3158). However, there are important di(cid:11)erences. The (cid:12)rst panel of Table 2 lists several examples of complex occupations that are routine-intensive (cid:0) they contain a number of (cid:12)nancial service occupations such as Accountants, Financial Managers, and Real Estate Sales occupations. One possible reason that they are designated as being quite routine is that these occupations are often embedded within a strict hierarchical (cid:12)rm structure. This may limit the latitude a(cid:11)orded to workers to make in- 9

Table 2: Comparison of Complexity and Routinization Routinizable Occupations with High Complex Content Occupation RoutineIndex ComplexityIndex Title Percentile Percentile FinancialManagers 82.825 96.109 RealEstateSalesOccupations 87.416 66.033 AccountantsandAuditors 95.502 78.977 InsuranceUnderwriters 95.976 65.348 StatisticalClerks 93.661 93.177 ClinicalLaboratoryTechnologistandTechnicians 74.922 73.236 OtherFinancialSpecialists 77.201 75.251 Non-Routinizable Occupations with Low Complex Content Occupation RoutineIndex ComplexityIndex Title Percentile Percentile WaitersandWaitresses 12.038 3.617 BaggagePorters,BellhopsandConcierges 9.357 26.968 RecreationFacilityAttendants 27.036 11.736 TaxiCabDriversandChau(cid:11)eurs 5.054 28.085 PersonalServiceOccupations 26.624 30.395 Door-to-doorSales,StreetSales,andNewsVendors 26.855 6.419 BusDrivers 3.775 12.672 Notes: Thetablereportsvaluesoftheroutineandcomplexityindicesforaselectionofoccupations. Theindexvalues areconvertedtopercentilesoftheoccupaton-leveldistribution. Seesections2.2and2.3forconstructionoftheroutine indexandthecomplexityindex. dependent decisions and requires them to work to set standards. Nevertheless, we think of such occupations as requiring some specialized knowledge and requiring the ability to perform some abstract problem solving (such as mathematical calculations). In other words, they are likely to recruit from a di(cid:11)erent pool of workers than occupations that are in competition with computers (such as some clerical workers or machine operators). The second panel of Table 2 lists examples of non-routine occupations with low complexity ratings. These include several service occupations 10

Table 3: Complexity, Routineness, Wages, and Employment Employment % Employment log(wage ) log(wage ) (cid:1)log(wage) Share Change 1980 2005 1980 2005 simple routine 1.925 2.041 0.116 0.188 0.169 -0.098 nonroutine 1.959 2.071 0.112 0.466 0.426 -0.086 complex 2.304 2.663 0.357 0.346 0.405 0.170 Notes: Wageandemploymentdatatakenfrom19805%sampleoftheUSCensusandthe2005ACS.Samplerestricted tonon-institutionalizedmalesaged16-64inthemainlandUnitedStates. Complexoccupationsde(cid:12)nedasthosewhose complexityindexisabovethe66thpercentileintheoccupation-levelcomplexitydistribution. Allotheroccupationsare de(cid:12)nedassimple. such as Waiters and Waitresses or Bus Drivers. While these occupations are di(cid:14)cult to replace with processing technology (and hence are relatively non-routine), we consider them to be simple as they do not require many higher-level skills nor do they involve much abstract problem solving. As a consequence, we think of them as entering a similar labor market to those who work in simple, routine occupations. Table 3 builds on the results presented in Table 1 by separating all simple occupations into two groups: routine and non-routine. Following Autor and Dorn (2013) routine occupations are those for which the routine task intensity de(cid:12)ned in (1) is ranked in the top third amongst all occupations. The distinction between simple routine and simple non-routine occupations will play an important role in our empirical analysis since it can be used to test the hypothesis of complextaskbiasedtechnologicalchangeagainstthehypothesisofroutine-biasedtechnologicalchange. The underlying theoretical framework will be developed in Section 4. The table shows mean wages as wellasaveragewageandemploymentgrowthforthethreeoccupationalcategories(cid:0)simpleroutine, simple non-routine, and complex (cid:0) and yields the following insights: 1. Wage levels and wage growth are higher in complex occupations than in simple occupations; 2. Within the simple occupations, wage levels as well as wage growth are the same for routine occupations and non-routine occupations; 3. There is reallocation from simple occupations to complex occupations over time; 11

4. Within the simple occupations, the routine occupations experienced a larger percent decline in employment over time than the non-routine occupations. 3 Empirical Analysis This section presents the results from a detailed empirical analysis of the relationship between wages, wage- and employment growth, and task complexity at the occupational level in the 1980- 2005 time period. Our empirical analysis consists of estimating separate regressions for our outcomes on measures of task complexity and routinization. We experiment with two ways of controlling for task complexity: (i) a continuous normalized measure of task complexity; speci(cid:12)cally, a percentileinthedistributionofourtaskcomplexityindexcomputedviaPCA,and(ii)acomplexity dummy. Results from both of these approaches are presented in the tables below. We also o(cid:11)er a detailed analysis of robustness to adding more controls, splitting the sample in various ways, and disaggregating the data to a (cid:12)ner level. Importantly, for the wage growth and employment growth regressions we show results from speci(cid:12)cations that include a (cid:13)exible polynomial in the 1980 average occupational wage, a variable that is often used in the literature as a measure of the \absolute" skill content of an occupation.14 3.1 Task Content of Occupations and Wage Levels Westartbyconsideringtherelationshipbetweenthetaskcomplexityofanoccupationanditsplace in the wage distribution. Table 4 reports results for individual-level regressions of log wages on the task complexity index and the routine task intensity index, together with (cid:12)xed e(cid:11)ects for age, education, and race. Both task indices are converted to percentiles and normalized to lie between zero and one.15 Results are reported for both the 1980 and 2005 cross-sections. There is a large and signi(cid:12)cant relationship between the task complexity of the occupation in which an individual works and their wage level. Since we use the percentile of the complexity index as the explanatory variable of interest, a coe(cid:14)cient value of 0.35 for the 1980 cross section has the interpretation that the mean wages of individuals in the most complex occupations are 35% higher than the mean 14We use a 3rd order polynomial. Adding higher orders does not change the results. 15Age consists of four categories (16-28, 29-40, 41-52, and 52-64), education consists of four categories (less than high school, high school, some college, and college), and race is consists of two categories (white and nonwhite). 12

wages of individuals in the least complex occupations. In the 2005 cross-section this gap increases to 71%. For both years the routineness of an individual’s occupation has no signi(cid:12)cant relationship with the mean wage after controlling for complexity. In the analysis that follows we focus on the relationship between complexity and both wageand employment growth. Because we do not use panel data that follow individuals over time this requires aggregating to the occupation level. For comparability with the individual-level results for wage levels we (cid:12)rst show an occupation-level analogue to Table 4. Table 5 shows results for regressions of the log of mean occupational wages on task complexity and routine task intensity. The regressions include an array of demographic controls. These include the share of workers in an occupation with a college or high school degree, the share of workers in an occupation who are married or who are non-white, the occupational female employment share, as well as the average age and mean number of children for workers in the occupation. Once again the task complexity index has a robust positive relationship with wage levels. The gap between the mean wage in the most and the least complex occupation is 10% in 1980 and 40% in 2005. This is robust to controlling for the routineness of an occupation, which does not have a signi(cid:12)cant relationship with the occupation wage level. Table 5 also shows results for speci(cid:12)cations where the complexity index is replaced by a complexity dummy. Here the results are stronger for the 2005 cross-section, with complex occupations having wages that are 8.6-11.5 percent higher than those in simple occupations, after controlling for demographic factors. 13

Table 4: Individual-Level Wage Regression, 1980 and 2005 Dependent Variable: Log Wages Independent 1980 2005 Variable Complexity Index 0.347*** 0.711*** (7.25) (14.32) Routine Index -0.0154 0.0157 (-0.34) (0.31) N 2664259 673783 Notes: Theregressionsinclude(cid:12)xede(cid:11)ectsforage(4categories: 16-28,29-40,41-52,53-64), educationlevel(lessthanhighschool,highschool,somecollege,college),andrace(white, nonwhite). Standarderrorsclusteredatoccupationlevel. t-statisticsareinparentheses. (cid:3)p<0:1;(cid:3)(cid:3)p<0:05;(cid:3)(cid:3)(cid:3)p<0:01. 3.2 Task Content of Occupations, Wage Growth, and Employment Growth Table 6 shows results from baseline regressions of 1980-2005 wage growth on occupational task content. The independent variables in columns (i)-(iii) are the occupation task complexity index and the Autor and Dorn (2013) routine task intensity index (both converted to percentiles and normalized to lie between zero and one), a third-degree polynomial in the 1980 wage level, and the same set of occupation-level demographic means included in Table 5. Complexity has a positive and highly signi(cid:12)cant relationship with wage growth. This e(cid:11)ect is robust to the inclusion of the 1980 wage level and the routineness index as control variables. Average wage growth between 1980 and 2005 in the most complex occupations is 30-35 percentage points higher than in the least complex occupations. It is notable that complexity has a signi(cid:12)cant relationship with wage growth even though the regressions include controls for the share of workers in an occupation with a college degree. In columns (iv) and (v) in Table 6 the complexity index is replaced with an indicator variable for complexity. Since the cuto(cid:11) value of our complexity index that separates complex occupations from simple occupations is rather arbitrary, we show results from using the 14

Table 5: Occupation-Level Wage Regression with Occupational Demographic Controls (A) Dependent Variable: Log Wages in 1980 (B) Dependent Variable: Log Wages in 2005 Complex Variable: Complex Variable: Complex Variable: Complex Variable: Indep. Index Indicatory Index Indicatory Variable (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) Complexity 0.102* 0.106* 0.00228 0.0235 0.401*** 0.416*** 0.115*** 0.0862** Variable (1.71) (1.75) (0.08) (0.79) (5.31) (5.45) (3.29) (2.19) Routine 0.0131 0.00442 0.00846 0.0512 0.0394 0.0317 Index (0.41) (0.14) (0.26) (1.28) (0.95) (0.76) Female -0.143*** -0.147*** -0.154*** -0.155*** -0.128** -0.143*** -0.159*** -0.174*** Share (-3.52) (-3.51) (-3.68) (-3.71) (-2.53) (-2.76) (-2.97) (-3.24) College 0.260*** 0.265*** 0.325*** 0.295*** 0.530*** 0.553*** 0.715*** 0.676*** Share (3.49) (3.50) (4.64) (3.74) (5.71) (5.85) (8.01) (6.61) High School 0.427*** 0.423*** 0.468*** 0.478*** 0.361** 0.345** 0.441*** 0.568*** Share (3.50) (3.45) (3.84) (3.97) (2.35) (2.24) (2.80) (3.64) Non-white -0.284 -0.282 -0.269 -0.279 -0.172 -0.164 -0.0910 -0.139 Share (-1.38) (-1.37) (-1.30) (-1.35) (-0.67) (-0.64) (-0.35) (-0.52) Married 0.884*** 0.868*** 0.938*** 0.922*** 0.568* 0.509 0.701** 0.717** Share (3.47) (3.37) (3.66) (3.60) (1.79) (1.59) (2.14) (2.17) Mean 0.00845** 0.00851** 0.00835** 0.00844** 0.0104** 0.0106** 0.00822 0.00991* Age (2.16) (2.17) (2.11) (2.14) (2.09) (2.13) (1.61) (1.92) Mean # -0.0710 -0.0644 -0.0661 -0.0699 0.0437 0.0692 0.0789 0.0583 Children (-0.64) (-0.57) (-0.59) (-0.62) (0.31) (0.49) (0.54) (0.39) N 315 315 315 315 310 310 310 310 yComplexoccupationsarede(cid:12)nedasthoseabovethe50thpercentile(columns(iii)and(vii))orabovethe66thpercentile (columns(iv)and(viii))ofthecomplexityindex. Notes: Demographicvariablesareoccupation-levelmeansoftheshareofworkersinanoccupationwithacollege/high-school degree,theshareofworkersinanoccupationwhoarenon-white,theshareofworkersinanoccupationwhoaremarried,the shareoffemaleworkersinanoccupation,themeanageofworkersinanoccupation,andthemeannumberofchildrenof workersinanoccupation. t-statisticsareinparentheses. Signi(cid:12)cancelevelsare: (cid:3)(cid:3)(cid:3) 1%,(cid:3)(cid:3) 5%,(cid:3) 10%. 15

50th percentile in column (iv) and the 66th percentile in column (v).16 Wage growth in complex occupations is 7-14 percentage points higher than in simple occupations under the two cuto(cid:11) levels, while routineness once again has no signi(cid:12)cant relationship with wage growth. We repeat our baseline regressions using employment growth rather than wage growth as a dependent variable, and the results are reported in Table 7. The relationship between employment growth and complexity is weaker than the wage growth results shown in Table 6. The relationship between task complexity and employment growth is positive in all columns, however the coe(cid:14)cient is not signi(cid:12)cant. It is quite notable that after controlling for complexity there is no signi(cid:12)cant relationship between routineness and employment growth. Group-Level Estimation. So far our empirical analysis has been performed on data aggregated to the occupation level. Another empirical approach would be to rely on panel data that includes individuals of di(cid:11)erent cohorts in 1980 and 2005. This would enable us to estimate occupationspeci(cid:12)c age- and time e(cid:11)ects from worker-level data. Unfortunately, such data do not exist, at least not with an appropriate sample size. We approximate this type of data by disaggregating our repeated cross-sections to a much (cid:12)ner level, de(cid:12)ned by occupations and \groups." Groups are de(cid:12)ned by gender, education, race, and age. We de(cid:12)ne four categories for education: (i) individuals with less than a high school diploma, (ii) individuals with a high school diploma only, (iii) individuals with some college education, but no degree; and (iv) individuals with a college degree. We also de(cid:12)ne four categories for age: (i) 16 to 28, (ii) 29 to 40, (iii) 41 to 52, and (iv) 52 to 64. Finally, we use two categories for race: white and non-white. For each occupationdemographic cell we compute average wage and total employment changes from 1980 to 2005 using the 1980 5% Census and the 2005 ACS.17 This yields a total of 15142 cells. We estimate our baseline wage and employment growth regressions on the disaggregated data, but with (cid:12)xed e(cid:11)ects for the categories.18 The results are reported in Tables 8 and F.1 (in Appendix F), respectively. In all of these regressions the standard errors are clustered at the occupation level. When we regress wage growth on our disaggregated data the relationship between complexity and wage growth identi(cid:12)ed thus far remains. The most complex occupations are predicted to have 16The (cid:12)ndings are robust to the choice of the cuto(cid:11) and additional results are available upon request. 17Weusethesamesamplerestrictionsasbefore. However,inordertohaveenoughnumberofobservationsineach cell we use both men and women in this analysis. 18To be clear, the regressions include gender (cid:2) education (cid:2) race (cid:2) age (cid:12)xed e(cid:11)ects. 16

Table 6: Occupation-Level Wage Growth Regression with Occupational Demographic Means Dependent Variable: Change in Log Wages 1980-2005 Complex Variable: Complex Variable: Independent Index Indicatory Variable (i) (ii) (iii) (iv) (v) Complexity Variable 0.304*** 0.316*** 0.347*** 0.138*** 0.0683** (4.94) (5.07) (5.74) (5.02) (2.18) Routine Index 0.0398 0.0336 0.0262 0.0161 (1.21) (1.05) (0.81) (0.48) Female Share 0.00599 -0.00561 -0.0299 -0.0267 -0.0504 (0.15) (-0.13) (-0.71) (-0.63) (-1.15) College Share 0.270*** 0.288*** 0.287*** 0.349*** 0.381*** (3.56) (3.73) (3.52) (4.37) (4.35) High School Share -0.102 -0.115 0.0629 0.119 0.235* (-0.82) (-0.91) (0.50) (0.94) (1.81) Non-white Share 0.106 0.112 0.0181 0.100 0.0551 (0.51) (0.54) (0.09) (0.49) (0.26) Married Share -0.244 -0.290 0.0537 0.232 0.209 (-0.94) (-1.11) (0.20) (0.87) (0.76) Mean Age 0.00207 0.00222 0.00364 0.000595 0.00271 (0.51) (0.55) (0.90) (0.15) (0.64) Mean # Children 0.0549 0.0747 0.00478 -0.0198 -0.00485 (0.48) (0.64) (0.04) (-0.17) (-0.04) Order of 1980 Wage Poly. 0 0 3 3 3 N =310 yComplexoccupationsarede(cid:12)nedasthoseabovethe50thpercentile(column(iv))orabovethe66thpercentile(column(v)) ofthecomplexityindex. Notes: Demographicvariablesareoccupation-levelmeansoftheshareofworkersinanoccupationwithacollege/high-school degree,theshareofworkersinanoccupationwhoarenon-white,theshareofworkersinanoccupationwhoaremarried,the shareoffemaleworkersinanoccupation,themeanageofworkersinanoccupation,andthemeannumberofchildrenof workersinanoccupation. t-statisticsareinparentheses. Signi(cid:12)cancelevelsare: (cid:3)(cid:3)(cid:3) 1%,(cid:3)(cid:3) 5%,(cid:3) 10%. 17

Table7: Occupation-LevelEmploymentGrowthRegressionwithOccupationalDemographicMeans Dependent Variable: Change in Employment Share 1980-2005 Complex Variable: Complex Variable: Independent Index Indicatory Variable (i) (ii) (iii) (iv) (v) Complexity Variable 0.00162 0.00135 0.00154 0.00000113 0.000876 (1.44) (1.19) (1.34) (0.00) (1.56) Routine Index -0.000871 -0.000822 -0.000961 -0.000783 (-1.44) (-1.34) (-1.57) (-1.27) Female Share 0.000152 0.000407 0.000207 0.000131 0.0000781 (0.20) (0.52) (0.26) (0.16) (0.10) College Share 0.000808 0.000419 0.000563 0.00136 0.000282 (0.58) (0.29) (0.36) (0.89) (0.18) High School Share -0.00114 -0.000878 -0.000129 0.000499 0.000791 (-0.50) (-0.38) (-0.05) (0.21) (0.33) Non-white Share -0.000418 -0.000536 -0.000877 -0.000595 -0.00102 (-0.11) (-0.14) (-0.22) (-0.15) (-0.26) Married Share -0.00478 -0.00375 -0.00189 -0.000950 -0.00167 (-1.00) (-0.78) (-0.37) (-0.19) (-0.33) Mean Age -0.00000104 -0.00000499 -0.00000580 -0.0000103 -0.00000498 (-0.01) (-0.07) (-0.08) (-0.13) (-0.07) Mean # Children 0.000758 0.000317 0.0000537 0.00000976 -0.0000621 (0.36) (0.15) (0.02) (0.00) (-0.03) Order of 1980 Wage Poly. 0 0 3 3 3 N =315 yComplexoccupationsarede(cid:12)nedasthoseabovethe50thpercentile(column(iv))orabovethe66thpercentile(column(v)) ofthecomplexityindex. Notes: Demographicvariablesareoccupation-levelmeansoftheshareofworkersinanoccupationwithacollege/high-school degree,theshareofworkersinanoccupationwhoarenon-white,theshareofworkersinanoccupationwhoaremarried,the shareoffemaleworkersinanoccupation,themeanageofworkersinanoccupation,andthemeannumberofchildrenof workersinanoccupation. t-statisticsareinparentheses. Signi(cid:12)cancelevelsare: (cid:3)(cid:3)(cid:3) 1%,(cid:3)(cid:3) 5%,(cid:3) 10%. 18

a wage growth that is 26-35 percentage points higher than in the least complex occupations. This is consistent with the coe(cid:14)cient values estimated in the occupation level data (Table 6) and still signi(cid:12)cant at the 1% level. There is also a positive, though insigni(cid:12)cant, relationship between routineness and wage growth. Table F.1 shows the results from the group-level regressions for employment. Complexity has a positive and signi(cid:12)cant relationship with employment growth, while occupations with higher levels of routine intensity are now predicted to have signi(cid:12)cantly lower levels of employment growth. It should be noted that the relatively small magnitude of the coe(cid:14)cients in these regressions is a result of the disaggregation, as the dependent variable is the share of overall employment in each occupation-gender-education-age-race cell. Overall, we conclude that the stylized facts motivating our de(cid:12)nition of complex-task biased technological change presented in section 2.3 are robust to disaggregation to the occupational level and inclusion of the 1980 wage level. In particular, task complexity is strongly positively related with both wage growth and wage levels, while wages within occupations of similar complexity are equalized across routine and non-routine occupations. Furthermore, we (cid:12)nd evidence that more complex occupations experienced higher employment growth, and labor in occupations of similar task complexity has reallocated slightly towards non-routine occupations. The relatively weak employment e(cid:11)ects suggest that the skill structure in the economy makes labor movements relatively inelastic with respect to the complex task wage premium. 3.3 Robustness In this section we provide some sensitivity analysis on our wage and employment growth results. 3.3.1 Complex-Task Biased Technological Change and the 1980 Wage Distribution A potential concern with our results is that they may be driven by a particular segment of the 1980 wage distribution. For example, Autor and Dorn (2013) argue that low-skill non-routine service sector jobs, which were at the bottom of the 1980 wage distribution, experienced substantial wage growth between 1980 and 2005. One may therefore wonder if our results do not hold for this part of the 1980 wage distribution and if they are mostly identi(cid:12)ed from formerly middle-wage and 19

Table 8: Group-Level Wage Growth Regression Dependent Variable: Change in Log Wages 1980-2005 Independent Variable (i) (ii) (iii) Complexity Index 0.258*** 0.273*** 0.349*** (10.98) (10.02) (12.59) Routine Index 0.0427 0.0440 (1.36) (1.49) Order of 1980 Wage Poly. 0 0 3 N =15142 Notes: Thetablereportsresultswhenoccupation-leveldataisdisaggregatedto occupation(cid:2)gender(cid:2)education(cid:2)race(cid:2)agecells(seesection3.2)for discussion. Regressionsincludegender(cid:2)education(cid:2)race(cid:2)age(cid:12)xede(cid:11)ects. Sandarderrorsclusteredattheoccupationlevel. t-statisticsareinparentheses. Signi(cid:12)cancelevelsare: (cid:3)(cid:3)(cid:3) 1%,(cid:3)(cid:3) 5%,(cid:3) 10%. high-wage occupations. We thus split the sample by terciles of the 1980 wage distribution. The results for a speci(cid:12)cation with a third degree polynomial in the 1980 wage are shown in Table 9. The coe(cid:14)cient on task complexity is quite robust and estimated with high precision in all three subsamples. It is thus clear that our results hold no matter the wage level at the beginning of the sample period. Furthermore, the routine dummy is negative, though insigni(cid:12)cant, in the (cid:12)rst two subsamples. It is positive and signi(cid:12)cant among high-paying occupations, however. This is most likely driven by outliers since there are very few routine occupations among traditionally highpaying occupations. Corresponding results for employment growth are shown in Table F.2. Again, we (cid:12)nd a robustly positive e(cid:11)ect of task complexity and a robustly negative e(cid:11)ect of routineness on employment growth for each tercile of the 1980 occupational wage distribution, though with insu(cid:14)cient statistical power to attain statistical signi(cid:12)cance. Interestingly, the employment e(cid:11)ect of task complexity is strongest for the tercile with the highest estimated wage e(cid:11)ect as well. 20

Table 9: Occupation-Level Wage Growth Regression by 1980 Wage Tercile Dependent Variable: Change in Log Wages 1980-2005 First Second Third Independent Tercile Tercile Tercile Variable (i) (ii) (iii) Complexity Index 0.553*** 0.490*** 0.624*** (8.35) (7.92) (5.43) Routine Index -0.0327 -0.0409 0.131* (-0.70) (-0.88) (1.90) Order of 1980 Wage Poly. 3 3 3 N 112 108 90 Notes: Thetablereportsresultsforoccupation-levelregressionsrunfordi(cid:11)erent tercilesofthe1980occupationalwagedistribution. t-statisticsarein parentheses. Signi(cid:12)cancelevelsare: (cid:3)(cid:3)(cid:3) 1%,(cid:3)(cid:3) 5%,(cid:3) 10%. 3.3.2 Regressions on Female-Only Sample In our baseline analysis we excluded women from our wage and employment data, except in the group-level analysis in the previous section. This was done so as to abstract from the e(cid:11)ects of increased female labor force participation and female wage growth during the sample. To examine the e(cid:11)ect of this data restriction we now repeat our analysis using a female-only sample from the Census and the ACS, otherwise sample restrictions and variable construction remain unaltered. Table F.3 reports results from the occupation-level wage growth regressions run on the femaleonly sample. The point estimates are similar to the corresponding results on the male sample reported in Table 6. Average wage growth in the most complex occupations is 36 to 38 percentage points higher than in the least complex occupations. When using the complexity dummies, instead of the index, the average wage growth for complex occupations is 9-12 percentage points higher than for simple occupations. Moreover, routine task intensity has no signi(cid:12)cant relationship with wage growth in the female-only sample. As was the case with the baseline sample, task complexity has a weaker relationship with em- 21

ployment than with wages. Table F.4 reports the results for the occupation-level employment growth regressions carried out on the female-only sample. While the estimated coe(cid:14)cient on complexity is always positive, it is not signi(cid:12)cant. In contrast, routineness has a negative relationship with the 1980-2005 employment growth that is signi(cid:12)cant at the 5% level. 4 Theoretical Framework 4.1 Overview We have documented four robust empirical facts about the evolution of the occupational wage and employment structure. These are: (i) wages, measured either in growth or in levels, are not signi(cid:12)cantly related to routine-task intensity once one conditions on task complexity; (ii) task complexity is strongly positively related to wage levels and wage growth; (iii) there has been a reallocation of labor from simple to complex occupations, and this employment growth e(cid:11)ect is weaker than the growth in the complexity wage premium; (iv) within the simple occupations, the share of non-routine occupations has increased. In this section we formulate an equilibrium model of the occupational wage and employment structure that can jointly rationalize these facts. To derive sharp theoretical results that clarify which modi(cid:12)cations to the canonical model of SBTC are required we keep the model stylized. In particular, we consider a structure with three productionprocessesonly, calledoccupations,thatdi(cid:11)erwithrespecttotheirtechnologiesandthat aggregate into a single (cid:12)nal output good. The three central features of the model are as follows. First, one of the occupation groups features capital-skill complementarity, where skill is measured by the ability to solve complex tasks. We call this group of occupations \complex". On the other hand, the ability to solve complex tasks is irrelevant in non-complex occupations. We refer to this groupofoccupationsas\simple". Second, tohighlightthedistinctionbetweentaskcomplexityand routineness, we divide simple occupations into two subgroups, namely simple-routine and simple non-routine occupations. Simple routine occupations are those that are gradually automated. Labor and capital are hence relatively substitutable. Simple non-routine occupations are akin to low-skill service jobs in Autor and Dorn (2013) and only require labor inputs. Third, workers are heterogeneous with respect to their skill endowment for performing complex tasks but are homogeneous in their ability to solve simple tasks. A direct consequence of this assumption is that 22

simple occupations, whether routine or non-routine, draw from the same homogenous pool of labor supply. Wages are thus equalized among workers optimally choosing this group of occupations. This setup can be interpreted as a hybrid of the Ricardian model in Autor and Acemoglu (2011) and of a model of SBTC with capital-skill complementarity as in Krusell et al. (2000). Indeed, the technology in the complex and the simple routine occupations is a simpli(cid:12)ed version of the productionfunctioninKruselletal.(2000),butwithskillsmeasuredbytheabilitytosolvecomplex tasks. We derive comparative statics results for the case of an increase in the factor productivity of labor in the complex occupations. We call this case Complex-Task Biased Technological Change. Because of a shift in the demand for complex labor, the complexity wage premium increases. At the same time, more workers now (cid:12)nd it optimal to move to the complex occupations, thereby worsening the skill composition and dampening the e(cid:11)ect on the wage premium. How large this supply e(cid:11)ect is depends on the characteristics of the complex-skill distribution. If this distribution is su(cid:14)ciently skewed, with a large mass at the lower tail, then the labor supply to the complex occupationsisrelativelyinelastic. Inthiscase,thee(cid:11)ectonthewagepremiumwillbelargewhilethe employmente(cid:11)ectwillberelativelysmall. Thiswidensthecomplexitywagepremiumbecauseofthe capital-complex-skill complementarity. The equilibrium adjustment of the employment structure in simple occupations is more complicated. Clearly, labor needs to (cid:13)ow from the simple to the complex occupations. Whether the decrease in simple routine- or non-routine labor inputs is larger in relative terms depends on the technologies. As it turns out, if capital and labor in simple routine occupations are su(cid:14)ciently substitutable and intermediate outputs from routine and non-routine occupations are su(cid:14)ciently complementary in the production of the (cid:12)nal good, then the share of non-routine labor increases relative to the share of routine labor. Takentogether, ourmodelfeaturesaproductionprocessinwhichworkerswithacertaintypeof skillgainfromtheintroductionofnewtechnologies, aproductionprocessinwhichnewtechnologies substitute for workers, thereby integrating the concept of automatization, and a third production process that absorbs a (potentially substantial) share of \displaced" workers because it is nonroutine but simple. Interestingly, automatization in our comparative statics exercise does not arise from cheaper or more productive capital, but from the reallocation of labor towards an occupation in which computers and workers are complements. 23

Atthispointitisworthwhilehighlightingthatwemaintaintheassumptionthatthedistribution over simple tasks is degenerate, for two main reasons. First, it serves to highlight that we think of simpleoccupationsasthoseinvolvingtasksthatmostpeopleneedtoperformatsomepointintheir dailyorweeklyroutine,suchasdriving,cleaning,preparingsimplemeals,archivingortransporting. As a consequence, simple non-routine occupations are a type of outside option available to anyone. Put di(cid:11)erently, skills in performing simple tasks are in abundant supply relative to higher-order skills. Second, the model presented below remains tractable even though we solve for general equilibrium with heterogeneous workers. An important consequence of this assumption is that our model only generates employment polarization, but not wage polarization. While this is consistent with the evidence for many non- US countries, such as for Canada (Green and Sand (2014)) or for Germany (Dustmann et al. (2009)), there is a large literature documenting polarization of the occupational wage structure in US data. We do not attempt to modify the model to generate wage polarization as well and focus on the novel set of stylized facts we have established above.19 4.2 The Model Weconsideraclosedeconomyinwhicha(cid:12)nalgoodY isproducedusingthreeintermediateproduction processes. Output from the three processes, de(cid:12)ned by the tasks that need to be performed, is (y ;y ;y ), where s stands for \simple", c stands for \complex", R stands for \routine" and NR c R NR stands for \non-routine". The mapping from intermediate to (cid:12)nal output is given by the function Y = F (y ;y ;y ): Y c R NR 19We conjecture that wage polarization can be delivered by our model as follows. Suppose that skills are twodimensional. Inparticular,skillsinperformingsimpleroutinetasksareheterogeneousandpositivelycorrelatedwith skills in performing complex tasks. Then complex-task biased technological change will induce the highest earners in simple routine occupations to move to the complex occupations. As a consequence, the wage in simple routine occupations will decrease, while the wage in simple non-routine occupations, which do not depend on heterogeneous skills, will remain constant. While this extension is interesting for quantitative analysis, it will be analytically intractable. 24

For reasons explained below, we impose the following functional form restrictions: F = (y ) (cid:13) (cid:1)(y )1(cid:0)(cid:13) ; (2) Y s c (cid:22) (cid:22) 1 y s = [(y R ) +(y NR ) ](cid:22) : (3) We will assume that (cid:13) = 0:5 throughout the rest of the analysis. Output can be used either for producing capital, with technology 1 K = (cid:1)Y; (4) (cid:25) (cid:18) K(cid:19) orfor(cid:12)nalconsumption. Capitaldepreciatesfullysothatoureconomycanbeviewedasasequence of static economies. We therefore do not use a time-subscript. Let C;S;K stand for aggregate inputs of labor performing complex or simple tasks and of capital, indexed appropriately in what follows. In specifying the production structure we assume that the elasticity of substitution between the capital input and the labor input is larger in the routine process than in the complex process. Hence, inputs of labor performing complex tasks are a relative complement with capital inputs. The non-routine process is modeled as in Autor and Dorn (2013), where it stands in for the manual non-routine labor intensive service sector. An example of such a production structure is a (cid:12)nal output good that is produced using machines that need to be operated (y ) and that produce intermediates that need to be transported, stored and sold (y ), R NR thereby requiring organization, e(cid:11)ective communication and management of the two processes (y ). c For analytical convenience we impose the following production structure on these process: y = ((cid:11) (cid:1)C) (cid:26) (cid:1)((cid:11) (cid:1)K )1(cid:0)(cid:26) ; c c k;c c 1 y = (cid:11) (cid:1)S +(cid:11) (cid:1)K ; R s;R R k;R R h i y = (cid:11) (cid:1)S : (5) NR s;NR NR Relative capital-skill complementarity in the complex process implies that (cid:26) 2 (0;1). There is a unit mass of workers who are endowed with skills for performing simple or complex tasks, denoted by (s;c). Each worker supplies one unit of labor inelastically. Skill endowments 25

of s are homogenous in the population, imposing the assumption that each worker has the same base level of skills at performing raw manual or simple communicative tasks, with implications discussed above in section 4.1. In contrast, skills at performing complex tasks are heterogeneous anddistributedwithCDFG(c),whichweassumetobeofthePareto-typewithparameters((cid:12);c ): m c (cid:12) m G(c) = 1(cid:0) , with c (cid:21) c : (6) m c (cid:16) (cid:17) The resource constraint that the mass of workers going to the complex process cannot be larger than one imposes the parameter restrictions c < ((cid:12) (cid:0)1)=(cid:12), with (cid:12) > 1. The parameters of the m Pareto distribution turn out to be important for explaining why strong wage growth in non-routine simple occupations can come with weak employment growth in this occupation group. Given these assumptions it is worth highlighting that the employment share of labor that goes to the simple occupations, S, is homogenous. In contrast, C is an aggregator of heterogenous labor going to the complex sector: C = 1 c(cid:1)dG(c) = (cid:12) (cid:1)(c ) (cid:12) (cid:1) cT 1(cid:0)(cid:12) : (7) m (cid:12)(cid:0)1 ZcT (cid:18) (cid:19) (cid:0) (cid:1) The threshold level c is endogenous and needs to be consistent with individual optimization (the T threshold worker is indi(cid:11)erent between working in simple and complex tasks) and the labor market equilibrium condition S = S +S R = G(c ). R N T The market structure is as follows. We treat this model economy as static so that we do not make any explicit assumptions about timing of events. Markets are perfectly competitive. One largerepresentative(cid:12)rmownsthetechnologyF . Itbuysintermediateinputsatpricesp ;p and Y c NR p from three types of (cid:12)rms, each of which holds one of the intermediate technologies, and sells its R (cid:12)nal output to consumers at price p . We treat the (cid:12)nal good as the numeraire, with normalized Y price p = 1. Labor and capital is hired in competitive factor markets. Y Sincethiseconomyisfrictionlesswecharacterizetheequilibriumallocationbysolvingthesocial planner’s problem. The planner’s problem is outlined in Appendix B. Evidently, evaluated at the (cid:12)rst-best allocation of labor and capital, all goods- and factor prices need to be equal to their marginal products. It is important to notice that in competitive equilibrium, w = p and NR NR 26

w = w . Both of these equations are equilibrium conditions, the (cid:12)rst of which states that NR R pro(cid:12)ts in the non-routine process need to be zero and the second of which is a law-of-one-price for labor in the two simple production processes. Of course, these conditions also come out directly from the social planner’s problem, as can be shown from its (cid:12)rst-order conditions. The equilibrium allocations do not admit closed-form solutions. Yet, the model can generate the empirical regularities documented above under a surprisingly clear restriction on the parameter space. De(cid:12)ne (cid:22)(cid:3) = (cid:12)=((cid:12)+(cid:26)) 2 (0;1). We then obtain the following result, proven in Appendix C. Proposition. Consider two stationary state equilibrium allocations of labor together with their factor prices, C0;S0;S0 ;w0;w0;w0 and C1;S1;S1 ;w1;w1;w1 . Assume that > R NR c R NR R NR c R NR (cid:22) > (cid:22)(cid:3). Then an in(cid:0)crease in the factor produc(cid:1)tivity(cid:0)of the labor input, (cid:11) (or o(cid:1)f the capital input, c (cid:11) ) in the complex technology, has the following e(cid:11)ect on the equilibrium allocations and factor k;c prices C1 > C0 S1 < S0 R R S1 < S0 NR NR S1 S0 NR > NR S1 S0 R R w0 = w0 R NR w1 = w1 R NR w1 w0 c > c : (8) w1 w0 NR NR (cid:4) 4.3 Discussion Probably the deepest of the results in the proposition is the decline of the non-routine labor share when measured relative to the entire economy but an increase when measured relative to the total labor share of simple occupations. This result thus deserves some discussion. To understand 27

the issue, suppose we set the parameter (cid:22) in equation (3) equal to zero so that the elasticity of substitution between all occupation-speci(cid:12)c inputs in the production of the (cid:12)nal good is equal to one. In this case the ratios of these intermediate inputs relative to total output produced, y =Y, j are all kept constant. Since the only input in the non-routine occupation is labor it follows directly that S increases whenever C increases. This is inconsistent with our stylized facts. We thus NR need to be able to control the complementarity between the two simple intermediate inputs in the production of the (cid:12)nal good. This is achieved via the speci(cid:12)cation in equations (2) and (3). Notice that it will be optimal to keep the ratio of y and y constant. A rise in y will thus have the C S S e(cid:11)ect of increasing the price of the simple intermediate inputs. With p = w = w , this NR NR R will have the e(cid:11)ect of increasing the relative cost of simple labor inputs. Since capital and labor are relatively substitutable in the routine occupation, there will be a strong substitution towards capital inputs. For SNR to increase while S decreases, (cid:22) can neither be too small nor too SR+SNR NR large. Indeed, ifit wastoo small, S wouldincreaseratherthan decrease. Ifitwastoolarge, then NR S would decrease even faster than S . This explains the condition on the structural parameters NR R in the proposition. An interesting result not mentioned in the proposition is that the model is consistent with a situation in which the relative wage (wC) increases dramatically whereas the equilibrium employwR ment share of the complex occupations C(cid:3) rises only slightly. This can be seen from the following equation, derived in Appendix C: (cid:12)(cid:0)1 (cid:12) w C(cid:3) = (cid:1)c(cid:12) (cid:1) c ; (9) (cid:12)(cid:0)1 m w (cid:18) (cid:19) (cid:18) R(cid:19) where c is the lower bound on labor in complex tasks, possibly zero, and (cid:12) > 1. Since equilibrium m relative wages can be characterized without solving for C(cid:3), as shown in Appendix C, this equation should be interpreted as structural. It describes the equilibrium relationship between the complex wage premium and the labor share of the complex occupation. The strength of this relationship is governed by the parameters of the Pareto skill distribution, (cid:12) and c . It is then clear that m one can (cid:12)nd restrictions on the parameters of this distribution such that dC(cid:3) (cid:25) 0 even though d(w =w ) (cid:29) 0. This will apply if c is close to zero while (cid:12) is su(cid:14)ciently large. With large C R m (cid:12), the Pareto distribution is concentrated near c , and with small c this point of concentration m m 28

is quite far away from the threshold level c . Intuitively, if a large share of the population has T very low skills at performing complex tasks, then the pool of labor optimally choosing the complex occupation is small and inelastic. As a consequence, demand shifts for complex labor have large e(cid:11)ects on relative prices, but small e(cid:11)ects on quantities. Several additional points are worth noting. First, we refer to the situation in which the factor productivity in the complex technology rises as Complex-Task Biased Technological Change (CBTC). In principle the distinction between (cid:11) and (cid:11) is vacuous given the technology, but c k;c given our focus on the reallocation of labor rather than of capital we emphasize the case in which CBTC is kick-started by an increase of the factor productivity of complex labor inputs. Second, there are a number of other parameters that can generate the same qualitative predictions in comparative statics exercises. Examples include a decrease in price of capital, (cid:25) , a case that may K be particularly relevant given the evidence in Krusell et al. (2000), or an increase of the factor productivity of capital relative to labor in the simple routine technology, (cid:11) =(cid:11) . Which of k;R s;R these channels has the largest e(cid:11)ect, and whether it can be identi(cid:12)ed, is an interesting question for future research. Third, any situation of complex-task biased technological change comes, by de(cid:12)nition, with an increase of C. As this can only be the case if the skill threshold cT decreases, the average skill for performing complex tasks decreases in the process of labor reallocation. We provide empirical evidence suggestive of this e(cid:11)ect in Appendix E. 5 Complexity and Social Skills In a recent paper, Deming (2015) focuses on the role that social interaction skills play in explaining labor demand shifts over the past 30 years. He argues that such skills serve to reduce workerspeci(cid:12)c coordination costs. Technological progress and automation have therefore implied that high-paying occupations increasingly require social skills. Consistent with this hypothesis, he (cid:12)nds that social skills have been increasingly rewarded over the last three decades, especially in jobs that combine social and cognitive skills. To compare our de(cid:12)nition of complexity with social skills we compute a measure analogous to the social skill index in Deming (2015). Following Deming (2015) we select four occupational descriptors from the O*NET indicative of social skills: \Coordination", \Negotiation", \Persuasion", and \Social Perceptiveness". We carry out a PCA 29

with one component on this data in order to compute social skill scores, which we in turn convert to percentiles between zero and one in order to yield a social skill index. Table 10: Comparison of Complexity and Social Skills Occupations with High Complex Content and Low Social Skill Content Occupation SocialSkill ComplexityIndex Title Percentile Percentile ComputerandPeripheralEquipmentOperators 48.497 74.395 AircraftMechanics 49.112 76.409 ProgrammersofNumericallyControlledMachineTools 49.125 67.812 PowerPlantOperators 49.648 71.556 MathematiciansandStatisticians 0.772 91.323 BiologicalTechnicians 46.732 73.283 Occupations with Low Complex Content and High Social Skill Content Occupation SocialSkill ComplexityIndex Title Percentile Percentile RetailSalespersons&SalesClerks 62.228 49.662 Door-to-doorSales,StreetSales,andNewVendors 68.335 6.419 BillandAccountCollectors 70.040 44.817 SupervisorsofClearningandBuildingServices 62.962 32.372 EligibilityClerkforGovernmentPrograms 56.290 44.825 Sheri(cid:11)s,Baili(cid:11)s,CorrectionalInstitutionO(cid:14)cers 56.283 43.533 Notes: The table reports values of the social skill and complexity indices for a selection of occupations. The index values are converted to percentiles of the occupation-level distribution. See sections 2.2 and 5 for the construction of thecomplexityandthesocialskillindices. Social skills are correlated with complexity (cid:0) the correlation coe(cid:14)cient between the two indices is 0.8951. There are, however, important di(cid:11)erences. The (cid:12)rst panel in Table 10 lists several examples of complex occupations with relatively low social skill content. These are principally technical occupations such as Mathematicians and Statisticians, Computer Operators, and Programmers. These occupations clearly require abstract problem solving skills despite not involving 30

Table 11: Complexity, Social Skills, Wages, and Employment Employment % Employment log(wage ) log(wage ) (cid:1)log(wage) Share Change 1980 2005 1980 2005 simple nonsocial 1.924 2.028 0.104 0.598 0.558 -0.068 social 2.220 2.430 0.210 0.055 0.037 -0.326 complex nonsocial 2.250 2.559 0.300 0.056 0.077 0.380 social 2.314 2.681 0.367 0.291 0.328 0.129 Notes: Wage and employment data is taken from the 1980 5% sample of the US Census and the 2005 ACS. The sample is restrictedtonon-institutionalizedmalesaged16-64inthemainlandUnitedStates. Complexoccupationsarede(cid:12)nedasthose whose complexity index is above the 66th percentile in the occupation-level complexity distribution. All other occupations are de(cid:12)ned as simple. Social occupations are de(cid:12)ned as those whose social skills index is above the 66th percentile in the occupation-levelsocialskillsdistribution. Allotheroccupationsarede(cid:12)nedasnonsocial. a great deal of social interaction. Conversely, the second panel in Table 10 lists several examples of simple occupations with high social skill measures. These principally comprise service occupations such as Salespersons, Cleaning Supervisors, and Bill Collectors (cid:0) occupations which are heavily dependent on interacting with other people whilst not requiring a great deal of speci(cid:12)c knowledge, management and organizational skills, or problem solving ability. Table 11 presents preliminary evidence regarding the extent to which complexity and social skills have a(cid:11)ected wage and employment growth in various occupations over the 1980-2005 time period. In particular, Table 11 shows average wage growth for 4 categories of occupations20: simple nonsocial, simplesocial, complexnonsocial, andcomplexsocial. Itisclearthatitisthecomponents of occupational complexity that principally explain wage patterns over the period. First, wage growth is signi(cid:12)cantly higher for complex rather than simple occupations regardless of their social skilltype. Second,theemploymentshareofbothcomplex-socialandcomplex-nonsocialoccupations increased between 1980 and 2005. At the same time, the employment share of both simple-social and simple-nonsocial occupations decreased. These results suggest that social skills principally contribute to higher wage and employment growth through their correlation with complexity. Tables12andF.5showresultsforthewage-andemploymentgrowthregressionswhenthesocial 20Socialoccupationsarede(cid:12)nedasthosethathaveasocialskillindexinthetop66thpercentamongstalloccupations. 31

skill index is included as a control. In both tables we show results from our baseline occupationlevel regression (column i), from an occupation-level regression with demographic controls (column ii), and the group-level (cid:12)xed e(cid:11)ects regression speci(cid:12)cation (column iii). From Table 12 it can be seen that controlling for social skills does not substantially alter the coe(cid:14)cient estimates on complexity. Complex tasks remain signi(cid:12)cant predictors of 1980-2005 wage growth both in the occupation-level regressions (with or without control for occupational demographic means) and in the group-level (cid:12)xed e(cid:11)ect regression. The estimated coe(cid:14)cient on social skill intensity is positive andmostlysigni(cid:12)cantaswell,albeitsmallerthanthecoe(cid:14)cientsontaskcomplexity. Whenitcomes to employment growth neither social skill intensity nor task complexity are signi(cid:12)cant predictors of employment growth. From this analysis we conclude that it is indeed possible to separately estimate the e(cid:11)ects of complextaskintensityandsocialskillintensityratherprecisely. Giventheresultsitisreasonableto conjecture that the two concepts are complementary. There is a substantial increase in the return to task complexity over and above the rise in the returns to social skills. Bringing together these two concepts to measuring occupational task content in a uni(cid:12)ed model of the occupational wage and employment structure is a promising avenue to pursue. 6 Conclusion This paper studies the relationship between task complexity and the occupational wage- and employment structure. Using O*NET data, we provide a novel characterization of occupations based on the extent to which they rely on complex tasks (cid:0) tasks that require higher-order skills, such as the ability to abstract, solve problems, make decisions, or communicate e(cid:11)ectively. We argue that this classi(cid:12)cation is insightful for understanding the wage structure in the cross-section as well as the observed wage and employment growth in the U.S. over the 1980-2005 time period. In particular, we document the following facts that are robust to the inclusion of a detailed set of controls, subsamples, and levels of aggregation. First, there is a positive relationship at the occupational level between task complexity and wage levels and wage growth. Second, in contrast with the literature studying RTBC, we show that, conditional on task complexity, routine-intensity of an occupation is not a signi(cid:12)cant predictor of wage levels and wage growth. Third, labor has 32

Table 12: Wage Growth Regression with Social Skills Dependent Variable: Change in Log Wages 1980-2005 Independent Variable (i) (ii) (iii) Complexity Index 0.427*** 0.277*** 0.279*** (6.63) (3.82) (4.54) Routine Index 0.0316 0.0409 0.0488 (1.03) (1.27) (1.60) Social Skill 0.164*** 0.110* 0.0752 (2.65) (1.73) (1.45) Controls None Occ Dem Group Means Level Order of 1980 Wage Poly. 3 3 3 N 310 310 15142 Notes: t-statisticsareinparentheses. Signi(cid:12)cancelevelsare: (cid:3)(cid:3)(cid:3) 1%,(cid:3)(cid:3) 5%,(cid:3) 10%. (i)occupation-levelregression. (ii)occupation-levelregressionwiththefollowingdemographiccontrols: shareofworkersinan occupationwithacollege/high-schooldegree,shareofworkersinanoccupationwhoare non-white,shareofworkersinanoccupationwhoaremarried,shareoffemaleworkersinan occupation,meanageofworkerinanoccupation,andmeannumberofchildrenofworkersin anoccupation. (iii)group-levelregressiononoccupation(cid:2)gender(cid:2)education(cid:2)race(cid:2)agecells(seesection 3.2fordiscussion). Regressionsincludegender(cid:2)education(cid:2)race(cid:2)age(cid:12)xede(cid:11)ects. Standarderrorsclusteredattheoccupationlevel. reallocated from occupations with lower complexity towards occupations with higher complexity over this period. Fourth, within groups of occupations with similar task complexity labor has reallocated to non-routine occupations over this period. We then formulate a model of Complex-Task Biased Technological Change with heterogeneous skills in performing complex tasks and show analytically that it can rationalize these facts. Two major conclusions emerge from our model. First, amongst the simple occupations, non-routine and routine jobs draw from the same pool of labor supply. As a result, wages are equalized across non-routine and routine occupations, conditional on an appropriate measure of skill complexity. This implies that non-routine work, such as low skill service jobs, are not shielded from the e(cid:11)ects 33

of automatization and computer adoption. Second, the strength of wage e(cid:11)ects from technological change relative to employment e(cid:11)ects is consistent with a heavily skewed distribution of skills for performing complex tasks. In particular, the model implies that this distribution should have a large mass at its lower tail. A result of this is that complex-task biased technological change can generate a situation in which a substantial share of the population is permanently trapped in low-paying jobs. 34

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APPENDICES A Principal Components Analysis Under the PCA, the complexity score for occupation o, C , is equivalent to 0 C = (cid:13) (cid:1)X ; (A.1) o o where (cid:13) is a 1 (cid:2) 35 vector of factor loadings and X is a 35 (cid:2) 1 vector of the selected O*NET o descriptors. The factor loadings are chosen so that C captures as much of the variance in X as o o possible. To be precise, (cid:13) is set so that (cid:13) = argmin kX (cid:0)C (cid:1)(cid:13)0k o o (cid:13) o X = argmin kX (cid:0)(cid:13) (cid:1)X (cid:1)(cid:13)0k: (A.2) o o (cid:13) o X The factor loadings are computed using O*NET information on 315 occupations.21 When computing (cid:13) we weight the occupations by their employment shares in 1980, which we compute from a 5 percent sample of the 1980 US Census.22 The estimated factor loadings can be seen in Table A.1. The complexity index that we use in our empirical analysis are the imputed complexity scores C o converted to percentile rankings between 0 and 1, using as weights the relative employment shares of each occupation. Appendix D lists both the weighted and the raw complexity indices for the complete set of occupations in our sample.23 21See footnote 12 in the text. 22The sample is non-institutionalized non-farm males aged 16 to 64 in the mainland United States. 23The weighted and raw complexity indices including the agricultural occupations are available upon request. 37

Table A.1: O*NET Questions and PCA Factor Loadings Descriptor Factor Loading O*NET Worker Abilities Oral Comprehension 0.1818 Written Comprehension 0.1848 Written Expression 0.1797 Fluency of Ideas 0.1813 Originality 0.1772 Problem Sensitivity 0.1799 Deductive Reasoning 0.1870 Inductive Reasoning 0.1814 Information Ordering 0.1761 Category Flexibility 0.1734 Mathematical Reasoning 0.1702 Category Flexibility 0.1734 Number Facility 0.1640 Memorization 0.1688 Speed of Closure 0.1629 Flexibility of Closure 0.1407 Perceptual Speed 0.0796 O*NET Skills Mathematics 0.1589 Science 0.1402 Critical Thinking 0.1835 Active Learning 0.1859 Complex Problem Solving 0.1867 Programming 0.1400 Judgement and Decision Making 0.1862 Systems Analysis 0.1832 Systems Evaluation 0.1847 O*NET Activities Monitor Processes, Materials or Surroundings 0.1106 Judging the Qualities of Things/Services/People 0.1520 Processing Information 0.1712 Evaluating Information to Determine Compliance with Standards 0.1493 Analyzing Data or Information 0.1807 Making Decisions and Solving Problems 0.1774 Thinking Creatively 0.1647 Updating and Using Relevant Information 0.1761 Developing Objectives and Strategies 0.1662 38

B Model (cid:12) Given full depreciation of capital, the social planner maximizes output. De(cid:12)ne B = c . The m maximization problem is: max (y ) (cid:13) (cid:1)(y )1(cid:0)(cid:13) (cid:0)(cid:25) (cid:1)K (B.1) s c K K;Kc;cT;SR n o subject to : (cid:22) (cid:22) 1 y s = [(y R ) +(y NR ) ](cid:22) y = ((cid:11) (cid:1)C) (cid:26) (cid:1)((cid:11) (cid:1)K )1(cid:0)(cid:26) (B.2) c c k;c c y = S NR NR 1 y = (cid:11) (cid:1)S +(cid:11) (cid:1)K R s;R R k;R R C = h 1 c(cid:1)dG(c) = (cid:12) i (cid:1)B(cid:1) cT 1(cid:0)(cid:12) (cid:12)(cid:0)1 ZcT (cid:18) (cid:19) S = G cT (cid:0)S = 1(cid:0)B(cid:1) cT (cid:0)(cid:12) (cid:0) (cid:0) S (cid:1) NR R R (cid:0) (cid:1) (cid:0) (cid:1) K = K +K : c R Noticethatwehavenormalized(cid:11) = 1sothatallfactorproductivityparametersarerelative s;NR to the factor productivity of labor inputs in the non-routine process. Expressions for relative wages can then be derived from the (cid:12)rms’ pro(cid:12)t maximization problems. C Proof of Proposition In the following it is convenient to de(cid:12)ne K y R S k (cid:17) and y = : R S S S R NR e From the (cid:12)rst-order condition for cT, (cid:13) = :5, and the expression for C in terms of cT: (cid:0)1 cT = (cid:12)(cid:0)1 (cid:1)(cid:26)(cid:1)S (cid:1)(y ) (cid:22) (cid:12) : (C.1) NR S (cid:12) (cid:1)B (cid:20)(cid:18) (cid:19) (cid:21) e 39

Substituting this back into C yields 1 (cid:12) (cid:1)B (cid:12) (cid:22) (cid:12)(cid:0)1 C = (cid:1)[(cid:26)(cid:1)S NR (cid:1)(y S ) ] (cid:12) : (C.2) (cid:12)(cid:0)1 (cid:18) (cid:19) e The (cid:12)rst-order condition for S is R (cid:11) (cid:1)(S )1(cid:0)(cid:22) (cid:1)(S ) (cid:0)1(cid:1)(y ) (cid:22)(cid:0) = 1; (C.3) s;R NR R R and the (cid:12)rst-order conditions for the two types of capital are (cid:25) Y = K (cid:1)(y ) (cid:22) (cid:1)(y ) (cid:0)(cid:22) (cid:1)(K )1(cid:0) S R R (cid:11) (cid:1)(cid:13) (cid:18) k;R (cid:19) (1(cid:0)(cid:13))(cid:1)(1(cid:0)(cid:26)) K = (cid:1)Y: (C.4) c (cid:25) (cid:18) K (cid:19) We can now combine the two conditions for the capital inputs to get: 1(cid:0)(cid:26) K = (cid:1)(y ) (cid:22) (cid:1)(y ) (cid:0)(cid:22) (cid:1)(K )1(cid:0) : (C.5) c S R R (cid:11) (cid:18) k;R (cid:19) From the (cid:12)rst-order condition for S , rewrite equation (C.4) as R (cid:25) (cid:11) Y = K (cid:1) s;R (cid:1)(y ) (cid:22) (cid:1)S (cid:1)(k )1(cid:0) (C.6) S NR R (cid:13) (cid:11) (cid:18) (cid:19) (cid:18) k;R(cid:19) e and equation (C.5) as (cid:11) K = (1(cid:0)(cid:26))(cid:1) s;R (cid:1)(y ) (cid:22) (cid:1)S (cid:1)(k )1(cid:0) : (C.7) c S NR R (cid:11) (cid:18) k;R(cid:19) e Next,evaluatetheaggregateproductionfunctionattheexpressionsforC andK derivedabove: c Y = A 1 (cid:1)(S NR ) (cid:13) (cid:1)((y S ) (cid:22) )(cid:22) (cid:13) (cid:1)[(y S ) (cid:22) (cid:1)S NR ](cid:16) (cid:12)(cid:0) (cid:12) 1 (cid:17) (cid:1)(cid:26)(cid:1)(1(cid:0)(cid:13)) (cid:1) (y s ) (cid:22) (cid:1)S NR (cid:1)(k R )1(cid:0) (1(cid:0)(cid:26))(cid:1)(1(cid:0)(cid:13)) ; h i e e e where (cid:12)(cid:0)1 (cid:12) (cid:1)B (cid:12) 1 (cid:26)(cid:1)(1(cid:0)(cid:13)) (cid:11) s;R (1(cid:0)(cid:26))(cid:1)(1(cid:0)(cid:13)) A 1 = (cid:26) (cid:12) (cid:1)(cid:11) c (cid:1) (1(cid:0)(cid:26))(cid:1) (cid:1)(cid:11) k;c : (cid:12)(cid:0)1 (cid:11) " (cid:18) (cid:19) # (cid:20) (cid:18) k;R(cid:19) (cid:21) 40

Combining this equation with (C.6) and collecting terms yields (cid:21) A (cid:1) (k )1(cid:0) k (cid:1)[S ] (cid:21)S = [(y ) (cid:22) ] (cid:21)y ; (C.8) 2 R NR s h i e with A 2 = (cid:25) K (cid:1) (cid:11) s;R 1(cid:0)(1(cid:0)(cid:26))(cid:1)(1(cid:0)(cid:13)) (cid:1) (cid:26) (cid:12)(cid:0) (cid:12) 1 (cid:12)(cid:1)B (cid:12) 1 (cid:1)(cid:11) c (cid:0)(cid:26)(cid:1)(1(cid:0)(cid:13)) (cid:1)[(1(cid:0)(cid:26))(cid:1)(cid:11) k;c ] (cid:0)(1(cid:0)(cid:26))(cid:1)(1(cid:0)(cid:13)) (cid:13) (cid:11) (cid:12) (cid:0)1 (cid:18) (cid:19) (cid:18) k;R(cid:19) " (cid:18) (cid:19) # (cid:21) = 1(cid:0)(1(cid:0)(cid:26))(cid:1)(1(cid:0)(cid:13)) > 0 k 1(cid:0)(cid:13) (cid:21) = (cid:26)(cid:1) > 0 S (cid:12) (cid:18) (cid:19) 1(cid:0)(cid:22) 1(cid:0)(cid:13) (cid:21) = (cid:13) (cid:1) (cid:0)(cid:26)(cid:1) : (C.9) y (cid:22) (cid:12) (cid:18) (cid:19) (cid:18) (cid:19) Asitturnsout,equilibriumdoesnothaveananalyticalsolution. Rather,wewillcharacterizethe equilibriumusingtwoequationsinthetwounknowns(S ;S )andthenstateseveralcomparative NR R statics results from implicit di(cid:11)erentiation. The (cid:12)rst equation is given by (C.8), which was derived above from (cid:12)rst-order conditions and the assumptions on technologies. The second equation relies on the labor market equilibrium condition. De(cid:12)ne s = SNR and express the production technology y as SR s e y (cid:22) (cid:22) R (y ) = +1: (C.10) S S (cid:18) NR(cid:19) e The (cid:12)rst-order condition for S in equation (C.3) can be used to show that R y R 1 1(cid:0) = ((cid:11) s;R ) (cid:0)(cid:22) (cid:1)(s) (cid:0)(cid:22) : (C.11) S (cid:18) NR(cid:19) e Combining these two equations we get (y S ) (cid:22) = ((cid:11) s;R ) (cid:0) (cid:22) (cid:22) (cid:1)(s) (cid:22)(cid:1) (cid:16) 1(cid:0) (cid:0) (cid:22)(cid:17)+1: (C.12) e e Here we substituted out yR . Plug the technology for y into (C.11) we can derive an expression SNR R 41

for k in terms of s: R e k R = (cid:11) s;R (cid:1) ((cid:11) s;R ) (cid:0) (cid:22) (cid:22) (cid:1)(s) (cid:1) (cid:16) 1(cid:0) (cid:0) (cid:22) (cid:22)(cid:17)(cid:0)1 1 : (C.13) (cid:11) (cid:20)(cid:18) k;R(cid:19) (cid:18) (cid:19)(cid:21) e Di(cid:11)erentiating (C.11) and (C.13) with respect to S and S yields NR R (cid:22) @(y S ) = ((cid:11) s;R ) (cid:0) (cid:22) (cid:22) (cid:1)(cid:22)(cid:1) 1(cid:0) (cid:1)(s) (cid:22)(cid:1) (cid:16) 1(cid:0) (cid:0) (cid:22)(cid:17)(cid:1)(s(cid:1)S R ) (cid:0)1 @S (cid:0)(cid:22) NR (cid:18) (cid:19) @(ye ) (cid:22) @(y ) (cid:22) S S = (cid:0) (cid:1)s e e @S @S R NR @ @ S ek R = 1 (cid:1)k e R 1(cid:0) (cid:1) e (cid:11) (cid:11) s;R (cid:1)((cid:11) s;R ) (cid:0) (cid:22) (cid:22) (cid:1) (cid:1) 1(cid:0) (cid:0) (cid:22) (cid:22) (cid:1)(s) (cid:1) (cid:16) 1(cid:0) (cid:0) (cid:22) (cid:22)(cid:17)(cid:1)(s(cid:1)S R ) (cid:0)1 NR (cid:18) k;R(cid:19) (cid:18) (cid:19) @k @k R R = (cid:0) (cid:1)s: e e (C.14) @S @S R NR e Total di(cid:11)erentiation of (C.8) with respect to S and S yields: NR R (cid:21) (1(cid:0) )(cid:1)(cid:21) @k @k A (cid:1) (S ) (cid:21)S (cid:1)(k )(1(cid:0) )(cid:1)(cid:21) k (cid:1) S dS + k (cid:1) R dS (cid:0) R (cid:1)s dS 2 NR R NR NR R S k @S @S (cid:20)(cid:18) NR(cid:19) (cid:18) R (cid:19) (cid:20)(cid:18) NR(cid:19) (cid:18) NR (cid:19) (cid:21)(cid:21) (cid:22) (cid:22) @(y ) @(y ) = (cid:21) (cid:1) [(y ) (cid:22) ] (cid:21)y(cid:0)1 (cid:1) S dS (cid:0) S (cid:1)s dS : e (C.15) y s NR R @S @S (cid:20)(cid:18) NR (cid:19) (cid:18) NR (cid:19) (cid:21) e e e e Bringing all terms involving dS to the left-hand side and all terms involving dS on the right- NR R handsideclari(cid:12)esthat @kR entersbothtermspositivelyand(cid:21) (cid:1) @(yS)(cid:22) negatively. Notingthatthe @SNR y @S eNR solution of the social planners’ problem will be interior because the technologies for (Y;y ;y ;y ) s c R satisfy Inada conditions and that @kR and @(yS)(cid:22) have the same sign we get @SNR @S eNR dS @k NR R > 0 if > 0 and (cid:21) < 0: (C.16) y dS @S R NR These conditions are satis(cid:12)ed if > (cid:22) and (cid:22) > (cid:22)(cid:3), where (cid:22)(cid:3) = (cid:12) . ((cid:12)+(cid:26)) It is important to note that this is a property of equilibrium, even though we have not used the aggregate resource constraint for labor inputs yet. The latter merely pins down the level of S (or R S ), while (C.8) determines implicitly the equilibrium relationship between S and S . NR NR R Next, use the labor market resource constraint S = 1(cid:0)B(cid:1) cT (cid:0)(cid:12) (cid:0)S together with (C.1): NR R (cid:0) (cid:1) S NR (cid:1) 1+ (cid:12) (cid:0)1 (cid:1)(cid:26)(cid:1) ((cid:11) s;R ) (cid:0) (cid:22) (cid:22) (cid:1)(s) (cid:22)(cid:1) (cid:16) 1(cid:0) (cid:0) (cid:22)(cid:17)+1 = 1 (cid:0)1: (C.17) S (cid:12) S (cid:18) R (cid:19) (cid:20) (cid:18) (cid:19) (cid:18) (cid:19)(cid:21) R e 42

This equation can be rearranged to express the term in square brackets as 1(cid:0)SR. Totally di(cid:11)eren- SNR tiating it with respect to s and S yields R 1(cid:0)S R ds+ s(cid:1)(cid:22)(cid:1) e 1(cid:0) (cid:1) (cid:12)(cid:0)1 (cid:1)(cid:26)(cid:1)((cid:11) s;R ) (cid:0) (cid:22) (cid:22) (cid:1)s (cid:22)(cid:1) (cid:16) 1(cid:0) (cid:0) (cid:22)(cid:17) (cid:0)1 ds = (cid:0) 1 2 dS R : S (cid:0)(cid:22) (cid:12) S (cid:18) NR (cid:19) (cid:18) (cid:18) (cid:19) (cid:18) (cid:19) (cid:19) (cid:18) R(cid:19) e e e e (cid:22)(cid:1) 1(cid:0) (cid:0)1 (cid:22)(cid:1) 1(cid:0) Now notice that the terms multiplying ds add up easily since s(cid:1)s (cid:16) (cid:0)(cid:22)(cid:17) = s (cid:16) (cid:0)(cid:22)(cid:17), which is exactly how s shows up in the term 1(cid:0)SR . In particular, SNRe e e e (cid:16) (cid:17) e 1(cid:0)S R +(cid:22)(cid:1) 1(cid:0) (cid:1) (cid:12) (cid:0)1 (cid:1)(cid:26)(cid:1)((cid:11) s;R ) (cid:0) (cid:22) (cid:22) (cid:1)s (cid:22)(cid:1) (cid:16) 1(cid:0) (cid:0) (cid:22)(cid:17) S (cid:0)(cid:22) (cid:12) (cid:18) NR (cid:19) (cid:18) (cid:19) (cid:18) (cid:19) (cid:12) (cid:0)1 (cid:1)(1(cid:0)(cid:22)) (cid:22) (cid:22)(cid:1) 1(cid:0) = 1+ (cid:1)(cid:26)(cid:1) 1+ (cid:1)((cid:11) s;R ) (cid:0)(cid:22) (cid:1)(s) (cid:16) e(cid:0)(cid:22)(cid:17) : (C.18) (cid:12) (cid:0)(cid:22) (cid:18) (cid:19) (cid:20) (cid:21) e A su(cid:14)cient condition for this term to be positive is > (cid:22). In this case we have ds < 0: (C.19) dS R e We thus (cid:12)nd that if > (cid:22), then the labor share of non-routine labor in the simple production processes decreases if S increases. R To complete the characterization of the equilibrium labor allocation, we derive comparative statics results for s in terms of model parameters. First rewrite equation (C.8) using (C.12) and (C.13) and the de(cid:12)nition of A as 2 e ((cid:11) s;R ) (cid:0) (cid:22) (cid:22) (cid:1)(s) (cid:1) (cid:16) 1(cid:0) (cid:0) (cid:22) (cid:22)(cid:17)(cid:0)1 (1(cid:0) )(cid:1)(cid:21) k (cid:1)(S NR ) (cid:21)S (cid:1) ((cid:11) s;R ) (cid:0) (cid:22) (cid:22) (cid:1)(s) (cid:22)(cid:1) (cid:16) 1(cid:0) (cid:0) (cid:22)(cid:17)+1 (cid:0)(cid:21)y = A 3 ; (C.20) (cid:18) (cid:19) (cid:18) (cid:19) e e where (cid:21)k 1 (cid:26)(cid:1)(1(cid:0)(cid:13)) A 3 = (cid:13) (cid:1) (cid:11) k;R (cid:1) (cid:26) (cid:12)(cid:0) (cid:12) 1 (cid:12) (cid:1)B (cid:12) (cid:1)(cid:11) c (cid:1)[(1(cid:0)(cid:26))(cid:1)(cid:11) k;c ](1(cid:0)(cid:26))(cid:1)(1(cid:0)(cid:13)): (cid:25) (cid:11) (cid:12)(cid:0)1 (cid:18) K(cid:19) (cid:18) s;R(cid:19) " (cid:18) (cid:19) # LetS = h(sj(cid:11) ;(cid:12);(cid:22); ;(cid:26))bethefunctionde(cid:12)nedimplicitlyby(C.17),withh0(sj(cid:11) ;(cid:12);(cid:22); ;(cid:26)) NR s;R s;R as de(cid:12)ned above. Also de(cid:12)ne LHS as the left-hand side of (C.20). Let x stand for any of the pae e 43

(cid:11) rameters entering A but not LHS. These are (cid:25) ; k;R ;(cid:11) ;(cid:11) . Then we get: 3 K (cid:11)s;R c k;c (cid:16) (cid:17) ds @A3 = @x : (C.21) dx @LHS @s e e If > (cid:22) and (cid:22) > (cid:22)(cid:3), then (cid:21) < 0 and it is straightforward to show that @LHS > 0. Hence, ds has y @s dx e the same sign as @A3 under these assumptions. This establishes the compar e ative statics results in @x the proposition regarding employment. In particular, any exogenous force that increases s comes with a decline in both S and S . R NR e Moving on to characterizing prices, we use the fact that all marginal revenue products need to be equal to marginal costs. For the three intermediate input prices we thus get 1(cid:0)(cid:22) Y y s p = (cid:13) (cid:1) (cid:1) (C.22) R y y (cid:18) s (cid:19) (cid:18) R(cid:19) 1(cid:0)(cid:22) Y y s p = (cid:13) (cid:1) (cid:1) (C.23) NR y S (cid:18) s (cid:19) (cid:18) NR(cid:19) Y p = (1(cid:0)(cid:13))(cid:1) (C.24) c y c (cid:18) (cid:19) and for wages we have w = p (C.25) NR NR 1(cid:0) y R w = p (cid:1)(cid:11) (cid:1) (C.26) R R s;R S (cid:18) R(cid:19) y c w = p (cid:1)(cid:26)(cid:1) : (C.27) c c C Furthermore, in equilibrium it must be the case that w = w , w = p : NR R R NR Equations (C.24) and (C.27) imply that Y w = (cid:26)(cid:1)(1(cid:0)(cid:13))(cid:1) (C.28) c C (cid:18) (cid:19) 44

and equations (C.22) and (C.26) yield w = (cid:13) (cid:1)(cid:11) (cid:1)Y (cid:1)y(cid:0)(cid:22)(cid:1)y (cid:22)(cid:0) (cid:1)S (cid:0)1 : R s;R s R R The (cid:12)rst-order condition for S from the social planner’s problem can be used to write R w = (cid:13) (cid:1)Y (cid:1)y(cid:0)(cid:22)(cid:1)S(cid:0)1 : (C.29) R s NR e The (cid:12)rst-order condition for cT from the social planner’s problem combined with equations (C.28) and (C.29) implies that w 1 c = : (C.30) w cT R Combining this equation with equation (7) yields (cid:12)(cid:0)1 (cid:12) w C(cid:3) = (cid:1)c(cid:12) (cid:1) c ; (C.31) (cid:12)(cid:0)1 m w (cid:18) (cid:19) (cid:18) R(cid:19) From above we know that dS dS R NR < 0; < 0: (C.32) dx dx The labor market equilibrium condition then implies that dC > 0: (C.33) dx Since (cid:12) > 1 this is only possible if dcT < 0 (C.34) dx characterizing our equilibrium result. In particular, dwc wR > 0: (C.35) dx 45

D Complexity Percentiles of Occupations Occupation List and Complexity Percentile Occupation ComplexityIndex,Weighted ComplexityIndex,Raw Vehiclewashersandequipmentcleaners .0016101 0 Clothingpressingmachineoperators .0019852 .0474957 Foodpreparationworkers .0022551 .058032 Janitors .0249187 .0918971 Shoemakers,otherprec. apparelandfabricworkers .0252782 .0925525 Housekeepers,maids,butlers,andcleaners .02768 .1111131 Crossingguards .027743 .1378214 Butchersandmeatcutters .032228 .1428061 Washing,cleaning,andpicklingmachineoperators .0323416 .1434333 Knitters,loopers,andtopperstextileoperatives .0328108 .1472788 Laundryanddrycleaningworkers .0338383 .1492647 Salesdemonstrators,promoters,andmodels .033879 .156003 Waitersandwaitresses .0361711 .1564893 Ushers .0362983 .1573397 Packersandpackagersbyhand .0393966 .158118 Moldersandcastingmachineoperators .0412176 .1644148 Paperhangers .0414369 .1648163 Textilesewingmachineoperators .0422301 .1682662 Miscellaniousfoodpreparationandserviceworkers .0467314 .1775591 Garbageandrecyclablematerialcollectors .0478686 .1876843 Mailcarriersforpostalservice .0521171 .197245 Metalplaters .0528155 .1987244 Mailandpaperhandlers .0528622 .1993897 Productionhelpers .0543581 .2025392 Parkinglotattendants .0547438 .2062236 Barbers .0562024 .2074238 46

Sawingmachineoperatorsandsawyers .0577174 .2196525 Garageandservicestationrelatedoccupations .061774 .2197336 Motionpictureprojectionists .0619409 .2236338 Otherminingoccupations .0628925 .2245478 Door-to-doorsales,streetsales,andnewsvendors .0641871 .2292543 Stockandinventoryclerks .0705001 .2321019 Foodroastingandbakingmachineoperators .0706147 .2356098 Welders,solderers,andmetalcutters .083701 .24098 Machineoperators,n.e.c. .1119686 .2418786 Helpers,surveyors .1121227 .2423221 Drywallinstallers .1135813 .2473086 Typists .1139037 .2494702 Mailclerks,outsideofposto(cid:14)ce .115208 .2496178 Machinefeedersando(cid:11)bearers .1165266 .2515694 Recreationfacilityattendants .1173587 .2522547 Painters,constructionandmaintenance .1231511 .2539865 Shoemakingmachineoperators .1234541 .2546685 Busdrivers .1267233 .2549169 Excavatingandloadingmachineoperators .1282058 .2579201 Telephoneoperators .1295526 .2632094 Messengers .1303752 .263628 Furniture/wood(cid:12)nishers,otherprec. woodworkers .1307821 .2640873 Laborers,freight,stockandmaterialhandlers,n.e.c. .1612356 .2652903 Hairdressersandcosmetologists .1624208 .2657102 Paintinganddecorationoccupations .1628932 .2679644 Concreteandcementworkers .1639893 .2697237 Cashiers .1680383 .2699966 Glaziers .1685899 .2710331 Slicing,cutting,crushingandgrindingmachine .1719594 .2746302 47

Proofreaders .1720419 .2796004 Bakers .1732495 .2810528 Furnance,kiln,andovenoperators,apartfromfood .1759559 .2817367 Dressmakers,seamstresses,andtailors .1766308 .2836869 Structuralmetalworkers .1780822 .2842702 Nail,tacking,shapingandjoiningmachops(wood) .178214 .2850213 Truck,delivery,andtractordrivers .2332571 .2881833 Paperfoldingmachineoperators .2334732 .2898981 Gardenersandgroundskeepers .238643 .2901271 Paving,surfacing,andtampingequipmentoperators .2401614 .2903215 Autobodyrepairers .2437769 .2934009 Engravers .243926 .2942845 Generalo(cid:14)ceclerks .2485348 .2970265 Forgeandhammeroperators .2488021 .3001972 Lathe,milling,andturningmachineoperatives .2521926 .3015528 Constructionlaborers .264245 .3023615 Cementingandgluingmachineoperators .2645649 .304257 Masons,tilers,andcarpetinstallers .2694101 .3055735 Baggageporters,bellhopsandconcierges .2696804 .3055973 Plasterers .2701079 .306403 Operatingengineersofconstructionequipment .2742835 .3064868 Drillersofearth .2747057 .3094935 Batchfoodmakers .2749797 .3130697 Windingandtwistingtextileandappareloperatives .2754852 .313157 Packers,(cid:12)llers,andwrappers .2764093 .3145595 Helpers,constructions .2780616 .3175598 Taxicabdriversandchau(cid:11)eurs .2808504 .3189189 Cooks .2906471 .3191219 Handmoldersandshapers,exceptjewelers .2918167 .3269784 48

Miners .2934508 .3280829 Crane,derrick,winch,hoist,longshoreoperators .2964257 .3283859 Punchingandstampingpressoperatives .2985013 .3297018 Photographicprocessworkers .2991731 .3306982 Extrudingandformingmachineoperators .2998369 .331729 Postalclerks,exludingmailcarriers .3030544 .3339394 Personalserviceoccupations,n.e.c .3039461 .3340037 Hotelclerks .304226 .3407545 Repairersofmechanicalcontrolsandvalves .3047346 .3428789 Assemblersofelectricalequipment .3195663 .343298 Machinerymaintenanceoccupations .3203659 .3446272 Insulationworkers .3212201 .3446951 Patternmakersandmodelmakers .3217962 .3466091 Animalcaretakers,exceptfarm .3222107 .3479617 Supervisorsofcleaningandbuildingservice .3237224 .3503228 O(cid:14)cemachineoperators,n.e.c. .3239973 .3514165 Dataentrykeyers .3244871 .351688 Meterreaders .3251612 .3527323 Weighers,measurers,andcheckers .3259872 .3529728 Industrialmachineryrepairers .3350245 .3545351 Guides .3351743 .355157 Receptionistsandotherinformationclerks .3357277 .3555206 Textilecuttinganddyeingmachineoperators .3358103 .3568808 Railroadbrake,coupler,andswitchoperators .337425 .3578726 Libraryassistants .3376905 .3616587 Teacher’saides .3378554 .3619579 Fileclerks .3387471 .3640199 Drillingandboringmachineoperators .3396919 .3683746 Payrollandtimekeepingclerks .3401749 .3705224 49

Bartenders .3428776 .371148 Correspondenceandorderclerks .3447219 .3719169 Billingclerksandrelated(cid:12)nancialrecordsprocessing .3455834 .3721412 Healthrecordtechnologistsandtechnicians .3456078 .3735193 Heattreatingequipmentoperators .3460346 .3745169 Misc. constructionandrelatedoccupations .3487912 .3751594 Typesettersandcompositors .3493497 .3758858 Heavyequipementandfarmequipmentmechanics .3531129 .3785861 Mixingandblendingmachineoperators .354895 .3786395 Smallenginerepairers .355472 .3809398 Recreationand(cid:12)tnessworkers .3556651 .3816842 Stevedoresandmisc. materialmovingoccupations .3596893 .3817274 Bookbinders .3599093 .3827012 Locomotiveoperators: engineersand(cid:12)remen .3616267 .3846796 Productioncheckers,graders,andsortersinmanufacturing .3709035 .3849652 Interviewers,enumerators,andsurveyors .3712956 .385058 Banktellers .3719943 .3872021 Dancers .3720301 .3878274 Roofersandslaters .3737694 .3886213 Mechanicsandrepairers,n.e.c. .3831168 .3894151 Plumbers,pipe(cid:12)tters,andsteam(cid:12)tters .3917227 .3924724 Upholsterers .3926257 .3927588 Carpenters .4123504 .3977388 Administrativesupportjobs,n.e.c. .4148578 .399947 Othermetalandplasticworkers .4174884 .3999856 Locksmithsandsaferepairers .4177947 .4042563 Pestcontroloccupations .4183996 .4078006 Secretariesandstenographers .4192881 .4078266 Cabinetmakersandbenchcarpeters .4204831 .4087574 50

Grinding,abrading,bu(cid:14)ng,andpolishingworkers .424457 .4128952 Rollers,rollhands,and(cid:12)nishersofmetal .4247807 .4160658 Healthandnursingaides .4280792 .4171047 Repairersofdataprocessingequipment .4288996 .4171405 Musiciansandcomposers .4299978 .4204387 Precisiongrindersand(cid:12)tters .4303453 .4211147 Legalassistantsandparalegals .4307436 .4226654 Publictransportationattendantsandinspectors .4309823 .4237073 Precisionmakers,repairers,andsmiths .4319676 .4237647 Childcareworkers .4325137 .4243256 Protectiveservice,n.e.c. .4328654 .4262462 Sheri(cid:11)s,baili(cid:11)s,correctionalinstitutiono(cid:14)cers .435336 .4262941 Humanresourcesclerks,exclpayrollandtimekeeping .4354915 .4267306 Shippingandreceivingclerks .4447515 .428109 Bus,truck,andstationaryenginemechanics .4475912 .429 Billandaccountcollectors .4481743 .4299577 Eligibilityclerksforgovernmentprog.,socialwelfare .4482474 .4325045 Retailsalespersonsandsalesclerks .4966205 .4343396 DentalAssistants .496669 .4376354 Drillersofoilwells .4981148 .4399363 Repairersofhouseholdappliancesandpowertools .4995348 .4415153 Railroadconductorsandyardmasters .5005776 .443033 Recordsclerks .5009044 .4443701 Transportationticketandreservationagents .5016944 .4447685 Boilermakers .5023338 .4487705 Machinists .5117255 .4497759 Guardsandpolice,exceptpublicservice .5188752 .4504754 Bookkeepersandaccountingandauditingclerks .5219113 .4512078 Announcers .5224794 .4535288 51

Telecomandlineinstallersandrepairers .5280938 .4583492 Separating,(cid:12)ltering,andclarifyingmachineoperators .529344 .4601226 Electricpowerinstallersandrepairers .5312842 .462637 Kindergartenandearlierschoolteachers .5313818 .4650418 Photographers .532622 .4656839 Insuranceadjusters,examiners,andinvestigators .5338447 .4667797 Athletes,sportsinstructors,ando(cid:14)cials .5344892 .4697548 Technicalwriters .5350577 .4705883 Dentalhygienists .5350676 .4718026 Plantandsystemoperators,stationaryengineers .5374832 .4729008 Elevatorinstallersandrepairers .5378498 .4753022 Automobilemechanicsandrepairers .5553351 .478068 Opticalgoodsworkers .5558305 .4812819 Superv. oflandscaping,lawnservice,groundskeeping .5561892 .4848577 Businessandpromotionagents .5564464 .4865477 Electricians .5675195 .4869483 Dentallaboratoryandmedicalapplicancetechnicians .5680903 .4935272 Art/entertainmentperformersandrelatedoccs .5685701 .4957203 Supervisorsofmotorvehicletransportation .56923 .497671 Painters,sculptors,craft-artists,andprint-makers .57053 .4983236 Waterandsewagetreatmentplantoperators .5711213 .5000399 Funeraldirectors .5718923 .5015252 Dispatchers .5732161 .5078909 Broadcastequipmentoperators .5739396 .50795 Otherplantandsystemoperators .5748871 .5093867 Shipcrewsandmarineengineers .5763842 .5096271 Toolanddiemakersanddiesetters .5802024 .5129167 Millwrights .5826892 .5142236 Productionsupervisorsorforemen .6170128 .5163915 52

Repairersofelectricalequipment,n.e.c. .6181906 .5170321 Customerservicereps,invest.,adjusters,excl. insur. .6199347 .5200379 Supervisorsofpersonalservicejobs,n.e.c .6202488 .5228023 Welfareserviceworkers .6203519 .5276881 Heating,airconditioning,andrefrigerationmechanics .6230185 .5285116 Designers .6260712 .5298232 Othersciencetechnicians .6269315 .5315494 Advertisingandrelatedsalesjobs .6281067 .5376239 Insurancesalesoccupations .6363132 .5380685 Repairersofindustrialelectricalequipment .6391367 .5385529 Writersandauthors .6394979 .5393205 Editorsandreporters .6413863 .5394176 Drafters .646362 .5413974 O(cid:14)cesupervisors .6533478 .5456049 Insuranceunderwriters .65348 .546587 Purchasingagentsandbuyersoffarmproducts .6538292 .5466031 Realestatesalesoccupations .6603308 .5472972 Managersofpropertiesandrealestate .662331 .5474688 Radiologictechnologistsandtechnicians .6628282 .5513899 Supervisorsofconstructionwork .6775198 .5614792 Librarians .6779959 .5638413 Programmersofnumericallycontrolledmachinetools .6781242 .5646561 Miscellanioustransportationoccupations .6782089 .565611 Actors,directors,andproducers .6789458 .5667997 Constructioninspectors .6797738 .5677375 Salessupervisorsandproprietors .7039372 .5694135 Buyers,wholesaleandretailtrade .7057255 .5711881 Primaryschoolteachers .7150567 .5715752 Powerplantoperators .7155595 .5721468 53

Materialrecording,sched.,prod.,plan.,expeditingcl .7192039 .5773472 Licensedpracticalnurses .7194566 .5794451 Explosivesworkers .7196467 .5831427 Teachers,n.e.c. .7216645 .5840338 Policeanddetectives,publicservice .7310947 .5924041 Specialeducationteachers .7312641 .5938933 Clinicallaboratorytechnologiesandtechnicians .7323585 .5957232 Biologicaltechnicians .7328334 .6006724 Healthtechnologistsandtechnicians,n.e.c. .7338486 .6040076 Secondaryschoolteachers .7401884 .6074831 Archivistsandcurators .7403287 .6088821 Computerandperipheralequipmentoperators .7439466 .6090996 Therapists,n.e.c. .7441803 .6091286 Occupationaltherapists .7442039 .6093953 Technicians,n.e.c. .7483711 .6143714 Other(cid:12)nancialspecialists .7525147 .6215262 Clergyandreligiousworkers .7585013 .6251798 Respiratorytherapists .7588941 .6283643 Surveryors,cartographers,mappingscientists/techs .7606438 .6301623 Vocationalandeducationalcounselors .7621104 .6345538 Aircraftmechanics .7640925 .6384776 Financialservicesalesoccupations .7660716 .6397019 Engineeringtechnicians .7746348 .640195 Chemicaltechnicians .7756594 .6405557 Socialworkers .7784598 .6432993 Accountantsandauditors .7897698 .645144 Fire(cid:12)ghting,(cid:12)reprevention,and(cid:12)reinspectionocc .7953491 .6453222 Purchasingmanagers,agents,andbuyers,n.e.c. .7990443 .6458427 Managementsupportoccupations .7993091 .6475878 54

Managersandspecialistsinmarketing,advert.,PR .8126259 .6494842 Supervisorsofmechanicsandrepairers .8158349 .6523172 Personnel,HR,training,andlaborrel. specialists .8200432 .6536342 Forestersandconservationscientists .8206129 .6545376 Managersineducationandrelated(cid:12)elds .8253328 .6579295 Physicaltherapists .825543 .662291 Managersandadministrators,n.e.c. .9084735 .6703479 Managementanalysts .9100308 .6734453 Humanresourcesandlaborrelationsmanagers .9128619 .6758255 Mathematiciansandstatisticians .9132312 .6762955 Airtra(cid:14)ccontrollers .9138585 .6771919 Computersoftwaredevelopers .9178438 .6786138 Otherhealthandtherapyoccupations .9181587 .6799001 Subjectinstructors,college .925038 .6813116 Veterinarians .9257077 .6862742 Speechtherapists .9257848 .6941292 Computersystemsanalystsandcomputerscientists .9288143 .6973373 Inspectorsandcomplianceo(cid:14)cers,outside .9311807 .6978745 Statisticalclerks .9317746 .6983281 Dieticiansandnutritionists .9318948 .6984047 Managersofmedicineandhealthoccupations .9329729 .7105789 Physicians’assistants .9333857 .7120637 Airplanepilotsandnavigators .9346732 .7129837 Registerednurses .935637 .7162699 Electricalengineers .9414794 .7180361 Dentists .9434849 .7194137 Pharmacists .9456243 .7206631 Lawyersandjudges .9542739 .7285635 Socialscientistsandsociologists,n.e.c. .9544347 .7329476 55

Operationsandsystemsresearchersandanalysts .955542 .7373657 Financialmanagers .9610853 .738309 Salesengineers .9619034 .7418968 Industrialengineers .965312 .7441369 Optometrists .9657143 .7482106 Atmosphericandspacescientists .9658464 .750657 Physicalscientists,n.e.c. .9659775 .7544398 Podiatrists .9660975 .7555497 Economists,marketandsurveyresearchers .9674464 .7582632 Architects .9693015 .7646669 Petroleum,mining,andgeologicalengineers .9697799 .7699337 Psychologists .9706449 .770106 Urbanandregionalplanners .9708155 .7740712 Agriculturalandfoodscientists .9711688 .7783705 Geologists .9719127 .7851528 Chemists .9734307 .7941574 Engineersandotherprofessionals,n.e.c. .9786969 .8180442 Chiefexecutives,publicadministrators,andlegislators .9793075 .828075 Mechanicalengineers .9830744 .8318534 Physicians .9918112 .8355613 Civilengineers .9955139 .8388404 Metallurgicalandmaterialsengineers .9959559 .8439432 Aerospaceengineers .9975579 .8576173 Medicalscientists .9978017 .8673735 Actuaries .9979488 .8832101 Biologicalscientists .99853 .8882928 Chemicalengineers .9995857 .9360058 Physicistsandastronomists 1 1 56

E Worker Sorting As discussed in Section 4, our model makes strong predictions about worker sorting. In the process of complex-task biased technological change the skill threshold that separates workers going to the complex occupations and those who do not falls. If there are observable worker characteristics that are correlated with the skill to solve complex tasks, then one may hope that one can test the prediction of a falling threshold. Unfortunately, with repeated cross-sectional data, this is di(cid:14)cult, for at least two reasons. First, a decrease in the skill threshold means that the average skill in either type of occupation falls. Second, observable characteristics that are likely to relate with the skill to solve complex tasks, such as educational attainment, have been subject to strong aggregate trends. We construct a test of the sorting mechanism generated by our model that addresses both issues as follows. We use two measures of worker characteristics that are likely related to the skill for solving complex tasks. The (cid:12)rst measure is the fraction of workers with some postsecondary education. This measure has the advantage that it is likely to be small in simple occupations and large in complex occupations. We thus expect a larger decrease of this measure in complex occupations, absent any aggregate trends in educational attainment. The second measure is the share of those with a high school degree. This measure has the advantage that individuals with a high school degree are most likely to be near the skill threshold that separates workers going to complex and simple occupations. To control for aggregate trends in educational attainment we compare the change in the share of the highly educated over the sample period between groups of simple and the complex occupations. This can be interpreted as the regression coe(cid:14)cient on the interaction of a complex occupation dummy and a time (cid:12)xed e(cid:11)ect in a di(cid:11)erence-in-di(cid:11)erence (DiD) regression. This assumption is likely violated if one compares changes in the educational composition betweenallcomplexandsimpleoccupations. Instead, weonlycompareworkersinoccupationsnear our exogenously set threshold for the task complexity de(cid:12)ning complex occupations, which we have assumed to be either the 50th or the 66th percentile. More precisely, we compare the growth of our observed skill measures among those working in occupations between the 45th and 65th percentile and those in occupations between the 67th and 87th percentile of the complexity distribution. For 57

Table E.1: Change in Average Education Outcomes by Occupation fraction with fraction with postsecondary education high school degree task complexity 45-65 0.141 0.125 percentile 67-87 0.063 0.059 task complexity 29-49 0.104 0.157 percentile 51-71 0.134 0.125 Notes: Thetablereportschangesintheshareofworkerswithapostsecondaryeducationor highschooldegreeamongstoccupationswhosecomplexityindexfallswithinthegiven percentilesintheoccupationleveldistribution. robustness, we repeat the exercise using occupations between the 29th and the 49th percentile on theonehandandthe51standthe71stpercentileontheotherhand. ResultsareshowninTableE.1. We (cid:12)nd that in accordance with our hypothesis, the share of both medium- and highly educated workers has grown faster in simple than complex occupations. One exception is the measure of highly educated when using the 50th percentile threshold. This may be the case because the demand for highly skilled individuals is too small in occupations below the 50th percentile to make a comparison with complex occupations meaningful. In particular, the common-trends assumption for the validity of the DiD design may be violated in this case. Overall, we conclude that in the aggregate the average skill of those going to complex occupations has decreased, consistent with Beaudry et al. (2016) who document a \de-skilling process" according to which traditionally lower-skilled occupations have seen a particularly large growth in the share of highly educated individuals.24 24Wehavealsoestimatedrichermodelsofthechangingeducationcompositionbetweensimpleandcomplexoccupations. In particular, using pooled individual level data for 1980 and 2005 we have run linear probability models of the complex occupation dummy on a dummy for high school educated workers, a dummy for workers with at leastsomepost-secondaryeducationalattainment,apolynomialinage,adummyfortheyear2005,andinteractions between the time- and education dummies. The results from these speci(cid:12)cations are in line with those documented in Table E.1. In particular, the share of high school educated workers, that is those likely to be most likely at the margin between simple- and complex occupation employment, has increased faster in simple occupations, holding constant the share of highly educated. Hence, there was a faster reallocation from low- to medium-skilled labor in simplethanincomplexoccupations. Interestingly,wealso(cid:12)ndthatyoungerworkersalsoreallocatedatahigherrate to complex occupations than older workers, which we view as further evidence in favor of our proposed mechanism if we view age as a variable correlated with human capital and skill. 58

Another, and potentially more powerful, approach to conduct a test of sorting as suggested by our model is using panel data. We use the 1980-1997 Panel Study of Income Dynamics (PSID) and consider two time periods: 1980-1985 and 1992-1997. We restrict the sample to male workers, aged 16-64, working in a complex occupation in period t, and having experienced a 3-digit occupational switch from period t(cid:0)1 to period t into their current complex occupation either from a simple occupation or from another complex occupation. We then run the following regression: lnw = (cid:12) +(cid:12) Dum +(cid:12) Dum +(cid:12) Dum (cid:3)Dum +(cid:12) X ; (E.1) t 0 1 sc 2 time 3 sc time 4 t where lnw is the log real hourly wage in period t, Dum is a dummy variable that takes the value t sc of one if the occupational switch into the current complex occupation is from a simple occupation and zero otherwise, Dum is a dummy variable that takes the value of one in the 1992-1997 time time period, and X is a vector of covariates that includes (cid:12)ve age groups, education, race, number t of children, and health. The parameter of interest is the coe(cid:14)cient on the interaction term. This speci(cid:12)cation can be motivated as follows. According to our model, workers going to complex occupations become over time, on average, less skilled at solving complex tasks. First, in the empirical model in (E.1) we use those who switch from simple to complex occupations as \standins" for such marginal workers. However, occupational switches may always come with systematic wage gains or losses, and these gains may have changed over time. Therefore, we use occupational switchers within complex occupations to control for this component. Second, the interaction term measures the extent to which the wage gap between these two groups of switchers has changed over time. Column (i) in Table E.2 provides the basic results from the regression. In the (cid:12)rst time period, within the group of occupational switchers into a complex occupation in period t, those that switched from a simple occupation had 34% lower wages in period t than those that switched from another complex occupation. The main result from our test is in the interaction coe(cid:14)cient (cid:0) in the second time period that wage gap increased by another 10 percentage points. In other words, switchersfromsimpletocomplexoccupationsearnadditional10percentagepointslessthan switchers from complex to complex occupations in the second period than in the (cid:12)rst period. 59

Table E.2: Change in Average Wages by Occupation Dependent Variable: Log Wages (i) (ii) Dum -0.339*** -0.129*** sc Dum 0.134*** 0.060** time Dum *Dum -0.101*** -0.118** sc time Age 0.131** Education 0.071*** Race -0.099*** Children 0.030*** Health -0.046*** signi(cid:12)cancelevel: (cid:3)(cid:3)(cid:3) 1%,(cid:3)(cid:3) 5% Notes: Regressionsrunon1980-1997PSIDdata Column (ii) in Table E.2, listing a speci(cid:12)cation where we control for several observables,25 does notchangeourmainresults: thewagegapbetweenswitchersfromcomplextocomplexoccupations and switchers from simple to complex occupations has increased over time. We interpret this result as indirect supporting evidence of the fact that the marginal worker that works in a complex occupation in the late 1990s has a lower level of skill complexity than the marginal worker in the early 1980s. 25Note also that since we restrict the sample to occupational switchers into a complex occupation, they all have the same occupational tenure. 60

F Tables and Figures Table F.1: Group-Level Employment Growth Regression Dependent Variable: Change in Employment Share 1980-2005 Independent Variable (i) (ii) (iii) Complexity Index 0.0000315*** 0.0000227** 0.0000246** (3.08) (2.30) (2.38) Routine Index -0.0000248* -0.0000252* (-1.94) (-1.97) Order of 1980 Wage Poly. 0 0 3 N =15142 Notes: Thetablereportsresultswhenoccupation-leveldataisdisaggregatedto occupation(cid:2)gender(cid:2)education(cid:2)race(cid:2)agecells(seesection3.2for discussion). Regressionsincludegender(cid:2)education(cid:2)race(cid:2)age(cid:12)xede(cid:11)ects. Sandarderrorsclusteredattheoccupationlevel. t-statisticsareinparentheses. Signi(cid:12)cancelevelsare: (cid:3)(cid:3)(cid:3) 1%,(cid:3)(cid:3) 5%,(cid:3) 10%. 61

Table F.2: Occupation-Level Employment Growth Regression by 1980 Wage Tercile Dependent Variable: Change in Employment Share 1980-2005 First Second Third Independent Tercile Tercile Tercile Variable (i) (ii) (iii) Complexity Index 0.00111 0.00128 0.00429* (0.88) (1.22) (1.92) Routine Index -0.00115 -0.00133* -0.000162 (-1.30) (-1.68) (-0.12) Order of 1980 Wage Poly. 3 3 3 N 114 111 90 Notes: Thetablereportsresultsforoccupation-levelregressionsrunfordi(cid:11)erent tercilesofthe1980occupationalwagedistribution. t-statisticsarein parentheses. Signi(cid:12)cancelevelsare: (cid:3)(cid:3)(cid:3) 1%,(cid:3)(cid:3) 5%,(cid:3) 10%. 62

Table F.3: Occupation-Level Wage Growth Regression with Occupational Demographic Means: Female-Only Sample Dependent Variable: Change in Log Wages 1980-2005 Complex Variable: Complex Variable: Independent Index Indicatory Variable (i) (ii) (iii) (iv) (v) Complexity Variable 0.365*** 0.364*** 0.380*** 0.0941*** 0.121*** (5.25) (5.14) (5.35) (2.75) (3.45) Routine Index -0.00457 -0.0182 -0.0421 -0.0279 (-0.09) (-0.36) (-0.82) (-0.54) Female Share -0.0477 -0.0465 -0.101** -0.115** -0.116** (-0.96) (-0.90) (-1.99) (-2.21) (-2.24) College Share 0.183** 0.181** 0.312*** 0.455*** 0.383*** (2.08) (2.00) (3.14) (4.68) (3.77) High School Share -0.0724 -0.0706 0.0860 0.213 0.267 (-0.47) (-0.45) (0.53) (1.28) (1.65) Non-white Share -0.214 -0.215 0.00986 0.0627 0.110 (-0.85) (-0.85) (0.04) (0.24) (0.43) Married Share -0.414 -0.409 0.133 0.305 0.348 (-1.32) (-1.29) (0.41) (0.91) (1.06) Mean Age 0.00290 0.00289 -0.000432 -0.00170 -0.00285 (0.59) (0.59) (-0.09) (-0.34) (-0.58) Mean # Children 0.244* 0.242* 0.131 0.137 0.104 (1.76) (1.72) (0.96) (0.97) (0.74) Order of 1980 Wage Poly. 0 0 3 3 3 N =310 yComplexoccupationsarede(cid:12)nedasthoseabovethe50thpercentile(column(iv))orabovethe66th percentile(column(v))ofthecomplexityindex. Notes: Demographicvariablesareoccupation-levelmeansoftheshareofworkersinanoccupationwitha college/high-schooldegree,theshareofworkersinanoccupationwhoarenon-white,theshareofworkersinan occupationwhoaremarried,theshareoffemaleworkersinanoccupation,themeanageofworkersinan occupation,andthemeannumberofchildrenofworkersinanoccupation. t-statisticsareinparentheses. Signi(cid:12)cancelevelsare: (cid:3)(cid:3)(cid:3) 1%,(cid:3)(cid:3) 5%,(cid:3) 10%. 63

Table F.4: Occupation-Level Employment Growth Regression with Occupational Demographic Means: Female-Only Sample Dependent Variable: Change in Employment Share 1980-2005 Complexity Variable: Complexity Variable: Independent Complexity Index Complex Indicatory Variable (i) (ii) (iii) (iv) (v) Complexity Variable 0.00179 0.00120 0.000970 0.000476 0.000796 (1.16) (0.77) (0.59) (0.63) (1.01) Routine Index -0.00245** -0.00243** -0.00245** -0.00233** (-2.10) (-2.07) (-2.10) (-1.98) Female Share -0.00353*** -0.00289** -0.00318*** -0.00321*** -0.00320*** (-3.16) (-2.51) (-2.68) (-2.71) (-2.70) College Share 0.00472** 0.00376* 0.00425* 0.00447** 0.00390* (2.40) (1.87) (1.83) (2.02) (1.68) High School Share -0.00307 -0.00215 -0.00126 -0.00118 -0.000953 (-0.90) (-0.63) (-0.34) (-0.32) (-0.26) Non-white Share 0.00453 0.00434 0.00584 0.00588 0.00614 (0.80) (0.77) (1.00) (1.01) (1.06) Married Share -0.00683 -0.00446 -0.00156 -0.00138 -0.00127 (-0.97) (-0.63) (-0.20) (-0.18) (-0.17) Mean Age 0.0000220 0.0000174 -0.000000999 -0.00000376 -0.0000122 (0.20) (0.16) (-0.01) (-0.03) (-0.11) Mean # Children 0.00229 0.00125 0.000523 0.000576 0.000397 (0.75) (0.41) (0.16) (0.18) (0.13) Order of 1980 Wage Poly. 0 0 3 3 3 N =315 yComplexoccupationsarede(cid:12)nedasthoseabovethe50thpercentile(column(iv))orabovethe66thpercentile (column(v))ofthecomplexityindex. Notes: Demographicvariablesareoccupation-levelmeansoftheshareofworkersinanoccupationwitha college/high-schooldegree,theshareofworkersinanoccupationwhoarenon-white,theshareofworkersinan occupationwhoaremarried,theshareoffemaleworkersinanoccupation,themeanageofworkersinanoccupation, andthemeannumberofchildrenofworkersinanoccupation. t-statisticsareinparentheses. Signi(cid:12)cancelevelsare: (cid:3)(cid:3)(cid:3) 1%,(cid:3)(cid:3) 5%,(cid:3) 10%. 64

Table F.5: Employment Growth Regression with Social Skills Dependent Variable: Change in Employment Share 1980-2005 Complex Variable: Independent Index Variable (i) (ii) (iii) Complexity Index 0.000493 0.000313 -0.0000316 (0.41) (0.23) (-0.11) Routine Index -0.000632 -0.000697 -0.000215 (-1.11) (-1.13) (-0.69) Social Skill 0.00205* 0.00194 0.0000888 (1.77) (1.58) (0.27) Controls None Occ Dem Grou Means Level Order of 1980 Wage Poly. 3 3 3 N 315 315 15142 Notes: t-statisticsareinparentheses. Signi(cid:12)cancelevelsare: (cid:3)(cid:3)(cid:3) 1%,(cid:3)(cid:3) 5%,(cid:3) 10%. (i)occupation-levelregression. (ii)occupation-levelregressionwiththefollowingdemographiccontrols: shareof workersinanoccupationwithacollege/high-schooldegree,shareofworkersinan occupationwhoarenon-white,shareofworkersinanoccupationwhoaremarried, shareoffemaleworkersinanoccupation,meanageofworkerinanoccupation,and meannumberofchildrenofworkersinanoccupation. (iii)group-levelregressiononoccupation(cid:2)gender(cid:2)education(cid:2)race(cid:2)agecells(see section3.2fordiscussion). Regressionsincludegender(cid:2)education(cid:2)race(cid:2)age(cid:12)xed e(cid:11)ects. Standarderrorsclusteredattheoccupationlevel. 65