The Allocation of Talent and U.S. Economic Growth

1. The Allocation of Talent and U.S. Economic Growth Chang-Tai Hsieh Erik Hurst Chad Jones Pete Klenow Spring 2016

2. Occupational Sorting Over Time Over last 50 years, remarkable convergence in occupational distribution between white men, women, and black. (See surveys in Altonji and Blank (1999) and Blau et al (2013)). In 1960, 94% of doctors and lawyers were white men. By 2010, the fraction was just over 60 percent. Many papers have focused on explaining differences in the occupational distribution across race-sex groups. No formal study has assessed the effect of these changes on aggregate productivity.

3. This Paper Measures the aggregate productivity effects from the changing allocation of talent of women and blacks from 1960 to 2010. Build a Roy model of occupational choice. Model includes many broad explanations for differences in occupational sorting across race-sex groups. (Focus on black and white; men and women). o Occupation specific labor market discrimination for each race-sex group. o Occupation specific barriers to human capital for each race-sex group. o Occupation specific preferences for each race-sex group o Productivity (preferences) for working in the home sector. Key assumption: Innate talent draws are similar across race-sex groups (in base case). Allow mean talent draws to differ across men and women in “brawny” occupations (robustness).

4. Modeling Choices Labor market discrimination: o Occupation specific “tax” on labor income for discriminated groups o Consistent with Becker (1957) o Keep track of the “tax” revenues Barriers to human capital accumulation: o “Tax” on occupation specific human capital expenditures for different groups. o Proxy for many stories: discrimination in schooling, social norms that steer certain groups away from certain occupations, differences in school quality across neighborhoods, etc. o Large literature on these specific stories o Keep track of the “tax” revenues

5. Modeling Choices Occupational Preferences: o Occupation specific preferences in utility function; differ by group o Johnson and Stafford (1998), Altonji and Blank (1999), and Bertrand (2011). Productivity/Preferences for home production: o Model it as productivity differences in home production – allow for time effect for all groups and differences across groups. o Large literature o Social Norms, home durables, changes in desired fertility, etc. Goal is to embed these broad features shown to be important in the literature into a more structural macro model. Distinguish the broad features of factors changing occupational choice. Goal is not to highlight a specific micro mechanism.

6. Where are the Productivity Gains Coming From? The labor market discrimination and barriers to human capital development act as a barrier to the allocation of talent. High (comparatively) productive women and blacks may have been deterred from choosing high skilled occupations in 1960. As the barriers declined, a better allocation of talent occurs. Productivity gains come from two sources: o Reduction in misallocation (right people are allocated to the right jobs) o Endogenous changes in human capital Similar stories can be told for preferences/home production efficiency. Yet, these also show up in utility or non-market production.

7. Findings Use data from the 1960-2000 Census plus the 2008-2010 ACS to discipline the model. Roughly 29 percent of the growth in US earnings per person (20 percent of GDP per worker) can be explained jointly by declines in barriers to human capital and declines in labor market discrimination for women and blacks. Most of the gains come from declining human capital barriers. Biggest gains came in the 1970s and 1990s. Relatively little gains post 2000. Counterfactuals suggest US growth may be slower going forward – less low hanging fruit. Declining allocation of talent for women and blacks were an important source of US productivity growth over last 50 years.

8. How We Will Proceed Develop a model of occupational sorting. Discuss model implications Show features of the data which will help us identify model. Compute productivity gains/conduct counterfactuals Show additional external data that matches model predictions pretty well. o Changing female labor supply elasticities from Blau and Khan (2007) o State measures of racial discrimination from Charles and Guryan (2008)

9. Why Do We Need A Model? Question: o Why not assess productivity gains in a back of the envelop way by multiplying change in wage gap by employed share of various groups. Answer: o White men’s wages may be affected by changing labor market conditions for other groups o Distinguish between various channels driving the changing occupational sorting of different groups. o The gender/racial wage gaps will almost certainly change for reasons not explaining occupational choice. (i.e., productivity changes sectors that “favor” women) o Allows for various counterfactuals.

10. Model

11. Continuum of workers in M market occupations or in the home sector (M+1 potential sectors) • Workers are indexed by occupation i, group g, and cohort c • 4 groups: white men (wm), white women (ww), black men (bm) and black women (bw). • Each worker possess heterogeneous abilities (some are good professors while others are good plumbers) • Basic allocation to be determined: matching workers with occupations • Life cycle structure • Human capital is endogenous Model

12. Some Notation τwig – employer “taste” for discrimination in sector i for group g τhig– “barrier” in human capital attainment associated with sector i for group g wi– wage per efficiency unit of human capital (endogenous) eig– schooling spending by group g associated with sector i (endogenous)

13. Workers C(c,t) – consumption of group g from cohort c at lifecycle point t. s(c) – time investment in schooling of cohort c (from group g choosing schooling in occupation i) zig– preference for occupation i by group g. β – parameter governing taste for consumption vs. leisure ϕi - return to time investments in human capital (another source of model growth in market output)

14. Timing Individuals draw and observe εi(their talent in each market sector i) for each market occupation and εhome(their productivity in the home sector). They also see current ϕi ,τhig , τwigand zig. They anticipate wiin first period of their life. The also see current slopes of occupational income profiles. Based on these, they choose their occupation, their s, and their e. The make schooling choices prior working (fund e by borrowing from future). Their occupation, pre-period human capital, and preferences stay constant over all periods of their life. Subsequent human capital accumulation is based on occupation specific experience. In each working period (1, 2, and 3), individuals choose whether to work in their chosen occupation or whether to work in the home sector. Make decisions based on Tighome, future τwigand future wig.

15. Workers

16. Workers Market Choice: (composite τ) Work at Home: (compare market consumption to home consumption) Measure of “home productivity” for cohort-group (could be preferences)

17. What Varies Across Occupations and/or Groups Occupation Specific wi= the wage per unit of total human capital in occupation i (endogenous) = the elasticity of human capital with respect to time invested in occupation i Occupation-Group or Cohort-Group Specific = labor market barrier (discrimination) facing group g in occupation i = barrier to building human capital facing group g in occupation i (fixed for a cohort) = preferences for occupation i by group g (fixed for a cohort) = productivity in home sector for group g and cohort c (fixed for a cohort)

18. The Distribution of Talent We assume Frechet for analytical convenience θ governs the dispersion of skills (estimated from data- higher θ less dispersion) εhome also drawn from a Frechet with same dispersion parameter Abstract from absolute advantage differences across people.

19. Occupational Choice Let denote the fraction of people in group g from cohort c who chose occupation i (when young). Model implies: τig(c,c) is the composite τ in occupation i for cohort c when they are young. Occupational sorting driven by: is the reward to working in an occupation for a person with average talent. Base assumption:

20. Labor Force Participation Let LFPig(c,t) denote the fraction of people in cohort c from group g at time t who chose occupation i and decided to work (as opposed to staying home) Observed occupational choice in market sector (this is data): Observed average occupational wage for young (t = c) (this is data)

21. Relative Propensities Relative occupational sorting (in market sectors): (data) (data) Relative occupational wages: (data) (constant across occ’s)

22. An Aggregate Firm Ai – productivity within each market occupation (major source of growth within model) Y - aggregate output (time subscripts suppressed throughout) σ - elasticity of substitution across sectors Hig – denotes total efficiency units of labor provided by group g to i (solved for in equilibrium)

23. An Aggregate Firm τwig – employer “taste” for discrimination in sector i for group g τhig– “barrier” in human capital attainment associated with sector i for group g wi– wage per efficiency unit of human capital (endogenous) eig– schooling spending by group g associated with sector i (endogenous) Utility of Owners of Firms Utility of Owners of “Schools”

24. Some Intuition Two groups: wm and ww. Assume wm face no distortions Assume occupations are perfect substitutes (σ ∞) s.t.wi = Ai. Assume no schooling time (ϕi), mean occupational talent in all occupations for all groups is same (Tig = 1), and no occupational preferences (zig = 0). earnings weighted average τ

25. Some Intuition To see effect of distortions on aggregate consumption and output, assume τh = 0 and (1-τiw) and Ai are jointly log normally distributed. Given the above: Aggregate output and consumption depend on both the mean and the variance of the τ’s. In more realistic examples (σ< ∞) , men’s wages will also be affected by changing barriers to women.

26. Competitive Equilibrium Given occupations, individuals choose c, e, and s to maximize utility. Each individual chooses the utility-maximizing occupation. Each individual choose to work each period. A representative firm chooses Hi to maximize profits The occupational wage per unit of human capital, wi, clears each labor market Aggregate output is given by the production function Perfect competition assumes that the “taxes” offset for the disutility of hiring/educating a group.

27. Data and Some Parameters

28. Data U.S. Census: 1960, 1970, 1980, 1990, and 2000 American Community Survey: 2008-2010 (pooled) Sample: o Include only black men, white men, white women, and black women o Include only individuals aged 25-55 (inclusive) o Exclude unemployed o Distinguish between full time and part time employees (part time workers are allocated 0.5 to home sector and 0.5 to their occupation). Occupations: o 67 consistently defined occupations (one of which is the home sector) o As robustness exercises, look at 350 occupations (1980 -2008) or only 20 occupations.

29. Examples of Base Occupational Classifications Health Diagnosing Occupations084     Physicians 085     Dentists 086     Veterinarians 087     Optometrists 088     Podiatrists 089     Health diagnosing practitioners, n.e.c. Health Assessment and Treating Occupations095     Registered nurses 096     Pharmacists 097     Dietitians Secretaries, Stenographers, and Typists313     Secretaries 314     Stenographers 315     Typists

30. Our Measure of “Wages” We measure earnings as sum of labor, business and farm income in the previous year. We restrict sample to individuals who worked at least 48 weeks during the prior year, who earned at least 1000 dollars (in 2007 dollars) in the previous year, and who reported working more than 30 hours per week. We define hourly wages as total annual earnings in prior year divided by total hours worked in prior year. All earnings are in constant dollars. When measuring aggregate wage gaps, we regress individual wages on race* sex dummies, cohort dummies, cohort*race-sex dummies, occupational controls and usual hours worked controls.

31. An Important Input: Estimating θandη Implications of Frechet: Use data on wages (adjusted for occupation and group dummies) to solve above numerically for each year. Adjust for top coding. Pin down η = 0.36 (using aggregate expenditure on schooling) Estimate θ(1-η) = 1.36 Implies θ = 2.12 Also, extensive margin labor supply elasticity = Using data from white men in 1990, get θ = 2.31

32. Cohort Life Cycle Young: Age 25-34 Middle: Age 35-44 Older: Age 45-54

33. Some Descriptive Results

34. Standard deviation of ln (pig(c,c)/pi,wm(c,c)); Focus on young

36. Inferring the Composite τ’s Assume talent draws are similar between men and women. Model implication 1: (data) (data) Note: Compute the composite τ for each group, in each occupation, during each time period.

38. Weighted Average of by group over time

39. Weighted Standard Deviation of by group over time

40. Parts 2: Estimate Preferences Model implications 2: (1) (2) (3) Term (1) is data. Term (2) conditions on labor market participation (inclusive of selection). Conditional on observed labor force participation, solve for preferences (term (3))

41. Weighted Average of z’s by group over time

42. Weighted Standard Deviation of z’s by group over time

43. Part 3: Separating Labor Market Discrimination from Human Capital Frictions Model implications 3: (1) (2) (3) (4) Terms (1) and (2) are data. Term 3 is the experience profile of wages for each group relative to white men. Estimate earnings growth within each occupation for white men (conditional on “experience”). Women have same profile holding experience constant – differ in experience.

44. Parts 4: Estimate Ωhome Model implications 4: Choose home productivity to match the labor supply of young – it is a cohort effect and then carries with them throughout their lifecycle.

45. Completing the Model and Doing Counterfactuals

46. Parameter Summary

47. Parameter Summary

48. Decomposing τ

49. Intuition: Lifecycle Wage Gaps for White Women (Relative to White Men), By Cohort

50. Decomposing τ