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 October 2013

2. Occupational Sorting Over Time Focus on a sample of individuals aged 25-55 and focus on following groups white men, white women, black men and black women: White Men in 1960: 94% of Doctors, 96% of Lawyers, and 86% of Managers White Men in 2008: 63% of Doctors, 61% of Lawyers, and 57% of Managers

3. Share of Each Group in High Skilled Occupations Shares are conditional on working in market sector. Unconditional shares of white women working in High-skill occupations goes from 2% to 15%.

4. Where Were the Other Groups Working in 1960 58% of working white women in Nursing, Teaching, Sales, Secretarial and Office Assistances, and Food Prep/Service. o The comparable number for white men was 17% (mostly sales) o 68% of white women stayed at home (9% of white men) 64% of working black men in Freight/Stock Handlers, Motor Vehicle Operators, Machine Operators, Farm, and Janitorial and Personal Services. o The comparable number for white men was 29% 51% of working black women in Household Services, Personal Services, and Food Prep/Services. o The comparable number for white men was 2%

5. Why Are There Differences in Occupational Sorting? Some Potential Candidates (which can result in labor “misallocation”): Differential discrimination in labor markets (Becker, 1957; Charles and Guryan, 2008) Differential barriers to human capital (formal and informal) accumulation o Discrimination in college admissions (Karabel, 2005) o Public schools for blacks were underfunded relative to whites (Card and Krueger, 1992) o Gender specific social norms that affect human capital investments (Fernandez, 2007) o Improved health care access for blacks when young (Chay, Guryan, and Mazumder, 2009)

6. Why Are There Differences in Occupational Sorting? Some Potential Candidates (which do not necessarily result in “misallocation”): Changes in occupational productivity that is group specific (e.g., “brain” vs. “brawn” technological change (Rendall, 2010)) Occupation specific technological change o Technological innovation took place in occupations were women/blacks had a relative comparative advantage (like the home sector). (Bound and Johnson, 1992 ; Greenwood, Seshadri, and Yorukoglu, 2005) Fertility/Flexibility Stories (may or may not be “misallocation”) o Innovation in fertility planning (Goldin and Katz, 2002) o Changes in labor market flexibility (Bertrand, Goldin, and Katz, 2010).

7. Why Are There Differences in Occupational Sorting? Some Potential Candidates (which do not result in “misallocation”): Preferences? o Not in the model (yet). o Preliminary results – implies wage should fall (wage gaps should increase) for those occupations into which women migrate (all else equal). o Is inconsistent with the data (as a first order story). May still be there but would imply that other forces that we document are even stronger.

8. How We Proceed Develop a model of occupational sorting. o Model will nest the potential stories about why differences in occupation choice can occur. o How talent for different occupations is distributed is a key input into the model choice (occupations are not chosen randomly) o Make assumptions so that the model can be taken to the data. Show that the model is consistent with many features of the data . o Prediction from the model about how wage gaps vary across occupations. o Show that the data are (roughly) consistent with this prediction.

9. How We Proceed 3. Use the model to decompose how much of the change in: o Wage gaps across groups o Occupational choice across groups o Aggregate earnings growth o Convergence of earnings in the South relative to the North are due to: a) Sector specific productivities (including brawn/brain differences) b) Group specific frictions or relative comparative advantage changes Within the latter explanations, perform counterfactuals assuming all changes are either labor market frictions, human capital frictions, or changes in relative comparative advantages across the groups. If time, show some results trying to tease among the latter stories.

10. Model

11. 4 groups (g): white men (wm), white women (ww), black men (bm), and black women (bw). The quantity of each group is qg. • Individuals draw iid talent εiin each of N occupations (i = occupation) Model Preferences Human Capital Consumption Note: Individuals choose i (occupation), s (time spent in schooling), and e (resource inputs into schooling).

12. 4 groups (g): white men (wm), white women (ww), black men (bm), and black women (bw). The quantity of each group is qg. • Individuals draw iid talent εiin each of N occupations (i = occupation) Model Preferences Human Capital Consumption Note: Individuals choose i (occupation), s (time spent in schooling), and e (resource inputs into schooling).

13. What Varies Across Occupations and/or Groups (So Far) 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 Specific = labor market barrier (discrimination) facing group g in occupation i = barrier to building human capital facing group g in occupation i = factor that augments the human capital function differentially by group g and occupation i Note: (1) The home sector is a separate occupation. (2) Wages (in a world with no distortions) reflect marginal products.

14. Timing Individuals draw and observe εifor each occupation. They also see ϕi, τhigand τwig They anticipate wi. Based on these, they choose their occupation, their s, and their e. Again, wiwill be determined in GE (production details later).

15. Identification Problem (Currently) In terms of the model: (1) is isomorphic to ; given that, we normalize o Interpretation of and differ. Empirically, we will be able to identify: Note: We cannot distinguish between , , and How we proceed with counterfactuals (later in talk): Assume = 0 so that all differences in are from barriers to human capital accumulation (assume zero profits in the human capital sector). Or, conversely, assume = 0 so that all differences in are from labor market barriers (assume zero profits in the different occupations). Note: In last part of the talk (if time allows), we will talk about some work we are doing to help to tease these two factors apart from each other.

16. The solution to the individual’s utility maximization problem, given an occupational choice: Individual Consumption and Schooling

17. The Distribution of Talent We assume Frechet for analytical convenience Commonly used for tractability (McFadden, 1974; Eaton and Kortum, 2002) For convenience, redefine so that: ρ governs correlation across an individuals skills (absolute advantage) θ governs the dispersion of skills (estimated from data- higher θ less dispersion) Assume θ is constant across all groups in all occupations.

18. The Distribution of Talent We assume Frechet for analytical convenience Tigscales the supply of talent for an occupation Benchmark case: Tig = Ti(identical talent distributions) Ti is observational equivalent to production technology parameters, so we normalize Ti = 1.

19. Occupational Choice Let pig denote the fraction of people in group g that work in occupation i. Model implies: Occupational sorting driven by: is the reward to working in an occupation for a person with average talent.

20. Equilibrium Wage Gaps Across Groups Let denote the average earnings in occupation i by group g. Implication: The wage gap between groups is same across occupations. Selection exactly offsets differences in T’s and τ’s across groups because of the Frechet assumption. Higher τig barriers in one occupation reduce a group’s wages proportionally in all occupations.

21. Notation: γ Related to the mean of the Frechet distribution for abilities.

22. Implication In models of occupational sorting with occupational talent draws, the wage gap between groups in an occupation is relatively uninformative about: o Occupation specific differences in distortions between groups (τ’s) o Occupation specific differences in comparative advantage between groups (T’s)

23. Inferring Occupation Specific Differences Between Groups Relative propensities to be in an occupation between groups: Given the available data, we can estimate:

24. Empirical Implication When doing counterfactuals below, we assume all the differences in occupational choice (in levels and changes) are either due to: (1) Changes in occupational productivities (via wi) and ϕ’s (2) Changes in T’s or changes in τ’s We can pin down the levels of τigfor each group by either: (a) normalizing Ti,wm = 1 and τi,wm= 1 (b) assuming zero profit by occupation in labor and human capital markets with white men always getting the subsidy. (c) assuming zero profits with most represented group getting subsidy.

25. Aggregates Human Capital Production Expenditure Note: qg is fraction of population in group g

26. Competitive Equilibrium Given occupations, individuals choose c, e, and s to maximize utility. Each individual chooses the utility-maximizing occupation. 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

27. Weaknesses of Setup No preference differences across groups (not yet) - Will have trouble fitting the wage data Talent of teachers does not affect human capital of students - Average quality of teachers (both men and women) is falling in our model. - Not due to fact that talented women in the 1960s are now doctors and lawyers (comparative advantage is not differentially correlated with absolute advantage across occupations). No dynamics. Do not focus on utility yet (only focus on productivity). Simple correlation between absolute ability and comparative advantage.

28. Evaluating the Sorting Model and Inferring

29. Data U.S. Census: 1960, 1970, 1980, 1990, and 2000 American Community Survey: 2006-2008 (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.

30. 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

31. Our Measure of “Wages” For annual aggregate wage gaps by group, we compute wages as individual earnings divided by hours worked in the previous years for those working full time during the previous year. o We condition wages on a quadratic in potential experience, a cubic in usual hours worked, and occupation dummies. When needed (basically for weighting), we impute wages for the home sector o Use relationship between education and earnings for different occupation and groups. o Use education and group to infer average wages in the home sector.

32. Test Model Implications: Changes By Schooling

33. Test Model Implications: Changes By Schooling

34. Note: Figure holds in changes (1960-2008) as well (Figure 2) and for other group/years.

35. Doctor

36. An Important Input: Estimating θ(1−η) Implications of Frechet: Use data on wages (adjusted for occupation and group dummies) to solve above numerically for each year. Attempt to control for “absolute advantage” across people

37. Estimating θ (1−η) Adjustment to WagesEstimates of θ(1−η): Base controls (assume ρ = 0) 3.11 Base controls + Adjustments 3.43 Assumptions about wage variation due to absolute advantage differences 25% 3.43 50% 4.14 75% 5.58 90% 8.36 Base controls: Potential experience, hours worked, occupation dummies, group dummies Adjustment: Transitory variation in wages, AFQT score, Education

38. Our Estimates of (η = 0.25): White Women

39. Our Estimates of (η = 0.25): Black Men

40. Summary: Means of Over Time (Weighted by Occupational Income Share)

41. Summary: Variance of Log Over Time (Weighted by Occupational Income Share)

42. Completing the Model and Doing Counterfactuals

43. A Note on Estimation Using model and available data, estimate 5*N parameters (where N is the number of occupations). Parameters of interest: Occupation-specific A’s, ’s, and (ww, bm, bw) Moments: o pi’s for each group 4*N−4 moments (pi’s sum to one) o Average wage (i) N average wages o wage gap (r) 3 wage gaps (ww, bw, bm) o Need to pin down the level of the ’s

44. Parameters

45. Main Findings: Percent of Growth Explained

46. Counterfactuals in the τhCalibration

47. Counterfactuals in the τw Calibration

48. Potential Remaining Productivity Growth From Changing Note: Counterfactual of setting 2008 to zero (relative to 2008 income).

49. Sources of Productivity Gains in the Model Changing allocation of human capital investments: o White men over-invested in 1960 o Women, blacks under-invested in 1960 o Less so in 2008 Changing allocation of talent to occupations: o Dispersion in τ’s for women, blacks in 1960 o Less so in 2008

50. A Simple (Naïve) Back of the Envelop Calculation How much of aggregate income growth can be simply accounted for by changing wage gaps of white women, black men, and black women? o Assume wages of white men are exogenous o Answer: 12.8% (as opposed to 15.9% - 20.4% in our base specifications). Why is this naïve? Many forces at work (some of which are opposing) o Ignores dispersion! Productivity gains coming from mean and dispersion. o Interaction of tau’s and T’s with productivity changes (A’s) o Ignores general equilibrium effects (men’s wages are distorted) Our estimates indicate that most of our gains are coming from change in dispersion of tau’s over time.