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 March 2012

2. Occupational Sorting Over Time Fraction of group (white men, white women, black men, black women) aged 25-55 working in the following occupations: Executives, Mgmt, Architects, Engineers, Math/Computer Science, Natural Scientists, Doctors, and Lawyers. 19602006-2008 White Men 17.9% (19.7%) 21.7% (24.9%) White Women 2.0 (6.2) 14.6 (21.2) Black Men 2.2 (2.7) 10.6 (14.8) Black Women 0.7 (1.7) 11.4 (15.7) * 93.7% (62.9) of doctors, 95.8% (61.1) of lawyers, 85.9% (57.2) of managers, and 98.8% (83.5) of engineers were white men in 1960 (2006-8). Data: U.S. Census and American Community Survey

3. 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) 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%

4. Wage Gaps Over Time: An Overview Log difference in annual earnings of full time workers, conditional on experience, hours and occupation controls (relative to White Men) 196019802008 White Women -0.58 -0.48 -0.26 Black Men -0.38 -0.22 -0.15 Black Women -0.88 -0.48 -0.31 Note: Large changes in schooling over this time period. Large differences in labor market participation over this time period.

5. Potential Questions of Interest Why does occupational sorting differ across groups? 2. Why did occupational sorting change differentially across groups? 3. What are the aggregate productivity effects – if any – of changes in occupational sorting across the groups? o Were there any aggregate productivity gains from women and blacks moving into different occupations over last 50 years? (Yes) o Does this mean that labor market outcomes were distorted in 1960? (Perhaps – but not necessarily)

6. 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)

7. Why Are There Differences in Occupational Sorting? Some Potential Candidates (which do not necessarily result in “misallocation”): Latent differences in occupational productivity by gender due to differences in “brain” vs. “brawn” (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).

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 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) • Individuals draw iid talent εiin each of I occupations (i = occupation) Model Preferences Human Capital Consumption Note: Individuals choose i, s, and e.

12. 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 Note: (1) The home sector is a separate occupation. (2) Wages (in a world with no distortions) reflect marginal products.

13. Identification Issues (Part 1) Creating a composite measure of the “frictions” Under certain assumptions, can identify but not or separately. 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.

14. The solution to the individual’s utility maximization problem, given an occupational choice, is: Individual and Human Capital Decisions

15. The Distribution of Talent Each person j gets an iid skill draw, εij, for each of the I occupations. We assume a Frechet distribution for analytical convenience Implies that the distribution of log wages has fat tails. Often used in discrete choice models (McFadden, 1974; Eaton and Kortum, 2002) for tractability. What is θ ? θ = governs the dispersion of skills o A higher θ implies more relative comparative advantage in given occupation o A higher θimplies less wage dispersion. o Assume θ is constant across all groups in all occupations. Note: We will estimate θ from the data.

16. The Distribution of Talent Each person j gets an iid skill draw, εij, for each of the I occupations. We assume a Frechet distribution for analytical convenience What is Tig? Ti = mean of “comparative advantage” for each group in occupation i. o If all groups were the same, without loss of generality, we could set the Ti’s of the Frechet distribution equal to 1 for all occupations (observationally equivalent to sector productivities) o We set Ti,wm = to 1 for all occupations (normalization). o We allow Ti,g to differ from 1 for other groups (relative occupational comparative advantage differences across groups).

17. The Distribution of Talent Each person j gets an iid skill draw, εij, for each of the I occupations. We assume a Frechet distribution for analytical convenience Note o The iid assumption is important when we use actual wage data to estimate θ. o Some of the dispersion in the wage data is potentially due to persistent differences in absolute advantage across people. o When estimating θ from the data, we attempt to control for such differences.

18. Occupational Choice Let pig denote the fraction of people in group g that work in occupation i in equilibrium. Model implies: Occupational sorting driven by: Misallocation of talent comes from the dispersion of τ’s across occupation-groups

19. Equilibrium Wage Gaps Across Groups Let denote the average earnings in occupation i by group g. Model says the occupational wage gap between any to groups is the same across all occupations. Selection exactly offsets differences in T’s and τ’s across groups because of the Frechet assumption. Frechet assumption is an extreme version of other distributional assumptions. Note: Higher average barriers (τ’s) reduce a group’s wages in all occupations.

20. 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)

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

22. Identification Issue 2 We cannot distinguish τ’s from T’s using this approach. 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 (2) Changes in T’s or changes in τ’s Note: Remember - we can pin down the levels of for each group by either: (a) normalizing Ti,wm = 1 or (b) assuming zero profit by occupation in labor and human capital markets.

23. What We Will Do in the Model Ask how much of the change in: Occupational sorting between groups Labor force participation between groups Average wage gaps between groups Aggregate income growth can be attributed to occupation specific productivities (which influence w’s) and versus T’s and τ’s (the ) Additionally: If due to T’s and τ’s, we conduct counterfactuals assuming it is all changing T’s or allchanging τ’s or some combination of both.

24. Some Interpretation Black Men vs. White Men Hard to tell a story where the T’s differ between the two groups. Means sorting differences are likely entirely due to τ’s. White Women vs. White Men T’s could differ (different skill endowments). Are they changing over time? Possibly (brain vs. brawn innovation). Big movements into lawyer, doctor, executive occupations! However T’s could be a short hand way to proxy for fertility timing innovations. Fertility timing can be more important of certain (high skilled) occupations. Changing τ’s could still be an potential important channel.

25. Evaluating the Sorting Model and Inferring

26. 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 70 consistently defined occupations (one of which is the home sector) o As robustness exercises, look at 350 occupations (1980 -2008) or only 20 occupations.

27. 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

28. Our Measure of “Wages” For annual aggregate wage gaps by group, we compute define 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.

29. Test Model Implications: Changes By Schooling

30. Test Model Implications: Changes By Schooling

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

32. Doctor

33. 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

34. Estimating θ(1−η) Adjustment to WagesEstimates of θ(1−η): Base controls 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

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

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

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

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

39. Completing the Model and Doing Counterfactuals

40. Aggregates Human Capital Production Expenditure Note: qg is fraction of population in group g We normalize population to 1.

41. 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

42. 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

43. Parameters

44. Counterfactuals in the τhCalibration

45. Counterfactuals in the τw Calibration

46. Summary: Productivity Gains from Changing

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

48. Sources of Productivity Gains in the Model Better allocation of human capital investments o White men over-invested in 1960 o Women, blacks under-invested in 1960 o Less so in 2006 Better allocation of talent to occupations: o Dispersion in τ’s for women, blacks in 1960 o Less so in 2008

49. A Simple (Naïve) Back of the Envelop Calculation How much of aggregate income growth can be explained by changing wage gaps of white women, black men, and black women (a decomposition): o 21.7% Why is this naïve? Many forces at work (some of which are opposing) o Ignores movements across sectors o Interaction with productivity changes (A’s) o Ignores selection effects o Ignores general equilibrium effects (men’s wages are distorted) Note: We are working on decomposing the individual magnitudes of the different mechanisms.

50. Wage Growth Due to Changing Factors Note: We are reporting percent of growth explained. Note: Results are not sensitive to η