The Allocation of Talent and U.S. Economic Growth

Chang-Tai Hsieh

Erik Hurst

Chad Jones

Pete Klenow

October 2013

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

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%.

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%

Why Are There Differences in Occupational Sorting?

Some Potential Candidates (which can result in labor “misallocation”):

1. Differential discrimination in labor markets (Becker, 1957; Charles and Guryan, 2008)

2. 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)

Why Are There Differences in Occupational Sorting?

Some Potential Candidates (which do not necessarily result in “misallocation”):

3. Changes in occupational productivity that is group specific (e.g., “brain” vs. “brawn” technological change (Rendall, 2010))

4. 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)

5. 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).

Why Are There Differences in Occupational Sorting?

Some Potential Candidates (which do not result in “misallocation”):

6. 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.

How We Proceed

1. 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.

2. 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.

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

4. 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.

5. If time, show some results trying to tease among the latter stories.

Model

Model

Preferences

Human Capital

Consumption

Note: Individuals choose i (occupation), s (time spent in schooling), and e (resource inputs into schooling).

(1 )U s c

• 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 εi in each of N occupations (i = occupation)

h h s e

(1 ) (1 )w hc wh e

Model

Preferences

Human Capital

Consumption

Note: Individuals choose i (occupation), s (time spent in schooling), and e (resource inputs into schooling).

(1 )U s c

• 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 εi in each of N occupations (i = occupation)

h h s e

(1 ) (1 )w hc wh e

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.

i

wigwig

igh

Timing

• Individuals draw and observe εi for each occupation.

• They also see ϕi, τhig and τw

ig

• They anticipate wi.

• Based on these, they choose their occupation, their s, and their e.

• Again, wi will be determined in GE (production details later).

Identification Problem (Currently)

In terms of the model:

(1) is isomorphic to ; given that, we normalize

o Interpretation of and differ.

(2) 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.

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1

hig

ig wig

wig

hig

ighhig 1igh

igh hig

igh

hig

ig

ig

wig

Individual Consumption and Schooling

The solution to the individual’s utility maximization problem, given an occupational choice:

*

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1

1* 1

1 1

1

1 (1 )

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( ) , (1 )

(1 )( , , )

i

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ii

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ig

i iig

ig

i i i iig i i

ig

s

w se

w sc

w s sU w

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.

11

1

1

( ) exp{N

igi ii

F T

1

1/ (1 ) and igigT T

1

1

( ) exp{N

i ig ii

F T

The Distribution of Talent

• We assume Frechet for analytical convenience

• Tig scales 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.

1

1

( ) exp{N

i ig ii

F T

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.

11/

1

(1 ) where

iig ig i i i

ig igIigjgj

w T w s sp w

w

(endogenous), , , i i ig igw T

igw

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.

1 1

11/

1

(1 )(1 )

w Nig i ig

sgig isg ig

w Hwage s w

q p

1 1.1

,,

jgig j

j wmi wm j

wwage

wwage

igwage

Notation: γ

• Related to the mean of the Frechet distribution for abilities.

1 11

(1 ) 1

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)

1 1.1

,,

jgig j

j wmi wm j

wwage

wwage

Inferring Occupation Specific Differences Between Groups

Relative propensities to be in an occupation between groups:

Given the available data, we can estimate:

(1 )

,

, ,

ig ig gi wm

i wm i wm ig wm

p T wage

p T wage

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, ,

,

ig i wm i wm wm

i wm ig ig g

T p wage

T p wage

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 τig for 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.

11

(1 )

, ,

,

ig i wm i wm wm

i wm ig ig g

T p wage

T p wage

Aggregates

Human Capital

Production

Expenditure

Note: qg is fraction of population in group g

1

G

i g ijg ijggH q h dj

1/

1( )

N

i iiY A H

1 1

N G

ijg ijgi gY c e dj

Competitive Equilibrium

1. Given occupations, individuals choose c, e, and s to maximize utility.

2. Each individual chooses the utility-maximizing occupation.

3. A representative firm chooses Hi to maximize profits

4. The occupational wage per unit of human capital, wi, clears each labor market:

5. Aggregate output is given by the production function

1/

1 1max

N N

i i i ii iA H w H

1

G

i g ijg ijggH q h dj

Weaknesses of Setup

1. No preference differences across groups (not yet)

- Will have trouble fitting the wage data

2. 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).

3. No dynamics.

4. Do not focus on utility yet (only focus on productivity).

5. Simple correlation between absolute ability and comparative advantage.

Evaluating the Sorting Model and Inferring 'ig s

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.

Examples of Base Occupational Classifications

Health Diagnosing Occupations 084     Physicians 085     Dentists 086     Veterinarians 087     Optometrists 088     Podiatrists 089     Health diagnosing practitioners, n.e.c.

Health Assessment and Treating Occupations 095     Registered nurses 096     Pharmacists 097     Dietitians

Secretaries, Stenographers, and Typists313     Secretaries 314     Stenographers 315     Typists

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. 

Test Model Implications: Changes By Schooling

Panel A: Occupational Similarity Index, Relative to White Men

Race-Sex Group 1960 20082008-1980Difference

White Women: High Educated 0.38 0.59 0.12

White Women: Low Educated 0.40 0.46 0.04

Panel B: Conditional Log Difference in Wages, Relative to White Men

Race-Sex Group 1960 20082008-1980Difference

White Women: High Educated -0.50 -0.24 0.16

White Women: Low Educated -0.56 -0.27 0.20

Test Model Implications: Changes By Schooling

Panel A: Occupational Similarity Index, Relative to White Men

Race-Sex Group 1960 20082008-1980Difference

White Women: High Educated 0.38 0.59 0.12

White Women: Low Educated 0.40 0.46 0.04

Panel B: Conditional Log Difference in Wages, Relative to White Men

Race-Sex Group 1960 20082008-1980Difference

White Women: High Educated -0.50 -0.24 0.16

White Women: Low Educated -0.56 -0.27 0.20

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

Doctor

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

2 2

21

(1 )(1 )variance of w1

mean of w 11

(1 )(1 )

11

(1 )

, ,

,

ig i wm i wm wm

i wm ig ig g

T p wage

T p wage

Estimating θ (1−η)

Adjustment to Wages Estimates 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

Our Estimates of (η = 0.25): White Women

Our Estimates of (η = 0.25): Black Men

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

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

Completing the Model and Doing Counterfactuals

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 min

' s

Parameters

Parameters Base Value Target/Range

θ(1-η) 3.44 Wage Dispersion*

η 0.25 Set Value [0, 0.5]

β 0.693 Mincerian return across occupations

σ 2/3 Set values [-90, 95]

min by year Schooling in lowest wage occupation

Main Findings: Percent of Growth Explained

Average Annual Wage Growth = 1.47 Due to τh’s Due to τw’s

Ti,g = Ti,wm in all occupations 20.4% 15.9%

Ti,g set to fit relative shares in brawny occ’s in all years 18.9% 14.1%

Ti,g set to fit relative shares in all occ’s in 2008 20.4% 12.3%

Only Focus on Growth in Market Sector 26.9% 23.5%

Only Focus on Data for Ages 25-35 28.7% 23.6%

11

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, ,

,

ig i wm i wm wm

i wm ig ig g

T p wage

T p wage

Counterfactuals in the τh Calibration

Counterfactuals in the τw Calibration

Potential Remaining Productivity Growth From Changing

Average Annual Wage Growth = 1.47

Due toτh’s

Due toτw’s

Increase in growth if remaining frictions went to zero

14.3% 10.0%

' s

Note: Counterfactual of setting 2008 to zero (relative to 2008 income). ' s

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

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.

Sensitivity of Gains to the Wage Gaps

Due toτh’s

Due toτw’s

Baseline 20.4% 15.9%

Counterfactual: wage gaps halved 12.5% 13.7%

Counterfactual: zero wage gaps 2.9% 11.8%

Wage Growth Due to Changing Factors

Actual Wage Growth

Due toτh’s

Due toτw’s

White Men 77.0 percent -5.8% -7.1%

White Women 126.3 percent 41.9% 43.0%

Black Men 143.0 percent 44.6% 44.3%

Black Women 143.0 percent 58.8% 59.5%

Robustness, τw Case (% of growth)

Base: σ = 2/3 σ = -90 σ = -1 σ = 1/3 σ = 0.95

15.9% 12.3% 13.3% 14.7% 18.4%

Base: η = 0.25

η = 0 η = 0.1 η = 0.5

15.9% 13.9% 14.8% 17.5%

η = 0.25

θ(1-η) = 3.44 θ(1-η) = 4.16 θ(1-η) = 5.61 θ(1-η) = 8.41

15.9% 14.6% 12.9% 11.2%

Robustness, τh Case (% of growth)

Base: σ = 2/3 σ = -90 σ = -1 σ = 1/3 σ = 0.95

20.4% 19.7% 19.9% 20.2% 21.0%

Base: η = 0.25

η = 0 η = 0.01 η = 0.05 η = 0.1 η = 0.5

20.4% 20.5% 20.5% 20.5% 20.5% 20.3%

η = 0.25

θ(1-η) = 3.44 θ(1-η) = 4.16 θ(1-η) = 5.61 θ(1-η) = 8.41

20.4% 20.7% 21.0% 21.3%

Gains when changing only the dispersion of ability (i.e, not simultaneously re-estimating model or solving for new τ’s)

Value of θ(1-η)Due to

τh’sDue to

τw’s

3.44 20.4% 15.9%

4.16 18.6% 15.1%

5.61 9.5% 8.0%

8.41 8.4% 3.9%

Robustness

Estimates are robust to the following:

• More Detailed Occupations (331 for 1980 onward)

• A broader set of occupations (20 in all years)

• Weight on consumption vs. time in utility (β)

Summary of Other Findings

Changing T’s and τ’s also led to:

• Decompose gains in each period to each group.

o Post 1980, essentially all gains come from changes to white women.

o Prior to 1980, about one-quarter of gains come from blacks.

• ~90% of the narrowing of the wage gaps

• ~70% of the rise in female LF participation

• Substantial wage convergence between North and South

Education Predictions (Not Used in Calibration at All)

1960Level

2008Level

Change2008 - 1960

ChangeRelative to WM

Model Prediction

(τh’s)

Model Prediction

(τw’s)

Model Prediction

(T’s)

White Men 11.11 13.47 2.35

White Women 10.98 13.75 2.77 0.41 0.62 0.60 0.63

Black Men 8.56 12.73 4.17 1.81 0.63 0.62 0.66

Black Women 9.24 13.15 3.90 1.55 1.11 1.10 1.16

Work in Progress/Things to Think About

• Distinguishing between T’s/τh’s and τw’s.

o Look at cohort vs. time effects.

o Assume T’s/τh’s are cohort effects and τw’s are time effects.

o What we are finding: mostly cohort effects for women and a mix for blacks.

• Absolute advantage correlated with comparative advantage?

o Talented 1960 women went into teaching, nursing, home sector?

o As barriers fell lost talented teachers and drew talented women out of the home sector?

o Effect on measured wage gaps? Loss of high quality inputs into children?

o Could explain Mulligan and Rubinstein (2008) facts.

Conclusion

• Changing labor market factors for blacks and women have had a non-trivial impact on the change in average earnings within the U.S. during the past 50 years. (~ 20% of U.S. growth attributable to T’s and τ’s).

• Developed a model of occupational choice with labor market differences across groups that can be taken to the data.

• General equilibrium factors can be important (selection and human capital decisions.)

• Can ask how much sector specific technological change (e.g., home production innovations) can explain relative patterns in labor force participation, educational attainment, and wage gaps relative to other stories.