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

The Allocation of Talent and U.S. Economic Growth

Chang-Tai Hsieh

Erik Hurst

Chad Jones

Pete Klenow

March 2012

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.

1960 2006-2008

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

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%

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)

1960 1980 2008

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.

Potential Questions of Interest

1. 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)

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. Latent differences in occupational productivity by gender due to differences in “brain” vs. “brawn” (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).

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 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

Preferences

Human Capital

Consumption

Note: Individuals choose i, s, and e.

(1 )U s c

• 4 groups (g): white men (wm), white women (ww), black men (bm), and black women (bw)

• Individuals draw iid talent εi in each of I occupations (i = occupation)

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

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

products.

i

wig

wig

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.

(1 )

1

hig

ig wig

hig w

ig

ig

hig

ig

wig

Individual and Human Capital Decisions

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

*

1

1*

1

1* 1

1 1

1

1 (1 )

( )

( ) , (1 )

(1 )( , , )

i

i

i

ii

i iig

ig

i iig

ig

i i i iig i i

ig

s

w se

w sc

w s sU w

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 θ implies less wage dispersion.

o Assume θ is constant across all groups in all occupations.

Note: We will estimate θ from the data.

( ) exp{ }i igF T




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).

( ) exp{ }i igF T




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.

( ) exp{ }i igF T

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

11/

1

(1 ) where

iig ig i i i

ig igIigjgj

w T w s sp w

w

(endogenous), , , i i ig igw T

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.

1 1.1

,,

jgig j

j wmi wm j

wwage

wwage

igwage

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

11

(1 )

, ,

,

ig i wm i wm wm

i wm ig ig g

T p wage

T p wage

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.

11

(1 )

, ,

,

ig i wm i wm wm

i wm ig ig g

T p wage

T p wage

' s

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 all changing τ’s or some combination of both.

' s

' s

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.

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 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.

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 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.

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 )variance of w1

mean of w 11

(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 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

Aggregates

Human Capital

Production

Expenditure

Note: qg is fraction of population in group g

We normalize population to 1.

1

G

i g ijg ijggH q h dj

1/

1( )

I

i iiY A H

1 1

I 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

I I

i i i ii iA H w H

1

G

i g ijg ijggH q h dj

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

ρ 2/3 Set values [-90, 95]

min by year Schooling in lowest wage occupation

Counterfactuals in the τh Calibration

Counterfactuals in the τw Calibration

Summary: Productivity Gains from Changing

Average Annual Wage Growth = 1.47

Due toτh’s

Due toτw’s

Due toT’s

Growth due to particular changes in

(Percent explained)

0.294

(20.0%)

0.233

(15.8%)

0.300

(20.4%)

Assume no τ’s in the “brawny” occupations

Growth due to particular changes in

(Percent explained)

0.262

(17.8%)

0.233

(13.4%)

' s

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

9.3% 4.3%

Assume no τ’s in the “brawny” occupations

Increase in growth if remaining frictions went to zero

7.2% 3.0%

' s

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

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

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.

Wage Growth Due to Changing Factors

Actual Wage Growth

Due toτh’s

Due toτw’s

Due toT’s

White Men 77.0 percent -4.3% -10.2% -5.8%

White Women 126.3 percent 39.4% 34.9% 41.9%

Black Men 143.0 percent 44.3% 40.8% 44.6%

Black Women 143.0 percent 57.0% 53.6% 58.8%

Note: We are reporting percent of growth explained.Note: Results are not sensitive to η

Robustness, τh Case (% of growth)

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

20.0% 15.9% 17.0% 18.6% 23.1%

Base: η = 0.25

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

20.0% 14.3% 15.1% 18.1% 19.3% 18.5%

η = 0.25

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

20.0% 18.8% 17.8% 17.0%

Base: β = 0.693 β = 0.5 β = 0.8

20.0% 20.0% 20.0%

Robustness, τw Case (% of growth)

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

15.8% 10.0% 11.7% 13.9% 19.9%

Base: η = 0.25

η = 0 η = 0.1 η = 0.5

15.8% 15.6% 15.6% 15.8%

η = 0.25

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

15.8% 15.2% 14.4% 13.6%

Base: β = 0.693 β = 0.5 β = 0.8

15.8% 15.8% 15.8%

Robustness to Broad or Detailed Occupation Codes

Baseline Broad Detailed

20.0% 20.1% 17.8%

Baseline: 67 occupations

Broad: 20 occupations

Detailed: 331 occupations (1980 onward)

Percent of Growth Explained (from 1980-2008 for comparability):

Baseline Broad Detailed

15.8% 14.4% 12.3%

h

w

Change in Female Labor Force Participation Due To Changing Factors

Change in Labor Force Participation For Women

Due toτh’s

Due toτw’s

Due toT’s

36.4 percentage points 37.4% 40.5% 27.7%

Note: We are reporting percent of growth explained.

Note: Women’s Labor Force Participation in 1960: 0.329Women’s Labor Force Participation in 2008: 0.692

Contribution of Each Group to Total Income Growth: τh

Percent of Growth Explained

Year

BaseModelGrowth

Setting All τh’s to

End Levels

Setting WM τh’s to End Levels

Setting WW τh’s to End Levels

Setting BM τh’s to End Levels

Setting BW τh’s to End Levels

1960-1980 33.3 percent

21.1% 4.2% 8.7% 3.4% 4.7%

1980-2008 49.8 percent

19.2% 1.5% 15.4% 0.8% 1.4%

1960-2008 99.7 percent

20.0% 2.6% 12.6% 1.9% 2.8%

Contribution of Each Group to Total Income Growth: τw


Year

BaseModelGrowth

Setting All τw’s to End Levels

Setting WM τw to End Level

Setting WW τw to End Level

Setting BM τw’s to End Level

Setting BW τw’s to End Level

1960-1980 33.3 percent

21.3% 1.8% 13.8% 2.1% 3.6%

1980-2008 49.8 percent

11.9% -0.7% 10.7% 0.4% 1.4%

1960-2008 99.7 percent

15.8% 0.3% 12.0% 1.1% 2.3%

Contribution of Each Group to Total Income Growth: T’s


Year

BaseModelGrowth

Setting All T’s to

End Levels

Setting WW T’s to End Level

Setting BM T’s to End Level

Setting BW T’s to End Level

1960-1980 33.3 percent 19.7% 11.3% 3.3% 5.1%

1980-2008 49.8 percent 20.9% 18.2% 0.9% 1.9%

1960-2008 99.7 percent 20.4% 15.3% 1.9% 3.2%

Education Predictions

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

Contributions to Northeast-South Convergence: τh

Percentage Points of Growth Explained

Year

Base ModelConvergencein P. Points

Setting All τh’s toEnd Levels

Setting BM and BW τh’s to

End Levels

1960-1980 20.7 2.9 3.3

1980-2008 -16.5 0.2 1.6

1960-2008 10.0 3.3 5.0

Contributions to Northeast-South Convergence: τw

Percentage Points of Growth Explained

Year

Base ModelConvergencein P. Points

Setting All τw’s toEnd Levels

Setting BM and BW τw’s to

End Levels

1960-1980 20.7 1.9 2.2

1980-2008 -16.5 0.0 1.0

1960-2008 10.0 2.1 3.2

Average “Quality” of Women in Occupation Relative to Men

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.

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

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