Demand-Driven Labor Market Polarization

Demand-Driven Labor Market Polarization

Diego Comin (Dartmouth)

joint work with

Ana Danieli (Northwestern)Marti Mestieri (Northwestern)

DartmouthFebruary 25, 2019

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US Labor Market Outcomes Have Polarized since 1980

• Labor market outcomes in the US have polarized since the1980s.

Wage Bill Wage EmploymentH M L H M L H M L

2016-1980 8.8 2.9 6.1 2.98 2.33 2.6 1.48 .18 .98Relative to M 5.9 3.2 .65 .25 1.3 .8

• What drives the increase in inequality and polarization?

I skilled biased technical changeI tradeI de-unionizationI computerization and digitization of the economic activityI changes in the school curriculae

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Demand-Driven Polarization

1 Novel mechanism based on nonhomotheticity of demand:

I Income grows → demand shifts to high-income-elastic sectors→ (relative intensity of high- and low-skill occupations inhigh-income elastic sectors)→ relative demand of high- andlow- skilled workers increases → polarization.

2 Establish new empirical findings:I High-income elastic sectors are intensive in high- and low-skill

occupations relative to middle-skillI Initial Wage bill of high- and low-skill occupations

concentrated in high-income elastic sectorsI This pattern persists

3 Quantify the effect of the mechanism using GE model:

I Demand-driven mechanism accounts for significant shares ofwage bill change from 1980-2016

• 100% of increase for low-• 50% of increase for high-• 60% of decline for medium-

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Correlation of Sectoral Growth with Income Elasticity

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High-Skill Factor Shares and Income Elasticity

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Low-Skill Factor Shares and Income Elasticity

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Middle-Skill Factor Shares and Inc. Elasticity

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High-Skill 1980 Wage Bill Shares and Income Elasticity

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Low-Skill 1980 Wage Bill Shares and Income Elasticity

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Middle-Skill 1980 Wage Bill Shares and Income Elasticity

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Related Literature

• Traditional mechanisms to explain polarization:

I Routinization hypothesis: Autor, Levy and Murnane (2003),. . .I Offshoring: Blinder (2007), Grossman and RH (2008),. . .

• Employment Shifts Between Sectors:

I Acemoglu and Autor (2011), Goos et al. (2014).

• Structural change and wage structure:

I Barany and Siegel (18), Lee and Shin (18), Buera et al. (15).I Nonhomothetic CES: Comin, Lashkari and Mestieri (2015).

• Other related mechanisms:

I Trade, skill premium, structural change: Cravino Sotelo (18).I Sectoral trade composition: Basco and Mestieri (2013).I Consumption Spillovers: Manning (04), Mazzolari and Ragusa

(13), Clemens et al. (16).I College-educated-specific demand elasticities: Leonardi (2015).

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Outline

1 (If asked) Occupation classification and income elasticityestimation

2 The multi-sector model: importance of compositional changefor job polarization

3 Demand system: what drives compositional change

4 Full-blown model with job assignment (to derive predictionsfor quantity and price polarization)

5 Extensions:

I Trade.I Looking back and ahead, from 1950 to 2036.

6 Conclusion

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We Estimate Income Elasticities using HH Survey Data

• Use household expenditure data: CEX Survey, 2000-2002.

• Study urban HH with age of head between 25 and 64.

I Keep if responses in 4 rounds, not incomplete, 5th-95thincome, positive total and food expenditure, . . .

• Convert final good expenditures reported in the CEX intovalue added using the BEA’s 2000 input-output tables.

• Obtain total expenditure Eht and expenditure shares xhst ofHH h in sector s during quarter t.

• Use as HH controls Zh dummies for:

I Age (25-37, 38-50, 51-64), number of earners (≤ 2, 2+),household size (≤ 2, 3-4, 5+), region of residence.

• Merge with BLS urban sectoral price series.

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We Estimate a Nonhomothetic CES Demand System

• Each sector s has a demand income elasticity parameter, εs .

I Normalized to 1 for one sector s, εs = 1.I Expenditure elasticity proportional to εs.

• There is a common price elasticity σ across sectors.

• Allow for heterogeneity in tastes: ζsht ≡ αs + ΓsXh + δr + δt .

• Estimate system of equations for all sectors s(6= s).

ln xhst = ζhst + (1− σ) ln

(phstphst

)+

(1− σ)(εs − 1) ln

(Eht

phst

)+ εs ln xhst + νhst .

I If εs = 1→ Homothetic CES.I System of equations, estimate using GMM.

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We Instrument Prices and Expenditures

• Want to isolate relative price variation coming from shifts inthe supply curve.

• Use average relative price in other regions controlling for timeand region dummies.

• Household expenditures have measurement error.

• Use HH annual income and HH income quintile asinstruments (∼ NPV).

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Estimation Results of Nonhomothetic CES

Price Elasticity σ 0.63 (0.01)

Income Elasticity Parameters εsEducation and Health Care (6) 3.50 (0.18)

Arts, Entertainment,Recreation and Food Services (7) 2.04 (0.08)

Government (G) 1.00

Finance, Professional, Information,other services (excl. gov’t) (FIRE, PROF, 51, 81) 0.98 (0.04)

Manufacturing (31G) 0.57 (0.04)

Retail, Wholesale Trade andTransportation (42, 44RT, 48T) 0.37 (0.04)

Construction (23) 0.14 (0.06)

Agriculture, Mining and Utilities (11,21,22) 0.10 (0.04)

Std. Err. Clustered at HH level in parenthesis. Number of HH is 20,843.

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We Classify Occupations According to Skill Intensity

• Use Acemoglu and Autor (2011) classification.

• 3 levels: H (high), M (middle) and L (low).

I Use average wage from 1980 CPS (5th to 95th).I Ranking stable over time.I Ranking occupations by years of schooling very similar.

• AA group finer occupations by their skill level:

I H: managerial, professional and technical occupationsI M: sales, clerical and administrative support occupations;

production, craft, repair and operative occupations; andI L: service occupations (food/cleaning, personal care,

protective).

• Use employment shares from decennial census.

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Illustration of mechanism

• Start with a one sector model

Yt = At

∏j∈H,M,L

Xαjt

jt ,

wjtXjt = αjtYt .

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wjtXjt

wj ′tXj ′t=

αjt

αj ′t. (1)

• Variation in relative wage bill must come from variation infactor intensity (αjt/αj ′t).

• Importance of trade, skilled biased technical change and othertheories that change the effective factor intensity.

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Multi-sector setting

Yst = Ast

∏j∈H,M,L

Xαjst

jst , (2)

with∑

j∈H,M,Lαjst = 1

wjtXjst = αjstPstYst ≡ αjstVAst . (3)

wjtXjt =∑s∈S

αjstVAst . (4)

αjstVAst = (αjs0 +4αjst)(VAs0 +4VAst) (5)

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4 (wjtXjt)

wj0Xj0=

Term 1︷︸︸︷∑s∈S

γjs04VAst

VAs0+


γjs04αjst

αjs0+


γjs0

[4VAst

VAs0

4αjst

αjs0

]

where γjs0 ≡αjs0VAs0∑

s∈Sαjs0VAs0

High Mid Low H−M L−M

Total Change 10.19 3.18 6.61 7.01 3.43

Term 1 7.05 4.66 7.09 2.39 2.43Term 2 0.45 -0.22 0.00 0.67 0.22Term 3 2.69 -1.26 -0.47 3.95 0.79

Contribution ∆VAst 62% 82%

• Term 2 generates little variation alone! Multi-sector is key.

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Preferences Drive Sectoral Reallocation of Production

• Representative household earns all wages.

• Nonhomothetic CES Preferences, implicitly defined:

I∑s=1

(ζsCεst )

1σ c

σ−1σ

st = 1,

I ζs > 0 constant taste parameter for i = 1, . . . , I .I σ is the elasticity of substitution.I εi governs nonhomotheticity of i .I If εi = 1− σ, we recover homothetic CES.I Parameter restriction (Hanoch, 75): ζi > 0, σ > 0,εi > 0 if σ ∈ (0, 1), εi < 0 if σ > 1.

I Preferences defined up to scaling factor in

1 nonhomotheticity: εi ≡ ξεi ,2 taste parameter: ζi ≡ Ωζi .

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Preferences Drive Sectoral Reallocation of Production• Representative household earns all wages.• Nonhomothetic CES Preferences, implicitly defined:

I∑s=1

(ζsCεst )

1σ c

σ−1σ

st = 1,

I ζs > 0 constant taste parameter for i = 1, . . . , I .I σ is the elasticity of substitution.I εi governs nonhomotheticity of i .I If εi = 1− σ, we recover homothetic CES.

S∑i=1

(ζiC

1−σt

) 1

σ cσ−1

σ

it = 1

I Parameter restriction (Hanoch, 75): ζi > 0, σ > 0,εi > 0 if σ ∈ (0, 1), εi < 0 if σ > 1.



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Preferences Drive Sectoral Reallocation of Production

• Representative household earns all wages.

• Nonhomothetic CES Preferences, implicitly defined:

I∑s=1

(ζsCεst )

1σ c

σ−1σ

st = 1,

I ζs > 0 constant taste parameter for i = 1, . . . , I .I σ is the elasticity of substitution.I εi governs nonhomotheticity of i .I If εi = 1− σ, we recover homothetic CES.I Parameter restriction (Hanoch, 75): ζi > 0, σ > 0,εi > 0 if σ ∈ (0, 1), εi < 0 if σ > 1.



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Sectoral Demand is Log-Linear• HH facing prices pst with budget constraint

∑s pstcst ≤ Et .

• Demand (Hicksian)

cst = ζs

(pstPt

)−σC εst .

• In terms of observables (marshallian)

cst = ζs(pst/Pt)−σ(Et/Pt)

εs

and

Pt =

[∑s∈S

(ζsp

1−σst

)χs(xstE

1−σt

)1−χs

] 11−σ

where xst = pstcst/Et and χs ≡ (1− σ)/εs .• Expenditure elasticity:

∂ ln cst∂ lnEt

= σ + (1− σ)εs∑s xstεs

.

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We Close the Model Imposing Market Clearing

• The representative household spends all its income

Et =∑s

∑j

wjtXjst .

• Goods consumed in each sector need to be produced ,

VAst = ζs(pst/Pt)−σ(Et/Pt)

εs . (6)

• Wage Bill for occupation j is

wjtXjt =∑s∈S

αjstVAst =∑s∈S

αjstζsEσ+εst p1−σ

st P−εst . (7)

We use Equations (6) and (7) for quantifying bare-bones model

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Quantification: Match 1980, then shock model to 2016

Initial Values

• Strategy: match 1980 (exactly).

• Demand parameters εs , σ from CEX (as discussed).

• Demand parameters ζs to match VA shares 1980 (BEA).

• αs,1980 inferred from wage bill.

I Hours worked from Census, wages from CPS.

Shock the 1980 Economy with 2016 Values

• Uniform increase in productivity, match increase in real PCE:

I Compute same way as in BEAs with Fisher price indeces.I Hold relative sectoral prices to 1980.

• Change prices pst to match change in relative prices (BEA).

• Hold αs,1980 for now.

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We Are Allowing only Variation in ∆VAst

Back to the Wage Bill Decomposition

4 (wjtXjt)

wj0Xj0=

Term 1: Comp.︷︸︸︷∑s∈S

γjs04VAst

VAs0+

Term 2: Factor Int.︷︸︸︷∑s∈S

γjs04αjst

αjs0+

Term 3: Covariance︷︸︸︷∑s∈S

γjs0

[4VAst

VAs0

4αjst

αjs0

]


s∈Sαjs0VAs0

are wage bill shares.

Zoom in Term 1: How important is Nonhomotheticity?

∑s∈S

γjs04VAst

VAs0=

Term1︷︸︸︷∑s∈S

γjs0

[4VAst

VAs0

]E

+


γjs0

[4VAst

VAs0

]ps

+∑s∈S

γjs0

[4VAst

VAs0

]E

[4VAst

VAs0

]ps︸︷︷︸

Term 3

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We Are Allowing only Variation in ∆VAst

Back to the Wage Bill Decomposition

4 (wjtXjt)

wj0Xj0=

Term 1: Comp.︷︸︸︷∑s∈S

γjs04VAst

VAs0+

Term 2: Factor Int.︷︸︸︷

HHHHH

HH

∑s∈S

γjs04αjst

αjs0+

Term 3: Covariance︷︸︸︷

XXXXXXXXXXXX

∑s∈S

γjs0

[4VAst

VAs0

4αjst

αjs0

]


s∈Sαjs0VAs0

are wage bill shares.

Zoom in Term 1: How important is Nonhomotheticity?

∑s∈S

γjs04VAst

VAs0=

Term1︷︸︸︷∑s∈S

γjs0

[4VAst

VAs0

]E

+


γjs0

[4VAst

VAs0

]ps

+∑s∈S

γjs0

[4VAst

VAs0

]E

[4VAst

VAs0

]ps︸︷︷︸

Term 3

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Quantification of the Mechanism Sectoral Growth Predictions

H M L H−M L−M

Total Value Added growth 10.19 3.18 6.61 7.01 3.43

VA only growth (Term 1) 7.05 4.66 7.09 2.39 2.43

Predicted change of. . .

Estimated Model 6.20 3.63 7.16 2.57 3.53Increase in Et 5.64 3.91 6.24 1.73 2.33Growth in pst 0.08 -0.06 0.16 0.14 0.21Interaction 0.48 -0.22 0.76 0.70 0.99

% Accounted, ↑ in Et 95% 105% 92% 81% 80%

• If we assign half of interaction to Et , account forI 81% of H–M,I 80% of L–M.

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Production Technologies

• Generalize production to

Yst = AstK1−βstst

∏j∈H,M,L

Xαjst

jst

βst

,

where Xjst denotes the number of efficiency units of labor areemployed in occupation j in sector s in year t.

• Demand is now

wjtXjst = βstαjstpstYst ,

rtKst = (1− βst) pstYst .

• Total wage bill in sector s is

J∑j=1

wjtXjst = βstpstYst

J∑j=1

αjst .

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Demand Side

• Continuum of households indexed by h from (0,1).

• Each household inelastically supplies a unit of labor to one ofthe three occupations.

• Household income is composed of the labor income plus therental income accrued from the capital it owns (Kht).

• We assume that capital is evenly distributed across households

• Every period household expenditure, Eht , equals householdincome.

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Preferences and Aggregate Demand

• Each household has nonhomothetic CES preferences as before.∑s∈S

(ζsU

εsht

) 1σ c

σ−1σ

hst = 1.

• Aggregate demand for sectoral output is

Cst =

∫ζsE

σ+εsht p−σst P−εsht dh.

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Occupational Choice

• Each HH draws a vector (ηL, ηM , ηH) of efficiency units ineach occupation

I Draws from iid log-normal.

• Price for each unit of skill: (wL, wM , wH).

• The optimal choice of the agent is to select occupation s.t.

maxj∈L,M,H

ηj wj.

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Equilibrium and Overview of Quantification

• Study competitive equilibrium.

• Demand elasticities εs , σ estimated from HH expendituresurvey (CEX).

• Use moments in the data for 1980 to set the values of themodel parameters.

I Sectoral prices and sectoral value added in 1980 come from theBEA.

I ζs is set to match sectoral consumption in 1980.

• αst , βst that is set to match the sectoral wage bill in eachsector in year t.

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Quantification

Initial Values

• Strategy: match 1980.

• Demand parameters εs , σ from CEX

• Demand parameters ζs to match VA shares 1980.

• Variance of log-normal for M and H to match relative wagesin 1980.

Changes to the 1980 Economy

• Explore how different shocks bring us to 2016.

• Uniform increase in labor productivity to match increase inpersonal consumption expenditure:

I Compute same way as in BEAs PCE with Fisher price indeces.

• αst , βst change by period and sector from the data.

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Results

Table: Full Quantitative Model

Year WLWM

WHWM

Ls Ms HsWLL∑k WkK

WMM∑k WkK

WHH∑k WkK

Exercise

Data 1980 0.74 1.24 0.095 0.653 0.252 0.068 0.630 0.3022016 0.80 1.49 0.129 0.488 0.383 0.088 0.421 0.491

Model 1980 0.74 1.24 0.095 0.653 0.252 0.068 0.630 0.3022016 0.86 1.44 0.133 0.543 0.324 0.101 0.483 0.416 E2016 0.77 1.41 0.095 0.582 0.323 0.066 0.524 0.411 α+β2016 0.87 1.57 0.125 0.499 0.376 0.091 0.416 0.493 E+β + α

Fraction of 2.17 1.32 0.88 0.93 0.95 1.15 1.02 1.01observedchange1

Contribution 0.85 0.55 1.13 0.63 0.5 1.26 0.6 0.51of E

Contribution 0.15 0.45 -0.13 0.37 0.5 -0.26 0.4 0.49of α+ β

(1) Fraction of the change produced by the full model, with changesin the level of expenditures, factor intensities and in the sectoral laborshares relative to total changed observed in the data.

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Extensions

1 Introduce trade.

I Most action comes from services, which are non-traded.I Correct total demand for sectoral net exports. Trade wedges

2 Backward exercise: 1950-1980. Results

I Account for the rise of middle-class.I Manufacturing was more of a luxury good in that period.

3 Other OECD countries.

I How much differences in levels of income account for differentpolarization experiences?

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Conclusions

• Sectoral growth between 1980-2016 is highly correlated withthe distribution of employment in high and low skilloccupations

• One consequence of this new empirical finding is that changesin sectoral composition of output induced by increase inexpenditures are a major driver of labor market polarization

• Our mechanism explains very significant share of changes inoccupational wage bills, relative wages and share of hoursworked from 1980-2016. For high- and low- skill occupationsthe mechanism accounts for around 50% and 100% ofobserved increases in data. For medium-skill occupations ourmechanism represents around 60% of the observed decline inthe data.

• Mechanism is robust to extensions and relevant for other timeperiods and countries.

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Trade Wedges

year Manufacturing Agriculture

1980 0.0082 -0.10022016 -0.1535 -0.0331

Go back

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Backward Exercise: 1950-1980

year WLWM

WHWM

Ls Ms HsWLL∑k WkK

WMM∑k WkK

WHH∑k WkK

Data 1980 0.74 1.24 0.095 0.653 0.252 0.068 0.630 0.3021950 0.70 1.15 0.106 0.731 0.163 0.075 0.736 0.189

Sim. 1980 0.74 1.24 0.095 0.653 0.252 0.068 0.630 0.302Sim. 1950 0.68 1.17 0.074 0.702 0.224 0.049 0.693 0.258 TFP

1950 0.79 1.18 0.122 0.660 0.218 0.094 0.651 0.254 α+β1950 0.72 1.06 0.100 0.730 0.171 0.073 0.743 0.184 TFP+β + α

Go back

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Subperiods

H−M L−M1980-2000: Overall 3.26 1.10

Incr Sect Shares 0.79 0.73Incr alpha 0.38 0.09Cov 2.09 0.28

2000-2016: Overall 3.75 2.33Incr Sect Shares 1.60 1.69Incr alpha 0.29 0.13Cov 1.86 0.51

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Demand-Driven Labor Market Polarization

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