,

The Macroeconomic Implications of Rising Wage

Inequality in the United States

Jonathan Heathcote Minneapolis Fed, and CEPR

Kjetil Storesletten

Oslo University, Frisch Center, and CEPR

Gianluca Violante

New York University, CEPR, and NBER

The transformation of the U.S. wage structure

1. An increase in the college wage premium

• _{Skill-biased demand shift in favor of college graduates} 2. A decline in the gender wage gap

• _{Gender-biased demand shift in favor of women}

3. An increase in residual wage dispersion

The transformation of the U.S. wage structure

1. An increase in the college wage premium

• _{Skill-biased demand shift in favor of college graduates}

2. A decline in the gender wage gap

• _{Gender-biased demand shift in favor of women} 3. An increase in residual wage dispersion

The transformation of the U.S. wage structure

1. An increase in the college wage premium

• _{Skill-biased demand shift in favor of college graduates}

2. A decline in the gender wage gap

• _{Gender-biased demand shift in favor of women}

3. An increase in residual wage dispersion

This paper

• _{Take these changes in the wage structure as “given”}

• _{Feed them into OLG, incomplete-markets model of US economy}

• _{Answer two sets of quantitative questions:} 1. Positive: What have been their macroeconomic implications,

ie implied changes in the equilibrium distributions of labor earnings, labor supply and consumption?

2. Normative: What have been their welfare implications for U.S. households?

This paper

• _{Take these changes in the wage structure as “given”}

• _{Feed them into OLG, incomplete-markets model of US economy}

• _{Answer two sets of quantitative questions:}

1. Positive: What have been their macroeconomic implications, ie implied changes in the equilibrium distributions of labor earnings, labor supply and consumption?

2. Normative: What have been their welfare implications for U.S. households?

This paper

• _{Take these changes in the wage structure as “given”}

• _{Feed them into OLG, incomplete-markets model of US economy}

• _{Answer two sets of quantitative questions:}

1. Positive: What have been their macroeconomic implications, ie implied changes in the equilibrium distributions of labor earnings, labor supply and consumption?

2. Normative: What have been their welfare implications for U.S. households?

This paper

• _{Take these changes in the wage structure as “given”}

• _{Feed them into OLG, incomplete-markets model of US economy}

• _{Answer two sets of quantitative questions:}

1. Positive: What have been their macroeconomic implications, ie implied changes in the equilibrium distributions of labor earnings, labor supply and consumption?

2. Normative: What have been their welfare implications for U.S. households?

Production technology

• _{Aggregate CRS technology in capital K and aggregate labor H:}

Yt = ZtK_tαH1

−α

t

• _{H is a CES aggregator of four types of labor input indexed by} gender g ∈ {m, f} and education e ∈ {h, l}:

Ht =

·

λ_tS ³(1 − λG_t )H_tm,h + λG_t H_tf,h´

θ−1

θ

+¡1 − λS_t ¢³(1 − λG_t )H_tm,l + λG_t H_tf,l´

θ−1

θ ¸ θ θ₋₁

I _λS

t and λGt capture skill and gender-biased demand shifts

Production technology

• _{Aggregate CRS technology in capital K and aggregate labor H:}

Yt = ZtK_tαH1

−α

t

• _{H is a CES aggregator of four types of labor input indexed by} gender g ∈ {m, f} and education e ∈ {h, l}:

Ht =

·

λ_tS ³(1 − λG_t )H_tm,h + λG_t H_tf,h´

θ−1

θ

+¡1 − λS_t ¢³(1 − λG_t )H_tm,l + λG_t H_tf,l´

θ−1

θ ¸ θ θ₋₁

I _λS

t and λGt capture skill and gender-biased demand shifts

Production technology

• _{Aggregate CRS technology in capital K and aggregate labor H:}

Yt = ZtK_tαH1

−α

t

• _{H is a CES aggregator of four types of labor input indexed by} gender g ∈ {m, f} and education e ∈ {h, l}:

Ht =

·

λ_tS ³(1 − λG_t )H_tm,h + λG_t H_tf,h´

θ−1

θ

+¡1 − λS_t ¢³(1 − λG_t )H_tm,l + λG_t H_tf,l´

θ−1

θ ¸ θ θ₋₁

I _λS

t and λGt capture skill and gender-biased demand shifts

Demographics and life-cycle

1. Overlapping cohorts, each one comprising a continuum of

individuals of different gender

2. Individuals decide on education

3. Individuals marry to form households (married couples)

4. Households jointly decide on labor supply, consumption/savings

5. Mandatory retirement

Education and matching

• _Education

I Discrete decision: pursuing college degree _{(e = h)} or lower

schooling degree (e = l)

I Agents draw idiosyncratic utility cost _{κ ∼ F}g(κ), and make

schooling decision by comparing values of the two options • _Matching

I Conditional on (e, g), individuals meet spouse stochastically

I Assortative matching: part of return to education realized in

Education and matching

• _Education

I Discrete decision: pursuing college degree _{(e = h)} or lower

schooling degree (e = l)

I Agents draw idiosyncratic utility cost _{κ ∼ F}g(κ), and make

schooling decision by comparing values of the two options

• _Matching

I Conditional on (e, g), individuals meet spouse stochastically

I Assortative matching: part of return to education realized in

Household problem: working age

Vj

t(st) = max ct,nm_t ,nf_t

n

u(ct, xt) + βζjEtVj

+1

t+1(st+1)

o

s.t.

xt = x(1 − nm_t ,1 − nf_t )

c_t + ζja_t+1 = a_t + (1 − τa)ra_t +

(1 − τn) X

g∈m,f

pg,e_t g exp(L(j) + η_tg + v_tg)ng_t

at+1 ≥ a

Household problem: retirement

Vj

t(at) = max ct

n

u(ct, xt) + βζjEtVj

+1

t+1(at+1)

o

s.t.

xt = x(1,1)

c_t + ζja_t+1 = a_t + (1 − τa)ra_t + (1 − τn)b

Calibration: preferences

u(ct, xt) =

c1_t−γ

1 − γ + ψ

x1_t−χ 1 − χ

xt = [(1 − nm_t )1

−_σ

+ (1 − nf_t )1−_σ

]1−1σ

• _{χ = σ = 3 simultaneously delivers:}

1. ratio of female to male mkt hours: 0.48

2. Frisch labor supply elasticities: 0.48 for men, 1.46 for women

3. added worker effect: corr(∆wm,∆hf) = −0.11

• _{γ = 1.5}

Calibration: preferences

u(ct, xt) =

c1_t−γ

1 − γ + ψ

x1_t−χ 1 − χ

xt = [(1 − nm_t )1

−_σ

+ (1 − nf_t )1−_σ

]1−1σ

• _{χ = σ = 3 simultaneously delivers:}

1. ratio of female to male mkt hours: 0.48

2. Frisch labor supply elasticities: 0.48 for men, 1.46 for women

3. added worker effect: corr(∆wm,∆hf) = −0.11 • _{γ = 1.5}

Calibration: preferences

u(ct, xt) =

c1_t−γ

1 − γ + ψ

x1_t−χ 1 − χ

xt = [(1 − nm_t )1

−_σ

+ (1 − nf_t )1−_σ

]1−1σ

• _{χ = σ = 3 simultaneously delivers:}

1. ratio of female to male mkt hours: 0.48

2. Frisch labor supply elasticities: 0.48 for men, 1.46 for women

3. added worker effect: corr(∆wm,∆hf) = −0.11

• _{γ = 1.5}

Calibration: education & matching

• _Education

I We set parameters of _Fg_(κ) in order to replicate the empirical

‘‘trends" of male and female college enrollment

• _Matching

I We set conditional meeting probabilities in order to replicate

Calibration: education & matching

• _Education

I We set parameters of _Fg_(κ) in order to replicate the empirical

‘‘trends" of male and female college enrollment

• _Matching

I We set conditional meeting probabilities in order to replicate

Calibration: technology & productivity

• _{Aggregate technology}

I Elasticity of substitution between college and HS labor: _1.43

I ©_λS

t , λGt

ª

: match empirical paths for male college premium, and gender wage gap

• _{Individual productivity}

I _{λω

t , λvt }: Minimum Distance between model and empirical

Calibration: technology & productivity

• _{Aggregate technology}

I Elasticity of substitution between college and HS labor: _1.43

I ©_λS

t , λGt

ª

: match empirical paths for male college premium, and gender wage gap

• _{Individual productivity}

I _{λω

t , λvt }: Minimum Distance between model and empirical

Changes in the wage structure

1970 1980 1990 2000 0.8 0.9 1 1.1 1.2 1.3 1.4

(A) Skill and Gender Bias

Year 1970 1975 1980 1985 1990 1995 2000 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3

(B) Residual Variance of Log Male Wages

Year

0.05 0.1 0.15 0.2

(C) Variance Decomposition

0.005 0.01 0.015 0.02 0.025

0.03 (D) Variance of the Persistent Shock Skill Bias (λS)

Gender Bias (λG)

PSID Data Model Fit

Persistent Component (cumulated) Transitory Component (λv) Measurement Error

Computational experiment

1. Initialize economy in steady-state (1960s)

2. Sequence Λt ≡

©

λS_t , λG_t , λω_t , λv_tª is the only time-varying input

3. Perfect foresight

4. Set {Zt} such that absent any behavioral response, dynamics of

Λt leave average output (and productivity) constant at initial

Female-male hours ratio

1970 1980 1990 2000 0.3

0.4 0.5 0.6

Female / Male Hours Worked

Year

0.35 0.4 0.45 0.5 0.55 0.6

Decomposition

Pers Trans SB GB

Hours dispersion

1970 1980 1990 2000

−0.1 −0.05 0 0.05

0.1 (A) Variance of Log Male Hours

Year 1970 1980 1990 2000

−0.1 −0.05 0 0.05

0.1 (B) Variance of Log Female Hours

Year

−0.1 −0.05 0 0.05

0.1 (C) Decomposition

−0.1 −0.05 0 0.05

0.1 (D) Decomposition

Wage-hours correlation

1970 1980 1990 2000

−0.2 −0.1 0 0.1 0.2

(A) Male Wage−Hour Correlation

Year 1970 1980 1990 2000

−0.2 −0.1 0 0.1 0.2

(B) Female Wage−Hour Correlation

Household earnings and consumption

1970 1980 1990 2000

−0.15 −0.1 −0.05 0 0.05 0.1

0.15(A) Variance of Log Household Earnings

Year 1970 1980 1990 2000

−0.06 −0.04 −0.02 0 0.02 0.04

0.06(B) Variance of Log Household Consumption

Year

1970 1980 1990 2000

−0.15 −0.1 −0.05 0 0.05 0.1

0.15 (C) Decomposition

1970 1980 1990 2000

−0.06 −0.04 −0.02 0 0.02 0.04

0.06 (D) Decomposition CPS: Mean=0.32

PSID: Mean=0.28 Model: Mean=0.23

Welfare

1965 1970 1975 1980 1985 1990 1995 −10

−5 0 5 10

(B) Welfare Gain by Household Type (Relative to 1965 Cohort)

Year of Labor Market Entry

% Lifetime Consumption

1965 1970 1975 1980 1985 1990 1995 −4 −3 −2 −1 0 1 2 3 4

(A) Average Welfare Gain (Relative to 1965 Cohort)

Year of Labor Market Entry

% Lifetime Consumption

−10 −5 0 5 10

(D) Decomposition for (HS,HS)

% Lifetime Consumption

−3 −2 −1 0 1 2 3

4 (C) Decomposition

% Lifetime Consumption

Aggregate labor productivity

1965 1970 1975 1980 1985 1990 1995 2000 2005 −10

−5 0 5

10 Aggregate Labor Productivity

Year

Percentage Change from 1965

−10 −5 0 5

10 Decomposition

Percentage Change from 1965

Pers Trans SB GB

Two views from the public policy arena

1. “While there is no doubt that some people have been left

behind,[...] the good new is that most of the inequality reflects an increase in returns to investing in skills - workers completing more school, [...] and acquiring new capabilities.”

Ed Lazear

2. “Over the past three decades the lives of ordinary Americans

have become less secure, and their chances of plunging from the middle class into acute poverty ever larger [...] People aren’t

nearly as much better off as they would be if the gains from economic growth had been broadly distributed.”

Two views from the public policy arena

1. “While there is no doubt that some people have been left

behind,[...] the good new is that most of the inequality reflects an increase in returns to investing in skills - workers completing more school, [...] and acquiring new capabilities.”

Ed Lazear

2. “Over the past three decades the lives of ordinary Americans

have become less secure, and their chances of plunging from the middle class into acute poverty ever larger [...] People aren’t

nearly as much better off as they would be if the gains from economic growth had been broadly distributed.”

Facts I

1970 1980 1990 2000 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

2 (A) College Wage Premium

Year

Male Female

1970 1980 1990 2000 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65

1.7 (B) Gender Wage Gap

Year

0.15 0.2 0.25 0.3

0.35 (C) Fraction of Coll. Grad. (age 25−29)

Male Female 0.3 0.35 0.4 0.45 0.5 0.55 0.6

Facts II

1970 1975 1980 1985 1990 1995 2000 2005 −0.1

−0.05 0 0.05 0.1

(A) Variance of Log Wages

Year 1970 1975 1980 1985 1990 1995 2000 2005 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06

0.08 (B) Variance of Log Hours

Year

1970 1975 1980 1985 1990 1995 2000 2005 −0.2 −0.15 −0.1 −0.05 0 0.05 0.1

(C) Correlation btw Log Wages and Hours

1970 1975 1980 1985 1990 1995 2000 2005 −0.15 −0.1 −0.05 0 0.05 0.1 0.15

(D) Variance of Household Log Earnings and Equivalized Consumption Male [0.34]

Female [0.3] Male [0.11]_{Female [0.24]}

Male [−0.16]