Overview Empirical Evidence Model Calibration Quantitative Results

The Macroeconomic Implications of Rising WageInequality in the United States

by Heathcote, Storesletten and Violante (JPE, 2010)

presented bySalvatore Lo Bello (UC3M)

Macro Reading Group - UC3M

7 June, 2017

Overview Empirical Evidence Model Calibration Quantitative Results

Rising Wage Inequality: Should we Worry?

The structure of relative wages in the US has undergone amajor transformation in the period 1970–2000.

American workers faced:1 A rising college premium;2 A shrinking gender gap;3 An increase in residual wage inequality.

→ Question: what are the implications for themacroeconomy and for the household welfare?

Main Idea: concerns for inequality (fact 3) may be mitigatedby the fact that households can actually take advantage ofsome of the drivers of inequality (fact 1 and 2).

Overview Empirical Evidence Model Calibration Quantitative Results

This Paper in a Nutshell

Develop an OLG model economy with incomplete markets.

Quantitative exercise: shock the steady–state economy withobserved changes in relative prices of labor (due todemand shifters) and level of volatility of wage process.

The model replicates several trends quite well:1 Rise in relative hours worked by women;2 Little dispersion in hours worked of men;3 Rise in correlation between wage and hours worked;4 Increase in consumption dispersion << increase in earnings

dispersion.

Welfare effects are on average positive: +3.1% of lifetimeconsumption!

Biggest driver: rise in college premium.Large heterogeneity: high–school couples lose 1.9%.

Overview Empirical Evidence Model Calibration Quantitative Results

Model Inputs

Overview Empirical Evidence Model Calibration Quantitative Results

Model Targets

Overview Empirical Evidence Model Calibration Quantitative Results

Preliminaries

Time is discrete: t = 0, 1, ... and continues forever.

Continuum of individuals who differ in: gender g ∈ {m, f },age j ∈ J = {1, 2, ..., J}.

Equally many females and males. Survival probabilities ζ j .

Life–cycle has 4 stages:1 Education (endogenous); [j = 0]2 Matching (exogenous); [j = 0]3 Work (endogenous savings, consumption, labor supply choices

within the household); j ∈ {1, ..., jR − 1}4 Retirement. j ∈ {jR , ..., J}

Unitary model: no disagreement within the household.

Overview Empirical Evidence Model Calibration Quantitative Results

Education & Matching

Education

Discrete education choice between college degree (e = h) orlower degree (e = l).

Utility cost of attending college κ, drawn from gender– andcohort– specific distribution F g

t (κ).

egt (κ) =

{h if Mg

t (h)− κ ≥ Mgt (l)

l otherwise

College enrollment rate: qgt = F gt (Mg

t (h)−Mgt (l)) ∈ [0, 1].

Matching

Mmt (h) = πmt (h, h)V 0

t (h, h) + πmt (h, l)V 0t (h, l),

Mmt (l) = πmt (l , h)V 0

t (l , h) + πmt (l , l)V 0t (l , l).

Overview Empirical Evidence Model Calibration Quantitative Results

Work & Retirement

Expected lifetime value for each spouse in newly formedhousehold:

V 0t (em, ef ) = E

[Vt(e

m, ef , 1, 0, ymt , yft

]

Problem of working household:

Vt(em, ef , j , at , ymt , y

ft ) = max

ct ,at+1,nmt ,nft

u(ct , nft , n

mt )+

βζ jEt

[Vt+1(em, ef , j + 1, at+1, y

mt+1, y

ft+1)

]s.t.

ct + ζ jat+1 = [1 + (1− τ a)r ]at+

(1− τn)[pm,em

t ε(j , ymt )nmt + pf ,ef

t ε(j , yft )nft ]

at+1 ≥ a ct ≥ 0 nmt , nft ∈ [0, 1].

Overview Empirical Evidence Model Calibration Quantitative Results

Productivity Process

Men and women face the same experience profile and thesame process for idiosyncratic productivity.

yt = {ηt , vt} (stacked vector, 2 components):

yt = ηt + vt (1)

ηt =ρηt−1 + ωt (2)

vt and ωt drawn from distributions with mean zero andvariances λvt and λωt .

Shocks are imperfectly correlated within an household.

The sequences {λvt , λωt } capture time variation in thedispersion of shocks.

Overview Empirical Evidence Model Calibration Quantitative Results

Technology

The consumption good is produced by a representative firm:

Yt = ZtKαt H

1−αt ,

where Ht is a CES aggregator of four types of labor:

Ht =[λSt

(λGt H

f ,ht + (1− λGt )Hm,h

t

) θ−1θ

+

(1− λSt )(λGt H

f ,lt + (1− λGt )Hm,l

t

) θ−1θ] θ

θ−1

The sequences {λGt , λSt } capture gender–biased andskill–biased demand shifts.

The sequence {Zt} adjusts to keep average labor productivityconstant, absent any behavioral response.

Overview Empirical Evidence Model Calibration Quantitative Results

Calibration

Overview Empirical Evidence Model Calibration Quantitative Results

Sequences of Shocks

Overview Empirical Evidence Model Calibration Quantitative Results

Hours Dynamics

Overview Empirical Evidence Model Calibration Quantitative Results

Wage–Hours Correlations

Overview Empirical Evidence Model Calibration Quantitative Results

Earnings and Consumption Variance

Overview Empirical Evidence Model Calibration Quantitative Results

Welfare Effects

Welfare effects using the educ. costs (κ’s) of initialsteady–state.

Overview Empirical Evidence Model Calibration Quantitative Results

Welfare Effects with Myopic Beliefs

Consider a model in which agents are surprised each period bythe λ’s.

Importantly, recalibrate the sequence of κ’s, to ensure sameenrollment rates.

Myopic agents fail at reaping most of the benefits fromskill–biased technical change.

Overview Empirical Evidence Model Calibration Quantitative Results

Concluding Remarks

Since the 1970’s, the US economy has experienced astructural change in the wage distribution.

Developed a neoclassical growth model with incompletemarkets and OLG.

Model can account for salient trends in inequality of laborsupply and consumption.

The model delivers welfare gains from the changes in thewage distribution.

Policy implications: fighting earnings inequality is notnecessarily welfare–improving.

→ Should be able to distinguish between sources of inequality!