[PPT] - Consumption and Labor Supply with Partial Insurance: An Analytical PowerPoint Presentation

SLIDE 1

Consumption and Labor Supply with Partial Insurance: An Analytical Framework

Jonathan Heathcote Federal Reserve Bank of Minneapolis, CEPR Kjetil Storesletten Federal Reserve Bank of Minneapolis, CEPR Gianluca Violante New York University, CEPR, and NBER Conference in Honor of Thomas Sargent and Christopher Sims Federal Reserve Bank of Minneapolis, May 4-5 2012

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 1 /20

SLIDE 2

Measurement of risk sharing

Three broad questions:

1. Fraction of individual shocks that transmits to consumption
2. Insurability nature of the recent increase in US inequality
3. Life-cycle shocks vs. initial conditions in determining inequality

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 2 /20

SLIDE 3

Measurement of risk sharing

Two complementary approaches:

1. Structural model ⇒ risk sharing as equilibrium outcome

◮ Sensitive to assumed market structure and insurance channels

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 3 /20

SLIDE 4

Measurement of risk sharing

Two complementary approaches:

1. Structural model ⇒ risk sharing as equilibrium outcome

◮ Sensitive to assumed market structure and insurance channels

2. Quantify overall risk sharing from data ⇒ agnostic about sources

◮ Requires long, high-quality panel data on (c, y)

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 3 /20

SLIDE 5

Our approach: Bewley meets Deaton

1. Structural equilibrium model with non-contingent bond, labor

supply, and redistributive taxation

2. Flexible financial market structure that does not hardwire agents’

access to insurance

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 4 /20

SLIDE 6

Our approach: Bewley meets Deaton

1. Structural equilibrium model with non-contingent bond, labor

supply, and redistributive taxation

2. Flexible financial market structure that does not hardwire agents’

access to insurance Analytical tractability

Closed-form equilibrium cross-sectional (co-)variances of (w, h, c)

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 4 /20

SLIDE 7

Our approach: Bewley meets Deaton

1. Structural equilibrium model with non-contingent bond, labor

supply, and redistributive taxation

2. Flexible financial market structure that does not hardwire agents’

access to insurance Analytical tractability

Closed-form equilibrium cross-sectional (co-)variances of (w, h, c)

Labor supply data informative about risk-sharing

Like c, h react differently to insurable vs. uninsurable shocks to w

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 4 /20

SLIDE 8

ECONOMIC ENVIRONMENT

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 5 /20

SLIDE 9

Demographics and preferences

Perpetual youth demographics with constant survival probability δ
Preferences over sequences of consumption and hours worked:

Eb

∞

t=b

(βδ)t−bu(ct, ht; ϕ) u (ct, ht; ϕ) = c1−γ

t

− 1 1 − γ − exp(ϕ) h1+σ

t

1 + σ where ϕ ∼ Fϕ,b is distaste for work relative to consumption

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 6 /20

SLIDE 10

Technology and individual endowments

Technology: linear in aggregate effective labor

◮ Competitive labor market: wage = individual productivity

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 7 /20

SLIDE 11

Technology and individual endowments

Technology: linear in aggregate effective labor

◮ Competitive labor market: wage = individual productivity

Individual wage: sum of two orthogonal components (in logs):

log wt = αt + εt

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 7 /20

SLIDE 12

Technology and individual endowments

Technology: linear in aggregate effective labor

◮ Competitive labor market: wage = individual productivity

Individual wage: sum of two orthogonal components (in logs):

log wt = αt + εt αt = αt−1 + ωt with ωt ∼ Fω,t

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 7 /20

SLIDE 13

Technology and individual endowments

Technology: linear in aggregate effective labor

◮ Competitive labor market: wage = individual productivity

Individual wage: sum of two orthogonal components (in logs):

log wt = αt + εt αt = αt−1 + ωt with ωt ∼ Fω,t εt = κt + θt with θt ∼ Fθ,t κt = κt−1 + ηt with ηt ∼ Fη,t At labor market entry, agents draw α0 ∼ Fα0,b and κ0 ∼ Fκ0,b

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 7 /20

SLIDE 14

Private risk-sharing

1. Non-state-contingent bond traded in zero net supply
2. Insurance claims tarded against shocks to ε only
Captures other (residual) insurance arrangements:

financial markets, spousal labor supply, family transfers, etc. Partial insurance: between bond economy and complete markets

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 8 /20

SLIDE 15

Government

Government: runs a progressive tax/transfer scheme

◮ Redistribution and financing of (non-valued) expenditures Gt ◮ Two-parameter function maps pre-government earnings (y = wh) to disposable earnings (˜ y) ˜ y = λy1−τ τ measure the degree of progressivity

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 9 /20

SLIDE 16

EQUILIBRIUM

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 10 /20

SLIDE 17

Equilibrium

In equilibrium, there is no bond trade among households
Sharp dichotomy between shocks:

◮ (αt, ϕ) uninsured privately, while εt perfectly insured

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 11 /20

SLIDE 18

Equilibrium

In equilibrium, there is no bond trade among households
Sharp dichotomy between shocks:

◮ (αt, ϕ) uninsured privately, while εt perfectly insured

We can solve for equilibrium allocations and prices in closed-form

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 11 /20

SLIDE 19

Link to Constantinides and Duffie (1996)

(i) CRRA prefs, (ii) unit root shocks to log disposable income, (iii)

zero initial wealth, (iv) wealth in ZNS ⇒ no bond-trade equilibrium

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 12 /20

SLIDE 20

Link to Constantinides and Duffie (1996)

(i) CRRA prefs, (ii) unit root shocks to log disposable income, (iii)

zero initial wealth, (iv) wealth in ZNS ⇒ no bond-trade equilibrium

Our environment micro-founds unit root disposable income:
1. Primitive exogenous process: wages
2. Labor supply: exogenous wages → endogenous earnings
3. Non-linear taxation: pre-tax earnings → after-tax earnings
4. Private risk-sharing: earnings → post-trade disposable income
5. No bond-trade: disposable income = consumption

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 12 /20

SLIDE 21

Hours worked

log ha

t (ϕ, α, ε)

= − ˆ ϕ + 1 − γ

σ + γ
α + 1
σ ε + Ha

t

where ˆ ϕ ≡

ϕ

σ+γ

and

1

σ ≡ 1−τ

σ+τ

Hours worked decrease in effort cost

ϕ

Response to ε proportional to tax-modified Frisch elasticity
Response to α depends on γ which controls wealth effect

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 13 /20

SLIDE 22

Consumption

log ca

t (ϕ, α, ε)

= −(1 − τ) · ˆ ϕ + (1 − τ) · 1 + σ

σ + γ
α + Ca

t

Independent of the insurable shock ε
Effect of ˆ

ϕ mediated by tax progressivity

Response to α mediated by labor supply and tax progressivity
Random walk, displays excess smoothness relative to PIH

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 14 /20

SLIDE 23

ANSWERS TO THE THREE QUESTIONS

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 15 /20

SLIDE 24

Pass-through coefficient

Pass-through from permanent wage shocks to consumption:

φw,c

t

≡ cov(∆ct, ωt + ηt) var(ωt + ηt)

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 16 /20

SLIDE 25

Pass-through coefficient

Pass-through from permanent wage shocks to consumption:

φw,c

t

≡ cov(∆ct, ωt + ηt) var(ωt + ηt) = (1 − τ) · 1 + σ

σ + γ ·

vωt vωt + vηt ◮ progressive taxation → 0.73 ◮ labor supply → 0.87 ◮ private insurance → 0.63

Overall, we estimate: φw,c

t

= 0.40

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 16 /20

SLIDE 26

Risk-sharing over time

1970 1975 1980 1985 1990 1995 2000 2005 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 Variance of Log Wages Year Data Model 1970 1975 1980 1985 1990 1995 2000 2005 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 Insurable Fraction of Cross−sectional Wage Dispersion Year 1970 1975 1980 1985 1990 1995 2000 2005 0.05 0.1 0.15 0.2 0.25 0.3 Variance of Log Consumption Year Data Model

vart(w) = vart(α) + vart(ε) + vµy + vµh vart(c) = (1 − τ)2vart( ˆ ϕ) + (1 − τ)2 1 + σ

σ + γ

2 vart(α) + vµc

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 17 /20

SLIDE 27

Risk-sharing over time

1970 1975 1980 1985 1990 1995 2000 2005 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 Variance of Log Wages Year Data Model 1970 1975 1980 1985 1990 1995 2000 2005 −0.3 −0.25 −0.2 −0.15 −0.1 −0.05 0.05 0.1 Correlation between Log Wages & Log Hours Year Data Model 1970 1975 1980 1985 1990 1995 2000 2005 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 Insurable Fraction of Cross−sectional Wage Dispersion Year

vart(w) = vart(α) + vart(ε) + vµy + vµh covt(w, h) = 1 − γ

σ + γ
vart(α) + 1
σ vart(ε) − vµh

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 18 /20

SLIDE 28

Lifecycle inequality decomposition

Total Variance Percent Contribution to Total Variance Initial Heterogeneity Life-Cycle Measurement Preferences Productivity Shocks Error var(log w) 0.35 40 50 10 var(log h) 0.11 46 6 15 33 var(log c) 0.16 17 30 20 33

All components are orthogonal ⇒ decomposition is unique

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 19 /20

SLIDE 29

Why preference heter. is a source of inequality

covt(w, h) = 1 − γ

σ + γ
vart(α) + 1
σ vart(ε) − vµh

< 0 covt(h, c) = (1 − τ)vart( ˆ ϕ) + (1 − τ) (1 + σ) (1 − γ) ( σ + γ)2 vart(α) > 0 γ = 1.5 ⇒ vart( ˆ ϕ) > 0

Heathcote-Storesletten-Violante, ”Consumption and Labor Supply with Partial Insurance”

p. 20 /20