Partial Insurance ECON 34430: Topics in Labor Markets T. Lamadon (U - - PowerPoint PPT Presentation

Partial Insurance

ECON 34430: Topics in Labor Markets

• T. Lamadon (U of Chicago)

Fall 2017

Blundell Pistaferri Preston (2008) Consumption Inequality and Partial Insurance

Intro

Blundell, Pistaferri, Preston (2008)

1 Understand the level of inequality using both income and

consumption inequality

2 Understand how individual smooth income shocks:

• complete markets delivers too much insurance
• self-insurance too little

3 Lay out a model, estimate on data using consumption and

earnings

4 analyze the level of partial insurance against income

transatory and permanent income shocks

• big difference between income and consumption inequalities
• particularly after 1985

• inequality is very different across cohorts
• initial conditions are very different

Plan of attack

Blundell, Pistaferri, Preston (2008)

1 Specify an income and consumption process 2 Construct a panel of consumption and earnings 3 Estimate the consumption rule 4 Evaluate how observables change how consumption responds

to earning shocks

The Income Process

Blundell, Pistaferri, Preston (2008)

• Log real income is as follows:

log Yit = Zitbt + Pit + νit where Z is a set of observables and Pit is the permanent component: Pit = Pit−1 + ζit

• ζit is serially uncorrelated and νit is an MA(q)

νit =

q

• j=0

θj ǫit−j with θ0 = 1

• define income net of predictable individual components:

yit = log Yit − Zitbt

Consumption rule

Blundell, Pistaferri, Preston (2008)

• We define the following consumption rule:

∆cit = φitζit + ψitǫit + ξit

• cit is consumption net of predictable components
• the impact of permanent and transitory shocks are allowed to

be different and vary with time

• ξit is an independent income shock
• φit and ψit are the partial insurance coefficients
• can be derived from quadratic utility, or approximation to

CRRA

Partial Insurance parameters

Blundell, Pistaferri, Preston (2008)

• extreme cases are given by :
• full insurance φit = ψit = 0
• hand to mouth φit = ψit = 1
• in general, the closer the parameters to 0, the more insurance
• in the case of self insurance
• using CRRA utility,linear approximation
• φit ≃ πit and ψit ≃ γt,L · πit
• πit is share of future labor income to human capital and wealth
• ξit can be interpreted as shocks to higher moment
• γt,L ≃ r/(1 + r)(1 + θ1))
• simulations give that πit ∈ [0.8, 0.95]
• finding φ < π and/or ψ < γπ represents partial insurance

beyond self insurance

Moments for income

Blundell, Pistaferri, Preston (2008)

• assuming that ζit, νit and ξit are uncorrelated
• we get:

cov(∆yt, ∆yt−1) = var(ζt) + var(∆νt) for s=0 cov(∆νt, ∆νt+s) for s = 0

• this variances can be computed for sub-groups
• if ν is MA(q), cov(∆νt, ∆νt+s) = 0 for |s| > q + 1

Moments for consumption

Blundell, Pistaferri, Preston (2008)

• we get:

cov(∆ct, ∆ct+s) = φ2

t var(ζt) + ψ2 t var(ǫt) + var(ξt)

for 0 for s = 0

• consumption growth inequality can grow for 2 reasons:
• decrease in the amount of insurance φt, ψt ր
• increase in the variance of the shocks var(ǫt), var(ξt) ր
• Finally the co-movement is given by

cov(∆ct, ∆yt+s) = φtvar(ζt) + ψtvar(ǫt) for 0 φtcov(ǫt, ∆νt+s) for s = 0

Identification

Blundell, Pistaferri, Preston (2008)

• The model is identified in the simple case using 4 periods
• if MA(q), need to add more periods
• can allow for measurement error, only get a lower bound on ψt
• variances of the shocks to income do not require consumption

data (using consumption can improve efficiency of the estimator)

Data

Blundell, Pistaferri, Preston (2008)

• select continuously married couples headed by a man, age 20

to 65

• combine PSID and CEX to build a panel of income and

consumption

• PSID only contains food consumption but CEX is only

repeated cross-section

• the paper imputes non-durable and durable comsumption for

the PSID using a demand function estimated on CEX

• importantly, they allow for the demand to depend on time,

prices and observables

Demand estimation results

BPP 2008

Var in imputed versus CEX

BPP 2008

• the variances seem to match

Variances of income growth

BPP 2008

• strong increase in the

variance of income growth, by 30% by 1985

• second and higher order cov

are small, indicating MA(1)

Variances of consumption growth

BPP 2008

• variance of consumption

growth is also increasing

• ver the years
• PSID did not collect

consumpption data 1987-1988

Covariances of growths

BPP 2008

• the co-variance increases in

the 80s, flattens after

• cov(∆ct, ∆yt+1) should

reflect insurance against transitory shocks

Insurance

Blundell, Pistaferri, Preston (2008)

• estimate the parameters of the process
• assume MA(1) for transitory and estimate θ
• allow for variances to be time specific and by education, or

cohort

• ψ and φ are allowed to vary before and after 1985
• test if they are identical, and fail to reject!
• Estimation uses minimum distance with diagonal weights (off

diagonal can be worse, see Altonji and Segal)

Insurance results

BPP 2008

• estimates of θ are small 0.11 to 0.17
• φ indicates some partial insurance: a 10% permanent income

shock generates a 6.4% change in consumption

• ψ is more inline with PIH and suggest almost full insurance
• insurance is greater for college educated
• note here that φ is a bit lower in the second part of the sample

Income Shocks Variance results

BPP 2008

• variance of the permanent shock doubles around the 1980
• transitory shocks seems stable at first and growing towards

the end of the sample

Permanent shock variance over time

BPP 2008

Model fit

BPP 2008

Taxes, Transfers and Labor Supply

BPP 2008

• how are coefficients affected when only including male

earnings, or pre-tax earnings?

• reduction in second column indicates important role of taxes
• reduction in third column indicates that family labor supply is

an important channel of insurance

Importance of transfers

BPP 2008

Inequality Growth Decomposition

BPP 2008

• In the first half of the sample increase is mostly due to

permanent shocks var(∆ct) = φ2var(∆ζt) with some attenuation due to φ < 1

• In the second the change is mostly in transitory shocks

var(∆ct) = ψ2var(∆ǫt) but ψ ≃ 0 so we do not get a large increase in var(∆ct)

• Note that ignoring the difference between transitory and

permanent shocks would result in an average over ψ and φ that would change overtime

• constant insurance against each shock would be interpreted

as changing insurance.

Private transfers, Low Wealth and total expenditure

BPP 2008

• private transfers seem unimportant (column 2)
• low wealth households have a harder time insuring their

consumption

• this is true for both transitory and permanent shocks

Median income by cohort in the US

Guvenen, Kaplna, Song and Weidner

Guiso Pistaferri Schivardi Insurance within the firm (2005)

Firm productivity regression

GSP 2005

Earnings regression

GSP 2005

Results

GSP 2005

Results and conclusion

GSP 2005

• 10% shock to value added → 0.7% permanent shock to

earnings

• transitory shocks appear to be insured
• they quantify firm insurance to be worth 9% consumption!
• what about the employment response ?
• how to think of contracting environment?

References