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 Y it = Z it b t + P it + ν it where Z is a set of observables and P it is the permanent component: P it = P it 1 + ζ it ζ it is serially uncorrelated and ν it is an MA(q) ν it = q θ j ɛ it j with θ 0 = 1 j =0 define income net of predictable individual components: y it = log Y it Z it b t
Consumption rule Blundell, Pistaferri, Preston (2008) We define the following consumption rule: c it = φ it ζ it + ψ it ɛ it + ξ it c it is consumption net of predictable components the impact of permanent and transitory shocks are allowed to be different and vary with time ξ it is an independent income shock φ it and ψ it 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 φ it = ψ it = 0 - hand to mouth φ it = ψ it = 1 in general, the closer the parameters to 0, the more insurance in the case of self insurance - using CRRA utility,linear approximation - φ it π it and ψ it γ t,l π it - π it is share of future labor income to human capital and wealth - ξ it can be interpreted as shocks to higher moment - γ t,l r/(1 + r)(1 + θ 1 )) - simulations give that π it [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 ζ it, ν it and ξ it are uncorrelated we get: cov( y t, y t 1 ) = { var(ζt ) + var( ν t ) for s=0 cov( ν t, ν t+s ) for s 0 this variances can be computed for sub-groups if ν is MA(q), cov( ν t, ν t+s ) = 0 for s > q + 1
Moments for consumption Blundell, Pistaferri, Preston (2008) we get: cov( c t, c t+s ) = { φ 2 t var(ζ t ) + ψ 2 t var(ɛ t) + var(ξ t ) for 0 0 for s 0 consumption growth inequality can grow for 2 reasons: - decrease in the amount of insurance φ t, ψ t - increase in the variance of the shocks var(ɛ t ), var(ξ t ) Finally the co-movement is given by { φt var(ζ cov( c t, y t+s ) = t ) + ψ t var(ɛ t ) for 0 φ t cov(ɛ t, ν t+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 ψ t 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 over 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( c t, y t+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( c t ) = φ 2 var( ζ t ) with some attenuation due to φ < 1 In the second the change is mostly in transitory shocks var( c t ) = ψ 2 var( ɛ t ) but ψ 0 so we do not get a large increase in var( c t ) 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