Household Risk and Insurance over the Life Cycle

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1 Household Risk and Insurance over the Life Cycle Andrés Erosa IMDEA Social Sciences Institute Luisa Fuster IMDEA Social Sciences Institute Gueorgui Kambourov University of Toronto and NBER July 9, 2012

2 Motivation The household is an important entity for studying the various risks individuals face (labor productivity, health) the way individuals react to and insure against these risks the effect of various government policies (e.g., UI, social programs) aggregate (Frisch and Hicks) labor supply elasticities

3 Motivation The focus has mostly been on individual risk and insurance, in isolation. Many papers on individual risk (labor productivity, health) and the way individuals insure against them. Labor supply responses are one way to offset this risk: Low (2005), Pijoan-Mas (2006), Erosa, Fuster, and Kambourov (2011) Low, Meghir, and Pistaferri (2010) look in greater detail at the sources of risk (employer mobility).

4 Contribution 1. Estimate a quarterly wage process for husbands and wives within households Allow for correlation b/n husband and wife shocks Correct for selection bias in male and female participation Four household groups: HH, CH, HC, CC Study a relatively long time period: Use a fairly unrestricted sample Hyslop (AER, 2001); Low, Meghir, and Pistaferri (AER, 2010)

5 Contribution 2. Develop a life-cycle model of the household Quarterly model period Four household groups: HH, CH, HC, CC Intensive and extensive labor supply margin Labor productivity risk and incomplete markets Correlated wage shocks b/n husband and wife Unemployment shocks and labor market frictions Heathcote, Storesletten, and Violante (JPE, 2010); Guner, Kaygusuz, and Ventura (ReStud, 2011)

6 Contribution 3. Study the aggregate (Frisch and Hicks) labor supply response (Erosa et al, 2011) 4. Study the effect of government policies (across countries): Social security and labor supply late in the life cycle (Erosa et al, 2012) Unemployment Insurance (UI) Social Assistance Programs Supplemental Nutrition Assistance Program (SNAP) Temporary Assistance for Needy Families (TANF)

7 The Household Wage Process

8 Empirical Framework Household wages follow the process (for a given household education group): lnw m,it = X m,it ζ m + u m,it + ν m,it lnw f,it = X f,it ζ f + u f,it + ν f,it w j,it real hourly wage in period t X j,it observed variables such as age, race, region, time dummies ν j,it N(0,σ 2 ν j ) measurement error (trans. shock)

9 u j,it random walk stochastic shock: u m,it = u m,it 1 + ε m,it u f,it = u f,it 1 + ε f,it ε N 2 (0,Σ), where ( Σ = σ 2 ε m ρ εm,ε f σ εm σ εf ρ εm,ε f σ εm σ εf σ 2 ε f )

10 Estimation of the Wage Process The household wage process is estimated in FD: The selection equations are: lnw m,it = X m,it ζ m + ε m,it + ν m,it lnw f,it = X f,it ζ f + ε f,it + ν f,it Pm,it = Z m,it ξ m + π m,it Pf,it = Z f,it ξ f + π f,it, π N 2 (0,Π), where ( Π = 1 ρ πm,π f ρ πm,π f 1 ) Selection correlations: ρ εm,π m and ρ εf,π f

11 Selection-Corrected Residual Wage Growth E [ lnw m,it P m,it = 1,P m,it 1 = 1 ] = = X m,it ζ m + E [ (ε m,it + ν m,it ) P m,it = 1,P m,it 1 = 1 ] [ ] = X m,it ζ m + E (ε m,it π m,it > Z m,it ξ m, π m,it 1 > Z m,it 1 ξ m ( ) φ(z = X m,it ζ m,it ξ m ) m + σ εm ρ εm,π m Φ(Z m,it ξ m) = X m,it ζ m + σ εm ρ εm,π m Λ P m,it Probit on participation to estimate the inverse Mills ratio Λ P m,it OLS to obtain consistent estimates of ˆζ m g m,it = (lnw m,it X m,it ˆζ m ) = ε m,it + ν m,it g f,it = (lnw f,it X f,it ˆζ f ) = ε f,it + ν f,it

12 Moment Estimation: GMM { σ εm ;ρ εm,π m ;σ νm ;σ εf,σ νf ;ρ εf,π f ;ρ εm,ε f } Erosa, Fuster, and Kambourov (2012) show that: 1. E [ g m,it ] = σ εm ρ εm,π m ˆΛ P m,it ] [ 2. E [gm,it 2 = σε 2 m 1 ρε 2 m,π m (Z m,it ˆξ ] m )ˆΛ P m,it + 2σν 2 m 3. E [ g m,it+1 g m,it ] = σ 2 ε m ρ 2 ε m,π m ˆΛP m,it+1ˆλp m,it σ 2 ν m 4. E [ g f,it ] = σ εf ρ εf,π f ˆΛ P f,it ] [ 5. E [gf 2,it = σε 2 f 1 ρε 2 f,π f (Z f ˆξ ],it f )ˆΛ P f,it + 2σν 2 f 6. E [ g f,it+1 g f,it ] = σ 2 ε f ρ 2 ε f,π f ˆΛ P f,it+1ˆλ P f,it σ 2 ν f 7. E [ g m,it g f,it ] = σ εm σ εf [ ρ εm,ε f + ρ εm,π m ρ εf,π f ˆΛP m,it;f,it ]

13 Data: 1990 SIPP Monthly information on income and welfare program participation for individuals and households October 1989 August 1992 (8 waves) High-school: 22-61; College: Sample sizes: HH: 53,907. CH: 16,056. HC: 14,693. CC: 25,800.

14 Data: 1990 SIPP Merge couples into households (families) Probit on male participation: obtain the inverse Mills ratio, trend in log wages, and residual wage growth (controlling for selection in participation). Probit on female participation: obtain the inverse Mills ratio, trend in log wages, and residual wage growth (controlling for selection in participation). Bivariate probit on husband and wife participation: obtain inverse Mills ratio. Construct 7 moments using husband and wife residual wage growth. Estimate the 7 parameters of interest.

15 Estimation Results Group HH CH HC CC σ εm ρ εm,π m σ νm σ εf ρ εf,π f σ νf ρ εm,ε f

16 The Model

17 The Model The economy is populated by overlapping generations of households Households differ in education (e m,e f ) and labor productivity (z m,z f ) The education decision is exogenous and there are two types of education e i college and non-college The marriage decision is exogenous, and there are 4 types of households: HH, CH, HC, CC

18 Preferences Households value consumption c and leisure (l m,l f ). The period utility functions is: lm 1 σ u(c,l m,l f ) = lnc + ϕ m 1 σ + ϕ l 1 σ f f 1 σ F mp m>0 F f P f >0 F j fixed cost of work; P j participation indicator; An individual is endowed with 1 unit of time each period.

19 Household Risk 1. Labor productivity risk As described earlier. 2. Employment risk δ: job destruction rate for employed indiv. each period. λ: job offer rate for non-employed individuals each period. δ and λ are education- and gender-specific.

20 Government and Credit Markets Government taxes consumption, capital and labor income (τ c, τ k, τ h ). τ h proportional in this presentation. τ h progressive in the future. No borrowing. No insurance against idiosyncratic labor income risk.

21 Government Programs: Social Security Pay-as-you-go social security system. High-school retire at 62; College at 65. Payroll tax τ ss. Pension benefits b s (x) depend on education and the permanent labor productivity shock at the age of retirement.

22 Government Programs: Unemployment Insurance Individuals who exogenously separate from their job receive unemployment insurance, b u (x). b u (x) is received only for one period (quarter). b u (x) depends on last period s wage (the labor productivity shock). Individuals who quit their jobs (decide not to work) are not eligible for unemployment insurance.

23 Household s Employment Status e = (e m,e f ) e j for j {m,f } takes the values: 1: the individual starts the period with a job offer; 2: the individual is non-employed and eligible for UI; 3: the individual is non-employed and not eligible for UI; Then, the law of motion for e j is: 1 with probability 1 δ if n j > 0 and e = 1 e j = 1 with probability λ if (e 1) or (e = 1 and n = 0) 2 with probability δ if n j > 0 and e = 1 3 otherwise

24 Government Programs: Social Assistance Programs Universal program that is means-tested on family income The transfer T is T = { T 0.3 y if y y 0 otherwise T is the maximum payment; y is the poverty line; y is household income net of taxes and deductions.

25 The Household s Problem The household s state, x, for a given household group is: j m husband s age; j f wife s age; e m husband s employment status; e f wife s employment status; z m husband s labor productivity; z f wife s labor productivity; a household s assets;

26 The Household s Problem V (x) = max {c,n m,n f,a } {u(c,l m,l f ) + βe[v (x )]} s.t. a = (1 + r) a + w(z m n m P m + z f n f P f ) c + b s (x) + b u (x) T (x) a 0 l j = (1 n j ), j {m,f } P j = 1 if e j = 1 and 0 otherwise, j {m,f } e j = e (e j )

27 Preliminary Simulation Results: HH, σ = 2.0

28 Labor Supply Response HH CH lnz m lnz f lnz m lnz f Intensive margin lnn m lnn f Extensive margin Prob(P m = 0 P m = 1) Prob(P f = 0 P f = 1)

29 Conclusion Estimate a quarterly wage process, within the family, correcting for selection bias in participation Develop a life-cycle model of the household Preliminary simulation results

30 Conclusion The next step is to use the model to analyze household life-cycle risk and insurance aggregate labor supply responses (Erosa et al, 2011) labor supply late in the life cycle across countries (Erosa et al, 2012) the effects of government programs across countries (UI, taxes, social programs)

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