Household Responses to Individual Shocks: Disability and Labor Supply

Transcription

1 Household Responses to Individual Shocks: Disability and Labor Supply Gallipoli and Turner presented by Tomás Rodríguez Martínez Universidad Carlos III de Madrid 1 / 19

2 Introduction The literature of incomplete markets idiosyncratic risk is modeled as persistent perturbations in the wage process. This restricts the response of different types of risk - job, wage and health risk- to be the same. This paper: explicitly model health shocks and study the household labor supply response to it. 2 / 19

3 Introduction Empirically: Two facts are at odds with the standard intertemporal labor supply choices. Prime age single men respond much more negatively to a disability shock than married men ( labor supply). Secondary worker in the household does not increase labor supply (negligible added worker effect). Modify the standard model in two dimensions: Endogeneize wage growth by allowing learning by doing human capital accumulation. Allow for optimal sharing of house work activity. 3 / 19

4 Introduction The mechanism: The health shock decreases productivity at home and in the market. Human capital accumulation creates incentive for the primary earner keep their level of labor supply. The spouse provide hours at home instead of going to the market. 4 / 19

5 Empirical evidence 5 / 19

6 Empirical evidence Wages decrease for single men after a disability shock, but not for married men. 6 / 19

7 Model Overview A simple dynamic household model with endogenous marriage decision. For simplicity we allow only men to receive disability shock. Marriage market acts as random search. When agents marry they pool their assets, when they divorce they split assets evenly. Home production acts as a constraint: They do not derive any utility from it, but every period the household have supply a minimum of it. 7 / 19

8 Model Marriage Market Let j be age and x = (a, w, δ n, δ h ), where δ n, δ h is labor-limiting and home-limiting disability. Let x M be the state of a married household. A single agent meet with another marriageable partner of the same age with probability q. The single household value function is defined as: V s (j, x) = max (u(c, l) +βe[(1 q)v s (j + 1, x ) c,l,a ) +q V M (j + 1, x M (x f, x ))dxf M j, x M ] A marriage occurs iff: V M (j, x M ) > V S (j, x) for both agents. X M f 8 / 19

9 Model Marriage Market Married households maximize a joint objective function, for a given marriage contract λ: U(j, x M, λ, θ f (, θ) = max (1 λ)v M + λv M ) c f,l f,h f,c,l,h,a f where θ is the non-pecuniary value of marriage. Married man s individual value function is given by: V M = u(c, l, θ)+βe[ ω max { V M (j + 1, x M ), V s (j + 1, x (x M )) } +(1 ω)v s (j + 1, x (x M )) j, x M ] where ω is the probability the marriage terminates without husband s consent. 9 / 19

10 Model Intratemporal decision The couple s full maximization problem is defined by U(j, x M, λ, θ f, θ) s.t.: ξ 1 : (T l δ h h) w δ n + (1 + r)a M + b(.) + (T l f h f )w f c f c a M = 0 ξ 2a : l T δ h h ξ 2b : l f T h f ξ 3a : ω = ω(a M, w f, w ; δ h, δ n ) ξ 3b : ω f = ω f (a M, w f, w ; δ h, δ n ) ξ 4a : Ew = H(l, h w, δ h, δ n ) ξ 4a : Ew f = H(l f, h f w f ) ξ 5 : h = φ f (h f ) + φ(h) Where b(.) is a function that captures different benefits and H(.) is the human capital accumulation function. 10 / 19

11 Functional forms Individuals enter the model at age 19, work until 65 and live to a maximum age of 99. They die exogenously with age/gender specific survival probabilities. Individual utility: u = (1 γ j ) (c n η) 1 ω γ, θ are gender specific. l 1 ψ 1 ω + γ j 1 ψ + I ηθ, where Home production: φ(h) = h + ah q and φ(h f ) f = h f + a f h q f f Disability process: Summarize by two state variables. rsk: 3 states, low, high and chronic disability. ds: discretization of δ h, δ n. Transition matrix is age and rsk specific. The benefits function b(.) replicates Canadian disability, retirement and anti-poverty programs. 11 / 19

12 Functional forms Wage Dynamics Wages follow a combination of a random process and a human capital accumulation function. w it = R t H it H i,t+1 = κ it + (α 1 + α 2 n it + α 3 n 2 it)h it + ν i,t+1 where n it is average weekly hours worked in previous year. ν i,t+1 follows an AR(1) process with highly persistence and gender specific parameters. κ it is a deterministic wage profile. 12 / 19

13 Estimation The model is calibrated by first have some parameters assigned / estimated exogenously. Then, the rest of parameters are estimated using SMM. Parameters We will compare the full extended model with: The work horse model (without home production and human capital). Model w/o home production. Model w/o human capital. 13 / 19

14 Model Fit The model is able to replicate labor supply over the life-cycle. 14 / 19

15 Results 15 / 19

16 Results The workhorse model cannot replicate the response of labor supply and wages. 16 / 19

17 Results Home production is necessary to get the non-response of wives. Human capital accumulation is needed to get different responses of married and non-married. 17 / 19

18 Conclusion This paper studies the family labor supply in response to a disability shock. The standard model cannot take into account two puzzles: The absence of an added worker effect. The different response of married and single households. They propose modify the standard model in two dimension. Home production task sharing is needed to the absence of an added worker effect. Human capital accumulation helps to get difference responses of married and single household. 18 / 19

19 Thank you! 19 / 19

20 Appendix 1 Estimation 20 / 19