Intergenerational Persistence of Earnings: The Role of Early and College Education

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1 Intergenerational Persistence of Earnings: The Role of Early and College Education by Restuccia and Urrutia (AER, 2004) presented by Salvatore Lo Bello Macro Reading Group UC3M April 18, 2016

2 Intergenerational Persistence of Earnings Intergenerational elasticity of earnings is of great importance (degree of equality of opportunities). In the US, the IGE is estimated to be at least 0.4 (Solon 2000). This paper wants to identify and measure the major sources of intergenerational mobility. Early childhood education is crucial for future outcomes. Natural question: to which extent can HC investment explain the degree of mobility? (Early vs. college education). Use the model to study the effects of government expenditure and evaluate changes in policy.

3 Summary of Main Results Endogenous investment in education can explain: About half of earnings persistence. One fourth of earnings inequality. Early investments account for most of the persistence in earnings. College education generates most of the inequality in earnings.

4 Model Environment OLG economy, individuals live for 4 periods (2 as children, 2 as adults). Mass 1 of individuals of each age, constant population. Parent and child form an household unit, parents make decisions. Young parent decides amount (quality) of early education for child. Old parent decides whether to send child to college or not. Government spends for early education and subsidizes college education (need based scheme).

5 Young Parent s Problem State x y = (h y, π), where: h y = father s HC; π = child s innate ability (observable). V y (h y, π) = max {u(c y ) + βv o (h o, π, ˆπ)}, c y >0,e>0 τ = tax rate on labor earnings. w = wage rate. ˆπ = realized ability. G(.) =HC production function. e=early education expenditure. s.t. c y + e = (1 τ)wh y ˆπ = G(π, e, g) h o = ξh y

6 Old Parent s Problem (1/2) State x 0 = (h 0, π, ˆπ). V s0 V s1 s0 V o (h o, π, ˆπ) = max {Vo (x o ), E θ Vo s1 (x o, θ)}, s {0,1} o (x o ) = value of no college education. o (x o, θ) = value of college education θ. θ = college completion shock. E θ V s1 o (x o, θ) = q(ˆπ)v s1 o (x o, θ 1 ) + (1 q(ˆπ))v s1 o (x o, θ 0 ), q(ˆπ) = probability of college completion (q (ˆπ) > 0).

7 Old Parent s Problem (2/2) V s0 o (x o ) = max c 0>0 {u(c o) + βe π [V y (h y, π ) π]}, s.t. c o = (1 τ)(wh 0 + wh y ) h y = ˆπ V s1 o (x o, θ) = max c 0>0 {u(c o) + βe π [V y (h y, π ) π]}, s.t. c o + (1 κ(wh o ))f [θ n + (1 θ)n] = (1 τ)(wh o + wh y [θ(1 n) + (1 θ)(1 n)], h y = θ pˆπ + (1 θ)ˆπ

8 Firm s Problem max{y wh} H>0 s.t. Y = F (H)

9 Functional Forms u(c) = c1 σ 1 1 σ F (H) = AH G(π, e + g) = π(e + g) γ q(ˆπ) = min{ψ o (1 + ˆπ) ψ1, 1} κ(wh o ) = max{1 κ 0 wh o, 0} log(π ) = ρ log(π) + ɛ ɛ N(0, σ 2 π)

10 Calibration

11 HC Investments, Inequality and Persistence

12 College Enrollment Policy

13 Enrollment and Completion Rates

14 Sources of Intergenerational Persistence

15 Policy Experiments

16 Concluding Remarks Model of early HC investment and college education. Differences in (quality of) early education is the most important component of earnings persistence. Policies that reduce the extent of credit constraint at early stage reduce persistence. Need based college subsidy system gives incentives to poor families to invest in early education. Main limitations: no savings, no shocks, naive early education investment.

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