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Optimal Taxation with Risky Human Capital and Retirement Savings Radek Paluszynski 1 Pei Cheng Yu 2 1 University of Houston 2 University of New South Wales May 2019 Paluszynski & Yu Human Capital with Present Bias May 2019 1 / 27

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Optimal Taxation with Risky Human Capital and Retirement Savings

Radek Paluszynski1 Pei Cheng Yu2

1University of Houston 2University of New South Wales

May 2019

Paluszynski & Yu Human Capital with Present Bias May 2019 1 / 27

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Motivation

Classic PF problem: How to insure against risk in lifetime income? Two concerns: Income distributions different between college and non-college Recent studies suggest that individuals are present biased Current policies and proposals: Pay as You Earn Repayment Plan Retirement Parity for Student Loans Act

Paluszynski & Yu Human Capital with Present Bias May 2019 2 / 27

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This paper

Mirrlees taxation + education + present-biased agents Traditional Mirrlees taxation: unobservable productivity ⇒ efficiency vs. equity exogenous productivity + time-consistent agents This paper: education ⇒ endogenous productivity present-biased agents ⇒ paternalistic government New insights on policy design

Paluszynski & Yu Human Capital with Present Bias May 2019 3 / 27

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Preview of findings

1 Generous student loans to entice present-biased agents 2 Education dependent retirement policies ◮ help all college graduates save ◮ only help non-college grads with low-income with savings 3 Income tax quantitatively similar to time-consistent case 4 Retirement Parity for Student Loans Act 5 Potentially significant welfare gains Paluszynski & Yu Human Capital with Present Bias May 2019 4 / 27

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Related literature

1 Mirrlees taxation with behavioral bias: ◮ Farhi and Gabaix (2017), Lockwood (2018), Yu (2018), Moser and de

Souza e Silva (2019)

2 Optimal human capital policy ◮ Bovenberg and Jacobs (2005), Bohacek and Kapicka, (2008),

Grochulski and Piskorski (2010), Kapicka (2015), Gary-Bobo and Trannoy (2015), Findeisen and Sachs (2016), Stantcheva (2017), Koeniger and Prat (2018), Markis and Pavan (2018)

Paluszynski & Yu Human Capital with Present Bias May 2019 5 / 27

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Model

Paluszynski & Yu Human Capital with Present Bias May 2019 5 / 27

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Setup overview

Three periods: student → work → retire Student: Innate ability: γ ∈ {H, L} each with share πγ Education: e ∈ {eL, eH} Human capital: κ (e, γ) strictly increasing in e and γ Work: Productivity θ drawn from F (θ|κ)

◮ FOSD: for any θ and κ > κ′, F(θ|κ) < F(θ|κ′)

Production technology: y = θl Retire: Consume savings

Paluszynski & Yu Human Capital with Present Bias May 2019 6 / 27

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Present bias

(γ, θ)-workers have utility U1 (c1, c2, y; γ, θ, e) = u (c1) − h y θ

  • + βδ2u (c2)

γ-students have utility U0

  • {ct}t , e, y; γ
  • = u (c0)

+ βδ1 (e)

  • Θ
  • u (c1) − h

y θ

  • + 1δ2u (c2)
  • f (θ|κ (e, γ)) dθ

Key: Immediate gratification (β < 1) Disagreement between selves (time inconsistency)

Paluszynski & Yu Human Capital with Present Bias May 2019 7 / 27

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Government

Only observes education e and output y H-agents invest e = eH and L-agents invest e = eL Paternalistic: offset present bias Mechanism design approach:

  • Gov. designs: P = {c0 (γ) , c1 (γ, θ) , c2 (γ, θ) , y (γ, θ)}

Require P to be incentive compatible

Paluszynski & Yu Human Capital with Present Bias May 2019 8 / 27

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Incentive compatibility

Ex-post IC: workers report θ truthfully ∀γ, θ, θ′ U1(γ, θ) = U1(θ; γ, θ) ≥ U1(θ′; γ, θ) Ex-ante IC: students report γ truthfully U0 (H) = U0 (H; H) ≥ U0 (L; H)

Paluszynski & Yu Human Capital with Present Bias May 2019 9 / 27

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Planning problem

Paternalistic gov. maximizes

max

P

  • γ

πγ

  • u
  • c0 (γ)
  • + 1δ1 (eγ)
  • Θ
  • u (c1 (γ, θ)) − h

y (γ, θ) θ

  • + 1δ2u (c2 (γ, θ))
  • f (θ|κγ) dθ
  • subject to
  • γ

πγ

  • −c0 (γ) − eγ +

1 R1 (eγ)

  • Θ
  • −c1 (γ, θ) − 1

R2 c2 (γ, θ)

  • f (θ|κγ) dθ
  • ≤
  • γ

πγ

  • 1

R1 (eγ)

  • Θ

y (γ, θ) f (θ|κγ) dθ

  • ,

and ex-ante and ex-post IC constraints.

Paluszynski & Yu Human Capital with Present Bias May 2019 10 / 27

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Wedges

Assume Rtδt = 1 Savings wedge for γ-students: τ k

0 (γ) = 1 −

u′ (c0 (γ)) Eθ [u′ (c1 (γ, θ))] Savings wedge for (γ, θ)-workers: τ k

1 (γ, θ) = 1 − u′ (c1 (γ, θ))

u′ (c2 (γ, θ)) Labor wedge for (γ, θ)-workers: τ w(γ, θ) = 1 −

1 θh′ y(γ,θ) θ

  • u′ (c1 (γ, θ))

Paluszynski & Yu Human Capital with Present Bias May 2019 11 / 27

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Theoretical characterization

Paluszynski & Yu Human Capital with Present Bias May 2019 11 / 27

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Savings wedges: time-consistent case

Intertemporal distortion of γ-student: 1 u′ (c0 (γ)) = Eθ

  • 1

u′ (c1 (γ, θ))

  • u′ (c0 (γ)) < E [u′ (c1 (γ, θ))]

τ k

0 (γ) > 0 : restricted savings

◮ High savings ⇒ expensive to reward high output in future

Intertemporal distortion of (γ, θ)-worker: u′ (c1 (γ, θ)) = u′ (c2 (γ, θ)) τ k

1 (γ) = 0 : consumption smoothing

No uncertainty after work life ⇒ no need for distortions in future

Paluszynski & Yu Human Capital with Present Bias May 2019 12 / 27

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Savings wedges: present-biased students

For H-agents: 1 u′ (c0 (H)) > Eθ

  • 1

u′ (c1 (H, θ))

  • τ k

0 (H) is larger ⇒ intertemporal distortion exacerbated

For L-agents: 1 u′ (c0 (L)) < Eθ

  • 1

u′ (c1 (L, θ))

  • τ k

0 (L) is smaller ⇒ intertemporal distortion is weakened

Paluszynski & Yu Human Capital with Present Bias May 2019 13 / 27

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Discussion of savings wedge

Encouraging education investment:

  • 1. c0 ↑ for educated agents
  • 2. commitment device for educated agents
  • 3. additional distortions for uneducated agents

Therefore,

  • 1. increase τ k

0 of educated relative to uneducated

◮ Policy implication: generous student loans

  • 2. help educated agents smooth consumption

◮ Policy implication: subsidize retirement savings for college grads

  • 3. help uneducated commit only if output is likely from L-agent

◮ Policy implication: subsidize retirement savings of low income Paluszynski & Yu Human Capital with Present Bias May 2019 14 / 27

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Savings wedges: present-biased workers

For H-agents: u′

1 (c1 (H, θ))

u′

2 (c2 (H, θ)) > β

  • ffset present bias

For L-agents: there exists Γ such that u′

1 (c1 (L, θ))

u′

2 (c2 (L, θ))

           > β if Γ >

f (θ|κL,H) f (θ|κL)

= β if Γ =

f (θ|κL,H) f (θ|κL)

< β if Γ <

f (θ|κL,H) f (θ|κL)

More likely from L-agent than H-agent ⇒ offset present bias More likely from H-agent than L-agent ⇒ exacerbate present bias

Paluszynski & Yu Human Capital with Present Bias May 2019 15 / 27

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Discussion of savings wedge

Encouraging education investment:

  • 1. c0 ↑ for educated agents
  • 2. commitment device for educated agents
  • 3. additional distortions for uneducated agents

Therefore, increase τ k

0 of educated relative to uneducated

◮ Policy implication: generous student loans

help educated agents smooth consumption

◮ Policy implication: subsidize retirement savings for college grads

help uneducated commit only if output is likely from L-agent

◮ Policy implication: subsidize retirement savings of low income Paluszynski & Yu Human Capital with Present Bias May 2019 16 / 27

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Discussion of savings wedge

Encouraging education investment:

  • 1. c0 ↑ for educated agents
  • 2. commitment device for educated agents
  • 3. additional distortions for uneducated agents

Therefore, increase τ k

0 of educated relative to uneducated

◮ Policy implication: generous student loans

help educated agents smooth consumption

◮ Policy implication: subsidize retirement savings for college grads

help uneducated commit only if output is likely from L-agent

◮ Policy implication: subsidize retirement savings of low income Paluszynski & Yu Human Capital with Present Bias May 2019 16 / 27

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Labor wedge

τ w (H, θ) 1 − τ w (H, θ) = AH (θ) BH (θ) [CH (θ) − DH (θ) + EH (θ)] , τ w (L, θ) 1 − τ w (L, θ) = AL (θ) BL (θ) ×

  • CL (θ) −

1 − F (θ|κL,H) 1 − F (θ|κL)

  • DL (θ) + h (θ|κL)

h (θ|κL,H)EL (θ)

  • ,

where h (θ|κ) =

f (θ|κ) 1−F(θ|κ)

Intratemporal component: A, B, C (Diamond, 1998; Saez, 2001) Intertemporal component: D (Golosov et. al., 2016) Present-bias component: E

Paluszynski & Yu Human Capital with Present Bias May 2019 17 / 27

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Effects of present bias on labor wedge

Eγ(θ) = u′ (c1 (γ, θ)) βu′ (c2 (γ, θ)) − 1

  • disagreement component

− 1 − β β u′ (c1 (γ, θ)) φ

  • myopic component

. Myopic component: Present-biased students undervalue returns from education Lockwood (2018) Disagreement component: Present-biased worker views savings subsidies as ‘distortion’ Opposing forces: ambiguous effect on labor wedge

Paluszynski & Yu Human Capital with Present Bias May 2019 18 / 27

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Policy implementation

Paluszynski & Yu Human Capital with Present Bias May 2019 18 / 27

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Current policy debate on student loans

Consensus: ease student loan burden How? Employer Participation in Repayment Act of 2019

◮ employer helps repay student loans using pretax income

Retirement Parity for Student Loans Act of 2018

◮ employer contributes to 401(k) while employees repay student loans

This paper: foundation for Retirement Parity for Student Loans Act

Paluszynski & Yu Human Capital with Present Bias May 2019 19 / 27

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Retirement Parity for Student Loans Act

Education policy: Student loans: L (e) Income-contingent repayment: r (e, y) Retirement policy: Income-contingent social security benefits: a (y) 401(k): matching rate α and contribution limit ¯ s and αr (e, y) saved Taxes: Income tax: T (y) Tax deduction on student loans: g (r) Tax on bonds: T k (b) Tax on retirement account: T ra Optimum can be implemented with above policies

Comparison with literature Paluszynski & Yu Human Capital with Present Bias May 2019 20 / 27

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Numerical analysis

Paluszynski & Yu Human Capital with Present Bias May 2019 20 / 27

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Parameterizing the model

Symbol Meaning Value π(L) Share of low type 0.64 π(H) Share of high type 0.36 σ Risk aversion 2 η Frisch elasticity 0.5 Discount factors: Present-bias Time-cons. β Short-term factor 0.7 1.0 δ0(L) HS period 1 long-term factor 0.00 0.00 δ1(L) HS period 2 long-term factor 1.00 1.00 δ2(L) HS retirement long-term factor 0.254 0.142 δ0(H) COL period 1 long-term factor 0.115 0.151 δ1(H) COL period 2 long-term factor 0.885 0.849 δ2(H) COL retirement long-term factor 0.287 0.167 Functional forms: u(c) = c1−σ

1−σ , h(ℓ) = ℓ1+ 1

η

1+ 1

η Paluszynski & Yu Human Capital with Present Bias May 2019 21 / 27

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Estimating productivity distributions

Factual and counterfactual lifetime income distributions

◮ Cunha and Heckman (2007) Reference income distributions

Construct economy with “current policies”

◮ progressive income taxes ◮ Social security and corresponding taxes ◮ 401(k) with matching contributions ◮ (unconditional) college loan subsidy

Assume normal-lognormal-Pareto shape distributions Match income dist. of simulated agent populations.

Paluszynski & Yu Human Capital with Present Bias May 2019 22 / 27

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Parameterizing the productivity distributions

0.05 0.1 0.15 0.2 0.25 5 10 15 20 25 30 pdf productivity Distributions of skills in the model high school factual high school counterfactual college factual college counterfactual

Source: calibrated to fit income distributions in Cunha and Heckman (2007)

Paluszynski & Yu Human Capital with Present Bias May 2019 23 / 27

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Present-biased vs time-consistent agents

First-period savings wedge: Present-biased Time-consistent τ k

0 (L)

1.0000 1.0000 τ k

0 (H)

0.3232 0.2776 Second-period savings wedge:

◮ zero for time-consistent agents Paluszynski & Yu Human Capital with Present Bias May 2019 24 / 27

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Savings wedge

−0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0.1 0.2 50 100 150 200 250 300 350 400 450 lifetime income

Savings wedge in period 1

high school college

Paluszynski & Yu Human Capital with Present Bias May 2019 25 / 27

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Labor wedge: present-biased vs. time-cons.

0.2 0.4 0.6 0.8 1 50 100 150 200 250 300 350 400 450 lifetime income

Labor wedge in period 1

present biased − high school time consistent − high school time consistent − college present biased − college

Paluszynski & Yu Human Capital with Present Bias May 2019 25 / 27

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Welfare gains of optimal policies

Welfare gains relative to optimal policy for time-consistent agents? Gains in terms of fraction of lifetime consumption. Under what implementation of time-consistent policies?

◮ Laissez-faire savings ◮ Mandatory (but uncontingent) savings Paluszynski & Yu Human Capital with Present Bias May 2019 26 / 27

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Welfare gains of optimal policies

Welfare gains relative to optimal policy for time-consistent agents? Gains in terms of fraction of lifetime consumption. Under what implementation of time-consistent policies?

◮ Laissez-faire savings ◮ Mandatory (but uncontingent) savings

Table: Welfare gains over optimal policies for time-consistent agents

Mandatory savings Laissez-faire % increase in lifetime consumption 1.12 1.18

Paluszynski & Yu Human Capital with Present Bias May 2019 26 / 27

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Conclusion

Paluszynski & Yu Human Capital with Present Bias May 2019 26 / 27

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Extensions and future work

Extensions: Heterogeneous β Non-sophisticated agents Future work:

  • 1. Correct for the underestimation of high-income individuals
  • 2. Explore implementation with simple instruments

Paluszynski & Yu Human Capital with Present Bias May 2019 27 / 27

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Appendix

Paluszynski & Yu Human Capital with Present Bias May 2019 0 / 2

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Implementation in Literature

Findeisen and Sachs (2016): Income-contingent college loans Difference: FS focuses on TC ⇒ retirement policy not important for pre-work incentives Moser and Olea de Souza e Silva (2019): uses different savings tools to separate productivity

◮ low-productivity ⇒ social security, high-productivity ⇒ retirement

accounts

Difference: MO focuses on exogenous productivity ⇒ savings wedges in t = 1 are different

Back to implementation Paluszynski & Yu Human Capital with Present Bias May 2019 1 / 2

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Reference income distributions

(a) High school (b) College Source: Cunha and Heckman (2007)

Back to calibration Paluszynski & Yu Human Capital with Present Bias May 2019 2 / 2