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
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
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
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
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
Model Paluszynski & Yu Human Capital with Present Bias May 2019 5 / 27
Setup overview Three periods: student → work → retire Student: Innate ability: γ ∈ { H , L } each with share π γ Education: e ∈ { e L , e H } 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 = θ l Retire: Consume savings Paluszynski & Yu Human Capital with Present Bias May 2019 6 / 27
Present bias ( γ, θ )-workers have utility � y � U 1 ( c 1 , c 2 , y ; γ, θ, e ) = u ( c 1 ) − h + βδ 2 u ( c 2 ) θ γ -students have utility � � U 0 { c t } t , e , y ; γ = u ( c 0 ) � � � y � � + βδ 1 ( e ) u ( c 1 ) − h + 1 δ 2 u ( c 2 ) f ( θ | κ ( e , γ )) d θ θ Θ Key: Immediate gratification ( β < 1) Disagreement between selves (time inconsistency) Paluszynski & Yu Human Capital with Present Bias May 2019 7 / 27
Government Only observes education e and output y H -agents invest e = e H and L -agents invest e = e L Paternalistic: offset present bias Mechanism design approach: Gov. designs: P = { c 0 ( γ ) , c 1 ( γ, θ ) , c 2 ( γ, θ ) , y ( γ, θ ) } Require P to be incentive compatible Paluszynski & Yu Human Capital with Present Bias May 2019 8 / 27
Incentive compatibility Ex-post IC: workers report θ truthfully ∀ γ, θ, θ ′ U 1 ( γ, θ ) = U 1 ( θ ; γ, θ ) ≥ U 1 ( θ ′ ; γ, θ ) Ex-ante IC: students report γ truthfully U 0 ( H ) = U 0 ( H ; H ) ≥ U 0 ( L ; H ) Paluszynski & Yu Human Capital with Present Bias May 2019 9 / 27
Planning problem Paternalistic gov. maximizes � � � � max c 0 ( γ ) π γ u P γ � � � � y ( γ, θ ) � � + 1 δ 1 ( e γ ) u ( c 1 ( γ, θ )) − h + 1 δ 2 u ( c 2 ( γ, θ )) f ( θ | κ γ ) d θ θ Θ subject to � � � � � 1 − c 1 ( γ, θ ) − 1 � π γ − c 0 ( γ ) − e γ + c 2 ( γ, θ ) f ( θ | κ γ ) d θ R 1 ( e γ ) R 2 Θ γ � � � 1 � ≤ y ( γ, θ ) f ( θ | κ γ ) d θ π γ , R 1 ( e γ ) Θ γ and ex-ante and ex-post IC constraints. Paluszynski & Yu Human Capital with Present Bias May 2019 10 / 27
Wedges Assume R t δ t = 1 Savings wedge for γ -students: u ′ ( c 0 ( γ )) τ k 0 ( γ ) = 1 − E θ [ u ′ ( c 1 ( γ, θ ))] Savings wedge for ( γ, θ )-workers: 1 ( γ, θ ) = 1 − u ′ ( c 1 ( γ, θ )) τ k u ′ ( c 2 ( γ, θ )) Labor wedge for ( γ, θ )-workers: θ h ′ � � y ( γ,θ ) 1 θ τ w ( γ, θ ) = 1 − u ′ ( c 1 ( γ, θ )) Paluszynski & Yu Human Capital with Present Bias May 2019 11 / 27
Theoretical characterization Paluszynski & Yu Human Capital with Present Bias May 2019 11 / 27
Savings wedges: time-consistent case Intertemporal distortion of γ -student: � � 1 1 u ′ ( c 0 ( γ )) = E θ u ′ ( c 1 ( γ, θ )) u ′ ( c 0 ( γ )) < E [ u ′ ( c 1 ( 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 ′ ( c 1 ( γ, θ )) = u ′ ( c 2 ( 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
Savings wedges: present-biased students For H -agents: � � 1 1 u ′ ( c 0 ( H )) > E θ u ′ ( c 1 ( H , θ )) τ k 0 ( H ) is larger ⇒ intertemporal distortion exacerbated For L -agents: � � 1 1 u ′ ( c 0 ( L )) < E θ u ′ ( c 1 ( L , θ )) τ k 0 ( L ) is smaller ⇒ intertemporal distortion is weakened Paluszynski & Yu Human Capital with Present Bias May 2019 13 / 27
Discussion of savings wedge Encouraging education investment: 1. c 0 ↑ 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
Savings wedges: present-biased workers For H -agents: u ′ 1 ( c 1 ( H , θ )) 2 ( c 2 ( H , θ )) > β u ′ offset present bias For L -agents: there exists Γ such that f ( θ | κ L , H ) if Γ > > β f ( θ | κ L ) u ′ 1 ( c 1 ( L , θ )) f ( θ | κ L , H ) = β if Γ = u ′ 2 ( c 2 ( L , θ )) f ( θ | κ L ) f ( θ | κ L , H ) < β if Γ < f ( θ | κ L ) 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
Discussion of savings wedge Encouraging education investment: 1. c 0 ↑ 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
Discussion of savings wedge Encouraging education investment: 1. c 0 ↑ 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
Labor wedge τ w ( H , θ ) 1 − τ w ( H , θ ) = A H ( θ ) B H ( θ ) [ C H ( θ ) − D H ( θ ) + E H ( θ )] , τ w ( L , θ ) 1 − τ w ( L , θ ) = A L ( θ ) B L ( θ ) � � 1 − F ( θ | κ L , H ) � � D L ( θ ) + h ( θ | κ L ) × C L ( θ ) − h ( θ | κ L , H ) E L ( θ ) , 1 − F ( θ | κ L ) f ( θ | κ ) where h ( 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
Effects of present bias on labor wedge � u ′ ( c 1 ( γ, θ )) � u ′ ( c 1 ( γ, θ )) � � 1 − β E γ ( θ ) = β u ′ ( c 2 ( γ, θ )) − 1 − . β φ � �� � � �� � disagreement component 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
Policy implementation Paluszynski & Yu Human Capital with Present Bias May 2019 18 / 27
Recommend
More recommend
