Taxation under Learning-by-doing Miltos Makris Alessandro Pavan - PowerPoint PPT Presentation

Motivation Qualitative Analysis Quantitative Analysis Conclusions Appx: T V & R IC RA term SB Handicaps Taxation under Learning-by-doing Miltos Makris Alessandro Pavan Kent Northwestern November 2019

Motivation Qualitative Analysis Quantitative Analysis Conclusions Appx: T V & R IC RA term SB Handicaps Learning by Doing Learning-by-doing (LBD) : positive effect of time spent at work on productivity human capital investment side-product of labor supply LBD: significant source of productivity growth Dustmann and Meghir (2005) first 2 years of employment, wages grow, on average, by 8.5% in 1st year and 7.5% in 2nd Thompson (2012), Levitt et. al. (2013) reduction in unit costs from production, particularly strong in early years, “bounded learning”

Motivation Qualitative Analysis Quantitative Analysis Conclusions Appx: T V & R IC RA term SB Handicaps This Paper Dynamic Mirrleesian economy in which agents’ productivity own private information stochastic evolves endogenously over lifecycle (due to LBD) Novel effects on (labor) wedges Quantitatively significant impact on optimal tax codes level progressivity dynamics

Motivation Qualitative Analysis Quantitative Analysis Conclusions Appx: T V & R IC RA term SB Handicaps Related Literature Optimal Labor Income Taxation : Mirrlees (1971), Diamond (1998), Saez (2001)... static & exogenous productivity New Dynamic Public Finance: Albanesi and Sleet (2006), Golosov, Tsyvinski and Werning (2006), Kocherlakota (2005, 2010), Kapicka (2013), Farhi and Werning (2013), Golosov, Tsyvinski and Troshkin (2016) ... dynamic & exogenous productivity Taxation w. Human Capital Accumulation: Krause (2009), Best and Kleven (2013), Kapicka (2006, 2015), Kapicka and Neira (2016), Parrault (2017), and Stantcheva (2016, 2017)... future productivity is private information, stochastic and side-product of labor

Motivation Qualitative Analysis Quantitative Analysis Conclusions Appx: T V & R IC RA term SB Handicaps Summary of Main Results LBD leads to higher distortions (wedges) SB allocations can be (approximately) implemented by simple age-dependent taxes, invariant in past incomes Higher and less progressive tax rates than under current US tax code ... but lower and more progressive than without LBD

Motivation Qualitative Analysis Quantitative Analysis Conclusions Appx: T V & R IC RA term SB Handicaps Road Map Qualitative Analysis Model Labor distortions (wedges) Quantitative Analysis Optimal reform of calibrated economy Approximate implementation Role of stochasticity Counterfactual analysis: role of LBD on proposed reforms Conclusions

Motivation Qualitative Analysis Quantitative Analysis Conclusions Appx: T V & R IC RA term SB Handicaps Qualitative Analysis Qualitative Analysis

Motivation Qualitative Analysis Quantitative Analysis Conclusions Appx: T V & R IC RA term SB Handicaps Environment Two working periods/blocks t = 1 , 2: “young” and “old” Linear labor production Period-1 productivity: θ 1 privately observed at beginning of t = 1 drawn from cdf F 1 (density f 1 ) Period-2 productivity: θ 2 privately observed at beginning of t = 2 drawn from cdf F 2 ( ·| θ 1 , y 1 ) (FOSD) dependence on y 1 : LBD � � ζ ε 2 = θ ρ Example: θ 2 = θ ξ 1 l ζ 1 ε 2 = θ ξ 1 y ζ y 1 1 ε 2 1 θ 1

Motivation Qualitative Analysis Quantitative Analysis Conclusions Appx: T V & R IC RA term SB Handicaps Environment Period- t flow utility: v ( c t ) − ψ ( y t , θ t ) � � 1 + φ y t 1 e.g. ψ ( y t , θ t ) = where 1 / φ is Frisch elasticity 1 + φ θ t Discount factor (for both workers and planner): δ

Motivation Qualitative Analysis Quantitative Analysis Conclusions Appx: T V & R IC RA term SB Handicaps Setting up the problem Let θ 2 ≡ ( θ 1 , θ 2 ) and θ 1 ≡ ( θ 1 ) Worker expected life-time utility: � � δ t − 1 � � v ( c t (˜ θ t )) − ψ ( y t (˜ θ t ) , ˜ ∑ V 1 ( θ 1 ) = E θ t ) | θ 1 , y 1 ( θ 1 ) t Worker expected life-time tax bill: � � δ t − 1 � � y t (˜ θ t ) − c t (˜ θ t ) ∑ R 1 ( θ 1 ) = E | θ 1 , y 1 ( θ 1 ) t

Motivation Qualitative Analysis Quantitative Analysis Conclusions Appx: T V & R IC RA term SB Handicaps Setting up the dual Utilitarian problem Dual : planner maximizes tax revenues � R 1 ( θ 1 ) dF 1 ( θ 1 ) s.t. participation/redistribution constraint � V 1 ( θ 1 ) dF 1 ( θ 1 ) ≥ κ and incentive-compatibility constraints

Motivation Qualitative Analysis Quantitative Analysis Conclusions Appx: T V & R IC RA term SB Handicaps First Best: period-1 output For any θ 1 ψ y ( y 1 ( θ 1 ) , θ 1 ) = 1 + LD 1 ( θ 1 ) v ′ ( c 1 ( θ 1 )) where � � θ )+ v ( c 2 (˜ θ )) − ψ ( y 2 (˜ θ ) , ˜ LD 1 ( θ 1 ) ≡ δ ∂ θ 2 ) y 2 (˜ θ ) − c 2 (˜ | θ 1 , y 1 ( θ 1 ) E v ′ ( c 2 (˜ ∂ y 1 θ )) output driven by marginal production cost expressed in terms of tax revenues (consumption) output driven also by LBD impact on future tax revenues, and workers continuation utility LBD effect via change in conditional distribution ⇒ Higher period-1 output under LBD, for any given θ 1 (due to FOSD and increasing period-2 net surplus)

Motivation Qualitative Analysis Quantitative Analysis Conclusions Appx: T V & R IC RA term SB Handicaps Second Best When productivity is workers’ private information, FB not incentive compatible Higher productivity workers would mimic lower types to take advantage of cost differentials and skill persistence Need to give high types ”rents”: higher consumption (lower taxes) than under FB Value of distorting output: smaller rents to highly productive workers Under LBD: extra value in distorting period-1 output: smaller expected rents thanks to shift in period-2 distribution

Motivation Qualitative Analysis Quantitative Analysis Conclusions Appx: T V & R IC RA term SB Handicaps Labor Wedges Definition Period-1 Labor wedge: W 1 ( θ 1 ) ≡ 1 + LD 1 ( θ 1 ) − ψ y ( y 1 ( θ 1 ) , θ 1 ) . v ′ ( c 1 ( θ 1 )) Relative wedge: W 1 ≡ W 1 / ψ y ( y 1 ( θ 1 ) , θ 1 ) � v ′ ( c 1 ( θ 1 ))

Motivation Qualitative Analysis Quantitative Analysis Conclusions Appx: T V & R IC RA term SB Handicaps Relative Wedges (FOA) Period-1 wedges under SB allocations: W 1 ( θ 1 ) = [ RA 1 ( θ 1 ) − D 1 ( θ 1 )][ � � W RRN ( θ 1 )+Ω 1 ( θ 1 )] 1 where � W RRN : wedge under Rawlsian objective, RN agents, no LBD 1 Ω 1 : LBD effect RA 1 : correction due to higher costs of non-transferable utility D 1 : correction due to higher Pareto weights given to types above θ 1

Motivation Qualitative Analysis Quantitative Analysis Conclusions Appx: T V & R IC RA term SB Handicaps LBD Effect � � ∂ h 2 (˜ θ , y (˜ θ )) | θ 1 , y 1 ( θ 1 ) ∂ y 1 E Ω 1 ( θ 1 ) ≡ δ ψ y ( y 1 ( θ 1 ) , θ 1 ) “handicap” h 2 ( θ , y ) ≡ − 1 − F 1 ( θ 1 ) θ 1 f 1 ( θ 1 ) ρθ 2 ψ θ ( y 2 ( θ 2 ) , θ 2 ) : cost of rents associated with compensation to type ( θ 1 , θ 2 ) LBD contributes to higher expected period-2 handicaps ⇒ extra benefit of lowering y 1 ( θ 1 ) ⇒ higher wedges in early years Ω 1 ( θ 1 ) increasing in θ 1 , if θ 1 and y 1 strong complements and 1 − F 1 ( θ 1 ) θ 1 f 1 ( θ 1 ) / ψ y ( y 1 ( θ 1 ) , θ 1 ) not very decreasing ⇒ benefit of distorting y 1 downwards stronger for higher θ 1 ⇒ more progressivity

Motivation Qualitative Analysis Quantitative Analysis Conclusions Appx: T V & R IC RA term SB Handicaps Quantitative Analysis Quantitative Analysis

Motivation Qualitative Analysis Quantitative Analysis Conclusions Appx: T V & R IC RA term SB Handicaps Calibrated Economy T = 40 v ( c ) = log ( c ) � � 1 + φ y t 1 ψ ( y t , θ t ) = with φ = 2 ( Frisch elasticity = 0 . 5) 1 + φ θ t r = 1 − 1 β = 4 % with δ = β 20 θ 1 = h 1 ε 1 θ 2 = θ ρ 1 y ζ 1 ε 2 ε t iid Pareto-Lognormal ( λ , σ ) with mean 1 U.S. income tax estimation in Heathcote et. al. (2017) T ( y ) = y − e τ 0 y 1 − 0 . 181

Motivation Qualitative Analysis Quantitative Analysis Conclusions Appx: T V & R IC RA term SB Handicaps Parameters Using estimated moments in Huggett et. al. (2011) Param Value Target Moment Data Abs % Dev. ρ 0 . 4505 0 . 868 0 . 0015 % mean earn’s ratio ζ 0 . 2175 0 . 335 1 % Var. log-earn’s young 0 . 4795 0 . 435 0 . 009 % h 1 Var. log-earn’s old σ 0 . 5573 0 . 3175 1 . 7 % Gini earn’s young λ 5 . 9907 1 . 335 1 . 25 % mean/median earn’s young Table: Calibrated Parameters

Motivation Qualitative Analysis Quantitative Analysis Conclusions Appx: T V & R IC RA term SB Handicaps Second Best: Quantitative Analysis Optimal reform: 4 . 0409 % increase in consumption at all histories Inverse U-shape wedges as functions of (conditional) income percentile low-end LBD factor moderate skill persistence shock distribution close to Lognormal Increasing (conditional average) wedges over time high stochasticity and risk aversion / low-end LBD factor