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

• wn 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: θ1 privately observed at beginning of t = 1 drawn from cdf F1 (density f1) Period-2 productivity: θ2 privately observed at beginning of t = 2 drawn from cdf F2(·|θ1,y1) (FOSD)

dependence on y1: LBD

Example: θ2 = θ ξ

1 lζ 1 ε2 = θ ξ 1

• y1

θ1

ζ ε2 = θ ρ

1 yζ 1 ε2

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

Environment

Period-t flow utility: v(ct)−ψ(yt,θt) e.g. ψ(yt,θt) =

1 1+φ

• yt

θt

1+φ where 1/φ is Frisch elasticity 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 ≡ (θ1,θ2) and θ 1 ≡ (θ1) Worker expected life-time utility: V1(θ1) = E

• ∑

t

δ t−1 v(ct(˜ θ t))−ψ(yt(˜ θ t), ˜ θt)

• |θ1,y1(θ1)
• Worker expected life-time tax bill:

R1(θ1) = E

• ∑

t

δ t−1 yt(˜ θ t)−ct(˜ θ t)

• |θ1,y1(θ1)

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

• R1(θ1)dF1(θ1)

s.t. participation/redistribution constraint

• V1(θ1)dF1(θ1) ≥ 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 θ1 ψy(y1(θ1),θ1) v′(c1(θ1)) = 1+LD1(θ1) where LD1(θ1) ≡ δ ∂ ∂y1 E

• y2(˜

θ)−c2(˜ θ)+ v(c2(˜ θ))−ψ(y2(˜ θ), ˜ θ2) v′(c2(˜ θ)) |θ1,y1(θ1)

• utput driven by marginal production cost expressed in terms of tax

revenues (consumption)

• utput 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 θ1 (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: W1(θ1) ≡ 1+LD1(θ1)− ψy(y1(θ1),θ1) v′(c1(θ1)) . Relative wedge:

• W1 ≡ W1/ψy(y1(θ1),θ1)

v′(c1(θ1))

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

Relative Wedges (FOA)

Period-1 wedges under SB allocations:

• W1(θ1) = [RA1(θ1)−D1(θ1)][

W RRN

1

(θ1)+Ω1(θ1)] where

• W RRN

1

: wedge under Rawlsian objective, RN agents, no LBD Ω1: LBD effect RA1: correction due to higher costs of non-transferable utility D1: 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

Ω1(θ1) ≡ δ

∂ ∂y1 E

• h2(˜

θ,y(˜ θ))|θ1,y1(θ1)

• ψy(y1(θ1),θ1)

“handicap” h2(θ,y) ≡ − 1−F1(θ1)

θ1f1(θ1) ρθ2ψθ(y2(θ2),θ2): cost of rents

associated with compensation to type (θ1,θ2) LBD contributes to higher expected period-2 handicaps ⇒ extra benefit of lowering y1(θ1) ⇒ higher wedges in early years Ω1(θ1) increasing in θ1, if θ1 and y1 strong complements and

1−F1(θ1) θ1f1(θ1) /ψy(y1(θ1),θ1) not very decreasing

⇒ benefit of distorting y1 downwards stronger for higher θ1 ⇒ 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) ψ(yt,θt) =

1 1+φ

• yt

θt

1+φ with φ = 2 (Frisch elasticity= 0.5) r = 1− 1

β = 4% with δ = β 20

θ1 = h1ε1 θ2 = θ ρ

1 yζ 1 ε2

εt iid Pareto-Lognormal (λ,σ) with mean 1 U.S. income tax estimation in Heathcote et. al. (2017) T(y) = y −eτ0y 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 mean earn’s ratio 0.868 0.0015% ζ 0.2175

• Var. log-earn’s young

0.335 1% h1 0.4795

• Var. log-earn’s old

0.435 0.009% σ 0.5573 Gini earn’s young 0.3175 1.7% λ 5.9907 mean/median earn’s young 1.335 1.25%

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

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

Approximate Implementation

SB allocations implemented arbitrarily well by age-dependent taxes invariant in past incomes: T1(y1) = −B +y1 −eτ0,1y 1−τ1 and T2(y2) = y2 −eτ0,2y 1−τ2 Loss in consumption (relative to SB): 0.155% Optimal linear age-dependent taxes τ1 = 38% and τ2 = 46% loss in consumption (relative to SB): 0.1567%

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

Reform: Revenue-neutral Tax Rates

Income Percentile

0.2 0.4 0.6 0.8 1

• 0.1
• 0.05

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4First-period income tax rates

Income percentile

0.2 0.4 0.6 0.8 1 0.25 0.3 0.35 0.4 0.45 0.5

Second-period income tax rates

benchmark tax rate

• ptimal linear tax rate

quasi-optimal tax rate

Figure: Tax rates as functions of income percentile

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

Comparative Statics: Stochasticity

Income Percentile

0.2 0.4 0.6 0.8 1 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43

First-period tax rates

calibrvar var =0.34 var =0.22 var =0.14 var =0.08 var =0.05

Income percentile

0.2 0.4 0.6 0.8 1 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46

Second-period tax rates

Figure: Variations in stochasticity

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

Counterfactual: Importance of LBD

Similar calibration but with exogenous productivity θ2 = h2θ

ρ 1 ε2

Calibrated (conditional) distributions very close to those under LBD Higher persistence: ρ = 0.6 (with LBD, ρ = 0.4) Ignoring LBD: 15% overestimation of benefits of reforming US tax code SB allocations: implemented arbitrarily well by age-dependent taxes invariant in past incomes but with higher peroid-1 rates

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

Importance of LBD

Income Percentile

0.2 0.4 0.6 0.8 1 0.376 0.378 0.38 0.382 0.384 0.386 0.388 0.39 0.392 0.394

First-period quasi-optimal tax rates Income percentile

0.2 0.4 0.6 0.8 1 0.42 0.425 0.43 0.435 0.44 0.445 0.45 0.455 0.46 0.465 0.47

Second-period quasi-optimal tax rates

with LBD witout LBD

Figure: Quasi-optimal income tax rates with and without LBD

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

Conclusions

LBD: important qualitative and quantitative implications for level progressivity dynamics benefits in reforming US tax code Future work: sector-specific LBD heterogeneity hidden savings political economy constraints spillovers partial commitment ···

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

THANKS!

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

Multi-period Environment

T: length of working life in years (even number) Linear labour production Labour productivity in period τ: ϑτ ϑτ = θ1 for τ = 1,...,T/2 θ1 privately observed by worker at beginning of “young age” F1: cdf of initial distribution (density f1) ϑτ = θ2 for τ = T/2+1,...,T θ2 privately observed by worker at beginning of “old age” F2(·|θ1,y): cdf of θ2 - satisfies FOSD LBD: dependence on weighed average of output as young y Example: θ2 = θ ρ+ζ

1

l

ζε2 = θ ρ+ζ 1

• y

θ1

ζ ε2 = θ ρ

1 yζε2

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

Environment

Period-τ worker’s payoff: v(cτ)−ψ(yτ,ϑτ) Discount factor β Planner maximizes average expected life-time utility s.t. exogenous expected tax revenue requirements β = 1/(1+r)

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

Environment

LBD active in each of first T/2 years with declining weights

• βτ/

T/2

∑

τ=1

ˆ βτ When (ˆ β1, ˆ β2,..., ˆ βT/2) is proportional to (1,β,...,β T/2−1), consumption and earnings constant over each block of T/2 years Isomorphic to 2-period model discount factor δ = β T/2 period-t history: θ t with θ 1 = θ1,θ 2 = (θ1,θ2) allocation: (yt(θ t),ct(θ t))t=1,2 LBD: y = y1(θ1)

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

V & R

Worker expected life-time utility given allocation: V1(θ1) = v(c1(θ1))−ψ(y1(θ1),θ1)+ δ v(ct(θ1, ˜ θ2))−ψ(yt(θ1, ˜ θ2), ˜ θ2)

• F2(˜

θ2|θ1,y1(θ1)) Expected life-time tax bill: R(θ1) = y1(θ1)−c1(θ1)+ δ yt(θ1, ˜ θ2)−ct(θ1, ˜ θ2)

• F2(˜

θ2|θ1,y1(θ1))

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

Incentive Compatibility

v(c1(θ1))−ψ(y1(θ1),θ1)+δ

• (v(c2(θ1,θ2))−ψ(y2(θ1,θ2),θ2))dF2(θ2|θ1,y1(θ1)) ≥

v(c1( θ1))−ψ(y1( θ1),θ1)+ δ v(c2( θ1, θ2(θ2)))−ψ(y2( θ1, θ2(θ2)),θ2)

• dF2(θ2|θ1,y1(

θ1))

and

v(c2(θ1,θ2))−ψ(y2(θ1,θ2),θ2) ≥ v(c2(θ1, θ2))−ψ(y2(θ1, θ2),θ2)

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

Second Best: Impulse Responses

Impulse Responses

With θ2 = Z2(θ1,y1,ε2) = θ ρ

1 yζ 1 ε2

I 2

1 (θ,y1) = ∂Z2(θ1,y1,ε2) ∂θ1

= ρ θ2

θ1

where θ = (θ1,θ2) and ε2 = Z −1

2 (θ2;θ1,y1) = θ2 θρ

1 yζ 1

and I 1

1 (θ,y1) = 1

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

Second Best: Incentive Compatibility

Continuation utility (history θ = (θ1,θ2)): V2(θ) ≡ c2(θ)−ψ(y2(θ),θ2) For any θ1, IC-2 requires that V2(θ1,·) Lipschitz continuous and s.t. (e.g., Mirrlees) V2(θ1,θ2) = V2(θ1,θ 2)−

θ2

θ2

ψθ(y2(θ1,s),s)ds, y2(θ1,·) nondecreasing

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

Second Best: Incentive Compatibility

IC-1 requires that V1(θ1) = V1(θ 1) −

θ1

θ1

• ψθ(y1(s),s)ds +δE
• I 2

1 (˜

θ,y1(s))ψθ(y2(˜ θ), ˜ θ2)|s,y1(s)

• ds

and

θ1

ˆ θ1

• ψθ(y1(s),s)+δE
• I 2

1 (˜

θ,y1(s))ψθ(y2(s, ˜ θ2), ˜ θ2)|s,y1(s)

• ds ≤

θ1

ˆ θ1

• ψθ(y1(ˆ

θ1),s)+δE

• I 2

1 (˜

θ,y1(ˆ θ1))ψθ(y2(ˆ θ1, ˜ θ2), ˜ θ2)|s,y1(ˆ θ1)

• ds

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

Risk Aversion Effect

Increasing lifetime utility by v′(c1(θ1))Ω1(θ1) increases rents to all higher types One util compensation requires 1/v′(ct) units of consumption Risk aversion increases cost of increasing expected future information rents: RA1(θ1) > 1 Risk aversion contributes to amplification of LBD level effect risk aversion increases benefit of shifting future distribution towards lower types BUT, risk aversion leads also to an alleviation of LBD effects higher cost of future rents → lower future rents → lower need to shift future distribution

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

Redistribution Effect

Increasing lifetime utility by v′(c1(θ1))Ω1(θ1) is valued by an Utilitarian planner One social util costs

θ1

θ1 1 v′(c1(s))dF1(s) in revenue terms

This effect counteracts amplification effect of risk aversion

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

Recursive Problem

“Promised continuation payoff”: Πt+1(θ t) ≡

• Vt+1(θ t,θt+1)dFt+1(θt+1 | θt,yt(θ t))

“Marginal promise”: Zt+1(θ t) ≡ −Eλ[χ]|θt ∑τ=t+1 δ τ−t−1I τ

t (θ τ,yτ−1)ψθ(yτ,θτ)

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

Towards Recursive Problem

With these definitions we have: Vt(θ t) = v(ct(θ t))−ψ(yt(θ t),θt)+δΠt+1(θ t) and ∂Vt(θ t) ∂θt = −ψθ(yt(θ t),θt)+δZt+1(θ t)

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

The Recursive Problem

Qt

• θt−1,yt−1(θt−1),Πt(θt−1),Zt(θt−1)
• ≡ maxyt(·),Vt(·),Πt+1(·),Zt+1(·)

yt(θt)−v−1 Vt(θt)+ψ(yt(θt),θt)−δΠt+1(θt)

• +

δE

• Qt+1
• θt,yt(θt),Πt+1(θt),Zt+1(θt)
• |θt,yt(θt)
• subject to

∂Vt(θt) ∂θt = −ψθ(yt(θt),θt)+δZt+1(θt) Πt(θt−1) =

• Vt(θt)dF(θt | θt−1,yt−1(θt−1))

and for t > 1 Zt(θt−1) = −ψθ(yt(θt),θt)+δZt+1(θt)

• ×

×I t

t−1(θt,yt−1(θt−1))dFt(θt | θt−1,yt−1(θt−1))

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

Second Best under RN and Rawls: period-2 output

Given θ = (θ1,θ2), 1 = ψy(y2(θ),θ2)− f1(θ1) 1−F1(θ1)I 2

1 (θ,y1(θ1))ψyθ(y2(θ),θ2)

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

Second Best under RN and Rawls: period-1 output

Given θ1, 1+LD1(θ1) = ψy(y1(θ1),θ1)− f1(θ1) 1−F1(θ1)ψyθ(y1(θ1),θ1) +δ ∂ ∂y1 E

• f1(θ1)

1−F1(θ1)I 2

1 (˜

θ,y1(θ1))ψθ(y2(˜ θ), ˜ θ2))|θ1,y1(θ1)

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

Second Best: Handicaps

Expected tax revenues under risk neutrality (using IC): E

• ∑

t

δ t−1 yt(˜ θ t)−ψ(yt(˜ θ t), ˜ θt)−ht( ˜ θ t,yt(˜ θ t))

• −V1(θ 1),

first-period "handicap": h1(θ1,y1) ≡ −

f1(θ1) 1−F1(θ1)ψθ(y1,θ1)

second-period "handicap": h2(θ,y) ≡ −

f1(θ1) 1−F1(θ1)I 2 1 (θ,y1)ψθ(y2,θ2)

Handicaps: costs to planner from asymmetric information