Optimal Taxation with Behavioral Agents

Transcription

1 Optimal Taxation with Behavioral Agents Emmanuel Farhi and Xavier Gabaix Harvard Chicago, 2018

2 Our Paper Behavioral version of three pillars of optimal taxation theory: Ramsey (linear taxation to raise revenues and redistribute) Pigou (linear taxation to correct for externalities) Mirrlees (nonlinear taxation to raise revenues and redistribute) Unified treatment of behavioral biases with sufficient statistics: misperceptions of taxes internalities mental accounts, etc...

3 Outline Behavioral price theory Behavioral optimal tax formulas (Ramsey, Pigou, Mirrlees) Concrete lessons by specializing model Additional results (Diamond-Mirrlees, Atkinson-Stigltiz...)

4 Example: Decision vs. Experienced Utility Decision utility u s and experience utility u Agent behavior c (q,w) = arg maxu s (c) s.t. q c w c Ex. internalities from temptation, hyperbolic discounting...

5 Example: Misperception True prices q and perceived prices q s (q,w) Agent behavior (Gabaix 2014) c (q,w) = arg smax c R n q s (q,w)u (c) s.t. q c = w i.e. u (c(q,w)) = λq s (q,w) with λ such that q c(q,w) = w Implications: trade-off according to perceived relative prices u c 1 u c 2 = qs 1 q s 2 budget constraint satisfied q c = w

6 General Model: Behavioral Price Theory Two primitives: Marshallian demand function c(q,w) with q c(q,w) = w "experienced" utility function u(c) Indirect utility function v(q,w) = u(c(q,w)) Misoptimization wedge τ b = q u c (c(q,w)) v w (q,w) Slutsky matrix S C j (q,w) = c qj (q,w) + c w (q,w)c j (q,w) Behavioral Roy identity v q j (q,w) v w (q,w) = c j τ b S C j

7 Mapping to the General Model: Concrete Examples Decision vs. experienced utility model: misoptimization wedge τ b = us c v s w u c v w τ b i > 0 for tempting goods Slutsky Sij = S s ij Misperception model: misoptimization wedge τ b = q q s τ b i > 0 for goods with non-salient taxes Slutsky S H ij = k S r ik q s k (q,w) q j

8 Many-Person Ramsey (Diamond 1975) Social objective function L(τ) = W (v h (p + τ,w)) + λ [τ c h (p + τ,w) w] h Optimal tax formula 0 = L(τ) τ i Sufficient statistics: = [(λ γ h )ci h + λ(τ τ b,h ) S C,h i ] h social marginal welfare weight β h = W v hv h w social marginal utility of income γ h = W v hv h w + λ τ c h w substitution elasticities S C,h i weighted misoptimization wedge τ b,h = β h λ τb,h

9 Many-Person Ramsey (Diamond 1975) Optimal tax formula 0 = L(τ) τ i Three terms: = [(λ γ h )ci h + λ(τ τ b,h ) S C,h i ] h mechanical (λ γ h )c h i substitution λ τ S C,h i misoptimization λ τ b,h S C,h i Additional condition if lump sum taxes h (λ γ h ) = 0

10 Many-Person Ramsey (Diamond 1975) Assume symmetric Slutsky matrices S C,h ij = S C,h ji Then tax formula expressible in discouragement form h,j τ j S C,h ij c i = 1 γ ( γ h λ cov λ, Hch i c i ) h,j τb,h j S C,h ij c i

11 Pigou (Sandmo 1975) Externality ξ = ξ ((c h )) h=1...h, indirect utility v h (q,w,ξ ) Optimal tax formula 0 = L(τ ) τ i = [(λ γ ξ,h )ci h + λ(τ τ ξ,h τ b,h ) S C,h i ] h where τ ξ,h traditional externality wedge General model NOT subsumed by traditional theory of externalities

12 Nudges Nudge χ: influences demand c(q, w, χ), possibly utility u (c, χ), but not budget q c = w Ex. decision utility u s (c), perceived price q s, (q,w), nudgeability η 0 Agent behavior i.e. c (q,w, χ) = arg smax c u s,b s us (c) s.t. q c w u s (c) = ΛB s c (q s,c, χ) with Λ such that q c(q,w, χ) = w Nudge as a tax B s (q,c, χ) = q s, (q,w) c + χηc i Nudge as an anchor B s (q,c, χ) = q s, (q,w) c + η c i χ

13 Optimal Nudges Optimal nudge formula 0 = L χ = [λ(τ τ ξ,h τ b,h ) cχ h + β h uh χ ] h v h w Integrates nudges in canonical optimal taxation framework

14 Taking Stock So far: general taxation motive general behavioral biases generalize canonical optimal tax formulas sufficient statistics approach Now: specialize model: behavioral bias, taxation motive concrete lessons for taxes

15 Ramsey: Inverse Elasticity Rule Representative agent with quasilinear utility u(c) = c 0 + u i (c i ) i>0 Misperception of taxes τ s i = m i τ i (salience) Social objective, limit of small taxes (Λ = λ 1 small) 1 L(τ) = i 2 (τs i ) 2 ψ i y i + Λ i τ i p i y i where ψ i rational demand elasticity, y i expenditure with no tax

16 Ramsey: Inverse Elasticity Rule Behavioral elasticity m i ψ i Behavioral Ramsey formula τ i p i = Λ m 2 i ψ i Contrast with traditional Ramsey formula τ R i p i = Λ ψ i Taxation and salience: 1 m 2 i

17 Pigou: Dollar for Dollar Principle Representative agent with quasilinear utility One taxed good with price p and externality ξ c Inattention to tax τ s = mτ Behavioral Pigou formula τ = ξ m Contrast with traditional Pigou formula τ R = ξ Taxation and salience: Pigou 1 m vs. Ramsey 1 m 2

18 Ramsey and Pigou: Heterogeneous Attention Heterogeneous attention m h i Additional deadweight loss from misallocation Behavioral Ramsey and Pigou formula become τ i p i = ψ i E Λ [ ] = Λ mi h 2 ψ i (E [ ] mi h 2 [ ] ) + var m h i τ = E[ ξ h m h] [ E m h2] = E [ ξ h ] E [ m h] + cov ( ξ h,m h) E[m h ] 2 + var [m h ]

19 Pigou: Taxes vs. Quantity Restrictions Revisit traditonal presumption: Heterogeneity: Pigouvian taxes > quantity restrictions externality ξh mispereception mh Quasilinear + quadratic utility: social bliss point c h elasticity (slope) of demand Ψ

20 Pigou: Taxes vs. Quantity Restrictions Quantity restrictions better than taxation iff 1 Ψ var(c h ) ΨE [ ] [ ] ξ 2 h E m 2 h (E [ξh m h ]) 2 E [ ] mh 2 1. enough heterogeneity in attention (m h ) or externality (ξ h ) 2. not too much heterogeneity in preferences (c h ) 3. high demand elasticity (Ψ high)

21 Useful Simple Parametrization Experienced utility u h (c 0,C) = c 0 + U h (C) ξ Decision utility u s,h (c 0,C) = c 0 + U s,h (C) ξ Misperception τ s,h = τm h Internality wedge τ I,h = U s,h C (C) Uh C (C) Internality/externality wedge τ X,h = β h λ τi,h + τ ξ,h Misoptimization wedge τ b,h = τ I,h + τ τ s,h Optimal tax τ = ( M h S h,r (I (I M h) γ ξ,h h λ )) 1 [M h S h,r τ X,h (1 γh,ξ h λ )ch ]

22 Pigou: Principle of Targeting Traditional principle of targeting: tax eternality good do not tax complements do not subsidize substitutes Behavioral (heterogeneous attention): tax complements subsidize substitutes cf Allcott, Mullainathan, Taubinsky ( 14): if consumers partly forget about cost of gas when purchasing car, subsidize fuel efficiency, or mandate fuel-efficiency standards

23 Pigou: Principle of Targeting Use simple parametrization Two goods, negative externality from good 1 τ1 X = ξ > 0 and τ2 X = 0 Homogenous preferences, decision=experienced, heterogenous misperceptions, no redistributive or revenue raising motive Optimal tax on good 2 τ 2 = S 11 r S 12 r E [m 1,h] [ E [ m1h 2 ] E [m2h ] E [m 1h m 2h ]E [m 1h ] ] dete [M h S r M h ] τ2 = 0 with homogenous misperceptions τ 2 > 0 iff S12 r > 0 with heterogenous misperceptions (if not too correlated) τ X 1

24 Vouchers and Mental Accounts Two goods, food (1) and non-food (2) Internality from food (decisions vs. experienced utility) 1 u s (c 1,c 2 ) = cαs 1 cαs 2 2 α α 1 1 αα 2 2 vs. u (c 1,c 2 ) = cα 1 1 cα 2 2 α α 1 1 αα 2 2 with α1 s + αs 2 = α 1 + α 2 = 1 and α1 s < α 1 Mental accounting (perceived vs. actual budget constraint) c1 c 1 + c 2 + κ 1 ω1 d = w vs. c 1 + c 2 = w Transfers t and food voucher b w = w + t + b and ω1 d = α1w s + βb Government objective function [u (c (t,b))] 1 σ λ (t + b) 1 σ

25 Vouchers and Mental Accounts MPCF from voucher (α s 1 + β) > MPCF from transfer (αs 1 ), even if voucher inframarginal (c 1 > b) Given T = t + b, optimal voucher b w = α 1 α1 s β Higher overall transfers iff weak taste for redistribution (σ < 1) Higher welfare with vouchers.

26 Mistakes and Redistribution Assume h,s u s,h (c 1,c 2 ) = cα 1 1 c αh,s 2 2 α α 1 1 αα 2 2 and u h (c 1,c 2 ) = cα 1 1 cα 2 2 α α 1 1 αα 2 2 with α h,s 1 + α h,s 2 = α 1 + α 2 = 1 Samuelsonian welfare function h [u h,s (c h 1,ch 2 )]1 σ 1 σ Linear income tax τ z and a lump sum rebate

27 Mistakes and Redistribution Strong preference for redistribution(σ > 1): larger behavioral biases (reductions in A h ) for poor lead to more redistribution (higher τ z ) Reverse if weak preference for redistribution (σ < 1) Mistakes lower utility and marginal utility of wealth, ambiguous effect on social marginal utility of income γ h : ( ) v h (z) = A h z, A h α h,b α1 ( ) 1 α h,b α2 2 = 1 α 1 α 2 ( ) ( σ γ h = A h z A h = z σ A h) 1 σ

28 Internalities and Redistribution Use simple parametrization No externalities, mo misperceptions, decision=experienced except......good 1 only consumed by type h with internality τ I,h 1 > 0 Optimal tax τ 1 = 1 γh λ q 1 ψ 1 + γh λ τ I,h 1 q 1 Sign ambiguous, internality correction vs. redistribution Ex. sugary sodas (cf. also Lockwood and Taubinsky 15)

29 Aversive Nudges vs. Taxes Allow for misperceptions Use U h (c) = ah c 1 2 c2 Ψ Nudge as a tax c h (τ, χ) = c h 0 Ψ( m h τ + χη h ) Aversive nudge u h (c, χ) = u h (c) ι h χc 1 Tax dominates nudge iff λ γ h m h > ιh γ h η h Nudge the poor, tax the rich

30 Mirrlees (1971) General behavioral biases with non-linear income tax T (z) Behavioral Saez formula (Saez 2001) Sufficient statistics: traditional: elasticity of labor supply, welfare weights, hazard... behavioral: misoptimization wedge, behavioral cross-influence

31 Behavioral Saez Formula T (z ) τ b (z ) 1 T (z ) = 1 ζ c (z ) H(z ) z h (z ) ω(z,z) T (z) τ b (z) 1 T dz (z) z e z z ρ(s)ds ( 1 g(z) η(z) τb (z) 1 T (z) ) h(z) 1 H(z ), where ρ(z) = η(z) 1 ζ c (z) z, ω(z,z) = ζq c (z) z z z e z ρ(s)ds ρ(z )ζq c (z)dz z zh (z) ζ c (z ) z h (z ), and traditional Saez formula obtains with τ b (z) = ζ c Q z = 0.

32 Some Applications (See Paper) Nonzero taxes at top and bottom (bounded skills) Behavioral Saez top tax formula (unbounded skills) Possibility of negative marginal income tax rates rationalization of EITC if poor undervalue benefits of work see also Lockwood (JMP, in progress) Schmeduling (Liebman and Zeckhauser 2004): confusion of average for marginal tax rates

33 Additional General Results (See Paper) Endogenous attention: attention as a good, optimal/suboptimal attention typically lower taxes with endogenous attention Salience as policy choice: low salience to raise taxes high salience to correct for internalities or externalities

34 Additional General Results (See Paper) Diamond-Mirrlees (1971): traditional productive efficiency (ex. no taxes on intermediate goods) if complete set of taxes on final goods behavioral productive efficiency if complete set of salient taxes on final goods in both cases, no productive efficiency supply elasticities and incidence enter tax formulas Atkinson-Stiglitz (1976): traditional uniform commodity taxation if separable preferences behavioral not true anymore in general, e.g. tax more non-salient goods and high internality goods

35 Conclusion Traditional optimal taxation theory: general using traditional price theory unification tax formulas with sufficient statistics concrete lessons Behavioral optimal taxation theory: general using behavioral price theory unification tax formulas with old and new sufficient statistics new concrete lessons