Taxing Top Incomes in a World of Ideas

Transcription

1 Taxing Top Incomes in a World of Ideas Chad Jones September 24, / 43

2 The Saez (2001) Calculation Income: z Pareto(α) Tax revenue: T = τ 0 z+τ(z m z) where z m is average income above cutoff z Revenue-maximizing top tax rate: z m z + τz m(τ) = 0 mechanical gain behavioral loss Divide by z m elasticity form and rearrange: τ 1 = 1+α η zm,1 τ where α = z m z m z. 1 / 43

3 τ 1 = 1+α η zm,1 τ Intuition Decreasing in η zm,1 τ: elasticity of top income wrt 1 τ Increasing in 1 α = z m z z m : change in revenue as a percent of income = Pareto inequality Diamond and Saez (2011) Calibration α = 1.5 from Pareto income distribution η = 0.2 from literature τ d-s 77% 2 / 43

4 This Paper How does this calculation change when: New ideas drive economic growth The reward for a new idea is a top income Creation of ideas is broad A formal research subsidy is imperfect (Walmart, Amazon) Adds new terms to the Saez (2001) calculation τ w Lowers revenue from other brackets Also lowers consumption throughout the economy The efforts of a relatively small number of entrepreneurs is responsible for the bulk of economy-wide income growth 3 / 43

5 Literature Review Human capital: Badel and Huggett, Kindermann and Krueger Superstars/inventors: Scheuer and Werning, Chetty et al Spillovers: Lockwood-Nathanson-Weyl Mirrlees w/ Imperfect Substitution: Sachs-Tsyvinski-Werquin Inventors and taxes: Akcigit-Baslandze-Stantcheva, Moretti and Wilson, Akcigit-Grigsby-Nicholas-Stantcheva Growth and taxes: Stokey and Rebelo, Jaimovich and Rebelo 4 / 43

6 Basic Setup 5 / 43

7 Overview BGP of an idea-based growth model. Romer 1990, Jones 1995 Semi-endogenous growth Basic R&D (subsidized directly), Applied R&D (top tax rate) BGP simplifies: static comparison vs transition dynamics Three alternative approaches to the top tax rate: Revenue maximization Maximize welfare of median worker Maximize utilitarian social welfare 6 / 43

8 The Economic Environment Consumption goods produced by labor L and applied ideas A: Y = A γ L (1) Applied ideas produced from entrepreneurs, effort e, talent z, and basic research B: A = ν a E[ez]S a B β (2) Fundamental ideas produced from basic research: B = ν b S b (3) L, S a, S b exogenous. e, z endogenous (unspecified for now) 7 / 43

9 Nonrivalry of Ideas (Romer): Y = A γ L Constant returns to rival inputs (L) Given a stock of nonrival blueprints/ideas A Standard replication argument Increasing returns to ideas and rival inputs together γ > 0 measures the degree of IRS Hints at why effects can be large One computer or year of school 1 worker more productive One new idea any number of people more productive Distortions of the computer/schooling have small effects. Distorting the creation of the idea... 8 / 43

10 BGP from a Dynamic Growth Model Production of basic ideas Ḃ t = bs λ bt Bφ b t Production of applied ideas Ȧ t = ā(e(ez)s at ) λ A φ a t B α t BGP implies that stocks are proportional to flows: A and B are proportional to S a and S b (to some powers) S a, S b, L all grow at the same exogenous population growth rate. 9 / 43

11 Output = Consumption: Combining (1) - (3): Y = ( νe[ez]s a S β b) γ L. (4) Output per person (S a S β b )γ Intuition: y depends on stock of ideas, not ideas per person LR growth = γ(1+β)n where n is population growth Taxes distort E(ez), not S a or S b here Simplicity Cutoff rich nonlinear tax could get it right? Middle rate right number become entrepreneurs / 43

12 Nonlinear Income Tax Tax Revenue T = τ 0 [wl+w b S b + w a E(ez)S a ]+(τ τ 0 )[w a E(ez) w]s a Full growth model: entrepreneurs paid a constant share of GDP w a E(ez)S a Y = ρ and Y = wl+w b S b + w a E(ez)S a Therefore T = τ 0 Y+(τ τ 0 )[ρy ws a ] 11 / 43

13 The Top Tax Rate that Maximizes Revenue 12 / 43

14 Revenue-Maximizing Top Tax Rate Two key equations: T = τ 0 Y+(τ τ 0 )[ρy ws a ] Y = ( νe[ez]s a S β b) γ L Choose τ to maximize tax revenue (given τ 0 for now) A higher τ reduces the effort of entrepreneurs, Leads to less innovation which reduces everyone s income (Y) which lowers tax revenue received via τ 0 13 / 43

15 Solution max T = τ 0 Y(τ)+(τ τ 0 )[ρy(τ) ws a ] τ FOC: (ρ ρ) Y + Y mechanical gain τ [(1 ρ)τ 0 +ρτ] = 0 behavioral loss where ρ ws a Y Rearranging with ρ ρ ρ τ rm = 1 τ 0 1 ρ ρ η Y,1 τ 1+ ρ ρ η Y,1 τ 14 / 43

16 Interpretation τ rm = 1 τ 0 1 ρ ρ η Y,1 τ 1+ ρ ρ η Y,1 τ vs τ ds = 1 1+α η zm,1 τ Remarks: Two key differences η Y,1 τ versus η zm,1 τ η Y,1 τ How GDP changes if researchers keep more η zm,1 τ How average top incomes change If τ 0 > 0, then τ is lower Distorting research lowers GDP lowers revenue from other taxes! 15 / 43

17 Guide to Intuition ρη Y,1 τ Behavioral effect via top earners (1 ρ)η Y,1 τ Behavioral effect via workers ρ ρ ρ Tax base for τ, mechanical effect 1 ρ Tax base for τ 0 16 / 43

18 What is η Y,1 τ? Y = ( νe[ez]s a S β b) γ L ηy,1 τ = γ ζ γ is the degree of IRS via ideas ζ is the elasticity of E[ez] with respect to 1 τ. Standard Diamond-Saez elasticity: ζ = η zm,1 τ How individual behavior changes when the tax rate changes Cool insight from PublicEcon: all that matters is the value of this elasticity, not the mechanism! So for now, just treat as a parameter (endogenized later) 17 / 43

19 Calibration Parameter values for numerical examples γ [1/8, 1] g tfp = γ(1+β) g S 1%. ζ 1 ζ {0.2, 0.5} Behavioral elasticity. Saez values τ 0 = 0.2 Average tax rate outside the top. ρ = 0.10 Share of income taxed at the top rate; top returns account for 20% of taxable income. ρ = 0.15 So ρ ρ = 1.5 as in Saez pareto parameter, α. 18 / 43

20 Revenue-Maximizing Top Tax Rate, τ rm Degree of Behav. Elas = 0.2 Behav. Elas = 0.5 IRS, γ τ 0 = 0 τ 0 = 0.2 τ 0 = 0 τ 0 = 0.2 1/ / / / 43

21 Intuition Suppose we double the keep rate 1 τ. What is the long-run effect on GDP? Answer: 2 η Y,1 τ = 2 γζ Baseline: γ = 1/2 and ζ = 1/6 2 1/ Going from τ = 75% to τ = 50% raises GDP by just 6%! With ρ = 10%, the revenue cost is 2.5% of GDP 6% gain to all > redistributing 2.5% to the bottom half! 6% seems small, but achieved by a small group of researchers working 15% harder / 43

22 Maximizing Worker Welfare Revenue-max ignores effect on consumption Worker welfare yields a clean closed-form solution 21 / 43

23 Choose τ and τ 0 to Maxmimize Worker Welfare Workers: c w = w(1 τ 0 ) u w (c) = θ log c Government budget constraint τ 0 Y+(τ τ 0 )(ρy ws a ) = ΩY Exogenous government spending share of GDP = Ω Therefore: max τ,τ 0 log(1 τ 0 )+log Y(τ) s.t. τ 0 Y+(τ τ 0 )(ρy ws a ) = ΩY. 22 / 43

24 First Order Conditions The top rate that maximizes worker welfare satisfies τ ww = 1 η Y,1 τ ( ) 1 ρ ρ τ ρ ρ (1 τ 0 ) Ω ρ 1+ ρ ρ η. Y,1 τ Three new terms relative to Saez: η 1 ρ ρ τ 0 Original term from RevMax η 1 ρ ρ (1 τ0 ) Direct effect of a higher tax rate reducing GDP reduce workers consumption η Ω ρ Need to raise Ω in revenue 23 / 43

25 Solution Combining with the Govt Budget Constraint: τ ww = [ ( )] 1 ρ ρ Ω ρ 1+ ρ 1 ρ 1+ ρ ρ η Y,1 τ + ρ 1 ρ η, Y,1 τ 1 η Y,1 τ Another intuition: when is flat tax optimal? τ τ 0 and κ κ 0 η Y,1 τ ρ 1 ρ. Increase κ raises GDP by η Y,1 τ Redistribution: take from ρ people, give to 1 ρ ρ Baseline parameters: 1 ρ = 1 9 and η Y,1 τ = 1 6 γ. So γ > 2/3 τ < τ / 43

26 Tax Rates that Maximize Worker Welfare Degree of Behavioral elast. = 0.2 Behavioral elast. = 0.5 IRS, γ τ ww τ 0 τ ww τ 0 1/ / / The top rate that maximizes worker welfare can be negative! 25 / 43

27 Maximizing Utilitarian Social Welfare 26 / 43

28 Entrepreneurs Utility function depends on consumption and effort: u(c, e) = θ log c ζe 1/ζ Researcher with talent z solves maxu(c, e) s.t. c,e c = w(1 τ 0 )+[w s ez w](1 τ)+r = w(1 τ 0 ) w(1 τ)+w s ez(1 τ)+r = w(τ τ 0 )+w s ez(1 τ)+r where R is a lump sum rebate. FOC: e 1 ζ 1 = θw sz(1 τ). c 27 / 43

29 SE/IE and Rebates Log preferences imply that SE and IE cancel: e τ = 0 Standard approach is to rebate tax revenue to neutralize the IE. Tricky here because IE s are heterogeneous! Shortcut: heterogeneous rebates that vary with z to deliver c z = w s ez(1 τ) 1 α e z = e = [θ(1 τ) α ] ζ, where α parameterizes the elasticity of effort wrt 1 τ governs tradeoff with redistribution 28 / 43

30 Utilitarian Social Welfare Social Welfare: SWF Lu(c w )+S b u(c b )+S a u(c z, e z )df(z). Substitution of equilibrium conditions gives SWF log Y+l log(1 τ 0 )+s[1 α(1 ζ)] log(1 τ) sζ(1 τ) α where s S a L+S b +S a, l 1 s, 29 / 43

31 Tax Rates that Maximize Social Welfare Proposition 2 gives the tax rates, written in terms of the keep rates κ 1 τ and κ 0 1 τ 0. Two well-behaved nonlinear equations: αζsκ α + κ κ 0 ( l ( ρ+ ρη) = η 1+ ρl ) + s[1 α(1 ζ)] 1 ρ 1 ρ κ 0 (1 ρ)+κ ρ = 1 Ω. 30 / 43

32 Maximizing Social Welfare: α = 1 κ FOC κ Government BC 0 κ κ / 43

33 Tax Rates that Maximize Social Welfare (α = 1) Behavioral elast. = 0.2 Behavioral elast. = 0.5 Degree of GDP loss GDP loss IRS, γ τ if τ = 0.75 τ if τ = / % % 1/ % % 1/ % % % % 32 / 43

34 Tax Rates that Maximize Social Welfare (α = 1/2) Behavioral elast. = 0.2 Behavioral elast. = 0.5 Degree of GDP loss GDP loss IRS, γ τ if τ = 0.75 τ if τ = / % % 1/ % % 1/ % % % % 33 / 43

35 Summary of Calibrtion Exercises Top rate, τ Exercise γ = 1/2 γ = 1 Saez revenue-maximization, τ 0 = Revenue-maximization w/ ideas Worker welfare (incl. worker consumption) Utilitarian welfare (incl. entrepreneur cons.) Incorporating ideas sharply lowers the top tax rate. 34 / 43

36 Extensions 35 / 43

37 Does Michael Jordan Create Ideas? Group M of top earners who do not create ideas Y = A γ (E(ez)M) ψ L 1 ψ Paid fraction ρ m of GDP. Total tax revenue: T = τ 0 Y+(τ τ 0 )[(w a E(ez) w)s a +(w m E(ez) w)m] = τ 0 Y+(τ τ 0 )[(ρ s +ρ m )Y w(s a + M)]. where ρ ρ s +ρ m. Same formula for τ applies; interpret ρ and ρ to include all top earners. MJ does not create ideas; ideas create MJ! 36 / 43

38 The Social Return to Research How big is the gap between equilibrium share and optimal share to pay for research? Jones and Williams (1998) social rate of return calculation here: ( 1 r = g Y +λg y ρ s (1 τ) 1 ) γ After tax share of payments to entrepreneurs should equal γ Simple calibration: τ = 1/2 r = 39% if ρ s = 10% Consistent with SROR estimates e.g. Bloom et al. (2013) But those are returns to formal R&D / 43

39 Evidence on Growth and Taxes? Important and puzzling!!! Stokey and Rebelo (1995) Growth rates flat in the 20th century Taxes increased a lot! But other things were not equal! Massive government investments in basic research after WWII Decline in basic research investment in recent decades? Short-run vs long-run? Shift from goods to ideas may reduce GDP in short run / 43

40 Growth in U.S. GDP per person (smoothed) PERCENT YEAR 39 / 43

41 Taxes in the United States PERCENT Top marginal tax rate (left scale) Total government revenues as a share of GDP (right scale) PERCENT / 43

42 GEMS Entrepreneurs versus Taxes ENTREPRENEURS, PERCENT OF YEAR OLDS (GEMS) 8 Iceland 7 6 United States Canada 5 Luxembourg Norway Switzerland Turkey Portugal Ireland United Kingdom Greece Spain Japan Italy Germany Netherlands Finland Austria France Belgium Sweden Denmark EFFECTIVE TOP TAX RATE, / 43

43 Environment for Full Growth Model Final output Production of variety i Resource constraint (l) Resource constraint (N) Population growth Entrepreneurs Managers Applied ideas Basic ideas Talent heterogeneity Y t = A t 0 x ρ it di(e(ez)m t) 1 ρ x it = l it lit di = L t L t + S bt = N t N t = N exp(nt) S at = S a exp(nt) M t = M exp(nt) Ȧ t = ā(e(ez)s at ) λ A φ a t B α t Ḃ t = bs λ bt Bφ b t z i F(z) Utility (S a, M) u(c, e) = θ log c ζe 1/ζ 42 / 43

44 Conclusion Lots of unanswered questions What is the right top tax rate? Many other considerations... Why is evidence on growth and taxes so murky? What is true effect of taxes on growth and innovation? Akcigit et al (2018) makes progress... Still, innovation is a key force that needs to be incorporated Taxes affect entrepreneurship and innovation Innovation is largely responsible for economic growth Distorting the behavior of a small group of innovators can affect all our incomes To Do: Endogenize S b financed by government? 43 / 43