Taxing Top Incomes in a World of Ideas Chad Jones September 2019 - PowerPoint PPT Presentation

Taxing Top Incomes in a World of Ideas Chad Jones September 2019 0 / 47

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 + τ z ′ m ( τ ) = 0 mechanical gain behavioral loss • Divide by z m ⇒ elasticity form and rearrange: 1 τ ∗ = 1 + α · η z m , 1 − τ z m where α = z . z m − ¯ 1 / 47

1 τ ∗ = 1 + α · η z m , 1 − τ • Intuition ◦ Decreasing in η z m , 1 − τ : elasticity of top income wrt 1 − τ α = z m − ¯ z ◦ Increasing in 1 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 / 47

Overview • Saez (2001) and following literature “Macro”-style calibration of optimal top income taxation • 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) ◦ A small number of entrepreneurs ⇒ the bulk of economy-wide growth • ↑ τ lowers consumption throughout the economy via nonrivalry 3 / 47

Literature • 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 / 47

This paper does not calculate “the” optimal top tax rate • Many other considerations: ◦ Political economy of inequality ◦ Occupational choice (other brackets, concavity) ◦ Top tax diverts people away from finance to ideas? ◦ Social safety net, lenient bankruptcy insure the downside ◦ How sensitive are entrepreneurs to top tax rates? ◦ Empirical evidence on growth and taxes ◦ Rent seeking, human capital • Still, including economic growth and ideas seems important 5 / 47

Basic Setup 6 / 47

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 “workers” ◦ Maximize utilitarian social welfare 7 / 47

Environment for Full Growth Model � A t 0 x 1 − ψ di ( E ( ez ) M t ) ψ Final output Y t = it Production of variety i x it = ℓ it � Resource constraint ( ℓ ) ℓ it di = L t Resource constraint ( N ) L t + S bt = N t N t = ¯ Population growth N exp ( nt ) S at = ¯ Entrepreneurs S a exp ( nt ) M t = ¯ Managers M exp ( nt ) ˙ a ( E ( ez ) S at ) λ A φ a t B α Applied ideas A t = ¯ t B t = ¯ ˙ bt B φ b bS λ Basic ideas t z i ∼ F ( z ) Talent heterogeneity u ( c , e ) = θ log c − ζ e 1 /ζ Utility ( S a , M ) 8 / 47

The Economic Environment • Consumption goods produced by managers ˜ M , labor L , and nonrival “applied” ideas A : Y = A γ ˜ M ψ L 1 − ψ (1) • Applied ideas produced from entrepreneurs, effort e , talent z , and basic research ideas B : ˙ a ( E ( ez ) S at ) λ A φ a t B α A t = ¯ t • Fundamental ideas produced from basic research: B t = ¯ ˙ bt B φ b bS λ t • ˜ M , L , S a , S b exogenous. e , z endogenous (unspecified for now) 9 / 47

Nonrivalry of Ideas (Romer): Y = A γ ˜ M ψ L 1 − ψ • Constant returns to rival inputs ˜ M , 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... 10 / 47

BGP from a Dynamic Growth Model • 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. • Stock of applied ideas (being careless with exponents wlog) A = ν a E [ ez ] S a B β (2) • Stock of basic ideas B = ν b S b (3) 11 / 47

Output = Consumption: • Combining (1) - (3) with ˜ M = E [ ez ] M : � � γ ν E [ ez ] S a S β ( E [ ez ] M ) ψ L 1 − ψ Y = b ◦ Output per person y ∝ ( 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 ) : ◦ ψ effect is traditional, but ψ small? ◦ γ effect via nonrivalry of ideas, can be large! 12 / 47

Nonlinear Income Tax Revenue T = τ 0 [ wL + wS b + w a E ( ez ) S a + w m E ( ez ) M ] � �� � all income pays τ 0 + ( τ − τ 0 )[( w a E ( ez ) − ¯ w ) S a + ( w m E ( ez ) − ¯ w ) M ] � �� � income above ¯ w pays an additional τ − τ 0 • Full growth model: entrepreneurs paid a constant share of GDP w a E ( ez ) S a w m E ( ez ) M = ρ s and = ρ m . Y Y and Y = wL + w b S b + w a E ( ez ) S a + w m E ( ez ) M , ρ ≡ ρ s + ρ m ⇒ T = τ 0 Y + ( τ − τ 0 ) [ ρ Y − ¯ w ( S a + M )] 13 / 47

Some Intuition • Entrepreneurs/managers paid a constant share of GDP w a E ( ez ) S a w m E ( ez ) M = ρ s and = ρ m . Y Y � � γ ν E [ ez ] S a S β ( E [ ez ] M ) ψ L 1 − ψ • Production: Y = b • Efficiency: Pay ∼ Cobb-Douglas exponents. IRS means cannot! • Jones and Williams (1998) social rate of return calculation: � � ρ s ( 1 − τ ) − 1 1 ˜ r = g Y + λ g y γ ⇒ After tax share of payments to entrepreneurs should equal γ ρ s ( 1 − τ ) versus γ is one way of viewing the tradeoff 14 / 47

The Top Tax Rate that Maximizes Revenue 15 / 47

Revenue-Maximizing Top Tax Rate • Key policy problem: T = τ 0 Y + ( τ − τ 0 ) [ ρ Y − ¯ max w ( S a + M )] τ s.t. � � γ ν E [ ez ] S a S β ( E [ ez ] M ) ψ L 1 − ψ Y = b • A higher τ reduces the effort of entrepreneurs/managers ◦ Leads to less innovation ◦ which reduces everyone’s income ( Y ) ◦ which lowers tax revenue received via τ 0 16 / 47

Solution T = τ 0 Y ( τ ) + ( τ − τ 0 ) [ ρ Y ( τ ) − ¯ max wS a ] τ • FOC: + ∂ Y ( ρ − ¯ ρ ) Y ∂τ · [( 1 − ρ ) τ 0 + ρτ ] = 0 � �� � � �� � mechanical gain behavioral loss ρ ≡ ¯ w ( S a + M ) where ¯ Y • Rearranging with ∆ ρ ≡ ρ − ¯ ρ 1 − τ 0 · 1 − ρ ∆ ρ · η Y , 1 − τ τ ∗ rm = ρ 1 + ∆ ρ η Y , 1 − τ 17 / 47

Solution 1 − τ 0 · 1 − ρ ∆ ρ · η Y , 1 − τ 1 τ ∗ rm = τ ∗ ds = vs ρ 1 + ∆ ρ η Y , 1 − τ 1 + α · η z m , 1 − τ • Remarks: Two key differences ◦ η Y , 1 − τ versus η z m , 1 − τ η Y , 1 − τ ⇒ How GDP changes if researchers keep more η z m , 1 − τ ⇒ How average top incomes change ◦ If τ 0 > 0 , then τ ∗ is lower Distorting research lowers GDP ⇒ lowers revenue from other taxes! 18 / 47

Guide to Intuition η Y , 1 − τ The economic model ρ η 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 19 / 47

What is η Y , 1 − τ ? � � γ ν E [ ez ] S a S β ( E [ ez ] M ) ψ L 1 − ψ Y = ⇒ η Y , 1 − τ = ( γ + ψ ) ζ b • γ = degree of IRS via ideas • ψ = manager’s share = 0.15 (not important) • ζ is the elasticity of E [ ez ] with respect to 1 − τ . ◦ Standard Diamond-Saez elasticity: ζ = η z m , 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) 20 / 47

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 re- turns account for 20% of taxable income. ρ = 0 . 15 ρ So ∆ ρ = 1 . 5 as in Saez pareto parameter, α . 21 / 47

Revenue-Maximizing Top Tax Rate, τ ∗ rm Behavioral Elasticity Case 0.20 0.50 Diamond-Saez: 0.80 0.67 No ideas, γ = 0 τ 0 = 0 : 0.96 0.93 τ 0 = 0 . 20 : 0.92 0.85 Degree of IRS, γ 1/8 0.86 0.74 1/4 0.81 0.64 1/2 0.70 0.48 1 0.52 0.22 22 / 47

Revenue-Maximizing Top Tax Rate, τ ∗ rm Behavioral Elasticity Case 0.20 0.50 Diamond-Saez: 0.80 0.67 No ideas, γ = 0 τ 0 = 0 : 0.96 0.93 τ 0 = 0 . 20 : 0.92 0.85 Degree of IRS, γ 1/8 0.86 0.74 1/4 0.81 0.64 1/2 0.70 0.48 1 0.52 0.22 23 / 47

Revenue-Maximizing Top Tax Rate, τ ∗ rm Behavioral Elasticity Case 0.20 0.50 Diamond-Saez: 0.80 0.67 No ideas, γ = 0 τ 0 = 0 : 0.96 0.93 τ 0 = 0 . 20 : 0.92 0.85 Degree of IRS, γ 1/8 0.86 0.74 1/4 0.81 0.64 1/2 0.70 0.48 1 0.52 0.22 24 / 47