Increasing the overall tax progressivity or the tax rate on the top 1% of earners can increase government revenues. However, increasing the tax rate on just the top 1% raises revenues more substantially - by 16% compared to 5% from increasing overall progressivity. This is because directly targeting top earners brings in more income tax revenue. Both tax changes modestly lower labor supply and the capital stock.

1. Revisiting tax on top income
Ay¸se ˙Imrohoro˘glu Cagri S. Kumru Arm Nakornthab
USC Marshall ANU ANU
EUI

2. Taxing top income
• Increase in income inequality
• Renewed interest in optimal marginal tax rates of top earners
• Different papers with significantly different results
• Diamond and Saez (2011): marginal tax rates on top earners 73%.
• Badel and Huggett (2015) and Guner, Daneri, and Ventura (2016):
52%-49% and 35%
• Kindermann and Kruger (2017): 90%.

3. Taxing top income
• Need a model that can generate a reasonable income and wealth
distribution
• Kindermann and Kruger (2017): superstars with temporary
productivity shocks
• Badel and Huggett (2015) : risky human-capita investments
• Guner, Daneri, and Ventura (2016): Superstars for life
• We model entrepreneurs

4. Taxing top income
• Entrepreneurs earn 17% of total income and
• 40% of the top 1% income earners are entrepreneurs
• Follow Cagetti and DeNardi (2009) to generate the appropriate
distribution of wealth inequality
• Endogenize labor supply of workers and the entrepreneurs

5. Taxing top income
• We examine two changes in the tax code
• Increasing the overall tax progressivity
• Increasing the tax rate for the top 1% of earners
• For both reforms find the revenue and welfare maximizing tax rates

6. Taxing top income
Figure 1: Tax Rates

7. Model
• Simplified life-cycle model
• Young and old cohorts in the economy with stochastic aging
• young stay young with probability πy and
• get old with a probability 1 − πy

8. Model
• Old
• continue to live with a constant probability πo and
• die with a probability 1 − πo
• When the old die, their offsprings receive their assets as bequests
• Each household has only one offspring
• Young individuals: either be a worker or an entrepreneur
• Old individuals: stay as an entrepreneur (if an entrepreneur
before) or become a retiree

9. Technology
• Two production sectors: corporate and entrepreneurial sector
• People have two types of abilities, working or entrepreneurial
• Types are stochastic and positively correlated over time
• Entrepreneurs can borrow (depending on their current wealth),
invest in capital, hire labor, and produce
• The return from the production technology depends on
entrepreneurial ability

10. Technology
• When the entrepreneur invests kt , the output is given by
f(kt , nt ) = θt kγ
t (lt + nt )1−γ
ν
• 0 ≤ γ ≤ 1 : share of entrepreneurial capital
• θt : entrepreneurial productivity
• ν < 1 indicates the decreasing returns to scale
• lt : entrepreneurs own labor
• nt : hired labor

11. Technology
• Corporate sector
F(Kc
t , Lc
t ) = A(Kc
t )α
(Lc
t )1−α
• capital in the corporate sector: KC
t
• labor in the corporate sector: LC
t

12. Government
• Collects taxes,
• Pays a pension benefit p to each retiree,
• Provides goods and services as a fraction g of output

13. Government: The total amount of income tax
(Benabou (2002))
Tt (Yt ) =



(1 − λY−τ
t )Yt + τbal
t Yt + τk
t rt at if Yt < YH
(1 − λY−τ
H )YH + τbal
t YH + τk
t rt at + τH ∗ (Yt − YH ) if Yt > YH
• Yt : total taxable income (labor+capital income)
• τbal
t : proportional income tax rate (State and local tax)
• τk
t : corporate income tax
• τ : governs the curvature of the tax function.
• yH : income threshold for those having income in top 1%
• τH : the marginal tax rate at top 1%

14. Young Individual’s Problem
• Young individuals: either a worker or an entrepreneur.
• The value function of a young individual:
VY
t (at , yt , θt ) = max VY,e
t (at , yt , θt ), VY,w
t (at , yt , θt )
• VY,e
t (at , yt , θt ): Value fn. young entrepreneur
• VY,w
t (at , yt , θt ): Value fn. young worker

15. Young Worker’s Problem
VY,w
t (at , yt , θt ) = max
ct ,lt ,at+1
{u(ct , 1−lt )+βπy Et VY
t+1(at+1, yt+1, θt+1) +β(1−πy )VO,r
t+1 (at+1)}
subject to
Yw
t = wt lt yt + rt at ,
(1 + τc
t )ct + at+1 = wt lt yt + (1 + rt )at − Tt (Yw
t ),
0 ≤ lt ≤ 1,
0 ≤ at+1,

16. Young Entrepreneur’s Problem
VY,e
t (at , yt , θt ) = max
ct ,lt ,kt ,nt ,at+1
{u(ct , 1 − lt ) + βπy Et VY
t+1(at+1, yt+1, θt+1)
+β(1 − πy )Et VO
t+1(at+1, θt+1)}
subject to
Ye
t = θt kγ
t (lt + nt )1−γ
ν
− δkt − rt (kt − at ) − wt nt ,
(1 + τc
t )ct + at+1 = Ye
t − Tt (Ye
t ) + at ,
0 ≤ at+1,
0 ≤ nt ,
0 ≤ lt ≤ 1,
0 ≤ kt ≤ (1 + d)at .
• Ye
t : entrepreneur’s total profit
• d : exogenous borrowing limit

17. Old Individual’s Problem
• Old individuals choice
• stay as an entrepreneur (if was an entrepreneur previously) or
• become a retiree
VO
t (at , θt ) = max VO,e
t (at , θt ), VO,r
t (at )

18. Old Retiree’s Problem
VO,r
t (at ) = max
ct ,at+1
{u(ct , 1) + βπoVO,r
t+1 (at+1) + β(1 − πo)Et [VY
t+1(at+1, yt+1, θt+1)]}
subject to
(1 + τc
t )ct + at+1 = (1 + rt )at + p − Tt (rt at + p)
0 ≤ at+1.
VY
t+1(at+1, yt+1, θt+1): the offspring’s value function

19. Old Entrepreneur’s Problem
VO,e
t (at , θt ) = max
ct ,lt ,kt ,nt ,at+1
{u(ct , 1 − lt ) + βπoEt [VO
t+1(at+1, θt+1)]
+β(1 − πo)Et VY
t+1(at+1, yt+1, θt+1) }
subject to
Ye
t = θt kγ
t (lt + nt )1−γ
ν
− δkt − rt (kt − at ) − wt nt ,
(1 + τc
t )ct + at+1 = Ye
t − Tt (Ye
t ) + at ,
0 ≤ at+1,
0 ≤ nt ,
0 ≤ lt ≤ 1,
0 ≤ kt ≤ (1 + d)at .

20. Calibration
• Workers productivity : Enhanced version of Kaplan (2012)
• Idiosyncratic labor productivity, y takes 6 values
• (0.16, 0.30, 0.57, 1.08, 2.05, 11.48)
• Highest earning realization y6 has a very low probability of
happening
• Choose the productivity matrix to match the labor earnings Gini
(0.51)

21. Calibration
• Entrepreneurs’ productivity: Enhanced version of Cagetti and De
Nardi (2009)
• Two productivity types θ1 and θ2
• θ2 is a highly successful entrepreneur (θ1 = 1.8, θ2 = 2.75)
• Match the Income Gini of the entrepreneurs (data: 0.66)
• Match the % of entrepreneurs on top 1% of income (data: 40%)

22. Calibration
Transition function for entrepreneurs
θ0: No entrepreneurial ability


π(θ0|θ0) π(θ1|θ0) π(θ2|θ0)
π(θ0|θ1) π(θ1|θ1) π(θ2|θ1)
π(θ0|θ2) π(θ1|θ2) π(θ2|θ2)

 =


0.98 0.023 0
0.24 0.76 0.000075
0 0.025 0.9775



23. Calibration
Table 1: Fixed parameters
Parameter Value
Preferences, technology, and demographics
Risk aversion σ 1.5
Inverse of Frisch elasticity σ2 1.67 Frisch elasticity = 0.59
Capital share α 0.33
Probability of staying young πy 0.978 Av. working life: 45 years
Probability of staying old πo 0.911 Av. retirement life: 11 years
Depreciation δ 0.06
Entr. return to scale ν 0.88
Entr. borrowing constraint d 0.5
Labor income process and social security payments
Autocorrelation ρ 0.958
Pension (as a % of average income) p 40%

24. Calibration
Table 2: Fixed parameters
Parameter Value
Public purchases, government debt, and taxes
Government debt / total capital D 0.27
Consumption tax τc 5%
State and local tax τbal
5%
Revenue requirement λ 0.911
Tax progressivity τ 0.053

25. Calibration
Table 3: Calibrated Parameters
Calibrated parameter Value
Discount factor β 0.9396
Entrepreneurial ability {θ0, θ1, θ2} {0, 1.8, 2.75}
Entr. transition probabilities transition matrix
Entr. capital share γ 0.45
Disutility from working χ 1.9
Standard deviation of productivity shock σy 0.18
Value of highest productivity y6 11.5
Probability of having highest productivity π6 0.002
Probability of staying highest productivity π66 0.9307

26. Benchmark Economy
Table 4: Target moments
Targets Data Model
Capital to output ratio 2.9 2.9
% Entrepreneurs 7.5-7.6 7.2
% Exiting Entrepreneurs 22-24 24
% Workers to Entrepreneurs 2-3 2.34
% Hiring entrepreneurs 57.4-64.6 65
% Average worked hours 33 33.4

27. Benchmark Economy
Table 5: Target moments
Targets Data Model
Income distribution
Income Gini 0.55 0.56
Entr. income Gini 0.66 0.62
Worker earnings Gini 0.51 0.51
99-100% income 17.2 21.2
95-99% income 16.6 18.9
% entr. on top 1% income 40 35.3
Wealth distribution
Wealth Gini 0.85 0.84
99-100% wealth 34.1 34.5
95-99% wealth 26.8 28.7
% People at zero wealth 7-13 13.8
Ratio of median net worth entr. to workers 5.3-6.5 5.2

28. Benchmark Economy
Table 6: Income distribution in the benchmark economy
Share of income (in %)
Income quintiles Top
0-20% 20-40% 40-60% 60-80% 80-100% 90-95% 95-99% 99-100% Gini
Data 3 6.5 10.9 18.1 61.4 10.7 16.6 17.2 0.58
Model 4.1 7.7 11.5 16.9 59.8 8.5 18.9 22.2 0.56

29. Benchmark Economy
Table 7: Wealth distribution in the benchmark economy
Share of wealth (in %)
Wealth quintiles Top
0-20% 20-40% 40-60% 60-80% 80-100% 90-95% 95-99% 99-100% Gini
Data -0.7 0.7 3.3 9.9 86.7 13.5 26.8 34.1 0.85
Model 0.2 0.8 3.8 7.9 87.2 13.1 28.7 34.5 0.84

30. Benchmark Economy
Table 8: Share of tax payments in benchmark economy
Share of tax (in %)
Income quintiles
0-20% 20-40% 40-60% 60-80% 80-100%
Data 0.3 2.2 6.9 15.9 74.6
Model 1.2 3.4 6.6 11.4 77.5

31. Results: Changes in Tax Rates
What are the consequences of increasing the overall progressivity
of taxes versus increasing the tax rate of the richest 1% on
• Government revenues
• Find the revenue maximizing τ
• Find the revenue maximizing τH
• Welfare
• Find the welfare maximizing τ
• Find the welfare maximizing τH

32. Results: Revenue maximization
Table 9: Changes in Progressivity-Revenue Maximizing
Progressivity τ=0.035 τ=0.05 τ=0.07 τ=0.09 τ=0.10 τ=0.12 τ=0.15
Output 104.4 100.3 99.0 94.9 94.0 91.8 88.4
Labor supply 104.8 100.0 99.9 99.0 98.9 98.4 98.0
Capital 109.6 101.3 97.3 86.3 84.9 80.9 74.7
Revenues
Federal income tax 96.0 99.0 102.7 105.27 105.33 104.0 97.7
State and local taxes 102.9 100.1 98.2 96.9 96.2 94.6 92.0
Corporate income tax 23.0 80.4 196.6 275.8 296.3 350.3 415.9
All taxes 98.9 99.5 101.0 102.0 101.8 100.5 96.2
Worker avg. hours worked 104.8 100 99.4 99 98.9 98.4 98.1
Entr. avg. hours worked 100.7 100 95.2 94 91.5 87.7 86.2
Labor supply in corp sector 106 100.3 97.8 96.7 98.2 100.1 102.4
Labor supply in entr. sector 101.5 99.7 100.4 100.6 99.6 98.1 95
Capital in corp sector 111.9 101.5 91.1 84.5 84.3 81.9 78.2
Capital in entr. sector 107.1 100.7 93.7 88.2 85.5 79.9 71.2

33. Results: Revenue maximization
If the purpose is revenue maximization: Increase the tax rate on top
1% of income earners
• Revenues from federal income increase by
• 5% when progressivity is increased
• 16% when the top tax rate is increased
Why?

34. Results: Revenue maximization
• Both changes in taxes (increase in τ and the increase in τH)
• Lower the labor supply by similar amounts (around 1%)
• Capital stock declines by
• 15% if overall progressivity is increased
• 8% if the top tax rate is increased

35. Results: Revenue maximization
• Why does capital stock react differently?
• Remember only 35% of entrepreneurs are on the top 1%
• When overall progressivity is increased more entrepreneurs are hit
• Capital stock of the entrepreneurs declines by
• 14.5% when overall progressivity is increased
• 11.2% when the top tax rate is increased

36. Results: Revenue maximization
• Also, even though labor supply declines are similar in both tax
experiments
• Hours worked by entrepreneurs reacts differently
• Declines by 8.5% when overall progressivity is increased
• Declines by 2.3% when the top tax rate is increased
• Thus, the decline in output is smaller with an increase in τH
instead of an increase in τ

37. Results: Welfare Maximization
If the purpose is welfare maximization: Increase the overall
progressivity (τ = 0.15)
Why?

38. Results: Welfare Maximization
• Share of tax payments by the lower income people much lower
with (τ = 0.15)
Table 10: Share of tax payments
Income Quantiles Bench. τ = .15 τH = 0.55
0-20% 1.2 -4.2 0.9
20-40% 3.4 -3.2 2.7
40-60% 6.6 0.1 5.5
60-80% 11.4 5.2 9.8
80-100% 77.5 102.2 81.0

39. Results: Welfare Maximization
• Wealth distribution for the lower income people better with
(τ = 0.15)
Table 11: Wealth Distribution
Wealth Quantiles Bench. τ = .15 τH = 0.55
0-20% 0.2 0.1 0.2
20-40% 0.8 1.6 1.0
40-60% 3.8 5.7 4.2
60-80% 7.9 11.2 9.2
80-100% 87.2 81.4 85.4

40. Results: Welfare Maximization
• Both changes in taxes do the following
• While overall output declines
• Consumption of certain groups rise
• Hours worked by certain groups fall
• Variance of consumption declines

41. Results: Welfare Maximization
• Consider the largest group YW (73.4% of the population)
• Changes in consumption and hours worked varies across income
quantiles
• With τ = .15
• there is a 45% increase in the average consumption of the YW in
the 34-66% income quantile while a 7% decline in hours worked.
• With τH = 0.55
• Consumption of YW in the 34-66% income quantile increases by
39% while hours worked declines by 3%

42. Results: Welfare Maximization
• Variance of consumption for those in the bottom 99% of the
income distribution
• About 60% lower with τ = 0.15
• About 20% lower with τH = 0.55

43. Results: Wealth Inequality
If the purpose is to reduce wealth inequality: Increase the overall
progressivity (τ = 0.15)
• Benchmark Wealth Gini: 0.84
• With τ = 0.15: Wealth Gini: 0.79
• With τH = 0.55: Wealth Gini: 0.82

44. Optimal Tax Rates
Table 12: Tax rates - welfare maximizing
Marginal Tax Rates
Percentiles of income Benchmark τ=0.15 τH =0.55
Top 10% 16.9 29.6 20.1
Top 5% 19.5 35.6 22.3
Top 1% 22.9 42.2 55.0

45. Optimal Tax Rates: Comparing Different Papers
Comparing different papers
• Guner et al. [2016]: change overall progressivity of income
(capital+labor) tax function to find revenue maximizing tax
schemes
• They find federal income marginal tax rate of 36.6% for the richest
5% of households
• For the same type of experiment we find 35.6%

46. Optimal Tax Rates: Comparing Different Papers
• Badel and Huggett [2015] analyze the change in the top tax rate
on general income (capital and labor)
• They find: tax rate of 49% for top 1%
• For the same type of experiment we find 55%

47. Optimal Tax Rates: Comparing Different Papers
• Kindermann and Krueger [2017] alter the top tax rate on labor
earnings and calculate both revenue and welfare maximizing rates
• They find 90% optimal revenue and welfare maximizing tax rate
for the richest 1% of the population
• If we tax only the labor income we find the optimal tax rate on the
richest 1% as 80%

48. Conclusions
• Model with entrepreneurship
• Realistic income and wealth distribution
• Higher marginal tax rates than what is observed
• Lower than some estimates in the literature