Top MTR. Threshold/Averag e Income. US Top Marginal Tax Rate and Top Bracket Threshold. Top MTR (Federal Individual Income Tax)

Transcription

1 Source: IRS, Statistics of Income Division, Historical Table 23

2 Top Marginal Tax Rate and Top Bracket Threshold Top MTR (Federal Individual Income Tax) 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% Top MTR Threshold/Averag e Income 0% Top Bracket Threshold/Average Income 1 Source: statistics computed by the author

3 $50,000 Tax/Transfer System, single parent with 2 children, 2009 $50,000 $40,000 $40,000 Welfare: TANF+SNAP Disposable arnings $30,000 $20,000 $10,000 $30,000 $20,000 $10,000 Tax credits: EITC+CTC Earnings after Fed+SSA taxes 45 Degree Line $0 $0 $0 $10,000 $20,000 $30,000 $40,000 $50,000 Gross Earnings (with employer payroll taxes) Source: Federal Govt

4 SAEZ ELASTICITIES AND INCOME TAXES 209 -Before reform schedule - - After reform schedule Slope 1- r - Slope I-t_-dt -i _ - ~Uncompensated change 0 Before tax income z FIGURE 1 Source: Saez (2001), p. 209 High income tax rate perturbation

5 FIGURE 2 Ratio mean income above z divided by z, z m /z, years 1992 and 1993 Coefficient z m /z year 1992 year 1993 Coefficient z m /z year 1992 year $0 $100K $200K $300K $400K $500K Wage Income z 1 $10K $100K $1,000K $10,000K Wage Income z Source: Saez (2001), p. 211

6 -Before reform schedule - After reform schedule E._ ~~~~~~Slope I-,r-dr Substitution effect Income effect z*+dz* Before tax income z Source: Saez (2001), p. 216 FIGURE 3 Local marginal tax rate perturbation

7 FIGURE 4 Hazard Ratio (1 H(z))/(zh(z)), years 1992 and year 1992 year Coefficient (1 H(z))/(zh(z)) Source: Saez (2001), p. 219 $0 $100,000 $200,000 $300,000 $400,000 $500,000 Wage Income z

8 FIGURE 5 Optimal Tax Simulations 1 Utilitarian Criterion, Utility type I 1 Utilitarian Criterion, Utility type II Marginal Tax Rate ζ c =0.25 ζ c =0.5 Marginal Tax Rate ζ c =0.25 ζ c =0.5 0 $0 $100,000 $200,000 $300,000 Wage Income z 0 $0 $100,000 $200,000 $300,000 Wage Income z Marginal Tax Rate Rawlsian Criterion, Utility type I ζ c =0.25 ζ c =0.5 Marginal Tax Rate Rawlsian Criterion, Utility type II ζ c =0.25 ζ c =0.5 0 $0 $100,000 $200,000 $300,000 Source: Saez (2001), p. 224 Wage Income z 0 $0 $100,000 $200,000 $300,000 Wage Income z

9 Reform: Increase τ 1 by dτ 1 and c 0 by dc 0 =z 1 dτ 1 Disposable Income c 1) Mechanical fiscal cost: dm=-h 0 dc 0 =-H 0 z 1 dτ 1 2) Welfare effect: dw=g 0 H 0 dc 0 =g 0 H 0 z 1 dτ 1 3) Fiscal cost due to behavioral responses: db=-dh 0 τ 1 z 1 = dτ 1 e 0 H 0 τ 1 /(1-τ 1 ) z 1 c 0 +dc 0 c 0 0 Slope 1-τ 1 45 o z1 Optimal phase-out rate τ 1 : dm+dw+db=0 à τ 1 /(1-τ 1 ) = (g 0-1)/e 0 Earnings z

10 Starting from a Means-Tested Program Consumption c G 0 45 o w* Earnings w Source: revised version of Saez (2002), p. 1050

11 Consumption c Starting from a Means-Tested Program Introducing a small EITC is desirable for redistribution G 0 45 o w* Earnings w Source: revised version of Saez (2002), p. 1050

12 Consumption c Starting from a Means-Tested Program Introducing a small EITC is desirable for redistribution Participation response saves government revenue G 45 o w* 0 Earnings w Source: revised version of Saez (2002), p. 1050

13 Consumption c Figure 3a: Optimal Tax/Transfer Derivation c 2 c 1 c o w1 w 2 Wage w Source: revised version of Saez (2002), p. 1052

14 Figure 3a: Optimal Tax/Transfer Derivation (assuming g 1 >1) Consumption c Welfare Effect: h 1 g 1 dc 1 >0 c 2 Fiscal Effect: -h 1 dc 1 <0 c 1 +dc 1 c 1 c o w1 w 2 Wage w Source: revised version of Saez (2002), p. 1052

15 Figure 3a: Optimal Tax/Transfer Derivation (assuming g 1 >1) Consumption c Net Welfare effect: h 1 dc 1 (g 1-1)>0 c 2 Labor Supply: dh 1 w 1 τ 1 <0 c 1 +dc 1 c 1 c o w1 w 2 Wage w Source: revised version of Saez (2002), p. 1052

16 Figure 3a: Optimal Tax/Transfer Derivation (assuming g 1 >1) Consumption c Net Welfare effect: h 1 dc 1 (g 1-1)>0 c 2 Labor Supply: dh 1 w 1 τ 1 <0 c 1 +dc 1 c 1 c 0 At the optimum: dh 1 w 1 τ 1 + h 1 dc 1 (g 1-1)=0 implies τ 1 /(1-τ 1 )=(1-g 1 )/e 1 < o w1 w 2 Wage w Source: revised version of Saez (2002), p. 1052

17 2. Optimal Tax/Transfer System (no min wage) Consumption c c 2 c 1 c o w1 w 2 Wage w Source: Lee and Saez (2008)

18 2. Set Min wage w=w 1 and increase c 1 by dc 1 Consumption c Welfare Effect > Direct Fiscal Effect if govt values redistribution to low skill workers c 2 c 1 +dc 1 c 1 c 0 45 o 0 w=w 1 w 2 Wage w Source: Lee and Saez (2008)

19 2. Desirability of Min Wage with Optimal Taxes Consumption c Welfare Effect > Direct Fiscal Effect if govt values redistribution to low skill workers c 2 c 1 +dc 1 c 1 dc 1 >0 makes low skilled job w 1 more attractive would reduce w 1 through demand effects c o w=w1 w 2 Wage w Source: Lee and Saez (2008)

20 2. Desirability of Min Wage with Optimal Taxes Consumption c Welfare Effect > Direct Fiscal Effect if govt values redistribution to low skill workers c 2 c 1 +dc 1 c 1 With min wage set at w 1, dc 1 >0 does not affect labor supply because w 1 cannot go down c o w=w1 No indirect fiscal effect Welfare increases w 2 Wage w Source: Lee and Saez (2008)

21 Consumption c 3. Pareto Improving Policy when τ 1 >0 and min wage binds c 2 c 1 τ 1 >0 = Tax on low skilled work: c 1 -c 0 < w c o w w 2 Wage w Source: Lee and Saez (2008)

22 Consumption c 3.Pareto Improving Policy when τ 1 >0 and min wage binds c 2 c 1 c 0 Reduce w while keeping c 1, c 2 constant: No direct fiscal effect of dw, dw 2 as h 1 dw+h 2 dw 2 =0 (no profits) and tax=(w-c 1 ) h 1 +(w 2 -c 2 ) h 2 45 o dw<0 0 dw 2 >0 Wage w Source: Lee and Saez (2008)

23 3. Pareto Improving Policy when τ 1 >0 and min wage binds Consumption c Unemployment decreases New Workers better off and pay more taxes Pareto Improvement c 2 c 1 c 0 Reduce w while keeping c 1, c 2 constant: No direct fiscal effect of dw, dw 2 as h 1 dw+h 2 dw 2 =0 (no profits) and tax=(w-c 1 ) h 1 +(w 2 -c 2 ) h 2 45 o dw<0 0 dw 2 >0 Wage w Source: Lee and Saez (2008)

24 Optimal Top Income Tax Rate (Mirrlees 71 model) Disposable Income c=z-t(z) Top bracket: Slope 1-τ z*-t(z*) Reform: Slope 1-τ dτ 0 Source: Diamond and Saez JEP'11 z* Market income z

25 Optimal Top Income Tax Rate (Mirrlees 71 model) Disposable Income c=z-t(z) Mechanical tax increase: dτ[z-z*] z*-t(z*) Behavioral Response tax loss: τ dz = - dτ e z τ/(1-τ) 0 z* z Market income z Source: Diamond and Saez JEP'11

26 Empirical Pareto Coefficient z* = Adjusted Gross Income (current 2005 $) a=zm/(zm-z*) with zm=e(z z>z*) alpha=z*h(z*)/(1-h(z*)) Source: Diamond and Saez JEP'11

27 Top 1% Income Share (%) A. Top 1% Income Shares and Top MTR Top 1% (excl. KG) Top MTR Top Marginal Tax Rates Year Source: Piketty, Saez, and Stantcheva NBER'11

28 Top 1% Income Shares (%) B. Top 1% Income Shares and Top MTR Top 1% (excl. KG) MTR K gains Top 1% Share (incl. KG) Top MTR Marginal Tax Rates (%) Year Source: Piketty, Saez, and Stantcheva NBER'11

29 Real Income per adult (1913=100) C. Top 1% and Bottom 99% Income Growth Top 1% Top MTR Bottom 99% Marginal Tax Rate (%) Year Source: Piketty, Saez, and Stantcheva NBER'11

30 Top 1% Income Share (%) Top Marginal Tax Rate (%) A. Top 1% Share and Top Marginal Tax Rate in Source: Piketty, Saez, and Stantcheva NBER'11

31 Top 1% Income Share (%) Top Marginal Tax Rate (%) B. Top 1% Share and Top Marginal Tax Rate in Source: Piketty, Saez, and Stantcheva NBER'11

32 Change in Top 1% Income Share (points) Change in Top Marginal Tax Rate (points) A. Changes Top 1% Share and Top Marginal Tax Rate Source: Piketty, Saez, and Stantcheva NBER'11

33 GDP per capita real annual growth (%) Change in Top Marginal Tax Rate (points) B. Growth and Change in Top Marginal Tax Rate Source: Piketty, Saez, and Stantcheva NBER'11

34 Disposable Income c=z-t(z) Small band (z,z+dz): slope 1- T (z) Reform: slope 1- T (z) d Mechanical tax increase: d dz [1-H(z)] Social welfare effect: -d dz [1-H(z)] G(z) d dz Behavioral response: z= -d e z/(1-t (z)) Tax loss: T (z) z h(z)dz = -h(z) e z T (z)/(1-t (z)) dzd 0 z z+dz Pre-tax income z Source: Diamond and Saez JEP'11

35 Reform: Increase 1 by d 1 and c 0 by dc 0 =z 1 d 1 Disposable Income c g 0 >>1 welfare effect >> mechanical fiscal cost c 0 +dc 0 c 0 Slope o z1 Earnings z Source: Diamond and Saez JEP'11

36 Reform: Increase 1 by d 1 and c 0 by dc 0 =z 1 d 1 Disposable Income c g 0 >>1 welfare effect >> mechanical fiscal cost Fiscal cost due to behavioral responses proportional to 1 /(1-1 ) and elasticity e 0 =(1-1 )/H 0 dh 0 /d(1-1 ) c 0 +dc 0 c 0 0 Slope o z1 Optimal phase-out rate 1 : 1 = (g 0-1)/(g 0-1+ e 0 ) Example: if g 0 =3 and e 0 =0.5, 1 =80% Earnings z Source: Diamond and Saez JEP'11

37 Reform: Increase 1 by d 1 and c 0 by dc 0 =z 1 d 1 Disposable Income c 1) Mechanical fiscal cost: dm=-h 0 dc 1 =-H 0 z 1 d 1 2) Welfare effect: dw=g 0 H 0 dc 1 =g 0 H 0 z 1 d 1 3) Fiscal cost due to behavioral responses: db=-dh 0 1 z 1 = d 1 e 0 H 0 1 /(1-1 ) z 1 c 0 +dc 0 c 0 0 Slope o z1 Optimal phase-out rate 1 : dm+dw+db=0 1 /(1-1 ) = (g 0-1)/e 0 Earnings z

38 Disposable Income c Starting from a positive phasing-out rate 1 >0: 1) Increasing transfers by dc 1 at z 1 is desirable for redistribution: net effect (g 1-1)h 1 dc 1 > 0 if g 1 >1 2) Participation response saves government revenue 1 z 1 dh 1 = e 1 1 /(1-1 ) h 1 dc 1 >0 Win-win reform if intensive response is small c 0 Optimal phase-out rate 1 : (g 1-1)h 1 dc 1 + e 1 1 /(1-1 ) h 1 dc 1 = 0 Slope /(1-1 ) = (1-g 1 )/e 1 < 0 if g 1 > o z2 z 1 Earnings z

39 EITC Amount as a Function of Earnings EITC Amount ($) Subsidy: 40% Subsidy: 34% Phase-out tax: 16% Married, 2+ kids Single, 2+ kids Married, 1 kid Single, 1 kid No kids Phase-out tax: 21% Source: Federal Govt Earnings ($)

40 Source: Piketty, Thomas, and Emmanuel Saez (2012)

41 Table 2: Equality of Opportunity vs. Utilitarian Optimal Tax Rates Fraction from low background (=parents below median) above each percentile Equality of Opportunity Implied social welfare weight G(z) above each percentile Implied optimal marginal tax rate at each percentile Utilitarian (log- utility) Utilitarian social welfare weight G(z) above each percentile Utilitarian optimal marginal tax rate at each percentile (1) (2) (3) (4) (5) Income percentile z= 25th percentile 44.3% % % z= 50th percentile 37.3% % % z= 75th percentile 30.3% % % z= 90th percentile 23.6% % % z= 99th percentile 17.0% % % z= 99.9th percentile 16.5% % % Notes: This table compares optimal marginal tax rates at various percentiles of the distribution (listed by row) using an equality of opportunity criterion (in column (3)) and a standard utilitarian criterion (in column (5)). Both columns use the optimal tax formula T'(z)=[1- G(z)]/[1- G(z)+α(z)*e] discussed in the text where G(z) is the average social marginal welfare weight above income level z, α(z)=(zh(z))/(1- H(z)) is the local Pareto parameter (with h(z) the density of income at z, and H(z) the cumulative distribution), and e the elasticity of reported income with respect to 1- T'(z). We assume e=0.5. We calibrate α(z) using the actual distribution of income based on 2008 income tax return data. For the equality of opportunity criterion, G(z) is the representation index of individuals with income above z who come from a disadvantaged background (defined as having a parent with income below the median). This representation index is estimated using the national intergenerational mobility statistics of Chetty et al. (2013) based on all individuals born in with their income measured at age For the utilitarian criterion, we assume a log- utility so that the social welfare weight g(z) at income level z is proportional to 1/(z- T(z)). Source: Saez and Stantcheva (2014)

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44 T(z) Individual Income Tax T(z) is continuous in z slope 39.6% slope 10% slope 15% 0 taxable income z

45 T (z) Marginal Income Tax T (z) is a step function 39.6% 10% 15% 0 taxable income z

46 c= z-t(z) after-tax and transfer income Budget Set slope=1-t (z) -T(0) 0 z pre-tax income z

47 c= z-t(z) τ p =participation tax rate (1 τ p )z -T(0) z 0 pre-tax income z

48 Labor Supply Theory c = consumption Indifference Curve c = wl + R R slope= w Marshallian Labor Supply l(w, R) 0 l labor supply l

49 Labor Supply Theory c = consumption utility u slope= w Hicksian Labor Supply l c (w, u) 0 labor supply l

50 c Labor Supply Income Effect R+ R η = w l R 0 R l(w, R+ R) l(w, R) 0 labor supply l

51 c Labor Supply Substitution Effect utility u slope= w + w slope= w ε c = w l l c w > 0 l c (w, u) l c (w + w, u) 0 labor supply l

52 c Uncompensated Labor Supply Effect ε u = ε c + η income effect η 0 slope= w + w slope= w substitution effect: ε c > 0 l(w, R) 0 l(w + w, R) labor supply l

53 c= z-t(z) Effect of Tax on Labor Supply T(z) < 0: income effect l T (z) > 0: substitution effect l slope=1-t (z) T(z) > 0: income effect l T (z)>0: substitution effect l -T(0) 0 z pre-tax income z

54 Tax Revenue R R = τ Z(1 τ) τ = e Laffer Curve with e = 1 τ Z dz d(1 τ) 0 τ 1 τ: Tax Rate

55 utility Utilitarianism and Redistribution u c 1 + c 2 2 u(c 1 ) + u(c 2 ) 2 0 c 1 c 1 + c 2 c 2 2 consumption c

56 Labor Supply Theory c = consumption Indifference Curves c = (1-t)z+R R Slope=1-τ Marshallian Labor Supply z(1-τ,r) 0 earnings supply z

57 c = consumption Labor Supply Theory utility u Slope=1-τ Hicksian Labor Supply z c (1-τ,u) 0 earnings supply z

58 c Labor Supply Income Effect η=(1 t) z/ R 0 R+ R R z(1-τ,r+δr) z(1-τ,r) 0 Earnings z

59 c Labor Supply Substitution Effect utility u slope= 1-τ+dτ slope=1-τ ε c = (1-τ)/z z c / (1-τ)>0 z c (1-τ,u) z c (1-τ+dτ,u) 0 Earnings z

60 c Uncompensated Labor Supply Effect Slutsky equation: ε u = ε c + η slope=1-τ+dτ income effect η 0 slope=1-τ R substitution effect: ε c >0 0 Earnings z

61 c= z-t(z) Effect of Tax on Labor Supply T(z) < 0: income effect z T (z) > 0: substitution effect z slope=1-t (z) T(z) > 0: income effect z T (z)>0: substitution effect z -T(0) 0 z pre-tax income z