Revisiting Tax on Top Income

Transcription

1 Revisiting Tax on Top Income Ayşe İmhrohoğlu, Cagri Kumi and Arm Nakornthab, 2017 Presented by Johannes Fleck November 28, 2017

2 Structure of the paper (and today s presentation) 1. Research question 2. Model Main elements Agent s problem Sequential illustration Analytical description (quilibrium) Baseline calibration 3. Policy experiments (Maximize revenues) Maximize welfare Discussion 4. Conclusion Forward guidance: This is NOT a published paper (yet)

3 Research question

4 Research question What is the optimal marginal tax rate on top incomes? Literature displays strikingly large variation in answers Diamond and Saez [2011]: 73% Badel and Huggett [2015]: 49% Guner, Lopez-Daneri and Ventura [2016]: 42% Kindermann and Krueger [2017]: >90% This paper aims to contribute two related inquiries What answer emerges in a model with entrepreneurial activity? In this model is increasing overall or top progressivity more optimal?

5 Model

6 Model: main elements 1. Demographics: simplified life-cycle with intergenerational altruism young and old cohorts, aging is stochastic when old dies, offspring receives bequest and re-enters as young each household has only one offspring measure of all agents normalized to 1 2. Preferences: u(c t, 1 l t ) = c1 σ 1 t 1 σ 1 + χ (1 lt)1 σ 2 1 σ 2 3. Technology: competitive corporate and entrepreneurial sectors each period stochastic work and entrepreneurial ability (yt, θ t) after shock agents decide to be (corporate) worker or entrepreneur work income: y t MPL of F (Kt c, Lc t ) = A(K t c)α (L c t ( )1 α entrepreneurial income: f (k t, n t) = θ t k γ t (lt + nt)1 γ) ν (l: own labor; n: hired labor; k: own and borrowed capital) 4. Market incompleteness: risk free assets, borrowing constraints individual risk is uninsurable

7 Model: main elements 5. Government: closes the model (does not optimize!) xpenditures: consume g, pay pension p, service debt (1 + rt)d t Revenues: Dt+1, linear consumption tax τt c, income tax T t given by { (1 λyt τ )Y t + τt bal Y t + τt k r ta t if Y t < Y H T t(y t) = (1 λy τ H )Y H + τ bal t Y H + τ k t r ta t + τ H (Y t Y H ) if Y t > Y H Y H : top 1% income threshold, τt bal : linear state and local gov t tax 6. ffects of changing the tax code? Policy experiments I to IV: Objective τ (Overall progressivity) τ H (Marginal rate top 1% ) Maximize Revenue I II Maximize Welfare III IV

8 Model: agent s problem W W W R R R A! AG! DATH! DI! SHOCK Ω Young Agent enters the economy with Old asset endowment a0 work (corporate) productivity y0 entrepreneurial productivity θ0

9 Model: agent s problem W W W R R R A! AG! DATH! DI! SHOCK Ω Young Agent decides to work as (corporate) Worker or ntrepreneur Old

10 Model: agent s problem W W W R R R A! AG! DATH! DI! SHOCK Ω Young Old At the start of every period each agent draws productivities (y t, θ t ) They are independent and governed by π(y t+1 y t ) and π(θ t+1 θ t ) After observing, agent decides to work as Worker or ntrepreneur

11 Model: agent s problem W W W R R R A! AG! DATH! DI! SHOCK Ω Young The decision problem remains the same each period Old

12 Model: agent s problem W W W R R R A! AG! DATH! DI! SHOCK Ω Young With exogenous probability 1 π y agent gets hit by an age shock Old

13 Model: agent s problem W W W R R R A! AG! DATH! DI! SHOCK Ω Young In the period following the age shock Old a Worker becomes Retiree an ntrepreneur may continue as ntrepreneur or become Retiree

14 Model: agent s problem W W W R R R A! AG! DATH! DI! SHOCK Ω Young The decision problems of R and remain the same in every period Old

15 Model: agent s problem W W W R R R A! AG! DATH! DI! SHOCK Ω Young Old

16 Model: agent s problem W W W R R R A! AG! DATH! DI! SHOCK Ω Young With exogenous probability 1 π 0 agents get hit by a death shock Old

17 Model: agent s problem W W W R R R A! AG! DATH! DI! SHOCK Ω Young In the period after the death shock, R and re-enter the economy Their initial endowments are a0: given by parental choice of a t+1 y0: computed using invariant distribution of y t θ0: conditional on parent s θ t but following same Markov process ("This reflects the fact that the offspring inherits her parent s business") Old

18 Model: agent s problem W W W R R R A! AG! DATH! DI! SHOCK Ω Young Old Completes illustration of all individual decisions

19 Model: young agent problem { } V Y (a t, y t, θ t ) = max Vt Y,W (a t, y t, θ t ), Vt Y, (a t, y t, θ t )

20 Model: young worker problem { Vt Y,W (a t, y t, θ t ) = max u(c t, 1 l t ) + βπ y t [Vt+1(a Y t+1, y t+1, θ t+1 )] c t,l t,a t+1 } + β(1 π y )V O,R t+1 (a t+1) s.t. 0 l t 1 0 a t+1 (1 + τ c t )c t + a t+1 = w t l t y t + (1 + r t )a t T t (Y W t ) Y W t = w t l t y t + r t a t

21 Model: young entrepreneur problem { Vt Y, (a t, y t, θ t ) = max u(c t, 1 l t ) + βπ y t [Vt+1(a Y t+1, y t+1, θ t+1 )] c t,l t,k t,n t,a t+1 } + β(1 π y ) t [Vt+1(a O t+1, θ t+1 )] s.t. 0 l t 1 0 a t+1 0 n t (1 + τ c t )c t + a t+1 = Y t Y t 0 k t (1 + d)a t + a t T t (Y t ) = θ t ( k γ t (l t + n t ) 1 γ) ν δkt r t (k t a t ) w t n t

22 Model: old agent problem { } V O (a t, θ t ) = max Vt O,R (a t ), Vt O, (a t, θ t ) Recall: This is NOT the problem of a retiree but of an old agent who was an entrepreneur in the period before aging or who currently is an (old) entrepreneur

23 Model: old retiree problem s.t. { Vt O,R (a t ) = max u(c t, 1) + βπ O V O,R c t+1 (a t+1) t,a t+1 0 a t+1 (1 + τ c t )c t + a t+1 = (1 + r t )a t + p T t (Y O t ) Y O t = r t a t + p + β(1 π O ) t [V Y t+1(a t+1, y t+1, θ t+1 )] }

24 Model: old entrepreneur problem { Vt O, (a t, θ t ) = max u(c t, 1 l t ) + βπ O t [Vt+1(a O t+1, θ t+1 )] c t,l t,k t,n t,a t+1 } + β(1 π O ) t [Vt+1(a Y t+1, y t+1, θ t+1 )] s.t. 0 l t 1 0 a t+1 0 n t (1 + τ c t )c t + a t+1 = Y t Y t 0 k t (1 + d)a t + a t T t (Y t ) = θ t ( k γ t (l t + n t ) 1 γ) ν δkt r t (k t a t ) w t n t

25 Model: Competitive equilibrium in stationary steady state Some notation and model specific features States and distributions agent s state vector st = (a t, y t, θ t, ξ t) where ξ t {YW, Y, O, R} entire state space is given by S = R+ Y Θ Ξ transition matrix Γt(s t, s t+1) given by optimal policies and exogenous processes π(y t+1 y t) and π(θ t+1 θ t) agent distribution Φ t+1 = Γ t(s t, s t+1) Φ t In stationary steady state Φt = Φ Dt = D

26 Model: Competitive quilibrium A C is a set of value functions, agent policies, factor inputs and prices, government debt and taxes such that given r, w, tax function T ( ), tax rates τ c, τ bal, τ k and pensions p allocations ct, a t, l t, k t, n t max agent s problem s t S rt = MPK C δ = MPK δ wt = MPL C = MPL capital markets clear: kt(s t)dφ t(s t) + K c t + D t = a t(s t)dφ t(s t) labor market clears: nt(s t)dφ t(s t) + L c t = l t(s t)dφ t(s t) government budget holds: [Tt(Y s ) + τ c t c t(s t)]dφ t(s t) + D t = g t + p π R + (1 + r t)d t resource constraint holds: g+ c t(s t)dφ t(s t)+ a t+1(s t)dφ t(s t)=f (K c t, L c t )+ f (k t, n t)dφ t(s t) Φ associated with saving policy, π(yt+1 y t) and π(θ t+1 θ t) is Φ government debt is constant (at D )

27 assets. The degree of decreasing returns to scale,, is set to 0.88 as in Bassetto Model: baseline - fixed parameters The entrepreneurial capital share,,is chosen to equal Table 1: Fixed Parameters Parameter Value Preferences, technology, and demographics Risk aversion Inverse of Frisch elasticity Capital share 0.33 Technology A 1 Probability of staying young y Probability of staying old o Depreciation 0.06 ntr. return to scale 0.88 ntr. borrowing constraint d 0.5 Labor income process and social security payments Autocorrelation ndowments Pension/average annual income p 40% Parameter values come from various papers Public purchases, government debt, and taxes In order to generate income and wealth distributions and the share of entrepren Fraction of government spending to output g top 1% of income realistically, we introduce highly productive workers and highl Fraction of government debt to total capital D 0.27 entrepreneurs to the model. In every period, a worker is endowed with one uni Consumption tax c 5% xcept: Age and death shock probabilities so that average working and retirement periods are 45 and 11 years (80% young in eq.) Capital tax k 7.4% Technology A 1 Probability of staying young y Probability of staying old o Depreciation 0.06 ntr. return to scale 0.88 ntr. borrowing constraint d 0.5 Labor income process and social security payments Autocorrelation Pension/average annual income p 40% Public purchases, government debt, and taxes Fraction of government spending to output g Fraction of government debt to total capital D 0.27 Consumption tax c 5% Capital tax k 7.4% State and local tax bal 5% Revenue requirement Tax progressivity State and local tax bal 5% 13 Revenue requirement Tax progressivity ts nerate income and wealth distributions and the share of entrepreneurs at the ome realistically, we introduce highly productive workers and highly successful

28 Table 2 summarizes the parameters calibrated to match the seventeen targets in the data that are presented the next section. Model: baseline - calibrated parameters Table 2: Calibrated Parameters Calibrated parameter Value Discount factor ntrepreneurial ability { 0, 1, 2} {0, 1.8, 2.75} ntr. transition probabilities see eq. 33 ntr. capital share 0.45 Disutility from working 1.9 Standard deviation of productivity shock y 0.18 Value of highest productivity y Probability of having highest productivity Probability of staying highest productivity Superstars Features of andthe transitions Benchmark to match conomy empirical earnings and savings work ability: [ ] In this section, we discuss the aggregate and distributional properties of the benchmark economy. In top order transitions: to conduct meaningful policy experiments regarding changes in the progressivity and π(ythe 6 ytop 6 C ) tax = rate, 0.002, we π(y need 6 y to 6) make = 0.931; sure that the model delivers realistic income π(y 3 C y 6) = 0, π(y 3 y 6) = entrepreneurial ability: [ ] top transitions: π(θ 2 θ 0) = 0, π(θ 2 θ 1) = , π(θ 2 θ 2) =

29 Table 4 summarizes the key macroeconomic aggregates in the benchmark economy. In data. Model: baseline - targets Table 3: Target Moments Targets Data Model Capital to output ratio %ntrepreneurs %xitingentrepreneurs %Workerstoentrepreneurs %Hiringentrepreneurs %Averageworkedhours Income distribution Income Gini ntr. income Gini Worker earnings Gini % income % income %entr.intop1% Wealth distribution Wealth Gini % wealth % wealth %Peopleatzerowealth Ratio of median net worth entr. to workers

30 Overall our model matches income and wealth distributions quite well. Table 6: Wealth Distribution in the Benchmark conomy Table 4: Macroeconomic Share of wealth (in Aggregates %) Wealth Variable quintiles Value Top 0-20% 20-40% 40-60% Capital 60-80% % 90-95% 289.5% 95-99% % Gini Data Government 9.9 debt % Model Consumption % Investment 17.4% Table 7 shows the distribution Government of income consumption taxes paid in the 3.5% data and the model generated Average hours worked 33% distribution. 11 The distribution of tax payments is more concentrated than the income Interest rate 0.27% distribution but is less concentrated than the wealth distribution. In the data, first and Tax revenues second income quantiles are responsible - Consumption for 2.5% tax of income 4.0% tax payments. In the model this equal to 4.6%. Also in the data, -Labortax fifth income quantile is responsible 8.9% for 74.6% of income tax payments. The corresponding value -Proportionalcapitaltax in the model is 77.5%. 7.9% The concentration in income tax payments is the natural consequence Pensionof system the concentration in income and wealth distribution. -Totalpensionpayment 11.8% Model: baseline - macro and taxes Table 7: Share of Tax Payments in the Benchmark conomy Tables 5 and 6 summarize the model-generated income Share ofand tax wealth (in %) distributions together with their counterparts in the data. 9 The Income standard quintiles life-cycle models often fail to generate 0-20% 20-40% 40-60% 60-80% % income and wealth distributions correctly at the upper end. 10 Our model with workers and Data entrepreneurs is able Model to generate 1.2 a 3.4 realistic6.6 wealth 11.4 and income 77.5distribution.

31 Policy xperiments

32 P I and II: maximize revenue Idea of policy experiments: Fix λ at baseline value and search for optimal τ or τ H I Change overall progressivity τ = % revenues (relative to baseline) P I - full results II Change top progressivity τ H P II - full results = % revenues (relative to baseline)

33 P III and IV: maximize welfare Figure 3: Welfare Maximizing (welfare computed in consumption equivalent terms) To delve deeper into the reasons behind the welfare results, in Table 16, we display the income III Change and wealthoverall distributions progressivity in the three(lhs) economies considered: the benchmark economy, the economy τ = where 0.15welfare +4.25% is maximized CV (relative by changing to baseline) the overall progressivity P III - full resultsof taxes (t = 0.15), and the economy where the welfare-maximizing marginal income tax rate for the IV Change top progressivity (rhs) top 1% is found to be equal to 55%. While the income distribution is not very different across these τh three = 0.55 economies, +0.72% the wealth CV distribution (relative todisplays baseline) P IV - full results important differences. While the Wealth Gini in the benchmark economy is 0.84, the second economy where the overall

34 falls by 38.6%. Average consumption by the richest 1% young workers decrease by 2 elfare gains we observe. Although young and old entrepreneurs are Hours affected worked quite declines for most groups, except for those on the top 1% of incomes. ly, their small share in the population reduces their impact on the Variance overallof welfare consumption declines for all except the old workers. P III and IV - more details Table 13: Consumption and Hours - Welfare Maximizing Progressivity Panel A Average consumption Average hours worked xperiment =0.15 YW Y OW O YW Y O whole economy top 1% N/A bottom 99% % % N/A % 79.3 N/A 92.9 N/A 89.8 N/A N/A Panel B Variance consumption Variance hours worked YW Y OW O YW Y O whole economy bottom 99% Table 15: Consumption and Hours - Welfare-Maximizing Tax at the Top Panel A Average consumption Average hours worked xperiment H =0.55 YW Y OW O YW Y O whole economy top 1% N/A bottom 99% % % N/A N/A N/A 0-33% 89.2 N/A N/A 99.0 N/A N/A Panel B Variance consumption Variance hours worked YW Y OW O YW Y O whole economy bottom 99% Comparison of the Two Tax xperiments Our results indicate that the optimal tax rate that targets the richest 1% of the popu generates a moderate welfare gain (CV increases by 0.72%) compared to the expe Authors: welfare 28 changes driven by changes in income and wealth where the overall progressivity is increased (CV increases by 4.25%). Figure 3 summ the welfare results from these experiments. Panel A displays the welfare gain/loss income distribution not very different across these three economies increase the progressivity of taxes by varying. Panel B,summarizes changes in wel we increase the tax rate that applies to the top 1% of income levels. wealth distribution displays important differences: wealth share of the top 10% decreases and the wealth share of most of the lower quantiles increases in the overall progressivity case 30

35 P III and IV - more details: income and wealth Table 16: Changes in Wealth and Income Distribution - Welfare Maximizing Benchmark =0.15 H=0.55 Wealth distribution Wealth quintiles 0-20% % % % % Top 10% % % Wealth Gini Income distribution (all) Income quintiles 0-20% % % % % Top 10% % % Income Gini

36 P III and IV - more details: taxes Table 17: Share of Tax Payments and Tax Rates - Welfare Maximizing Percentiles of income Benchmark =0.15 H =0.55 Average tax rate Top 10% Top 5% Top 1% Marginal tax rate Top 10% Top 5% Top 1% Share of tax payments Income quintiles 0-20% % % % %

37 Conclusion

38 Conclusion 1. The paper explores a policy question but motivation is scarce 2. Some assumptions would benefit from additional details (robustness) endogenous borrowing constraint for entrepreneurs own and hired labor perfect substitutes for entrepreneurs stochastic aging induces additional precautionary savings 3. Thorough analytical characterization of model absent 4. Assessment of tax reforms is entirely numerical... variance of agent s after-tax income? cost of insurance via labor and asset market? elaboration on elasticities? (labor and capital supply, activity) comparison of results to papers such as KK 2017 hardly adequate

39 Thanks for your attention

40 P I: results Table 8: Changes in Progressivity-Revenue Maximizing Progressivity =0.035 =0.05 =0.07 =0.09 =0.10 =0.12 =0.15 Output Labor supply Capital Revenues Federal income tax State and local taxes Corporate income tax All taxes Additional targets Interest rate Worker avg. hours worked ntr. avg. hours worked Labor supply in corp sector Labor supply in entr. sector Capital in corp sector Capital in entr. sector %entr. in overall economy We find that revenues from the federal income tax schedule is maximizedreturn when = 0.10 and tax revenues from all sources are maximized when =0.09. Both values are

41 P II: results Table 9: Changes in Tax for Top 1% - Revenue Maximizing Marginal tax for top 1% H =0.2 H =0.4 H =0.55 H =0.6 H =0.8 Output Labor supply Capital Revenues Federal income tax State and local taxes Corporate income tax All taxes Additional targets Interest rate Worker avg. hours worked ntr. avg. hours worked Labor supply in corp sector Labor supply in entr. sector Capital in corp sector Capital in entr. sector %entr. in overall economy Table 10 summarizes the average and marginal income tax rates and share ofreturn tax payments for various income quantiles for three economies: 1) the benchmark, 2) the economy

42 revenue by 3.2% and the total tax revenue by 5.8%. P III: results Table 12: Changes in Progressivity - Welfare Maximizing Progressivity Output Labor supply Capital Revenues Federal income tax State and local taxes Corporate income tax All taxes Local tax rate, bal Average CV CV (All) CV (Work) CV (ntr.) Additional targets Interest rate Worker avg. hours worked ntr. avg. hours worked Labor supply in corp sector Labor supply in entr. sector Capital in corp sector Capital in entr. sector %entr. in overall economy = = = = = = = Table 13, explores the forces behind the welfare gains despite the fact that there are return large drops in economic aggregates. In our model, there are four distinct groups: young workers (YW), young entrepreneurs (Y), old workers (OW), and old entrepreneurs (O).

43 of taxes. This fact also contributes to the smaller welfare gains found in this case. P IV: resultstable 14: Changes in Tax for Top 1% - Welfare Maximizing Marginal tax for top 1% H =0 H=0.2 H=0.4 H=0.55 H=0.7 H=0.8 Output Labor supply Capital Revenues Federal income tax State and local taxes Corporate income tax All tax Local tax rate, bal Average CV All Workers ntr Additional targets Worker avg. hours worked ntr. avg. hours worked Labor supply in corp sector Labor supply in entr. sector Capital in corp sector Capital in entr. sector %entr.inoveralleconomy return