Heterogeneity and Government Revenues: Does Tax Progressivity - - PowerPoint PPT Presentation

Heterogeneity and Government Revenues: Does Tax Progressivity Matter?

Nezih Guner, Martin Lopez Daneri and Gustavo Ventura

ICREA-MOVE, U. Autònoma de Barcelona and Barcelona GSE (Spain) Central Bank of Chile (Chile) Arizona State University (USA)

SED - 2013 - Seoul

Motivation

In the recent crisis, many governments increase or propose to

increase top marginal tax rates to raise revenue.

Recent policy debate on taxing the top earners (Diamond and

Saez, 2011)

How much more revenue can a government raise by making

income taxes more progressive?

How does the answer depend on average level of taxes? How does the answer depend on underlying labor supply

elasticities?

What we do

Build a standard Aiyagari-Bewley-Huggett economy. Parameterize this model to be consistent with facts on

inequality and taxes paid for the US economy.

Parametric representation of e¤ective taxes paid – Heathcote,

Storesletten and Violante (2012). Use this framework to compute how government revenue

changes with progressivity of income taxes.

Related Literature

Large literature on optimal progressivity of income taxes

Conesa and Krueger (2006), Conesa, Kitao, and Krueger

(2009), Diamond and Saez (2011), Heathcote, Storesletten and Violante (2012), Bakis, Kaymak and Poschke (2012), Badel and Huggett (2013) Literature on the La¤er curve – linear taxes

Trabandt and Uhlig (2010), Feve, Matheron, Sahuc (2012)

Taxes in the U.S.

Use Internal Revenue Service (IRS) micro data to document

the relation between income and taxes paid – Guner, Kaygusuz and Ventura (2013)

A representative sample of U.S. households No top-coding Information on, among other things, income and taxes paid

Taxes in the U.S.

Tax Rates Statistic All % with zero taxes 24.7% Median Tax rate 7.3% Mean Tax rate 7.4% Tax Rate De…ning Bottom 80% 12.3% Bottom 90% 15.9% Bottom 95% 18.5% Bottom 99% 25.4%

Taxes in the U.S.

Distribution of Income and Tax Liabilities Quantiles Income Taxes Paid Bottom 1% 0.0% 0.0% 1-5% 0.1% 0.0% 5-10% 0.4% 0.0% Quantiles 1st (bottom 20%) 2.0% 0.3% 2nd (20-40%) 6.1% 1.9% 3rd (40-60%) 11.3% 5.7% 4th (60-80%) 19.1% 13.1% 5th (80-100%) 61.3% 79.1% Top 90-95% 10.6% 11.2% 95-99% 15.0% 19.4% 1% 20.9% 35.8%

Taxes in the U.S.

What is the relation between income and taxes paid? Heathcote, Storesletten and Violante (2012) propose the

following relation T(I) = (1 λI τ)I = I λI 1τ

The average tax rate is given by

t(I) = 1 λI τ

Estimate this relation from micro data with I represented as

multiples of mean household income.

0.25

Average Tax Rates for Married Households, Data

0.2 0 15 0.15 verage Tax Rates 0.1 Av 0.05 0.2 1 1.8 2.6 3.4 4.2 5 5.8 6.6 7.4 8.2 9 9.8 Multiples of Mean Household Income

0.25

Average Tax Rates for Married Households, Data and Parametric Estimates

0.2 0.15 0.1 verage Tax Rates

Data HSV

0.05 Av

HSV

0.2 1 1.8 2.6 3.4 4.2 5 5.8 6.6 7.4 8.2 9 9.8 ‐0.05 Multiples of Mean Household Income

0.35

Marginal Tax Rates for Married Households (data and the parametric estimates)

0.3 0.25 0 15 0.2 Título del eje

data hsv

0.1 0.15 0.05 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 4.5 4.75 5 5.25 5.5 5.75 6 6.25 6.5 6.75 7 7.25 7.5 7.75 8 8.25 8.5 8.75 9 9.25 9.5 9.75 10

Model

Life-cycle economy, j = 1, ...., JR, ....J. Population structure is stationary, with population growing at

rate n.

Agents face idiosyncratic earnings risk and life uncertainty. Agents can save in the form of riskless capital, but they are

not allowed to borrow.

There are no annuities markets.

Model

Agents value consumption and dislike work

u(c, l) = log(c) ϕ l1+ 1

γ

1 + 1

γ

Labor productivity of an age-j agent with a current

idiosyncratic shock z is given by e(z, j)

Labor productivity evolves according to

ln e(z0, j) = γj + z0, and z0 = ρz + ε, ε~N(0, σ2

ε ).

At age-1, agents draw their initial z from N(0, σ2

z).

Model – Government

There is a government that taxes household income with a

progressive tax schedule T(.).

An additional ‡at tax on total household income τl. An additional ‡at tax on capital income τk. A social security tax τp on labor earnings that …nance the

social security system.

Budget constraint for an agents with e(z, j) and assets a

c + a0 = we(z, j)(1 τp) + a(1 + r) τkar T(we(z, j) + ar) τl(we(z, j) + ar)

Model – Production

Standard

Yt = K α

t (AtLt)1α,

with At = A0(1 + g)t.

Aggregate Resource Constraint

Ct + Kt+1 + G = K α

t (AtLt)1α + (1 δ)Kt.

Accidental bequests are wasted (or taken by the government).

Parameter Values

Model period is a year, JR = 45 (age 65), J = 81 (age 100) Productivity growth — g = 0.022 Population growth — n = 0.011 Survival probabilities – U.S. Life Tables Capital Share — α = 0.35 Depreciation — δ = 0.04

Parameter Values

fγjgJR

j=1 — Hansen (1993)

Set ρ = 0.973 and σ2

ε = 0.02 — Heathcote, Storesletten and

Violante (2010)

Parameter Values

Four parameters left: fβ, γ, ϕ, σ2

z)

Set γ = 1 (for now) Choose β = 0.973 to match K/Y = 2.94 Choose ϕ = 8 so that labor supply is 1/3 Choose σ2

z = 0.55 to match earnings Gini

Target for Earnings Gini 0.44 – Heathcote, Perri and Violante

(2010)

Parameter Values

E¤ective tax function

T(I/I) = (1 λ(I/I)τ)(I/I) = I/I λ(I/I)1τ

λ = 0.925, τ = 0.070 — Guner, Kaygusuz and Ventura (2013)

Set τl = 0.05 — Guner, Kaygusuz and Ventura (2013) Set τk = 0.075 — revenue collected is 1.74% GDP

(Corporate Income Tax, Cooley and Prescott 1995)

Set τp = 0.086 – social security contributions/labor income

Benchmark Economy

Distribution of Income, Data and Model Quantiles DATA MODEL Bottom 1% 0.0% 0.16% 1-5% 0.1% 0.75% 5-10% 0.4% 0.34% Quantiles 1st (bottom 20%) 2.0% 1.8% 2nd (20-40%) 6.1% 5.6% 3rd (40-60%) 11.3% 11.1% 4th (60-80%) 19.1% 21.1% 5th (80-100%) 61.3% 60.2%

Benchmark Economy

Distribution of Income, Data and Model Quantiles DATA MODEL 1st (bottom 20%) 2.0% 1.8% 2nd (20-40%) 6.1% 5.6% 3rd (40-60%) 11.3% 11.1% 4th (60-80%) 19.1% 21.1% 5th (80-100%) 61.3% 60.2% Top 90-95% 10.6% 14.6% 95-99% 15.0% 18.2% 1% 20.9% 8.4%

Benchmark Economy

Federal Income Taxes are about 8% of GDP as they are in

the data. Distribution of Tax Liabilities, Data and Model Quantiles DATA MODEL 1st (bottom 20%) 0.3% 0% 2nd (20-40%) 1.9% 0% 3rd (40-60%) 5.7% 2.0% 4th (60-80%) 13.1% 14.0% 5th (80-100%) 79.1% 84% Top 90-95% 11.2% 18.6% 95-99% 19.4% 28.6% 1% 35.8% 17.7% top 10% 66% 65%

Government Revenue

How does government revenue changes by τ? Benchmark values are λ = 0.925 and τ = 0.07

Distribution of Tax Liabilities Quantiles τ = 0.07 τ = 0.08 τ = 0.1 τ = 0.14 1st (bottom 20%) 0% 0% 0% 0% 2nd (20-40%) 0% 0% 0% 0% 3rd (40-60%) 2.0% 0.2% 0% 0% 4th (60-80%) 14.0% 13.4% 9.2% 1.3% 5th (80-100%) 84% 86.4% 90.8% 98.7% Top 90-95% 18.6% 19.1% 20% 31.5% 95-99% 28.6% 21.6% 21.5% 34.7% 1% 17.7% 18.4% 19.9% 22..3% top 10% 65% 67.1% 71.4% 78.5%

0.300

Average Tax Rates for Married Households, Role of 

0.250 0.150 0.200 0.100 verage Tax Rates

HSV tau =0.09 tau=0.08 tau = 0.04

0.050 Av ‐0.050 0.000 0.2 1 1.8 2.6 3.4 4.2 5 5.8 6.6 7.4 8.2 9 9.8 ‐0.100 Multiples of Mean Household Income

105

Income Taxes

101 103 99 95 97

lambda = 0.925, tau = 0.07, BM

91 93 89 91 87 0.035 0.04 0.05 0.06 0.07 0.08 0.085 0.09 0.1 0.11 0.12 0.13 0.14

TAU

125

Labor, Capital and Mean Income

115 120

lambda = 0.925, tau = 0.07, BM

110 100 105

Labor Supply Mean Income Capital

90 95 85 80 0.035 0.04 0.05 0.06 0.07 0.08 0.085 0.09 0.1 0.11 0.12 0.13 0.14

TAU

101

Total Taxes (income, local, capital)

100 100.5 99 99.5 98 98.5 97.5 98

lambda = 0.925, tau = 0.07, BM

96.5 97 96 0.035 0.04 0.05 0.06 0.07 0.08 0.085 0.09 0.1 0.11 0.12 0.13 0.14

TAU

Government Revenue

Can government increase federal income taxes by making the

tax system more progressive? Yes.

But the increase is small. Large declines in capital and labor. As a result, total tax revenue (federal, local and capital) does

not increase with τ.

130.00

Income Taxes, role of 

120.00 125.00 115.00 105.00 110.00

lambda = 0.925, BM lambda = 0.9

100.00 90.00 95.00 85.00 0.035 0.07 0.1 0.15

120

Total Taxes, role of 

115 110 105

lambda = 0.925, BM lambda = 0.9

105 100 95 0.035 0.07 0.1 0.15

TAU

Government Revenue

At higher levels of λ, there is even less room to increase

revenue by increasing τ.

As λ increases, τ that maximized total tax revenue is smaller.

Conclusions

Can government increase federal income taxes by making the

tax system more progressive?

We build a standard Aiyagari-Bewley-Huggett economy to

answer this question.

Government revenue can increase with progressivity but the

gains are very small.

To do list: i) match the distribution of tax liabilities, iii) role

• f labor supply elasticities, iii) other types of changes in

progressivity (taxing top 1%), iv) welfare

Parameters Parameter Value Comments

Population Growth Rate (n) 1.1 U.S. Data Productivity Growth Rate (g) 2.22 U.S. Data Survival Probabilities (sj)

• U.S. Data

Discount Factor (β) 0.972 Matches K/Y = 2.94

• Lab. Supply Elasticity (γ)

1 Literature estimates. Disutility of Market Work (ϕ)

• Matches hours worked, 1/3

Age-earnings pro…les, fγjg

• Hansen (1993)

Persistence of earnings shocks, ρ 0.973 Heathcote et al (2010) Variance of earnings shocks, σ2

ε

0.02 Heathcote et al (2010) Variance of initial draws, σ2

z

0.55 Match overall earnings Gini Capital Share (α) 0.35 U.S. Data Depreciation Rate (δ) 0.04 Matches I/Y Tax function parameter, λ 0.925 Guner et al (2013) Tax function parameter, τ 0.07 Guner et al (2013) Payroll Tax Rate (τp) 0.086 U.S. Data Capital Income Tax (τk) 0.075 Matches corporate taxes Local Taxes (τ ) 0.05 Guner et al (2013)

A Static Example

Let preferences be represented by

γ 1 + γ l1+ 1

γ

γ is the (Frisch) elasticity of labor supply.

Individuals are heterogenous in the wage rates they face.

Wage rates are log-normally distributed. log(w) s N(0, σ2)

Finally, the tax function is given by

t(I/I) = 1 λ(I/I)τ

A Static Example

Labor Supply Decision

l

γ 1+γ

Taxes collected from a household with wage rate w are

wl

• "

1 λ

• wl
• E(w)l
• τ#

It follows that aggregate revenues are

R(τ) = l

• E(w) λ

[

A Static Example

After some algebra

R(τ) = l

• exp

1 2 σ2

• λ exp

1 2 (1 + τ2 τ)σ2

• FOC for τ
• γ

(1 + γ)(1 τ) = λ σ2 (2τ 1) 2 [ exp((1/2) σ2(τ τ2)) λ

• Revenue maximizing τ is increasing in γ (decreasing in labor

supply elasticity), decreasing in σ2 and increasing λ (decreasing in average taxes).