David Seim. Tax Rates, Tax Evasion and Cognitive Skills

Tax Rates, Tax Evasion and Cognitive Skills

David Seim

IIES, Stockholm University

October 2012

D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012

Introduction

Earnings responses to taxes:

(i) Real substitution responses

(ii) Reporting responses (legal and illegal)

Tax system complex: ability to respond possibly affected by cognitiveability


This Paper

Identify the effects of a tax change on substitution and evasion.

Study whether the cognitively able are more likely to evade.


Motivation

Crucial to understand tax evasion for giving policy recommendationson how to reduce evasion.

Need to know tax elasticity of both taxable net wealth and actual netwealth to determine optimal tax rate.

If the ability to evade taxes differs across people:

I The tax incidence will fall disproportionally on the less able.

I Heterogenous effects on wealth inequality within skill groups.


Contribution

Provide an empirical measure of tax evasion.

Find tax elasticities of evasion on the order of 1 - 3.5 in both astructural and reduced form framework.

Use military enlistment data on cognitive skills to establish thatcognitively able are more likely to evade the wealth tax.


Roadmap

I STRUCTURAL APPROACH

I Develop a model of savings and evasion.

I Estimate model using bunching at kink points.

I Administrative data on taxable net wealth for the Swedish population.

II REDUCED FORM APPROACH

I Use new measure of tax evasion.

I Apply a D-in-D framework exploiting tax reforms.


III BOUNDED RATIONALITY AND TAX RESPONSES

I Construct model of cognitive skills, savings and evasion building onChetty et al. (2007).

I Use Swedish military enlistment data on cognitive skills to test themodel’s predictions.


Related Literature

Optimal taxation: Feldstein (1999), Saez (2001), Chetty (2009).

Tax evasion: Allingham and Sandmo (1972), Clotfelter (1983),Slemrod (1985), Slemrod (2001).

Methodology: Saez (2010), Chetty et al. (2011).

Cognitive costs: Chetty et al (2007), Liebman and Luttmer (2011).


STRUCTURAL APPROACH


Model

Individuals have homothetic utility function

ui (c1, c2) =c1−δ

1,i

1− δ+ β

c1−δ2,i

1− δ

where c1,i is consumption today, c2,i is consumption tomorrow, β isthe discount factor, 1

δ is the IES.


Agents’ budget constraints

c1,i = yi − s

c2,i = (1 + r) ((1− τ) (s − e) + e − C (e, s))

where yi is income, distributed with continuous and differentiableCDF F (y), s is savings, r is the deterministic interest rate, τ is taxon taxable savings.

Agents can evade taxes τ by choosing e < s subject to a costfunction C (e, s).


Cost Function

Builds on Slemrod (2001).

C (e, s) =(es

)γ 1

1 + γpe

where p > τ and γ measures curvature of cost.

e∗i =

(τ

p

) 1γ

s∗i


Mean Evasion as Function of Net WealthEvasion = max{Third Party Reported Net Wealth− Taxable Net Wealth, 0}

010

0000

2000

0030

0000

4000

00Ev

asio

n

1500000 2500000 3500000 4500000Third Party Reported Net Wealth


Model

In equilibrium,

s∗i =

β1δ (1 + r)

1−δδ

(1− τ

(1−

(τp

) 1γ γ

1+γ

)) 1−δδ

1 + β1δ (1 + r)

1−δδ

(1− τ

(1−

(τp

) 1γ γ

1+γ

)) 1−δδ

yi

and taxable net wealth becomes

s∗i − e∗i =

β1δ (1 + r)

1−δδ

(1− τ

(1−

(τp

) 1γ γ

1+γ

)) 1−δδ

1 + β1δ (1 + r)

1−δδ

(1− τ

(1−

(τp

) 1γ γ

1+γ

)) 1−δδ

(1−

(τ

p

) 1γ

)yi


Linear Tax Scheme, τ = τ0

s − e

After Tax Net Wealth, c2 = (s − e)− T (s − e)IC High

IC Low

Slope 1− τ0


Progressive Tax Scheme with τ = τ1 > τ0 for s − e >= z∗

s − e

After Tax Net Wealth, c2 = (s − e)− T (s − e)

IC High 1

IC High 2

IC Low

Slope 1− τ0

Slope 1− τ1

z∗ z∗ + ∆z


Simulated Savings Using Swedish Data on Income, τ = 0

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 105

0

1000

2000

3000

4000

5000

6000

s−e

Freq

uenc

y


Simulated Savings Using Swedish Data on Income,τ = 0.015 above SEK 150000

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 105

0

1000

2000

3000

4000

5000

6000

s−e

Freq

uenc

y


Agents with

y ∈

[f (τ0) , f (τ1)

]bunch at the kink point. (Where f (τ) is given here .)


Number of agents bunching:

B =

∫ z∗+∆z

z∗h0 (s)ds

≈ ∆zh0 (z∗) + h0 (z∗ + ∆z)

2

≈ ∆zh0

or, equivalently,

B

h0

≈ z∗

1 + β1δ R

1−δδ

(1− τ1

(1−

(τ

1p

) 1γ γ

1+γ

)) 1−δδ

1 + β

1δ R

1−δδ

(1− τ0

(1−

(τ

0p

) 1γ γ

1+γ

)) 1−δδ

×(1− τ0

(1−

(τ

0p

) 1γ γ

1+γ

)) 1−δδ(1−

(τ

0p

) 1γ

)(1− τ1

(1−

(τ

1p

) 1γ γ

1+γ

)) 1−δδ(1−

(τ

1p

) 1γ

)D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012

Solve for structural parameter γ as a function of:

(i) known parameters: z∗, τ0 , τ1 ,

(ii) the excess bunching around the kink point: Bh

0

,

(iii) intertemporal parameter δ, discount factor β.

(iv) cost p.


Institutional Background and Data

Figure: MTR since 1992

z∗

1.5

Taxable Net Wealth

Marginal Tax Rate %


Movement in Tax Bracket Cutoff Across Years

Singles

Couples filing jointly

1998 1999 2000 2001 2002 2003 2004 2005 2006

1000

1500

2000

2500

3000

3500

Year

SEK 1000


Declaring Wealth


Table: Perceptions of Tax Cheating in Sweden, in %

Very Quite Not very Not at all Don’tcommon common common common know

Federal inc. tax 8.6 26.6 32.5 8.8 22.1Corporate tax 10.4 29.0 20.6 3.5 34.8Inheritance tax 11.2 30.3 24.5 6.2 26.2Wealth tax 18.7 37.2 15.6 3.8 23.5Estate tax 4.7 17.3 35.2 16.6 24.8Gas tax 2.7 9.6 31.4 25.0 29.8

Source: Survey by Hammar et al. 2006.


Distribution of Third Party Reported Net Wealth,2002-2006

2000

3000

4000

5000

Freq

uenc

y

1500000 16250001250000 1375000 1750000Third Party Reported Net Wealth, SEK (2002−2006)


Distribution of Taxable Net Wealth, 2002-2006

2000

3000

4000

5000

Freq

uenc

y

13750001250000 1500000 17500001625000Taxable Net Wealth, SEK (2002−2006)


Estimating Excess Bunching

I Follow previous literature

I Estimate the counterfactual as a polynomial excluding points aroundthe kink.

II Nonparametric way

I Compute the number of people tax liable using third party reported netwealth but not using taxable net wealth.


Method I

Cj

(1 + I [j > 0]

BN∑∞j=1

)=µ0 + µ1Zj + µ2Z

2j + . . .+ µ7Z

7j +

0∑i=−R

ρi I [Zj = i ] + ε0j

where Cj is number of people in net wealth bin j , Zj is taxable net wealthrelative to kink point in 5000 kronor intervals, R measures the lower boundof the bunching that is allowed (measured in 5000 kronor).

Estimator of b = Bh0

given by:

BN

h0

=

∑0j=−R Cj − C 0

j∑0j=−R

Cj

R+1


Empirical Results; Bunching

6000

8000

1000

012

000

1400

0Fr

eque

ncy

−50 −40 −30 −20 −10 0 10 20 30 40 50Taxable Net Wealth Relative to Tax Bracket Cutoff (SEK 5000)

b=0.536 (0.0923)


Bunching results, 2002-2006

2000

3000

4000

5000

Freq

uenc

y

−50 −40 −30 −20 −10 0 10 20 30 40 50Taxable Net Wealth Relative to Tax Bracket Cutoff (SEK 5000)

b=0.6565 (0.0991)


Does Bunching Track the Tax?Bunching in 2001:

400

600

800

1000

1200

Freq

uenc

y

1000000 15000001250000Taxable Net Wealth



050

010

0015

00Fr

eque

ncy

15000001000000 12500000Taxable Net Wealth Relative to Tax Bracket Cutoff (SEK 5000)



2001 kink

2001 kink infl. adj.

2001 kink invested in riskfree interest rate

2006 kink

2001 kink inv−ested in stocks

400

600

800

1000

1200

Freq

uenc

y

1000000 1250000 1500000Taxable Net Wealth



400

600

800

1000

1200

1400

Freq

uenc

y

15000001000000 1250000Taxable Net Wealth


Method II

Estimator of B is given by:BN =

∑Ni I [z∗ − R < Zi < z∗ & Si > z∗].

where Zi is taxable net wealth of i , Si is third-party reported netwealth, R is lower bound of allowed bunching.

Estimator of h0 is given by: h0 =∑0

i=−R Pi

R+1

where Pi denotes the number of people in third party reported netwealth bin i .

B = 1.009 (0.0189)


Calibration and Results

Elasticity of intertemporal substitution= 0.25

p ∈ [0.02, 1]

β = 0.98, (1 + r) = 1.04

Bunching, Bh0

= 1.009

gives γ = [0.42, 0.93] and εe,τ = [2.37, 1.08]


REDUCED FORM


Define evasion as e = max{s − (s − e), 0}.

Methodology (Gruber and Saez, 2002):

I Regress ∆ log evasion over X years on ∆ log net-of-tax rates (NTR).

I Instrument for ∆ log NTR using the simulated change from holding netwealth levels constant at base year levels.

First stage strong: Coefficient= 0.690 and t = 350.


Table: Elasticities Estimates from Variation in Tax Bracket Cutoff

Dependent var:∆ log Evasion 2y 2y 3y 3y∆ log NTR -1.966*** -2.247*** -3.917*** -4.587***

(0.665) (0.664) (0.749) (0.747)Age Fixed Effects X X X XYear Fixed Effects X X X XRegion Fixed Effects X XWage spline X XBase Year Evasion spline X X X XObservations 1919253 1919253 1508141 1508141

Standard errors clustered at household level.


BOUNDED RATIONALITY


Let agents internalize θi ∈ [0, 1] of the tax in optimization.

θHIQ > θLIQ .

Perceived constraints:

c1 = y − s

c2 = R

((1− θiτ) (s − e) + e −

(es

)γ pe

1 + γ

)Let first period consumption adjust

c1 = y − s − τR (1− θi ) (s − e) .


Predictions:

(i) The amount of bunching increases with θ, i.e. highly skilled agentsbunch more.

(ii) Conditional on bunching, the distribution of taxable net wealth doesnot differ across cognitive skill-groups.


Military Enlistment Data

Enlistment mandatory for men at age 18.

Two days of physical, cognitive and noncognitive tests.

Cognitive test consists of:I Logical skillsI Verbal skillsI Spatial skillsI Technical comprehension


Heterogenous Responses by Cognitive Skills

0.0

5.1

.15

Frac

tion

of B

unch

ers

1000000 1500000 2000000 2500000 3000000Pre wealth

High Skilled Low Skilled

Fraction of Bunchers, by Cognitive Skills


Heterogenous Responses by Cognitive Skills

.01

.02

.03

.04

Frac

tion

of B

unch

ers

0 2 4 6 8 10Cognitive Skills


Table: Dependent var: indicator for evading the tax through bunching,logit-model

(1) (2) (3) (4)Sample: All All 2002 − 2006 2002 − 2006Cognitive Skills 0.015 0.063* 0.103*** 0.127***

(0.025) (0.034) (0.040) (0.044)Cognitive Skills Sq. -0.064*** -0.051*

(0.023) (0.028)Third Party Rep. NW. X XThird P.R. NW. - spline X XYear Fixed Effects X X X XAge Fixed Effects X X X XRegion Fixed Effects X X X XFamily Fixed Effects X X X XEducation Fixed Effects X XObservations 60800 60800 34265 34265

Standard errors clustered on the household level.


Distribution of Taxable Net Wealth Among Bunchers,2002-2006

050

010

0015

00Fr

eque

ncy



Distribution of Taxable Net Wealth Among Bunchers, HighSkilled, 2002-2006

020

4060

80Fr

eque

ncy



Distribution of Taxable Net Wealth Among Bunchers, LowSkilled, 2002-2006

05

1015

20Fr

eque

ncy



Are people with high cognitive ability better at locating atthe kink?

Define two skill groups (high and low cognitive skills):

I Mann-Whitney U test of equal distributions gives P-value for equalityof distributions = 0.4064

Use discrete variable with nine cognitive skill groups:

I Kruskal-Wallis test gives P-value for equality of distributions = 0.4668


Conclusion

Approach tax evasion from three angles.

Findings:I Bunching identifies structural tax elasticity of evasion of 1− 2.5.

I Reduced form estimates on the order of 2− 4.5.

I Cognitive skills matter for the extent of evasion.

Actual revenue from tax increase is 88 % of the mechanical revenue(ignoring real and evasion responses).


Final Remarks

STRUCTURAL APPROACHI Functional form assumptions, relies on parameter values being correct.

REDUCED FORMI Identifying assumption: Changes in tax rates not correlated with base

year net wealth.


Appendix

Agents with

y ∈

[ z∗

1 + β1δ R

1−δδ

(1− τ0

(1−

(τ

0p

) 1γ γ

1+γ

)) 1−δδ

β

1δ R

1−δδ

(1− τ0

(1−

(τ

0p

) 1γ γ

1+γ

)) 1−δδ(1−

(τ

0p

) 1γ

) ,

z∗

1 + β1δ R

1−δδ

(1− τ1

(1−

(τ

1p

) 1γ γ

1+γ

)) 1−δδ

β

1δ R

1−δδ

(1− τ1

(1−

(τ

1p

) 1γ γ

1+γ

)) 1−δδ(1−

(τ

1p

) 1γ

)]

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David Seim. Tax Rates, Tax Evasion and Cognitive Skills