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 cognitive
ability


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 recommendations
on how to reduce evasion.

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

If the ability to evade taxes diﬀers across people:

The tax incidence will fall disproportionally on the less able.

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 a
structural and reduced form framework.

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


Roadmap

I STRUCTURAL APPROACH
Develop a model of savings and evasion.
Estimate model using bunching at kink points.
Administrative data on taxable net wealth for the Swedish population.

II REDUCED FORM APPROACH
Use new measure of tax evasion.
Apply a D-in-D framework exploiting tax reforms.


III BOUNDED RATIONALITY AND TAX RESPONSES

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

Use Swedish military enlistment data on cognitive skills to test the
model’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
1−δ 1−δ
c1,i c2,i
ui (c1 , c2 ) = +β
1−δ 1−δ
where c1,i is consumption today, c2,i is consumption tomorrow, β is
the discount factor, 1 is the IES.
δ


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 diﬀerentiable
CDF F (y ), s is savings, r is the deterministic interest rate, τ is tax
on taxable savings.
Agents can evade taxes τ by choosing e < s subject to a cost
function C (e, s).


Cost Function

Builds on Slemrod (2001).

e γ 1
C (e, s) = pe
s 1+γ
where p > τ and γ measures curvature of cost.

1
τ γ
ei∗ = si∗
p


Mean Evasion as Function of Net Wealth
Evasion = max{Third Party Reported Net Wealth − Taxable Net Wealth, 0}
400000
300000
Evasion
200000
100000
0

1500000 2500000 3500000 4500000
Third Party Reported Net Wealth


Model

In equilibrium,
1−δ
1 δ
1 1−δ
τ γ γ
β (1 + r )
δ δ 1−τ 1− p 1+γ
si∗ = 1−δ yi
1 δ
1 1−δ
τ γ γ
1 + β (1 + r )
δ δ 1−τ 1− p 1+γ

and taxable net wealth becomes
1−δ
1 δ
1 1−δ γ
τ γ
β (1 + r )
δ δ 1−τ 1− p 1+γ
1
τ γ
si∗ − ei∗ = 1−δ
1− yi
1 1−δ
1 δ p
τ γ γ
1 + β (1 + r )
δ δ 1−τ 1− p 1+γ


Linear Tax Scheme, τ = τ0
After Tax Net Wealth, c2 = (s − e) − T (s − e)
IC High
IC Low

Slope 1 − τ0

s −e


Progressive Tax Scheme with τ = τ1 > τ0 for s − e >= z ∗
After Tax Net Wealth, c2 = (s − e) − T (s − e)
IC High 1
IC Low
IC High 2

Slope 1 − τ1

Slope 1 − τ0

s −e
z∗ z ∗ + ∆z


Simulated Savings Using Swedish Data on Income, τ = 0
6000

5000

4000
Frequency

3000

2000

1000

0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
s−e 5
x 10


Simulated Savings Using Swedish Data on Income,
τ = 0.015 above SEK 150000
6000

5000

4000
Frequency

3000

2000

1000

0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
s−e 5
x 10

Agents with
y ∈ f (τ0 ) , f (τ1 )

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


Number of agents bunching:
z ∗ +∆z
B= h0 (s) ds
z∗
h0 (z ∗ ) + h0 (z ∗ + ∆z)
≈ ∆z
2
˜
≈ ∆z h0
or, equivalently,
 1−δ

1 δ
1 1−δ τ1 γ γ
1 + β R δ δ 1 − τ1 1− p 1+γ

B
≈ z∗  ×
˜
h0 1
1−δ
δ
1 + β δ R 1−δ
1
δ 1 − τ0 1−
τ0 γ γ 
p 1+γ

1−δ
1 δ 1
τ0 γ γ τ0 γ
1 − τ0 1− p 1+γ
1− p
1−δ
1 δ 1
τ1 γ γ τ1 γ
1 − τ1 1− p 1+γ
1− p


Solve for structural parameter γ as a function of:

(i) known parameters: z ∗ , τ0 , τ1 ,

B
(ii) the excess bunching around the kink point: ˜
h0
,

(iii) intertemporal parameter δ, discount factor β.

(iv) cost p.


Institutional Background and Data

Figure: MTR since 1992
Marginal Tax Rate %

1.5

Taxable Net Wealth
z∗


Movement in Tax Bracket Cutoﬀ Across Years
SEK 1000

3500

Couples ﬁling jointly
3000

2500

2000

1500
Singles
1000

1998 1999 2000 2001 2002 2003 2004 2005 2006
Year

Declaring Wealth


Table: Perceptions of Tax Cheating in Sweden, in %
Very Quite Not very Not at all Don’t
common common common common know
Federal inc. tax 8.6 26.6 32.5 8.8 22.1
Corporate tax 10.4 29.0 20.6 3.5 34.8
Inheritance tax 11.2 30.3 24.5 6.2 26.2
Wealth tax 18.7 37.2 15.6 3.8 23.5
Estate tax 4.7 17.3 35.2 16.6 24.8
Gas 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
5000
4000
Frequency
3000
2000

1250000 1375000 1500000 1625000 1750000
Third Party Reported Net Wealth, SEK (2002−2006)


Distribution of Taxable Net Wealth, 2002-2006

5000
4000
Frequency
3000
2000

1250000 1375000 1500000 1625000 1750000
Taxable Net Wealth, SEK (2002−2006)


Estimating Excess Bunching

I Follow previous literature

Estimate the counterfactual as a polynomial excluding points around
the kink.

II Nonparametric way

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


Method I

ˆ
BN
Cj 1 + I [j > 0] ∞ =µ0 + µ1 Zj + µ2 Zj2 + . . . + µ7 Zj7 +
j=1
0
ρi I [Zj = i] + ε0
j
i=−R

where Cj is number of people in net wealth bin j, Zj is taxable net wealth
relative to kink point in 5000 kronor intervals, R measures the lower bound
of the bunching that is allowed (measured in 5000 kronor).
B
Estimator of b = h0 given by:

0 ˆ
ˆ
BN j=−R Cj − Cj0
=
hˆ 0 ˆ
Cj
0
j=−R R+1


Empirical Results; Bunching

14000
12000
Frequency
10000

b=0.536 (0.0923)
8000
6000

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


Bunching results, 2002-2006

5000
4000
Frequency

b=0.6565 (0.0991)
3000
2000

−50 −40 −30 −20 −10 0 10 20 30 40 50


Does Bunching Track the Tax?
Bunching in 2001:
1200
1000
Frequency
800
600
400

1000000 1250000 1500000
Taxable Net Wealth


Bunching in 2002:
1500
1000
Frequency
500
0

1000000 12500000 1500000


Bunching in 2001:
1200

2006 kink
1000

2001 kink infl. adj. 2001 kink inv−
ested in stocks
Frequency

2001 kink invested in riskfree interest rate
800
600

2001 kink
400

1000000 1250000 1500000
Taxable Net Wealth


Bunching in 2006:
1400
1200
1000
Frequency
800 600
400

1000000 1250000 1500000
Taxable Net Wealth


Method II

Estimator of B is given by:
BN = N I [z ∗ − R < Zi < z ∗ & Si > z ∗ ].
ˆ
i

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

0
ˆ i=−R Pi
Estimator of h0 is given by: h0 = R+1

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

ˆ
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
ˆ
B
Bunching, h = 1.009
0

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):
Regress ∆ log evasion over X years on ∆ log net-of-tax rates (NTR).
Instrument for ∆ log NTR using the simulated change from holding net
wealth 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 X
Year Fixed Effects X X X X
Region Fixed Effects X X
Wage spline X X
Base Year Evasion spline X X X X
Observations 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
e γ pe
c2 = R (1 − θi τ ) (s − e) + e −
s 1+γ

Let ﬁrst period consumption adjust

c1 = y − s − τ R (1 − θi ) (s − e) .


Predictions:

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

(ii) Conditional on bunching, the distribution of taxable net wealth does
not 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:
Logical skills
Verbal skills
Spatial skills
Technical comprehension


Heterogenous Responses by Cognitive Skills

.05 .15
Fraction of Bunchers
0 .1
Fraction of Bunchers, by Cognitive Skills

1000000 1500000 2000000 2500000 3000000
Pre wealth

High Skilled Low Skilled


Heterogenous Responses by Cognitive Skills

.04
Fraction of Bunchers
.02 .01 .03

0 2 4 6 8 10
Cognitive Skills


Table: Dependent var: indicator for evading the tax through bunching,
logit-model
(1) (2) (3) (4)
Sample: All All 2002 − 2006 2002 − 2006
Cognitive 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 X
Third P.R. NW. - spline X X
Year Fixed Effects X X X X
Age Fixed Effects X X X X
Region Fixed Effects X X X X
Family Fixed Effects X X X X
Education Fixed Effects X X
Observations 60800 60800 34265 34265
Standard errors clustered on the household level.


Distribution of Taxable Net Wealth Among Bunchers,
2002-2006
1500
1000
Frequency
500
0

500000 1000000 1500000
Taxable Net Wealth


Distribution of Taxable Net Wealth Among Bunchers, High
Skilled, 2002-2006
80
60
Frequency
40
20
0

500000 1000000 1500000
Taxable Net Wealth


Distribution of Taxable Net Wealth Among Bunchers, Low
Skilled, 2002-2006
20
15
Frequency
105
0

500000 1000000 1500000
Taxable Net Wealth


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

Deﬁne two skill groups (high and low cognitive skills):
Mann-Whitney U test of equal distributions gives P-value for equality
of distributions = 0.4064

Use discrete variable with nine cognitive skill groups:
Kruskal-Wallis test gives P-value for equality of distributions = 0.4668


Conclusion

Approach tax evasion from three angles.

Findings:
Bunching identiﬁes structural tax elasticity of evasion of 1 − 2.5.
Reduced form estimates on the order of 2 − 4.5.
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 APPROACH
Functional form assumptions, relies on parameter values being correct.

REDUCED FORM
Identifying assumption: Changes in tax rates not correlated with base
year net wealth.


Appendix

Agents with
 1−δ

1 δ
1 1−δ τ0 γ
z ∗ 1 + β R δ δ 1 − τ0 1− p
γ
1+γ


y∈ 1−δ
,
1 δ 1
1 1−δ τ0 γ γ τ0 γ
β R δ δ 1 − τ0 1− p 1+γ
1− p
 1−δ

1 δ
1 1−δ τ1 γ
z ∗ 1 + β R δ δ 1 − τ1 1− p
γ
1+γ


1−δ
1 δ 1
1 1−δ τ1 γ γ τ1 γ
βδR δ 1 − τ1 1− p 1+γ
1− p

Back


David Seim. Tax Rates, Tax Evasion and Cognitive Skills

Recomendados

Recomendados

Más contenido relacionado

La actualidad más candente

La actualidad más candente (14)

Destacado

Destacado (20)

Más de Eesti Pank

Más de Eesti Pank (20)

Último

Último (20)

David Seim. Tax Rates, Tax Evasion and Cognitive Skills