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
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
This Paper
Identify the effects of a tax change on substitution and evasion.
Study whether the cognitively able are more likely to evade.
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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.
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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.
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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.
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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.
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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).
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
STRUCTURAL APPROACH
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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.
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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).
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
Linear Tax Scheme, τ = τ0
s − e
After Tax Net Wealth, c2 = (s − e)− T (s − e)IC High
IC Low
Slope 1− τ0
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
Agents with
y ∈
[f (τ0) , f (τ1)
]bunch at the kink point. (Where f (τ) is given here .)
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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.
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
Institutional Background and Data
Figure: MTR since 1992
z∗
1.5
Taxable Net Wealth
Marginal Tax Rate %
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
Declaring Wealth
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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.
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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)
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
Distribution of Taxable Net Wealth, 2002-2006
2000
3000
4000
5000
Freq
uenc
y
13750001250000 1500000 17500001625000Taxable Net Wealth, SEK (2002−2006)
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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.
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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)
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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)
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
Does Bunching Track the Tax?Bunching in 2001:
400
600
800
1000
1200
Freq
uenc
y
1000000 15000001250000Taxable Net Wealth
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
Does Bunching Track the Tax?Bunching in 2002:
050
010
0015
00Fr
eque
ncy
15000001000000 12500000Taxable Net Wealth Relative to Tax Bracket Cutoff (SEK 5000)
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
Does Bunching Track the Tax?Bunching in 2001:
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
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
Does Bunching Track the Tax?Bunching in 2006:
400
600
800
1000
1200
1400
Freq
uenc
y
15000001000000 1250000Taxable Net Wealth
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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)
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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]
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
REDUCED FORM
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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.
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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.
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
BOUNDED RATIONALITY
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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) .
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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.
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
Heterogenous Responses by Cognitive Skills
.01
.02
.03
.04
Frac
tion
of B
unch
ers
0 2 4 6 8 10Cognitive Skills
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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.
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
Distribution of Taxable Net Wealth Among Bunchers,2002-2006
050
010
0015
00Fr
eque
ncy
500000 1000000 1500000Taxable Net Wealth
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
Distribution of Taxable Net Wealth Among Bunchers, HighSkilled, 2002-2006
020
4060
80Fr
eque
ncy
500000 1000000 1500000Taxable Net Wealth
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
Distribution of Taxable Net Wealth Among Bunchers, LowSkilled, 2002-2006
05
1015
20Fr
eque
ncy
500000 1000000 1500000Taxable Net Wealth
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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).
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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.
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012
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
)]
Back
D. Seim (IIES, Stockholm University) Tax Rates, Tax Evasion and Cognitive Skills October 2012