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A proposal for a simple average-based progressive taxation system
Dirk-Hinnerk Fischer* 
Simona Ferraro*
Simona Ferraro
Affiliation: Tallinn University of Technology, Tallinn, Estonia
 0000-0001-5175-5348
Preliminary communication | Year: 2019 | Pages: 141 - 165 | Volume: 43 | Issue: 2 Received: January 9, 2019 | Accepted: April 1, 2019 | Published online: June 10, 2019
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FULL ARTICLE
FIGURES & DATA
REFERENCES
CROSSMARK POLICY
METRICS
LICENCING
PDF
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21.43/1
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30/1.4
|
45/2.0998
|
|
Yo
|
76,809
|
76,809
|
76,809
|
|
Y1
|
165,850
|
165,850
|
165,850
|
|
T(Yo)
|
39,510
|
38,460
|
37,683
|
|
T(Y1)
|
90,002
|
86,395
|
83,602
|
|
ATR (Yo)
|
0.51
|
0.50
|
0.49
|
|
ATR(Y1)
|
0.54
|
0.52
|
0.50
|
|
ARP
|
0.02
|
0.02
|
0.01
|
Source: LIS 2007 Data for Germany Notes: authors’ own calculation
|
2007
|
Germany
|
|
Tax
rate
|
|
Quantile
|
Income
in thousand €
|
x
|
Formula
I
|
Formula
II
|
|
1
|
4.5
|
0.10
|
3.09
|
|
|
5
|
8.4
|
0.19
|
5.71
|
|
|
10
|
10.9
|
0.25
|
7.39
|
|
|
25
|
18.0
|
0.41
|
12.25
|
|
|
50
|
31.5
|
0.71
|
21.43
|
|
|
75
|
51.9
|
1.18
|
35.30
|
|
|
Cut
for (4)
|
73.5
|
1.67
|
50.00
|
|
|
90
|
76.8
|
1.74
|
52.27
|
50.10
|
|
95
|
99.0
|
2.25
|
67.37
|
50.58
|
|
99
|
165.9
|
3.76
|
112.87
|
52.10
|
Source: Luxembourg Income Survey (LIS) 2007 Notes: authors’ calculation based on LIS
|
2010
|
Germany
|
|
Tax
rate
|
|
Quantile
|
Income
in thousand €
|
x
|
Formula
I
|
Formula
II
|
|
1
|
4.3
|
0.1
|
2.9
|
|
|
5
|
8.8
|
0.2
|
5.89
|
|
|
10
|
11.3
|
0.25
|
7.6
|
|
|
25
|
18.0
|
0.40
|
12.17
|
|
|
50
|
31.9
|
0.71
|
21.43
|
|
|
75
|
54.1
|
1.21
|
36.42
|
|
|
Cut
for (4)
|
74.3
|
1.67
|
50
|
|
|
90
|
81.3
|
1.82
|
54.72
|
50.16
|
|
95
|
101.4
|
2.27
|
68.24
|
50.61
|
|
99
|
161.5
|
3.62
|
108.64
|
51.95
|
Source: Luxembourg Income Survey (LIS) 2007 Notes: authors’ calculation based on LIS
|
2007
|
Estonia
|
|
Tax
rate
|
|
Quantile
|
Income
in thousand €
|
x
|
Formula
I
|
Formula
II
|
|
1
|
0.7
|
0.05
|
1.60
|
|
|
5
|
2.4
|
0.18
|
5.51
|
|
|
10
|
2.7
|
0.22
|
6.45
|
|
|
25
|
4.6
|
0.35
|
10.71
|
|
|
50
|
9.2
|
0.71
|
21.43
|
|
|
75
|
16.3
|
1.26
|
37.87
|
|
|
Cut
for (4)
|
21.5
|
1.67
|
50.00
|
|
|
90
|
24.5
|
1.90
|
56.86
|
50.22
|
|
95
|
30.8
|
2.38
|
71.53
|
50.72
|
|
99
|
46.6
|
3.60
|
108.03
|
51.93
|
Source: Luxembourg Income Survey (LIS) 2007 Notes: authors’ calculation based on LIS
|
2010
|
Estonia
|
|
Tax
rate
|
|
Quantile
|
Income
in thousand €
|
x
|
Formula
I
|
Formula
II
|
|
1
|
0.7
|
0.06
|
1.79
|
|
|
5
|
2.4
|
0.19
|
5.68
|
|
|
10
|
3.4
|
0.27
|
8.02
|
|
|
25
|
4.6
|
0.37
|
11.09
|
|
|
50
|
8.9
|
0.71
|
21.43
|
|
|
75
|
16.9
|
1.34
|
40.32
|
|
|
Cut
for (4)
|
20.9
|
1.67
|
50.00
|
|
|
90
|
25.3
|
2.02
|
60.51
|
50.35
|
|
95
|
33.3
|
2.65
|
79.50
|
50.98
|
|
99
|
49.99
|
3.98
|
119.52
|
52.31
|
Source: Luxembourg Income Survey (LIS) 2007 Notes: authors’ calculation based on LIS
Source: DeStatis dataset (2015).
|
Income
group in thousand €
|
Average
income per group
in thousand €
|
Nr.
of taxpayers
in thousand
|
SPT
(1)
result
|
Tax
rate SPT
in %
|
Total
group tax volume real
in million €
|
Total
group tax volume under SPT
in million €
|
|
0-2.5
|
0.8
|
25.8
|
0.01
|
0.21
|
60.4
|
0.045
|
|
2.5-5.0
|
3.8
|
47.2
|
0.06
|
0.93
|
35.4
|
1.6
|
|
5.0-7.5
|
6.3
|
71.8
|
0.10
|
1.55
|
44.2
|
7.0
|
|
7.5-10
|
8.8
|
160.1
|
0.15
|
2.18
|
78.2
|
30.7
|
|
10.-12.5
|
11.3
|
665.1
|
0.19
|
2.78
|
204.4
|
208.6
|
|
12.5-15
|
13.7
|
863.7
|
0.23
|
3.39
|
495.2
|
402.6
|
|
15-20
|
17.5
|
1,789.2
|
0.29
|
4.32
|
2,220.2
|
1,352
|
|
20-25
|
22.5
|
2,134.1
|
0.37
|
5.56
|
4,013.5
|
2,667.3
|
|
25-30
|
27.5
|
2,333.1
|
0.45
|
6.79
|
6,093
|
4,355.6
|
|
30-37.5
|
33.6
|
3,148.9
|
0.55
|
8.30
|
11,898.9
|
8,783.9
|
|
37.5-50
|
43.3
|
3,737
|
0.71
|
10.69
|
21,890.6
|
17,291.6
|
|
50-75
|
60.6
|
3,818
|
0.99
|
14.97
|
38,271.8
|
34,625
|
|
75-100
|
85.7
|
1,531
|
1.41
|
21.17
|
26,260.2
|
27,776.1
|
|
100-125
|
110.9
|
657
|
1.83
|
27.39
|
16,703.8
|
19,952.9
|
|
125-175
|
145.1
|
486.2
|
2.39
|
35.86
|
18,583.7
|
25,306
|
|
175-250
|
205.5
|
230.3
|
3.38
|
50.05
|
14,160.7
|
23,677.8
|
|
250-375
|
299.3
|
114.4
|
4.93
|
51.60
|
11,147.5
|
17,668.1
|
|
375-500
|
428.8
|
38.7
|
7.06
|
53.73
|
5,685.9
|
8,923.9
|
|
500-1,000
|
668.2
|
37.7
|
11.01
|
55.00
|
8,977.1
|
13,870
|
|
1,000-2,500
|
1,463.4
|
12.2
|
24.11
|
55.00
|
6,339.8
|
9,829.8
|
|
2,500-5,000
|
3,408.8
|
2.6
|
56.16
|
55.00
|
2,924.7
|
4,788.4
|
|
5,000-
|
12,887.6
|
1.4
|
212.31
|
55.00
|
5,459.8
|
9,888
|
|
|
|
|
|
|
201,549.1
|
231,407
|
Sources: Based on DeStatis dataset (2015) Notes: authors’ own calculation, under the exclusion of donations; tax rate multiplier of 15 and a societal tax multiplier of 3.33 ̅ - in order to reflect a reasonably similar total tax volume.
|
Income group
in thousand €
|
Average income per group
in thousand €*
|
Nr. of taxpayers
in thousand
|
SPT Formula result**
|
Tax rate SPT**
|
Total group tax volume
real
in million € **
|
Total group tax volume
under SPT
in million €**
|
|
0-1.7
|
0.6
|
68.8
|
0.04
|
0.53
|
0
|
0.2
|
|
1.7-3.2
|
2.5
|
47.0
|
0.14
|
2.11
|
473.0
|
245.7
|
|
3,2.-6.4
|
4.7
|
128.0
|
0.26
|
3.96
|
1,289.2
|
2,364.3
|
|
6.4-12.8
|
9.3
|
176,925
|
0.53
|
7.90
|
1,782.2
|
12,967.2
|
|
12.8-19.2
|
15.5
|
79,832
|
0.88
|
13.17
|
804.3
|
16,269.1
|
|
19.2-25.6
|
21.9
|
31,954
|
1.24
|
18.64
|
322.2
|
13,055.3
|
|
25.6-32
|
28.4
|
14,092
|
1.61
|
24.13
|
141.7
|
9,647.8
|
|
32-63.9
|
41.7
|
15,556
|
2.36
|
35.44
|
156.5
|
22,960.5
|
|
63.9-127.8
|
82.4
|
2,359
|
4.67
|
53.00
|
23.9
|
10,298.2
|
|
127.8-191.7
|
151.7
|
282
|
8.61
|
55.00
|
2.8
|
2,353.,6
|
|
191.7- 255.7
|
222.3
|
61
|
12.61
|
55.00
|
0.569
|
745.9
|
|
255.7-320
|
286.5
|
30
|
16.25
|
55.00
|
0.569
|
472.7
|
|
320-383.5
|
350.5
|
22
|
19.88
|
55.00
|
1.6
|
424.1
|
|
383.5-639.1
|
480.8
|
31
|
27.27
|
55.00
|
0.569
|
819.7
|
|
639.1-3,195.6
|
952.6
|
21
|
54.03
|
55.00
|
4.200
|
1.100
|
|
Above 3,195.6
|
4,534.4
|
2
|
257.19
|
55.00
|
1.9
|
498.8
|
|
Total
|
|
|
|
|
569.2
|
48.8
|
Sources: Based on (Estonian Tax and Customs Board, 2013) * Estimation based on standard distribution ** Estimation – if applicable: based on the same parameters as Table 6
Source: Luxembourg Income Survey (LIS) for years 2007 and 2010
Source: Luxembourg Income Survey (LIS) for years 2007 and 2010
Table 1Average rate of progression DISPLAY Table
Table 2Simple progressive tax results Germany 2007 DISPLAY Table
Table 3Simple progressive tax results Germany 2010 DISPLAY Table
Table 4Simple progressive tax results Estonia 2007 DISPLAY Table
Table 5Simple progressive tax results Estonia 2010 DISPLAY Table
Graph 1Taxation volume per income group in billion € DISPLAY Graph
Table 6SPT in comparison with the German tax code in 2011 DISPLAY Table
Table 7SPT in comparison with the Estonian tax code in 2012 DISPLAY Table
Table A1Descriptive statistics for Germany DISPLAY Table
Table A2Descriptive statistics for Estonia DISPLAY Table
* We would like to thank the participants of the FairTax special session of the conference “Enterprise and Competitive Environment 2017” for their comments on a draft of this paper. We would also like to thank Ton Notermans of Tallinn University of Technology for his advice on the paper as well as the two anonymous referees.
1 Friedman wrote: “I find it hard, as a liberal, to see any justification for graduated taxation solely to redistribute income” (Capital and Freedom).
2 Russia in 2001, Serbia in 2003, Slovak Republic and Ukraine in 2004, Romania and Georgia in 2005.
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June, 2019
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