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Income tax statistics analysis: A comparison of microsimulation versus group simulation

  1. Heiko Müller  Is a corresponding author
  2. Caren Sureth  Is a corresponding author
  1. Ruhr-University of Bochum, Germany
  2. University of Paderborn, Germany
Research article
Volume 2(1) Spring 2009
Cite this article as: H. Müller, C. Sureth; 2009; Income tax statistics analysis: A comparison of microsimulation versus group simulation; International Journal of Microsimulation; 2(1); 32-48. doi: 10.34196/ijm.00010
5 tables

Tables

Table 1
Example of grouped data provided by the German Statistical Office, positive and negative income from different sources and assessed income tax. (1995 income distribution, basic tax scale)
taxable income from… to under …DM negative income from different sources positive income from different sources Assessed income tax Amount assessed using 1990 tax scale
number of taxpayers sum in DM ’000 number of taxpayers sum in DM ’000 number of taxpayers sum in DM ’000 sum in DM ’000
Under 1 266,105 −12,415,250 621,453 9,126,448 8,061 890 -
1–5,670 70,316 −710,317 1,722,122 12,318,096 166,060 54,234 -
5,670–8,154 29,302 −315,997 750,329 9,407,202 375,611 135,333 180,739
8,154–12,096 42,971 −495,175 1,133,053 18,737,618 633,921 529,002 965,929
12,096–12,366 2,634 −32,123 65,535 1,272,609 64,297 59,071 83,707
12,366–13,068 6,541 −72,121 159,406 3180,959 155,468 171,071 219,226
13,068–18,036 48,221 −574,758 943,652 22,260,815 933,305 1,795,389 1,837,818
18,036–25,002 77,933 −939,391 1,217,176 36,818,996 1,215,761 4,031,413 4,018,826
25,002–30,023 61,778 −738,561 929,610 33,453,121 929,514 4,411,434 4,408,774
30,023–40,013 132,580 −1,389,631 2,146,192 91,273,023 2,146,147 14,380,689 14,380,662
40,013–50,004 113,496 −1,334,815 1,659,698 86,684,169 1,659,673 15,650,731 15,660,133
50,004–55,728 53,055 −612,021 599,575 36,517,684 599,574 7,160,721 7,173,713
55,728–58,644 21,470 −264,002 231,363 15,215,855 231,360 3,100,941 3,108,599
58,644–60,048 9,722 −135,733 98,916 6,747,897 98,916 1,399,886 1,403,312
60,048–66,366 38,500 −507,366 352,999 25,532,735 352,999 5,449,135 5,465,481
66,366–70,038 18,540 −282,451 152,869 11,943,497 152,866 2,644,972 2,652,440
70,038–75,006 21,053 −316,026 158,898 13,170,377 158,898 3,001,504 3,013,301
75,006–100,008 61,821 −1,177,064 365,395 35,597,184 365,365 8,730,816 8,784,647
100,008–120,042 20,876 −575,376 94,303 11,909,994 94,301 3,263,494 3,299,181
120,042–240,084 34,145 −1,370,692 107,606 19,967,383 107,577 6,268,572 6,458,174
240,084–480,168 9,642 −669,580 23,523 8,923,469 23,518 3,294,257 3,488,455
480,168–1,000,026 3,404 −402,661 7,793 5,920,376 7,787 2,337,854 2,549,395
1,000,026 or more 2,059 −687,475 4,302 15,232,935 4,299 6,096,409 7,226,559
total 1,146,162 −26,018,587 13,545,766 531,212,441 10,485,277 93,967,818 96,379,068

  1. Source: German Statistical Office, Wiesbaden.

Table 2
Tax scale based micro and group simulation of tax revenue for the basic tax scale. (1995 income distribution)
TI class no. taxable income (DM) 1990 tax scale 1996 tax scale
income tax in (DM ' 000) relative difference (%) relative difference (%)
microsimulation (German Statistical Office) group simulation
1 under 1 - - 0.0000 0.0000
2 1–5,670 - - 0.0000 0.0000
3 5,670–8,154 180,739 180,734 −0.0028 0.000
4 8,154–12,096 965,929 965,970 0.0042 0.0000
5 12,096–12,366 83,707 83,706 −0.0012 −0.0685
6 12,366–13,068 219,226 219,228 0.0009 0.0083
7 13,068–18,036 1,837,818 1,837,820 0.0001 0.0022
8 18,036–25,002 4,018,826 4,018,823 −0.0001 0.0008
9 25,002–30,023 4,408,774 4,408,747 −0.0006 −0.0003
10 30,023–40,013 14,380,662 14,381,434 0.0054 0.0034
11 40,013–50,004 15,660,133 15,660,329 0.0013 0.0010
12 50,004–55,728 7,173,713 7,173,689 −0.0003 −0.0003
13 55,728–58,644 3,108,599 3,108,590 −0.0003 −0.0003
14 58,644–60,048 1,403,312 1,403,312 0.0000 0.0001
15 60,048–66,366 5,465,481 5,465,480 0.0000 −0.0005
16 66,366–70,038 2,652,440 2,652,457 0.0006 0.0006
17 70,038–75,006 3,013,301 3,013,302 0.0000 0.0001
18 75,006–100,008 8,784,647 8,782,625 −0.0230 −0.0230
19 100,008–120,042 3,299,181 3,298,992 −0.0057 −0.0058
20 120,042–240,084 6,458,174 6,458,172 0.0000 0.0000
21 240,084–480,168 3,488,455 3,488,455 0.0000 0.0003
22 480,168–1,000,026 2,549,395 2,549,390 −0.0002 0.0000
23 1,000,026 or more 7,226,559 7,226,536 −0.0003 −0.0003
Total (ALL BANDS) 96,379,068 96,377,792 −0.0013 −0.0018

  1. Source: German Statistical Office, Wiesbaden; own calculations.

Table 3
Tax base based micro and group simulation of tax revenue and the financial effects using TI tables in case of vertical loss offset restriction. (1995 income distribution)
TI class no. Percentage difference in the results of microsimulation (German Statistical Office) relative to the discrete group model
interpolation by TIig interpolation by TIi
basic tax scale splitting tax scale basic tax scale splitting tax scale
1 −1.4182 −100.0000 194.1274 263.1967
2 −34.5701 −35.6779 −37.4919 −38.2353
3 −20.3230 −17.8262 −19.9858 −17.7484
4 −14.7191 −11.8263 −15.0016 −11.6785
5 −9.4212 −7.9040 −9.4722 −7.8956
6 −11.7048 −7.3189 −11.7094 −7.3079
7 −9.8775 −6.5023 −10.5133 −6.4304
8 −6.3505 −4.3696 −6.3986 −4.9910
9 −5.1233 −2.9831 −5.2855 −3.0239
10 −3.6476 −2.7450 −3.6717 −3.1454
11 −3.3690 −2.6741 −3.8018 −3.1458
12 −2.4027 −2.4326 −2.7062 −2.4803
13 −2.7901 −2.3300 −2.8571 −2.3755
14 −2.3323 −2.4959 −2.4071 −2.5000
15 −2.6210 −2.4570 −2.7292 −2.5696
16 −2.5111 −2.2322 −2.7662 −2.2305
17 −2.0388 −2.1054 −2.1141 −2.1570
18 −1.6480 −1.7187 −2.6890 −2.5163
19 −0.1687 −0.1625 −0.5135 −0.3792
20 −0.1687 −0.0181 −2.3527 −0.7592
21 −0.0071 −0.0080 −0.5272 −0.1134
22 −0.0038 −0.0037 0.0445 0.2148
23 −0.0010 −0.0010 −5.2218 0.0058
total −1.9124 −3.7316 2.6085 3.0275
total without class 1 1.9282 −1.8186 −3.5040 −2.1424
financial effects −6.8567 −14.5591 14.6799 13.0822
financial effects without class 1 −7.5351 −7.4848 −7.7054 −7.6267

  1. Source: German Statistical Office, Wiesbaden; own calculations.

Table 4
Tax scale based micro and group simulation of tax revenue using a sample of the original microdata and grouped data of TAI tables. (1995 income distribution)
TI class no. Percentage difference in results reported
(i) by sample relative to TAI tables (ii) by group simulation relative to microsimulation
number of taxpayers taxable income calculated income tax
basic tax scale splitting tax scale basic tax scale splitting tax scale basic tax scale splitting tax scale
1 1.4916 −0.0093 0.0934 0.0690 0.0000 0.0000
2 0.8065 −0.000 0.4750 0.0010 0.0000 0.0000
3 0.0927 −0.0020 0.0891 −0.0023 0.0702 −1.0534
4 0.0692 −0.0005 0.0687 −0.0009 0.0723 −0.2947
5 −0.0458 0.0226 −0.0451 0.0233 −0.0455 −0.1903
6 0.0984 −0.0266 0.0993 −0.0269 0.1007 −0.2267
7 0.0482 0.0040 0.0493 0.0036 0.0502 −0.1414
8 0.0784 −0.0015 0.0780 −0.0016 0.0777 −0.0970
9 0.0649 0.0030 0.0659 0.0030 0.0657 −0.0680
10 0.0386 −0.0010 0.0391 −0.0008 0.0447 −0.0544
11 0.0324 0.0001 0.0325 −0.0002 0.0338 −0.0445
12 0.0332 −0.0019 0.0333 −0.0023 0.0329 −0.0392
13 0.0073 0.0176 0.0073 0.0171 0.0070 −0.0172
14 0.0788 0.0000 0.0790 0.0005 0.0792 −0.0323
15 0.0212 0.0000 0.0216 0.0001 0.0217 −0.0311
16 −0.0373 0.0077 −0.0384 0.0084 −0.0383 −0.0203
17 0.0761 −0.0106 0.0754 −0.0105 0.0751 −0.0378
18 0.0235 0.0019 0.0228 0.0021 −0.0006 −0.0384
19 0.0064 −0.0073 0.0057 −0.0075 −0.0004 −0.0302
20 −0.0046 −0.0094 −0.0130 −0.0072 −0.0162 −0.0180
21 0.0467 0.0000 0.0369 0.0000 0.0357 −0.0048
22 0.0000 0.0000 0.0000 0.0000 0.0000 −0.0021
23 0.0000 0.0000 0.0000 0.0000 0.0001 −0.0003
total 0.2782 −0.0007 0.0388 −0.0020 0.0269 −0.0477

  1. Source: German Statistical Office, Wiesbaden; own calculations.

Table 5
Tax base based micro and group simulation of tax revenue and the financial effects using a sample of the original microdata and grouped data of TAI tables in the case of vertical loss offset restrictions. (1995 income distribution)
TI class No. Percentage deviation of the microsimulation results of the German Statistical Office from those of the discrete group model
negative income taxable income modified taxable income calculated income tax on modified taxable income
  basic tax scale splitting tax scale basic tax scale splitting tax scale basic tax scale splitting tax scale basic tax scale splitting tax scale
1 −0.95 −1.34 −75.05 −63.24 73.73 147.02 189.31 136.41
2 −50.78 −37.57 −31.18 −18.79 −46.11 −31.99 −68.99 −59.58
3 −13.07 −11.43 0.06 −1.08 −7.96 −6.68 −29.48 −26.05
4 9.25 −1.37 1.27 1.43 11.13 0.25 −5.83 −12.02
5 17.25 14.01 19.80 8.50 18.53 10.45 6.81 2.77
6 29.06 13.51 18.99 8.29 23.66 10.09 11.29 3.09
7 8.07 9.75 6.03 8.85 6.91 9.20 −3.36 2.21
8 −7.58 0.06 −4.93 2.19 −5.88 1.68 −12.15 −3.06
9 −11.46 5.50 −3.57 0.41 −5.95 1.39 −11.73 −1.15
10 9.25 16.26 8.10 6.99 8.37 8.56 4.61 6.37
11 1.33 58.41 10.69 23.48 8.74 29.04 4.37 28.36
12 1.42 40.82 0.07 14.03 0.31 18.20 −1.98 17.20
13 22.78 20.50 16.16 4.24 17.33 6.74 14.63 5.40
14 5.67 12.35 11.61 0.79 10.48 2.56 7.42 0.83
15 8.27 −5.75 4.16 −6.05 4.87 −6.00 2.51 −8.32
16 −0.56 −23.20 1.82 −16.78 1.38 −17.81 −1.34 −20.12
17 28.67 −30.56 13.76 −22.04 16.32 −23.39 15.32 −25.64
18 21.9 −55.51 5.5 −33.95 8.49 −37.79 9.1 −40.88
19 36.01 −32.40 16.81 −26.38 20.69 −27.50 22.11 −27.81
20 −24.27 1.15 −17.82 −0.42 −19.11 −0.15 −19.82 −0.25
21 75.79 9.33 3.77 0.89 16.45 2.18 17.94 2.33
22 −2.36 47.36 −1.76 0.51 −1.85 7.03 −1.85 7.42
23 −68.43 −40.02 −15.47 1.35 −20.20 −2.53 −20.31 −2.59
total −0.17 −0.35 19.30 5.31 26.87 9.74 2.80 −1.21
total without class 1 0.55 0.18 0.25 −1.20 21.85 5.37 −3.15 −3.95
financial effects 16.47 2.31
financial effects without class 1 −5.09 −8.79

  1. Source: German Statistical Office, Wiesbaden; own calculations.

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