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Methodology, Taxes and benefits

Research articles · Jun 30, 2009

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

Heiko Müller, Caren Sureth

Faculty of Economics, Universitätsstr, Ruhr-University of Bochum, Germany; Faculty of Business Administration and Economics, University of Paderborn, Germany

Volume 2(1) Spring 2009

Cite 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

Abstract

Microsimulation based on income tax statistics may be useful in tax reform discussions. Unfortunately, access to appropriate data is still rather restricted and expensive for ad-hoc analyses, and individual data is often even not available at all. In this paper we take Germany and its data situation as a proxy for many countries. restrictions in terms of tax data availability. Analyzing how much reliability and robustness of results we lose if we employ group simulation instead of microsimulation, we compare both methods. Investigating tax scale effects by the group model leads to very good results. Determining the financial effects of modified tax bases, the deviation from the microsimulation results increases, especially if tax base cuts vary between taxpayers. In addition, we take account of the class of taxpayers with a negative taxable income. Neglecting this class we identify a systematic underestimation of the financial consequences of a modified tax base with the group model assuming a progressive tax scale. If the group simulation data is not arranged according to the taxable income, but rather according to the total amount of income, we also find a tendency towards higher deviations from the microsimulation results. Quantifying the tax revenue effects of alternative tax settings the group simulation model represents a good compromise between the desire to capture the complex reality and the achievable accuracy when facing limited resources and data. Furthermore, for those cases in which group simulation is the appropriate tool, we provide a very simple method to interpolate a suitable income distribution and thereby the tax distribution within the classes. This interpolation makes future estimates of tax revenues a lot easier. We conclude that, although microsimulation in general is the superior approach, a group simulation model remains of interest, especially for analyses of rather old data and cross-country analyses, when sufficiently detailed data for micro analyses is missing.

This article contains 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

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

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

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

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

Source: German Statistical Office, Wiesbaden; own calculations.