Annex
The explanatory variables for the kNN method
1. Region: West and Central Hungary in contrast with North Hungary 2. Sole proprietor in full time (dummy)
3. Turnover under 20 million HUF (dummy) 4. Turnover under 25 million HUF (dummy)
5. Non-registered production1 or tips in households sector (dummy)
6. Group of industries 1 (1. Agriculture, 2. Industry, 3. Construction, 4. Services)
7. Group of industries 2 (1. Agriculture, 2. Construction, 3. Retail trade, 4. Services1 –
industries in fields of 64–88 NACE code, 5. Services2 – services without retail trade and Services 1, 6. Industry)
8. Group of industries 3 (1. Agriculture, Wholesale trade, Accommodation and food service
activities, Real estate activities, 2. Construction, 3. Retail trade, Legal and accounting activities, Activities of head offices, 4. Other industries)
9. Average GVA of corporations per employee at four digit level of NACE, million
HUF/person
10. Ratio of purchases and sales
11. Average GVA of corporations per employee at two digit level of NACE, million
HUF/person
12. Ratio of the GVA and output of corporations at two digit level of NACE
13. Ratio of the average turnover of sole proprietors to that of corporations at two digit level of
NACE
14. Relative output of missing corporations in 2008 at four digit level of NACE
15. Natural logarithm of the ratio of corporations GVA and output at four digit level of NACE 16. Natural logarithm of the average of corporations GVA per employee at two digit level of
NACE
17. Natural logarithm of the average ratio of sole proprietors’ and corporations’ turnover at two
digit level of NACE
18. Natural logarithm of purchases, million HUF 19. Natural logarithm of sales, million HUF 20. Natural logarithm of turnover, million HUF 21. Natural logarithm of other costs, million HUF
22. Natural logarithm of the sum of entrepreneurial withdrawals and wages, million HUF 23. Natural logarithm of total costs, million HUF
24. Natural logarithm of the ratio of GVA and output for individuals and for corporations at
two digit level of NACE
25. Natural logarithm of the ratio of GVA for individuals and for the mean of corporations at
two digit level of NACE
1 The non-registered output of households includes the production in fields of agriculture, hotels and
28. Natural logarithm of material to other costs
29. Natural logarithm of the ratio of the difference between turnover and material cost to the
total cost
30. Natural logarithm of the ratio of the difference between turnover and material cost to the
other cost
31. Natural logarithm of labour input (person)
32. Natural logarithm of the difference between turnover and material cost per labour input,
(million HUF/person)
33. Natural logarithm of wages and entrepreneurial withdrawals per labour input (million
HUF/person)
34. Natural logarithm of wages per labour input (million HUF/person) 35. Natural logarithm of the ratio of wages to the total cost
36. Year of establishment
37. Natural logarithm of the basis of payable VAT (million HUF)
Table A1 The parameters of linear regression
Explanatory variables*
Agriculture and transportation
Retail trade Construction Industry
Services without transportation and retail trade
Constant 1 070.20
(367.54)
–80 548.41 (41 798.36)
Sole proprietor in full time (dummy) 540.72
(258.17)
634.10 (223.22) Turnover under 20 million HUF
(dummy)
–1 984.17 (445.21)
Purchases, million HUF 9.34
(4.98)
43.78 (8.59)
Sales, million HUF –0.32
(0.20)
–124.37 (45.47)
–71.80 (11.04)
Turnover, million HUF –6.40
(5.19)
16.71 (8.18)
30.72 (8.96)
Total cost, million HUF –43.45
(12.23) Other cost, million HUF –15.65
(6.75)
–1.99 (0.88)
20.84 (14.83)
–106.90 (22.22)
(Continued on the next page.)
(Continuation.)
Explanatory variables*
Agriculture and transportation
Retail trade Construction Industry
Services without transportation and retail trade
Sum of entrepreneurial withdrawals and wages, million HUF
440.71 (116.91)
5.63 (2.43)
–157.21 (66.49)
–388.56 (99.35)
481.44 (79.84) Quotient of the ratios of purchases and
sales for individuals and for the mean of corporations at four digit level of NACE
22.91 (15.25)
40.84 (28.03)
Quotient of the ratios of intermediate consumption and output for individuals and for the mean of corporations at two digit level of NACE
–227.86 (116.72)
–19.79 (11.06)
256.11 (52.47)
–438.75 (143.61)
234.97 (91.09)
Ratio of differences between turnover and material cost to the total cost
–93.08 (34.20) Ratio of differences between turnover
and material cost to the other cost
1.36 (0.99)
138.14 (28.42) Difference between turnover and
material cost per labour input, million HUF/person
–6.83 (3.09)
–116.82 (15.83)
29.09 (19.53) Ratio of the difference between
turnover and material cost per labour input for individuals to that of the mean of corporations at four digit level of NACE
31.58 (11.15)
–529.15 (96.49)
–253.61 (67.43)
Ratio of GVA per labour input for individuals to that of the mean of corporations at two digit level of NACE
0.04 (0.03)
0.32 (0.06)
0.48 (0.11)
0.35 (0.04)
Ratio of material costs to other costs 8.31 (5.84)
0.63 (0.24)
–30.78 (16.88)
220.24 (86.10)
7.87 (2.70)
Labour input, person –477.09
(124.03) Sum of entrepreneurial withdrawals and
wages per labour input, million HUF/person
46.87 (12.03)
–373.00 (122.01) Wages per employee, million
HUF/person
–1 200.25 (434.82)
–20.83 (15.49)
1 395.81 (665.12)
Year of establishment 0.05 (0.01)
41.53 (20.90) Basis of payable VAT, million HUF 0.45
(0.24)
35.91 (11.70)
140.43 (38.44) Natural logarithm of purchases, million
HUF
704.85 (565.82)
–92.36 (27.49)
510.92 (169.74)
672.92 (179.77)
284.76 (73.53) Natural logarithm of sales, million HUF –714.64
(579.02)
58.64 (27.11) Natural logarithm of turnover, million
HUF
27.53 (9.95)
–595.16 (168.95) Natural logarithm of the sum of
entrepreneurial withdrawals and wages, million HUF
–408.90 (200.81)
–26.61 (8.59)
–509.72 (287.76)
–327.14 (180.34) Natural logarithm of total cost, million
HUF
501.53 (210.77)
1 370.30 (393.20) Natural logarithm of other cost, million
HUF
–342.33 (196.64) Natural logarithm of the ratio of GVA
per labour input for individuals to that of the mean of corporations at two digit level of NACE
–84.57 (60.24)
–117.08 (70.80)
–188.49 (104.92)
–137.57 (39.48)
Natural logarithm of the quotient of ratios of purchases and sales for individuals and for the mean of corporations at four digit level of NACE
–760.20 (577.80)
76.55 (32.76)
Natural logarithm of the quotient of ratios of intermediate consumption and output for individuals and for the mean of corporations at two digit level of NACE
27.35 (14.16)
–418.95 (121.84)
Natural logarithm of the ratio of material cost to the other cost
–24.93 (8.62)
–493.89 (119.53)
–1 052.53 (221.88) Natural logarithm of the ratio of the
difference between turnover and material cost to the total cost
24.53 (34.20)
–652.82 (224.72)
–1 505.05 (386.45)
(Continued on the next page.)
(Continuation.)
Explanatory variables*
Agriculture and transportation
Retail trade Construction Industry
Services without transportation and retail trade
Natural logarithm of labour input, person
996.64 (417.99)
1 262.75 (341.05)
–955.91 (272.12) Natural logarithm of the ratio of the
difference between turnover and material costs per labour input for individuals and that of the mean of corporations at four digit level of NACE
–34.20 (10.51)
624.70 (232.05)
Natural logarithm of wages per employee, million HUF/person
–579.23 (223.61)
–720.56 (360.33)
934.69 (413.93)
–1 187.35 (147.57) Natural logarithm of wages per total
cost
763.50 (256.74) Natural logarithm of the basis of
payable VAT, million HUF
–670.46 (194.93) Natural logarithm of the ratio of the
difference between turnover and material cost to the other cost
617.75 (248.78)
Adjusted R2 0.43 0.51 0.52 0.82 0.46
Sample size 314 280 220 84 394
Dependent variable Undeclared
VAT (thousand
HUF)
Ratio of undeclared
VAT and purchases
Undeclared VAT (thousand
HUF)
Quotient of undeclared VAT and ratio of purchases
and sales
* Owing to the multicollinearity of the explanatory variables, the partial interpretation of the parameters is not possible. However, the use of these parameters is justified since the analysis aims only to estimate undeclared VAT.
Note. The standard errors are in parenthesis.
Natural logarithm of turnover 0.829 (0.004)
0.765 (0.018)
Adjusted R2 0.87 0.70
Sample size 7 415 783
Note. The standard errors are in parenthesis.
Table A3 The output and GVA of sole proprietors, 2011
(million HUF)
Industry
The economic performance of VAT-subject sole proprietors
Category N7 Category N5
Total sum of sole proprietors’ economic
performance Figure calculated from
tax returns data Estimated data for VAT evasion
Output GVA Number of VAT evaders
Undeclared
VAT Output GVA Output GVA Output GVA Output GVA
Agriculture 190 278 80 265 5 456 4 212 15 721 24 486 56 769 28 875 13 215 6 715 275 983 140 340 Industry 169 011 76 313 3 617 3 552 13 775 19 616 88 793 52 076 15 457 8 926 287 038 156 930 Construction 114 438 62 045 5 754 4 491 14 067 19 207 161 785 101 765 35 428 22 447 325 718 205 464 Retail trade 111 463 60 851 10 389 7 798 30 735 36 133 70 202 47 880 20 226 13 795 232 626 158 659 Transportation 175 633 97 028 3 228 2 730 5 696 10 931 20 208 12 031 7 045 4 194 208 583 124 184 Services without
transportation
and retail trade 251 387 121 871 12 233 10 849 43 703 51 258 818 995 585 496 122 670 86 607 1 236 754 845 232 Total 1 012 210 498 374 40 677 33 631 123 698 161 630 1 216 752 828 122 214 041 142 684 2 566 702 1 630 810
Note. The discrepancies between the figures Total and the actual column totals result from rounding.
