1. Taxes and benefits
Download icon

The siena microsimulation model (SM2) for net-gross conversion of EU-silc income variables

  1. Gianni Betti  Is a corresponding author
  2. Gabriella Donatiello  Is a corresponding author
  3. Vijay Verma  Is a corresponding author
  1. University of Siena, Italy
  2. ISTAT, Italy
Research article
Volume 4(1) Spring 2011
Cite this article as: G. Betti, G. Donatiello, V. Verma; 2011; The siena microsimulation model (SM2) for net-gross conversion of EU-silc income variables; International Journal of Microsimulation; 4(1); 35-53. doi: 10.34196/ijm.00044
2 figures and 9 tables

Figures

Figure 1
Download asset Open asset
Basic relationship between net and gross amounts.
Table 4
Download asset Open asset
Common structure of the iterative model.

Tables

Table 1
Gross-to-Net conversion algorithm.
Income measure Total By component a
1 GROSS b G=ΣGi ← Gi
2 Social Insurance contribution Si = Si(Gi)
3 GROSS TAXABLE H=ΣHi ← Hi = Gi − Si
4 Component-specific deductions Di = Di(Hi)
Aggregation over components and individuals in tax unit
5 TAXABLE INCOME Y=Σyi ← Yi = Hi − Di
6 Common deductions D0 = D0(H)
7 Taxable income (after deduction) Y0 = Y − D0
8 Tax due (before credits) W0 = W0(Y0)
9 Common tax credits C0 = C0(Y0)
10 TAX DUE W = W0 − C0
11 Component-specific tax credits C = ΣCi ← Ci = Ci(Yi)
12 TAX PAID X = W − C
13 TOTAL NET INCOME N = H − X
14 Tax rate (descriptive) R0 = X/H
15 TAX RATE = TAX DUE/ TAXABLE INCOME R = W/Y
Disaggregation – personal income by component
16 Proportionate tax by component Xi = (R*Yi) – Ci
17 NET INCOME BY COMPONENT Ni = Hi – Xi
  1. a

    The functional relationships in this column may be somewhat more complex or varied.

  2. b

    Gross including employers’ social insurance contribution (SS) is: GG = G + SS(G1)

Table 2
Forms of reporting of an income component.
Income component (i) subject to tax and social insurance contributions
Form (Xi) in which data on the income component have been collected:
  Gi gross income (before tax and social insurance contributions, if applicable)
  Hi gross taxable (before tax, but after social insurance contributions, if any)
  Ni net income (after deducing ‘final’ tax and social insurance contributions, i.e., as the final amount actually received)
Income received after retentions at source:
  XTi taxed at source (but no social insurance contribution); Ti = tax at source
  XSi Social insurance contributions (but not tax) at source; Si = social insurance contributions at source
  XTSi both tax and social insurance contributions at source; Ti + Si
Table 3
Calculation of Hi according to the form in which the component is specified.
Set H
given value Pi = XSi Hi = XSi Simple iteration, generally separately for each component
Gi Hi = Gi − Si(Gi)
XTi Hi = Gi − Si(Gi) where Gi = XTi + Ti(Hi)
XTSi Hi = XTSi + Ti(Hi)
Set N
given value Pi = Ni Hi = Yi + Di(Hi)
where
Yi = [Hi − Ni + Ci(Yi)] / R		 Double iteration
(i) with assumed R, for each component in turn
(ii) for determining R, common to all pooled components

  1. Set N: set of income components which are subject to income tax (irrespective of whether the component is also subject to social insurance contributions), and for which the ‘final net’ amount (Xi = Ni) has been specified in the data collected.

  2. Set H: all other income component (not subject to tax, or for which the data has been collected in a form other than

Table 5
Examples of special deductions and tax credits.
Form of taxation of component i Special deduction Special tax credit
1 Tax exempt Di = Hi −
2 Taxed at flat rate fi Di = Hi Ci = −fi × Hi
3 Tax-exempt at flat rate fi − Ci = +fi × Hi
4 Deductions for expenses + common deductions −
5 Tax credit for expenses − + common tax credits
6 Special tax not related to income − − common tax credits
7 Double taxation at flat rate fi − Ci = −fi × Hi
8 Part ΔSi of social insurance contributions subject to tax −ΔSi −

  1. Different forms may apply to cases like 3, 4 and 7: for instance the tax rate being a more general function of the amount of income involved for the component concerned.

Table 6
Main components of income, and tax and social insurance deductions in the Italian fiscal system (year 2003).
N Income Components Social Insurance Contributions (Si) Tax Included in common pool Component-specific
Deduction (Di) Tax Credits (Ci)c
1 Employment income Employer’s S0(G1)
Employer’s S0(G1)		 IRPEF a X D1(Y1)
2 Self-employment income S2(G2) IRPEF X D2(Y2) −f2(H2) IRAP d
3 Pensions IRPEF X D3(Y3)
4 Non-financial capital income IRPEF X
5 Property (rental and cadastral) income IRPEF c X
6 Financial Capital income Taxed at source (flat rate K6) H6 −K6 × H6
Education related benefits, Unemployment benefits IRPEF X
7 Family benefits, Sickness invalidity benefits d, Housing allowances, Any other personal benefits. Tax exempt H7
Assets
8 Property value ICI (on value of real estate) −f8(value)
  1. a

    Above a certain limit and if it not taxed at source

  2. b

    Additional tax on self-employment income (IRAP, Tax on income from production activities). f(..) stands for "a function of"

  3. c

    On total cadastral and on 85% of the rental income

  4. d

    Part of the benefits may be taxable

Table 7
EU-SILC target variables: distribution of income by component.
Ratio net/gross
6.1.1.1.1.1   Income from work 64.5
PY010 employee cash or near cash income 85.9
employer’s SI contribution
employee’s SI contribution
PY050 cash benefits or losses from self-employment 76.3
Self-employed SI contribution
6.1.1.1.1.2   Property income 80.7
HY090 interest, dividends, profit from capital investments in unincorporated business 81.1
HY040 income from rental of a property or land 80.2
6.1.1.1.1.3   Taxable benefits 88.6
PY090 unemployment benefits 92.5
PY100 old-age benefits 88.7
PY110 survivor’ benefits 87.9
PY130 disability benefits 90.2
6.1.1.1.1.4   Tax-exempt social transfers 100.0
PY140 education-related allowances 100.0
HY050 family related allowances 100.0
HY060 social assistance 100.0
HY070 housing allowances 100.0
HY080 regular inter-household cash transfer received 100.0
Total 71.3
Table 8
Comparison with external sources: distribution of total gross income.
SM2 ISTAT Error (% point)
Gross including SI 100.0 100.0
SI contributions 15.9 15.7 0.2
− Employers’ contribution 9.9 11.4 −1.5
− Employees’ contribution 3.5 2.8 0.7
− Self -employment contribution 2.5 1.6 0.9
Gross taxable 84.1 84.3 −0.2
Personal income tax and financial tax 12.8 12.0 0.8
Net income 71.3 72.2 −0.9

  1. Sources: ISTAT: National Accounts (2003); SM2: Model run using Italy EU SILC Wave 1 (2003) as input

Table A.1
Main components of income, and tax and social insurance deductions: Spain (year 2003)
Income component ECHP/SILC variable Social insurance contribution Taxed at source Tax-exempt
1 Employees’ income (PI1111/PY010), regular wage/salary earnings excluding lump-sum Employers’ contribution f ; Employees contribution; Unemployment. Insurance. g X a
2 Unemployment benefits (PI131/PY090) X a
3 Pensions (PI132/PY100 + PY110) includes old age and survivor’s benefits (2 EU-SILC variables) X a
4 Family related benefits (PI133/HY050) X a
5 Sickness invalidity benefits (PI134/PY120 + PY130) (2 EU-SILC variables) X a X b
6 Other taxable personal benefits (PI136/PY150) X a
Flat rate taxed withholding
7 Employees’ lump-sum income (PI1112) X c
8 Self-employment income (PI112/PY050) Self-employed social insurance X d
9 Capital income includes both financial and non-financial capital income (PI121/HY090) X d,e
10 income from renting out buildings or land (PI122/HY040) X d,e
Tax exempt
11 Education related benefits (PI135/PY140) X
12 Housing benefits (HI138/HY070) X
13 Social assistance (HI137/HY060) X
14 Private transfer received (PI123/HY080) X
  1. a

    All these components are taxed at source following the same rules as applied to employment income. The tax rate for deduction at source is determined on the basis of incomes from components 1–6, taken one at a time. By contrast, the final tax rate (IRPF) is determined on the basis of pooled income from all taxable components 1–10.

  2. b

    Some benefits in these categories are tax exempt, e.g. when the individual is completely disabled, or receive sickness benefit due to HIV

  3. c

    Taxed at source at the same rate as determined on the basis of (and applied to) employee’s income.

  4. d

    Taxed at source at a fixed (flat) rate, depending on the component concerned.

  5. e

    Certain (in particular non-financial) forms of capital income are not subject to withholding at source. Also special or local withholding rates apply to some forms. Similarly, only a part of rental income is subject to withholding. Assumption in the application using available data: As it was not possible to distinguish between different forms of capital income, in our application to ECHP data all capital income was treated in a uniform way as financial capital income.

  6. f

    Employee’s ‘gross income’ (including tax and social insurance contributions of the employee), plus employer’s social insurance contribution gives ‘labour cost’.

  7. g

    Assumption in the application using available data: It was assumed that unemployment insurance contributions are made by all employees, but only during the time they are in employment. In reality, not all persons in employment may make this contribution because it is not obligatory. On the other hand, persons may continue to make this contribution also during any periods of unemployment. Such variations are not available in data such as ECHP at the micro-level.

Table A.2
Main components of income, and tax and social insurance deductions: France (year 2003)
Income from employment
     Total Cost of Labour GG1
     Gross wages G1 = GG1 − S0
     Wages Net of Social Insurance Contributions H1 = G1 − S1
Income net of social contributions
     Net Income H − H8 a
     Total Net Income H
Tax base and tax
     Revenus Catégoriels Yg = (H − Hs) + ΔS
     Revenus Catégoriels Net Yn = Yg − (D1 + D2 + D3 + D4)
     Taxable Income Y = Yn − (D5 + D6 + D7 + D0)b
     (basis for Quotient Familial and Income Taxation)
     Quotient Familial Q
     Net Income taxes (IR) X = Q × W(Y/Q) − (C + C0)
Income after tax N′ = H − X
Disposable Income N = N′ + H8
Constructing the income components in SM2
Gross income (including employers’ SI contributions) GG = G + S8
Employers’ social insurance contributions S8
Gross income (excluding employers’ SI contributions) Gi; G = ΣGi
Income component (i)
     1. Employment income
     2. Self-employment income
     3. Pensions
     4. Unemployment benefits
     5. Invalidity benefits
     6. Capital income ‘A’; Capital income ‘B’ (in fact all capital income treated as ‘A’)
     7. Other incomes: including property and rental income
     8. Benefits ‘A’; Benefits ‘B’ (in fact all benefits treated as ‘B’)
Social insurance contributions (other than employers’) Si; taxable part ΔSi
Gross taxable income Hi = Gi − Si; H = ΣHi
     Component-specific deductions Di; D = ΣDi
     Net taxable income Yi = Hi − (Di − ΔSi) ; Y = ΣYi = H − D
     Common deductions D0; Y0 = Y − D0
     Common tax credits C0
     Quotient Familial Q
     Tax due W = Q × W0(Y0/Q) − C0
     Component-specific tax credits Ci; C = ΣCi
Tax to be paid X = W − C
Total net income N = H − X
     Net by component Ni = Hi − [{Yi (W/Y)} − Ci]
  1. a

    H8 are tax and social insurance (SI) exempt benefits; hence H8 = N8

  2. b

    D5 to D7 are in fact zero (no component-specific deductions)

Download links

A two-part list of links to download the article, or parts of the article, in various formats.

Downloads (link to download the article as PDF)

Download citations (links to download the citations from this article in formats compatible with various reference manager tools)

Open citations (links to open the citations from this article in various online reference manager services)