According to Reg. (EU) 2019/1700 Annex II, precision requirements for all data sets are expressed in standard errors and are defined as continuous functions of the actual estimates and of the size of the statistical population in a country or in a NUTS 2 region. For the income and living conditions domain, the estimated standard errors of the following indicators are examined according to certain parametres set:

• Ratio at‐risk‐of‐poverty or social exclusion to population

• Ratio of at‐persistent‐risk‐of‐poverty over four years to population

• Ratio at‐risk‐of‐poverty or social exclusion to population in each NUTS 2 region

EU-SILC is a complex survey involving different sampling designs in different countries. In order to harmonize and make sampling errors comparable among countries, Eurostat (with the substantial methodological support of Net-SILC2) has chosen to apply the "linearization" technique coupled with the “ultimate cluster” approach for variance estimation.

Linearization is a technique based on the use of linear approximation to reduce non-linear statistics to a linear form, justified by asymptotic properties of the estimator. This technique can encompass a wide variety of indicators, including EU-SILC indicators. The "ultimate cluster" approach is a simplification consisting in calculating the variance taking into account only variation among Primary Sampling Unit (PSU) totals. This method requires first stage sampling fractions to be small which is nearly always the case. This method allows a great flexibility and simplifies the calculations of variances. It can also be generalized to calculate variance of the differences of one year to another.

The main hypothesis on which the calculations are based is that the "at risk of poverty" threshold is fixed. According to the characteristics and availability of data for different countries we have used different variables to specify strata and cluster information. In particular, countries have been split into 3 groups:

1) BE, BG, CZ, IE, EL, ES, FR, IT, LV, HU, PL, PT, RO, SI, UK and HR whose sampling design could be assimilated to a two-stage stratified type we used DB050 (primary strata) for strata specification and DB060 (Primary Sampling Unit) for cluster specification;

2) DK, DE, EE, CY, LT, NL, LU, AT, SK, FI, CH whose sampling design could be assimilated to a one stage stratified type, DB050 is used for strata specification and DB030 (household ID) for cluster specification;

3) MT, SE, IS, NO, whose sampling design could be assimilated to a simple random sampling, DB030 is used for cluster specification and no strata;

In order to limit measurement errors and improve the quality of individual income measurement in SILC, data concerning (taxable) income and social security benefits, which were collected by means of surveys until 2007, have since been collected by means of matching with tax and social security data (DGFIP, CNAF, CNAV and CCMSA).

However, this matching is not exhaustive: since matching takes place on the basis of addresses, young adults aged 18 to 25 who are included in their parents’ tax return at an address other than the reporting address may be difficult to find (these young people are asked about the amount of their wage). Likewise, people who have moved house since 1 January of the reporting year may be difficult to find.

Where matching cannot be performed (around 4% of individuals for tax data), tax and social welfare income are imputed.

Finally, only social benefits on the one hand and income declared to the IR on the other hand are obtained by matching. As a result, the questionnaire still contains some amounts of income exempted from income tax and absent from the social source: income from apprentices, school grants, exempted overtime, ....

In the case of social security benefits, all family and housing benefits are covered. This is not the case for the minimum old-age pension. Indeed, CNAV and MSA only pay 70% of the total amount.

Non-response errors are errors due to an unsuccessful attempt to obtain the desired information from an eligible unit. Two main types of non-response errors are considered:

1) Unit non-response which refers to the absence of information of the whole units (households and/or persons) selected into the sample. According to Annex VI of the Reg.(EU) 2019/2242

• Household non-response rates (NRh) is computed as follows:

NRh=(1-(Ra Rh)) 100

Where Ra is the address contact rate defined as:

Ra= Number of address/selected person (including phone, mail if applicable) successfully contacted/Number of valid addresses/selected person (including phone, mail if applicable) selected and Rh is the proportion of complete household interviews accepted for the database

Rh=Number of household interviews completed and accepted for database/Number of eligible households at contacted addresses (including phone, mail if applicable)

• Individual non-response rates (NRp) is computed as follows:

NRp=(1-(Rp)) * 100

Where Rp is the proportion of complete personal interviews within the households accepted for the database

Rp= Number of personal interview completed/Number of eligible individuals in the households whose interviews were completed and accepted for the database

• Overall individual non-response rates (*NRp) is computed as follows:

NRp=(1-(Ra Rh Rp)) 100

For those Members States where a sample of persons rather than a sample of households (addresses, phones, mails etc) was selected, the individual non-response rates will be calculated for ‘the selected respondent.

2) Item non-response which refers to the situation where a sample unit has been successfully enumerated, but not all the required information has been obtained.

The data processing programs incorporate data consistency and format checks (some check programs provided by Eurostat have been recoded in R within the processing chain).