EU statistics on income and living conditions (EU-SILC) methodology - monetary poverty of elderly people - Statistics Explained

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# EU statistics on income and living conditions (EU-SILC) methodology - monetary poverty of elderly people

This article is part of a set of articles describing the methodology applied for the computation of the statistical indicators pertinent to the subject area of Monetary poverty of elderly people (ilc_pn) within the overall domain of Income and living conditions. For these indicators, the article provides a methodological and practical framework of reference. The indicators relevant to the subject area of monetary poverty of elderly people are the following:

• At-risk-of-poverty rate of older people
• At-risk-of-poverty rate for pensioners
• Dispersion around the at-risk-of-poverty threshold (for selected age groups)
• Gender differences in the at-risk-of-poverty rate
• Relative median income ratio
• Gender differences in the relative median income ratio
• Aggregate replacement ratio
• Gender differences in the aggregate replacement ratio
• Inequality of income distribution S80/S20 income quintile share ratio
• Relative median at-risk-of-poverty gap of elderly people

Moreover, since the indicators are of multidimensional structure and can be analysed simultaneously along several dimensions, the separate datasets providing these indicators along with the different combinations of dimensions are also presented.

### Description

• At-risk-of-poverty rate of older people refers to the share of elderly persons who are at risk of monetary poverty, i.e. with an equivalised disposable income (after social transfers) below the at-risk-of-poverty threshold, which is set at 60 % of the national median equivalised disposable income after social transfers.
• At-risk-of-poverty rate for pensioners refers to the percentage of retired persons who are at-risk-of-poverty over the total population of retired people.
• Dispersion around the at-risk-of-poverty threshold (for selected age groups) refers to the share of elderly persons with an equivalised disposable income (after social transfers) below the 50 % and 70 % at-risk-of-poverty threshold (i.e. 50 % or 70 % of the national median equivalised disposable income after social transfers). Three age groups are used to define older (elderly) people: 60 years and over (60+), 65 years and over (65+) and 75 years and over (75+).
• Gender differences in the at-risk-of-poverty rate refers to the absolute difference between the the at-risk-of-poverty rates for males and females living in single-person households.
• Relative median income ratio refers to the ratio of the median equivalised disposable income of people aged 65 or over to the median equivalised disposable income of those aged less than 65. The relative median income ratio is also given for people aged 60 and over compared to persons aged less than 60 years.
• Gender differences in the relative median income ratio refers to the absolute gender differences in the relative median income ratio for persons living in single-person households.
• Aggregate replacement ratio refers to median individual pension income of population aged 65-74 relative to median individual earnings from work of population aged 50-59, excluding other social benefits.
• Gender differences in the aggregate replacement ratio refers to the absolute differences in the aggregate replacement ratios for males and females.
• Inequality of income distribution S80/S20 income quintile share ratio refers to the ratio of total income received by the 20% of the country's population with the highest income (top quintile) to that received by the 20% of the country's population with the lowest income (lowest quintile). Income must be understood as equivalised disposable income. The ratio is given for the population aged less than 65 and 65 or over.
• Relative median at-risk-of-poverty gap of elderly people refers to the poverty gap of elderly people (aged 65 or over and 75 or over), which is measured as the difference between the median equivalised disposable income of elderly people who are at-risk-of-poverty and the poverty threshold itself (60% of median equivalised income), expressed as a percentage of the threshold.

### Statistical population

The statistical population consists of all persons living in private private households. Persons living in collective households and in institutions are generally excluded from the target population.

However, for the calculation of the at-risk-of-poverty rate for older people when broken down by tenure status and the dispersion around the at-risk-of-poverty threshold, all persons aged 60 (or 65 or 75) years or over living in private households are included.

The at-risk-of-poverty rate for pensioners covers all persons aged 18 years or over living in private households who are pensioners (i.e. retired persons), excluding those persons with less than 7 months declared in the calendar of activities are excluded.

The reference population for the aggregate replacement ratio and the gender differences in the aggregate replacement ratio comprises all persons at-work aged between 50 and 59 years and all pensioners between 65 and 74 years living in private households, excluding those with less than 12 months declared in the calendar of activities are excluded. Additionally, people between 65 and 74 years with missing values for pension income or people between 50 and 59 years with missing value for working income are excluded.

The relative median at-risk-of-poverty gap of elderly people consists of all elderly people aged (a) 65 years or over or (b) 75 years or over living in private households.

In any case, people with missing values for equivalised income and for any of the different dimensions that the indicators are presented, are excluded from calculations.

### Reference period

All indicators are collected and disseminated on an annual basis and refer to the survey year.

The reference period for all dimensions along with the indicators are disseminated is the survey year, except for age, income, activity status, household type. As far as age is concerned, it refers to the age of the respondent at the end of the income reference period, based on which the household type is also derived. The income reference period is a fixed 12-month period (such as the previous calendar or tax year) for all countries except the United Kingdom, for which the income reference period is the current year, and Ireland, for which the survey is continuous and income is collected for the last twelve months. For income and activity status, the reference period is the income reference period.

### Unit of measurement

The number of elderly persons at risk of poverty (in thousands) is provided. The percentage of elderly persons at-risk-of-poverty is also given.

Regarding the dispersion around the at-risk-of-poverty threshold, the number (in thousands) and the percentage of elderly persons with an equivalised income below the 50 % and 70 % at-risk-of-poverty threshold is provided.

Gender differences in the at-risk-of-poverty rate are provided as absolute differences between males and females. In this dataset the percentage of males and females at-risk-of-poverty living in single-person households is also given.

The unit of measurement of the relative median income ratio, the aggregate replacement ratio and the inequality of income distribution S80/S20 income quintile share ratio is the ratio.

Gender differences in the relative median income ratio and in the aggregate replacement ratio are provided as absolute differences. In these datasets the median income ratio and the aggregate replacement ratio for males and females is also given.

The poverty gap of elderly people is made available as a percentage.

### Dimensions

The separate datasets provide each indicator along with the Geopolitical entity and time dimensions and the dimensions presented below.

The at-risk-of poverty rate of older people is presented along with the following dimensions:

• age group (less than 60, 60 or over, less than 65 and 65 or over and less than 75 and 75 and over) and sex
• αge group (60 or over, 65 years or over, 75 years or over) sex and tenure status

The at-risk-of-poverty rate of pensioners is presented broken down by age group (18 years or over, 65 or over), sex and activity status

The dispersion around the at-risk-of-poverty threshold is presented broken down by age group (60 or over, 65 years or over, 75 years or over) and sex

The gender differences in the at-risk-of-poverty rate are presented broken down y age group (60 or over, 65 years or over, 75 years or over), sex and household type (only for single-person households)

The relative median income ratio is presented broken down by selected age groups (60+, 65+) and sex

The gender differences in the relative median income ratio are presented broken down by age group (60+ or 65+ or 75+), sex and household type (only for single-person households)

The aggregate replacement ratio as well as the gender differences in the aggregate replacement ratio are presented broken down by sex

The inequality of income distribution S80/S20 income quintile share ratio is presented broken down age group (less than 65 and 65 or over) and sex

The relative median at-risk-of-poverty gap of elderly people is presented broken down by age group (65 or over and 75 or over) and sex

### Calculation method

1. At-risk-of-poverty rate of older people:

At-risk-of-poverty rate (ARPT) broken down by each combination of dimensions (k) $(ARPT_{at\_k})$ is calculated as the percentage of people (or thousands of people) in each k who are at-risk-of-poverty (calculated for different cut-off points) over the total population in k.

The weight variable used is the Adjusted Cross Sectional Weight (RB050a).

$ARPTagex_{at\_k}=\frac{\sum\limits_{i=j\_at\_k}\;RB050a_i}{\sum\limits_{i\_at\_k}\; RB050a_i}\times 100$

$ARPTagex_{at\_k}=\frac{\sum\limits_{i=j\_at\_k}\;RB050a_i}{1000}$

where j denotes the population, or subset of population, who is at risk of poverty and, agex takes the values: less than 60, 60 or over, less than 65 and 65 or over and less than 75 and 75 and over.

With regard to the calculation of the at-risk-of poverty rate of older people, the following methodological issues should be taken into consideration:

• Unless specified, at-risk-of-poverty rates are assumed to be ‘after social transfers’ (i.e. they include social benefits such as pensions and unemployment benefits).
• Income poverty risk at a given point in time may not necessarily imply low living standards in the short term, for example if the persons at risk have access to savings, to credit, to private insurance, tax credits, to financial assistance from friends and relatives etc. In particular, the cumulative impact of extended periods at risk is to be further assessed.
• An approach based on relative income poverty gives a proxy for the risk of being affected by poverty within each country, but makes it more difficult to compare the situation between countries than would be the case with a common threshold.
• Income based indicators are presented for individuals by reference to their household distribution: no information is available about the actual distribution of income between household members. The attribution of the household income to each of its members may impede a detailed analysis of the sex dimension.
• Measuring incomes at the level of private households may have certain implications. The exclusion of collective households might lead to an underrepresentation of certain groups (the elderly, persons with disabilities).

2. At-risk-of-poverty rate for pensioners:

At-risk-of-poverty rate (ARPTretired) for pensioners (over the age of 18) broken down by each combination of dimensions (k) $(ARPTretired_{at\_k})$is calculated as the percentage of retired people in each k who are at-risk-of-poverty over the total population of retired people in that k.

The weight variable used is the Personal Cross Sectional Weight (PB040). ￼

$ARPTretired_{at\_k}=\frac{\sum\limits_{i=j\_at\_k}\;PB040_i}{\sum\limits_{i\_at\_k}\; PB040_i}\times 100$

where j denotes the population, or subset of population, who is at risk of poverty.

With regard to the calculation of the at-risk-of poverty rate for pensioners, the following methodological issues should be taken into consideration:

• Unless specified, at-risk-of-poverty rates are assumed to be ‘after social transfers’ (i.e. they include social benefits such as pensions and unemployment benefits).
• Income poverty risk at a given point in time may not necessarily imply low living standards in the short term, for example if the persons at risk have access to savings, to credit, to private insurance, tax credits, to financial assistance from friends and relatives etc. In particular, the cumulative impact of extended periods at risk is to be further assessed.
• An approach based on relative income poverty gives a proxy for the risk of being affected by poverty within each country, but makes it more difficult to compare the situation between countries than would be the case with a common threshold.
• Income based indicators are presented for individuals by reference to their household distribution: no information is available about the actual distribution of income between household members. The attribution of the household income to each of its members may impede a detailed analysis of the sex dimension.
• Measuring incomes at the level of private households may have certain implications. The exclusion of collective households might lead to an underrepresentation of certain groups (the elderly, persons with disabilities).

3. Dispersion around the at-risk-of-poverty threshold:

The dispersion around the at-risk-of-poverty threshold (ARPT50agex, ARPT70agex) broken down by each combination of dimensions (k) $(ARPT50agex_{at\_k},\;ARPT70agex_{at\_k}$ is calculated as the percentage of older people in k who are at-risk-of-poverty over the total population of older people in that k.

The weight variable used is the Adjusted Cross Sectional Weight (RB050a).

$ARPT50agex_{at\_k}=\frac{\sum\limits_{i=j\_at\_k}\;RB050a_i}{\sum\limits_{i\_at\_k}\; RB050a_i}\times 100$

$ARPT70agex_{at\_k}=\frac{\sum\limits_{i=j\_at\_k}\;RB050a_i}{\sum\limits_{i\_at\_k}\; RB050a_i}\times 100$

where j denotes the population, or subset of population, with an equivalised income below the 50% and 70% at-risk-of-poverty threshold and agex takes the values: 60 years and over, 65 years and over, 75 years and over.

No methodological issues pertain to the calculation of the dispersion around the at-risk-of-poverty threshold.

4. Gender differences in the at-risk-of-poverty rate:

In this dataset, two indicators are produced. The one concerns the at-risk-of-poverty rate of older people and the other the absolute differences in the at-risk-of-poverty rates between males and females living in single person households.

a. At-risk-of-poverty rate broken down by each combination of (k) for single-person households $(ARPT_{at\_k})$ is calculated as the percentage of people in each age group and sex who are at-risk-of-poverty over the total population in that k.

The weight variable used is the Personal Cross Sectional Weight (PB040).

$ARPT_{at\_k}=\frac{\sum\limits_{i=j\_at\_k}\;PB040_i}{\sum\limits_{i\_at\_k}\; PB040_i}\times 100$

where j denotes the population, or subset of population, who is at risk of poverty.

b. The absolute gender differences in the at-risk-of-poverty rate for single person households broken down by each combination of dimensions (k) $(ARPTdiff_{at\_k})$ is calculated as the difference between males and females in the at-risk-of-poverty rate for single person households in that k.

$ARPTdiff_{at\_k}=ARPT_{at\_k/MALE}-ARPT_{at\_k/FEMALE}$

With regard to the calculation of the gender differences in the at-risk-of-poverty rate, the following methodological issues should be taken into consideration:

• The indicator is calculated for single person households and then broken down by sex (total, male, females). The use of single person households avoids making assumptions about the intra-household allocation of incomes, which might affect the conclusions drawn from this indicator. However, the use of single person households is likely to introduce an age bias. Results for the single households cannot be assumed to hold for all household types.

5. Relative median income ratio of a selected age group (60+, 65+):

Relative median income ratio over a selected age group (60+ or 65+) broken down by each combination of dimensions (k) $(EQ\_INC20relage)$ is calculated as the ratio of the median equivalised disposable income after social transfers (EQ_INC20) of people aged above the selected age (i.e. 60 or 65) over the median equivalised disposable income after social transfers (EQ_INC20) of people aged below the selected age.

$EQ\_INC20relage_{at\_k}=\frac{EQ\_INC20_{MEDIAN\_at\_GEage/k}}{EQ\_INC20_{MEDIAN\_at\_LTage/k}}$

where age takes the values 60 and 65.

With regard to the calculation of the relative median income ratio, the following methodological issues should be taken into consideration:

• Compared to the aggregate replacement ratio, the median relative income ratio is broader in scope. This applies both to the income concept and to the age groups that are considered.
• In the calculation of the aggregate replacement ratio, income of elderly is restricted to pensions; income of the younger age group is limited to earnings. For the median relative income ratio, all sources of income are considered.
• Moreover, the median relative income ratio considers two broad age groups (0 to 64 compared to population aged 60 or over or 65 or over), whereas the aggregate replacement ratio focuses on the population aged 65 -74 for the elderly and the population aged 50-59 for the younger age group.

6. Gender differences in the relative median income ratio of a selected age group (60+, 65+, 75+):

In this dataset, two indicators are produced. The one concerns the relative median income ratio for persons living in single person households and the other the absolute differences in the relative median income ratio between males and females living in single person households.

a. Relative median income ratio (60+, 65+, 75+) for single-person households broken down by each combination of dimensions (k) $(EQ\_INC20rel60,\;EQ\_INC20rel65,\;EQ\_INC20rel75 )$ is calculated as the ratio of the median equivalised disposable income after social transfers (EQ_INC20) of people aged above the selected age (i.e. 60 or 65 or 75) over the median equivalised disposable income after social transfers (EQ_INC20) of people aged below the selected age.

$EQ\_INC20relage_{at\_k}=\frac{EQ\_INC20_{MEDIAN\_at\_GEage/k}}{EQ\_INC20_{MEDIAN\_at\_LTage/k}}$

b. The absolute gender differences in the relative median income ratio for single-person households is calculated as the difference between males and females in the relative median income ratio of a selected age group (60+, 65+, 75+) for single-person households:

$EQ\_INC20relagediff=EQ\_INC20relage_{MALE}-EQ\_INC20relage_{FEMALE}$

where age takes the values 60, 65 and 75.

With regard to the calculation of the gender differences in the relative median income ratio, the following methodological issues should be taken into consideration:

• The relative median income ratio is calculated for single-person households. For this indicator a total and a breakdown by sex as well as the absolute difference in the relative median income ratio have to be calculated.
• The use of single-person households avoids making assumptions about the intra-household allocation of incomes, which might affect the conclusions drawn from this indicator. However, the use of single person households is likely to introduce an age bias. Results cannot be assumed to hold for all household types.
• For the age breakdown of people aged 75 and more, there may be some potential statistical difficulties due to the size of samples, and non-coverage of collective households by household surveys.

7. Aggregate replacement ratio:

The aggregate replacement ratio broken down by each combination of dimensions (k) $(AGRR_{at\_k})$ is calculated as the ratio of the median pension income $(INCPEN_MEDIAN)$ for people aged between 65 and 74 years old to the median working income $(INCWRK_MEDIAN)$ for people aged between 50 and 59 years.

$AGRP_{at\_k}=\frac{INCPEN_{MEDIAN\_at\_65-74/k}}{INCWRK_{MEDIAN\_at\_50-59/k}}$

With regard to the calculation of the gggregate replacement ratio, the following methodological issues should be taken into consideration:

• Compared to the median relative income ratio, the aggregate replacement ratio is narrower in scope. This applies both to the income concept as to the age groups that are considered.
• Equivalisation is not performed to gross income, because it is inappropriate. No account is taken of differences in household composition or size, which may affect the adequacy of the income.
• Pension income covers pensions from individual private plans, old age benefits and survivor benefits.
• Other social benefits include unemployment-related benefits; family-related benefits; benefits relating to sickness or invalidity; education-related allowances; any other personal social benefits. Work income includes income from wage and salary employment and income from self-employment.
• No account is taken of other income sources like investment income or social transfers between households.

8. Gender differences in the aggregate replacement ratio:

In this dataset, two indicators are produced. The one concerns the aggregate replacement ratio and the other the absolute differences in the aggregate replacement ratio between males and females.

a. The aggregate replacement ratio broken down by sex $(AGRR_{at\_sex})$ is calculated as the ratio of the median pension income $(INCPEN_MEDIAN)$ for people aged between 65 and 74 years old to the median working income $(INCWRK_MEDIAN)$ for people aged between 50 and 59 years.

$AGRP_{at\_sex}=\frac{INCPEN_{MEDIAN\_at\_65-74/sex}}{INCWRK_{MEDIAN\_at\_50-59/sex}}$

b. The absolute gender differences in the aggregate replacement ratio are calculated as the difference between males and females in the aggregate replacement ratio:

$AGRPdiff=AGRP_{MALE}-AGRP_{FEMALE}$

With regard to the calculation of the gender differences in the aggregate replacement ratio, the following methodological issues should be taken into consideration:

• Gender differences in the aggregate replacement ratio need to be interpreted carefully, particularly in relation to earnings of women aged 50-59. For example, if the female aggregate replacement ratio is higher than for males, this does not necessarily refer to a pension’s policy issue.
• The aggregate replacement ratio is a crude measure of comparison of the pension income of individuals in the upper age group and the income from work of persons in the lower age group. It should be taken into account that this aggregate calculation does not in fact compare the situation of the same individuals before and after the cut-off age.

9. Inequality of income distribution S80/S20 income quintile share ratio:

The S80/S20 income quintile share ratio broken down by each combination of dimensions (k) $(S80\_20_{at\_k})$ is calculated as the weighted ratio of the equivalised disposable income after social transfers (EQ_INC20) of people belonging in the fifth (top) income quintile to the equivalised disposable income after social transfers (EQ_INC20) of those belonging in the first (lowest) income quintile.

The weight variable used is the Adjusted Cross Sectional Weight (RB050a).

$S80\_20_{at\_k}=\frac{\sum\limits_{\forall i\_in\_fifth\_quintile}RB050a_i\times\;EQ\_INC20_{i\_k}}{\sum\limits_{\forall i\_in\_first\_quintile}RB050a_i\times\;EQ\_INC20_{i\_k}}$

With regard to the calculation of the he inequality of income distribution S80/S20 income quintile share ratio , the following methodological issues should be taken into consideration:

• The quintile shares are sensitive to outliers. Extreme incomes, especially at the top end of the distribution, can have a strong influence on this indicator.
• The value this indicator takes when calculated separately for the two age groups does not necessarily imply anything about the distribution of income within one country's population. Rather, it measures solely the distribution of income within a particular age group, treating the complementing age group as though it was not present. One cannot add the inequality of both groups to obtain the overall inequality.
• As the quintiles are calculated at the level of the individuals (not the households) in the sample, individuals in the same age group within the same household could be sorted into different adjoining quintiles, even though their equivalised disposable income would be equal by definition.

10. Relative median at-risk-of-poverty gap of elderly people:

Relative median at-risk-of-poverty gap of elderly people (RAROPG) broken down by each combination of dimensions (k), $(RAROPG_{at\_k})$ is calculated as the difference between the median equivalised disposable income of people below the at-risk-of-poverty threshold (EQ_INC20median/at_poor_k) and the at-risk-of-poverty threshold (ARPT60), expressed as a percentage of the at-risk-of-poverty threshold, in each k.

$RAROPG_{at\_k}=\frac{ARPT60_k-EQ\_INC20_{median/at\_poor\_k}}{ARPT60_k}\times100$

With regard to the calculation of the relative median at-risk-of-poverty gap of elderly people, the following methodological issues should be taken into consideration:

• The poverty gap represents the poverty gap of the ‘median person’ who is at risk of poverty. However, it does not convey any information on the distribution of the poverty gap among the population at-risk-of-poverty.
• The median poverty gap is preferred to the total poverty gap or mean poverty gap, in as far as the latter are more sensitive to extremely low and negative incomes, (which may be due to income measurement errors).
• The poverty gap is expressed as a percentage of the at-risk of poverty threshold in order to make data comparable across countries.

Moreover, there are some methodological limitations that pertain to the following dimensions accompanying the indicators: Age, Activity status, Household type, Tenure status.

### Main concepts used

For the production of the indicators relevant to the subject area of monetary poverty for elderly people, the variables listed below are also involved in computations:

### SAS program files

SAS programming routines developed for the computation of the EU-SILC monetary poverty for elderly people datasets along with the different dimensions, are listed below.

Dataset SAS program file
At-risk-of-poverty rate of older people by sex and selected age groups (ilc_pnp1) pnp1.sas
At-risk-of-poverty rate of older people by age and sex (ilc_pns1) pns1.sas
At-risk-of-poverty rate for pensioners (ilc_pns6) pns6.sas
At-risk-of-poverty rate of older people by tenure status (ilc_pns7) pns7.sas
Dispersion around the at-risk-of-poverty threshold by sex and selected age groups (ilc_pns8) pns8.sas
Gender differences in the at-risk-of-poverty rate (ilc_pnp9) PNP9.sas
Relative median income ratio (65+) (ilc_pnp2) PNP2.sas
Relative median income ratio (60+) (ilc_pns2) PNP2.sas
Gender differences in the relative median income ratio (65+) (ilc_pnp10) PNP10.sas
Gender differences in the relative median income ratio (60+) (ilc_pns11) PNS11.sas
Aggregate replacement ratio (ilc_pnp3) PNP3.sas
Gender differences in the aggregate replacement ratio (ilc_pnp11) PNP9.sas
Inequality of income distribution S80/S20 income quintile share ratio (ilc_pns4) pns4.sas
Relative median at-risk-of-poverty gap of elderly people (ilc_pns5) pns5.sas
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