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Income inequality in life expectancy and disability-free life expectancy in Denmark
  1. Henrik Brønnum-Hansen,
  2. Else Foverskov,
  3. Ingelise Andersen
  1. Faculty of Health and Medical Sciences, Department of Public Health, University of Copenhagen, Copenhagen, 1014 Denmark
  1. Correspondence to Henrik Brønnum-Hansen, Faculty of Health and Medical Sciences, Department of Public Health, University of Copenhagen, Øster Farimagsgade 5, Copenhagen 1014, Denmark; Henrik.Bronnum-Hansen{at}


Background Income has seldom been used to study social differences in disability-free life expectancy (DFLE). This study investigates income inequalities in life expectancy and DFLE at age 50 and 65 and estimates the contributions from the mortality and disability effects on the differences between income groups.

Methods Life tables by income quintile were constructed using Danish register data on equivalised disposable household income and mortality. Data on activity limitations from the Danish part of the Survey of Health, Ageing and Retirement in Europe (SHARE) was linked to register data on income. For each income quintile, life table data and prevalence data of no activity limitations from SHARE were combined to estimate DFLE. Differences between income quintiles in DFLE were decomposed into contributions from mortality and disability effects.

Results A clear social gradient was seen for life expectancy as well as DFLE. Life expectancy at age 50 differed between the highest and lowest income quintiles by 8.6 years for men and 5.5 years for women. The difference in DFLE was 12.8 and 11.0 years for men and women, respectively. The mortality effect from the decomposition contributed equally for men and slightly more for women to the difference in expected lifetime without than with activity limitations. The disability effect contributed by 8.5 years for men and 8.0 years for women.

Conclusion The income inequality gradient was steeper for DFLE than life expectancy. Since income inequality increases, DFLE by income is an important indicator for monitoring social inequality in the growing share of elderly people.

  • Functioning and disability
  • Social inequalities
  • Health expectancy
  • Health inequalities
  • Quality of life

Statistics from


Income inequality increases in almost all world regions, but at different rates.1 In Denmark, income inequality measured using the Gini coefficient has grown from 0.221 in 1987 to 0.291 in 2018 (

Life expectancy has increased in the European countries for more than 100 years although there have been periods of stagnation.2 It is known that income and mortality are strongly linked which is reflected in growing life expectancy with increasing income.3–7 Income inequality in Denmark is low. Nevertheless, increasing income inequality is seen simultaneously with a differential speed of the increase in life expectancy depending on income level. Thus, the mortality pattern differs markedly between income quartiles, and the gap between the lowest and the highest income quartile in life expectancy at age 0 grew from 5.5 to 9.7 years for men and from 5.3 to 5.7 years for women during the period from 1986 to 2014.7

Health expectancy indicators have gained importance as supplement to life expectancy when monitoring overall population health.8 Health expectancy combines information on morbidity and mortality, and the indicator thus has the advantage of considering both quantity and quality of remaining years of life. Previous studies have reported educational inequality in health expectancy for a vast number of countries,9 (for a systematic review of studies published since year 2000). A study comprising eight European countries found that for all countries, life expectancy and disability-free life expectancy (DFLE) increased by level of education and that the educational differences were much smaller in life expectancy than in DFLE.10 A recent review comprising 29 studies from European countries identified socioeconomic inequalities in life expectancy and health expectancy at age 50 and confirmed that people in a more advantaged position can expect a longer life, more years in good health and less in bad health.11 However, limited research exists on income inequality in health expectancy.12–14 Apart from these few studies, it has not been investigated whether the income gradient in DFLE is steeper than that of life expectancy. We know that this is the case for the educational gradient, but although education and income are associated, the two indicators of socioeconomic position are not interchangeable. In fact, there is no clarification as to which measure of socioeconomic position shows the largest or smallest gap in DFLE or other health expectancy indices.15 Income may be a more relevant indicator for people’s social position in later stages of the life course as it captures their current standing, which is not necessarily in accordance with a stratification based on educational credentials often obtained during youth.

The present study aimed to evaluate differentials in life expectancy and DFLE by income among people aged 50 and 65 years using register data on income and mortality for the entire population of Denmark to construct income-specific life tables and Danish survey data on activity limitations from the Survey of Health, Ageing and Retirement in Europe (SHARE) linked with register data on income to establish income-specific data on disability prevalence by age and gender.


Data sources

We used data from the Danish part of SHARE, a cross-national panel dataset covering 27 European countries.16 The fifth wave of the Danish SHARE survey was conducted in 2013–2014 (n=4097, response rate=61%) and we additionally included data from respondents who participated in the fourth wave from 2010 to 2011 but were missing in the 2013–2014 data collection (n=324). After exclusion of 84 people younger than 50 years of age at the time of the data collection, the final sample included 4337 people aged 50 or older.

REGLINK-SHAREDK is a Danish research infrastructure that links national register data to the Danish participants in SHARE by using the unique personal identification number assigned to all citizens ( REGLINK-SHAREDK was used to get consistent and valid income data on the survey participants.


Equivalised disposable household income in 2015–2016 was calculated based on data from the Danish Tax and Customs Administration for all citizens stored at Statistics Denmark.17 Equivalised disposable household income was defined using the Eurostat definition and calculated as the total household income after deduction of taxes and social contributions divided by the number of ‘equivalent adults’ reflecting the size and the age composition of the household by weighting all members of the household (using the modified Organisation for Economic Co-operation and Development (OECD) scale): 1.0 to the first adult; 0.5 to the second adult and each subsequent person aged 14 and over; 0.3 to each child aged under 14.( The total household income consists of income from work, government transfers, private pensions, interest as well as other types of wealth-based incomes such as equity income.

Equivalised disposable household income was divided into quintiles.


Register data on mortality in 2015–2016 for the complete Danish population was used to construct income-quintile-specific life tables. Thus, income grouping was established by dividing individuals into income quintiles within each combination of gender and age and life tables were created for each gender and quintile by linkage to mortality data using the unique personal identification number.

Activity limitation

To measure health status, the Global Activity Limitation Indicator (GALI) was used. GALI has been found to be a valid indicator for activity limitations and is widely used in analysis of DFLE.18 19 The question in SHARE is ‘For the past six months at least, to what extent have you been limited because of a health problem in activities people usually do?’. Respondents were coded as being limited if they answered ‘severely limited’ or ‘limited, but not severely’.


Income-quintile-specific life table data were combined with data on prevalence of no activity limitations by income quintiles to estimate DFLE at age 50 and 65 by the Sullivan method.20 For each gender and income quintile person-years in the age intervals, 50–54, …, 75–79 and 80+ were multiplied by age-specific prevalence of no activity limitations, and person-years without activity limitation were estimated by standard life table methods.20 Differences in DFLE between the highest income quintile and lower income quintiles were further decomposed into the contributions from the mortality effect and the disability effect. We used the decomposition method suggested by Andreev, Shkolnikov and Begun.21 The method is a stepwise replacement algorithm and has recently been described by van Raalte and Nepomuceno.22 Because the sequence of replacements can be performed in different order resulting in different solutions, the final components have to be averaged over all possible permutations. We followed the suggested strategy to run the replacement sequence in ascending order of ages and averaged the final components from two decompositions of the difference in DFLE between two income quintiles.

Different death rates in a specific age interval between persons in two income quintiles imply a difference in person-years between the two income quintiles and furthermore a difference in the number of survivors in the succeeding age intervals which contributes to life expectancy difference between the quintiles. All the age-specific contributions to the difference in person-years between the two income quintiles add up to the difference in life expectancy and contribute to the difference in expected lifetime with/without activity limitations between the two income quintiles (the mortality effect). The age-specific differences in the proportion of people with/without limitations contribute to the other component of the decomposition (the disability effect).


Figure 1 shows mean equivalised disposable household income for the entire population of Danes aged 50 or older in 2015–2016 within the four income quintiles. The income of the richest 20% was about four times higher than that of the poorest 20% and even though we are using a measure of household income women had a somewhat lower income compared to men. This may be because one-third of the population above 50 is living alone. Thus, as in other developed countries, there are still gender differences in income in Denmark.

Figure 1

Mean annual equivalised disposable household income (in 1000 euros) among Danes aged 50 or older in 2015–2016.

The difference between the richest and poorest income quintiles in life expectancy at age 50 was 8.6 years for men and 5.5 years for women (table 1). For men, the difference in life expectancy between the fifth quintile (the richest) and the fourth, third and second quintiles was 1.4, 3.2 and 5.5 years, respectively. For women, the difference was 2.3, 3.6 and 4.8 years, respectively. Table 1 also depicts a clear social gradient in DFLE at age 50 with the difference between income quintile 5 and income quintiles 1, 2, 3 and 4 being, respectively, 12.8, 8.2, 3.3 and 1.7 years for men and, respectively, 11.0, 9.3, 6.5 and 4.3 years for women.

Table 1

Life expectancy (LE) and expected lifetime without activity limitations y (DFLE) and with activity limitations (LE–DFLE) at age 50 by income quintile. Differences decomposed into contributions from mortality and disability effects. Denmark, in 2013–2014*

The contribution from the mortality effect to the difference of 12.8 years without activity limitations (DFLE) between income quintiles 1 and 5 for men was 4.3 years while the disability effect contributed 8.5 years (table 1). The contribution from the mortality effect of the difference of 4.2 years in life expectancy with disability (LE–DFLE) was 4.3 years. For women, the mortality effect contributed 3.0 years to the difference of 11.0 years in DFLE between income quintiles 1 and 5 and 2.5 years to the difference of 5.5 years with activity limitations between income quintiles 1 and 5, while the disability effect contributed 8.0 years. Figure 2 visualises the results from the decomposition.

Figure 2

Differences in life expectancy and expected lifetime with and without activity limitations at age 50 decomposed into contributions from the mortality and the disability effects. Income quintiles 1, 2, 3 and 4 compared with income quintile 5.

Figure 3 shows life expectancy and DFLE at age 65, which is the pension age for the study population (see details in online appendix table). Life expectancy between the highest and lowest income quintiles differed by 4.7 and 3.3 years for men and women, respectively, whereas DFLE differed by 6.1 and 5.6 years, respectively. A clear social gradient in DFLE at age 65 was seen, and it was also apparent when looking at the proportion of lifetime without activity limitations (DFLE/LE) except for women in the lowest quintile for whom the estimate (48.4%) was somewhat higher than that of the second income quintile (42.2%). No significant gender difference in the proportion was observed.

Figure 3

Life expectancy, expected lifetime without and with activity limitations at age 65 and proportion (in percent) of life years without limitations by income quintile, Denmark, 2013–2014 (details in online appendix table).

Supplemental material


This study shows that life expectancy for 50-year-old Danes differed by 8.6 for men and 5.5 years for women between the lowest and the highest income quintiles. However, the highly aggregated life expectancy indicator blurs important details in the social inequality, for instance, in causes of death and lifespan variations.7 23 24 Furthermore, life expectancy does not tell us anything about the health-related quality of life for the remaining lifetime. Integrating life table data and health prevalence data adds this extra component of quality of life to life expectancy. We used GALI to constitute the indicator of DFLE and found remarkable differences between income quintiles and an even steeper gradient for DFLE than life expectancy. Thus, although life expectancy of the poorest 20% of men was 8.6 years shorter than that of the richest 20% at age 50, the reduced lifespan of the poorest 20% was furthermore burdened by 4.2 more years with activity limitations compared to the richest 20% (LE–DFLE, table 1). A similar inequality applied to women.

We examined income inequality in life expectancy and expected lifetime without and with activity limitations at age 50, that is, in an age interval covering some years before retirement and the remaining lifetime after retirement. The results for the 65-year-olds contributes with knowledge about income inequality in the expected total number of retirement years and among these the number of years without and with activity limitations. Not surprisingly, the social inequality remains after pension age, which points to the relevance of a flexible retirement age taking social differentials in morbidity and mortality into account.

Among the few other studies on income differentials in health expectancy, inequalities between income groups were also reported; however, the findings from these studies cannot directly be compared with our results. In the Netherlands, in the period up to 2010, life expectancy differed by 7 years between persons with less than 14 000 euros and persons with more than 28 000 euros of disposable income. Disease-free life expectancy differed by 14 years between the two income groups as age at onset of disability on average was 62 for men and 61 for women in the low-income group, while it was 76 and 75 for men and women in the high-income group.14 A study of active life expectancy among older adults living in the municipal of Beijing in the 1990s defined socioeconomic position by different indicators.13 Men aged 55 in the highest (dichotomised) income group on average lived 37% longer than men in the lower-income group and could furthermore expect 44% more active life years. Among women, there was no statistically significant difference in life and active life expectancy between the income groups.13 In Brazil, a study of disease-free life expectancy among elderly in 1998 and 2008 used household income quintiles to stratify by socioeconomic position. However, the differences between income quintiles in life expectancy without four selected health conditions were erroneous because the same age-specific mortality rates were applied for all income quintiles.12

Danish studies on social inequality in health expectancies where social stratification was based on education or occupation have recently been published.25–27 The difference in life expectancy between 65-year-old men with high and low educational levels was 2.4 years in 2014. For 65-year-old women, the difference was 2.2 years. The difference in DFLE between people with high and low educational levels at age 65 was 2.9 and 3.4 years for men and women, respectively.26 The high and low educational groups were defined by a tripartition according to the highest completed education. This study used the same data sources from 2013 to 2014 and the same measure of disability (GALI) as the current study, and although no formal statistical comparison can be made, the results suggest that income inequalities in DFLE may be larger than educational inequalities. A mortality study that compared educational quartiles and income quartiles suggested that life expectancy difference between educational quartiles 1 and 4 was less than between income quartiles 1 and 4.28 Recently, a study on occupational inequality in DFLE used the same data sources as the present study. Here, it was found that partial DFLE between the ages of 50 and 75 differed by about 4.5 years when comparing Danes in high-skilled white-collar occupations and low-skilled blue-collar occupations.27

Socioeconomic position is usually defined based on either income, education or occupation depending on the purpose of the study. Different choices have their own relative advantages and drawbacks.15 29 The present study investigates health expectancy among middle-aged and older persons including a large share who have left the labour market and whose education was achieved many years ago. Thus, income may be more apt to capture the current social and material standing of this age group. Nevertheless, income is rarely used in DFLE studies, mainly because information is unstable across ages due to changes in personal careers and financial fluctuations. Furthermore, using income to measure social position in studies of social inequality in health and mortality may pose a risk of reverse causality, as the occurrence of illness may cause income reduction and increase risk of death, which can lead to differences being overestimated. Changes in the mortality pattern due to a possible income reduction close to death have previously been examined in the Danish population by comparing the age at death distributions between current income and income 5 years before the calendar year of mortality. The change in social inequality in the mortality patterns was negligible.7 A similar conclusion was reached in a sensitivity analysis in a Finnish study on trends in life expectancy by income quintiles.4 An alternative to using disposable household income might be register data on wealth. We choose to focus on household income (which in this case also includes income from private pensions, interest as well as other types of wealth-based incomes such as equity income) because it gives a good indication of day-to-day material resources. The correlation coefficient between household income and household wealth in our population of Danes aged 50 or older was moderate (0.42 for men and 0.56 for women), suggesting that the importance of income and wealth for DFLE may differ. One reason could relate to negative household wealth being a lot more common in our population (24%) compared to negative disposable household income (0.2%). Considering that a certain income often is necessary to incur debt, it is likely that there is no big overlap between people in the bottom of the wealth distribution and people in the bottom of the income distribution.

A strength of the present study is that income-quintile-specific life tables were unbiased because the register data used to link income and mortality comprises consistent information on all Danes. Furthermore, to ensure consistency between mortality data and survey data, SHARE was enriched with the same register data on income as used for the life tables. The SHARE survey also includes information on household income, but the information is missing for 32% of the participants and differs substantially from the register data. The survey health data we used might be biased due to a relatively low participation rate of 61% in the fifth SHARE wave. However, the impact of non-participation is expected to underestimate social inequalities due to differential response rate and differential health status, which involves under-reporting by people in low-income groups.


The study quantified the well-documented and persisting social inequality in health in Denmark and found that the income gradient for DFLE was steeper than that for life expectancy. Income has seldom been used to investigate social differences in DFLE. Although income inequality in Denmark is modest, it is growing. Due to the clear association between income and health, life expectancy and DFLE by income are important indicators for monitoring social inequality in the growing share of elderly people. Considering that these indicators reveal substantial inequalities, policymakers are encouraged to work towards ensuring that elderly people with a low income can maintain an adequate standard of health and living.

What is already known on this subject

Social inequality in health and mortality increases in Europe and other regions of the world.

Studies have shown large inequalities in disability-free life expectancy between educational groups.

Few studies have estimated income differentials in disability-free life expectancy.

What this study adds

This study is an example of a rare opportunity to split the study population into income groups free of bias as income information is not self-reported but register-based.

Using equivalised disposable household income divided into quintiles demonstrates a steep social gradient in disability-free life expectancy among middle-aged and older persons.

The income gradient in disability-free life expectancy is steeper than the gradient in life expectancy, in accordance with what has been found for the educational gradient.


The authors acknowledge the crucial work performed by the secretariat of the Public Health Database at Department of Public Health at University of Copenhagen in regard to operating and establishing project data. A special thanks to Charlotte Ørsted Hougaard for management and handling the REGLINK-SHAREDK. The paper uses data from SHARE Waves 1, 2, 3 (SHARELIFE), 4 and 5 (DOIs: 10.6103/SHARE.w1.611, 10.6103/SHARE.w2.611, 10.6103/SHARE.w3.611, 10.6103/SHARE.w4.611, 10.6103/SHARE.w5.611, 10.6103/SHARE.w6.611), see Börsch-Supan et al 16 for methodological details.16 The SHARE data collection has been primarily funded by the European Commission through FP5 (QLK6-CT-2001-00360), FP6 (SHARE-I3: RII-CT-2006-062193, COMPARE: CIT5-CT-2005-028857, SHARELIFE: CIT4-CT-2006-028812) and FP7 (SHARE-PREP: N°211909, SHARE-LEAP: N°227822, SHARE M4: N°261982). Additional funding from the German Ministry of Education and Research, the Max Planck Society for the Advancement of Science, the US National Institute on Aging (U01_AG09740-13S2, P01_AG005842, P01_AG08291, P30_AG12815, R21_AG025169, Y1-AG-4553-01, IAG_BSR06-11, OGHA_04-064, HHSN271201300071C) and from various national funding sources is gratefully acknowledged (see



  • Contributors HB-H planed and designed the study. EF processed the SHARE data. HB-H conducted the analysis and drafted the work. All authors contributed to interpretation of the results and revision of the manuscript.

  • Funding The study was financed by grants from Helsefonden (The Health Foundation), Grant number 17-B-0281.

  • Competing interests None declared.

  • Patient consent for publication Not required.

  • Ethics approval The use of microdata from the national registers accessed from Statistics Denmark follows the rules and regulations of the General Data Protection Regulation and is not subject to authorisation from the National Committee on Health Research Ethics, as the investigations do not involve personal contact and informed consent is not required for register-based studies in Denmark. However, the processing and linking of data was approved by the Danish Data Protection Agency. In Denmark, the National Committee on Health Research Ethics does not require ethical approval to use SHARE Wave 5 as it is solely based on survey data and does not include any samples of biological materials from humans ( However, the SHARE project is submitted to continuous ethics reviews. From wave 4 and onwards, SHARE has received ethical approval from the Ethics Council of the Max Planck Society. The last ethics approval was granted on March 4, 2016 (

  • Provenance and peer review Not commissioned; externally peer reviewed.

  • Data availability statement No data are available.

  • Supplemental material This content has been supplied by the author(s). It has not been vetted by BMJ Publishing Group Limited (BMJ) and may not have been peer-reviewed. Any opinions or recommendations discussed are solely those of the author(s) and are not endorsed by BMJ. BMJ disclaims all liability and responsibility arising from any reliance placed on the content. Where the content includes any translated material, BMJ does not warrant the accuracy and reliability of the translations (including but not limited to local regulations, clinical guidelines, terminology, drug names and drug dosages), and is not responsible for any error and/or omissions arising from translation and adaptation or otherwise.

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