The social component of vulnerability, reflecting the individual’s involvement in social relations and the conditions of the individual’s social life, can act as a predictor of subjective well-being. At that, the lack or complete absence of social bonds can lead to vulnerability. (Ko and Jung 2021) investigated the impact of social vulnerability on the level of life satisfaction among older people in South Korea. To assess life satisfaction, the authors of the study used variables such as participation in social life, including volunteering and visiting community centers and clubs, meeting with friends, and living alone and interacting with other people. The study revealed a negative impact of low social activity on life satisfaction. (Berg et al. 2006) used data from Sweden and found that the quality of social links correlates significantly with the subjective well-being of older people.

(Yang et al. 2016) found a significant negative impact of social vulnerability and frailty on the life satisfaction studying 1970 individuals over the age of 65 years. The performed regression analysis showed that frailty is negatively associated with life satisfaction, and the influence is stronger in the 65–79 age group than in the group consisting of individuals over 80 years old. The obtained result indicates a weakening of the influence of physical vulnerability on life satisfaction with age. However, this difference is revealed only for persons belonging to the second and third social vulnerability terzils.

Financial well-being also acts as a factor of vulnerability. For older people, the problem of a lack of financial resources may be relevant due to the fact that with retirement, individual incomes can sharply decline. In this regard, for some of the elderly continuing to work and maintaining employment status becomes a necessity, which can lead to a deterioration in the quality of life, despite the additional income.

In (Hsu and Wu 2020), it was found that a significant predictor of life satisfaction is the feeling of financial security. The authors show that older people who do not lack income have higher life satisfaction than other groups. Similarly, Wallace (2008) found a positive relationship between income and subjective well-being.

Nevertheless, the relationship between the indicators under consideration is not always present. For example, (Pimquart and Sörensen 2020) found a weak correlation between life satisfaction and income. The authors attribute this result to the fact that older individuals adjust their needs to financial constraints.

(Strawbridge et al. 1998) and (Yang et al. 2016) showed that physical vulnerability is associated with lower life satisfaction. Similarly, (Gwozdz and Sousa-Poza, 2010) found that low self-assessment of health negatively affects subjective well-being.

At the same time, in (Kolosnitsyna et al. 2014), based on data from the Russian Longitudinal Monitoring Survey (RLMS — HSE), it was demonstrated that the health index has a negative relationship with life satisfaction only in the subsample of older women; and in (Enkvist et al. 2012), stroke, dementia, and heart disease did not affect life satisfaction in a sample of individuals aged 78–98 years.

The aim of this study is to assess the impact of vulnerability on life satisfaction of older persons, however, for a more accurate consideration of this relationship, it is necessary to take into account the influence of other individual socio-demographic characteristics, for example, sex, age, place of residence, and marital status, which also often act as predictors of the level of subjective well-being.

In (Guriev and Zhuravskaya 2009) it was revealed that in countries with transitional economies, life satisfaction monotonically decreases with age, while in other countries this dependence is U-shaped with a minimum at the age of 40 years. When contolled for individual indicators such as education and employment, the relationship between age and life satisfaction in countries with transitional economies also becomes U-shaped, but the minimum shifts to the right and settles at the age of 60 years.

(Kolosnitsyna et al. 2014), while studying the influence of socio-economic characteristics on life satisfaction among older people in Russia, did not reveal a significant effect of age on the dependent variable in the entire sample: the correlation turned out to be significantly positive only in the sub-sample of women. There was also no significant relationship between education and life satisfaction — as in the (Pinquart and Sörensen 2000), where, according to the results of empirical analysis, the relationship between education and life satisfaction was weak. However, the authors showed that the quality of contact with children is a more important determinant of life satisfaction in the older population in comparison with its frequency.

Marital status can also be a predictor of life satisfaction: when looking at a subsample of men, (Berg et al. 2006) found that in men, the status of widower was associated with a lower level of life satisfaction. The influence of marital status on subjective well-being was also identified in (Enkvist et al. 2012). According to the results of a survey of 681 respondents aged 78–98 years, the authors showed that living together with a spouse or partner has a positive effect on life satisfaction.

The same study failed to confirm the hypothesis about the influence of place of residence on life satisfaction (ibid.). However, (Zaidi et al. 2009) showed a negative relationship between the size of the settlement and subjective well-being, and the life satisfaction of residents of large cities was lower than that of representatives of smaller settlements. In addition, life satisfaction was found to be positively associated with the possession of various durable goods such as a car, a computer, etc. A negative relationship between urban life and subjective well-being was also revealed in (Kolosnitsyna et al. 2014), where it turned out that city dwellers are less satisfied with life than rural ones. Another important predictor of life satisfaction was an employment (ibid.): a significant positive relationship between these two variables was revealed in the subsample of women. In contrast, (Wallace 2008) found that retired individuals are more satisfied with their lives than those employed.

Thus, individual characteristics can have a significant impact on life satisfaction and excluding them can lead to biased estimates in empirical analysis of subjective well-being.

In the course of systematizing research on the impact of vulnerability on life satisfaction, we considered the main components of vulnerability: social, financial, and physical. As a result of the analysis of previous studies, the following hypotheses were formulated for testing on Russian data:

Hypothesis 1. The frequency of contact with friends is positively associated with the life satisfaction of older people.

Hypothesis 2. The better the financial situation of older people, the higher their life satisfaction.

Hypothesis 3. Frailty is negatively associated with life satisfaction among older people.

Hypothesis 4. There are significant differences in the effect of frailty on life satisfaction in different age groups.

The empirical analysis bases on the spatial data of the first wave of the WHO Study on Global Ageing and Adult Health (WHO SAGE), conducted in Russia in 2007–2010.

Tables 3 and 4 in the Appendix provide descriptive statistics for the main quantitative and categorical variables. On average, individuals are more likely to be satisfied with their lives: 57% of the respondents included in the sample note that they are rather satisfied, and 3% are very satisfied with their life. 63% of the respondents in the sample are women, and the most numerous age group is the 50–59-year-olds. Persons aged 60–74 and 75–89 years old account for 41% and 17%, respectively.

Most of the considered individuals live in urban areas (77%), have high school education or equivalent (52%) and live with a partner (60%). In addition, 63% of individuals are unemployed. 15% of the respondents in the sample have a household member in need of additional support.

Individuals in the sample generally note that they have sufficient income to cover their own needs. When considering variables related to the social component, we observe low participation in public life: in the past year, 93% of individuals attended groups, clubs, societies, and other social events no more than twice.

Within the framework of this study, the physical component of vulnerability is measured using the Frailty Index presented in (Rockwood et al. 2005; Searle et al. 2008) and calculated in terms of accumulated health deficits. Deficits are defined as the presence of symptoms, disease, or functional limitations that lead to increased susceptibility to external factors and an increased risk of adverse outcomes.

The authors of the above-mentioned studies note that this index is significantly associated with an increased risk of death when at least 30 variables are included in the calculation. The more parameters are taken into account when calculating the index, the higher the accuracy of the frailty assessment, while the inclusion of less than 10 indicators in the calculation does not allow obtaining a stable assessment. However, the variables included in the calculation must meet several conditions. First, deficits must be related to the health of the individual. Second, the occurrence of deficits should be positively associated with age. In addition, the deficits should not be massively manifested too early, and their combination should cover various indicators of an individual’s health, not just any one of its components such as, for example, mental health.

To assess the vulnerability components, the variables presented in the authors’ original methodology were compared with the indicators available in the WHO SAGE spatial data. Taking into account the results of previous studies and the criteria for selecting variables, the author picked 39 indicators representing 6 main domains:

• general health indicators;
• medical symptoms;
• functional performance indicators;
• indicators of daily activities;
• diagnosed diseases;
• body mass index.

The number of variables included in the calculation of the Frailty Index is defined by the availability of the necessary information in the WHO SAGE questionnaire, their compliance with the above-mentioned criteria, as well as the number of missing answers within each indicator. Similar variables were included in the calculation by other authors when assessing frailty using data from the WHO SAGE (Biritwum et al. 2016; Harttgen et al. 2013). In this study, the indicators of walking speed and grip force were not taken into account when calculating the index due to the large number of missing values. A full description of all variables used for constructing the Frailty Index is available in Table 5 in the Appendix.

In the course of the data processing, the variables were re-coded in accordance with the recommendations for calculating the Frailty Index presented in the literature. Thus, general health was considered through self-assessment, where “0” means very good, and “1” — very poor health. Medical symptoms, such as memory impairment, physical pain, problems with sleep and vision (at short and long distances), were evaluated in a similar way.

The assessment of daily activities was carried out on the basis of the following indicators: difficulties in getting dressed, when washing and bathing, when getting up from a lying position, and others. To assess functional activity, the author considered difficulties in walking a distance of 100 m, climbing a flight of stairs, and some other activities. 9 variables responsible for the presence of diagnosed diseases, for example, arthritis, stroke, diabetes, and others were reduced to a binary form, where “1” means the presence of a diagnosed disease, and “0” — absence of a diagnosis.

To calculate the body mass index (BMI), a generally accepted formula was used, according to which the respondent’s weight in kilograms must be divided by the respondent’s height in meters squared. Then, depending on the obtained value, the presence of under- or overweight (“1”) or absence of this health deficit (“0”) was determined. If the calculated value of the body mass index turned out to be less than 18.5 or more than 30, then it was assigned a value of 1, and with an index from 25 to 30 — 0.5. The rest of the values, defined as the norm, were assigned to 0.

The Frailty Index is estimated as the arithmetic mean of all indicators, where the sum of all accumulated deficits is divided by their number. Given the number of variables used in this article, the formula can be rewritten as follows:

(formula 1)

Thus, the frailty index was calculated for each of 2,640 individuals aged 50–89 years old.

To test the study hypotheses, the author estimated models introducing the Frailty Index, as well as indicators of social and financial vulnerability, as the controls. In addition, to test Hypothesis 4, the author constructed auxiliary regressors, which are the product of a binary variable of an individual’s belonging to a particular age group and the corresponding value of the Frailty Index. In order to prevent multicollinearity, some of the variables were excluded from the models; namely, these are the binary variables reflecting the presence of a partner, high school education, and age group of 60–74 years old which act as reference groups when considering marital status, education, and age group, respectively. All regressions were constructed using robust standard errors.

As a first step, the author estimated the following OLS model:

(formula 2)

In the presented model, on the left, Life satisfaction is the dependent variable, and X_i is a vector of regressors that includes both indicators of vulnerability and individual demographic and socio-economic characteristics of individuals.

Taking into account the discrete form of the dependent variable and the results of earlier studies, the author of the study also estimates ordered choice models where the probability that life satisfaction will take one of the values from 1 to 5 is calculated using the normal or logistic distribution function.

Table 6 in the Appendix presents the results of estimating the OLS regression, as well as ordered selection models. The values for each variable reflect the estimates of the coefficient values within each of the models.

According to the obtained results, the significance and direction of influence of almost each of the variables on life satisfaction are robust across the models. Since the dependent variable is discrete and the proportion of correctly predicted outcomes was slightly higher for the ordered logit model, further interpretation of the results is carried out on its basis.

Evaluation of the regression models showed that vulnerability has a significant impact on life satisfaction in older people. In Table 7 in the Appendix, the marginal effects for all considered variables are presented. For binary variables, the marginal effect was calculated as a change in the probability of falling into a certain group of life satisfaction as a result of a change in the variable from 0 to 1, and for discrete variables — as a result of a change from 1 to the considered value.

The results of the regression analysis support three out of four hypotheses of the study: about the influence of the frequency of meetings with friends, financial situation, and frailty on subjective well-being. Thus, greater involvement in social life and communication with friends is associated with higher levels of life satisfaction at an older age. The ordered logit model shows that regular interaction with friends is associated with a higher probability of being in the group of more satisfied individuals: it is 5.6 percentage points higher than in the group of those who meet with their friends less frequently. At the same time, a more active social life is not a significant predictor of subjective well-being. In addition, the presence in the household of an individual in need of care or support is negatively associated with life satisfaction of older persons: the likelihood of being included in the group of those who are more likely to be dissatisfied with life in this group is 2 percentage points higher than of those who do not have a relative who is in the need of care.

Hypothesis 2 is confirmed — a significant relationship is revealed between financial position (as an indicator of financial vulnerability) and life satisfaction: the higher it is, the higher the likelihood of falling into a group with high subjective well-being, while the lack of funds to cover daily needs is associated with a lower probability of being satisfied with life. An increase in the likelihood of being among the most satisfied with life by 1.6 percentage points is observed when the material well-being quintile changes from minimum to maximum, i.e., when there is a significant improvement in living conditions. At the same time, having a job negatively affects life satisfaction, and this relationship is significant at a 10% level.

Frailty is negatively associated with life satisfaction: the higher the frailty of older persons, the lower their assessment of subjective well-being. With an increase in the frailty index by 0.1, there is a decrease in the likelihood of falling into the group of those who are satisfied with life by 10 percentage points.

Hypothesis 4 on the presence of differences in the impact of vulnerability on life satisfaction among representatives of different age groups is confirmed only partially, for the group of elderly individuals and at a 5% significance level. Thus, all other things being equal, an increase in the physical vulnerability of individuals at the age of 75–89 years old has a greater negative effect on their subjective well-being in comparison with the group of individuals at the age of 60–74 years old.

Since it was frailty as an indicator of physical vulnerability that turned out to be the variable that most strongly differentiates life satisfaction among older people, the author additionally considers differences in probabilities of falling into groups with high and low levels of subjective well-being across frailty groups. In order to obtain more coherent results, the dependent variable was converted to a binary form: the value “1” was assigned to groups that noted that they were “satisfied” (4) or “very satisfied” with their life (5), and “0” — to those who reported the value of 1, 2, or 3 in the question about life satisfaction. To estimate the predicted probability in the regressions, the author calculated average values of the Frailty Index for the first and third quartiles (25th and 75th percentiles) of frailty and averaged the individual indicators.

The predicted probabilities are shown in Table 1. For the first quartile of the fragility index with a lower degree of physical vulnerability, the probability of falling into the group of those satisfied with their life is 0.72, and for physically vulnerable individuals the probability of being in the group of those satisfied with life is 1.5 times lower. Moreover, in the third quartile, there is a higher probability of being in the group of people dissatisfied with life (0.52) than in the group of people who highly assess their well-being (0.48).

The analysis revealed that the strongest relationship with life satisfaction among older people is observed for vulnerability factors, while the relationship between individual demographic and socio-economic variables and life satisfaction is weak. Place of residence turns out to be a significant factor: living in a city is associated with a lower probability of choosing an ambiguous answer (yes and no) about life satisfaction in comparison with living in rural areas.