Research Article |
Corresponding author: Rafael A. Akhtemzyanov ( rafael-css@yandex.ru ) © 2023 Rafael A. Akhtemzyanov.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Akhtemzyanov RA (2023) An Econometric Assessment of the “Punishment” for Singlehood in Russia: Risks or New Opportunities in Life? Population and Economics 7(1): 33-53. https://doi.org/10.3897/popecon.7.e89168
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The paper focuses on the effect of having a marriage partner on health and well-being of Russians as compared with their single compatriots. The health status variation between those who are married and those who are single can be explained both by the protective effect of marriage and marriage selection. Using the Cox proportional hazards model on the self-perceived health data from the RLMS 2004-2019 individual questionnaire, while controlling for socioeconomic factors, lifestyle, and living arrangements, we have found that the protective effect of marriage is non‑existent in men, except for a short-term impact of marital transitions. Women are “punished” for their singlehood due to a lack of a partner in their young age, or being in an unregistered union, or the loss of a breadwinner spouse at the age of 50 to 64. In contrast, women over 65 benefit from singlehood.
Singlehood, marriage, marital status, health, survival analysis
The paper focuses on the effect of having a marriage partner on health and well-being of Russians as compared with their single compatriots. The relationship between the marital status and the health status of a person has been well studied in different countries and supported by data. For example, the health indicators are on average better in those who are married than those who are not, while the mortality rates are lower for both men and women in all age groups (
Singlehood itself, associated with the absence of a marriage partner, can be broken down in two types: primary, resulting from not getting married, and secondary, arising upon withdrawal from marriage. In the Russian literature, the effect of having a partner on health and well-being is mainly considered in terms of simple comparison of average indicators (such as self-perceived health or life satisfaction) for the population grouped by the current marital status, gender, and age (
Our contribution can help shed some light on the positive and negative effects of living with a partner, as well as assess the size of the singlehood “penalty” for Russians.
The spread of gender egalitarianism and tertiary education along with the revolution in the gender roles in societies are the most important reasons for singlehood and childlessness, according to literature. For example,
The findings of the effect of the growing gender equality in access to education and career opportunities and of the lagging gender norms and traditions on singlehood and childlessness are also supported by the panel data from Germany (
Therefore, the level of education is an important socioeconomic parameter, as it is associated with the probability of falling into the group of singles. Next, we review the literature which examines more broadly the effects of the so-called marital transitions, i.e., entering into or withdrawal from marriage, with a view to identifying their positive or negative effects.
Empirical evidence suggests that the initial period of marriage features “bonuses” to health, physical and mental, while dissolution of marriage is associated with “penalties.” The mechanisms of the protective effect of marriage on health include improved psychological status, reduced probability of depression (
Thus, in the short term, entering into marriage is linked with health benefits, while, on the contrary, divorce seems to be a negative stressful life event, leading to deterioration of health, both physical and mental.
The consequences of marriage dissolution go beyond the above-mentioned short-term negative effects of the change in the marital status. A number of longitudinal studies applying the survival analysis have reported higher health risks for both those who for whatever reason withdrew from marriage and those who have never been married.
A number of studies have reported increased risks of cancer in single women (
Summarizing the empirical results obtained by the authors, we can assume that the single lifestyle is associated with an increased risk of developing chronic diseases and death as compared to having a marriage partner. The use of survival analysis, namely the Cox proportional hazards model, seems justified here, because it is better in this case than a simple linear regression or matching, and the reasons for that are as follows. Firstly, the survival analysis allows to account for censored observations, that is, individuals who dropped from the survey and whose future is untraceable, which is often the case in longitudinal studies. Secondly, it is easier to consider the long-term effects of the marital status on health by comparing the survival of groups of respondents according to their marital status over the period of survey. Thirdly, characteristics of the participants may change, e.g., as caused by getting married, changing a job, having children, etc., and the survival analysis allows constructing models to account for such changes, which improves the accuracy of results.
We use the Cox proportional hazards model to analyse the relationship between the marital status and health risks. The main source of data is the RLMS, which offers a broad set of questions on various aspects of the life of Russians. All the necessary control variables are only available from 2004 through 2019, so we rely on the annual observations for the waves 13-27, respectively.
The regressors that we further use in our models are the transformed variables taken from the RLMS questionnaire. Thus, the self-perceived health status is the main health variable. In addition, we consider a wide range of control characteristics: education, income, employment, lifestyle and bad health habits, type of population centre, etc.
As mentioned above, we apply the Cox proportional hazards model with time-varying covariates, especially in order to timely account for changes in the variable of interest, i.e., the respondent’s marital status. If the marital status changes during a certain wave of the survey (e.g., by getting married), then we will be able to track this down immediately (i.e., capture the marital transition), which is impossible to do in the standard Cox model. In our case, the model equation looks as follows:
hi (t) = h0(t) * exp[marsti * β(t) + Xi * γ(t)]
where
t – age of person (model time)
hi (t) – estimated risk of the i-th person to categorize as a low self-perceived health status
h 0(t) – risk to categorize as a low self-perceived health status, the same for all persons
Xi – matrix of control variables for the i-th person
marsti – marital status of the i-th person
γ(t) – coefficient vector for control variables, according to the age group
β(t) – coefficient vector for the variable of interest: marital status, according to the age group
We use the deterioration in the self-perceived health status as a failure event in our models, i.e., moving from the “rather satisfied with one’s health” group to the “dissatisfied with one’s health” group. Since the self-perceived health status is a categorical variable, we use it to construct a binary variable. Thus, respondents with the self-perceived health at “very good,” “good,” or “fair” fall into the good health category while those with the same at “poor” or “very poor”, into the poor health category.
There are several reasons for the above breakdown: firstly, it allows for a large sample size across all age-sex groups. Annex
For convenience, the control variables used in the model can be divided into the following three blocks:
Furthermore, control for the year of birth and fixed effects for each wave of the survey were introduced in all the specifications. Such a set of control variables generally covers different aspects of life. As we will see later, even in the absence of detailed medical information on the respondents’ health status, consecutively introducing control variables to the model does explain the protective effect of marriage in many cases, making it statistically insignificant. Therefore, even allowing for the fact that the problem of endogeneity may still be present due to self-selection into marriage, the available controls allow to successfully handle it.
The marital status of the respondent is the variable of interest here. We use the “in a registered marriage” group as a control group (with which we compare all the others). Therefore, all the estimates we obtain further below in the models are the risks of health deterioration for the groups with different marital statuses as compared with those who are in a registered marriage. Besides, we extended the model by introducing the variables to describe the marital transitions over the past three years, namely entering into a registered marriage and withdrawal from marriage through widowhood or divorce. This timeframe was chosen based on the empirical literature on marriage transitions and the duration of their effect on health (
Inasmuch as, consistent with the theory of the previous chapter, we expect different values of the protective effects of marriage for different age-sex groups, and also in order to meet the proportionality condition, which is one of the assumptions of the Cox model, we added binary variables to the model for the following three age groups: 30-49 years, 50-64 years, and 65+ years, with a view to estimating age-heterogeneous effects both for the marital status and for the control variables. This is the method which Therneau et al. (2017) recommend for simulated time-dependent hazard ratios. We chose age-group breakdown thresholds based on the methodology to be found in
Thus, based on the RLMS questionnaire, we found all of the most important variables that were controlled for in the previous studies.
Annex
We obtained the following results (Table
M 30-49 | M 50-64 | M 65+ | W 30-49 | W 50-64 | W 65+ | |
Never married | 1.38 | 0.57 | 0.57 | 1.45** | 1.22 | 1.02 |
Living together, not in a registered marriage | 1.28 | 0.88 | 0.88 | 1.01 | 1.46*** | 1.06 |
Divorced and unmarried | 1.27 | 0.79 | 0.79 | 0.98 | 1.17 | 0.92 |
Widowed | 0.79 | 1.07 | 1.07 | 0.98 | 1.32** | 0.80** |
In a registered marriage, not living together | 1.51 | 1.13 | 1.13 | 1.32 | 1.93* | 0.31 |
Events | 1 828 | 2 744 | ||||
Observations | 33 811 | 41 797 | ||||
*0.1 **0.05 ***0.01 |
In order to draw substantive conclusions, we tested the assumptions of the estimated models (see Annex
For convenience, let us consider each of the marriage statuses one by one as classified in the RLMS questionnaire.
The effect for men in the complete specification model was not significantly different from zero in all age groups, and most of the protective effect of marriage for them was explainable by introducing variables relating to the living arrangements: parental status and living alone, which correlated with the marital status. Notably, the introduction of lifestyle and habits-related variables into the model did very little for the size of effect for men in this age group. It is likely that these factors have a significant effect in older ages. For example, in the 65+ age group, it was the introduction of lifestyle variables that explained the entire effect for primarily single men. For women, the effect remained stable even upon introducing additional groups of controls. Given this control, never-married women aged 30-49 had about a 45% higher risk of lower self-perceived health than married women. Still being single while most of the peers are already in a relationship can cause additional anxiety and stress which lead to health problems. That is true for the Russian women in their younger working ages. However, as women age 50 or older, their non-marriage will no longer impact the probability of health deterioration; we did not find a significant effect even in the baseline specification. This can be explained by two reasons: first, at older ages, the decision not to get married is already an informed choice and therefore does not lead to any significant stress, and second, with age, a person simply gets adapted to living alone so that the costs of this lifestyle will decrease.
We deliberately did not cluster this category with those who have officially registered their relationships. Of course, those who live together but are not married are not single and nevertheless, it was interesting to see whether there are any effects for this group of individuals, or it is possible not to single them out into a category of its own in the future. In men, as before, no protective effect of marriage was found. For women in the younger age group, the effect initially identified in the baseline model completely disappeared when the new blocks of control variables were introduced. But at older ages (50-64) it remained robust, with a 46% higher risk of lower self-perceived health.
Initially, we expected higher risks for divorced individuals in all age-sex groups since the reviewed empirical literature (
Therefore, parting with an unloved partner, for all its costs, does not create additional health hazards. It seems that the main risk factor for the divorced persons is deterioration of their living arrangements (in particular, they live alone much more often) and development of bad habits, and it is through that channel that deterioration of health further takes place (of course, this hypothesis of ours also needs to be additionally tested). Furthermore, divorce, on average, occurs at an older age than marriage so that deterioration of health can partly be explained with the age factor as well.
There were few widowed respondents in the younger age groups and this simple fact means that the confidence intervals of the model were wide, making it difficult to find causal relationships for these groups. In pre-retirement age women, the loss of a partner, a breadwinner of the family, indeed, increases the risks of health problems by approximately 46%. However, at age 65+, by contrast, the effect is positive, with approximately a 20% reduction in the risks of health deterioration. As with the divorced, the widowed women are on average more likely to live alone, and on average they are older. By that age, they will often have adult children who can take care of them, and they would not bear the burden of loneliness even if they live without a partner. Moreover, they do not need to take care of their ill spouses, which also creates a protective effect from living alone for women of retirement age.
This group was the smallest compared to the others (see Annex
The following conclusion can be made from all the above: in Russia, the protective effect of marriage is much weaker than the literature initially allowed to expect. And in most cases the protective effect of marriage disappears when controls are introduced for the socioeconomic status, living arrangements, and habits.
In men, the protective effect of marriage was not found in any age group. Women have a greater propensity for prioritizing family over career and, therefore, have a hard time living alone due to not having a partner at their young age or if they live in an unregistered relationship at the pre-retirement age. They face a health risk due to their loss of a breadwinner spouse at ages 50-64. But then after the age of 65, widows face lower health risks than married women, which we initially did not expect to find.
Next, we will discuss the limitations of this analysis and possible directions of future research that would clarify the nature of “punishment” for singlehood in Russia.
The main limitation we encountered in conducting this study relates to the non-binary nature of the dependent variable, i.e., self-perceived health status. We developed a strategy for dichotomizing this variable based on the literature exploring the specifics of using the health variable in the RLMS and bringing it to a binary form, as well as for technical reasons (please, refer to Data and Empirical strategy). However, it is not technically possible to conduct a robustness analysis for selecting a threshold between what would be considered good health and poor health and, in particular, which category the “fair” health status should fall into, because in this case the sample size for all age-sex groups is simply not sufficient for the robustness analysis itself to be considered substantive.
A whole number of studies have looked into the extent to which a self-perceived health status truly reflects a person’s health rather than a subjective perception thereof. For example,
On the other hand, there is evidence to suggest that self-perceived health status used in RLMS is a good predictor of mortality (
The straightforward selection of the development of chronic diseases as a dependent variable presents a number of technical and substantive problems. Firstly, the presence (or absence) of a particular chronic disease conveys little about the person’s overall health status. In such cases, one can control for numerous medical characteristics of health: blood pressure, haemoglobin, body mass index and others, many of which are not to be found in the RLMS questionnaire. Secondly, the RLMS data on the presence of chronic diseases are of low quality. Thus, there are many respondents in the sample who forgot to mention the presence of certain diseases in each wave of the survey. Therefore, an additional cleansing and correction of the chronic disease data is required before those can be used to conduct a longitudinal study, which can also create additional limitations for the extrapolation of the results.
The connection between singlehood and well-being is still insufficiently covered in the scientific literature. Most papers including this one focus specifically on the direct effect of the marital status on health while ignoring other aspects of life, such as development of bad habits, changes in living arrangements, losing or finding a job, income dynamics, etc. The survival analysis methodology allows to assess the connection between the single lifestyle and the above as well as many other aspects of human well-being in order to get a broader picture of the “punishment” for being single in Russia, the magnitude of the “punishment” and its time-dependent behaviour along with its interplay with general changes in lifestyles and the behaviour in the marriage market.
Compared to the previously obtained empirical evidence suggesting a very large protective capacity of marriage in terms of health, we have found from the fresh data on the Russian population that it is not as prominent as originally expected. The three blocks of control variables that we used explain most of the differences between the marriage status groups. This means that in many cases the differences in the health dynamics between the single and the married Russians are explained by marital selection and changes in lifestyles and habits, rather than by the protective function of marriage. Having said this, at present, the differences between the single and the married Russians are still detectable in the data. And therefore, the institution of marriage is still an important factor in the health dynamics of Russia’s population.
Therneau T., Crowson C., Atkinson E. (2023) Using time dependent covariates and time dependent coefficients in the Cox model. CRAN Packages, Survival. https://cran.r-project.org/web/packages/survival/vignettes/timedep.pdf
Regressors | ||
---|---|---|
Name of Variable | Description | Units, Scale |
Variables of Interest | ||
Marst | Current marital status | 1) Never married 2) In a registered marriage 3) Living together, not married 4) Divorced and unmarried 5) Widowed 6) In a registered marriage, but not living together |
marriage | Binary variable for those who have got married over the past 3 years | 0) No 1) Yes |
Divorce | Binary variable for those who have divorced over the past 3 years | 0) No 1) Yes |
widowhood | Binary variable for those who have become widowed over the past 3 years | 0) No 1) Yes |
Block 0: fixed effects and technical control variables | ||
Wave | Survey wave index | 13-27 waves |
Born | Year of birth cohorts | Respondent’s year of birth |
age_group | Respondent categories by age (for heterogeneous effects and model calibration). Methodology used: (Franke S., Kulu H., 2018) | 1) 30-49 years 2) 50-64 years 3) 65+ years |
Block 1: Socioeconomic control variables | ||
Educ | Level of education. Represented in the model as a set of dummy variables | 0) Basic general 1) Secondary or Vocational secondary 2) Tertiary |
Income | Monthly income in 2020 rubles. Obtained by nominal income adjustment for CPI | RUB ‘000 |
Job | Employment | 0) no 1) yes |
Block 2: control variables for living arrangements | ||
Status | Type of population centre | 1) regional centre 2) city 3) urban-type settlement 4) village |
Alone | Respondent living alone? Obtained from household data | 0) no 1) yes |
children_old | Number of children from 18 years and upwards | Number |
children_young | Number of children under 18 years | Number |
Block 3: control variables for lifestyle | ||
Alcohol | alcohol use | 0) no 1) yes |
cigarettes | tobacco use | Cigarettes per day |
Phys | Physical activity level | 0) No physical exercise 1) Occasional physical exercise, or better |
Dependent variable (failure event) | ||
Name of variable | Description | Units, Scale |
event_health | Falls into “rather poor” self-perceived health category (health > 3) | 0) no 1) yes |
health | M 30-49 | M 50-64 | M 65+ | W 30-49 | W 50-64 | W 65+ |
1 | 2.0 % | 0.6 % | 0.4 % | 1.2 % | 0.3% | 0.1% |
2 | 45.2 % | 20.0 % | 7.9 % | 35.8 % | 12.1% | 3.7% |
3 | 48.2 % | 64.8 % | 55.0 % | 57.5 % | 69.8% | 49.2% |
4 | 4.2 % | 13.1 % | 30.3 % | 5.2 % | 16.3% | 39.3% |
5 | 0.4 % | 1.5 % | 6.4 % | 0.3 % | 1.5% | 7.7% |
Total | 100 % | 100 % | 100 % | 100 % | 100% | 100% |
Total, persons | 32 569 | 18 503 | 10 354 | 39 498 | 27 885 | 25 134 |
Women 30+ | |||||||
---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | ||
observations | 4972 | 44041 | 8357 | 11962 | 22613 | 572 | |
age | 48.03 (15.56) | 49.15 (13.03) | 45.63 (11.83) | 51.77 (13.05) | 69.00 (12.03) | 49.52 (12.78) | |
income | 23.10 (18.03) | 19.54 (17.03) | 20.44 (18.11) | 24.60 (18.67) | 18.25 (11.78) | 23.67 (17.86) | |
eduс (%) | 0 | 792 (16.0) | 5005 (11.4) | 1284 (15.4) | 1226 (10.3) | 8409 (37.3) | 82 (14.4) |
1 | 2456 (49.5) | 25762 (58.6) | 5179 (62.1) | 7200 (60.4) | 10629 (47.2) | 329 (57.6) | |
2 | 1713 (34.5) | 13224 (30.1) | 1876 (22.5) | 3503 (29.4) | 3503 (15.5) | 160 (28.0) | |
job (%) | 0 | 2003 (40.3) | 17738 (40.3) | 2933 (35.1) | 4389 (36.7) | 17887 (79.2) | 205 (35.8) |
1 | 2966 (59.7) | 26288 (59.7) | 5422 (64.9) | 7568 (63.3) | 4700 (20.8) | 367 (64.2) | |
status (%) | 1 | 2410 (48.5) | 17308 (39.3) | 3374 (40.4) | 5806 (48.5) | 9620 (42.5) | 284 (49.7) |
2 | 1014 (20.4) | 11908 (27.0) | 2322 (27.8) | 3536 (29.6) | 5728 (25.3) | 143 (25.0) | |
3 | 405 (8.1) |
3050 (6.9) | 455 (5.4) |
822 (6.9) |
1340 (5.9) | 42 (7.3) |
|
4 | 1143 (23.0) | 11775 (26.7) | 2206 (26.4) | 1798 (15.0) | 5925 (26.2) | 103 (18.0) | |
alone (mean (SD)) | 0.25 (0.43) | 0.00 (0.06) | 0.01 (0.12) | 0.27 (0.44) | 0.42 (0.49 | 0.18 (0.39) | |
children_old (mean (SD)) | 0.25 (0.53) | 1.18 (1.08) | 0.90 (1.02) | 1.07 (0.88) | 1.70 (1.09) | 1.21 (1.14) | |
children_young (mean (SD)) | 0.30 (0.58) | 0.61 (0.89) | 0.59 (0.87) | 0.35 (0.62) | 0.06 (0.29) | 0.48 (0.77) | |
cigarettes | 2.00 (5.05) | 1.31 (4.29) | 3.75 (6.76) | 2.54 (5.83) | 0.79 (3.51) | 2.96 (6.38) | |
alcohol | 0.58 (0.49) | 0.62 (0.49) | 0.69 (0.46) | 0.63 (0.48) | 0.48 (0.50) | 0.73 (0.45) |
|
phys | 0.23 (0.42) | 0.21 (0.41) | 0.18 (0.39) | 0.25 (0.43) | 0.18 (0.38) | 0.24 (0.43) | |
health (mean (SD)) | 2.86 (0.73) | 2.89 (0.66) | 2.85 (0.64) | 2.97 (0.67) | 3.40 (0.72) | 2.98 (0.69) |
Men 30+ | |||||||
---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | ||
observations | 3384 | 43864 | 8075 | 3503 | 2312 | 288 | |
age | 39.03 (9.36) | 50.34 (13.56) | 46.58 (12.43) | 48.52 (11.92) | 70.49 (12.30) | 48.02 (12.77) | |
income | 20.04 (19.77) | 28.65 (21.50) | 24.94 (20.19) | 20.88 (19.55) | 21.61 (15.91) | 24.48 (21.05) | |
eduс (%) | 0 | 773 (23.0) | 7737 (17.7) | 1887 (23.4) | 649 (18.6) | 971 (42.1) | 53 (18.5) |
1 | 1936 (57.5) | 25546 (58.3) | 5094 (63.3) | 2256 (64.6) | 935 (40.6) | 167 (58.2) | |
2 | 657 (19.5) | 10504 (24.0) | 1068 (13.3) | 589 (16.9) | 399 (17.3) | 67 (23.3) | |
job (%) | 0 | 1548 (45.7) | 14665 (33.4) | 2476 (30.7) | 1647 (47.1) | 1862 (80.7) | 110 (38.2) |
1 | 1836 (54.3) | 29177 (66.6) | 5598 (69.3) | 1853 (52.9) | 445 (19.3) | 178 (61.8) | |
status (%) | 1 | 1446 (42.7) | 16595 (37.8) | 3242 (40.1) | 1500 (42.8) | 989 (42.8) | 173 (60.1) |
2 | 737 (21.8) | 11992 (27.3) | 2227 (27.6) | 950 (27.1) | 506 (21.9) | 57 (19.8) | |
3 | 214 (6.3) |
3110 (7.1) | 420 (5.2) |
235 (6.7) |
163 (7.1) |
12 (4.2) |
|
4 | 987 (29.2) | 12167 (27.7) | 2186 (27.1) | 818 (23.4) | 654 (28.3) | 46 (16.0) | |
alone (mean (SD)) | 0.17 (0.37) | 0.00 (0.06) | 0.01 (0.09) | 0.38 (0.48) | 0.49 (0.50) | 0.36 (0.48) | |
children_old (mean (SD)) | 0.01 (0.15) | 1.11 (1.08) | 0.78 (1.02) | 0.88 (0.94) | 1.66 (1.04) | 0.81 (1.01) | |
children_young (mean (SD)) | 0.06 (0.27) | 0.63 (0.89) | 0.54 (0.82) | 0.40 (0.68) | 0.05 (0.30) | 0.57 (0.91) | |
cigarettes | 10.31 (10.13) | 9.06 (10.54) | 13.26 (10.82) | 11.95 (10.47) | 6.50 (9.91) | 12.13 (11.21) | |
alcohol | 0.77 (0.42) | 0.76 (0.43) | 0.80 (0.40) | 0.77 (0.42) | 0.69 (0.46) | 0.80 (0.40) |
|
phys | 0.24 (0.43) | 0.21 (0.40) | 0.17 (0.38) | 0.22 (0.42) | 0.20 (0.40) | 0.23 (0.42) | |
health (mean (SD)) | 2.66 (0.73) | 2.80 (0.70) | 2.74 (0.67) | 2.86 (0.73) | 3.30 (0.78) | 2.91 (0.77) |
Men 30+ | Women 30+ | |||||
1 | 2 | 3 | 1 | 2 | 3 | |
marst = 1, age_group = 1 | 0.48*** | 0.34* | 0.32 | 0.42*** | 0.29* | 0.37** |
marst = 3, age_group = 1 | 0.32** | 0.21 | 0.25 | 0.24** | 0.18 | 0.01 |
marst = 4, age_group = 1 | 0.51*** | 0.41** | 0.24 | 0.20 | 0.12 | -0.02 |
marst = 5, age_group = 1 | -0.40 | -0.44 | -0.23 | 0.23 | 0.21 | -0.02 |
marst = 6, age_group = 1 | 0.79* | 0.55 | 0.41 | 0.94*** | 0.79*** | 0.28 |
marst = 1, age_group = 2 | -0.47 | -0.57* | -0.57 | 0.20 | 0.15 | 0.20 |
marst = 3, age_group = 2 | -0.05 | -0.07 | -0.13 | 0.32*** | 0.30*** | 0.38*** |
marst = 4, age_group = 2 | -0.11 | -0.18 | -0.23 | 0.18* | 0.16 | 0.16 |
marst = 5, age_group = 2 | -0.02 | -0.08 | 0.07 | 0.28*** | 0.28*** | 0.28** |
marst = 6, age_group = 2 | 0.13 | 0.10 | 0.12 | 0.70*** | 0.66*** | 0.66* |
marst = 1, age_group = 3 | -1.83** | -1.86** | -0.57 | -0.12 | -0.12 | 0.02 |
marst = 3, age_group = 3 | -0.10 | -0.10 | -0.13 | -0.03 | -0.02 | 0.06 |
marst = 4, age_group = 3 | -0.39** | -0.36 | -0.23 | -0.15 | -0.14 | -0.08 |
marst = 5, age_group = 3 | -0.28** | -0.23 | 0.07 | -0.16** | -0.16** | -0.22** |
marst = 6, age_group = 3 | 0.40 | 0.44 | 0.12 | -0.82 | -0.90 | -1.18 |
marriage = 1, age_group = 1 | 0.02 | 0.01 | -0.07 | -0.10 | -0.10 | -0.16 |
marriage = 1, age_group = 2 | -0.10 | -0.11 | -0.12 | 0.05 | 0.04 | 0.10 |
marriage = 1, age_group = 3 | -0.17** | -0.18** | -0.21** | -0.08 | -0.09* | -0.13 |
divorce = 1, age_group = 1 | -0.12 | -0.15 | -0.18 | 0.06 | 0.07 | 0.12 |
divorce = 1, age_group = 2 | 0.01 | -0.01 | 0.15 | 0.11 | 0.10 | 0.07 |
divorce = 1, age_group = 3 | 0.08 | 0.06 | -0.01 | 0.09 | 0.07 | -0.10 |
widowhood = 1, age_group = 1 | 0.24* | 0.24* | 0.30** | -0.02 | -0.05 | -0.03 |
widowhood = 1, age_group = 2 | 0.02 | 0.03 | -0.17 | -0.02 | -0.06 | -0.23** |
widowhood = 1, age_group = 3 | 0.06 | 0.05 | -0.02 | 0.04 | 0.02 | 0.08 |
Robust SE | Yes | Yes | Yes | Yes | Yes | Yes |
FE waves | Yes | Yes | Yes | Yes | Yes | Yes |
Control 1 | Yes | Yes | Yes | Yes | Yes | Yes |
Control 2 | No | Yes | Yes | No | Yes | Yes |
Control 3 | No | No | Yes | No | No | Yes |
Events | 2639 | 2639 | 1828 | 5177 | 5177 | 2744 |
Concordance | 0.632 | 0.641 | 0.663 | 0.585 | 0.59 | 0.607 |
Observations | 45,042 | 45,039 | 33,811 | 63,467 | 63,464 | 41,797 |
Wald Test | 412.06*** (df = 51) | 510.52*** (df = 69) | 491.13*** (df = 77) | 256.08*** (df = 37) | 277.81*** (df = 46) | 274.96*** (df = 55) |
Max. Possible R2 | 0.52 | 0.52 | 0.48 | 0.48 | 0.36 | 0.29 |
*0.1 **0.05 ***0.01 |
Men 30+ | |||
Chisq | df | p | |
wave | 12.618 | 13 | 0.478 |
born | 0.659 | 1 | 0.417 |
marst*age_group | 12.890 | 15 | 0.611 |
marriage*age_group | 2.326 | 3 | 0.508 |
divorce*age_group | 2.071 | 3 | 0.558 |
widowhood*age_group | 4.837 | 3 | 0.184 |
educ*age_group | 12.921 | 6 | 0.044 |
income*age_group | 3.543 | 3 | 0.315 |
job*age_group | 3.595 | 3 | 0.309 |
status*age_group | 11.509 | 9 | 0.242 |
alone*age_group | 6.935 | 3 | 0.074 |
children_old*age_group | 2.741 | 3 | 0.433 |
children_young*age_group | 3.222 | 3 | 0.359 |
cigarettes*age_group | 0.101 | 3 | 0.992 |
alcohol*age_group | 2.825 | 3 | 0.419 |
phys*age_group | 1.463 | 3 | 0.691 |
GLOBAL | 90.656 | 77 | 0.137 |
Women 30+ | |||
Chisq | df | p | |
born | 0.00856 | 1 | 0.926 |
marst*age_group | 24.21359 | 15 | 0.062 |
marriage*age_group | 2.37526 | 3 | 0.498 |
divorce*age_group | 1.07182 | 3 | 0.784 |
widowhood*age_group | 0.53934 | 3 | 0.910 |
educ*age_group | 7.34928 | 6 | 0.290 |
income*age_group | 4.82144 | 3 | 0.185 |
job*age_group | 2.24149 | 3 | 0.524 |
alone*age_group | 0.16425 | 3 | 0.983 |
children_old*age_group | 1.74844 | 3 | 0.626 |
children_young*age_group | 1.84474 | 3 | 0.605 |
cigarettes*age_group | 5.48372 | 3 | 0.140 |
alcohol*age_group | 1.32902 | 3 | 0.722 |
phys*age_group | 6.37845 | 3 | 0.095 |
GLOBAL | 65.32298 | 55 | 0.161 |
The basic assumptions underlying the Cox proportional hazards model (
We tested the first assumption by constructing correlation matrices for the control variables (Figure
In men, the self-perceived health status declines with age, so does the percentage of the employed. Single or widowed men, as expected, were more likely to live alone in the household. All the variables were characterised by weak to moderate correlation, indicating no strong (0.7 or more) collinearity between the control variables.
Women, too, experience a decline in the self-perceived health status and loss of employment (probably due to retirement) as they age. The widowed category was on average older and more likely to be associated with living alone. There were no strongly correlated factors there too. Therefore, the first assumption of regressor independence holds for the models for both men and women.
It should be noted that the paired Pearson correlation coefficients are a measure of the linear relationship between the variables and may not always be accurate. Moreover, no substantive conclusions can be drawn from them, and we use them only to better trace the characteristics of the data, test the factors for collinearity and identify potential data errors.
Correlation matrix for the control variables. Men aged 30+. Source: author’s calculations based on RLMS data
We tested the second assumption by means of the proportionality test in Cox models as proposed by (
We graphically tested the third assumption of linearity by plotting the martingale residuals as a function of model predictions. It should be noted that our variable of interest, marital status, is a categorical rather than a continuous variable, while linearity is only tested for continuous explanatory variables. Therefore, we directly tested the entire model for linearity, rather than each continuous variable one by one. See Annex
Correlation matrix for the control variables. Women aged 30+. Source: author’s calculations based on RLMS data
Thus, all the basic assumptions of the Cox proportional hazards model are met for the above models.
Akhtemzyanov Rafael Anvarovich – bachelor, Lomonosov Moscow State University, Faculty of economics, Moscow, 119991, Russia. Email: rafael-css@yandex.ru