I. Introduction

Many previous studies have concluded that population aging leads to an increase in consumption or income inequality, which is explained by the permanent income hypothesis (Deaton and Paxson, 1997; Schultz, 1997; Luo et al., 2018). These results are based on a conventional model that analyzes compositional effects given inter-age differences in the means and variances of income (Lam, 1997; Lam and Levison, 1992). Schultz (1982) devised a decomposition method for analyzing the interactions among income, the number of adults per household, and the number of surviving children. Several other studies have also considered the effects on income inequality of the pooling of income by husbands and wives (Lam, 1997; Lam and Levison, 1992; Lehrer and Nerlove, 1981; Liu and Chang, 1987; Ogawa and Bauer, 1996; Pong, 1991). The effects of population aging on income inequality incorporating the responses of public transfer systems have also been explored (von Weizsäcker, 1996).

Depending on the responses of public and private transfer systems, however, analyses limited to compositional effects may be misleading. Some earlier work shows that public transfers can help reduce inequality (Anderson et al., 2017; Aaberge et al., 2019; Doumbia and Kinda, 2019; Sidek, 2021). Although empirical evidence that private transfers reduce inequality remains insufficient, Lee and Mason (2011) note the role of private transfers in reducing inequality.1 The prospect of population aging has motivated reforms of many public transfer systems in Latin America, Europe, and the U.S. Although the ultimate effect of reforms on the corresponding redistributive features remains uncertain, Gruber and Wise (2001) conclude that population aging has led to a decline in the share of resources going to the elderly. They estimate that in OECD countries, an increase in the share of the elderly population by 1 percent leads to a rise in spending on the elderly by 0.47 percent. Similarly, Razin, Sadka, and Swagel (2002) conclude that a rise in the overall dependency ratio is leading to a decline in social transfers. In contrast, Preston (1984) argues that the elderly in the U.S. may claim a disproportionate share of public resources as their numbers and political power increase.2

In many countries, the familial support system is as important as or more important than the public system. Familial support systems are similar to public support systems in that they are vulnerable to the same demographically induced “fiscal pressures.” As the number of surviving pensioners (parents) increases and the number of workers (offspring) declines within any family, either workers (offspring) must increase the share of their resources devoted to supporting pensioners (parents) (higher “taxes”) or pensioners (parents) must experience a decline in the share of their resources derived from relying on workers (offspring) (reduced benefits). On theoretical grounds, however, the effect of population aging on family transfers is uncertain. Given a sufficiently high degree of altruism, families may adjust their intergenerational transfers to distribute resources equally among all members. However, if altruism is weak or intergenerational transfers are motivated by non-altruistic concerns, income differences within the family may widen in response to population aging (Altonji, Hayashi, and Kotlikoff, 2000; Becker and Tomes, 1976; Cox, 1987; Ermisch, 2003; Frankenberg, Lillard, and Willis, 2002; Lillard and Willis, 1997; McGarry and Schoeni, 1997).

An important distinction between public and familial support systems is that the financial burden of a public system is spread across all workers or taxpayers, whereas the financial burden of a family system is concentrated only on those with surviving parents. As mortality rates improve, providing familial support to the elderly becomes a responsibility shared by a larger share of workers. Population aging leads to a ‘broadening of the tax base’ because the proportion of workers with a surviving parent increases. The effect of increased life expectancy is reinforced by the compression of the age of death. As the variance in the age of death declines, so does the variance in the proportion of workers with surviving parents.

Given these considerations, it is far from clear how the familial support system and income inequality will respond to population aging. These issues are addressed in this paper by (1) developing a new empirical strategy for estimating the effects of population aging, income, and other socio-economic variables on living arrangements; (2) extending the standard model of income inequality to incorporate the responses in one aspect of the familial support system – the formation of multi-generational households (or extended households); and (3) applying the models to South Korea (hereafter Korea), where familial support systems have long been important and where public support systems are also currently being rapidly developed. In particular, this paper complements these previous studies by incorporating the responses of familial support systems to changes in the age distribution of the population.

Building on this framework, the paper develops a theoretical model in which income inequality within family cohorts can be decomposed into two additive components – a compositional effect associated with population aging and a pooling effect that reflects the extent to which families share income through the formation of extended households. The model predicts that population aging influences not only the demographic composition of family cohorts but also the mechanisms through which income is pooled within households. Importantly, the magnitude and direction of these effects depend on whether population aging arises primarily from the decline in fertility or from the mortality improvement, as each process alters the structure and functioning of familial support systems in distinct ways.

An empirical analysis using Korean data provides evidence consistent with these theoretical predictions. Population aging, driven mainly by the fertility decline, tends to increase the proportion of individuals living in extended households, thereby reducing income inequality through enhanced intra-family pooling. However, recent trends away from extended households suggest a weakening of the inequality-reducing benefits of shared living arrangements. Overall, the findings support the view that co-residence within extended families serves as a stabilizing mechanism that mitigates the inequality pressures typically associated with demographic change.

Although the major emphasis of this paper is methodological, the analysis of inequality in Korea is of interest in its own right. Korea has experienced rapid demographic and economic change. The total fertility rate (TFR) in Korea declined from 4.53 births per woman in 1970 to replacement level by 1983, and it fluctuated at around 1.60 during the 1980s. However, it decreased sharply again, from 1.65 to 1.18, from the early 1990s to the early 2000s. After the early 2000s, the TFR remained between 1.09 and 1.30 until the mid-2010s; however, it fell below 1 (0.98) in 2018, eventually dropping to 0.84 in 2020 and 0.72 in 2023, the lowest level in the world. On the other hand, life expectancy in Korea increased continuously, from 62.3 (men 58.70, women 65.80) in 1970 to 83.5 (men 80.5, women 86.5) in 2020, which is the second-highest among OECD countries. Since 1960, the Korean economy has been one of the most rapidly growing economies in the world. Yet despite these and other equally dramatic social changes, income inequality has been steady and low. Between 1992 and 2009, the Gini coefficient (market income) increased continuously from about 0.25 to 0.32. Nonetheless, the Gini coefficient declined by about 5 percent between 2010 and 2016, the period analyzed in this paper, except for 2016 (Yun, 2017). Understanding how Korea achieved such rapid economic growth while avoided rising income inequality is a crucial policy questions, and this paper suggests that the answer may lie, in part, in the adaptive responses of the familial support system.

The paper is organized as follows. Section 2 models the effects of age structure, income, and other variables on living arrangements, which is useful for dealing with certain economic indicators, such as inequality. Section 3 extends the standard method for analyzing the compositional effect of age structure on income inequality to incorporate the effects of income pooling, which occurs when family members establish multi-generational households. Section 4 uses Korean data to estimate the effects of demographic and economic variables on living arrangements and income inequality. Section 5 concludes the paper and discusses reservations and problems.

II. Living Arrangements and Co-residence Model

B. Multi-generational Families

Two aspects of the family cohort are relevant to living arrangements: (1) the proportion who are members of multi-generational families ( ), and (2) the share of pensioners in multi-generational families (). Here and in the remainder of this section, the family cohort index 𝑎 is dropped for simplicity of notation; however, all variables and parameters are specific to a family cohort. It is more convenient to analyze the old-age dependency ratio of multi-generational families ( ), which is a monotonic transform of the share of pensioners.

Below, first we show that, under many but not all circumstances, population aging leads to an increase in the proportion of the family cohort belonging to multi-generational families. Second, under many but not all circumstances, population aging leads to an increase in the old-age dependency ratio within multi-generational families. Third, the effects depend on whether fertility or mortality change underlies population aging.

For any family cohort with no migration, the population of the pensioner generation is given by M(a+g,t)=s(a,t)M(g,t-a), where s(a,t) is the survival rate. The population of the worker generation is M(a,t)=f(a,t)M(g,t-a), where f(a,t) is similar to the net reproduction rate, e.g., the fertility rate. When dropping the age and year indexes to simplify notation, the age composition of the family cohort is measured by the dependency ratio, D=M(a+g,t)/M(a,t)=s/f. The proportion of persons belonging to a multi-generational family is expressed as follows:

where α is the proportion of pensioners who belong to a multi-generational family, i.e., the proportion with at least one surviving offspring, and β is the proportion of workers who belong to a multi-generational family, i.e., the proportion with at least one surviving parent.

As is apparent from the equation of D=M(a+g,t)/M(a,t)=s/f, changes in the age distribution have a compositional effect that depends on whether pensioners or workers are more likely to have intergenerational links. The proportion with intergenerational links depends, in turn, on survival and fertility. Members of the pensioner generation will have no intergenerational links if they are celibate or pre-deceased by their children. Improvements in survival during the working ages will lead to a decline in the proportion of pensioners who have been pre-deceased by their children; i.e. (∂α/∂S_k>o), where S_k is the proportion surviving from birth to age a . Reductions in fertility may lead to an increase in the proportion of pensioners who are childless(∂α/∂f>0). However, the fertility effect of childlessness is typically expected to emerge over a longer-term perspective.

There is no obvious reason why the proportion of workers belonging to multi-generational families would be influenced by fertility. Changes in survival, however, have a direct influence on the proportion of workers with a surviving parent. In a one-sex population, the relationship between the survival rate 𝑠 and the proportion of workers with a surviving parent is trivial; i.e., β=s. This systematically underestimates the proportion of workers with a surviving pensioner in a two-sex population unless the mortalities of mothers and of fathers are perfectly correlated. For this reason, we relax the one-sex assumption maintained elsewhere in this paper. It can be shown that if s is the survival rate and ϕ is the correlation between the survival of mothers and fathers, then the following holds:6

Lemma #1

The elasticity of β with respect to 𝑠 is expressed as shown below.

If the survival of husbands and wives is positively correlated or independent (0≤ϕ≤1) , then an increase in the survival rate leads to an increase in the proportion of workers with surviving parents (∂β/∂s≥0). Likewise, the elasticity is positive but less than one (0≤ƞ_β≤1).

The partial effect of population aging on the proportion of the family cohort who are members of multi-generational families can now be assessed using equation (1). First, consider the effect of population aging due to an increase in survival.

Lemma #2

Using α' to represent ∂α/∂s(>0 ) and β' to represent ∂β/∂s(>0 ) :

If α>β, population aging due to an increase in survival leads to an increase in the proportion of the family cohort belonging to multi-generational families . Also, note that even if α<β, the partial effect will be positive if the effects of survival on α and β , i.e., α' and β', are sufficiently great. However, if α<β and α' and β' are not large, the partial effect would be negative. Also considered is the effect of population aging due to an increase in fertility.

Lemma #3

Letting α'' represent ∂α/∂f :

If α>β and α″ is small, i.e., if fertility has a negligible effect on the rate of childlessness, population aging due to the fertility decline also leads to an increase in the proportion of the family cohort belonging to multi-generational families; i.e., <0 if α>β and α″ is small. However, if the fertility decline leads to a sufficiently large increase in the proportion of the pensioner generation who are childless, the proportion of persons belonging to multi-generational families will decline.

C. Age Structure of Multi-generational Families

The second availability measure relevant to this analysis is the age structure of multi-generational families, denoted by . The relationship between the age structure of the population (D) and the age structure of multi-generational families () is expressed as follows:

Lemma #4

The partial effect of a change in the age structure of multi-generational families due to a change in the survival rate is given by

where is the elasticity of 𝛼 with respect to 𝑠, which is greater than zero, and is the elasticity of β with respect to s , which is between zero and one.

In the polar case, i.e., with ƞ_α equal to zero and η_β equal to 1, a change in the survival rate has no effect on the age structure of multi-generational families; i.e., = 0. In more realistic cases, an increase in the dependency rate due to improving survival leads to a rise in the dependency ratio in multi-generational families; i.e., >0.

Lemma #5

Letting α″ represent ∂α/∂f and represent the elasticity of α with respect to f , the partial effect of a change in the age structure of multi-generational families due to a change in fertility is expressed as shown below.

The partial effect of a change in the age structure of multi-generational families due to a change in fertility is negative if α″<0 i.e., <0 if α″<0. However, if the fertility decline is accompanied by a significant rise in childlessness, then this could be positive.

III. Co-residence and Income Inequality Model

With inter-dependence between population aging and the co-residence variables established, we can address the effects of population aging and co-residence on income inequality. This section analyzes how income inequality is influenced by the proportion of family members living in extended households and the age structure of extended households.

Income inequality can be measured by the coefficient of variation (CV), which has well-known properties and has been previously used to analyze the effects of population aging (von Weizsäcker, 1995) and household composition (Lam, 1997) on income inequality. The analysis employs the OLF model, as explained in Section I, and proceeds in two steps. First, we consider income inequality for family cohorts. Second, the results for family cohorts are used to construct estimates of the population as a whole.

Given the mean(E(Y_K)) and variance(V(Y_K)) of income for family cohorts, income inequality for the population depends only on compositional effects. Applying the conventional formula to family cohort data (Goldstein and Lee, 2014) gives

where V(Y) is the variance in per adult household income for the population, E(Y) is the mean income per adult, 𝒰_k is the proportion of the adult population belonging to the family cohort of age k, and CV is the coefficient of variation. The values are summed over the age interval for the worker generation (from 𝑎 to a+g) because, as noted above, the ages of the worker generation are used to index family cohorts.

Before equation (4) can be employed, however, we must determine how the family cohort variables V(Y_k) and E(Y_k) are influenced by the age composition and living arrangements of family cohorts. Each family cohort consists of two generations, workers aged k and pensioners aged k+g with mean incomes of E() and E(), respectively, and corresponding variances of V() and V(). These values are taken as given throughout the analysis. The proportion of family members who are workers is designated by and the proportion who are pensioners by where +=1 (𝑎≤k<𝑎+g).

The mean income of the family cohort, expressed as

is a simple weighted average of the mean incomes of the worker and parent generations. It is independent of living arrangements.

The variance of income for the family cohort is influenced by both the age structure and living arrangements. It is this relationship that is key to understanding how changes in living arrangements influence income inequality within the family cohort and the broader population. The remainder of this section analyzes how changes in the age structure and living arrangements influence V(Y_k).

The analysis is greatly eased through a number of simplifying assumptions. First, we assume that households come in one of two forms. Nuclear households consist of a single worker or a single pensioner. Extended households consist of a single worker and a fractional portion of a pensioner. Second, the decision to establish an extended household is independent of the income of either the worker or the pensioner. The incomes of workers and pensioners who belong to the same family are assumed to be correlated. A positive correlation, for example, leads to positive covariance between the incomes of workers and pensioners living in extended households, but this does not arise because income influences the decision to coreside.

Given these simplifying assumptions, the variance of income per adult is given by:

The coefficients, 𝑤_𝑖, and the variables that determine them all vary across family cohorts, but 𝑘 has been dropped to ease notation. The coefficients depend on the age structure of the family cohort – the proportion of members who are workers (m^w) and pensioners (m^p) ; the age structure of extended households – the proportion of members who are workers () and pensioners () ; and the proportion of cohort family members who live in extended households (). All four coefficients are non-negative; i.e., w_i≥0 for i=1,2,3,4. The first three coefficients sum to one. Hence, the variance in per adult income, V(Y_k), is determined, in part, as the weighted average of the variances of the incomes of the family members, V() and V(), and the covariance between their incomes, C(, ) the difference-in-variances component. The fourth right-hand-side term, {E()-E()}², captures the effect of differences in the average incomes of workers and parents, the difference-in-means component.

The effect of changes in the age structure of the family cohort is identical to that found in conventional models (Lam, 1997). An increase in the relative size of the age group with the higher income variance leads to an increase in the difference-invariance component. A shift towards a more balanced age distribution leads to an increase in the difference-in-means component.

Lemma #6

Formally, the partial effect of aging as measured by an increase in the proportion of family members belonging to the pensioner generation is given by:

The effect of living arrangements is captured by the multiplicative term in equation (6), referred to here as the pooling effect. The pooling effect increases with the age balance in extended household membership (), reaching a maximum when there are equal numbers of workers and pensioners, and also increases with the proportion of family cohort members who live in extended households ().

Defining R=V()/V() and ρ as the correlation between the income of parents and workers, equation (6) can be rewritten as follows:

Lemma #7

The partial effect of an increase in the proportion living in extended households is expressed as shown below.

If ρ=R=1, then is zero; otherwise, it is always negative.7 Hence, the partial effect of an increase in the proportion of the family cohort living in extended households reduces the variance in income; i.e., .

Lemma #8

The partial effect of an increase in the proportion of pensioners in extended households is given by:

If the share of pensioners is less than one-half, the partial effect is unambiguously negative, as noted earlier, ≤0. Hence, for <0.5. As an empirical matter in Korea, the proportion of pensioners who live in extended households () is very low. Hence, we can expect with some certainty that the partial effect of an increase in the proportion of pensioners in extended households reduces the variance in income; i.e., . However, as the proportion of cohort family members who live in extended households () is rapidly decreasing, the effect would be smaller now than the past.

IV. Empirical Analysis

The analysis of this research consists of two distinct elements. First, we estimate the effects of population aging and other variables on living arrangements. Second, we estimate the effects of living arrangements and population aging on income inequality.

B. Results

1. Living Arrangements

Regression estimates for the proportion of family cohort members living in extended households(ln ) are reported in Table 1; for the dependency ratio in extended households(ln ), these values are given in Table 2. All regressions are estimated using ordinary least squares. The estimated regression equation takes the following general form:

where denotes either or , depending on the specification.

TABLE 1

REGRESSION RESULTS FOR THE PROPORTION LIVING IN MULTI-GENERATIONAL HOUSEHOLDS (ln )

Note: 1) These estimates include year dummies; 2) ***, **, and * denote the 1%, 5%, and 10% significance level, respectively; 3) Standard errors are given in parenthesis.

TABLE 2

REGRESSION RESULTS FOR DEPENDENCY RATIO IN MULTI-GENERATIONAL HOUSEHOLDS (ln )

Note: 1) These estimates include year dummies; 2) ***, **, and * denote the 1%, 5%, 10% significance level, respectively; 3) Standard errors in parenthesis.

For each dependent variable, results from four specifications are reported. Specifications 1 and 2 capture the effects of the age structure using the dependency ratio and its square, respectively. Specifications 3 and 4 introduce adult survival into the model in order to analyze the separate effects of fertility and survival.

In all specifications, we include the year of birth of the worker generation of the family cohort (Cohort), the natural log of the average earnings of members of the worker generation (ln labwork), the ratio of the average earnings of the pensioner generation to the average earnings of the worker generation (Incrat), the sex ratio of the pensioner generation (Sexratio), and single-year age dummy variables(δ𝑎). The coefficients of the age dummies are not reported in the table.

The coefficient of the natural log of workers’ average earnings(lnlabwork) captures the effect of general increases in earnings because the ratio of pensioners’ average earnings to workers’ average earnings is controlled. In specification 4, the estimated coefficient of lnlabwork is -0.833, which is statistically significant at the 1% significance level. This magnitude implies that a 1% increase in workers’ earnings is associated with approximately a 0.83% decrease in the proportion of family members living in extended households. The statistically significant negative coefficient is consistent with the standard view that higher income leads to an increase in the demand for privacy. Individuals with higher incomes are willing to give up the gains from economies of scale or public goods captured by extended households. A rise in the earnings of pensioners relative to workers (Incrat) has no discernible effect on the proportion of family members living in extended households. The estimated coefficients are not consistent according to the specification. Specifications 1 and 2 show a positive effect, whereas specifications 3 and 4 show a negative effect. Thus, we find no support for the altruism hypothesis. Note, however, that current earnings may poorly measure the economic status of the pensioner generation. The effects of pensioners’ wealth may be more supportive of the altruism hypothesis, as has been the case in other studies (Borsch-Supan et al., 1996). Adequate wealth measures by generation are not available in the data.10 The cohort effect (Cohort) is positive (except for specification 1), and the sex ratio of the pensioner generation (Sexratio) has a statistically significant negative effect, as anticipated. A lower proportion of cohorts with substantial surplus males were living in extended, multi-generational households.

Based on specifications 1 and 2, we can identify that the dependency ratio has a positive, statistically significant effect on the proportion of the family cohort living in multi-generational households. The elasticity rises gradually with the dependency ratio. This provides support for a central feature of this paper – population aging may reduce income inequality by encouraging relatively more co-residence. Specifications 3 and 4 address whether the source of population aging, declining fertility or mortality, matters. The analysis presented above shows that the effects on the availability of a decline in fertility or an increase in survival are not identical. Moreover, changes in fertility and survival may influence co-residence in ways other than through their effects on kinship availability.

This issue is addressed empirically by including both the dependency ratio and the proportion of the pensioner generation surviving. Given ln 𝑠, the coefficient(s) of the ln D terms give the partial effect of an increase in D due to a decline in fertility. A rise in the dependency ratio due to a decline in fertility produces an increase in the proportion of family cohort members residing in extended households, although the elasticity declines with the dependency ratio.

The estimated coefficients of the ln s terms in specifications 3 and 4 are partial effects controlling for the dependency ratio and the net reproduction rate, e.g., the fertility rate, because lnD=ln s − ln f. Two distinct effects related to survival are captured by the coefficients. The first is that the availability effects of survival are different than the availability effect of fertility. The second is that changing survival may capture other changes correlated with survival but unrelated to the availability effects of fertility. An example is that changes in health status may be captured by survival rates (Zimmer, Martin and Chang, 2002), although the evidence on how health status affects living arrangements is mixed (Borsch-Supan et al., 1992; Palloni, 2001). Thus, one possible interpretation of the coefficients is possible. This result implies that the availability effects of increased survival are much smaller than the availability effects of the decline in fertility.

Noting that ln D=ln s-ln f, the elasticity of with respect to s is equal to

and the elasticity of with respect to f is equal to

where β_i is the ith estimated coefficient of specification 4 in Table 1.

The elasticity of with respect to s increases as the survival rate and the fertility rate increase. On the other hand, the elasticity of with respect to f increases as the survival rate increases and as the fertility rate decreases. In addition, the elasticity of with respect to f is still negative for all values of s and f observed here.11 The bottom line is that population aging resulting from a decline in fertility leads to an increase in the proportion of people living in extended households. Also, population aging resulting from the rise in survival leads to an increase in the proportion of people living in extended households, although the effect of survival is less significant than the effect of fertility.

The analysis of reported in Table 2 uses the same specifications used for .The cohort effect (Cohort) is negative for all specifications. Workers’ average earnings(ln labwork) have a statistically significant positive effect on the dependency ratio in multigenerational households. In specification 4, the estimated coefficient of lnlabwork is 0.326 and statistically significant at the 5% significance level. This implies that a 1% increase in workers’ average earnings is associated with approximately a 0.33% increase in the dependency ratio within extended households. The positive coefficient suggests that higher aggregate income among workers may enable families to sustain a larger number of dependents—particularly elderly members—within multigenerational settings. In contrast, a rise in the earnings of pensioners relative to workers (Incrat) leads to a significant (except for specification 3) decline in the dependency ratio in multigenerational households. In specification 4, the coefficient of Incrat is -0.532 and statistically significant at the 1% significance level. This magnitude indicates that a 1% increase in the relative earnings of pensioners is associated with roughly a 0.53% decrease in the dependency ratio in multi-generational households, implying that as the elderly become more financially independent, the economic necessity of co-residence and within-household dependency weakens. The negative and highly significant effect is consistent with the notion that greater income security among pensioners reduces intergenerational economic dependence. A large surplus in the male pensioner population leads to a decrease in the proportion of pensioners in extended households (Sexratio).

The elasticity of with respect to D is close to one in specifications 1 and 2. This is consistent with a straightforward demographic model of the age composition of extended households.

Similar to equations (9) and (10), noting that lnD=ln s-ln f, the elasticity of with respect to 𝑠 is equal to

and the elasticity of with respect to f is equal to

where β_i is the ith estimated coefficient of specification 4 in Table 2.

The elasticity of with respect to 𝑠 declines as the survival rate and the fertility rate increase, but it is positive for all values of s and f observed here. Also, the elasticity of with respect to f decreases as the survival rate increases and as the fertility rate decreases, but it is also still negative for all values of s and f observed.12 The bottom line is that population aging due to a decline in fertility or survival increase leads to a rise in the dependency ratio in multi-generational households.

2. Effect of Living Arrangements and Population Aging on Income Inequality

Table 3 presents the regression estimates of the variance of income per adult (V(Y_k)) on the proportion of family cohort members () and of pensioners () living in extended households. All regressions are also estimated using ordinary least squares. The estimated regression equation takes the following general form:

where V(Y_k) denotes the variance of income per adult.

The results contain five specifications for the variance of income per adult. Specification 1 captures the effects of the proportion of family cohort members living in extended households. Specification 2 captures the effect of the proportion of pensioners living in extended households. Specification 3 introduces comprehensive models in order to analyze the separate effects of living arrangements and population aging. In addition, specifications 4 and 5 are the results of a robustness analysis of Specifications 1 and 3 using the proportion of family cohort numbers estimated by specification 4 of Table 1 () and the natural log of the old-age dependency ratio (ln D) instead of the proportion of family cohort numbers () respectively.

In all specifications, similar to Tables 1 and 2, we include the year of birth of the worker generation of the family cohort (Cohort), the natural log of the average earnings of members of the worker generation (ln labwork), the ratio of the average earnings of the pensioner generation to the average earnings of the worker generation (Incrat), the sex ratio of the pensioner generation (Sexratio), and single-year age dummy variables(δ_𝑎). The coefficients of the age dummies are not reported in the table.

Similar to Tables 1 and 2, the coefficient of the natural log of workers’ average earnings(ln labwork) captures the effect of general increases in earnings because the ratio of pensioners’ average earnings to workers’ average earnings is controlled. In Table 3, the estimated coefficients of the natural log of workers’ average earnings(ln labwork) is 6.607, which is statistically significant at the 1% level of significance. This implies that a 1% increase in workers’ average earnings is associated with a roughly 6.6 unit rise in the variance of income per adult. The magnitude of this effect suggests that overall income growth among the working generation tends to widen within-household and cross-generational income dispersion. Higher worker earnings may amplify the heterogeneity in economic well-being across family cohorts, particularly when some households benefit more than others from labor market gains. Similarly, the estimated coefficient of the ratio of the average earnings of pensioners to workers (Incrat) is 3.533, also statistically significant at the 1% level. This result indicates that a 1% increase in pensioners’ earnings relative to workers’ earnings leads to an approximately 3.5 unit increase in the variance of income per adult. The positive and significant effect implies that as the income of the elderly rises relative to that of workers, income dispersion within the population widens, possibly reflecting divergent income trajectories between pensioner and worker generations. This finding is consistent with the broader evidence that increasing income among pensioners contributes to greater cross-cohort income inequality, as observed in other contexts with aging populations (e.g., Borsch-Supan et al., 1996). The cohort effect (Cohort) is significantly negative, indicating higher income variance in the working generation than in the pensioner generation. Also, the sex ratio of the pensioner generation (Sexratio) has a negative effect, but it is not statistically significant.

TABLE 3

REGRESSION RESULTS FOR THE VARIANCE OF INCOME PER ADULT (V(Y_k)) ON THE PROPORTION OF FAMILY COHORT MEMBERS LIVING IN MULTI-GENERATIONAL HOUSEHOLDS () AND THE PROPORTION OF PENSIONERS LIVING IN MULTI-GENERATIONAL HOUSEHOLDS ()

Note: 1) The unit of variance of income is trillion; 2) These estimates include year dummies; 3) ***, **, and * denote the 1%, 5%, 10% significance level, respectively; 4) Standard errors in parenthesis.

Based on specifications 1 and 3, as explained by Lemma #7, we can identify that the partial effect of an increase in the proportion of the family cohort living in extended households reduces the variance in income; i.e., In addition, specifications 2 and 3, as explained by Lemma #8, show that the partial effect of an increase in the proportion of pensioners in extended households reduces the variance in income, i.e., , as we anticipated, although this outcome is not statistically significant. These statistically insignificant results can be accepted when considering how they reflect the Korean situation. These results also more clearly support the main argument of this paper – that co-residence and population aging reduce income inequality.

V. Conclusions

Analyzing income inequality, including in the Korean case, is a challenging exercise. Many aspects of the Korean economy and society have experienced rapid change, but income inequality has remained at relatively low levels, experiencing modest fluctuations over the past few decades. Explaining why something has not changed is significantly more difficult than explaining why it has.

There are aspects of this research that are perhaps of more general interest. First, we have shown that inequality for family cohorts can be modeled as two additive components – a direct population aging effect that captures compositional effects and a pooling effect that captures the manner in which families pool their income by forming multi-generational households. Second, the pooling effect is determined by two features of living arrangements. An increase in the proportion of family members living in extended households leads to a more favorable pooling effect. Third, on a priori grounds, the components of the pooling effect should be influenced by population aging. Thus, the effects of population aging are not limited to compositional effects. Fourth, the effect of population aging depends on whether a decline in fertility or a decline in mortality is the primary source of population aging. In many developing countries, the fertility decline is sufficiently recent such that low-fertility cohorts are just beginning to reach older ages. As they do, the implications of low fertility for familial support systems will become increasingly important.

The analysis in this paper does provide some answers to that difficult question. First, population aging may have led to a greater increase in the proportion living in extended households; however, improvements in survival have a weaker effect on the proportion living in extended households compared to the fertility decline. A possible explanation for this is that improvements in health led to an increase in the proportion of living independently, partially offsetting the availability effects associated with population aging. Second, the higher income of workers in Korea could have led to more of a shift away from extended households. This result may be linked to the fact that individuals with higher incomes are willing to give up the gains from economies of scale or public goods captured by extended households. On the other hand, a rise in the earnings of pensioners relative to workers has no discernible effect on the proportion of family members living in extended households. Finally, an increase in the proportion of the family cohort living in extended households reduces the variance in income. Furthermore, an increase in the proportion of pensioners in extended households may reduce the variance in income. These results support the argument that co-residence and population aging may reduce income inequality.

Although we briefly addressed income inequality in Korea in this paper in relation to living arrangements and population aging, the future of income inequality in Korea is still an interesting and broad issue that we should continuously explore. The effects of population aging on income inequality may be ambiguous in the coming decades. As the effects of low fertility take hold, the extended household effect may also rise with favorable implications for inequality. On the other hand, other forces, such as strengthening public support systems, may undermine the familial support system in Korea, leading to greater income inequality.

The analysis reported here relies on important simplifying assumptions that require qualification of the conclusions. Perhaps the most important is the assumption that co-residence decisions are made independently of income. To the extent that pensioners with atypically low incomes relative to their offspring are more likely to form extended households, income inequality will be reduced by more than that implied by our simple model. On the other hand, as this study confirmed using the Korean case, to the extent that lower-income workers are more likely to establish extended households, income inequality will be reduced by less than that implied by our simple model. A priority in future work, then, is to analyze a more complete and realistic model of income inequality.

A second problem with the application of the simple model is that it involves an unknown parameter – the correlation between the current incomes of pensioners and workers within extended households. Several studies have estimated the correlation between the earnings of parents and their offspring at similar stages in their lifecycle, but we are not aware of estimates of the correlation of the current income of workers and their mostly retired parents.

In addition, there are important aspects of income inequality that are not addressed by this study. We have excluded children and young adults from our study. In most countries, including Korea, there are important changes in the age at which offspring enter the labor force, marry, and establish separate households. Previous research has shown that changes in the age structure at younger ages have important implications for income inequality (Lam, 1997; Lam and Levison, 1992). However, the influence of incorporating changes in living arrangements on income inequality has largely been neglected. Likewise, fertility differentials may have important implications for per capita income inequality. It should also be noted that many pensioners live together with or near their adult children, not necessarily for economic reasons, but to help with childcare and other forms of family support. Such intergenerational coresidence motivated by caregiving arrangements may partly confound the interpretation of multi-generational living as a purely economic response to income or demographic changes. While addressing this issue is beyond the scope of our study, it would be meaningful to explore the interplay among caregiving roles, living arrangements, and income distribution in future research. More broadly, population aging and its implications for old-age support are only one of the important ways in which demographic change affects income inequality.

The analysis is limited to inequality in current income, whereas inequality in lifetime income may be a more preferred welfare measure. Age structure has no implications for inequality in lifetime income; however, as von Weizsäcker (1995) notes, changes in transfers induced by population aging do affect lifetime income inequality. Although we do not explore this issue here, the response of familial support systems may affect both current and lifetime income inequality.