2.1 What care do the elders have?

Many people over 65 need help. One of the key measures to evaluate whether or not an individual needs help from others is to see if they can perform Instrumental Activities of Daily Living, or commonly known as, iADLs. Examples of iADLs include doing laundry, shopping, and managing medications.Footnote ⁶ Both NHATS and HRS track if respondents have difficulty with iADLs. Around 23% of respondents from NHATS and 15% of respondents from HRS reported having some difficulty with at least one iADL. Another way to infer if an elder person needs care is, simply, to see if they have a caregiver. In 2015, at least 17.5% of NHATS respondents have unpaid caregivers (i.e. one or more unpaid caregivers answered the accompanied NSOC survey). Through the family module of 2014HRS, 15% of the respondents received some help and care from their adult children. While neither captures all of the caregivers an elder used, we can interpret the percentages as the lower bounds for the fraction of elders that needed caregivers.

When considering the care that people need as they age, we often think about LTC and nursing homes. However, a relatively small fraction of elders with care needs live in care facilities. According to 2015 NHATS, about 5% of people over age 65 live in nursing homes, about 7% receive some form of residential care but are not in nursing homes, and an overwhelming 88% reside in their communities. Similarly, in 2014HRS, 9% of respondents aged 65 and above spent any time in a nursing home in the last two years, including the 4% who were living in nursing homes at the time of the survey.

Medicaid covers some LTC options including nursing homes, but it does not lift the elder care responsibilities completely away from the families. First of all, most elders with some care need are not eligible for Medicaid. According to HRS, 89% of all the respondents over 65, 74% of those with difficulty at least one iADL, and 77% of those who received care from children are not covered by Medicaid. For the eligible elders, Medicaid alone does not always fulfill all of a patient’s need for care. 2014HRS shows that more than one-third of the Medicaid patients still received care from family members.

2.2 Who provides the care?

When nursing homes and Medicaid do not fully cover care needs, who are providing help and care to the elders? According to 2015 NHATS/NSOC, the biggest caregiver/helper group by far is the adult children.Footnote ⁷ Table 1 shows the share of unpaid caregivers by their relationships to the elders. Out of all the unpaid caregivers NSOC surveyed, 56% are adult children, with more daughters (38%) than sons (18%), in comparison to the 22% who are spouses or partners. From the care receiver’s perspective, close to half of elders have at least one daughter caregiver compared to a third with a spouse/partner caregiver. This shows that adult children are actively involved in caregiving, especially daughters. On the intensive margin, spouse/partner caregivers spend more hours per day and more days providing care than any other groups of caregivers. Still, the amount of time adult children spend on caregiving is sizeable, especially since they are much younger than the spouse/partner caregivers and are more likely to have other obligations.

Table 1. Unpaid caregivers for people over 65

Source: 2015 National Health and Aging Trends Study (NHATS), National Study of Caregiving (NSOC). In both tables, “Daughter” includes biological daughter, daughter-in-law, and stepdaughter. Similarly, “Son” includes biological son, son-in-law, and stepson. For the purpose of this paper, we do not distinguish the differences among these subgroups. Care time is imputed from average hours per day and average days per month.

According to 2015HRS, on average, daughters spent 66 hours helping the respondents last month, and sons spent 57 hours.Footnote ⁸ These estimates are slightly higher than those in NSOC, but generally comparable. In conclusion, empirical evidence suggests that a considerable fraction of adult children spend a nontrivial number of hours helping their parents, playing an essential role in fulfilling their parents’ care needs.

2.3 Caregiving and employment

Since adult-child caregivers are mostly at working ages, the natural question that follows is how caregiving and work affect one another. The effect of caregiving on employment is somewhat inconclusive in the empirical literature, especially on the intensive margin (Lilly et al. Reference Lilly, Laporte and Coyte2007), but the hypothesis is that caregiving takes time away from work. Furthermore, some papers that study the aggregate implications of caregiving (see Barczky and Kredler, Reference Barczky and Kredler2018; Kydland and Pretnar, Reference Kydland and Pretnar2019) model caregiving and working as binary decisions where agents choose one or the other. We believe, however, that the tradeoff between work and care is more nuanced.

In Table 2, we present the labor supply and caregiving data for unpaid caregivers with known employment status in 2015 NSOC. Around half of the adult-child caregivers worked in the last week, 47% for daughters and 52% for sons. This is comparable to the employment rates for their age and gender groups in the general population. Meanwhile, based on the reported work hours from those that do work, many work full-time jobs (40 hours or more each week). Furthermore, when asked if caregiving has kept them from doing paid work, only 13% of daughters and 9% of all caregivers answered “yes,” meaning that the vast majority of the unpaid caregivers did not feel they worked less as a result of caregiving.

Table 2. Caregiving and employment

Source: 2015 National Study of Caregiving (NSOC). In both tables, “Daughter” includes biological daughter, daughter-in-law, and stepdaughter. Similarly, “Son” includes biological son, son-in-law, and stepson. For the purpose of this paper, we do not distinguish the differences among these subgroups. “Worked Last Week” refers to the fraction of unpaid caregivers that worked for pay in the last week.

We then break down employment status by care intensity, measured in number of care hours per day. Adult-child caregivers who are helping more hours per day are generally associated with lower employment rates. However, we would like to point out that relatively high fraction of caregivers still work while providing care. If we consider caregiving as a job, 4-8 hours a day would be more than some part-time jobs, and more than 8 hours a day is equivalent to or more than a full-time job. This means that while some intensive caregivers had to choose between caregiving and work, more caregivers, including some intensive caregivers, did not, or could not, stop working. We show this from another perspective by breaking the data down by working status. Caregivers who did not work last week provided more care than those that did work. But on average, caregivers who worked are still providing around 4 hours of care a day, which is equivalent to a part-time job.

It is worth noting that a higher number of adult-child caregivers choose to work than spouse caregivers, but provide at least as much care if not more.Footnote ⁹ Among the adult children, daughters provided more care than sons, and a higher proportion of sons worked than daughters. This is consistent with the empirical findings that women are more likely to be affected by caregiving responsibilities. In conclusion, without claiming causality in any direction between caregiving and employment, we want to emphasize the fact that for most adult children, caregiving and work coexist. The tradeoff happens among work, caregiving, and leisure, not necessarily and exclusively between caregiving and work.

2.4 What motivates adult children to help parents?

To think about how adult children make caregiving decisions, we first think about why adult children help their parents in general. In the theoretical literature on intergenerational transfers, altruism, and bequest expectation are used most often (see Cardia and Michel, Reference Cardia and Michel2004; Mukherjee, Reference Mukherjee2022). Altruism usually means that the well-being of the parent generation is part of adult children’s utility. Both mechanisms indicate that adult children would get something in return for their transfer, utility, or future wealth. We would like to propose a third scenario regarding care-related transfer and refer to it as “need-based altruism.” This altruism motivates children to help parents fulfill their care needs. Parents with means can meet much or all of their needs using the formal care market, while parents with little means rely more on the adult children to provide care. Given the fixed amount of care need, adult children decide how to provide care. The main theoretical difference between the “need-based altruism” and the traditional altruism is that under “need-based altruism," adult children will not help beyond the level of the need, while the traditional altruism will motivate adult children to give until marginal utility becomes small. The latter may be more appropriate describing certain transfer behavior, such as gifting and spending time with parents. But given the nature of caregiving, we think of care-related transfer as a “need-based” decision.Footnote ¹⁰

To show some empirical patterns consistent with our suggestion of “need-based altruism," we now turn to the data on time and financial transfers from adult children to parents. Using the 2014 RAND HRS data, we graph the probability and mean of care time and overall financial transfers from children to respondents by parental asset, as shown in Figure 1. We use asset in the old household as a proxy for parents’ ability to fill their own care needs.Footnote ¹¹ Panel (a) shows that parents with relatively low asset are more likely to receive care time and financial transfers from children. Specifically, parents in the lowest quintile are three times more likely to have children giving money to them or caring for them. Panel (b) shows that the magnitude of both types of giving, measured by time and financial transfers from children in the last month, is also negatively related to parental asset.Footnote ¹² These results are consistent with our assumption that children with more financially endowed parents face less parental care need, and thus provide less care support.

To sum up this section, we would like to highlight four empirical patterns about elderly care. First, many elders need care, but only a small fraction reside in facilities such as nursing homes. It is common to use unpaid caregivers to assist elders with daily activities, such as grocery shopping and doing laundry. Second, adult children account for more than half of those unpaid caregivers, with majority of them being daughters. They spend a large amount of time caring for parents. The two datasets we looked at show an average care hours of 57 to 66 per month. Third, for adult children caregivers, caregiving and work coexist. Children who provide significant amount of care (more than 8 hours per week) are less likely to be in the labor force, but the overall employment rate among caregivers is high (47%). Fourth, parents in better financial situations receive less care support from children. Specifically, parents in the lowest asset quintile receive more than three times care than those in the highest asset quintile.

Motivated by these empirical findings, we build a theoretical model with the following features. First, elders use a combination of formal care (i.e. nursing home services) and informal care to meet their total care needs. Second, elders use own assets to purchase formal care. If eligible, elders benefit from a government program, similar to Medicaid, and have their care fulfilled through public provision. When private purchase and governmental subsidization are not enough, adult children step in to provide care. Third, children choose time allocation among work, caregiving, and leisure, allowing work and caregiving coexist. We present the details of the model in the next section.

Figure 1. Transfer to parents, by parental assets.

3.1 Care Production

Each household faces a probability of a health shock, $\bar{h}$ . When shocked, $\bar{h}=1$ , the parent loses her ability to perform some daily activities and requires a fixed amount of care, $H$ . Care is produced as:

\begin{equation*}H= s_{i,f} + s_{i,d}\end{equation*}

where $s_{i,f}$ is the amount of formal care purchased from the care market, and $s_{i,d}$ is the amount of informal care provided by adult children. For simplicity, we assume these two types of care are perfect substitutes. Informal care requires two inputs from children, time $t$ and money $m$ . Time input refers to when children spend their own time caring for parents, such as getting their groceries, taking them to doctor appointments, or simply helping them with household chores. Money input is the cost associated with care provision (i.e. gasoline) and the expenditure on informal care-related services (i.e. ordering food deliveries and paying for house cleaning). We allow the adult children to choose a combination of time and money inputs to highlight how people approach care provision based on their opportunity cost of time. We set a standard c.e.s. home production function for informal care with time and money as inputs:

\begin{equation*}s_{i,d} = \left[\alpha t_i^{\theta } + (1-\alpha ) (\eta m_i)^{\theta }\right]^{1/\theta }\end{equation*}

where $\alpha$ and $\theta$ are the weight and substitutability parameters, respectively. Parameter $\eta$ acts as a scalar for monetary input. These parameters are important to household decisions when responding to a health shock, and hence we choose their values carefully to reflect observed household behavior in the data. We discuss more details on our approach to set these parameter values in the calibration section.

3.2 Labor Market

The economy has a care sector and a non-care sector. All men work full-time in the non-care sector with wages based on their productivity per unit of time, $w_{i,m}$ . Women, or adult daughters, choose which sector to work in and how much to work. Let ( $e_{i,c}$ , $e_{i,nc}$ ) denote their labor efficiencies in the care and the non-care sectors, respectively. We allow labor efficiencies in the two sectors to be correlated:

(1) \begin{equation} ln(e_{i,c}) = ln (e_{i,nc}) + \epsilon _e, \quad \epsilon _e \sim N (0, \sigma _c^2\big) \end{equation}

The market wage rate per efficiency unit of labor in the care sector is $w_c$ , which is set in the care sector, separate from that in the non-care sector $w_{nc}$ . This allows us to capture the fluctuations of care market wage, driven by demographic shifts and policy interventions. Women observe the market wage rates in both sectors when making labor supply decisions, and they choose to work in the sector that pays more, so for individual $i$ , her wage per unit of time is $w_{i,f}=max(w_ce_{i,c},w_{nc}e_{i,nc})$ .

Spousal income is directly correlated to women’s non-care sector labor efficiency. We use the intro-household wage ratios observed in the ACS to pin down spousal wages and discuss this process in detail in the calibration section. We also allow intergenerational wage persistence by linking the non-care sector labor efficiency of the adult daughter and her parent in each household.

3.3 Firms and Output

There are competitive firms producing consumption goods and care service, respectively. Labor is the only input for production in both non-care and care sectors. We normalize the price of consumption goods to 1, and let $p$ be the price of care. Firms in the non-care sector face the following problem:

(2) \begin{equation} \max _{L_{nc}}\pi _{nc} = A_{nc}L_{nc}-w_{nc}L_{nc} \end{equation}

and the competitive nature of the market results in $w_{nc} = A_{nc}$ . Firms in the care sector face the following problem:

(3) \begin{equation} \max _{L_{c}}\pi _{c} = pA_{c}L_{c}-w_{c}L_{c} \end{equation}

which results in $w_{c} = pA_{c}$ . Therefore, when both markets are in an equilibrium,

\begin{equation*}\frac {w_c}{w_{nc}}=\frac {pA_c}{A_{nc}}\end{equation*}

which shows that the relative wage in the care sector is proportional to the care price.

Total output in the economy is the summation of consumption goods and care services,

(4) \begin{equation} Y=A_{nc}L_{nc}+pA_{c}L_{c}. \end{equation}

3.4 Government

In the USA, besides the parents themselves, some health insurers also pay for formal care. In the case of Alzheimer’s disease, a progressive chronic condition that requires long-term and potentially intensive care, public insurers, mostly Medicaid, pays more than 70% of formal LTC expenditure in 2013 (Chandra et al. Reference Chandra, Coile and Mommaerts2023).Footnote ¹³ In our model, care refers to the general care elder parents could use as they age, and LTC would be an important component. So it is necessary for us to acknowledge and include the role public programs play in providing care in an aging population. For simplicity, we model a public care program that mimics Medicaid, which helps pay for formal care for eligible parents. If eligible, this program would fulfill the total care need of the parent. Specifically, if one’s wage is below the wage threshold set by the program, this public care program kicks in and purchases $H$ units of care from the market on behalf of the parent.Footnote ¹⁴ In other words, for parents covered by this program, their households no longer have care needs to fill. The program is funded by income taxes, and the government runs a balanced budget. For households, $j$ , with parents who are eligible for Medicaid:

(5) \begin{equation} \tau Y = \sum _{j} pH. \end{equation}

3.5 Agents’ problems

Adult children are the main decision-makers in our model. They face a time constraint across work, $n$ , care, $t$ , and leisure, $l$ .Footnote ¹⁵ Care time is 0 when they do not experience a parental health shock. If the household receives a health shock ( $\bar{h}=1$ ), parents need $H$ units of care. In this case, the parent checks her Medicaid eligibility first. If she is eligible ( $\overline{w_i} \lt W$ ), the public program purchases all the care needed. If the parent is not eligible, she spends a fixed proportion of her endowment, $\psi$ , to purchase care, $s_{i,f}$ .Footnote ¹⁶ When her need is not fulfilled through the formal care she purchased for herself ( $s_{i,f} \lt H$ ), adult daughters would provide informal care, $s_{i,d}=H-s_{i,f}$ , to fill the gap. Adult children’s problem can be described as:

(6) \begin{equation} \max \limits _{n_i,t_i,m_i} ln(c_i) + \nu ln(l_i) \end{equation}

subject to

\begin{align*} & n_i + t_i + l_i = 1 \\ & c_i + m_i = ( w_{i,f} n_i + w_{i,m}*0.4 ) (1-\tau ) \\ & \left[\alpha t_i^{\theta } + (1-\alpha ) (\eta m_i) ^{\theta }\right]^{1/\theta } = \begin{cases} H-s_{i,f} &\text{ if }\bar{h}=1, s_{i,f} \lt H, \text{ and }\overline{w_i} \geq W\\ 0 &\text{if else}\\ \end{cases} \end{align*}

$0.2 \le n_i \le 0.4, \quad c_i, l_i, t_i \geq 0.$ Footnote ¹⁷

4.1 Exogenous parameters

The first four rows in Table 3 show the parameters we use to generate the wage structure in the non-care sector. We use wage data from the 2007 ACS to create the labor efficiency distribution of women in the non-care sector.Footnote ¹⁸ To generate spousal wages, we determine the intra-household wage ratios from the wages of married couples in the ACS, and then produce estimates of $\beta _1$ and $\beta _2$ in the following regression:

(7) \begin{equation} ln\left(\frac{w_{i,m}}{w_{i,f}}\right) = \beta _1 + \beta _2 ln(w_{i,f}). \end{equation}

Using the generated female wages, $w_{i,f}$ , and the estimates of $\beta _1$ and $\beta _2$ from the regression, we calculate the spousal wages for each household in the model.

In our model, due to intergenerational wage persistence, children with higher wages tend to have parents with more financial resources. Those children, on average, bear less care burden because we assume parents spend a fixed amount of income on care. We model persistence in labor efficiency between the parent and children generations as follows:

(8) \begin{equation} ln(e_{i,nc}) = \rho _1+ \rho _2 ln(\overline{e_{i,nc}})+ \epsilon _d, \quad \epsilon _d \sim N \left(0, \sigma _d^2\right) \end{equation}

where $\bar{ }$ represents the parent generation within the household. The fifth to seventh parameters in Table 3 govern this persistence. Based on the empirical work by Grawe (Reference Grawe2004), we set the labor efficiency persistence parameter, $\rho _2$ , to 0.47. Conditional on this choice, the constant term, $\rho _1$ , and the standard deviation of efficiency shocks, $\sigma _d$ , are set at values so that women’s wage distribution is stable across generations and follows the same distribution as the data.

The probability of a parental health shock is set to the fraction of 2015 NHATS respondents who have difficulty with at least one iADL. This is the population of our interest who require regular help from others. We apply the shock probability of 22% uniformly across the population.

4.2 Endogenous parameters

We use nine targeted moments to discipline the remaining nine parameters, as presented in Table 4. While all the nine parameters affect all the moments simultaneously, each moment is most sensitive to a particular parameter, so we will discuss them in pairs.

The first two moments describe the female employment status. The overall female employment rate is calculated using the 2007 ACS data. The weight of leisure in the utility function, $\nu$ , reflects the general attitude toward work and helps target the overall employment rate of 57%. In the empirical section, we show that while providing care affects some daughters’ availability to work, many stay in the labor force. We calculate and target the employment rate of caregivers, 47%, using employment status reported by NSOC caregivers. The scalar of adult daughter’s monetary input in the care production function, $\eta$ , is closely and positively related to this moment. As $\eta$ increases, monetary input becomes more productive relative to time input, which results in less use of own time for care and leaves more daughter caregivers in the labor force.

We proceed to the next three moments that capture the size and pay of formal care. According to 2007 ACS, 4.7% of employed female work in the care sector. We include people working in the following occupations as care workers: nursing, psychiatric, and home health aides (ACS occupation code 3600), personal and home care aides (ACS occupation code 4610), and personal care and service workers (ACS occupation code 4650).Footnote ¹⁹ This employment share partly depends on the total need for care, thus we use the care requirement, $H$ , to target this moment. The next two moments are from the 2007 ACS as well, and they capture the wage distribution of care workers. As implied by equation (3) in the firm’s problem, the wage per efficiency unit of labor in the care sector, $w_c$ , is proportional to the care labor productivity, $A_c$ . Therefore, we use this parameter to target the mean wage of care workers. We also calculate care workers’ wage variance and use the variance in care efficiency shock, $\sigma _e$ , to target this moment.

The next two moments are related to the care time provided by adult daughters. We limit the NSOC sample to daughter caregivers whose parents have difficulty with at least one iADL (the definition of health shock in the model). We find that the average informal care is 42.45 hours per month, which is 0.11 in the context of the model.Footnote ²⁰ This moment is directly and positively related to $\alpha$ , the weight of time input in the informal care production function. The estimated value of $\alpha$ is 0.77, showing a slightly higher weight of time input relative to monetary input when daughters provide care.

The model predicts a negative relationship between adult children’s wage and the amount of care time they offer, through two channels. First, the opportunity cost of care time increases as children’s wage increases, leading to less caregiving by children. Secondly, due to the built-in income persistence within households, children with higher wages tend to have parents with higher savings. This reduces the care burden on children after parental purchase of formal care, resulting in less informal care needed from children. This pattern between children caregivers’ wage and their caregiving time is consistent with what we find in the data using the 1994 Parent Module in the HRS.Footnote ²¹ We report the average care time within each wage quartile in Table 5 and show the negative correlation between care hours and the caregiver’s wage. Using this information, we also calculate the caregiver’s wage elasticity of care time to be –0.74. To target this moment, we use the substitutability parameter, $\theta$ , in the care production function. When $\theta$ is high, time input is more substitutable by monetary input, and children with higher wages are more likely to spend money versus own time in the production of informal care, leading to a steeper negative elasticity. Our estimation of $\theta =0.94$ shows that the two types of care inputs are quite substitutable. Rupert et al. (Reference Rupert, Rogerson and Wright1995) use PSID data to study the household production sector and estimate the substitutability between home consumption and market consumption goods, similar to our care time and care spending by children.Footnote ²² Their estimates of the substitutability parameter, like ours, are sufficiently greater than 0, particularly for married couples.

Table 5. Care hours for parents in the previous year, by caregiver’s wage quartiles

Source: 1994 Health and Retirement Study (Parent Module), wage estimated from full HRS panel

The last two moments in Table 4 correspond to the formal and informal care usage among households. We use parameter $\psi$ to capture the proportion of parental endowment that is spent on care and choose its value to target the usage of informal care.Footnote ²³ Barczyk and Kredler (Reference Barczyk and Kredler2019) provide a cross-country overview on LTC provision. Using data from the HRS, they show that informal care plays the most important part in the USA and report that 76% of care receivers use either informal care exclusively or a mix of informal and formal care. An increase in $\psi$ allows more parental spending on care, which reduces the care burden on children and the fraction of households relying on informal care. Lastly, we use the wage limit parameter on Medicaid eligibility to target the fraction of people receiving benefits from Medicaid. According to 2015 NHATS, 15.4% of its respondents are covered by state Medicaid program.Footnote ²⁴ We use this number as our target and set the wage threshold for Medicaid at 15th percentile of the parental wage distribution.

The baseline calibration implies an equilibrium care price $p = 16.2$ and the tax rate $\tau = 0.49\%$ .Footnote ²⁵ We choose these two parameter values simultaneously with all the endogenously estimated parameters above by iterating on the care price until it satisfies the care market-clearing condition, and on the tax rate until it balances the government budget constraint.

4.3 Untargeted moments

In this section, we report and discuss our model results in other dimensions. We check the fitness of the model by comparing our estimates of some untargeted moments with their empirical counterparts.

4.3.2 Usage of formal and informal care

Barczyk and Kredler (Reference Barczyk and Kredler2019) compare care arrangements across countries and show that people in the USA, similar to those in Southern European countries (i.e. Italy and Spain), rely heavily on informal care. Their estimates show that 64% of care cases use informal care primarily and 24% of care cases use formal home care or nursing home care. We present the fraction of each type of care arrangement in the population from Barczyk and Kredler (Reference Barczyk and Kredler2019) next to the results from our model in Table 6.

Table 6. Care arrangements (%)

Note: Barczyk and Kredler (Reference Barczyk and Kredler2019) count the cases with more than 80% of total care hours being informal as “informal care” and the cases with less than 20% of care hours being informal as “formal care." All other cases fall in the category of “mix IC and FC." We adopt the same rules for categorization.

Our estimates in the benchmark follow a similar pattern as Barczyk and Kredler (Reference Barczyk and Kredler2019)’s empirical findings. The majority of the households with care need rely on informal care. Note that our formal care fraction is lower than Barczyk and Kredler (Reference Barczyk and Kredler2019). This is partly due to our setup that private care spending is a fixed proportion of parental endowment. We choose such linear relationship to remain focused on the question at hand, but this simplification underestimates the care spending for rich households and thus the total formal care usage.

4.3.4 Time allocation of workers

Kydland and Pretnar (Reference Kydland and Pretnar2019) document the time allocation of workers who provide informal care and those who do not. Using data from the 2003-2016 American Time Use Survey (ATUS), they show that caring for another adult leads to 1.22 hours per week less on work and 3.96 hours less on leisure. We compare our estimates of those measures to theirs in Table 7.

Table 7. Time allocation

Note: Informal care in Kydland and Pretnar (Reference Kydland and Pretnar2019) includes care provided to any infirm adult, not just to the elderly. They choose the data point for “adult care” instead of “elder care” for the larger sample size.

Care time is much higher in our benchmark due to our focus on elderly care.Footnote ²⁷ Workers in our model also have lower labor supply than the sample in the ATUS. This is partly because we aim to capture the labor and care decisions of married adult daughters who have old parents, and this subgroup tends to work less than the representative sample in the ATUS. Regarding the effects of informal care on workers’ time allocation, our results are consistent with the empirical pattern shown in Kydland and Pretnar (Reference Kydland and Pretnar2019). While caregiving crowds out both work hours and leisure time, it has a larger impact on leisure. In the next section, we show that work hour response is highly heterogeneous among households, so the decrease from 0.217 to 0.215 in Table 7 does not reflect the trend for all in our model.

5.1 Household response

We generate a benchmark economy using parameter values in Tables 3 and 4. Figure 2 shows the impact of parental health shock on adult children households. The x-axis is the highest potential market wage (between care and non-care sectors) for adult daughters, including those who do not work. We see that, in general, the shocked households have lower consumption, leisure, work hours, and utility, though the differences are not uniform. For women with the lowest wages, they do not work regardless of parental shock, and any informal care is provided with time input exclusively, resulting in lower leisure but no change in consumption. For women with higher wages, they use a combination of time and money inputs to meet the care needs, resulting in lower labor supply and lower consumption. This echoes the empirical findings in the literature that people who spend a considerable amount of time providing care are usually less attached to the labor market and have relatively low wages (see Lilly et al. Reference Lilly, Laporte and Coyte2007; Leigh, Reference Leigh2010; Wang, Reference Wang2021). Facing a parental health shock, some low-wage working women drop out of the labor force and split the extra time between care and leisure. This explains the excess leisure among some shocked households, relative to their counterparts, in panel (b). The higher a women’s wage, the more likely her parent is not eligible for Medicaid; with a higher opportunity cost of time, she relies more on monetary input, so the more her consumption and overall utility decrease from a parental health shock.

Figure 2. Benchmark household response, by wage.

Figure 3. Benchmark care arrangement, by wage.

Meanwhile, the impact of a parental health shock on leisure is substantial. As we presented in the empirical section, most caregivers in NSOC do not claim that caring for parents hindered their participation in paid work. Our results suggest that much of the consequence of caregiving is a reduction in leisure, rather than in work hours. Kydland and Pretnar (Reference Kydland and Pretnar2019) use the 2003-2016 ATUS data and present the time use differences between caregivers and non-caregivers. Their results show that caregivers cut leisure time (3.96 hours per week) more than work time (1.22 hours per week). Our model generates a similar pattern and further shows a large negative impact on utility.

5.2 Care arrangement

We now look within the shocked households and show how they make care arrangements in Figure 3. Panel (a) shows that the residual care needs from parents, or informal care needs, first increase with children’s wages because the parents are less likely to be eligible for Medicaid, but then decrease with children’s wages because the parents are more able to purchase care themselves. This pattern is confirmed in panel (e), where public spending on care through the Medicaid program decreases and private spending on care through parental purchases increases. As a result, as described in panel (d), formal care use decreases quickly as public spending decreases at first, and then increases slightly as private spending starts to pick up. Regarding the informal care provision, most children rely on own time to give care as panel (b) follows a similar pattern with panel (a). Only children with higher wages use care-related spending to help parents, as shown in panel (c). This tradeoff between the time and money usage in meeting the parental needs is consistent with our model prediction in Appendix A. We then conduct a welfare analysis and show the results in panel (f) of Figure 3. For all affected adult children, we calculate their welfare loss as the percentage decrease in consumption that would lead to the same utility loss caused by the parental health shock. For the households not covered by Medicaid, the welfare loss ranges from 8.3% to 18.9%.

6.1 Aging population

We are currently experiencing one of the biggest demographic transitions in recent history. According to the Current Population Survey, the mothers of baby boomers had three children on average, whereas the baby boomers themselves had two. This means the children of baby boomers would have, on average, one fewer sibling to share parental care duties with. This can be interpreted as a 50% increase in $H$ in our setting.Footnote ²⁸ Consider people aged 18 to 64 as the working-age population and those above 65 as the elderly. In 2007, for each elderly person, there are 5.2 working-age people. According to the population projection from census, by 2060, for each elderly person, there will be 2.4 working-age people. This means that the overall elderly care burden will go up by 115%. $^{28}$ Combined with the new $H$ , we increase the shock probability by 43% to reflect this change.Footnote ²⁹ The top panel of Table 8 shows the changes in these parameter values.

Table 8. Aging population

Table 9. Care arrangement, by adult daughters’ wage quintiles

With the adjusted values of $H$ and shock probability, our model generates an economy that mimics a more aged population. We report and compare some care arrangement and labor market statistics in the benchmark and the aged economy in Table 8. Informal care needs increase by 63.2%, and this higher need is met by a 62.6% increase in time input and a 79.6% increase in monetary input. The latter is mostly driven by adult children households with high wages. There is a decrease in overall employment from 54.5% to 51.1% as some adult children withdraw from the labor market to provide care. Within this smaller workforce, the employment share of the care sector increases by 91.9%, resulting from the increased need for formal care. This is also reflected in output, where the non-care sector output decreases by 1.8%, while the care sector output increases by 85.3%. Total output decreases by 1% after a larger care sector compensates for nearly half of the decrease in the non-care sector.Footnote ³⁰ Kydland and Pretnar (Reference Kydland and Pretnar2019) find a much bigger negative effect on output due to caregiving in an aging population.Footnote ³¹ Our model, abstracting from the demographic change in the labor market, is not suited to study aggregate output, but it shows a channel through which the negative impact of caregiving on output can be dampened by the expansion of care sector.

To further demonstrate how households are affected by population aging, we present outcomes of adult children who experience a parental health shock by wage quintile in the benchmark economy and in the aging experiment in Table 9. All affected households have higher informal care needs, and thus bear higher time and monetary inputs and welfare losses in an aged economy. Though the increase in parental care needs is uniform, the increase in residual informal care needs is heterogeneous. Households in higher wage quintiles rely more on formal care in benchmark, so when the shock becomes more intense and parents are not able to afford more formal care, they experience a larger change in informal care. Meanwhile, the way adult children provide informal care in the households with time and monetary inputs continues to follow the trend in the benchmark. For households in lower wage quintiles, who rely almost entirely on time input in both scenarios, the increase in time input is proportional to the increase in informal care. For households in higher wage quintiles, because they are more able to use care-related spending to provide care, they choose to disproportionately rely on monetary input. This is shown by the substantial percentage increase in monetary inputs for the 4th (165.4%) and 5th (79.3%) quintile households.

As all affected adult children have to step up to fulfill the extra care needs, welfare loss from the parental health shock increases for all. We notice the largest informal care burden change, an increase of 68.5%, happens to the highest-wage quintile, which translates to the largest welfare loss. This result is partly attributable to our assumption that parents spend fixed amount of money on care, even when care need intensifies. This assumption may be less fair for parents who have more financial flexibility to purchase care and would buy more care in an aged economy, leading to an overestimation of the impact on high-wage households.

6.2 Government policy

In this section, we explore the role of government interventions in an aging population. We first describe how we implement each policy and then compare the impacts of the policies on households and the aggregate economy.

6.2.1 Care services subsidy

We first explore the effects of a care service subsidy that allows parents to buy more care while holding their total care spending constant. Let $\gamma$ be the subsidy rate. Formal care purchase by household $i$ increases from $s_{i,f}$ to $\frac{s_{i,f}}{(1-\gamma )}$ . This subsidy, similar to the Medicaid program, is funded by a flat labor income tax. Therefore, each subsidy rate, $\gamma$ , corresponds to a new labor tax rate, $\tau _s$ , that allows the program to be budget neutral:

\begin{equation*}\tau _s Y = \sum _{j} pH + \frac {\gamma }{1-\gamma } \sum _{i}(ps_{i,f}) \end{equation*}

where total output and total income, $Y$ , are constructed as in equation (4). Households $j$ are those who are eligible for Medicaid, and households $i$ are those that are affected by a parental health shock. For a given subsidy rate, we solve the equilibrium care price and the corresponding tax rate by iterating on them simultaneously until the care market clears and the government budget is balanced. We do this for subsidy rates from 0.1 to 0.5 and graph the results in Figure 4.

The government subsidy program reduces the cost of market care, therefore, households use more formal care and hence, the informal care burden on adult children decreases. This effect is more pronounced for high-wage households as their parents have higher care purchase to start within the benchmark. This is reflected in the bigger impact of higher subsidy rates for these households in Figure 4. We choose the scenario where $\gamma =0.2$ , $\tau _s =0.0129$ and compare it to other programs.

Figure 4. Household care decisions and care market, by subsidy rate, $\gamma$ .

6.3 Comparison and discussion

In Table 10, we present key results for five scenarios: the benchmark, the aged population with no policy intervention, the aged population with each of the three policy interventions, care subsidy, Medicaid expansion, and caregiver allowance. To better compare across scenarios, we normalize public spending in formal care purchase and aggregate outputs in the benchmark to 1. The top half of the table summarizes the changes in assumptions for the scenarios. The main difference across these experiments is how the government engages with care. In the care subsidy program and the Medicaid expansion program, the government interacts directly with the formal care market, by lowering the price of care for households and purchasing extra care, respectively. This increases the average formal care use from 0.038 to 0.041. The caregiver allowance, on the other hand, is relatively small and only for the intensive caregivers whose parents buy very little care, so the program does not affect formal care use.

Table 10. Policy scenario comparison in aged population

In the second half of Table 10, we present some key results from the experiments. First, we look at informal care needs and average time and monetary inputs from adult children. Population aging increases the average informal care needs from 0.068 to 0.111, on top of the increase in formal care from 0.031 to 0.038. The care subsidy and Medicaid expansion programs both cause a shift from informal care to formal care. While having a similar overall effect on informal care, the care subsidy and the Medicaid expansion affect different households. The subsidy has a larger impact on households who buy more care. The adult children in those households are most likely to fulfill care needs with monetary input, so we observe the largest decrease in average monetary input under the subsidy program. Medicaid expansion, on the other hand, affects low-income households, where adult children tend to previously mostly use own time to give care. By lifting the care burden completely from another 2.3% of the population, the Medicaid expansion causes a bigger cut in care time relative to care-related spending. Caregiver allowance, in contrast to the previous programs, has little effects on care provision (formal vs. informal) and informal care production (time vs. monetary input) in our model. A slight decrease in care-related spending comes from the income effect of the higher labor tax that all the adult children are paying to finance the intervention. Care price, endogenous in our model, is higher in an aged population and in the policy scenarios with higher formal care use.

We now look at the implications of the experiments on the aggregate economy. Employment rate increases under care subsidy and Medicaid expansion from an expanded formal care sector, reflected by the larger care output (from 0.018 without intervention to 0.2 with intervention). In all the aged scenarios, non-care output mostly remains unchanged and total output is boosted by the care sector, especially under the care subsidy and Medicaid expansion experiments.

To further understand the welfare impact of these different policy options, we calculate the percentage change in welfare caused by the three interventions and present the results in Figure 5.Footnote ³² Both care subsidy and Medicaid expansion increase welfare, though they have different redistributional effects. The benefit of care subsidy increases steadily with wage whereas Medicaid expansion largely affects households in the lower wage deciles. The caregiver allowance, on the other hand, has quite muted welfare effects in comparison because it does not directly reduce caregiving burden for adult children in our model. For households in the highest-wage decile, who pay a higher labor tax for the program but are not eligible for the allowance, a welfare loss occurs.

Overall, households are more responsive to the subsidy and Medicaid programs, given their direct influence on formal care purchase. Welfare improves under both policies, though the impact varies across households. Designed to directly help informal caregivers, care allowance has minimum effects on household behaviors and their welfare. Potentially, the policy effects could be amplified if we were to reduce the size of the beneficiary group and allow a more generous benefit for eligible caregivers. Still, care allowance would be the most costly way, among all interventions we consider, to provide a relief to caregiving adult children.

Figure 5. Welfare loss comparison.