Parents with an Unemployed Adult Child: Consumption, Income, and Savings Effects

Abstract The risk of labor market, health, and asset-value shocks comprise profound retirement savings challenges for older workers. Parents, however, may experience added risk if their children experience adverse labor market shocks. Prior research has shown that parents support their children financially through an unemployment spell. In this paper, we also provide evidence of financial support from parents and investigate if this financial support is accompanied by adjustments to parental consumption, income, or savings behavior. With longitudinal data on mothers and children from the Panel Study of Income Dynamics, we use within-mother variation in behavior to identify the effect of a child’s labor market shock on parent outcomes. We find evidence of a decline in consumption, an increase in labor supply, and a decrease retirement savings, though the results are heterogenous among mothers. Our results point to aggregate inefficiencies and inequities that may result from family risk sharing.


Introduction
Families often serve as the first line of defense against adverse events -for example, spouses enter the labor force or increase their hours of work when a partner is laid-off (Cullen and Gruber, 2000), grandparents provide child care or loans when a child is sick (Bianchi et al., 2010), and parents respond to the economic needs of their children through various forms of assistance, such as offering co-residence or sending money (Wiemers, 2014;Kaplan, 2012;McGarry, 2016;Edwards, 2017). It is generally assumed, either explicitly or implicitly, that the providers of assistance are not made worse off by helping their family members, if for no other reason than they willingly elect to do so.
Past research explores the motivations for family assistance, especially between parents and children. Parents are either altruistically motivated or they are motivated by exchange and give to a child in the current period in order to receive from the child in the future. In the former, a child's consumption enters the parents utility function, and the latter, a parent's future consumption and thereby utility is higher. 1 However, the voluntary aspect of the provision of family assistance does not make it costless. And critically, individual utility optimization does not guarantee an efficient allocation of risk or an equitable distribution of insurance in an economy.
In this paper, we directly approach the potential costs, inefficiencies, and inequities of aiding family members. We examine parental behavior in the year that an adult, non-residential child experiences an unemployment spell. Using the 1985-2013 waves ofthe Panel Study on Income Dynamics, a longitudinal dataset that allows for parent-child linkages across households within the same wave of the survey, we measure the concurrent changes to the parent's consumption, income, and savings during child's unemployment. Due to quality concerns in the matching process, we examine mothers only. However, all but one outcome is measure on the household-level. For this reason, we describe our results as parent behavior, though it is captured through mothers.
Given that we can observe mothers over long periods, we regress an adult child's unemployment on parents' outcomes and include mother, year, and mother-age fixed effects, which control for unobserved individual, time-period and life-cycle characteristics of the mothers that could be correlated with job loss of the children. Identification comes from within-mother variation in outcomes and the incidence of a child's unemployment spell.
Our analysis includes four classes of dependent variables that attempt to quantify the flow of financial assistance to children and any concurrent changes in parents' outcomes. Specifically, we examine the effect of a child's unemployment on the following parental behaviors: assistance to children (measured in reported cash transfers), consumption (measured in household food consumption), income (measured in labor supply and program participation), and savings (measured in savings rates and asset values).We do, however, find results in each category, though they vary by the age and situation of the parent.
We corroborate the findings of previous studies and show that parents are more likely to send a cash transfer to a child if they have an unemployed child. Separately, and not conditional on transfer sending, we find large drops in usual household food consumption, 1 There are numerous papers discussing, debating, and demonstrating altruism and exchange motives in both theory and empirics, starting with Becker (1974). Examples can be found in Cox (1990), Rosenzweig and Wolpin (1994), Altonji et al. (1997) and more recently McGarry (2016). A discussion of the motives can be found in Bianchi et al. (2010).
labor supply increases, but little change in program participation in Social Security and food stamps (Supplemental Nutrition Assistance, or SNAP), or savings in the year of a child's spell. We then look for heterogeneous effects based on the age and work status of the mother, as well as the nature of the unemployment spell of the child, and find that the main results are driven by younger, working-age mothers, who additionally reduce savings in the year of a child's spell.
The myriad measures examined here are still only partial measures of the extent of financial assistance provided to unemployed workers by parents and the effect it has on parents, as it is limited by what we observe in the survey. The array of significant changes to parent behavior detected in our study, however, suggests that the costs incurred providing family assistance and the effects of risk bearing may be large. A parent who willingly changes her behavior in order to help a child, though it may be optimal from the point of view of her utility, may still be suboptimal in the distribution and cost of risk in the economy. Given the state of financial insecurity among the working-age population and retirement security of the near-retired population, suboptimal distribution of risk is a large concern.
2 Data The Panel Study of Income Dynamics (PSID) is a 1968-representative sample of 5000 households in the U.S. that were surveyed annually survey from 1968-1996 and biennially since 1997.
It follows original sample members, their descendants, and co-resident relatives over time.
The PSID sample grows every year as children of the respondents move out and form their own households, which are added to the panel. This unique sampling frame enables us to see detailed information on parents and their non-resident children concurrently for long periods of time. While the level of detail afforded by family lineage is a key advantage to using the PSID, it has two major caveats relevant for our analysis.
First, while members of the original 1968 sample and their biological descendants are continuously followed, family members of those descendants are not. For example, a woman moves out of her parents house (in the PSID sample), gets married, and has a child. Her child, partner, and self are in the PSID. Her husband's parents are not. If she gets divorced and moves out, she and her child remain in the PSID, but her ex-husband does not. In general, a divorce or partner dissolution in which a non-sample member moves from the house means that that member will omitted in the future survey. We therefore miss parent-child relationships of divorced or separated parents who are not living with the member of the household that is biologically linked to the original PSID sample. This is a larger issue for fathers, since mothers are considerably more likely to maintain custody of children.
In addition, the PSID does not collect equal amounts of information on everyone in the household. The full household roster is asked a set of basic demographic and status questions, but detailed information, such as labor supply, is only gathered about the head in early waves and only heads and spouses in later waves. If an adult moves in with a family member, the move is observed, but the detail is lost. Hence, we cannot detect if a worker became unemployed and moved back in with family because he will no longer be a head of household, and will not report the prior year's labor force information. Hence, our analysis excludes any study of co-residence.

Mothers
From the full PSID sample, we create an analytical sample of 38,004 person-year observations of mothers matched to independently living adult children between 1985-2013. Details of the matching process, including matching rates and a comparison of dependent and covariate variables across matched and unmatched mothers, are discussed in Appendix B. Our analysis relies on mother-child pairs only. We are able to match mothers at a much higher rate than fathers, and most of the matched fathers were in households with previously matched mothers.
Hence, the only excluded parents from our sample are single, custodial fathers and divorced, non-custodial fathers. The former makes up a very small share of the population 2 and there is prior evidence that divorced fathers are much less likely to provide financial assistance to adult children (Amato et al., 1995). Moreover, with the exception of individual labor supply, all of the dependent variables that we measure are household summaries; we only need to observe one parent to capture any changes to partner behavior. calendar-year totals. The first group of variables are cash transfers sent and received by the household. Heads and wives separately provide estimates of the amount of money they sent to a family member, and their relation to that member. 5 They also each provide a total of how much they received from family, but do not specify who it was from. We combine transfers sent and received from heads and wives into a household summary measure. For parsimony, we refer to 5 This total excludes legal transfers, such as alimony and child support. a year in which a positive transfer amount was reported as a single transfer, though it could be multiple disbursements within the year. While they are younger, mothers' households are net senders of transfers; 8.5 percent of working-age mothers report sending a transfer to a child in a year and 6.9 percent received a transfer. As they age, they become net receivers; only 3.5 percent of older mothers report sending a transfer to a child but 5.2 percent report receiving a transfer.
The These variations could reflect economies of scale in larger households, changes in preferences towards or ability to afford more expensive food, as well as reductions in food consumption overall. However, it likely also reflects a measurement issue. Usual household food consumption is measured over a year, but family size is measured at the time of survey. If the family size changed over the course of the year, the members contributed to consumption, but may not be included in family size, depending on when they exited or entered. For this reason, we show per capita consumption in this summary, but will not use it as a dependent variable in our analysis.

Figure 1 Year of Birth of Three Age Groups of Mothers
Source: Author's Analysis of PSID data, 1985PSID data, -2013. Mom group 1 are mothers who are age 62 and less, mom group 2 are mothers who are 62-70, and mom group 3 are mothers who are 70 and older. Mothers can transition between groups.
The third group of variables summarizes sources of income, including the total weeks worked in the year, the share of mothers whose household has any Social Security Income, 6 and the share who receive Food Stamps/Supplemental Nutrition Assistance (SNAP In summary, our sample straddles mothers of varying financial resources and flexibility, from younger mothers who are working and contributing to savings, older mothers who are on Social Security income and drawing down their savings, and the mothers who are transitioning between the two states.

Unemployed Adult Children
We define an unemployment spell as a calendar year in which the child was unemployed for at least one week. 7 We further restrict unemployment spells not to be concurrent with the final year of schooling, to avoid anticipated unemployment spells. Figure 2 shows the distribution of ages of unemployed adult children in our sample the year they experienced a non-entry unemployment spell and the distribution of the age of their mothers in that year. Unemployment peaks between the ages of 24-33, and then gradually declines among older workers; half of spells occur before age 30. For mothers, unemployment among children is centered around a peak at age 57, occurring as early as 40 and as late as age 85. 8 The demographic characteristics of unemployed adult children matched to mothers in our sample, as well as characteristics of the spell, are summarized in Table 2 for all unemployed adult children, and grouped by the age of their mother. The average age of unemployed children is 32.2, with a nearly even split of men and women, though the child's average age increases with the age of the mothers, from 28.8 years old to 44.9. Similar to mother's age predicting the sources and scope of financial resources available to her, child's age is indicative of the needs and constraints of her household. For example, although marriage rates are similar for each set of unemployed children, the share with children of their own at home drops from 67.6 percent to 49.3 percent. In addition, 50.2 percent of unemployed children of working-age mothers have 6 The PSID varies in its collection of information regarding Social Security income, asking about individual receipt in some years and family receipt in others. We use household-level summaries in all years for consistency, but that means we cannot identify the recipient within the household for most years of the survey. 7 We use the term spell for parsimony; it could in fact be multiple spells within the annual total. 8 Appendix Figure A1 shows Figure 2 as a scatter plot of the age of mothers matched with the age of their unemployed adult child, which shows the same concentration between 20-30 among childrenand 40-60 among mothers. more education than their mother, but this increases to 63.1 percent for the oldest mothers.
Hence, the relative position of mothers to children is different among the threegroups.
We also examine events that are concurrent with the year of the child's unemployment spell that could lead to financial assistance from parents. Self-reporting of disability joint with an unemployment spell is rare, with less than one percent of spells for children or working-age and retiring mothers, and 1.9 percent of spells for children of the oldest mothers. More common is the concurrent reporting of a new child in the unemployed household in the year of a spell, averaging 11.1 percent of spells for children of working-age mothers and 4.1 percent for children of oldest mothers. Also more common is for a child's unemployment to coincide with that child's divorce, averaging 10.1 percent of spells, and fairly consistent across the age groups.
Due to the timing of the survey window, we can only identify that both events (unemployment and birth/divorce) occurred within the same calendar year and not which preceded the other, and it could be the case that the unemployment spell is prompted by the birth of a new child or divorce. Finally, 30.8 percent of unemployment spells occur within the year that a sibling is also unemployed; this share varies less by age of mom, from 30.9 percent, to 31.7 percent, to 28.5 percent.
To understand more about the nature of the child's unemployment, we also examine the characteristics of the spell itself. First, we show the reason given for the spell. The PSID varies in who was administered the question eliciting the reason for unemployment; in certain years the head had to be unemployed at the time of the survey, in other years not. Hence, the categories include that the spell was associated with displacement, either layoff or firm closing; the spell was voluntary; or, the nature of the spell is not known. Of the known spells, a roughly even   force attachment is high; 75.8 percent remain in the labor force in the year following an spell of unemployment. Hence, the majority of unemployed children in our sample are full-time, full-year workers who experience a short spell and then return to work in the following year.In summary, unemployed children have similar demographic variation as their mothers do, but their spells and labor force attachment is comparatively much more uniform.

Empirical Model
Our estimation strategy can be generalized in the following way. Given parent p, in year t, with child c: Where Y pt is the parents' outcome of interest, X pt is a set of parental covariates, X ct is a set of child covariates, θ p is individual (parent) fixed-effect and µ t is calendar year fixed-effect. 9 Our model relies on within-person variation in Y pt , identified from UC ct , a dummy variable equal to one if the mother had an adult child who was unemployed for at least one week in year t. We test four groups of dependent variables: transfers, income, consumption and saving. We operationalize these outcomes in a number of ways. For transfers we measure both the real dollar amount and a dummy for transfers sent to children or received from family by the mother's household; income is measured through the mother's labor supply, as well as the mother's household labor supply, and program income from Social Security and Supplemental Nutrition Assistance; consumption is measured by usual household food consumption in dollars and logs; and savings includes the mother's individual contributions to retirement savings and household IRA and vehicle wealth.
Given the use of individual fixed effect for the mother, we include in X pt changes in mothers' observed marital status, self-reported disability, unemployment rate in her state, retirement status, work status, age fixed effects, and a dummy variable for any unemployment in the mother's household, experienced by either herself or by her partner or spouse. X ct is a vector of child characteristics that may be related to parental assistance outside of unemployment, specifically, dummies for if a child got married, divorced, had a child, or became disabled.
The identifying assumption of equation (1) is that UC ct is exogenous. That is a strong assumption, for two primary reasons. First, the availability of assistance from parents could prompt unemployment among children. We cannot account for this directly, but we can measure the extent to which behavioral changes in parents are induced before or after the spell, in effect testing for pre-trends. The model in equation (1) can be expanded to UC ct j , Where j are the years before or after the spell in j = 0 and j ∈ [-3,3]. Hence, the estimates of γ j capture the time path of the dependent variable in the years preceding and following an adult child's reported unemployment. This method of identification-event study with fixed effects-is similar to studies of wages before and after displacement (Stevens, 1997) as well as outcomes before and after hospitalization (Dobkin et al., 2018).
The second issue with the exogeneity assumption of UC ct is that parents likely have a belief, or prediction, of their child's unemployment probability. Parental fixed effects control for any time-invariant aspect of this, but not for updated or evolving opinions. To the extent that this is occurring, then the interpretation of γ changes, ranging from the response to a fully exogenous income shock to the child's household, to a perfectly anticipated income reduction to the child's household. Our model cannot determine how random a child's spell is to parents, and where in the range of potential interpretation γ lies. We can, however, investigate how the estimated γ varies by the nature of the unemployment spell of the child, such as those who indicate that their unemployment was the result of displacement versus a voluntary quit. We will test differences in our analysis among these and other subgroups. As we present results, and in particular subgroup results, we will be careful to note the strength of identification and assumption of exogeneity. Yet, whatever behavioral changes are induced among parents are still informative to understanding the cost of risk bearing.

Results
In this section we present the results of equation (1) on the full sample of mothers for the categories of dependent variables: financial assistance, consumption, income, savings. We then discuss the results across all categories for key subgroups of mothers and children. The data support myriad dependent variables, or forms of dependent variables; we present only select results in the paper and omit those in which we did not have significant findings, but are careful to note those omissions, and include those results in the appendix.

Financial Assistance
We first estimate equation (1) when Y pt are measures of financial assistance from mother to child. Prior literature has established that parents send financial assistance to their children in certain instances, including unemployment (Cox andWay, 2011, Edwards, 2017); we want to confirm that finding within our sample before examining other outcomes. We use two measures of transfers in Y pt , presented in Table 3: the first as a dummy variable for any transfer sending, and the second as the real dollar amount of the transfer. The estimated γ when transfers are a dummy variable in column 1 is 0.018 (.004), or a 1.8 percentage-point increase off of a mean rate of 7.0 percent, a 25 percent increase in the probability of sending a transfer. In column 2, we show similar estimates when Y pt is the dollar amount of the transfer sent; the results are comparable to the first regression. There is a large and precisely estimated coefficient for the total population of mothers, at $77.844 (25.561). Off of a mean of $329, this is equivalent to a 22 percent increase in the amount of transfers sent to a child in the year of a child's unemployment spell.
In Figure 3, we show the coefficient estimates for the parental transfer dependent variable when UC ct is the time-path before and after unemployment, the event study from equation (2).
The markers are the point estimate of the regression coefficient and the bars are the standard errors; three years, the omitted variable, is zero. The transfer amount dependent variable shows Year fixed effects refer to the year of the spell, age fixed effects refer to the age of the mother, and individual fixed effects to the mother.
a spike in the year of the spell, but the years outside the spell are not positive. Hence, there is little evidence that parents pre-finance spells or may continue to assist even after the spell is completed. 10 To further understand the financial flows between parents and children, we also examine whether unemployed children effected the probability of mothers receiving a transfer, rather than sending one. There was no significantly estimated effect (neither decrease or increase), for either measure of transfers. 11 Our finding that parents are more likely to send a transfer to a child in the year they experience an unemployment spell corroborates similar results in previous studies. One shortcoming of the results presented here is that they are likely not exhaustiveof the total financial assistance sent from parents to children; the transfer themselves may be an underreporting of cash assistance, and by definition exclude any cohabiting or any in-kind transfers. Regardless, they do establish that parents financially assist unemployed children and that that assistance does not precede spells, providing support for exogeneity in the unemployment spell. We can turn to our research question, how this assistance is financed, and if we can observe any change in behavior.

Effect on Consumption
Consumption is the most basic measure of welfare, and it is also an adjustment that all individuals, even those on a fixed income, can make in response to an income shock. Most accounting of consumption and household expenditures are not captured in the PSID and, in the years when more consumption measures are available, they are not measured frequently or consistently, save annual household spending on food. Although this it only measures part of total household consumption, food consumption has been used in prior studies to proxy for overall consumption, notably in the Gruber (1997) study of the consumption smoothing effects of unemployment insurance.
In the third and fourth columns of Table 3, we estimate equation (1) Figure 4 shows the event study coefficients for the log dependent variable. Consumption declines in the year of the spell; the decline persists for the two years following before regaining its former level. 12 A sustained drop in consumption in mothers' households after the spell has 12 The exact coefficients (and errors) are: three years prior, 0.01 (0.011); two years prior, -0.016 (0.008); year prior omitted; year of, -0.039 (0.008); one year following, -0.020 (0.01); two years following, -0.028 (0.008); three years following, -0.006 (0.011). The dollar amount event studylooks similar; those coefficient estimates can be found in Appendix Table 3. ended could reflect either a continued need for assistance or a change in expectations about future need. Our estimates cannot comment further on which is the case. Regardless, a drop in consumption among a parent's household associated with an adult child's unemployment is a major finding, contributing to our understanding of how risk and income shocks are absorbed across family networks, to the extent that consumption shocks are shared across households.

Effect on Income Behavior
There are two measures of income behavior in the PSID that we can examine through the empirical framework in equation (1). Labor supply, as measured through the weeks worked per year and hours worked per week; and program participation in Social Security and SNAP.
Asset and dividends, such as from the sale of a car, we consider dis-saving, rather than income, and discuss in that section.
The coefficient estimates from equation (1) when Y pt is mothers' total weeks employed in a year are presented in Table 3. As noted previously, an average of 49.2 percent of mothers are working in any given year. In the fifth column of Table 3, we test the individual reported weeks employed by the mother. The coefficient estimate of γ on child's unemployment is a 0.381 increase in the number of weeks worked, on a base mean of 25.0 weeks, or 1.5 percent. This is a small though precisely estimated increase in labor supply in the year a child experiences unemployment. However, we do not find that there is an increase in the usual hours worked per week, in the subsequent column, which shows an imprecise point estimate of 0.058 (0.147).
We offer a few explanations of why weeks would adjust upward, but hours would not. First, they are measured differently. The survey asks for the number of weeks employed in the prior year, as well as the usual hours worked per week. The former is an accounting of time while the latter is not. Second, there may be less of a margin to adjust hours per week, either because it is not compensated or it is not feasible. A salaried employee, for example, may increase their earned income by taking less time off, but likely would see no earnings return to working longer hours. Workers in our sample are mostly at full-time hours. Conditional on working, 42 percent of mothers in our sample report working exactly forty hours per week and an addition 21 percent reportworking more than 40 hours. By comparison, conditional on working, half of mothers report working fewer than 48 weeks in the year prior. 13 To further understand the labor supply effects, we also examined the weeks worked per year and usual hours worked summed over the household (that is, including partner labor supply), as well as the weeks vacation taken in the prior year. None yielded any significant results for the full sample. 14 In Figure 5, we present the coefficients from the event study in equation (2) for the total weeks employed of mothers to determine if the increase in labor supply precedes the unemployment spell or persists following. There is no increase in weeks employed in the years leading up to a child's unemployment spell, a large increase in the year of the spell, and noisy 13 A histogram of usual hours per week for working mothers can be found in figure A7 of the Appendix. A histogram of weeks employed in the prior year can be found in A6. 14 Results presented in Appendix Table 1. estimates of the years following, though they weakly suggest that weeks worked remains high relative to the years prior to the child's spell. 15 The second income behavior we examine is from program participation in Social Security or SNAP. The margins by which mothers and their households can alter their behavior in order to increase income via either program is very small, given the eligibility constraints and observed claiming behavior. Individuals may not claim Social Security retirement benefits until age 62, the Early Retirement Age (ERA), and most claim by age 70. Individuals of any age can apply for Social Security disability benefits, if they demonstrate they have previously worked but can no longer. In our sample, we measure household Social Security income, which would capture receipt for retirement or disability of any household member. The coefficient estimates from equation (1) when Y pt is a dummy for any Social Security income are presented in the final column of Table 3. The result is positive, but imprecise, at 0.005 (0.004).
The other program, SNAP, has income-based eligibility requirements. To increase SNAP in the year of a child's unemployment, a mother would have to have been eligible but not claiming household benefits until the year of the child's spell, a very small margin. In addition, average SNAP receipt in our sample is low, at 7.0 percent. We do not find any significant results.

Effect on Savings
The last set of behaviors that we examine is savings. Savings variables were measured in each wave beginning in 1999, and take two forms. First, there is a measure of retirement savings contributions; the PSID asks what percent of income is put towards a pension. Second, there are measures of asset values of components of total wealth: home equity, debt, stock, farm or business income, other real estate, IRAs, and vehicles. For these regressions, we add to equation (1) a five-knot linear spline controlling for total household wealth.
To start, Table 4 shows the coefficient estimates when Y pt is the unconditional percentage of income contributed to retirement savings. We find there is an imprecisely estimated decrease in savings rates of -0.068 (0.047), off a sample mean of 0.6 percent. In Figure 6, we present the coefficients from the event study in equation (2) for the percentage of income contributed to retirement savings. None of the coefficients are precise, though they show a pattern year-of-spell only decline. 17 Next, we examine asset values of mothers' households in the year of child's unemployment spell. Although the PSID has seven asset measures, we present results for two: vehicle value and IRA value. Very few mothers have any farm/business income or real estate outside of a primary home; the distribution of both are highly skewed. The results for stock value, debt, and home equity were imprecise and insignificant. They also may not logically be expected to respond to unemployment of a child. Stocks are reasonably liquid, but few mothers report any stock assets, and may be constrained in selling based on the value at the time relative to when purchased. Mothers may take on debt if they are not borrowing constrained and can afford the interest. And home equityis not a reasonably liquid asset, especially relative to a vehicle or an

IRA. 18
The coefficient estimates when Y pt is vehicle value are presented in the second column of Table 4. We find an imprecisely estimated decline in vehicle value of -$324.56 (262.568). However, in Figure 7, we show the coefficient estimates from the event study of equation (2); the decline in vehicle value does not precede a child's unemployment, but decreases, significantly estimated at -$567.436 (275.268), in the two years following, before returning to the baseline level. 19 A decline in vehicle value does not necessarily indicate that a car was sold; it could also be the case that a decline in vehicle value is capturing that parents have transferred ownership of a car, perhaps to their children. The post-spell decline in vehicle value is the only instance in which there is no significant result in the year of the spell, only following. Although it could be the case that changes to this asset have a lagged adjustment period, it could also be spurious; we will test whether the subgroups illustrate which is the case. Finally, in the last column of

Subgroup Analysis
In the previous sections of results, we estimate the effect of having an unemployed child on various dependent variables for the full sample of mothers. In this section of results, we examine those previously estimated effects across key subgroups of unemployed children and their mothers. For both, we introduce the division in the treatment effect by substituting the single dummy U ct of child's unemployment with a vector UC ct . For example, to investigate how the main effect varies by the reason of unemployment, we execute: In the top half of Tables 5 and 6, we present estimates when UC ct spans reason for the child's unemployment, the labor supply before the spell, the duration of the spell, and the labor supply after the spell. We show this for each of the key dependent variables.  Standard errors listed. The regressions shown include but do not show estimates for child covariates (marital status, disability status, birth of a child) and mother's household covariates (presence of an unemployment member, marital status, disability status, employment status, and local unemployment rate).

Subgroups of Child Spells
In any empirical study of unemployment, endogeneity is a large concern. The unemployment of the child and the mother behavior that we measure may be correlated. We control for mother fixed effects, an exhaustive list of mother and parent covariates, as well as year and age-of- Standard errors listed. The regressions shown include but do not show estimates for child covariates (marital status, disability status, birth of a child) and mother's household covariates (presence of an unemployment member, marital status, disability status, employment status, and local unemployment rate).  Table 6) hours per week, SSA income, pension contribution, vehicle value, or IRA value.
In other words, mothers evince a similar response, at least in terms of transfers, for both more exogenous (displacement) and more endogenous (voluntary) unemployment, and similar effects on food consumption whether we restrict to more exogenous spells (displacement) or not (not known). This is evidence that parents respond to the decline in income of the child, whether it is a shock or not.
To further understand this, we look at the labor supply of the child in the year before the spell. A key note: in the main results, we excluded spells that were coincidental with school exit.
We add them here so that, rather than compare spells with probable variations in endogeneity, compare spells with certain variation in anticipation. School exit is known to the mother, whereas a child that had been working becoming unemployed, for whatever reason, is likely less anticipated. Interestingly, the estimate on transfers is largest for these anticipated spells, at 0.038 (0.015) and $187.329 (95.266), but no other dependent variable has precise estimates. This could suggest that mothers assist their children in unemployment regardless of why the spell occurred, but the changes in other behavior are associated with spells that were not anticipated.
Indeed, we compare school exit spells with those preceded by work, or no work, labeled here as entry, though it could be re-entry. Spells that follow at least a year of working show an increase in the probability of transfer sending at 0.011 (0.005), decline in food at -$285.200 (69.609) and -0.044 (0.012, an increase in weeks employed at 0.714 (0.247), and (see Table 6) a decrease in pension contribution at -0.121 (0.056). Comparatively, (re)entry spells have a decline in consumption at -$288.043 (108.125) and -0.045 (0.015), but no other precisely estimated concurrent changes to mother behavior. This is more significant variation than we see by examining spells of different duration, less than 4 week, 5 -25 weeks, or 26 weeks or more.
Transfers are more likely regardless, and the only significant estimates are the decline in food consumption associated with mid-length spells; none of the rest of the dependent variables show precision across spell length. Most surprisingly, the amount of transfers sent are not even precise for particularly long spells.
Finally, we examine the result of the spell, whether it was followed by a year in which the child remained in the labor force, or if the spell preceded an exit from the labor force.
The increase in sending a transfer is slightly larger if the child remains in the labor force at 0.018 (0.004) compared to 0.011 (0.005), but the size of the increase is slightly larger for labor force exit at $90.714 (34.527) compared to $60.214 (25.463). The decline in food is smaller for spells followed by continued laborforce participation, at -$194.352 (50.509) and -0.029 (0.008), compared to -$347.161 (75.984) and -0.063 (0.015). However, we place less of an emphasis on exact point estimate than we do on direction and precision; regardless of labor force decisions following a spell, we document an increase in financial assistance and decline in consumption in the year of the spell. This is in contrast to labor supply. The increase in mother's labor supply is precisely estimated for spells associated with child labor force exit, at 0.746 (0.277), but not with child labor force participation, at 0.148 (0.169).
Taken together, the comparisons of the coefficient estimates of subgroups of child spells present a more textured understanding of the main effects presented previously. In general, the increase in financial assistance is mostly insensitive to the type or nature of spells; mothers are more likely to help their children regardless. Response to an exogenous shock seems identical to the response to an endogenous one, similarly anticipated versus not.
But the secondary effects show more dispersion. The next most consistent estimates are the corresponding decline in household food consumption, but there is not a precisely estimated decline for spells that are voluntary or spells coincidental with schoolexit. This would suggest that the decline in food consumption that we identify is associated with more exogenous and less anticipated shocks. On the other hand, the increase in mother's employment is only precise when the spell was preceded by employment. Yet, we cannot make the same type of comparison to potential exogenous responses, since there is no discernible increase in weeks worked associated with displaced spells. Arguably the more interesting estimate is the large in increase in mother's labor force when spells are associated with child's labor force exit, as it could indicate, not at all investigated further in this analysis, an intrafamily, inter-household labor supply decision. The remaining dependent variables are little informed by the subgroup analysis based on the nature of spell, only one, pension contribution, has any precisely estimated effect.

Subgroups of Mothers
In the bottom half of Tables 5 and 6, Table 6) increase in having any Social Security income at 0.011 (0.005), decrease in retirement savings rates at -0.136 (0.062), and decrease in vehicle value at -$629.627 (323.912).
Given their subsample means, this reflects a 1.4 percent increase in labor supply, an 11.8 percent increase in likelihood of household Social Security income, a 15.1 percent decline in retirement savings rates, and a 3.4 percent decline in vehicle value. Our interpretation is that younger mothers, who are more likely to be working and therefore more likely to be saving, have more margins to adjust their behavior than older mothers, who are retiring or retired.
Yet, the increase in the likelihood of household Social Security income is surprising. Given that we measure any Social Security income in the household, an increase could happen through either claiming benefits, or the addition to the household of a member already receiving Social Security income. The former, given the age of the mother, would have to imply an increase in Disability claims, as they are not old enough to claim Old Age Insurance.
To further investigate, we show in the next set of rows how the main results vary by the work status of the mother. Again, there is consistently estimated increase in financial assistance and decline in food consumption regardless of mother's work status.The labor supply results show an increase in weeks worked for both working and non-working mothers, the former increasing 1.910 (0.224) weeks, or 4.5 percent, and the latter 0.480 (0.244) weeks. This is evidence that the unemployment spell of a child is associated with an increase in labor supply of mothers on both the intensive and extensive margins, though the latter is likely temporary. Working mothers also show an increase in usual hours worked, at 1.103 (0.225), but non-working moms show no significant change in usual hours, at 0.114 (.200). Given the scope of measurement between total weeks worked and usual hours worked, we conclude that there is support for the conclusion that working mother have a sustained increase in labor supply, but that non-working mothers, though with some measurable increase, do not become re-attached to the labor force.
Social Security increases, on the other hand, appear to be driven by non-working mothers; the estimate of the likelihood of household income from Social Security is 0.153 (0.068), compared to the imprecise 0.034 (0.078) for working moms. Like in the previous section of subgroup results in which we found that mother's labor supply increase is larger when children exit the labor force, further investigation of the increase in Social Security income to non-working mothers is outside the scope of this paper, but worth future study.
In terms of saving, we noted that the decline in retirement savings is large and significant for younger mothers, as is the decline in vehicle assets. However, IRA value only significantly declines for retirement age mothers at -$11955 (4364). This is quite a large estimate; though mean IRA value is highest for that age group, at $111,975, it still implies a decline of just under 10 percent. Again, we interpret the point estimate cautiously and put more emphasis on the direction. From the age subgroups, we can summarize that mothers decrease their retirement savings when their adult child becomes unemployed, either in their contributions or in the amount saved. However, none of these findings vary with work status, which we would expect, especially for pension saving rates.
Finally, we separate mothers by whether they have one or multiple children unemployed in the same year. Mothers with only one child who is unemployed or mothers with multiple children but only one unemployed at the time are conflated here. The increase intransfers is associated with a single unemployed child, whether measured in likelihood at 0.019 (0.004) or in size at $86.070 (26.472), potentially suggesting that mothers only financially support a single child. Yet, the decline in consumption, however measured, is much larger for mothers with multiplied unemployed children, at -$363.215 (106.970) and -0.054 (0.018), compared to -$240.929 (50.591) and -0.039 (0.008). Last, the increase in labor supply is similarly only positive and precisely estimated for mothers with a single child unemployed at 0.442 (0.164).
Like the differences across the types of unemployment spells, these mother-subgroup estimates add much to the understanding of our findings, though they speak less to identification and more to consistency. The increase in transfer assistance and the decrease in consumption are the most common results. The increase in labor supply depends on the situation of the mother, but is consistently estimated for the groups we expect, namely younger mothers and working mothers, with some indication that non-working mothers increase their labor supply as well. The savings results are less consistently estimated, and produce precision for some groups, such as the decline in savings rates among younger mothers and decline in IRA value among retirement-age mothers, but do not for others that we would expect, such as working mothers.

Robustness
Our results rely on a basic specification: using the longitudinal nature of the PSID to leverage individual fixed effects and identify the effect of unemployment on within-mother differences in the dependent variable. In Table 7, we decompose that specification. In the first column, we regress the dependent variable on a dummy for child's unemployment without any controls.
This can be read as the mean of the dependent variable among mothers in the year of the child's spell. We then add, successively, individual fixed effects, year and age fixed effects, mother controls, and child controls. The difference between the first and second columns can be read as, what do mothers look like in the year their child is unemployed, and is this different from other periods. The difference between the remaining columns is to test if anything else could be occurring that could explain that difference.
The trends in Table 7 echo what the subgroup analysis evinced-the most consistently estimated effects on mothers are the increase in sending a transfer, a decline in consumption, and an increase in labor supply, when measured through weeks. For the likelihood of sending a transfers and log consumption, the estimate is precise throughout, and similar in size and direction. For the amount of transfers and food, the estimate is not precise without individual fixed effects; this would make sense, as dollar amount of food and transfers has high, and skewed, variation. Interestingly, both measures of labor supply are negative in the first column and then positive, and in the case of weeks, and precise, once fixed effects are added. This suggests that mothers with an unemployed child work less than those who do not have an unemployed child, though it is higher than usual.
In the final two columns, we examine subsets of mothers-only those who ever have a child become unemployed, and only those who are ever observed sending financial assistance to children, in effect, reducing the sample to only affected mothers, or only mothers who are potentially more salient to be affected. There is little difference between the full specification and the sample restricted to mothers who ever have a child experience a spell. This is likely due to the fact that 84.2 percent of mothers have an unemployed child at some point, and our full sample only reduces to N=30,372 person years, from N=38,004. However, in the final column, we see large differences when the sample is reduced to the 35.8 percent of mothers who are ever there is a large behavioral response associated with a child's unemployment. However, their response is consistent with prior estimates, in that the most robust effects are for consumption and labor supply, but not savings.
As a separate robustness exercise, and a simple test of internal validity of our findings, is to examine if the estimates are compatible across categories. That is, assuming a simple budget constraint: Where in a given period income and assets net of consumption, savings, and transfers is zero, any change to one component is equaled by a change in another component, so that the remainder is still zero.
This equation does not hold in our findings. When looking at the mean effect for mothers of all ages, and including only precise estimates, we find transfers to children increase by $78, consumption on food decreases by $255, and labor supply increases by 1.9 days. The gap is larger for working-age moms, who transfer $67 but drop food consumption by $257, work 2.5 more days that year, and reduce retirement savings by 15.1 percent. Clearly, point estimates should be interpreted with caution, and greater emphasis placed on the direction, rather than size of the estimate. Yet aside from estimate precision, the increase in income and declines in consumption, savings, and assets are not similar in size to the transfers given to children in our analysis; this has (at least) two possible explanations.
First, our categories are only partially measured. For example, using reported estimates of cash transfers sent to children in a year likely misses most forms of in-kind assistance, including the direct purchase of goods and services or non-monetary gifts, such as buying food or paying rent for a child, co-financing arrangements, such as giving a child access to a credit that the parent pays for, and the provision of services, such child care or transportation. 20 It is possible that parents report the cash equivalent of that assistance in response to the survey question about sending money to children, but we have no means for assumingwhether they do or do not; yet, given the regular under-reporting of transfers (Meyer et al., 2009) it is unlikely that all transfers are fully captured. Partial measurements across categories likely explains why our simple budget constraint test did not equal out. However, we cannot say more about this within our data.
A second, and not exclusive, explanation is that parental adjustments in behavior to income, consumption, and savings do not only account for the financial exigencies of sending transfers in one period, but also the updated expectations of future need, or increased risk going forward. The estimates from the event study in equation (2)  The difference in post-spell behavior may be interpreted as risk-adjusting behavior, rather than financing behavior.

Discussion
In this paper, we examine the transfer, income, consumption, and savings behavior of mothers in the year that an adult child experiences an unemployment spell. The broad conclusion is that a child's unemployment is associated with significantly altered mother's behavior in sending of transfers, food consumption, and labor supply, and for certain groups, retirement savings contributions. It speaks to the strength of the PSID that analysis of a large set of dependent variables is supported. However, we note throughout that these we are only able to opera-20 As noted previously, our study excludes co-residence as a transfer and co-resident unemployed children.
tionalize dependent variables to a certain degree, and each broad category can only be partly represented. We also note, as many others have, that the PSID itself has numerous sample issues, including attrition (Zabel, 1998;Fitzgerald, 2011). For this reason, we acknowledge that our investigation, as a first step, is suited to the PSID, but that follow-up analysis for a particular category, such as savings, be conducted in a separate, more focused dataset.
We are cautious in assigning causality to our results. Within the numerous specifications and subgroups we examine, the most fitting exogeneity test-no pre-trend in the event study and significance for displaced spells only-is not met by any of our dependent variables. Transfer sending and food decreases are significantly estimated for non-displaced spells, while labor supply is not significantly estimated for displaced (or any reason subgroup) of spells. However, a looser test, with significance for unanticipated spells only, is met by labor supply and partially met by food consumption. But, we are also cautious in dismissing causality. As a researcher, we examine the behavior and reasoning mothers and children report to the survey, but cannot assume that this is what mothers and children report to each other. If we think of the shock to the mother as being random and unanticipated unemployment of a child, it is not necessarily the case that that is only true if the unemployment was also random and unanticipated to the child. We conclude that the causal relationship among our findings is not strong, but also not clear. It is likely that we are picking up both exogenous and endogenous response of mothers, and do not have a sufficient means to differentiate them. Still, the key finding is that there are large changes in mothers' labor market, consumption and savings behavior in the year of a child's spell.
Despite the estimated effects on mothers, we do not undertake a welfare analysis, beyond showing a drop in food consumption. We simply assume that changes in behavior are offset by the utility gained by having children with higher welfare. It is an open question whether a sense of familial obligation, altruism, or an exchange relationship is the underlying motivation for transfers and subsequent changes in parental behavior. Regardless of motivation, it is clear that mothers are likely to help their children, and they are likely to make changes to their consumption, income, or savings in order to, or as they, do so.
Welfare of the mother, however, does not translate into the optimal distribution of risk.
Our results suggest potential sources of sub-optimality. First, parents are bearing, and paying for, the labor market risk of their children as they themselves enter a time period associated with higher risk-the risk of retirement insecurity. We show that younger mothers reduce their retirement savings contributions and decrease their vehicle asset value in the year of a child's spell. Both are tantamount to reductions, even if marginal, in their own retirement security. It is not clear that this is efficient bearing of labor market risk across the economy, and our results call for further research into the aggregate consequences of the risk sharing we demonstrate, either on labor or credit markets of young workers or outcomes in retirement of their parents.
However, risk sharing to this degree could be suboptimal in numerous other ways. Distributionally, family risk sharing caps the insurance of one family member by the wealth of another, or conversely, the wealth of one family member by the risk of another. This has numerous implications. First, it is logically the case that if a person's insurance is capped by her parents' income, then the most under-insured are those with the most upward income mobility. A worker who earns twice as much as her parents has less insurance than a worker who earns half as much as her parents. Second, unemployment risk is not distributed randomly in either the income or wealth distributions, meaning that risk may concentrate among those families with less means to face it. Those differences raise both efficiency and equity concerns.
Our paper makes the novel contribution in identifying the concurrent changes in parents behavior in the year of a child's spell. It motivates further research on the incidence and consequences of risk sharing more generally, both to the individuals insured and the individuals insuring, as well aggregate risk distributions.

Data and materials
The dataset analysed in the current study is from publicly available data published by the Institute for Social Research at the University of Michigan. Analytic file used to create sample and results are available from the corresponding author.           Year fixed effects refer to the year of the spell, age fixed effects refer to the age of the mother, and individual fixed effects to the mother. to the year of the spell, age fixed effects refer to the age of the mother, and individual fixed effects to the mother.

Appendix
household, if it is not herself. 1 Given the practice of survey inclusion in the PSID, we are at risk of losing information on male single parents, but that is a very small population.
To show the representativeness of the analytical sample, a comparison of matched mothers, women who indicated that they had children but who were unmatched, and remaining females is shown in Table 2. We limit the age of the compared women to when they are 40-80 years old, since that is approximately the age span of our sample. 2 Matched mothers are older than unmatched mothers; the average age of matched mothers in column 1 is 62 years old, compared to 51.3 for unmatched mothers and 56.7 for remaining women. Matched mothers are also observed at older ages, the minimum and maximum age at which they are observed in the PSID range on average from 34.9 to 68, compared to 29.6 to 57.8 for unmatched. This makes intuitive sense, matched mothers have independently living children, which makes them older than mothers with children still at home. The age difference between matched and unmatched mothers explains many of the remaining demographic differences between the groups.
Across all three sets of women, there are similar shares of white individuals (74.4, 70.9, 73.8 percent). Matched mothers, however, have less education than unmatched mothers, with 69.6 percent having a high school degree or less, compared to 43.2 percent for unmatched mothers and 37.1 percent for remaining women. This suggests that our sample is not only observed at older ages but also in earlier time periods, relative to the rest of the women in the PSID, and is important for interpreting our results. It is not surprising then that, given that matched mothers are older and observed earlier, 59.6 percent of matched mothers are married, a lower share than the 67.6 percent of unmatched mothers and 44.3 percent of remaining women, but have a much higher share of widows, at 18 percent, compared to 7.4 percent and 10.6 percent. In addition, a much lower share of matched mothers are working (45.6 percent) than unmatched (67.1 percent) and remaining women (58.7 percent).
The bottom half of Appendix Table 1 summarizes the dependent variables used in this analysis. Differences across matched mothers, unmatched mothers, and remaining women can be mostly attributed to age differences.
Appendix Source: Authors' Calculations of PSID data. Table excludes women who are younger than 40 or older than 80 years old. Matched mothers are linked via family id and person number to a child's observation in at least one wave. Unmatched mothers indicated in survey response that they had at least one child, but was not matched to a separate child observation. Sample weighted using core weights.