Risk-Sharing within Families: Evidence from the Health and Retirement Study

Transcription

1 Rik-Sharing within Familie: Evidence from the Health and Retirement Study Ş. Nuray Akın and Okana Leukhina December 14, 2014 We report trong empirical upport for the preence of elf-interet-baed rik haring within extended familie in the U.S. A tandard model of elf-interet-baed rik haring predict that the hare of current family income conumed by a child poitively depend on that child permanent income. It follow that parental tranfer to children that are expected to earn more over the period of rik-haring arrangement hould exhibit le enitivity to the recipient income fluctuation. We tet thi ditinguihing prediction of elf-interet-baed rik haring by exploiting the variation of tranfer receipt among ibling, oberved over eventeen year of longitudinal data panned by the Health and Retirement Study. JEL Code: D1, E2 Keyword: Rik haring, informal inurance arrangement, inter vivo tranfer Acknowledgement: We thank David Blau, Donna Gillekie, Gulcin Gumu, Ocar Mitnik, Edward Norton, Chri Parmeter, Marika Santoro, David Weil and Mu-Jeung Yang for helpful dicuion. Leukhina gratefully acknowledge the financial upport from the Demography and Economic of Aging Reearch program ponored by the National Intitute of Health) and the Center for Retirement Reearch at Boton College. We alo thank Steven McMullen and Rihabh Kirpalani for valuable reearch aitance on aembling the dataet. Akin: Univerity of Southern California, Marhall School of Buine, Dept of Finance and Buine Economic, Bridge Hall - 308, MC-0804, 3670 Troudale Parkway, Ste. 308, Lo Angele, CA 90089, .nuray.akin@marhall.uc.edu; Leukhina: Univerity of Wahington, Department of Economic, Box , 305 Savery Hall, Seattle, WA 98195, oml@u.wahington.edu.

2 1. Introduction It i well etablihed that coniderable rik haring take place within network of family and friend, both in the U.S. and in le developed countrie. However, the precie nature of informal rik-haring arrangement i not well undertood ee Cox and Fafchamp 2008)). Informal rikharing arrangement are bound to interact with ocial inurance and income reditribution policie. Therefore, elucidating the nature of uch arrangement i important for the purpoe of effective policy deign. In thi paper, we invetigate whether the informal rik-haring arrangement are founded upon altruim or elf-interet. Our firt contribution i to contruct a longitudinal dataet of monetary tranfer between adult children and their parent in the U.S. and to document their empirical pattern. Our dataet i baed on the eventeen year period panned by the Health and Retirement Study HRS) and contain information on the incidence of within-family help proviion and frequency of contact, a well a the economic and demographic characteritic of individual. 1 The long panel dimenion of the dataet enable u to ditinguih between the altruitic and elf-interet motive of rik haring, a we explain below. Our econd contribution i to derive a tetable implication which i unique to the elf-interetbaed rik haring SIRS), and inconitent with the altruitic framework. To implify the comparion, we focu on frictionle environment that lead to efficient rik-haring arrangement. In both framework, family member face random income tream, but conume a contant hare of total family income, ay θ j, regardle of their current income. It follow that tranfer amount repond negatively to the recipient current income, with the magnitude of thi repone dampened by θ j. There i, however, an important ditinction. Only in the cae of SIRS, conumption hare, and therefore tranfer receipt, are linked to agent permanent income. In the altruitic framework, conumption hare are intead determined by preference parameter. Our final contribution i to tet thi unique feature of SIRS in HRS data. To thi end, we focu on familie with at leat two adult children, and exploit the oberved variation in tranfer receipt among ibling. The fact that we oberve familie over a long period of time allow u to control for the unoberved difference among adult children and enable u to proxy their permanent income. We find that tranfer amount depend negatively on the recipient current income, but thi dependence weaken with the recipient permanent income. While the firt of the two finding i conitent with the preence of rik haring in general, the econd finding i conitent only with elf-interet-baed arrangement. Previou tudie of rik-haring arrangement focued on teting it efficiency. Thee tudie teted and rejected the hypothei that individual conumption i completely independent of idioyncratic income hock e.g. Altonji et al. 1992), Hayahi et al. 1996), Altonji et al. 1997)) 1 We are aware of only two other tudie that pan the eventeen year period of HRS: Leukhina and Santoro 2011) and McGarry 2012). Both tudie explore the dynamic apect of giving. McGarry 2012) emphaize that controlling for unobervable difference which the panel dimenion allow u to do make an important difference in etimating the effect of income on tranfer amount. 2

3 baed on within-family tranfer data in the U.S. 2 More recently, however, high quality conumption data ha become available in many developing countrie, revealing ubtantial, although imperfect, conumption moothing within network of friend and family. 3 In repone to thee finding, it ha become common to modify SIRS model via limited commitment. Thi modification allow the agent to walk away from contractual arrangement for the option of living in autarky. It impede on rik pooling and effectively break down the efficiency reult. 4 In fact, SIRS model with limited commitment have been hown to uccefully account for individual conumption and income dynamic in developing countrie e.g. Ligon et al. 2001), Udry 1994), Cox and Eer 1998), Foter and Roenzweig 2001), Fafchamp 1999)). 5 Thi evidence alo favor elf-interet-baed arrangement. Our paper i related to the trand of literature that document within-family tranfer flow in the U.S. and invetigate the underlying motive. The early contribution focu on documenting empirical pattern of within-family flow, e.g. Cox 1990), Gale and Scholz 1994), McGarry and Schoeni 1995), Dunn and Phillip 1997). 6 In addition to the two motive tudied here, the tandard explanation of tranfer flow include the exchange motive. Parent could tranfer money to adult children in exchange for their help or attention. 7 In our empirical model, we control for the exchange motive by including help proviion a a determinant of tranfer flow. We find the exchange motive to be ignificant, which i conitent with the finding in Cox 1987) and Norton and Van Houtven 2006). To the bet of our knowledge, the elf-interet-baed motive of rik haring ha not been examined againt the altruitic motive. One likely reaon i that both motive have been dimied on the bai of empirical evidence againt efficiency of rik haring. Such concluion i premature ince impediment to perfect rik pooling can be eaily introduced to both model, uch a limited commitment in the cae of SIRS model, dicued above, and temporary liquidity contraint in the cae of altruitic model ee McGarry 2012)). It i important to point out that the empirical upport for elf-interet-baed arrangement preented here doe not rule out the preence of altruitic linkage. Altruim may play an important role in forming and utaining the rik-haring unit and facilitating informational flow within Cox 2 Mace 1991) tudie conumption moothing in the conumption expenditure urvey. 3 See Cochrane 1991), Deaton 1992), Townend 1994), Udry 1994), Grimard 1997) and Fafchamp and Lund 2003). 4 The ame modification could be introduced in our theoretical analyi without changing our main concluion. 5 Theoretical work on elf-interet-baed rik haring include Poner 1980), Kotlikoff and Spivak 1981), Kimball 1988), Coate and Ravallion 1993), Kehoe and Levine 1993), Kocherlakota 1996), Ligon et al. 2001). See Attanaio and Rio-Rull 2010) for a compete dicuion of rik-haring model. 6 McGarry 1999) and Bernheim and Severinov 2003) offer explanation for the puzzle reported in Dunn and Phillip 1997): while bequet are divided evenly, inter vivo tranfer favor the le fortunate children. 7 The trategic motive can be claified a an exchange motive. It arie if parent value their children attention and hold extra wealth or give money in order to induce children phone call and viit. Bernheim et al. 1985) document a tatitically ignificant poitive relationhip between attention received and the amount of parental beqeathable wealth, although Perozek 1998) claim that thi relationhip i not robut to including child and family characteritic. Tranfer can be alo motivated by the joy of giving Andreoni, 1989). Thi motive would induce flow independent of children income, which i inconitent with empirical obervation. 3

4 and Fafchamp, 2008). On a final note, undertanding within-family link i important becaue of their macroeconomic implication. In fact, everal tudie aign a ignificant role to within-family link in accounting for aggregate pattern. In De Nardi 2004) and Nihiyama 2002), intergenerational link help the model replicate the oberved wealth ditribution. Kotlikoff and Summer 1981) and Munnell and Sunden 2003) attribute a major part of capital formation to intergenerational flow. In Weil 1994), intergenerational link reconcile lower aggregate aving rate of countrie with older population with the lack of ignificant diaving by the elderly. 8 We organize the paper a follow. In Section 2, we decribe the dataet and report the main pattern of tranfer flow. In Section 3, we derive the ditinguihing feature of SIRS. In Section 4, we preent our empirical trategy. We preent our reult in Section 5 and conclude in Section Data The Health and Retirement Study HRS) i a panel data of the live of older American. It include the original HRS urvey of 7,703 houehold born between 1931 and 1941, conducted in 1992 and repeated every two year ince, and the Aet and Health Dynamic of the Oldet Old AHEAD) urvey of 6,046 houehold born prior to 1923, conducted in 1993 and A ha become cutomary, we merge the 1993 and the 1995 AHEAD wave with the 1994 and 1996 HRS wave. Thee two cohort tudie were officially merged in 1998 and expanded with two new cohort, the Children of the Depreion cohort and the War Babie cohort. The biannual data collection i ongoing. Each cohort ample i repreentative when properly weighted. The tudy contain detailed information on the demographic, health tatu, houing, family tructure and tranfer flow, employment tatu, work hitory and current employment, diability, retirement plan, wealth, wealth compoition, income, health and life inurance. Table 1 ummarize the age ditribution of the head of the houehold repondent), by wave. The mot uer-friendly compilation of HRS i the RAND HRS data file, contructed and treamlined by the RAND corporation from raw HRS file. Thi dataet i enriched with variou imputation of houehold variable. The RAND HRS data file, however, doe not include tranfer flow or child characteritic, needed for our analyi. We obtain thee directly from raw HRS file, made acceible through the Univerity of Michigan Intitute for Social Reearch. 9 We proceed a follow. For each wave, we tart with raw houehold-member file that include information on the repondent children and their houehold. We gather additional relevant information from helper, tranfer to, and tranfer from data file. We then merge wavepecific child-level file together to create a longitudinal dataet, uing the appropriate houehold and peron identifier. Finally, we merge onto the reulting child-level dataet the RAND HRS 8 Alo ee Boworth et al. 1991) 9 See 4

5 Table 1: Age Ditribution of Repondent Parent) in HRS, by Cohort and Wave Cohort over 69 over 71 over 74 over 76 over 78 over 80 over 82 over 84 6 over 69 over 71 over 74 over 76 over 78 over 80 over 82 over 84 Note: Cohort 1 through 6 refer to the early baby boomer cohort, the war babie cohort, the original HRS cohort, the children of the depreion cohort, the AHEAD cohort and finally the AHEAD-aged poue of the original HRS cohort. data file verion J) containing detailed parental information. 10 Houehold-member file contain information regarding repondent children characteritic, uch a their family income, education, age, number of own children, and frequency of contact with parent. Monetary tranfer flow are recorded between the repondent houehold and hi/her children. Tranfer refer to giving money, helping pay bill, or covering pecific type of cot uch a thoe for medical care or inurance, chooling, down payment for a home and rent. 11 Tranfer to file contain information regarding monetary tranfer from parent to their children or grandchildren). Tranfer from file contain information regarding monetary tranfer from children to their parent. 12 We aign tranfer made to grandchildren to their parent houehold. All monetary value in thi paper are tranlated into 2008 dollar uing the conumer price index CPI). Finally, the helper file can be ued to identify repondent children or grandchildren) who either provided phyical help to their parent or paid for hired help. Frequency of help and the amount of compenation, if any, are pecified whenever help i recorded. We count grandchildren help a help coming from their parent. To treamline our empirical analyi, we focu on repondent houehold parent) that did not change their ubhouehold identifier throughout the period examined, i.e. houehold that did not plit due to divorce in the period they were urveyed. Thi retriction eliminate only 7 percent of houehold. 10 See Jdd.pdf). 11 The two quetion identifying tranfer to children are a follow. Including help with education but not hared houing or hared food [or any deed to a houe], ince previou wave [or in the pat two year] did you [or your huband/wife/partner ] give financial help totaling $500 or more to a child [or her/hi children/grandchildren]? About how much did that amount to for [a given child] ince the previou wave/in the lat two year? For the firt two wave, tranfer flow over $100) are recorded over the pat year, a oppoed to two year. For conitency, we multiply thee amount by 2. The two quetion identifying tranfer from children are imilar. 12 When the exact tranfer amount i unavailable, a bracket i reported. We fill in the unavailable amount with imputed value from tranfer imputation file, available for all wave except the lat two. For the lat two wave, we impute tranfer amount a the wave-pecific average among tranfer within the relevant bracket. 5

6 Table 2: Total Tranfer Flow Child-level tatitic average no. of urvey wave 5.11 fraction ever receiving a tranfer 0.46 average total tranfer received 19,782 fraction ever giving a tranfer 0.08 average total tranfer given 5,697 Note: Total tranfer refer to the um of tranfer received or given over the period the child i preent in the urvey. Average amount are calculated baed on poitive amount. Child family income i inferred a the midpoint of the reported interval. To be conitent acro wave, we work with 5 income value: 5,000, 22,500, 52,500, 85,000, 105, Summary Statitic We retrict our attention to children of age 18 to 54. The average length of preence in the urvey i 5.11 wave, or roughly 10 year. Table 2 ummarize frequency and magnitude of tranfer flow. Nearly half of the children received at leat one tranfer during their preence in the urvey. Conditional on having received at leat one tranfer, the average total tranfer amount over the entire time period the child i preent in the urvey i nearly $20, Therefore, downward parent-to-child) flow are ubtantial in magnitude and incidence. On the contrary, only 8 percent of children are recorded to give at leat one tranfer to their parent during their preence in the urvey, with the average magnitude of the total tranfer at $5,697. Therefore, the upward tranfer are much le frequent and maller in magnitude. In fact, the incidence of parent-to-child tranfer i approximately 6 =0.47/0.08) time greater than the incidence of the child-to-parent tranfer. For the remainder of thi ection, we treat a child in a given wave a a unit of obervation, effectively pooling child-level data acro all wave. Table 3 report ummary tatitic by wave. Recall that all dollar amount are quoted in 2008 dollar and tranfer amount refer to the period elaped ince the previou wave. The table reveal that tranfer flow from parent to children are ubtantial in ize, even at wave level frequency. In every wave, around 20 percent of children receive a tranfer, in the average amount of $8,717. There appear no trend in frequency or magnitude of giving over time, depite the fact that the mean child age change from 30 in the firt wave to 39 in the lat wave. The ummary tatitic alo diplay that very few children, only 2 percent, help their parent with their daily tak. Only 4 percent of children that help get paid for their help. In 13 Thee value repreent income value we choe to refer to the income bracket pecified in wage 3: [0, 10, 000), [10, 000, 35, 000), [35000, 70000), [70, 000, 100, 000), [100, 000, +). Whenever income imputation are available wave 2 and 3), we aign the income midpoint according to the bracket implied by the imputed value. For wave 4-9, the lat two bracket are merged into one, [70, 000, +). We aign the value of 85, 000 to thi bracket. The AHEAD cohort of wave 2 i miing information on child family income, intead reporting child income. Finally, wave 1 give limited bracket, therefore we only ue information from people falling into the firt two bracket, for conitency. 14 Note that all average tranfer amount are computed baed on poitive tranfer. 6

7 Table 3: Tranfer Flow and Help Proviion by Year fraction average fraction fraction of average fraction average wave receiving tranf. rec-d helping helper paid helper pay giving tranf. given ,255 N/A N/A N/A N/A N/A , , , , , , , , , , , , , , , , ,060 Avg , ,047 Note: For each wave of the child-level urvey, the table report the incidence of tranfer inflow children receiving) and outflow children giving), the average tranfer amount excluding zero tranfer), the incidence of help proviion children helping parent) and pay for help. other word, children receive ubtantial amount of money from the parent depite the fact that they do not help. Approximately 2 percent of children are reported giving money to the parent in any given wave, in the average amount of $4,047. Table 4 report tranfer flow by child age. The probability of receiving a tranfer decline with age, with tranfer incidence dropping off quickly at younger age, and lowly at older age. Excluding current tudent from the ample ha a ignificant impact only on the younget age group, for which the incidence of tranfer receipt decline by 3%, with a $3,000 reduction in the average amount. There i a trong aociation of tranfer flow and parental wealth. A reported in Table 5, children with wealthier parent receive more money from their parent. In any given wave, nearly 40 percent of children with parent in the top decile of aet receive a tranfer, in the average amount of $16,153. Both incidence and average amount of thee tranfer are nearly twice the ize of the average tranfer incidence and magnitude. The aet value of the top decile i ignificantly greater than the value of the aet in the econd decile, conitent with large wealth inequality preent in the U.S. Thi i one likely reaon why tranfer receipt rie mot harply a we move from the 9 th to the 10 th top) decile of parental wealth. Interetingly, while the child-to-parent tranfer incidence decline in parental wealth level, the average tranfer amount actually rie. Finally, in Table 6, we ummarize tranfer flow by the interval of child family income. To ummarize tatitic here, we merge together the top two income interval. 15 The probability of tranferring money to one parent rie lightly with the child income cla. The probability of receiving a tranfer from the parent decline with the child income category. Thee fact are uggetive of the preence of rik haring, although they do not peak directly to the motive 15 Only 1 percent of child-wave unit are in the top income category [100,000, +). 7

8 Table 4: Tranfer Flow by Children Age Group age fraction average fraction average receiving tranf. rec-d giving tranf. given , , , , , , , , , , , , , ,668 Avg , ,047 Note: Baed on child-level obervation pooled acro urvey wave, the table report the incidence of tranfer inflow children receiving), tranfer outflow children giving), and the average tranfer amount excluding zero tranfer), by children age group. Table 5: Tranfer Flow by Decile of Parental Wealth decile of fraction average fraction average parental wealth receiving tranf. rec-d giving tranf. given , , , , , , , , , , , , , , , , , , , ,882 Note: Baed on child-level obervation pooled acro urvey wave, the table report the incidence of tranfer inflow children receiving), tranfer outflow children giving), and the average tranfer amount excluding zero tranfer), by parental wealth decile. 8

9 Table 6: Tranfer Flow by Children Income child family fraction average fraction average income receiving tranf. rec-d giving tranf. given 0-10, , ,883 10,000-35, , ,260 35,000-70, , ,952 70, , , ,463 Avg , ,200 Note: Baed on child-level obervation pooled acro urvey wave, the table report the incidence of tranfer inflow children receiving), tranfer outflow children giving), and the average tranfer amount excluding zero tranfer), by child family income. underlying the rik-haring arrangement. Note that the incidence of tranfer received and the average amount of thee tranfer drop mot ignificantly when children move from the firt income cla to the econd. An intereting pattern emerge in the top three categorie of child family income. Although the incidence of receiving a parental tranfer decline with child family income, the amount of tranfer, conditional on receipt, increae. Thi pattern i not inconitent with the rik-haring arrangement dicued in Section 2. Negative financial hock may not hit often in the highet child income category, but the amount of payment that a rik-haring contract pecifie may be high if the extended family total reource are alo high. 3. Theoretical Background Our goal i to invetigate the SIRS motive for within-family tranfer flow. Since the altruitic model alo implie rik-haring, we review both framework here. We then explicitly derive the unique prediction of the SIRS framework, which i not hared by the altruitic framework. Thi prediction form the bai for our empirical pecification. To implify the comparion, we focu on frictionle environment both of which lead to efficient rik-haring arrangement, which, a dicued earlier, ha been rejected by the data. We then dicu how the SIRS model can be modified via variou friction to break down the efficiency reult Self-interet-baed rik haring SIRS) Parent and children can be linked through elf-interet-baed arrangement. Kotlikoff and Spivak 1981) i one work decribing how intra-family arrangement can induce rik haring, even in the abence of altruitic behavior. A in inurance market, family member can et up contract that dicipline rik-haring arrangement. Preumably, enforceability and advere election iue are eaily reolved within familie, in contrat to formal inurance market. 9

10 We draw on a tandard model of rik haring e.g. Krueger 2012)). Suppoe that a parent and an adult child overlap for T period and face random income. In any given date t, one of the following event can be realized, t {1, 2,..., S}, each occurring with probability π t ), Σ π t ) = 1. We aume that hock are identically ditributed and independent acro time, and denote by t = 0, 1, 2,..., t ) the ummary of event realization up to time t. The event probabilitie determine probabilitie of different event hitorie π t). To be mot general, income of agent i at time t depend on a given realization of event up to that time: y pt t ) and y kt t ). The aggregate income aociated with a particular hitory i Y t t ) = y pt t ) + y kt t ). Conider the rik-haring framework under the aumption of the Arrow-Debreu market. Given hitory-dependent price { p t t )}, each agent, parent and child i = p, k), chooe the hitorydependent conumption allocation { t,t c it t )} in period t = 0 to maximize hi own utility ubject t,t to hi lifetime budget contraint:.t. max {c it t )} t,t t T π t ) β t ln c it t )) t T p t t ) c it t ) = T c it t ) 0 for all t and all t. t p t t ) y it t ), The firt order condition implifie to πt )β t c it t ) = λ i p t t ) for all t, and t, where λ i i the multiplier on the budget contraint of agent i. Hence, we have πt )p 0 0 )β t π 0 )p t t ) = c it t ) c i0 0 ), which immediately implie that cptt ), i.e. the ratio of conumption between the two agent i contant over time and c kt t ) = c p0 0 ) c k0 0 ) acro event hitorie. It follow from the market clearing condition that, in every event hitory, agent i conume a contant hare θ i of total family endowment. The propoition below formalize thi reult and etablihe that the agent conumption hare are given by their expected lifetime contribution to family reource. Propoition 1 Under elf-interet-baed arrangement, agent i {k, p} conume a contant hare of total family endowment c it t ) = θ i [ ypt t ) + y kt t )], 1) where the conumption hare θ i i given by the preent value of hi expected lifetime contribution to family reource: θ i = T t π t) β t y it t ) y pt t )+y kt t ) T βt. 2) Proof. See the appendix. In other word, the larger i the child permanent contribution to family reource, the larger hare of reource he conume under any given event hitory. Hence, for the rik-haring model 10

11 under the aumption of perfect commitment and no information friction, the optimal parent-tochild tranfer, which we denote by T R, i given by T R kt t ) = θ k [ ypt t ) + y kt t )] y kt t ). 3) Clearly, θ k mitigate the effect of current income fluctuation on the current tranfer, a larger θ k making tranfer le enitive to temporary income fluctuation. Intuitively, a relatively wealthy child high θ k ) will be compenated le for temporary drop in income becaue he i affected more by the correponding temporary drop in total family reource. Formally, comparing two event hitorie t and ŝ t uch that y kt ŝt ) > y kt t ) and, everything ele equal, we have dt R kt dy kt T R ŝt ) kt T R kt t ) y kt ŝ t ) y kt t = θ k 1 < 0, ) that i, the repone of the child tranfer to the poitive change in hi income realization i negative but poitively depend on θ k, i.e. dt R kt dy kt decreae in θk. Thi model eaily extend to the environment with J children, in which we index children by j {1, 2,...J}. Each child i entitled to a fixed fraction of the current total family endowment, given by the hare of total reource that he contribute where the hare i given by θ j = c jt t ) = θ j [ ypt t ) + y 1t t ) + y 2t t ) y Jt ], 4) T π t ) β t y jt t ) y pt t ) + y 1t t ) + y 2t t / ) y Jt The optimal tranfer to child j i therefore t T β t. 5) T R jt t ) = θ j [ ypt t ) + y 1t t ) + y 2t t ) y Jt ] yjt t ). 6) Clearly, θ j mitigate the effect of current income fluctuation on the current tranfer. Thi contitute the eence of our empirical tet for the rik haring motive of giving. The extenion to multiple children allow for the intuitive acro-children interpretation. The permanently rich and poor children will be compenated unevenly for the ame drop in their current income. The rich child will receive le compenation, becaue he i affected more by the correponding drop in total family reource. Similarly, the rich child will experience a maller decline in the tranfer received in the cae of a rie in current income, becaue he benefit more from the correponding rie in total family reource. 11

12 3.2. Altruim-baed rik haring The altruitic motive of within-family flow i probably the mot prominent in the literature, dating to Becker 1974). Conider the following model of one parent and one child. The parent maximize hi utility, which include the utility of hi child weighted by α. For implicity, there i no borrowing or lending. A in the rik haring model, parent and child overlap for T period and face a random income proce. The notation i a above. The altruitic parent houehold olve 16 max {c pt t ),c kt t ),T R t t )} t,t T β t π t ) [ ln c pt t )) + α ln c kt t ))] t.t. c pt t ) + T R t t ) = y pt t ) for all t and all t, c kt t ) = y kt t ) + T R t t ) for all t and all t, c it t ) 0 for all t, t, and i The olution involve equalizing marginal utilitie for the parent and child, a well a etting the marginal rate of ubtitution of conumption acro period equal to the interet rate i.e. conumption moothing acro time). It follow from the market clearing condition that c pt t ) = c kt t ) = T R t t ) = 1 ypt t ) + y kt t )), 7) 1 + α α ypt t ) + y kt t )), 1 + α 1 αypt t ) y kt t )). 1 + α It i traightforward to ee that children will receive greater tranfer under event hitorie that imply low income realization dt R kt dy kt < 0). Parent will give more in period in which their income are high dt R kt dy pt > 0), in particular in period in which their income are higher than their children income. The model eaily extend to the environment with J children. In thi cae, the hare of each child conumption in total family income i fixed and independent of date and tate, a formalized in the propoition below. Note that thi hare decreae in the number of children. Propoition 2 Under altruitic arrangement, conumption of child j i a contant hare of total family endowment: Proof. See the appendix. c jt t ) = α y pt t ) Jα J j=1 y jt t ). 8) 16 Since the parent can chooe a negative tranfer, we want to make ure the child will not prefer autarky to thi altruitic arrangement, i.e., that T β t π t) ln y ) t kt t + T R )) t t implied by the parent optimal choice i greater or equal to T β t ln y )) t kt t. 12

13 3.3. Dicuion At the firt glance, the SIRS model and the pure altruitic model appear to predict identical conumption allocation and tranfer. To ee that, compare 4) with 8). We ee that θ j in the SIRS model correpond to α 1+αJ in the altruitic model. The ditinguihing prediction of the SIRS model, however, i that the child conumption hare, θ j, i determined by that child permanent contribution to family income, while the conumption hare in the altruitic model, α 1+αJ, i determined by the utility weight that parent aign to their children. Therefore, while in both model, children conumption hare govern the repone of their tranfer amount to income fluctuation, only in the rik-haring model thi repone depend on the child permanent contribution to family income. Thi ditinguihing feature of the rik-haring model i the eence of our empirical tet. The detailed dicuion of our methodology follow in Section 4. A explained in the Introduction, previou literature rejected efficient rik haring, although it ha been found that coniderable rik haring doe take place within network of family and friend. Cox and Fafchamp 2008) argue that SIRS model can be eaily modified to break down efficiency of rik-haring. 17 Enforcement or informational friction can be eaily introduced in environment of elf-interet-baed interaction to make thee model conitent with imperfect inurance arrangement oberved in the data. For example, limited commitment model tem from the abence of contractual enforcement intitution. Attention i then retricted to contract that enure that agent never want to opt out of agreed-upon arrangement for living in autarky. Such retriction would appear a T π t ) β t u c it t )) t T t π t ) β t u y it t )) in our SIRS model, where c it t ) refer to conumption under the agreed-upon rik-haring arrangement. Ligon et al. 2001) explain how to derive the olution. Even under thi modification, the permanent income of agent i will affect the average hare of conumption he i entitled to. Intuitively, to induce participation of permanently richer agent, they mut be offered more conumption. Model with informational friction will alo lead to imperfection of inurance. Whatever modification are introduced, however, the ditinguihing prediction of the SIRS model teted here, i.e. that tranfer enitivity depend on the child contribution to total family reource, i likely to urvive. The reaon for thi i that thi ditinguihing prediction depend only on the preence of a poitive link between one contribution to family reource and one claim to thoe reource. And thi link i very robut, a it i eential for inducing rik haring between agent with unequal permanent income. 17 McGarry 2012) propoe a modification to the altruitic model that make it conitent with imperfection in rik haring. 13

14 4. Method The SIRS framework, and in particular the parent-to-child optimal tranfer 6), motivate the following empirical pecification, which we etimate uing the longitudinal HRS child-level data: ) T R it = β 0 + β 1 y it + β 2 ˆθi y it + β 3 child it + β 4 extended family it + fe i + µ t + ε it. 9) The child tranfer at time t depend on child family current income, it interaction with the etimate of the child θ i, time-dependent child family characteritic, time dependent characteritic of extended family, child family fixed effect fe i ), and time effect µ t ). The panel dimenion allow u to control for unoberved factor that vary acro children but are fixed over time. Child fixed effect will capture the influence on tranfer flow of factor that tend to be fixed over time, uch a the quality of the child relationhip with hi/her parent, frequency of contact between them, and proximity of reidency. Certainly, frequency of contact and geographical proximity may change over time, but information on thee two quantitie i not conitently available acro wave. 18 Therefore, we chooe not to include thee variable a eparate control. Among the child time-dependent characteritic, we include the number of own children and a dummy indicating whether or not the child or hi family member are lited in the helper-level file a helper, regardle of whether or not they received compenation for their help directly. Extended family refer to the child parent and ibling houehold, i.e. the remaining member of the rik-haring unit. To be conitent with 6), among the extended family control, we include the product of ˆθ i and total extended family reource excluding y it. We arrive at thi meaure by multiplying the proxy ˆθ i by the um of the current parental income and current income of the child ibling familie. We alo include parental total wealth among extended family characteritic. Our rationale for thi incluion i that parental wealth will help improve the proxy for total available reource. 19 Finally, we include retirement tatu for the parental houehold, which we define a an indicator that parental houehold annual earning are below $1,000. The child and time fixed effect model i etimated by including wave dummie µ t ) on the right hand ide of 9). Time effect would capture omitted variable that vary over time but not acro individual, uch a, for example, change in etate tax law, which are likely to influence inter vivo tranfer flow. For the empirical analyi, we need to approximate the empirical counterpart of θ i, defined in 2), i.e. child i contribution to the expected total value of family reource. Rik-haring unit are compried of extended family network coniting of parental houehold and houehold of grown year old) children. In order to take advantage of the oberved variation in tranfer received by ibling, we retrict attention to extended family network with at leat two eligible 18 Frequency of contact i unavailable in wave 1, 2 and 8, while geographical proximity i only available in the firt three wave. 19 Recall that in our model, the conumption good i perihable, and therefore, income and wealth are equivalent. In practice, thi i not the cae. 14

15 Figure 1: Ditribution of Entitlement Share Proxie adult children, each one appearing in at leat two wave. The former retriction i needed for the preence of variation acro ibling, and the latter retriction enure that the longitudinal dimenion i exploited. In the reulting dataet, children are oberved for 5.3 wave on average, or roughly 12 year. To approximate θ i, we firt compute the child contribution to total family reource in each wave, i.e. ˆθ it = y it / y 1t + y 2t y Jt + y pt ). We then average thee quantitie over the wave in which the child i preent, ˆθ i = T t=1 ˆθ it. The average ˆθ in the ample i 0.16, and it ditribution i depicted in the hitogram below. In Section 5, we explore an alternative meaure of θ i. 5. Main Reult Our main objective i to tet for the preence of influence of ˆθ i, our meaure of the child contribution to the rik-haring unit permanent reource, on tranfer reponivene dt R it /dy it. According to the SIRS model outlined in Section 3.1, thi derivative i negative, but it depend poitively on θ i. Therefore, the SIRS motive of giving implie that β 1 < 0 and β 2 > Table 7 in the appendix contain the main etimation reult. It report etimation for five different pecification. We reject the null hypothee that β 1 = 0 and β 2 = 0 againt their repective alternative, that β 1 < 0 and β 2 > 0, at a 0.5% ignificance level acro all five pecification. The firt pecification i the mot parimoniou one. It exclude the time effect, and time dependent child and extended family characteritic: T R it = β 0 + β 1 y it + β 2 ˆθi y it ) + fe i + ε it. 10) A expected, we etimate a negative coefficient on child income ) and a poitive coef- 20 Becaue the precie meaure of child family income i not available, we are not able to obtain the actual etimate for dt R j/dy j. Intead, we aim to etimate whether or not it depend on the child contribution to permanent family reource. 15

16 ficient on the interaction term ˆθ i y it ). Note that ince the average ˆθ i 0.16, the etimated total effect of child income on the tranfer received, evaluated at the average ˆθ, i negative, ) = The null hypothee that β 1 = 0 and β 2 = 0 are rejected againt their repective alternative, that β 1 < 0 and β 2 > 0, at 0.5% ignificance level. The econd pecification include the time effect: ) T R it = β 0 + β 1 y it + β 2 ˆθi y it + fe i + µ t + ε it. Thi reult in a lightly higher etimate of β 2, but both of the null hypothee are till rejected at 0.5% ignificance level. The lat three pecification exclude the time effect, but include time-dependent child and extended family characteritic. The third pecification include the children number of own children, the etimate on which i poitive and highly ignificant. It alo include parental wealth, the coefficient on which i alo poitive and ignificant. 21 The forth pecification generalize the third pecification by alo including the interaction term of ˆθ with the total income of other member of the rik-haring unit, the coefficient on which i etimated to be poitive, conitent with the implication of the model, although it i not highly ignificant. It alo include the dummy for retirement of both parent, which i not found to be a ignificant determinant of tranfer flow. Finally, the fifth pecification generalize the forth pecification by including the helper dummy, which indicate whether or not a child, or any of hi children, provided phyical help or paid for a hired helper) to the parent. Incluion of thi variable control for the potential preence of the exchange motive of giving upheld by Norton and Van Houtven 2006). 22 In each of the lat three pecification, which control for time dependent characteritic, the coefficient on the interaction term rie to The main reult i that acro all pecification, we find that the coefficient on child family current income i highly ignificant and negative, while the coefficient on the interaction term i highly ignificant and poitive. Thi reult provide empirical upport for the hypothei that dt R it /dy it depend poitively on the child contribution to the aggregate reource, therefore lending upport to the SIRS motive of giving. A a part of enitivity analyi, we have alo etimated 10) uing the fixed effect Poion regreion, which take into account the fact that tranfer are nonnegative. The null hypothee that β 1 = 0 and β 2 = 0 were rejected againt their repective alternative, that β 1 < 0 and β 2 > 0, with an even greater ignificance. 23 We alo repeated our analyi with a net child tranfer on the left hand ide of 10), where the net child tranfer i defined a the difference between the tranfer received by the child and the tranfer given to the parent. Uing the net tranfer i actually better 21 With the incluion of total parental wealth, the number of obervation decreae, becaue total parental aet are unavailable in Wave 3. If we work with parental financial aet, information on which i available in all wave, our main reult are not affected ignificantly. 22 Including the help proviion variable reduce the number of the obervation effectively ued in the regreion becaue help information i not available in Wave Coefficient on child income and the interaction term were 1.2) 10 5 and 1.55) 10 5 with tandard error 1.3) and 7) 10 10, repectively. Coefficient here ignify the change in the log of expected count. 16

17 aligned with the theoretical underpinning of 9). Once again, the reult were imilar. 24 Since mot related literature examine tranfer receipt probabilitie, we alo etimated the fixed effect logit model to obtain the effect of child income and the interaction term on the probability that the child obtain a tranfer. Once again, both null hypothei were rejected with great ignificance Differentiating the Rik-Sharing Motive from the Altruitic Motive Recall that both the altruitic and SIRS model imply that differential conumption hare acro children explain variation of derivative dt R j /dy j acro children, although differential conumption hare arie for different reaon. To differentiate the implication of the two model, it i ueful to conider the cae of the altruitic model where parent care equally for all of it adult children. In that cae, a can be een from 8), adult children with jut two other ibling would have an entitlement weight of 1/3. Adult children with 3 ibling would have an entitlement weight of 1/4. The altruitic model then implie that conumption hare are fixed acro ibling, and even acro unrelated children that have the ame number of ibling. In contrat, the SIRS model implie that conumption hare vary both acro ibling and acro unrelated children, and link them to the children contribution to their family total reource. In fact, becaue the number of ibling alo matter for conumption hare in the SIRS model a child making a fixed alary every period will be entitled to a larger hare of total family reource if he come from a maller family), our meaure of theta, ˆθ i, will duly correlate with family ize, and therefore with conumption hare predicted by the altruitic model. In order to ditinguih between the two model, or in other word, to be able to claim that the empirical evidence we find i uniquely conitent with the SIRS model, we need to eliminate family ize effect from the variation of ˆθ i. To do thi, we apply two different method. Firt, we plit the main ample into ample of children with a fixed number of ibling, and reetimate the main model on each ubample. Second, we reetimate the five pecification from Table 7 on the entire ample, but ue an etimate ˆθ i adjuted by family ize. Preciely, the adjuted ˆθ i capture child i contribution to family income relative to the average not aggregate) contribution of hi ibling. The reult obtained by applying the firt method are reported in Table 8. Since retricting the main ample to ubample defined by the number of adult children in the rik haring unit ubtantially reduce the number of obervation, we do not etimate the time effect, and among the time-dependent characteritic, we include only thoe that we found to be ignificant except helper dummie, which i not available in Wave 1). Thee characteritic are parental aet and the children number of own children. We report the reult for ubample of children with up to 6 other ibling. Once again, we ee trong evidence for the rik haring motive, even though variation of theta due to family ize i eliminated. The coefficient etimate on the current child 24 Coefficient on child income and the interaction term were.04 and with tandard error and 0.025, repectively. 17

18 family income i negative and tatitically ignificant p-value below 0.01), while the coefficient etimate on the interaction term i poitive and tatitically ignificant, with the p-value below 0.05 for all ubample, and below 0.01 for half of the ubample. The reult obtained by applying the econd method are reported in Table 9. We reetimate the five pecification, dicued in Table 7, on the entire ample, but ue a meaure of ˆθ i, which i adjuted by family ize. None of the main concluion are affected. In fact, the point etimate are very cloe to thoe reported in Table 7, with an exception of ˆβ 2, which change to accommodate the adjutment in the multiplier on child income from ˆθ to ˆθ adj ). Our preent attempt to eliminate family ize effect hould not be miinterpreted. We emphaize that family ize effect are important determinant of child conumption hare in the SIRS model, and conequently, they are important determinant of tranfer enitivity to child income fluctuation. We aim to eliminate family effect here only becaue their influence on tranfer enitivity i hared by the altruitic framework, and our goal i to tet whether or not tranfer enitivity i affected by factor unique to the rik haring framework. By eliminating family ize effect, we iolate the effect of children permanent income on the derivative dt R j /dy j, preent in the SIRS model, but not in the altruitic model. 6. Concluion To um up, we contruct a comprehenive longitudinal dataet of within-family giving and document inter vivo tranfer flow. Then, baed on the unique prediction of the elf-intereted rik-haring framework, we derive a dynamic empirical pecification, which allow u to tet for the preence of elf-interet-baed rik haring within extended familie in the U.S., thereby hedding light on ource underlying rik-haring arrangement. We find trong upport for the preence of elfinteret-baed rik haring. Thi evidence complement the literature that uncover evidence of elf-interet-baed arrangement in conumption data of le developed countrie. Our work further ugget that incorporating family tie through elf-interet-baed informal arrangement into exiting model ha the potential to help better explain aggregate conumption data in the U.S. and aid in the deign of effective ocial inurance policie. 25 Reference Altonji, J., F. Hayahi, and L. Kotlikoff 1992), I the Extended Family Altruitically Linked? Direct Tet Uing Micro Data, American Economic Review, 82, Altonji, J., F. Hayahi, and L. Kotlikoff 1997), Parental Altruim and Inter Vivo Tranfer: Theory and Evidence, Journal of Political Economy, 105, Kaplan 2012), for example, argue that informal rik haring arrangement help better explain aggregate data for young adult. 18

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