Dynastic Precautionary Savings

Transcription

1 Dynasti Preautionary Savings Corina Boar Clik here for the latest version Otober 9, 017 Abstrat This paper demonstrates that parents aumulate savings to insure their hildren against inome risk. I refer to these as dynasti preautionary savings. Using a sample of mathed parent-hild pairs from the Panel Study of Inome Dynamis, I test for dynasti preautionary savings by examining the response of parental onsumption to the hild s permanent inome unertainty. I exploit variation in permanent inome risk aross age and industry-oupation groups to onfirm that higher unertainty in the hild s permanent inome depresses parental onsumption. In partiular, I find that the elastiity of parental onsumption to hild s permanent inome risk ranges between and -0.06, and is of similar magnitude to the elastiity of parental onsumption to own inome risk. Motivated by the empirial evidene, I analyze the impliations of dynasti preautionary saving in a quantitative model of altruistially linked overlapping generations in whih parents and hildren interat strategially. I argue that strategi interations are important for generating the observed dynasti preautionary behavior. I use the model to i examine the size and timing of inter-vivos transfers and bequest, and ii perform ounterfatual experiments to isolate the ontribution of dynasti preautionary savings to wealth aumulation and intergenerational transfers. I am extremely grateful to my advisor Mark Bils for inspiration, enouragement and guidane throughout this projet, and to Yongsung Chang and Narayana Koherlakota for their generous advie. For helpful omments and onversations, I thank Mark Aguiar, George Alessandria, Yan Bai, Jay Hong, Marios Karabarbounis, Peter Klenow, Maria Cristina de Nardi, Romans Pans, Yena Park, Ronni Pavan, Matthew Rognlie, Kjetil Storesletten, Gianlua Violante, partiipants at the Chiago Fed Rookie Conferene and the Minneapolis Fed Junior Sholar Conferene, as well as many seminar partiipants at various other institutions. Department of Eonomis, Prineton University; orina.boar@gmail.om 1

2 1 Introdution The age profile of expenditures of retired parents is bakloaded. Explanations suh as unertain lifespans and medial expenses, or inreasing monetary transfers from hildren are partial ontributors, but a substantial gap remains. Setion.4 ontains a detailed disussion of these observations. This paper proposes dereasing inome unertainty of hildren as a justifiation for the onsumption pattern of retired parents. The argument derives from the theory of preautionary saving, aording to whih, when faed with inome unertainty, individuals postpone urrent onsumption in favor of aumulating preautionary savings as insurane against bad inome realizations. As unertainty resolves over time, onsumption inreases, thus generating a onsumption profile that is bakloaded over age. For parents in the data, this bakloading postdates the resolution of unertainty in their own inome stream, but oinides with times at whih their hildren are in the beginning or prime of their areers and still resolving their inome risk. In the fae of this unertainty, altruisti parents sarifie urrent onsumption to aumulate savings to insure their hildren. I refer to these as dynasti preautionary savings. Over time, as hildren s inome unertainty resolves, that form of savings delines, inreasing the onsumption of retired parents. In this paper, I seek evidene on dynasti preautionary savings using parent-hild pairs from the Panel Study of Inome Dynamis PSID. In partiular, I examine how a parent s onsumption responds to the unertainty of his hild s permanent inome. To that end, I first propose a measure of permanent inome unertainty losely related to the theoretial definition of permanent inome. Seond, I ondut a regression analysis of the effet of dynasti unertainty on parental onsumption on the sample of mathed parents and hildren. I find a negative and statistially signifiant relationship, whih I interpret as evidene for dynasti preautionary saving. I then build a model of altruistially linked overlapping generations in whih parents engage in dynasti preautionary saving. I use the model to verify the plausibility of the empirial estimates, and to ondut ounterfatual experiments and evaluate poliy proposals. The measure of inome unertainty onsidered in this paper is defined as the standard deviation of the foreast error of permanent inome. This measure is meant to apture the fat that when individuals make onsumption deisions, they are unertain about the evolution of their entire future inome stream. Therefore, it is the unertainty about permanent inome that is relevant for their hoies. I assume that individuals foreasts make rational use of the same onditioning information available to the eonometriian. Intuitively, the higher the unertainty, the more diffiult it is to foreast earnings aurately, whih translates into a larger standard deviation of the foreast error. Beause of issues suh as sample attrition and measurement error in inome, I fous on the properties of permanent inome unertainty aross age and work setors a setor is defined as an industry-oupation pair, instead of individual level. I find that

3 permanent inome unertainty is dereasing over age. On average, more than half of it is resolved by the age of 40. Moreover, there is substantial variation aross setors, both in terms of the level of unertainty and the speed at whih it resolves with age. I assign permanent inome unertainty measures to both parents and hildren based on their age and the setor in whih they work in a given year. The onsumption data used in the estimation is drawn diretly from the PSID for the later years, while for the earlier waves I use the Consumer Expenditure Survey CEX to impute total onsumption based on an inverted food demand equation. From the variation in permanent inome unertainty aross age and setors, I find that parental onsumption indeed responds negatively to the hild s permanent inome unertainty. In partiular, the elastiity of parental onsumption to dynasti unertainty is This magnitude implies that parents of hildren younger than 40 onsume on average $, 945 less per year beause at that stage most of hildren s inome unertainty is yet to be resolved. Building on the heterogeneity of permanent inome risk aross setors, the regression result implies that parents of hildren working in riskier setors have a lower onsumption. For example, when omparing two otherwise idential parents of two otherwise idential hildren, with the only differene being that the hild of one of them is a servies worker while the hild of the other one works in the finane setor, I find that the onsumption of the latter parent is on average 7% lower beause of the dynasti unertainty differene. I take a number of steps to address several endogeneity onerns. Firstly, I explore the sensitivity of the results to ontrolling for health status, as it may be the ase that mortality risk is orrelated with the setor in whih an individual works. Seondly, it may be the ase that hildren who know that their parents aumulate dynasti preautionary savings hoose to work in riskier setors. I examine the impat of suh seletion issues by i exluding from the sample the parent-hild pairs in whih the hild is self-employed and ii ontrolling for the initial setor of the hild. In this last ase an additional soure of identifiation is given by the hanges in a hild s setor over the areer. I find that while the estimates of dynasti preautionary savings are approximately 1 perentage point lower under these speifiations, the effet is still signifiant. In addition to these exerises, I also verify the robustness of the results to a series of alternative speifiations whih inlude ontrolling for the importane of the bequest motive, maroeonomi and loal labor market onditions, as well as using different onsumption and permanent inome unertainty measures. Motivated by the empirial evidene, I explore the impliations of dynasti preautionary saving in a partial equilibrium model of altruistially linked overlapping generations. I use the model to i evaluate the plausibility of the empirial estimates, and ii perform ounterfatual experiments to isolate the ontribution of dynasti preautionary savings to wealth aumulation and intergenerational transfers. There are three ingredients required for dynasti preautionary savings to emerge in a model: inome risk, 3

4 inomplete markets, and altruism à la Barro 1974, with the parent plaing a weight on the hild s utility from onsumption. 1 In light of existing evidene on imperfet risk-sharing within and between families, I model the deision making proess between the parent and the hild as a nonooperative game without ommitment. In my framework, individuals work in setors haraterized by different degrees of permanent inome unertainty. Eah period, parents and hildren deide individually, but sequentially, how muh to onsume and save. In addition, altruisti parents an provide monetary support to their hildren through expliit finanial transfers while they are alive inter-vivos transfers, and by leaving an inheritane upon their death. The model enables lear preditions about the wealth position of overlapping generations, as well as the size and timing of inter-vivos transfers, both of whih are relevant for ounterfatual experiments. The alloations of interest are given by the Markov-perfet equilibrium of the parent-hild repeated game. The alibrated model an reprodue the harateristis of the age profile of parental onsumption. In partiular, the onsumption of retired parents is bakloaded, whih is a lear indiator of dynasti preautionary saving, as in the model there are no other preautionary motives after retirement. I repeat the empirial exerise with model generated data and find that the response of parental onsumption to both own inome risk and hild s inome risk is of similar magnitude as in the data. In partiular, the model estimates fall well within the 95% onfidene interval of the empirial estimates. I examine the effet of the strategi interations between parents and hildren by solving a version of the model in whih these are absent. In the alternative model, the parent makes all onsumption-saving deisions for the family while he is alive. Consequently, the wealth position of different generations and the size of intergenerational transfers are indeterminate. In this framework, the dynasti preautionary saving motive is more important than the preautionary motive, ontrary to the empirial evidene. The model with strategi interations between parents and hildren also aounts reasonably well for the age pattern of inter-vivos transfers and the fration of parents making suh transfers, as well as for the size of end-of-life bequest. I use the model to quantify the ontribution of dynasti preautionary savings to wealth aumulation and intergenerational transfers. I find that a little over one fourth of aggregate wealth is held for dynasti preautionary reasons, and that most of the effet of dynasti unertainty on parental onsumption materializes in delayed rather than bequeathed onsumption. Moreover, dynasti unertainty is the main driver of intergenerational transfers. Lastly, the model predits that parents dynasti preautionary savings aount for one fourth of hildren s insurane against inome shoks. 1 The diretion of altruism i.e. from parent to hild, from hild to parent or two-sided is not essential. What matters is that the form of altruism onsidered extends the budget onstraint aross generations. Note that models with warm-glow bequest do not generate dynasti preautionary saving behavior in response to the hild s inome risk, as the parent only derives utility from the amount bequeathed. 4

5 Related literature This paper is related to three strands of literature. Firstly, it adds to the researh aimed at understanding household onsumption-saving behavior over the life yle, and espeially at older age. This literature advanes two main drivers of saving at older age: bequest motives and preautionary saving motives for mortality and medial risk. However, there is no onsensus regarding the strength of these two motives, nor their relative ontribution in shaping onsumption and savings late in life. Papers like Hubbard et al. 1995, Palumbo 1999, Nardi et al. 010 or Kopeky and Koreshkova 014 find that, given the signifiant medial spending risk faed by retirees, models without bequest motives an math well the wealth dynamis of middle-lass retirees. While this suggests that bequest motives are relatively negligible, Kopzuk and Lupton 007, Ameriks et al. 011, Lokwood 014 and De Nardi et al. 016 onlude that bequest motives are important drivers of retirees hoies. The saving motive analyzed in this paper falls under the umbrella of the bequest motive broadly defined. However, unlike in the previously mentioned papers in whih parental altruism an only manifest in the form of end-of-life bequests, here dynasti preautionary savings an also materialize in the form of inter-vivos transfers. Ameriks et al. 016 and Luo 016 examine the effets of suh transfers on late-in-life wealth aumulation, and find that parents save in order to help when their desendants most need it, rather than at the end of life. Seondly, this paper is related to the vast literature on preautionary savings. Some notable examples are Kimball 1990, Carroll and Samwik 1997, Gourinhas and Parker 00, Cagetti 003, Kennikell and Lusardi 005 and Hurst et al The losest onept to dynasti preautionary savings is the idea of preautionary bequests introdued by Strawzynski He shows that government intervention is a substitute for bequests that are intended to hedge the future generation against risk. In his paper, agents live for one period and hildren are born when the parent dies, whih means that there is essentially no differene between his framework and the reursive formulation of the problem of an infinitely lived agent. The subjetive disount fator is relabeled as degree of altruism and preautionary savings are relabeled as preautionary bequest. In this paper, I allow individuals to have both preautionary and dynasti preautionary saving motives at the same time. Thirdly, this paper omplements the literature that analyzes the insurane role of the family. Examples with rih empirial ontent are Altonji et al who strongly rejet family risk sharing, MGarry 1999 who finds that inter-vivos transfers are negatively orrelated with the reipient s urrent inome, flowing disproportionately to less welloff hildren, MGarry 016 who strengthens this onlusion with muh riher data and adds events suh as job loss and divore as strong preditors of parental transfers, Attanasio et al. 015 who find evidene of partial insurane within family networks, and Ameriks et al. 016 who designed and fielded a new survey to measure transfers See Carroll and Kimball 008 for a review of this literature. 5

6 from parents to desendants. More reently, there has been a revived interest in studying dynami models of families, espeially those that depart from the full ommitment assumption. 3 My paper omplements these efforts. While this departure is attrative from the perspetive of studying more realisti environments and obtaining riher preditions, it raises several hallenges, espeially if one is interested in environments in whih altruistially linked agents an save individually, as it is the ase in this paper. Barzyk and Kredler 014 disuss these hallenges at length. They propose a ontinuous time framework for studying suh environments, whih they subsequently use in Barzyk and Kredler 016 to analyze the role of family in evaluating long-term-are poliies. Fahle 015 also studies long-term are arrangements of the elderly in a dynami model of the family, but assumes hildren do not save. Kaplan 01 studies a model of young workers who have the option to move in and out of the parental home. He shows that this option is a valuable insurane hannel against labor market risk, whih failitates the pursuit of jobs with the potential for high earnings growth. His paper assumes parents annot ommit to transfers, but makes the simplifying assumption that they annot save either. Nishiyama 00 uses a setting with imperfetly altruisti overlapping households to analyze the role of inter-vivos transfers in shaping the wealth distribution, but rules out the possibility that transfers are used for saving. Differentely from the previous papers, in whih the parent hild interation is non-ooperative and without ommitment, Mommaerts 015 studies the effet of informal on insurane demand in a ooperative model of the family with limited ommitment. In my model, parents and hildren an save individually and there is no ommitment, but I make an assumption on the timing of their non-ooperative interation to deal with some of the onerns outlined by Barzyk and Kredler 014. The rest of the paper is organized as follows. Setion ontains the empirial exerise of the paper. Setion 3 explores dynasti preautionary savings further, in a quantitative model. Setion 4 onludes and disusses several avenues for extending this work. Evidene on Dynasti Preautionary Savings In this setion I provide empirial evidene on the existene of dynasti preautionary savings. The empirial exerise is aimed at exploring whether the onsumption of parents responds to the resolution of their hildren s earnings unertainty. 4 To apture that 3 Altig and Davis 199 and Altig and Davis 1993, among others, are examples that assume full ommitment. Ameriks et al. 016 and Luo 016 bypass suh onsiderations by assuming that parents derive warm-glow utility both from bequests and from inter-vivos transfers. 4 I fous on earnings rather than onsumption unertainty beause the latter is endogenous to individuals dynasti preautionary behavior. Speifially, high dynasti preautionary savings translate not only in lower urrent onsumption, but also in lower expeted onsumption unertainty. 6

7 unertainty, I fous on how labor earnings risk is ditated by workers age, industry and oupation..1 Measuring Permanent Inome Unertainty I begin with the measure of permanent inome risk. In the life yle framework, individuals maximize an intertemporal utility funtion subjet to a lifetime budget onstraint, whih speifies that permanent onsumption annot exeed permanent inome. The unertainty about an individual s own permanent inome triggers the aumulation of preautionary wealth. When the pure life yle framework is enrihed with altruism à la Barro 1974 i.e. the parent plaes a weight on the hild s utility from onsumption, unertainty about the permanent inome of future generations beomes relevant and it triggers the aumulation of dynasti preautionary wealth. I define permanent inome unertainty as the standard deviation of the foreast error of lifetime earnings. Intuitively, the higher the unertainty the more diffiult it is for an individual to foreast earnings aurately, whih translates into a larger standard deviation of the foreast error. I only fous on the human apital omponent of permanent inome, sine individual assets are known at the time the onsumption-saving deision is made. For simpliity, I abstrat from the unertainty assoiated to foreasting interest rates interest rates are used for disounting the future inome stream. 5 Inome unertainty at individual level I now desribe the measure of permanent inome risk of an individual i, who earns labor inome from age H to age H. At age h [H, H] the permanent inome of the { } H individual is the disounted sum of his remaining inome stream, y i j, and it is equal to Yh i yi h + yi h+1 R + yi h+ R yi H H R H h = y i j j=h R j h 1 5 I measure permanent inome unertainty diretly, without imposing any restritions on the statistial properties of the foreast errors. Alternatively, it an be assumed, as it is often the ase in the literature, that shoks to urrent inome an be deomposed into a permanent omponent z h persistent or random walk and a transitory omponent ε h usually iid as follows: ỹ h = z h + ε h z h = ρz h 1 + η h with ε h 0, σ ε and ηh 0, σ η. The parameters ρ, σ ε and σ η an then be used to alulate the standard deviation of the foreast error of lifetime earnings as I define it see Carroll and Samwik 1997 and Feigenbaum and Li 01 for estimates of these parameters at individual level, and Guvenen 007, Karahan and Ozkan 013 and Guvenen and Smith 014, among others, for estimates at population level, i.e. for ertain demographi groups. In fat, this is the proedure I implement in Setion 3 of this paper. Therefore, the measure of permanent inome unertainty that I define is not to be onfused with the standard deviation of the permanent omponent of urrent inome, σ η. The latter is only a omponent of the standard deviation of the foreast error of lifetime earnings. 7 j=h

8 where R is the gross risk-free interest rate fixed at population level i.e. not individual speifi and onstant over time. Assuming that urrent inome y i h is observed at the beginning of age h, the individual is unertain about the inome stream from age h + 1 { } H onward, y i j, whih he foreasts using the information set available at age h, denoted by Ih i to be defined later.6 Let ŷ i j,h j=h+1 y = E i j Ii h be the predited labor earnings at age j = h + 1,..., H, based on information set Ih i. I assume labor earnings are predited aording to the following projetion equation y i j y = E i j Ii h +e i j,h }{{} ŷ i j,h where e i j,h is the foreast error and is orthogonal to Ii h. The predited lifetime labor inome as of age h is the disounted sum of the predited inome stream and it is equal to Ŷ i h ŷi h,h + ŷi h+1,h R + ŷi h+,h R ŷi H H,h R H h = ŷ i j,h j=h R j h 3 where ŷ i h,h yi h, by assumption. Therefore, the error in foreasting lifetime labor earnings as of age h is the differene between realized and predited permanent inome, Yh i Ŷi h, and it is equal to E i h ei h+1,h R + ei h+,h R ei H,h R H h = H j=h+1 e i j,h R j h 4 The permanent inome unertainty for individual i at age h, denoted by Std i E i h, is defined as the standard deviation of this foreast error and is equal to Std i Eh i = H j=h+1 Var i e i j,h R j h + H 1 j=h+1 1 R j h H k=j+1 Cov i e i j,h ; ei k,h R k h 1 5 The derivation of this result an be found in Setion A.1 of Appendix A. Inome unertainty at setor level The measure of unertainty previously desribed is an estimate and is subjet to severe attenuation bias as preditor of behavior. Therefore, I follow the literature on 6 The assumption that y i h is observed at the beginning of age h is analogous to the reursive formulation of the life yle model in whih urrent labor inome is a state variable. 8

9 preautionary savings and projet it on influening fators suh as industry and oupation. 7 That is, I onstrut the measure of inome unertainty previously desribed at setor level, where a setor s is an industry-oupation pair. The permanent inome unertainty for an individual of age h working in setor s is then equal to Std s Eh i = H j=h+1 Var s e i j,h R j h + H 1 j=h+1 1 R j h H k=j+1 Cov s e i j,h ; ei k,h R k h where the generi term Var s e i j,h is the ross-setional variane of the foreast errors of all individuals of age h who are foreasting age j > h earnings and are in setor s at the time of the foreast. Similarly, the generi term Cov s e i j,h ; ei k,h is the ross-setional ovariane of the foreast errors of age j and age k earnings, made by age h individuals working in setor s at the time of the foreast. Note that this measure allows for setor hanges over the areer. What matters is the setor in whih an individual is at the time the foreast is made. Projeting individual level unertainty on setors mitigates the bias introdued by potential measurement error in earnings in the survey. If existent, measurement error ultimately shows up in the foreast errors used to alulate the permanent inome unertainty, and affets the distribution of permanent inome risk aross individuals of a given age, whih is one of the main soures of variation used to identify dynasti preautionary savings. If, given age, measurement error is assumed to be independent and identially distributed aross setors, and unorrelated with the true foreast error of labor earnings, then measuring permanent inome unertainty at setor level preserves the distribution of permanent inome unertainty aross setors. The formal disussion of this argument is deferred to Setion A. of the Appendix. 1 6 The ontent of the information set I h To ompute the foreast error of lifetime earnings a stand must be taken on the ontent of the information set I h used to predit labor earnings at ages j > h. I assume that individuals expetations make rational use of the same onditioning information available to the eonometriian. In the benhmark ase I employ a rather parsimonious struture of the information set by inluding harateristis of the individual that are know with ertainty at the time the future inome stream is predited. In partiular, I assume that age j labor earnings y j predited by an individual i of age h = H,..., j 1 7 See, for example, Carroll and Samwik 1998 and Kennikell and Lusardi 005, among others. Additional reasons for instrumenting are sample attrition and the fat that the PSID is not long enough to observe two generations parents and hildren over their entire areer. This would render extremely noisy estimates of individual level varianes and ovarianes. 9

10 and working in setor s are given by y i j = θ 0 + g θ 1, X i h + θ 3 t j +e }{{} ŷ j,h i j,h 7 where the funtion g is linear in the vetor of observables X i h. The latter inludes urrent and lagged inome, an age polynomial, dummies for urrent eduational attainment, marital status, rae and family size. Current and lagged inome y i h and yi h 1 are inluded to ontrol for the persistene of inome over time. Omitting them would result in larger foreast errors, as individuals on a steep inome profile would mehanially translate high observed inome into a large foreast error. Finally, t j is a time trend for the year when the individual is of age j and is meant to apture the effets of aggregate eonomi growth on future inome. I estimate equation 7 for eah setor s and use the errors e i j,h to ompute the setor level permanent inome unertainty as desribed in equation 6. The ontents of I h enumerated above inlude information that is available with ertainty to both the individual and the eonometriian. However, in reality it is possible that households plan ahead and know more than the eonometriian about their future self, espeially when the foreast horizon is small. In a first robustness exerise, I augment I h with a vetor of demographis X i j that are available in the survey and are likely to be known in advane by the individual. These inlude marital status, family size and eduational attainment at the projetion horizon j. Additionally, Guvenen 009 finds evidene inome growth rates are individual speifi. To the extent individuals learn about their speifi slopes over time, failing to aount for this magnifies foreast errors. In a seond robustness exerise, I attempt to ontrol for the effet of individual speifi growth rates by augmenting I h with the last foreast error of an individual. 8. Data desription Having laid out the theoretial framework for measuring permanent inome unertainty, I now turn to desribing the data sets used in the analysis. The data are drawn from two soures: the Panel Study of Inome Dynamis PSID and the Consumer Expenditure Survey CEX. I use the PSID to onstrut the setor level permanent inome risk measure previously desribed, and to form parent-hild pairs for the main estimation. I use the CEX to impute total onsumption in the years in whih the PSID only olleted information on food onsumption and housing. Sample seletion. The main data soure is the PSID, whih ontains longitudinal information on a representative sample of US individuals and families. The PSID started 8 For example, for an individual who is 3 and predits age 4 inome, the last foreast error he made and is aware of at the time of the foreast was at, when prediting age 3 inome. 10

11 in 1968, olleting information on a sample of approximately 5, 000 households. In the following years both the original families and their splitoffs hildren moving out of the parent household have been followed. This is the essential feature of the survey that makes it suitable for the analysis in this paper. The PSID data were olleted annually until 1996 and biennially starting in However, retrospetive information on labor inome in the past two years is olleted in eah of the biennial waves, so there are no gaps in labor inome indued by this hange in survey frequeny. To estimate the profile of inome unertainty I use all the waves of the survey, from 1968 to 013. I apply fairly standard riteria when onstruting the sample. First, I exlude households from the Survey of Eonomi Opportunity sample low-inome supplemental sample and latino sample to avoid any seletion issues. Seond, sine the unertainty measure previously defined refers to the human apital omponent of permanent inome, I fous on individuals of working age, so I restrit the sample to heads of age between and 65 who are either employed or not employed. Third, I exlude the observations with top oded annual earnings and I winsorize the earnings variable at the 99 th perentile to minimize the bias aused by outliers and measurement error. I express earnings in 1996 US dollars. Fourth, a stand must be taken regarding the treatment of respondents with zero earnings. Eliminating them would shut down the unertainty that omes from the extensive margin, thus underestimating the true unertainty of permanent inome. Instead, I impute labor earnings for suh observations based on an estimated transfer funtion, whih is disussed in detail in Setion A.3 of Appendix A. 9. Finally, I drop all entries with missing information in labor earnings and any of the demographi harateristis used in estimating equation 7, as well as all individuals with fewer than 3 observations. The resulting sample has 16, 476 observations orresponding to 9, 046 individuals. A setor s is defined as an industry-oupation pair, with the exeption of the unemployment setor whih inludes all individuals that are not employed at the time they make the inome foreast. Starting from 8 major industry groups listed in the first olumn of Table 1, I expand along 5 major oupation groups listed in the top row of the table. I aggregate some oupations further based on the distribution of annual labor earnings as summarized by the oeffiient of variation. The proedure yields a total of 17 setors 16 setors in Table 1, plus the unemployment setor. 10 In foreasting permanent inome, an individual is assigned to a setor based on his industry and oupation at the time the foreast is made. 11 This allows for transition between setors over the 9 I use the same estimated transfer funtion to impute earnings for observations with positive annual labor earnings smaller than $00, whih are likely to be measured with error 10 For a more detailed disussion of the setor lassifiation, see Setion A.4 in Appendix A. Tables 13 and 14 in Setion A.4 report desriptive statistis regarding the setor size and earnings distribution in eah setor. 11 For example, if an individual works as a onstrution worker at 5, his foreast errors as of age 5 will enter the measure of inome unertainty of onstrution workers of age 5. If at 6 he works as a transportation worker, his foreast errors as of age 6 enter the measure of inome unertainty of 11

12 ourse of a worker s areer. Table 1: Setor definition Industry/Oupation Exeutive and professional speialty oupations Tehniians and administrative support Sales and servies oupations Agriulture and Mining Setor 1 Prodution, operators, fabriators, and laborers Constrution Setor Setor 3 Manufaturing Setor 4 Setor 5 Setor 4 Setor 5 Transp. and Utilities Setor 6 Setor 7 Trade Setor 8 Setor 9 Setor 10 Setor 9 Finane Setor 11 Servies Setor 1 Setor 13 Setor 14 Setor 15 Publi administration Setor 16 Farming, forestry and fishing oupations Notes: Table entries are labels alloated to eah setor. The unemployment setor is labeled Setor 0. Parent-hild pairs. I test for the existene of dynasti preautionary savings on a sample of mathed pairs of parents and hildren, onstruted using the PSID Family Identifiation Mapping System. If a parent has n > 1 hildren, I treat that as n parent-hild pairs. There is a possibility that this affets the estimation results via two hannels. Firstly, parents of multiple hildren working in different setors an hedge against dynasti unertainty, biasing the estimates downwards. I explore the extent to whih this is true by repeating the empirial exerise on the sample of parents with one hild only. Seondly, errors might be serially orrelated between suh pairs, ontaminating the standard errors and impliitly the inferene. I aount for this by lustering the standard errors at parent level. The analysis requires demographi and eonomi information for both parent and mathed hild e.g. parent and hild inome, parent and hild setor, just to name a few. Therefore, I restrit the sample to those pairs in whih the hild is a splitoff. 1 In addition, given that the inome unertainty measure onstruted here refers to heads that are at least years old, I drop those pairs in whih the splitoff hild is not a head or is younger than. I also drop those pairs for whih the age differene between the parent and the hild is lower than 0 years or whih have fewer than 4 entries in the sample. The resulting sample has 155 parent-hild pairs observed between 4 and 1 times over the sample period. The oldest hild is 59 years old, while the age of parents ranges between 4 and 80 years old. transportation workers of age 6. 1 A splitoff hild is a hild who moved out from the parent s house and established his own household. Therefore, his demographi and eonomi information is olleted separately from the parent s. 1

13 Consumption series. The empirial exerise in this paper requires data on onsumption or savings. PSID olleted information on household wealth aross 11 interview waves. Researhers who use this information define savings as the hange in wealth net of debt between two time periods for example Dynan et al The measure thus obtained is rather noisy and limited to the ten existing wealth supplements. Instead, I hoose to fous on onsumption expenditure. This deision is motivated both by the fat that onsumption data is arguably less noisy, and by the fat that in some models of dynasti preautionary saving the wealth position of different generations is not identified. With this approah, I fae the problem that in the early waves of PSID information about onsumption is limited to spending on food and rent. To overome this, I follow the strategy of Blundell et al. 008, who use the CEX to estimate the demand for food available in both surveys as a funtion of total onsumption expenditure, relative pries and household harateristis, and then invert it to obtain a measure of total onsumption expenditure in PSID. Sine CEX data is only available starting 1980, I am able to onstrut the PSID measure of total onsumption from 1981 until 003 alendar years , with breaks in 1988 and 1989 when PSID did not ollet any information of food expenditure. The details of the proedure are disussed in Setion A.5 of Appendix A. For the survey years , the onsumption information in PSID is rih and onsistent enough in terms of the ategories to be used on its own. To aggregate the onsumption ategories olleted in the PSID, I use the guidelines in Andreski et al I onstrut two measures of onsumption expenditure. The first one inludes only expenditure on non-durable onsumption goods and servies food, utilities, personal are, transportation, health, eduation, et., and is the benhmark measure. The seond measure of onsumption also inludes expenditure on durables furniture, jewelry, ars, et.. I examine both measures beause expenditure on durables might affet utility for more than one period..3 Unertainty haraterization I now turn to haraterizing the age profile of permanent inome unertainty. I estimate the projetion equation 7 at the setor level using log annual labor earnings of the head as the dependent variable. That is, for eah setor s and for all h < j I run the following regression ln y i j = θ 0 + θ 1 X i h + θ 3 t j } {{ } ˆ ln y j,h +ε i j,h 8 where the ontents of X i h and t j are as previously desribed. The residuals ε i j,h obtained from this regression are used to onstrut the foreast errors e i j,h from equation 7 a- 13

14 ording to 13 j,h = exp ln y ˆ j,h exp e i ε i j,h 1 9 The foreast errors e i j,h are then used to ompute the permanent inome unertainty measure as desribed in equation 6, using R = 1.04 for disounting. I begin by examining the inome unertainty estimated under the baseline information set. Beause the unertainty measure defined in equation 6 is unit of measurement dependent in partiular, Std s E i h is measured in US dollars, in what follows I report the standard deviation of the foreast error divided by expeted permanent inome, Ŷ h,s. Expeted permanent inome is alulated as Ŷ h,s = H E s y i j Ii h j=h R j h = H j=h ŷ j,h R j h 10 where ŷ j,h is defined in equation 7. The expeted permanent inome is omputed under the assumption that H = 80. Individuals between 66 and 80 years old are treated as retired and thus not subjet to labor inome risk. 14 Their inome stream is given by the soial seurity inome of the head. 15 The average age profile of inome unertainty relative to permanent inome is displayed in Figure 1. Permanent inome unertainty is high when the individual is young and it delines during the twenties and thirties. By the age of 40 approximately half of the relative unertainty is resolved. Afterwards, unertainty dereases at a lower pae with only an extra 15% being resolved until mid fifties. As retirement age approahes, the resolution of unertainty aelerates. The figure implies that relative permanent inome unertainty is very high, with an average over age and setors of 56%. A similar magnitude is implied by a alibrated inome proess with relatively standard parameter values, as will be shown in Setion 3. The age profiles at setor level are displayed in Figures 1-13 in Appendix A. The orrelation between permanent inome unertainty and permanent inome aross setors is 0.61, meaning that setors that are subjet to high risk also exhibit high levels of permanent inome. The fat that unertainty is downward sloping over age is not an artifat of the narrowing foreast horizon. Figure displays the relative standard deviation of labor earnings foreasts, from the 1-year-ahead up to the 10-year-ahead foreast, by age. 13 If y = ŷ + e and ln y = ln ŷ + ε, then e = y ŷ = exp ln y exp ln ŷ = exp ln ŷ + ε exp ln ŷ = exp ln ŷ exp ε exp ln ŷ = exp ln ŷ exp ε % of the entries of age between 66 and 80 years old are retired. The rest of 3% are either employed or unemployed. 15 A retired individual is assigned to the setor in whih he last worked before retirement age. 14

15 S.d. of foreast error/permanent inome Raw unertainty Fitted unertainty Age Figure 1: Age Profile of Inome Unertainty Relative to Permanent Inome - baseline information set Notes: The Raw unertainty is obtained by averaging over the age profiles of unertainty at setor level weighted by the number of observations in eah setor Table 14 in Appendix A. The Fitted unertainty line is obtained by fitting a loal linear regression with bandwidth equal to to the Raw unertainty measure. Lastly, the dotted gray lines are the 95% onfidene interval. Speifially, the figure reports the average over setors s of Var s e i j,h E s y i j Ii h, where the foreast horizon is j h [1, 10] and the age at whih the foreast is made is h [, 55]. The fat that eah of the lines in the figure is upward sloping shows that the longer the foreast horizon is, the less preise the foreasts are. However, at older ages foreasts beome more preise, as implied by the lower relative standard deviations. I perform two robustness exerises with respet to the information set on whih inome foreasts are based and find very small effets. First, using a riher information set in foreasting inome redues measured permanent inome unertainty, on average, by approximately %. The differene is largest in the early twenties, with a redution of 4%. Seond, using past foreast errors in foreasting future inome has almost no effet on the measured permanent inome unertainty. I exploit differenes in unertainty aross age and setors to estimate the effet of own and dynasti unertainty on parental onsumption. This is a fruitful strategy insofar as there is enough variation in the level of permanent inome unertainty aross setors and in the speed at whih it resolves over age. To verify this, Figure 3 displays the oeffiient of variation aross setors, by age, of the level of permanent inome unertainty 15

16 S.d. of 10-year ahead foreast error rel. to inome Age Figure : Relative Standard Deviation of the 10-year-ahead Earnings Foreasts, by Age Notes: The lines in the figure are relative standard deviations of labor earnings foreasts, from 1-year to 10-years-ahead, by age. in gray and the 1-year hange in permanent inome unertainty in blak for the baseline information set. Variation aross setors in the level of inome risk is roughly onstant aross age groups, averaging at 36% and suggesting that level differenes in risk between different setors are an important soure of identifiation at all ages. For the slopes of the permanent inome risk the average over age is %. There is little variation aross setors in the speed at whih unertainty resolves in the twenties, suggesting that rapid resolution of unertainty early in the areer is a feature ommon to all industries and oupations. Under altruism, urrent generations internalize the inome unertainty of future generations. This means that parents lose to retirement, who fae little to no inome risk of their own, are still subjet to inome risk pertaining to their hildren s permanent inome. Moreover, even early in their areers, forward looking parents fae more inome risk than that assoiated to their own permanent inome. This ats towards flattening out the unertainty profile over the working life of an individual with hildren and an ative bequest motive, giving sope for preautionary saving, dynasti and for own insurane, until later in life. 16

17 0.8 Level Change 0.6 C.v. of unertainty Figure 3: Coeffiient of Variation of Inome Unertainty aross Setors, by Age Notes: The gray bars represent the oeffiient of variation of permanent inome risk as defined in equation 6 aross the 17 setors, by age. The blak bars represent the offieient of variation of the 1-year hange in permanent inome unertainty alulated as the ratio between the permanent inome risk at age h and permanent inome risk at age h 1. Age.4 Empirial Estimation A standard preautionary saving argument implies that one s onsumption responds negatively to unertainty related to the permanent inome. Extending this argument to inlude intergenerational onsiderations of the type entailed by altruism à la Barro 1974 implies that parental onsumption responds negatively to unertainty related to the hild s permanent inome. 16 Life-yle onsumption patterns for parents I begin my analysis of the relationship between parental onsumption and dynasti unertainty with an examination of the age profile of onsumption expenditure of parents. To that end, I estimate the following regression on the sample of respondents with hil- 16 This an our through one or two hannels, depending on how the parent-hild interation is modeled. For example, in a dynami version of Barro s setup, where the parent makes all the deisions for the family while alive and there are no strategi interations between the two parties, the hild s inome is an extension of the parent s inome and appears diretly in the family s budget onstraint. In setups in whih the parent and the hild make deisions separately, with or without strategi interations, the parent is subjet to flutuations in the hild s inome through the weight plaed on the hild s utility from onsumption. 17

18 dren: 17 ln C it = β 0 + β age f Age it + β Coh i + β t D t + β x X it + ε it 11 where C it is the equivalized onsumption expenditure of household i during year t, 18 f Age it is a quarti polynomial in the age of the household head, Coh i is a vetor of 10- year ohort dummies, D t is a vetor of year dummies and X it is a vetor of demographi and eonomi harateristis of the household that inludes a ollege dummy, a rae dummy, dummies for family size, and a dummy for weather the head of the household is working or not. The latter ontrols for the fat that retired or unemployed households have different onsumption preferenes or needs. 19 Finally, ε it is a residual that aptures all individual effets suh as measurement error, initial wealth, et. The left panel of Figure 4 displays the estimated age profile of parental onsumption i.e. the fourth-order age polynomial. Results are only shown for onsumption of non-durables and servies, but total onsumption expenditure exhibits a similar pattern. The onsumption profile has the hump-shaped pattern over the working life that has been previously doumented, with the peak ourring in the forties see, for example, Gourinhas and Parker 00. The new feature is the onsumption bakloading late in life, whih suggests that there is a preautionary motive at play in this stage of the life yle. 0 This pattern in onsumption is observed after retirement age the assumption is that retirement ours around age 65, when presumably the unertainty related to own permanent inome is resolved. However, it is possible that even though at this stage parents are no longer subjet to risk in their own inome, they still fae the unertainty pertaining to the permanent inome of their hildren. The fat that the latter is still resolving would shape the onsumption profile of parents as in the figure. Naturally, risk in hildren s inome is not the only type of unertainty elderly fae. Two other soures that have been previously examined in the literature are unertain medial expenses see Nardi et al. 016 for a survey. While the two do resolve with age, generating a bakloaded onsumption profile, they affet all individuals, whih means that the onsumption of non-parents should exhibit the same pattern. 1 To verify whether this is the ase, I run the same regression on the sample of non-parent house- 17 A respondent is lassified as parent if any of following riteria is met: 1 respondent has positive number of total births, respondent reported having a hild under 18 living in the household in any wave of the survey. All other respondents are lassified as non-parents. 18 Equivalized onsumption is obtained by dividing household onsumption by the OECD equivalene sale. The OECD equivalene sale is defined as ES = number of adult members number of hildren. 19 For example, Aguiar and Hurst 013 show that inputs into market work are an important driving fore of life yle onsumption expenditure. 0 A preautionary saving argument says that, when faed with inome risk, individuals postpone urrent onsumption in favor of aumulating preautionary savings. As unertainty resolves, onsumption starts inreasing, therefore displaying a bakloaded pattern. 1 One ould argue that unertainty about the lifespan or medial expenses affets the two groups differently. In partiular, medial evidene suggests that women who have had hildren tend to live longer see Barha et al

19 11 Thousands of 1996 US dollars Age Figure 4: Age Profile of Consumption Expenditure of Parents Notes: The figure shows the age profile of onsumption of non-durables and servies for parents in the blak solid line, together with the 95% onfidene interval in the gray dashed lines. The profiles are onstruted using the estimates of β age from equation 11. The satter plot is the nonparametri profile. The sample has 57, 980 observations. holds, and plot the average age profile of onsumption of non-parents in Figure 5. The figure shows that the onsumption of non-parents ontinues to deline after retirement, albeit at a lower rate. Note, however, that the results for non-parents are noisier, espeially at older age. This is a onsequene of the fat that the sample of non-parents is very small. In partiular, the sample of parents is 7.5 times higher than the one of non-parents. Conditional on individuals being older than 60, there are 13 times more parents than non-parents. The differene between the onsumption profiles of parents and non-parents late in life ould potentially be justified by inreasing monetary transfers from hildren to their parents. This is unlikely to be the sole, or even the main driver. Data on monetary transfers between parents and their hildren from the PSID Family Rosters and Transfers Module shows that only 5.% of respondents report having reeived monetary transfers from their hildren. This fration is inreasing in age albeit with large flutuations, but onditional on positive transfers there is no trend in the amount transfered. 19

20 17 15 Thousands of 1996 US dollars Age Figure 5: Age Profile of Consumption Expenditure of Non-Parents Notes: The figure shows the age profile of onsumption of non-durables and servies for non-parents in the blak solid line, together with the 95% onfidene interval in the gray dashed lines. The profiles are onstruted using the estimates of β age from equation 11. The satter plot is the nonparametri profile. The sample has 7, 730 observations. Estimates exploiting age and setoral differenes I now present the results of a regression analysis of the effet of dynasti unertainty on parental onsumption. The baseline speifiation for exploring this effet is ln pit = β p 0 + βp 1 σ p hs + β p σ hs + X pit β p 3 + X it β p 4 + ɛ p it 1 where pit is the logarithm of the onsumption of parent household i in year t, σ phs is the permanent inome unertainty of the parent and is assigned based on the age h and the setor s in whih the head of the parent household i is in year t, while σ hs is the permanent inome unertainty of the hild, assigned based on the age h and the setor s in whih the hild of the parent i is in year t.,3 The permanent inome unertainty is as desribed in equation 6 and is expressed in logarithm, to failitate the interpretation of the estimated oeffiients as elastiities. X pit and X it are vetors of demographi I assume that unertainty profiles previously doumented are time-invariant. This is mainly beause of data limitations, as the survey is not long enough to fully observe two generations. 3 A parent with n hildren appears in the sample as n parent-hild pairs. Beause in this ase it is very likely that residuals are orrelated within the family of a parent i with multiple hildren, I report standard errors lustered at parent level. 0