THE ECONOMIC MOTIVES FOR CHILD ALLOWANCES: ALTRUISM, EXCHANGE OR VALUE OF INDEPENDENCE?

Transcription

1 THE EONOMI MOTIVES FOR HILD ALLOWANES: ALTRUISM, EXHANGE OR VALUE OF INDEPENDENE? Lisa Farrell*, Paul Frijters** and Mihael A. Shields* * Department of Eonomis, University of Melbourne, Australia ** Tinbergen Institute, Free University Amsterdam, Netherlands August 00 (preliminary draft) Abstrat This paper looks inside the blak box of the family and examines the determinants of inter vivos transfers in the form of allowanes given to hildren. We onsider in a simple model two main ompeting explanations for the transfer of money from parents to hildren in the form of regular allowanes, namely altruism and exhange. We also extend the altruism framework to inlude unobserved hild heterogeneity in monetary autonomy or the 'value of independene'. We use a unique dataset drawn from the British Family Expenditure Survey, whih enables us to expliitly test both the inter-generational preditions of the various models, and through a study of siblings, we are also able to onsider the intra-household aspets of suh payments. Using both random (inter-household) and fixed-effet (intra-household) estimators, we find robust evidene of an n- shape relationship between a hild's external inome and the reeipt of allowanes from parents. Importantly, this estimated profile does not fit the prediations of simple models of altruism or exhange, but does fit an altruism model with unobserved heterogeneity. Further support for the importane of the value of independene is that girls and those with higher birth orders obtain muh higher allowanes, whereby we argue both girls and those born later mature earlier and are therefore likely to be ausally related to a high value of independene. We believe that further investigation of the motives underlying intra-household transfers is important for the design of poliies aimed at redistributing inome, suh as hild welfare payments. Keywords: hild Allowanes, Altruism, Exhange, Inter-Household, Intra-Household JEL lassifiations: orresponding author: Lisa Farrell, Department of Eonomis, University of Melbourne, Parkville, Melbourne, Australia, lfarrell@unimelb.edu.au. 1

2 1. Introdution This paper looks inside the blak box of the family and examines inter vivos transfers in the form of allowanes (poket money) given to hildren. The eonomi literature that onsiders intrahousehold transfers has mainly onentrated on bequest motives. Here, we onsider two ompeting explanations for the transfer of money from parents to hildren in the form of regular allowanes (poket money), namely altruism and exhange. In the ase of altruisti motives (Beker, 1981) parents are assumed to derive a warm glow from the transfer of household resoures to their hildren. They have others-regarding utility funtions. In the exhange model (Bernheim et al., 1985) allowanes are seen as payments to hildren for some servies they deliver to parents. The literature on bequests has been inonlusive regarding the motives for intra-household transfers. Tomes (1981) support s the altruisti motive by showing that the size of bequests are inversely related to the reipient s inome. In ontrast, Menhik (1980) suggests parents obey bequest norms. They simply divide bequests equally amongst siblings, rather than behaving in an altruisti manner. Bernheim et al (1985) finds evidene of bequests as an exhange mehanism through an analysis that quantifies hild servies as the frequeny of visits and phone alls to parents by hildren living outside of the home. He notes that the level of these servies is positively related to the size of the potential estate and that siblings ompete with eah other in this sense. Eonomists have, however, paid little attention to inter vivos transfers mostly due to a pauity of data with whih to explore the motives for suh transfers. Although ox (1989) looks at transfers between family units and finds evidene mostly in favour of exhange rather than altruism. Data on allowanes given to hildren provides an interesting way to re-examine these issues and to test the two ompeting motives: altruism versus exhange. The available evidene suggests that hildren begin to reeive allowanes, in the sense of regular transfers from other household members, between the age of 5 and 7 (Furnham and Thomas, 1984). hildren also reeive inome from other soures outside the household, i.e. from jobs both formal and informal (perhaps even illegal employment), and as gifts (e.g. birthday, hristmas and holiday money). These other soures of inome outside of the household are likely to affet the willingness of parents to transfer household resoures to hildren and the willingness of hildren to supply servies to parents in exhange for an allowane. Barnet-Verzat and Wolff (001) look at poket money in this ontext of altruism and exhange models. Their empirial results show that a whole host of motivations are relevant and present these results as one explanation for why there is a lak of onsensus among eonomists regarding the motives for inter vivos transfers. Here we ontribute to the altruism versus exhange debate by analysing allowanes in a unique data set that allows us to test both the inter-generational preditions of the models and seondly, through a study of siblings we are also able to onsider the intra-generational aspets of suh

3 payments. The analysis to date has onentrated on testing the ompeting hypothesis through their preditions regarding the inter-generational omparative statis only, negleting the intragenerational preditions of the models. Further investigation of the motives underlying intrahousehold transfers is important as this has important poliy impliations for poliies aimed at redistributing inome, suh as pensions and hild welfare payments. This paper proeeds as follows. Setion introdues the theories of altruism and exhange, and highlights the omparative statis of a model that ombines both explanations of parental allowane giving to hildren. The data and sample harateristis are desribed in Setion 3, and our eonometri modelling approahes are disussed in Setion 4. The results of the statistial analysis are presented in Setion 5, together with a theoretial framework that is onsistent with out empirial findings. Finally, we onlude in Setion 6.. Theoretial Bakground We will onsider two existing explanations of allowanes given to hildren by parents, altruism and exhange, whereby we extend the altruism model with the existene of unobserved heterogeneity. We first give the basi intuition for the two existing explanations, whih we ombine into in a single simple model. (i) Altruism The onept of interdependent utility funtions has a long history. With respet to family networks Beker (1981) first proposed the idea that parents may reeive utility from the well-being of their hildren. Thus they may be motivated to give hildren diret inome transfers in the form of regular allowanes. Suh inter-generational transfers are aimed at bringing together the living standards of parents and kids. Moreover, parents may wish to equalize well-being aross hildren in the household, thus using allowanes to at as a form of intra-generational ompensation. One empirial predition from altruism is that parent would ompensate hildren for having a low exogenous inome of their own. Indeed, in a general dynami model ox (1987) shows that a one unit inrease in parents inome together with a one unit derease in the hild s inome should lead to a one unit inrease in the transfer from the parent to the hild. Altonji et al. (1997) show empirially this ondition does not hold. They find that redistributing inome in this way leads to only a 0.13 inrease in the size of the transfer. (ii) Exhange Whilst altruisti motives are suffiient to explain the existene of allowanes it is not neessary to apply altruisti motives in order to invoke other-regarding behavior. Self-interested parents may 3

4 give allowanes as part of an impliit or expliit exhange ontrat where allowanes are paid in exhange for servies. These servies may simply be ompliane with parental regulations or attention given to the parent by the hild. In some households hildren may be involved in home prodution through ativities suh as providing hildare for younger siblings. Moreover, this exhange ontrat may be intertemporal in nature, suh as the promise to look after the parents in their old age, indeed if this is the servie that parents purhase then one would expet to see allowanes inrease as the hild gets older and therefore loser to leaving the family home. 1 The empirial preditions of the exhange motive will hinge on the marginal value of the time of the hild, whih will determine the prie of the servies, and the marginal value of the servie of the hild to the parent, whih will determine the willingness to pay. It would seem likely to expet that hildren with higher exogenous inome value their time more highly than others and that they would hene have a higher prie for their servies. If these servies are then normal goods, the payment should derease with its prie. If the servies are neessary goods, payment may inrease with the hild s inome. Hene the empirial predition on the relation between allowanes and external inome from exhange would ex ante seem ambiguous. We will ombine these two main arguments in a single model, adapted from ox (1989). The hild s utility funtion is: V= V( Y + A, S), (1) and the parent s utility funtion is: U = U( Y A, S, V( Y + A, S)). () P where A=allowanes and A 0, Y P = household inome, Y =the hild s inome and S= the servie hildren provided to parents suh that S 0. One should note that the inome of the hild and the parent is assumed to be exogenous. We make standard assumptions about these derivatives: 1. See ox (1990) and ox and Jappelli (1990) for the full exposition of the model in an intertemporal framework where parents at as lending agents to redit onstrained hildren. The predited effets of the inome variables remains unhanged in this framework. 4

5 > 0, < 0, > 0, + U U V ( YP A) ( YP A) ( Y A) V U U V V < 0, > 0, > 0, < 0, < 0 ( Y + A) V S S S (3) whih means that positive but dereasing marginal utility is derived from onsumption; the prodution of servies is assumed to have inreasing marginal utility ost for the hild; and the parent values the utility of the hild. As the leading example we have in mind, we take rossderivatives to be rather unimportant and the marginal utility of the servies and hild s utility to be onstant. This is for instane the ase when the parent s utility funtion is separable: UY ( ASVY,, ( + AS, )) = fy ( A) + S+ VY ( + AS, ) (4) P P Now, we shall deompose the transfer of the parent to the hild into an altruisti omponent and a payment for the servies of the hild: A= A0 + a( S). The altruisti omponent is defined as the transfer a parent would make even in the absene of any servies from the hild, i.e. the unonditional payment to the hild. This level will be determined by the first-order ondition of the maximization problem of the parent: du ( YP A0,0, V ) U U V ( Y + A0,0) = + = 0, (5) da0 ( YP A0) V ( Y + A0) whih an in our leading example be simplified as: f VY ( + A0,0) = ( Y A ) ( Y + A ) P 0 0 (6) whih is assured to have a unique solution beause 0 U ( Y A ) P 0 inreases as A 0 inreases whilst VY ( + A0,0) dereases due to the onavity of the utility funtions. What is easily seen is that the ( Y + A ) solution level of A0 will be dereasing in Y under any funtional form. If the marginal value of money to the parent is virtually onstant (i.e. parental inome is muh bigger than the transfer), this 5

6 inrease is on a one-to-one basis, as in ox (1987). In suh a ase, A 0 an be written as 0 A0 = max{0, A Y } where A 0 is found by solving (6) for Y =0. Now, the part of the transfer that is a payment for servies will have to take aount of the inentive ompatibility onstraint of the hild, i.e. the hild will only supply the desired amount of servie if the payment ompensates for the loss of utility. This means there must hold: VY ( + A+ as, ) VY ( + A,0) (7) 0 0 Obviously, a maximizing parent will set a(s) suh that this ondition is indeed binding, whih means that the impliit prie of S an be found by total differentiation of (7), yielding: da V V = / (8) ds S ( Y + A + a) 0 whih is a differential equation that, together with the initial ondition that a(0)=0, uniquely identifies a(s). What is immediate is that this impliit prie of extra effort is inreasing in Y A a and thereby in Y. What this implies for the total transfer is illustrated in the graph below for two possible assumptions on the type of good that S is. Under the first assumption, it is a normal good, whih means that less is spent on it the higher the prie. Under the seond assumption it is a neessary good, whih for instane arises if parent demand a fixed amount whatever its prie, whih would mean more is spent on it in total when its prie goes up. 6

7 FIGURE 1: Allowanes when there is Altruism and Exhange We an see the main arguments of the model in the ase of our leading example: when Y < A 0, then Y + A 0 is roughly onstant, and hene the prie of the servies is the same in the range. Although there an be some parental inome effets whih we ve ignored here (when the parent gives less to the hild, the parent has more to spend of its own and the marginal value of money dereases for the parent), these are not likely to be very important given the relatively low amounts of money transfers made to hildren. Hene, the amount of servies bought in is roughly onstant when Y < A 0, whih means total transfers go down linearly. When the altruisti transfer drops to 0, whih ours when Y = A 0, the parent only transfers money as a payment for servies. These will be delining with prie (and hene with Y ) when servies are a normal good and inreasing with prie when servies are a neessity. In our leading example we hene get the lear predition that transfers should go down as a hild s own inome inreases at low levels, whilst transfers may inrease or derease at high levels of the hild s inome, depending on the type of good that these servies are. If we are only prepared to make the general assumptions, all that we an safely say is that the transfers should go down initially and will only inrease with higher Y when the demand for servies is very prie-inelasti. 7

8 (iii) Altruism and the 'Value of Independene' So far it has been impliit that there is no heterogeneity in the population with respet to utility funtions and that the hild s external inome is exogenous. These assumptions are often implausible as there are likely to be unobserved fators that make some hildren value monetary transfers more than others and these unobserved fators may also push up the hild s own inome, leading to a statistial though non-ausal relationship. To make this expliit, we allow for unobserved heterogeneity in the utility funtion of the hild: V = V(( Y + A), γ, S) (9) where the unobserved parameter γ has a ontinuous distribution over the whole population. We label γ as the degree to whih individuals value independene. This means it is bounded between 0 and 1. The value of independene and the external inome of the hild are omplementary in the V utility funtion of the hild: 0. γ Y + A The value of independene and the external inome of the hild are furthermore likely to be statistially orrelated. This argument relies on several onsiderations. First we reognize that the hild s inome is itself made up largely of monetary gifts of other family members. Beause there is a hoie element to the type of transfer given to a kid, these monetary gifts are a substitute for inkind transfers, suh as lothes or toys: it may be the ase that the hild requests money instead of other types of gifts. Similarly, a large amount of inome earned by the hild itself indiates that the hild values being able to determine his or her own expenditures above relying on in-kind transfers. For these reasons the inome of the hild seems likely to be highly orrelated with some wish for monetary independene the part of the hild. Optimising behaviour of the hild thus translates into a positive orrelation between γ and Y. This means that the external inome of the hild may give information about the degree to whih the hild values his independene. What does this now mean for parental deision making? A maximising parent will now set the transfer suh that marginal values are equated: U U V(( Y + A), γ, S) = ( YP A) V ( Y + A) (10) 8

9 from whih we an see that, if γ were observed, parents will inrease their altruisti monetary V(( Y + A), γ, S) transfer to the hild with a high γ beause this inreases. If there is a positive ( Y + A) orrelation between γ and Y, i.e. if external inome onveys information about γ, this an lead to a spurious positive orrelation between Y and A in some interval (see Appendix for examples). There are two preditions of interest here. The first is that heterogeneity in the value of independene may explain some heterogeneity in transfers. We will in the empirial part hek this predition by looking for indiators of the value of independene. Our main indiator is the birth order of the hild in the household beause there is a lot of psyhologial evidene to suggest that the younger siblings mature faster than the older ones. The seond predition of this theory is that exluding indiators for the value of independene will bias the estimates of the effet of variables that orrelate with the value of independene. Amongst these is arguably the external inome of the hild. Now, there is atually not a lear predition as to the size or even diretion of this bias. In the appendix we illustrate the possibilities with two examples within a general lass. Under some assumptions on the utility funtion and the preise statistial relation between γ and Y, the bias is non-existent and in others the bias leads to a nonmonotoni relation between the external inome of the hild and the transfers to that hild. 3. Data and Sample harateristis This analysis is based on the urrently available and to our knowledge little used data on hildren s allowanes ontained in the British Family Expenditure Survey (FES). The FES is a nationally representative ross-setional survey that has been onduted on an annual basis sine Some 10,000 households are seleted eah year to take part in the FES, and the response rate is typially around 70%. The main aim of the survey is to provide a reliable soure of information on household expenditure, inome and other aspets of household finanes. To aount for seasonal differenes in expenditure fae-to-fae interviews are spread evenly over the year. Eah individual aged 16 or over in the households visited is asked to fill in an inome questionnaire and to keep diary reords of daily expenditure for two weeks. Parents are also asked to reord details of hildren s inome from outside the household and the amount of poket money they give to hildren. We pool aross the two years that ontain allowanes and other hild inome data at the level of eah individual hild in the household i.e. 1998/99 and 1999/00. Our data shows us the value of allowanes that the hild gets and any other monies reeived from outside the household, as well as various harateristis of the hild. The hildren in our The survey asked questions relating to other soures of hild inome for the first time in 1998/99. 9

10 sample are aged 0-15 years and we have a sample of 748 hildren evenly distributed by age and living in 4055 households. By mathing the hildren to the household we are also able to obtain a lot of information about the harateristis of the household. We are espeially interested in the sibling omposition of the household in order to be able to test the intra-generational preditions of our ompeting hypothesis regarding the motives for giving allowanes to hildren. As well as allowanes we observe monies reeived from outside the household. Some hildren in our sample have paid part-time jobs. Other hildren gain inome from informal work and many hildren have inome in the form of interest on hild bank aounts and building soiety aounts. hildren in our data set are also observed reeiving inome as ash gifts from people outside the household. The distintion between these soures of inome is unimportant for our task here, our theoretial framework only requires that we know the total inome the hild generates from outside of the household in order to be able to test between altruism and exhange as motives for parents giving hildren allowanes. Summary statistis of the raw data an be found in Table 1. We an see that aross all the hildren in our sample 18.91% of hildren reeive poket money, however, this proportion inreases with age. Indeed the proportion reeiving allowanes inreases steadily with age from 0.65% at age 1 to 9.6% at age 15. The size of the allowane follows a similar pattern. The average onditional allowane aross the sample is 3.45 per week and this rises from 0.61 per week at age 1 to 6.07 per week by age 15. There also appears to be a gender bias, at the mean levels of allowanes, with girls reeiving a higher average level of allowane that boys ( 3.69 ompared to 3.3). Britain's ethni minorities appear less likely to reeive regular allowanes but have higher average allowanes. [TABLE 1 ABOUT HERE] The relationship between allowanes and the level of external inome of the hild appears to be n-shaped. Only 16.60% of hildren with no external inome reeive an allowane, where as 33.73% of hildren with an external inome of 6-10 per week also reeive an allowane and this trails off to 3.89% for those with an external inome greater than 10. The average onditional allowane however is inreasing in the level of external inome. This is ompletely at odds with the altruisti explanation of allowanes. The exhange motive an fit either an inreasing or a dereasing relationship and is hene more in aordane with this initial finding. Regarding parental and household harateristis, we find the perentage of hildren reeiving allowanes and the size of the average allowanes is negatively related to the number of siblings in the household suggesting that hildren with siblings ompete for household resoures. Regarding 10

11 the marital status of the hild s parents the raw data suggests that hildren of lone parents are more likely to be reeiving an allowane than their two parent ounterparts but they reeive a lower onditional average amount. hildren with working mothers appear to be more likely to be in reeipt of an allowane and to reeive more. With respet to household inome we an see that the probability of reeiving an allowane and the size of the allowane is inreasing in household inome. Finally we onsider how the level of allowanes and the propensity to give an allowane hanges with the degree of 'external' altruism that the parents show. We apture this by the size of regular donations to harity made by the hild s parents. We an see that hildren of regular harity givers are more likely to reeive an allowane (4.48% ompared to 16.99%) but the onditional size of the allowane is not affeted. Figure below shows the relationship between the perentage of hildren who reeive an allowane and the perentage of hildren who have external inome, by age. We an see that there are very few hildren with allowanes at very young ages but there is a large inrease in the number of hildren reeiving an allowane after age six. This is onsistent with the available evidene that suggests that hildren begin to reeive allowanes in the sense of regular transfers from other household members, between the ages of 5 and 7 years of age (Furnham and Thomas, 1984). Between the ages of 0 and 6.5 years old a higher proportion of hildren have external inome than have an allowane. This is reversed for hildren between the ages of 6.5 and 13.5 years of age. However after age 13.5 years old more hildren have an external inome than reeive an allowane. This is onsistent with the fat that age 13 is the legal age at whih hildren in Britain are legally allowed to have paid employment. 11

12 FIGURE : The Relationship between Age and the Reeipt of Allowanes and External Inome Allowanes External inome % Reeiving Age 1

13 4. Inter and Intra-Household Empirial Models of hild Allowanes The fous of our empirial analysis is to model the provision of allowanes given to hildren. The theoretial models outlined in Setion suggest that the hild s exogenous inome will be a key fator in explaining the level of provision of allowanes aross hildren, although the desriptive statistis in Setion 3 suggest other fators may also be important suh as harateristis of the hild and the household in whih she lives. Thus our models of allowanes will have the following general form: A = f( Z, Y, H ) (11) Where A is the allowane reeived by hild, Z is a set of harateristis of hild, Y is the exogenous inome of the hild and H is a set of household and parental harateristis. (i) Inter-Household Estimates As noted in Setion 3 not all the hildren in our sample reeive an allowane and so our statistial framework needs to aount for this lustering of observations at zero. As our base model we therefore adopt a Tobit speifiation. We also explore the importane of unobservable household effets in determining the size of allowanes. This statistial framework is based on a random effets speifiation, whih allows us to investigate the level of orrelation between allowanes of hildren in the same household that is due to unobservable household effets. The panel dimension of our model arises from the fat that we observe eah hild and their siblings within the household. Given that the sampling frame of the FES is at the household level, we are able to reate a panel of data for households. This allows us to ontrol for the fat that there may be some unobservable household speifi effet that means the hildren in one household may be more likely to reeive an allowane than hildren in another household. We thus have a random effets Tobit model: A = X β + Y β + H β + ν (1) * h h 1 h h 3 h ν h = αh + ηh and A A * if A>0 = 0 if A 0 13

14 where * A h is the unobservable propensity to reeive an allowane for hild in household h; A h is the observed allowanes of hildren in household h; X,Y and H are vetor of exogenous harateristis; β 's are the assoiated vetors of oeffiients; α h is the household speifi unobservable effet and η h is a random error term. We assume a random effets speifiation, where η ~IN(0, σ ), and in order to marginalise the likelihood it is assumed that, onditional on h the ovariates, h α are (, σ ) IN and are independent of the η and the ov ariates. This implies 0 α that the orrelation between the error terms of hildren who live in the same household is a onstant given by: h σ ρ = orr( νhl, νhk ) = l k σ α α + ση (13) Thus, ρ represents the proportion of the total variane ontributed by the panel level variane omponent. A fuller disussion of the Random Effets Probit model and the assoiated likelihood funtion an be found in Arulampalam (1999). The likelihood is omputed using 0 point Gauss- Hermite quadrature (see Butler and Moffitt, 198). This model is again estimated for both the basi and extended regressor set in order to test the robustness of the oeffiients to the inlusion of the external altruism variable. Given the rihness of our data, the ovariates in the basi model are: Z = age (and it's square), gender and ethniity; Y = the hild's amount of external inome (external inome is entered as a quadrati, following extensive tests for funtional form); and H = years of eduation of the mother and father, age of the mother and father, the log of gross household weekly inome, number of siblings in the household, lone parent, working mother, regional of residene and degree of urbanization of residene. In one extended model we additionally inlude a variable representing the amount of regular haritable donations made by the adults in the household, whih should apture the parents degree of external altruism towards others outside of the household; given that external and internal altruism might be orrelated, this gives us a diret test of whether altruism may be involved and whih variables s oeffiients hange as a result of inluding suh an indiator. In a seond extended model we inlude birth order.. blab la very important blabla piks up value of independene. (ii) Intra-Household Estimates 14

15 A strong assumption in the random effet model is that the unobserved household harateristis are unrelated to observable harateristis. This assumption an be relaxed by looking at the alloation of allowanes within the household. In order to investigate the intra-household aspets of our ompeting hypotheses for the provision of allowanes, we estimate a fixed effets model. This will allow us to ompare differenes in the levels of allowanes aross siblings ontrolling for observable harateristis of the siblings. In this speifiation we are looking at the within household variation in the level of allowanes given to hildren rather than the between household variation that was aptured in the previous models. Here we use an OLS fixed effets model, given the problems with the available estimators for the onditional tobit fixed effets model 3. Our final speifiation is therefore: A = α + β X + β Y + β Z + ε (14) h h 1 h h 3 h h Where A h is the observed allowane of the siblings in the household, X, Y are vetors of exogenous harateristis whih are expeted to influene A h and whih vary aross hildren in the household; Z h is a vetor of variables that vary aross households but for eah household are onstant aross the hildren in that household; α h is an idiosynrati fixed effet whih aounts for inter-sibling differenes in unobserved explanatory variables- assuming these differenes are onstant over time and ε h is a random error term. It should be noted that we annot reover estimates of any explanatory variables that do not vary aross the hildren in the household i.e. those ontained in Z h. However the fixed effets estimator is robust to the omission of these hildinvariant regressors. In this model the oeffiient on the exogenous hild s inome variable tells us about parent s treatment of hildren within the household and thus aptures intra-generational aspets of the provision of allowanes. The fat that we an identify siblings means that our data uniquely allows us to investigate the intra-generational preditions of our ompeting hypothesis regarding the motives for giving allowanes to hildren. By using the fixed effet method we will be able to tell whether the relationships at the population level are tainted by simultaneity issues at the household level. We ould for instane think that some households have both very high unobserved savings and very rih friends. Suh an unobserved harateristi would presumably lead us to observe both high levels of exogenous inome for the hildren (in the form of monetary gifts from rih friends) and high transfers to the 3 The problem is that the estimators for the fixed-effet tobit model are not proven to be onsistent: there is no guarantee that the estimated oeffiients of the proedures of (Honore, 199) or (Honore and Kyriazidou, 000) onverge to the orret oeffiients. 15

16 hildren from the riher parents. At the population level, this would give us a positive relationship between exogenous inome and transfers. In the household-fixed effet analysis however, these unobserved household harateristis would be ontrolled for and the spurious relation between exogenous inome and transfers would fall away. 5. Results We now turn to the empirial results from our statistial models desribed in Setion 3. The results are qualitatively onsistent aross all speifiations. We will begin by onsidering the between household estimates before onsidering the results of the within household estimates. The parameter estimates for the inter-household estimators are presented in Table, and for the intra-household estimates in Table 3. We onsider three models in Table. The basi one exludes the variable that aptures a hild s parent s degree of external altruism through their observed donations to harity and it exludes birth order. We then add both sets of variables in the two other speifiations. We begin by disussing the key variables that allow us to draw onlusions regarding the motives for hild allowanes. 16

17 (i) Inter-Household Estimates Looking at the pooled tobit estimates for the extended variable set (olumn and 3) we find that allowanes inrease with external inome until external inome is about 6 after whih transfers derease. 4 Figure 3 shows the estimated profiles between hildren's external inome and allowanes, for the random-effets model that inludes the harity variable. FIGURE 3: The Estimated Effet of hild External Inome on unonditional allowanes and on allowanes for those with positive allowanes. Allowane and external inome 4.5 Allowane expeted allowane onditional expeted allowane lower bound of expeted allowane higher bound of expeted allowane Exteral inome note: the referene position is a 1 year old, where all other oeffiients are taken as fixed. The initial inrease in allowane as a response to inreasing external inome is inonsistent with the simple altruisti motivation for allowanes. This initial inrease ould be onsistent with the idea that parents have to pay higher amounts to reeive the servies of hildren who have other soures of inome when these servies are luxury goods. Yet, there is a level of external inome at whih this peaks and very rih hildren start to see the provision of allowanes derease as their inome rises further. The exhange motivation annot simultaneously fit this initial inrease in transfers and 4 We have extensively tested for the best funtional for hild's external inome. A quadrati speifiation leads to the highest log likelihood for all our models. We used a quadrati beause our model suggested a possible non-linear relation between exogenous inome and allowanes. 17

18 the subsequent derease. As shown in the appendix, altruism oupled with heterogeneity in the value of independene ould explain suh a non-monotoni relationship: at low levels of external inome, the signal about the value of independene is suffiiently strong to yield a positive relation between the transfer and external inome, whereas at high levels of external inome there is no extra information about the value of independene and the allowane redues. What diretly supports the importane of the value of independene is that higher birth orders have highly positive and signifiant oeffiients. We also see oeffiients of other variables that substantially hange as a result of inluding birth order. If we interpret this hange as implying that these variables previously piked up part of the value of independene, those variables whose oeffiient dereases from olumn to 3 would have to be positively related to the value of independene. This would apply for having a working mother, having a lone parent, having a high family inome, living in the ity (whih is the referene group for loation) and being non-white. It would seem quite plausible that all these indeed would be positively related to a value of independene. [TABLE ABOUT HERE] The random effets framework allows us to establish how muh of the variation in the hildren s poket money an be explained by unobservable household harateristis. Do some households atively give hildren allowanes whilst other households have preferenes for not giving allowanes to hildren? We find that the intra-household orrelation is substantial, for the basi model ρ =0.83 with t=85.5 and for the extended model ρ =0.830 with t= As expeted, allowanes are found to inrease with the age of the hild. This result is onsistent with the idea that older hildren will be more eonomially ative and thus their onsumption set inreases. However the negative oeffiient on the age squared term shows this inrease is at a dereasing rate. The gender dummy shows that boys appear to get lower allowanes than girls although the oeffiients are only signifiant for the random effets model. This result is inonsistent with a number of reent papers that have found that parents may favour boys when alloating family resoures. One suggested reason for boy favouring is that parents value hildren as an investment in the sense that they are able to appropriate future earnings from them (see, for example, Deaton, 1989). If it is the ase that, diret ommodity market-interations benefit hildren through an eduative proess of eonomi soialisation, as well as through inreased onsumption, then we might expet to see a gender bias direted towards higher allowanes among boys relative 18

19 to girls. Alternatively our result might be explained by the fat that adolesene, whih is often argued to our earlier for girls than boys, may be assoiated with eonomi as well as physial and emotional maturity in the eyes of parents. Hene gender may, quite apart from birth order with whih gender is obviously not orrelated, have a positive orrelation with the value of independene. We also ontrol for a number of harateristis of the hild s parents. The level of eduation of the parents appears to have no signifiant impat on the provision of allowanes to hildren, although the signs of these oeffiients are onsistent aross the models. The age of the parents is positively related to the size of allowanes (but is only signifiant in the random effets models). Looking at household inome we find little evidene that the size of a hild s allowanes are determined by the inome of the household in whih they live. This may be beause parents have an idea about the 'right' amount of inome that a hild should have given their age and so it is perhaps not surprising that allowanes are not responsive to household inome. We find that hildren of lone parents reeive higher allowanes (at the 10% level of signifiane) than hildren in two parent households. This results might be surprising given that lone parent households are known to be in the lower inome deiles, however we have already should that the level of allowanes is not orrelated with the level of inome in the household. We find no impat though of the presene of a working mother in the household. Again though, the drop in the oeffiients of these last 3 variables when we inlude birth order indiates that being a working mother, a lone parent and having higher family inome may be positively related to a high value of independene. Finally the result show that parents who are more altruisti towards people outside of the household in the sense that they donate more to harity are found to also give more to their hildren than parents who hoose not to donate to harity. This suggests that externally altruisti parents are also more generous in the allowanes they pass to their hildren. (ii) Intra-Household Estimates Next we will onsider the intra-generational preditions of our ompeting hypothesis regarding the provision of allowanes to hildren. Table 3 presents the results of this study, where the first striking aspet is that the signifiane of the found relationships has dropped substantially. This reflets the fat that there is not a lot of variation within the household to identify the underlying relationships with. However, taking the point estimates of the oeffiients, we an see that the oeffiients on the level of external inome of the hildren are very similar to those of the random effets speifiation. Within households those hildren that have higher exogenous inomes first 5 Our sample inludes a number of single hild households. To test the robustness of our intra-household orrelation findings, we have fitted the models inluding only those households for whih we have data on at least two hildren. 19

20 reeive more and only at high levels of exogenous inome do they start reeiving less. This suggest that i) there are no very important unobserved household harateristis that are responsible for the results in Table 1 and, and ii) the simple model of altruism and exhange annot by themselves explain the relations between exogenous inome and transfers under any speifiation. [TABLE 3 ABOUT HERE] The results looking at differenes aross siblings are also onsistent with the between household results, i.e. allowanes inrease with the age of the hild but at a dereasing rate. Male siblings are found to reeive statistially signifiantly lower allowanes than females in the same household. The results again strongly support the theory that the value of independene is important: those with higher birth orders obtain muh higher transfers within the household. The inlusion of birth order furthermore somewhat redues the importane of external inome though not by very muh. This in turn suggests that if external inome is related to a value of independene, it is an aspet of the value of independene not fully aptured by birth order. 6. onlusions In this paper we have used detailed household level data to investigate the motives for parental giving of allowanes to their hildren. The two main ompeting motives highlighted in the eonomi literature are altruism and exhange. Altruism means that parents gain a 'warm-glow' from the inreased utility that their hildren deriving from the allowane, whilst exhange is motivated by the giving of allowanes to hildren in order to 'buy' servies from them, suh as good behaviour. The former model predits that parents will give the most to hildren who have the least external inome, whilst the exhange model leads to ambiguous preditions. We have inluded to these standard models a third one in whih we ombine the existene of altruism with unobserved heterogeneity in the value of independene of the hild. Given the rihness of our data we have been able to expliitly test whih of these models is able to fit our data. In all speifiations we find an n-shaped relationship between external inome and the transfers. This most learly violates the initial arguments on altruism. Despite this, the data learly suggests that altruism indeed does inrease overall transfers to hildren and thereby that it is relevant. Our third model does allow for ases when this emerges, most notable when at low levels of external inomes an inrease in this external inome indiates a greater value of independene whih leads the parent to inrease its transfer to the hild. This is then a statistial relationship though, not a ausal one. The estimated ρ s are all quantitatively similar in magnitude and signifiane to those presented in Tables. 0

21 As a diret measure of the value of independene we have used birth order beause those born later in the household are likely to mature earlier. In the results we indeed find that those born later reeive muh higher transfers. Further evidene to support the idea that the value of independene is heterogeneous and an important preditor of transfers is the fat that girls obtain more transfers than boys beause girls are likely to be independent sooner than boys. It finally onurs with our finding that parents who are more generous to harity in general not only give higher transfers on average but are also more responsive in their transfer to the external inome of the hild Separate random and fixed-effet models were estimated, with the same ovariates as in Tables and 3, for observably altruisti parents and observable non-altruisti parents, where altruisti parents were defined as giving regularly to harity. The finding that altruisti parents display a muh stronger urvature (transfers inrease more rapidly with hild s inome at low levels and only very late tail off) than non-altruisti parents is onsistent aross both the inter-household and intra-household models. These additional results are available from the authors on request. 1

22 TABLE 1: Who Reeives Allowanes, and How Muh Do They Reeive? Reeiving Allowane (%) Average Allowane ( ) All (0.45) (0.11) hild harateristis Boys (0.63) Girls (0.65) Age = (0.37) Age = * (1.34) Age = * (.14) Age = * (.3) White 19.1 (0.47) Non-white 16.5 (1.4) hild external inome 10+ per week 3.89* (4.0) hild external inome 6-10 per week 33.73* (5.0) hild external inome 1-5 per week 7.38* (1.16) hild has no external inome (0.49) Parental and Household harateristis Three + siblings 16.55* (1.6) Two siblings 17.9 (0.91) One sibling (0.70) No siblings 0.18 (0.99) Both parents 18.7 (0.5) Lone parent (0.9) Working mother 1.03* (0.63) Non-working mother 16.0 (0.64) Total parental inome (75-100%).6* (0.97) Total parental inome (50-74%) (0.91) Total parental inome (5-49%) (0.87) Total parental inome (1-14%) (0.86) Parents regular harity givers 4.58* (0.99) Parents do not give to harity (0.13) 3.69* (0.17) 0.61 (0.17) 1.00* (0.10).65* (0.5) 6.07* (0.43) 3.4 (0.11) 3.81 (0.3) 5.85* (1.88) 5.16* (0.75) 3.3 (0.16) 3.46 (0.13).16* (0.18).90* (0.16) 3.34* (0.18) 4.4 (0.) 3.50 (0.13) 3.30 (0.17) 3.6* (0.1) 3.15 (0.19) 3.74* (0.) 3.47 (0.18) 3.4 (0.6) 3.06 (0.18) 3.41 (0.19) 3.47 (0.13) (0.50) Note: The standard error of the mean is given in parentheses. * indiates if there is a signifiant differene between boys and girls, age group relative to age=1, non-whites relative to whites, external inome amount relative to no external inome, number of siblings relative to only hild, lone parent hild relative to having both parents in the household, total parental inome quartile relative to the lowest quartile, parents regularly give to harities relative to those hildren whose parents do no give to harity.

23 TABLE : Household Random Effets Models of hild Allowanes Determinants of hild Allowanes Random Effets Random Effets Random Effets (1) () (3) β t β t β t hild harateristis Age Age squared Male Non-white External inome External inome squared Birth Order Seond born Third born Fourth both Fifth + born Parental and Household harateristis Number of siblings in household Years of eduation (Father) Years of eduation (Mother) Age (Father) Age (Mother) ln (Gross weekly inome) Lone parent Working mother haritable donations ( 's, weekly) Loational harateristis Region (1) YES YES YES YES YES YES Urban Rural onstant Log likelihood Rho Sample (in 4055 households) Notes: Absolute t-statistis given in parentheses. The omitted ategories are female, white, both parents in household, non-working mother, first born and living in a ity. 3

24 TABLE 3: Household Fixed Effets Models of hild Allowanes Determinants of hild Allowanes Fixed Effets Fixed Effets (1) () β t β t hild harateristis Age Age squared Male External inome External inome squared Birth Order Seond born Third born Fourth both Fifth + born onstant R-squared Rho orr(u,xb) Observations (household units)

25 Appendix 1: The Relationship between Allowanes (A) and hild Inome ( Y ) We strip down our model to the relevant bare-bone relationships: V = f(( Y + A+ b), γ ), U = YP A+ V (1a) and Y where we have taken parental inome so large that we an set the marginal value of money equal at all ranges for the parents (all the trade-offs between the utility of the hild and transfers is now in the funtion f), where servies are unimportant, and where the hild s external inome depends on the produt of γ and some non-negative random variable v. We will use g γ and g ν to denote the = γ v probability density funtions of γ and v. In the first equation, b is a positive onstant. If we take the value of independene that the parents assumes the hild has equal to the expeted value, the relation between A and Y follows from differentiating (10) for this ase: V(( Y + A+ b), E[ γ Y ]) da E[ γ Y ] E[ γ Y] ( Y + A+ b) = 1 + * dy Y V(( Y + A+ b), E[ γ Y]) ( Y + A+ b) from whih several items stand out immediately: unless hanges in Y onvey information about γ, then E[ γ Y ] Y will be 0 and da/ dy will beome negative. Only when E[ γ Y ] Y is suffiiently positive will there be a range for whih da / dy is positive. Intuitively, we would think that E[ γ Y ] Y would have to be positive at Y =0 and that minimal set of irumstanes under whih this ours is: E[ γ Y ] Y g (0)>0, g (1)>0, g (0)=0, lim lim g (x+m)/g (x) 0 γ γ ν x m ν ν beomes 0 at high levels of Y. A whih are a set of regularity onditions on the p.d.f. s of γ and v. Under these onditions, E[ γ Y ] E[ γ 0] = 0, E[ γ ] = 1,limY 0 =. Proofs of this are available on request, but the Y intuition is very basi: under these irumstanes, when Y is near 0 then all the mass of v will orrespond to γ being very lose to 0, and when Y beomes very large then all the mass of v will orrespond to γ being very lose to 1. 5

26 This result implies that we will then indeed have a negative da / dy when Y beomes large whilst E[ γ Y ] will be inreasing in Y for some prior range. We now show two examples to illustrate the relations we may empirially find: a) f = ln( γ ( Y + A+ b)) In this ase, the marginal utility of the hild is higher with a higher value of independene and Y will indeed onvey information about γ. Nevertheless, beause V(( Y A b), E[ γ Y]) = 0, E[ γ Y ] ( Y + A+ b) + + the information that Y onveys about γ is irrelevant and we would have da/ dy = 1. b) suppose f = ln(( Y + A+ b) γ ) and γ Uni[0,1] and ν σ. ln( ) N[0, ] da E[ γ Y]( Y + A+ b) In this ase we have = 1+. We then have after some additional dy Y E[ γ Y ] alulations: 1 γgg( Y / γ) dγ 1 γ ν 1.5σ 0 Ye 1 0 gg γ ν( Y / γ) dγ 0 E[ γ Y ] = γ p[ γ Y ] dγ = = where Φ(.) denotes the umulative standard normal distribution. Now, 1.5σ ( Y + A+ b) Ye Φ( ln Y / σ σ) da/ dy = 1 + / Y E[ γ Y ] Φ ( ln Y / σ σ) Φ ( ln Y / σ σ ) Φ ( ln Y / σ σ) whih displays an inverted u shape for some values of σ and b. A graphial example where σ =0.1 and b=0.15 is shown below. The inrease or derease in monetary transfers is likely to be ompensated by hanges in non-monetary transfers, but these are left out of the model for simpliity. 6