1 THE ECONOMIC MOTIVES FOR CHILD ALLOWANCES: ALTRUISM, EXCHANGE OR VALUE OF INDEPENDENCE? Lisa Farrell*, Paul Frijters** and Michael A. Shields* * Department of Economics, University of Melbourne, Australia ** Tinbergen Institute, Free University Amsterdam, Netherlands August 2002 (preliminary draft) Abstract This paper looks inside the “black box” of the family and examines the determinants of inter vivos transfers in the form of allowances given to children. We consider in a simple model two main competing explanations for the transfer of money from parents to children in the form of regular allowances, namely altruism and exchange. We also extend the altruism framework to include unobserved child heterogeneity in monetary autonomy or the 'value of independence'. We use a unique dataset drawn from the British Family Expenditure Survey, which enables us to explicitly test both the inter-generational predictions of the various models, and through a study of siblings, we are also able to consider the intra-household aspects of such payments. Using both random (inter-household) and fixed-effect (intra-household) estimators, we find robust evidence of an nshape relationship between a child's external income and the receipt of allowances from parents. Importantly, this estimated profile does not fit the predications of simple models of altruism or exchange, but does fit an altruism model with unobserved heterogeneity. Further support for the importance of the value of independence is that girls and those with higher birth orders obtain much higher allowances, whereby we argue both girls and those born later mature earlier and are therefore likely to be causally related to a high value of independence. We believe that further investigation of the motives underlying intra-household transfers is important for the design of policies aimed at redistributing income, such as child welfare payments. Keywords: Child Allowances, Altruism, Exchange, Inter-Household, Intra-Household JEL Classifications: Corresponding author: Lisa Farrell, Department of Economics, University of Melbourne, Parkville, Melbourne, Australia, 3010. E-mail: lfarrell@unimelb.edu.au. 2 1. Introduction This paper looks inside the “black box” of the family and examines inter vivos transfers in the form of allowances (pocket money) given to children. The economic literature that considers intrahousehold transfers has mainly concentrated on bequest motives. Here, we consider two competing explanations for the transfer of money from parents to children in the form of regular allowances (pocket money), namely altruism and exchange. In the case of altruistic motives (Becker, 1981) parents are assumed to derive a warm glow from the transfer of household resources to their children. They have others-regarding utility functions. In the exchange model (Bernheim et al., 1985) allowances are seen as payments to children for some services they deliver to parents. The literature on bequests has been inconclusive regarding the motives for intra-household transfers. Tomes (1981) support’s the altruistic motive by showing that the size of bequests are inversely related to the recipient’s income. In contrast, Menchik (1980) suggests parents obey bequest norms. They simply divide bequests equally amongst siblings, rather than behaving in an altruistic manner. Bernheim et al (1985) finds evidence of bequests as an exchange mechanism through an analysis that quantifies child services as the frequency of visits and phone calls to parents by children living outside of the home. He notes that the level of these services is positively related to the size of the potential estate and that siblings compete with each other in this sense. Economists have, however, paid little attention to inter vivos transfers mostly due to a paucity of data with which to explore the motives for such transfers. Although Cox (1989) looks at transfers between family units and finds evidence mostly in favour of exchange rather than altruism. Data on allowances given to children provides an interesting way to re-examine these issues and to test the two competing motives: altruism versus exchange. The available evidence suggests that children begin to receive allowances, in the sense of regular transfers from other household members, between the age of 5 and 7 (Furnham and Thomas, 1984). Children also receive income from other sources outside the household, i.e. from jobs both formal and informal (perhaps even illegal employment), and as gifts (e.g. birthday, Christmas and holiday money). These other sources of income outside of the household are likely to affect the willingness of parents to transfer household resources to children and the willingness of children to supply services to parents in exchange for an allowance. Barnet-Verzat and Wolff (2001) look at pocket money in this context of altruism and exchange models. Their empirical results show that a whole host of motivations are relevant and present these results as one explanation for why there is a lack of consensus among economists regarding the motives for inter vivos transfers. Here we contribute to the altruism versus exchange debate by analysing allowances in a unique data set that allows us to test both the inter-generational predictions of the models and secondly, through a study of siblings we are also able to consider the intra-generational aspects of such 3 payments. The analysis to date has concentrated on testing the competing hypothesis through their predictions regarding the inter-generational comparative statics only, neglecting the intragenerational predictions of the models. Further investigation of the motives underlying intrahousehold transfers is important as this has important policy implications for policies aimed at redistributing income, such as pensions and child welfare payments. This paper proceeds as follows. Section 2 introduces the theories of altruism and exchange, and highlights the comparative statics of a model that combines both explanations of parental allowance giving to children. The data and sample characteristics are described in Section 3, and our econometric modelling approaches are discussed in Section 4. The results of the statistical analysis are presented in Section 5, together with a theoretical framework that is consistent with out empirical findings. Finally, we conclude in Section 6. 2. Theoretical Background We will consider two existing explanations of allowances given to children by parents, altruism and exchange, whereby we extend the altruism model with the existence of unobserved heterogeneity. We first give the basic intuition for the two existing explanations, which we combine into in a single simple model. (i) Altruism The concept of interdependent utility functions has a long history. With respect to family networks Becker (1981) first proposed the idea that parents may receive utility from the well-being of their children. Thus they may be motivated to give children direct income transfers in the form of regular allowances. Such inter-generational transfers are aimed at bringing together the living standards of parents and kids. Moreover, parents may wish to equalize well-being across children in the household, thus using allowances to act as a form of intra-generational compensation. One empirical prediction from altruism is that parent would compensate children for having a low exogenous income of their own. Indeed, in a general dynamic model Cox (1987) shows that a one unit increase in parents income together with a one unit decrease in the child’s income should lead to a one unit increase in the transfer from the parent to the child. Altonji et al. (1997) show empirically this condition does not hold. They find that redistributing income in this way leads to only a 0.13 increase in the size of the transfer. (ii) Exchange Whilst altruistic motives are sufficient to explain the existence of allowances it is not necessary to apply altruistic motives in order to invoke other-regarding behavior. Self-interested parents may 4 give allowances as part of an implicit or explicit exchange contract where allowances are paid in exchange for services. These services may simply be compliance with parental regulations or attention given to the parent by the child. In some households children may be involved in home production through activities such as providing childcare for younger siblings. Moreover, this exchange contract may be intertemporal in nature, such as the promise to look after the parents in their old age, indeed if this is the service that parents purchase then one would expect to see allowances increase as the child gets older and therefore closer to leaving the family home.1 The empirical predictions of the exchange motive will hinge on the marginal value of the time of the child, which will determine the ‘price’ of the services, and the marginal value of the service of the child to the parent, which will determine the willingness to pay. It would seem likely to expect that children with higher exogenous income value their time more highly than others and that they would hence have a higher price for their services. If these services are then normal goods, the payment should decrease with its price. If the services are necessary goods, payment may increase with the child’s income. Hence the empirical prediction on the relation between allowances and external income from exchange would ex ante seem ambiguous. We will combine these two main arguments in a single model, adapted from Cox (1989). The child’s utility function is: = ( , ) V VY AS C + , (1) and the parent’s utility function is: ( , , ( , )) U UY ASVY AS =− + P C . (2) where A=allowances and A ≥ 0 , YP = household income, Yc =the child’s income and S= the service children provided to parents such that S ≥ 0 . One should note that the income of the child and the parent is assumed to be exogenous. We make standard assumptions about these derivatives: 1 . See Cox (1990) and Cox and Jappelli (1990) for the full exposition of the model in an intertemporal framework where parents act as lending agents to credit constrained children. The predicted effects of the income variables remains unchanged in this framework. 5 2 2 2 2 2 2 0, 0, 0, () ()() 0, 0, 0, 0, 0 ( ) P Pc c U UV YA YA YA V UUV V YA V S S S ∂∂ ∂ > <> ∂ − ∂ − ∂+ ∂ ∂∂∂∂ < >>< < ∂+ ∂ ∂ ∂ ∂ (3) which means that positive but decreasing marginal utility is derived from consumption; the production of services is assumed to have increasing marginal utility cost for the child; and the parent values the utility of the child. As the leading example we have in mind, we take crossderivatives to be rather unimportant and the marginal utility of the services and child’s utility to be constant. This is for instance the case when the parent’s utility function is separable: ( , , ( , )) ( ) ( , ) UY ASVY AS f Y A S VY AS PC P C − + = − ++ + (4) Now, we shall decompose the transfer of the parent to the child into an altruistic component and a payment for the services of the child: 0 A A aS = + ( ) . The altruistic component is defined as the transfer a parent would make even in the absence of any services from the child, i.e. the ‘unconditional payment’ to the child. This level will be determined by the first-order condition of the maximization problem of the parent: 0 0 0 00 ( ,0, ) ( ,0) 0 () () P C P C dU Y A V V Y A U U dA Y A V Y A − ∂+ ∂ ∂ ⎛ ⎞ = −+ = ⎜ ⎟ ∂− ∂ ∂+ ⎝ ⎠ , (5) which can in our leading example be simplified as: 0 0 0 ( ,0) ( )( ) C P C f VY A YA YA ∂ ∂ + = ∂− ∂+ (6) which is assured to have a unique solution because 0 ( ) P U Y A ∂ ∂ − increases as A0 increases whilst 0 0 ( ,0) ( ) C C VY A Y A ∂ + ∂ + decreases due to the concavity of the utility functions. What is easily seen is that the solution level of A0 will be decreasing in YC under any functional form. If the marginal value of money to the parent is virtually constant (i.e. parental income is much bigger than the transfer), this 6 increase is on a one-to-one basis, as in Cox (1987). In such a case, A0 can be written as i0 0 max{0, } A AY = − c where i A0 is found by solving (6) for YC =0. Now, the part of the transfer that is a payment for services will have to take account of the incentive compatibility constraint of the child, i.e. the child will only supply the desired amount of service if the payment compensates for the loss of utility. This means there must hold: 0 0 ( , ) ( ,0) VY A aS VY A C C + +≥ + (7) Obviously, a maximizing parent will set a(S) such that this condition is indeed binding, which means that the implicit price of S can be found by total differentiation of (7), yielding: 0 / ( ) c da V V dS S Y A a ∂ ∂ = − ∂ ∂++ (8) which is a differential equation that, together with the initial condition that a(0)=0, uniquely identifies a(S). What is immediate is that this implicit price of extra effort is increasing in YAa c + +0 and thereby in Yc . 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, which means that less is spent on it the higher the price. Under the second assumption it is a necessary good, which for instance arises if parent demand a fixed amount whatever its price, which would mean more is spent on it in total when its price goes up. 7 FIGURE 1: Allowances when there is Altruism and Exchange We can see the main arguments of the model in the case of our leading example: when i0 Y A c < , then i0 Y A c + is roughly constant, and hence the price of the services is the same in the range. Although there can be some parental income effects which we’ve ignored here (when the parent gives less to the child, the parent has more to spend of its own and the marginal value of money decreases for the parent), these are not likely to be very important given the relatively low amounts of money transfers made to children. Hence, the amount of services bought in is roughly constant when i0 Y A c < , which means total transfers go down linearly. When the altruistic transfer drops to 0, which occurs when i0 Y A c = , the parent only transfers money as a payment for services. These will be declining with price (and hence with Yc ) when services are a normal good and increasing with price when services are a necessity. In our leading example we hence get the clear prediction that transfers should go down as a child’s own income increases at low levels, whilst transfers may increase or decrease at high levels of the child’s income, depending on the type of good that these services are. If we are only prepared to make the general assumptions, all that we can safely say is that the transfers should go down initially and will only increase with higher Yc when the demand for services is very price-inelastic. 8 (iii) Altruism and the 'Value of Independence' So far it has been implicit that there is no heterogeneity in the population with respect to utility functions and that the child’s external income is exogenous. These assumptions are often implausible as there are likely to be unobserved factors that make some children value monetary transfers more than others and these unobserved factors may also push up the child’s own income, leading to a statistical though non-causal relationship. To make this explicit, we allow for unobserved heterogeneity in the utility function of the child: (( ), , ) V VY A S C = + γ (9) where the unobserved parameter γ has a continuous distribution over the whole population. We label γ as the degree to which individuals value independence. This means it is bounded between 0 and 1. The value of independence and the external income of the child are complementary in the utility function of the child: 2 0 C V γ Y A ∂ ≥ ∂∂ + . The value of independence and the external income of the child are furthermore likely to be statistically correlated. This argument relies on several considerations. First we recognize that the child’s income is itself made up largely of monetary gifts of other family members. Because there is a choice element to the type of transfer given to a kid, these monetary gifts are a substitute for inkind transfers, such as clothes or toys: it may be the case that the child requests money instead of other types of gifts. Similarly, a large amount of income earned by the child itself indicates that the child values being able to determine his or her own expenditures above relying on in-kind transfers. For these reasons the income of the child seems likely to be highly correlated with some wish for monetary independence the part of the child. Optimising behaviour of the child thus translates into a positive correlation between γ and YC . This means that the external income of the child may give information about the degree to which the child values his independence. What does this now mean for parental decision making? A maximising parent will now set the transfer such that marginal values are equated: (( ), , ) () () C P C U U VY A S YA V YA ∂ ∂ ⎛ ⎞ ∂ + γ = ⎜ ⎟ ∂− ∂ ∂+ ⎝ ⎠ (10) 9 from which we can see that, if γ were observed, parents will increase their altruistic monetary transfer to the child with a high γ because this increases (( ), , ) ( ) C C VY A S Y A ∂ + γ ∂ + . If there is a positive correlation between γ and Yc , i.e. if external income conveys information about γ, this can lead to a spurious positive correlation between Yc and A in some interval (see Appendix for examples). There are two predictions of interest here. The first is that heterogeneity in the value of independence may explain some heterogeneity in transfers. We will in the empirical part check this prediction by looking for indicators of the value of independence. Our main indicator is the birth order of the child in the household because there is a lot of psychological evidence to suggest that the younger siblings mature faster than the older ones. The second prediction of this theory is that excluding indicators for the value of independence will bias the estimates of the effect of variables that correlate with the value of independence. Amongst these is arguably the external income of the child. Now, there is actually not a clear prediction as to the size or even direction of this bias. In the appendix we illustrate the possibilities with two examples within a general class. Under some assumptions on the utility function and the precise statistical relation between γ and Yc , the bias is non-existent and in others the bias leads to a nonmonotonic relation between the external income of the child and the transfers to that child. 3. Data and Sample Characteristics This analysis is based on the currently available and to our knowledge little used data on children’s allowances contained in the British Family Expenditure Survey (FES). The FES is a nationally representative cross-sectional survey that has been conducted on an annual basis since 1957. Some 10,000 households are selected each year to take part in the FES, and the response rate is typically around 70%. The main aim of the survey is to provide a reliable source of information on household expenditure, income and other aspects of household finances. To account for seasonal differences in expenditure face-to-face interviews are spread evenly over the year. Each individual aged 16 or over in the households visited is asked to fill in an income questionnaire and to keep diary records of daily expenditure for two weeks. Parents are also asked to record details of children’s income from outside the household and the amount of pocket money they give to children. We pool across the two years that contain allowances and other child income data at the level of each individual child in the household i.e. 1998/99 and 1999/00. 2 Our data shows us the value of allowances that the child gets and any other monies received from outside the household, as well as various characteristics of the child. The children in our 2 The survey asked questions relating to other sources of child income for the first time in 1998/99. 10 sample are aged 0-15 years and we have a sample of 7482 children evenly distributed by age and living in 4055 households. By matching the children to the household we are also able to obtain a lot of information about the characteristics of the household. We are especially interested in the sibling composition of the household in order to be able to test the intra-generational predictions of our competing hypothesis regarding the motives for giving allowances to children. As well as allowances we observe monies received from outside the household. Some children in our sample have paid part-time jobs. Other children gain income from informal work and many children have income in the form of interest on child bank accounts and building society accounts. Children in our data set are also observed receiving income as cash gifts from people outside the household. The distinction between these sources of income is unimportant for our task here, our theoretical framework only requires that we know the total income the child generates from outside of the household in order to be able to test between altruism and exchange as motives for parents giving children allowances. Summary statistics of the raw data can be found in Table 1. We can see that across all the children in our sample 18.91% of children receive pocket money, however, this proportion increases with age. Indeed the proportion receiving allowances increases steadily with age from 0.65% at age 1 to 29.26% at age 15. The size of the allowance follows a similar pattern. The average conditional allowance across 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 allowances, with girls receiving a higher average level of allowance that boys (£3.69 compared to £3.23). Britain's ethnic minorities appear less likely to receive regular allowances but have higher average allowances. [TABLE 1 ABOUT HERE] The relationship between allowances and the level of external income of the child appears to be n-shaped. Only 16.60% of children with no external income receive an allowance, where as 33.73% of children with an external income of £6-10 per week also receive an allowance and this trails off to 23.89% for those with an external income greater than £10. The average conditional allowance however is increasing in the level of external income. This is completely at odds with the altruistic explanation of allowances. The exchange motive can fit either an increasing or a decreasing relationship and is hence more in accordance with this initial finding. Regarding parental and household characteristics, we find the percentage of children receiving allowances and the size of the average allowances is negatively related to the number of siblings in the household suggesting that children with siblings compete for household resources. Regarding 11 the marital status of the child’s parents the raw data suggests that children of lone parents are more likely to be receiving an allowance than their two parent counterparts but they receive a lower conditional average amount. Children with working mothers appear to be more likely to be in receipt of an allowance and to receive more. With respect to household income we can see that the probability of receiving an allowance and the size of the allowance is increasing in household income. Finally we consider how the level of allowances and the propensity to give an allowance changes with the degree of 'external' altruism that the parents show. We capture this by the size of regular donations to charity made by the child’s parents. We can see that children of regular charity givers are more likely to receive an allowance (24.48% compared to 16.99%) but the conditional size of the allowance is not affected. Figure 2 below shows the relationship between the percentage of children who receive an allowance and the percentage of children who have external income, by age. We can see that there are very few children with allowances at very young ages but there is a large increase in the number of children receiving an allowance after age six. This is consistent with the available evidence that suggests that children begin to receive allowances 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 children have external income than have an allowance. This is reversed for children between the ages of 6.5 and 13.5 years of age. However after age 13.5 years old more children have an external income than receive an allowance. This is consistent with the fact that age 13 is the legal age at which children in Britain are legally allowed to have paid employment. 12 FIGURE 2: The Relationship between Age and the Receipt of Allowances and External Income 0 10 20 30 40 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Age % Receiving Allowances External income13 4. Inter and Intra-Household Empirical Models of Child Allowances The focus of our empirical analysis is to model the provision of allowances given to children. The theoretical models outlined in Section 2 suggest that the child’s exogenous income will be a key factor in explaining the level of provision of allowances across children, although the descriptive statistics in Section 3 suggest other factors may also be important such as characteristics of the child and the household in which she lives. Thus our models of allowances will have the following general form: ( , , ) A fZYH c cc c = (11) Where Ac is the allowance received by child c, Zc is a set of characteristics of child c, Yc is the exogenous income of the child and Hc is a set of household and parental characteristics. (i) Inter-Household Estimates As noted in Section 3 not all the children in our sample receive an allowance and so our statistical framework needs to account for this clustering of observations at zero. As our base model we therefore adopt a Tobit specification. We also explore the importance of unobservable household effects in determining the size of allowances. This statistical framework is based on a random effects specification, which allows us to investigate the level of correlation between allowances of children in the same household that is due to unobservable household effects. The panel dimension of our model arises from the fact that we observe each child and their siblings within the household. Given that the sampling frame of the FES is at the household level, we are able to create a panel of data for households. This allows us to control for the fact that there may be some unobservable household specific effect that means the children in one household may be more likely to receive an allowance than children in another household. We thus have a random effects Tobit model: * 12 3 AX Y H hc hc hc hc hc = ++ + β β βν (12) ν hc h hc =α η+ and * if >0 0 if 0 c c c c A A A A ⎧⎪ ⎫⎪ = ⎨ ⎬ ⎩ ⎭ ⎪ ≤ ⎪14 where * Ahc is the unobservable propensity to receive an allowance for child c in household h; Ahc is the observed allowances of children in household h; X,Y and H are vector of exogenous characteristics; β 's are the associated vectors of coefficients; αh is the ‘household’ specific unobservable effect and ηhc is a random error term. We assume a random effects specification, where 2 ηhc ~ IN(0, ) σ c , and in order to marginalise the likelihood it is assumed that, conditional on the covariates, αh are ( ) 2 0,σ α IN and are independent of the and the covariates ηhc . This implies that the correlation between the error terms of children who live in the same household is a constant given by: 2 2 2 ( , ) hl hk corr l k α α η σ ρ νν σ σ == ≠ + (13) Thus, ρ represents the proportion of the total variance contributed by the panel level variance component. A fuller discussion of the Random Effects Probit model and the associated likelihood function can be found in Arulampalam (1999). The likelihood is computed using 20 point GaussHermite quadrature (see Butler and Moffitt, 1982). This model is again estimated for both the basic and extended regressor set in order to test the robustness of the coefficients to the inclusion of the external altruism variable. Given the richness of our data, the covariates in the basic model are: Z = age (and it's square), gender and ethnicity; Y = the child's amount of external income (external income is entered as a quadratic, following extensive tests for functional form); and H = years of education of the mother and father, age of the mother and father, the log of gross household weekly income, number of siblings in the household, lone parent, working mother, regional of residence and degree of urbanization of residence. In one extended model we additionally include a variable representing the amount of regular charitable donations made by the adults in the household, which should capture the parents’ degree of external altruism towards others outside of the household; given that external and internal altruism might be correlated, this gives us a direct test of whether altruism may be involved and which variables’s coefficients change as a result of including such an indicator. In a second extended model we include birth order .. blab la very important… blabla picks up value of independence. (ii) Intra-Household Estimates 15 A strong assumption in the random effect model is that the unobserved household characteristics are unrelated to observable characteristics. This assumption can be relaxed by looking at the allocation of allowances within the household. In order to investigate the intra-household aspects of our competing hypotheses for the provision of allowances, we estimate a fixed effects model. This will allow us to compare differences in the levels of allowances across siblings controlling for observable characteristics of the siblings. In this specification we are looking at the within household variation in the level of allowances given to children rather than the between household variation that was captured in the previous models. Here we use an OLS fixed effects model, given the problems with the available estimators for the conditional tobit fixed effects model3 . Our final specification is therefore: 1 23 A XYZ hc h hc hc h hc =α + +++ β β βε (14) Where Ahc is the observed allowance of the siblings in the household, X, Y are vectors of exogenous characteristics which are expected to influence Ahc and which vary across children in the household; Zh is a vector of variables that vary across households but for each household are constant across the children in that household; αh is an idiosyncratic fixed effect which accounts for inter-sibling differences in unobserved explanatory variables- assuming these differences are constant over time and hc ε is a random error term. It should be noted that we cannot recover estimates of any explanatory variables that do not vary across the children in the household i.e. those contained in Zh . However the fixed effects estimator is robust to the omission of these childinvariant regressors. In this model the coefficient on the exogenous child’s income variable tells us about parent’s treatment of children within the household and thus captures intra-generational aspects of the provision of allowances. The fact that we can identify siblings means that our data uniquely allows us to investigate the intra-generational predictions of our competing hypothesis regarding the motives for giving allowances to children. By using the fixed effect method we will be able to tell whether the relationships at the population level are tainted by simultaneity issues at the household level. We could for instance think that some households have both very high unobserved savings and very rich friends. Such an unobserved characteristic would presumably lead us to observe both high levels of ‘exogenous’ income for the children (in the form of monetary gifts from rich friends) and high transfers to the 3 The problem is that the estimators for the fixed-effect tobit model are not proven to be consistent: there is no guarantee that the estimated coefficients of the procedures of (Honore, 1992) or (Honore and Kyriazidou, 2000) converge to the correct coefficients. 16 children from the richer parents. At the population level, this would give us a positive relationship between exogenous income and transfers. In the household-fixed effect analysis however, these unobserved household characteristics would be controlled for and the spurious relation between exogenous income and transfers would fall away. 5. Results We now turn to the empirical results from our statistical models described in Section 3. The results are qualitatively consistent across all specifications. We will begin by considering the between household estimates before considering the results of the within household estimates. The parameter estimates for the inter-household estimators are presented in Table 2, and for the intra-household estimates in Table 3. We consider three models in Table 2. The basic one excludes the variable that captures a child’s parent’s degree of external altruism through their observed donations to charity and it excludes birth order. We then add both sets of variables in the two other specifications. We begin by discussing the key variables that allow us to draw conclusions regarding the motives for child allowances.17 (i) Inter-Household Estimates Looking at the pooled tobit estimates for the extended variable set (column 2 and 3) we find that allowances increase with external income until external income is about 6 after which transfers decrease.4 Figure 3 shows the estimated profiles between children's external income and allowances, for the random-effects model that includes the charity variable. FIGURE 3: The Estimated Effect of Child External Income on unconditional allowances and on allowances for those with positive allowances. Allowance and external income 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 1 3 4 5 6 8 9 10 12 13 14 15 Exteral income Allowance expected allowance conditional expected allowance lower bound of expected allowance higher bound of expected allowance note: the reference position is a 12 year old, where all other coefficients are taken as fixed. The initial increase in allowance as a response to increasing external income is inconsistent with the simple altruistic motivation for allowances. This initial increase could be consistent with the idea that parents have to pay higher amounts to receive the services of children who have other sources of income when these services are luxury goods. Yet, there is a level of external income at which this peaks and very rich children start to see the provision of allowances decrease as their income rises further. The exchange motivation cannot simultaneously fit this initial increase in transfers and 4 We have extensively tested for the best functional for child's external income. A quadratic specification leads to the highest log likelihood for all our models. We used a quadratic because our model suggested a possible non-linear relation between exogenous income and allowances. 18 the subsequent decrease. As shown in the appendix, altruism coupled with heterogeneity in the value of independence could explain such a non-monotonic relationship: at low levels of external income, the signal about the value of independence is sufficiently strong to yield a positive relation between the transfer and external income, whereas at high levels of external income there is no extra information about the value of independence and the allowance reduces. What directly supports the importance of the value of independence is that higher birth orders have highly positive and significant coefficients. We also see coefficients of other variables that substantially change as a result of including birth order. If we interpret this change as implying that these variables previously picked up part of the value of independence, those variables whose coefficient decreases from column 2 to 3 would have to be positively related to the value of independence. This would apply for having a working mother, having a lone parent, having a high family income, living in the city (which is the reference group for location) and being non-white. It would seem quite plausible that all these indeed would be positively related to a value of independence. [TABLE 2 ABOUT HERE] The random effects framework allows us to establish how much of the variation in the children’s pocket money can be explained by unobservable household characteristics. Do some households actively give children allowances whilst other households have ‘preferences’ for not giving allowances to children? We find that the intra-household correlation is substantial, for the basic model ρ =0.832 with t=85.25 and for the extended model ρ =0.830 with t=84.71.5 As expected, allowances are found to increase with the age of the child. This result is consistent with the idea that older children will be more economically active and thus their consumption set increases. However the negative coefficient on the age squared term shows this increase is at a decreasing rate. The gender dummy shows that boys appear to get lower allowances than girls although the coefficients are only significant for the random effects model. This result is inconsistent with a number of recent papers that have found that parents may favour boys when allocating family resources. One suggested reason for boy favouring is that parents value children 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 case that, direct commodity market-interactions benefit children through an educative process of economic socialisation, as well as through increased consumption, then we might expect to see a gender bias directed towards higher allowances among boys relative 19 to girls. Alternatively our result might be explained by the fact that adolescence, which is often argued to occur earlier for girls than boys, may be associated with economic as well as physical and emotional maturity in the eyes of parents. Hence gender may, quite apart from birth order with which gender is obviously not correlated, have a positive correlation with the value of independence. We also control for a number of characteristics of the child’s parents. The level of education of the parents appears to have no significant impact on the provision of allowances to children, although the signs of these coefficients are consistent across the models. The age of the parents is positively related to the size of allowances (but is only significant in the random effects models). Looking at household income we find little evidence that the size of a child’s allowances are determined by the income of the household in which they live. This may be because parents have an idea about the 'right' amount of income that a child should have given their age and so it is perhaps not surprising that allowances are not responsive to household income. We find that children of lone parents receive higher allowances (at the 10% level of significance) than children in two parent households. This results might be surprising given that lone parent households are known to be in the lower income deciles, however we have already should that the level of allowances is not correlated with the level of income in the household. We find no impact though of the presence of a working mother in the household. Again though, the drop in the coefficients of these last 3 variables when we include birth order indicates that being a working mother, a lone parent and having higher family income may be positively related to a high value of independence. Finally the result show that parents who are more altruistic towards people outside of the household in the sense that they donate more to charity are found to also give more to their children than parents who choose not to donate to charity. This suggests that externally altruistic parents are also more generous in the allowances they pass to their children. (ii) Intra-Household Estimates Next we will consider the intra-generational predictions of our competing hypothesis regarding the provision of allowances to children. Table 3 presents the results of this study, where the first striking aspect is that the significance of the found relationships has dropped substantially. This reflects the fact that there is not a lot of variation within the household to identify the underlying relationships with. However, taking the point estimates of the coefficients, we can see that the coefficients on the level of external income of the children are very similar to those of the random effects specification. Within households those children that have higher exogenous incomes first 5 Our sample includes a number of single child households. To test the robustness of our intra-household correlation findings, we have fitted the models including only those households for which we have data on at least two children. 20 receive more and only at high levels of exogenous income do they start receiving less. This suggest that i) there are no very important unobserved household characteristics that are responsible for the results in Table 1 and 2, and ii) the simple model of altruism and exchange cannot by themselves explain the relations between exogenous income and transfers under any specification. [TABLE 3 ABOUT HERE] The results looking at differences across siblings are also consistent with the between household results, i.e. allowances increase with the age of the child but at a decreasing rate. Male siblings are found to receive statistically significantly lower allowances than females in the same household. The results again strongly support the theory that the value of independence is important: those with higher birth orders obtain much higher transfers within the household. The inclusion of birth order furthermore somewhat reduces the importance of external income though not by very much. This in turn suggests that if external income is related to a value of independence, it is an aspect of the value of independence not fully captured by birth order. 6. Conclusions In this paper we have used detailed household level data to investigate the motives for parental giving of allowances to their children. The two main competing motives highlighted in the economic literature are altruism and exchange. Altruism means that parents gain a 'warm-glow' from the increased utility that their children deriving from the allowance, whilst exchange is motivated by the giving of allowances to children in order to 'buy' services from them, such as good behaviour. The former model predicts that parents will give the most to children who have the least external income, whilst the exchange model leads to ambiguous predictions. We have included to these standard models a third one in which we combine the existence of altruism with unobserved heterogeneity in the value of independence of the child. Given the richness of our data we have been able to explicitly test which of these models is able to fit our data. In all specifications we find an n-shaped relationship between external income and the transfers. This most clearly violates the initial arguments on altruism. Despite this, the data clearly suggests that altruism indeed does increase overall transfers to children and thereby that it is relevant. Our third model does allow for cases when this emerges, most notable when at low levels of external incomes an increase in this external income indicates a greater value of independence which leads the parent to increase its transfer to the child. This is then a statistical relationship though, not a causal one. The estimated ρ ’s are all quantitatively similar in magnitude and significance to those presented in Tables 2. 21 As a direct measure of the value of independence we have used birth order because those born later in the household are likely to mature earlier. In the results we indeed find that those born later receive much higher transfers. Further evidence to support the idea that the value of independence is heterogeneous and an important predictor of transfers is the fact that girls obtain more transfers than boys because girls are likely to be independent sooner than boys. It finally concurs with our finding that parents who are more generous to charity in general not only give higher transfers on average but are also more responsive in their transfer to the external income of the child. 6 . 6 Separate random and fixed-effect models were estimated, with the same covariates as in Tables 2 and 3, for observably altruistic parents and observable non-altruistic parents, where altruistic parents were defined as giving regularly to charity. The finding that altruistic parents display a much stronger curvature (transfers increase more rapidly with child’s income at low levels and only very late tail off) than non-altruistic parents is consistent across both the inter-household and intra-household models. These additional results are available from the authors on request. 22 TABLE 1: Who Receives Allowances, and How Much Do They Receive? Receiving Allowance (%) Average Allowance (£) All 18.91 (0.45) 3.45 (0.11) Child characteristics Boys 19.03 (0.63) 3.23 (0.13) Girls 18.80 (0.65) 3.69* (0.17) Age = 1 0.65 (0.37) 0.61 (0.17) Age = 5 8.87* (1.34) 1.00* (0.10) Age = 10 32.42* (2.14) 2.65* (0.25) Age = 15 29.26* (2.23) 6.07* (0.43) White 19.21 (0.47) 3.42 (0.11) Non-white 16.52 (1.42) 3.81 (0.32) Child external income £10+ per week 23.89* (4.02) 5.85* (1.88) Child external income £6-£10 per week 33.73* (5.02) 5.16* (0.75) Child external income £1-£5 per week 27.38* (1.16) 3.32 (0.16) Child has no external income 16.60 (0.49) 3.46 (0.13) Parental and Household characteristics Three + siblings 16.55* (1.26) 2.16* (0.18) Two siblings 17.92 (0.91) 2.90* (0.16) One sibling 19.43 (0.70) 3.34* (0.18) No siblings 20.18 (0.99) 4.42 (0.22) Both parents 18.72 (0.52) 3.50 (0.13) Lone parent 19.49 (0.92) 3.30 (0.17) Working mother 21.03* (0.63) 3.62* (0.12) Non-working mother 16.20 (0.64) 3.15 (0.19) Total parental income (75-100%) 22.62* (0.97) 3.74* (0.22) Total parental income (50-74%) 19.19 (0.91) 3.47 (0.18) Total parental income (25-49%) 17.13 (0.87) 3.42 (0.26) Total parental income (1-14%) 16.70 (0.86) 3.06 (0.18) Parents regular charity givers 24.58* (0.99) 3.41 (0.19) Parents do not give to charity 16.99 (0.50) 3.47 (0.13) Note: The standard error of the mean is given in parentheses. * indicates if there is a significant difference between boys and girls, age group relative to age=1, non-whites relative to whites, external income amount relative to no external income, number of siblings relative to only child, lone parent child relative to having both parents in the household, total parental income quartile relative to the lowest quartile, parents regularly give to charities relative to those children whose parents do no give to charity. 23 TABLE 2: Household Random Effects Models of Child Allowances Determinants of Child Allowances Random Effects (1) Random Effects (2) Random Effects (3) β |t| β |t| β |t| Child Characteristics Age 1.984 15.57 1.989 15.41 2.187 16.50 Age squared -0.075 11.17 -0.075 11.06 -0.075 11.03 Male -0.430 2.53 -0.435 2.53 -0.415 2.56 Non-white -0.690 1.34 -0.826 1.64 -1.902 4.29 External income 0.250 2.15 0.241 2.05 0.253 2.27 External income squared -0.020 2.55 -0.020 2.49 -0.020 2.60 Birth Order Second born - - - - 0.728 3.92 Third born - - - - 1.987 5.94 Fourth both - - - - 2.922 4.75 Fifth + born - - - - 5.240 5.08 Parental and Household Characteristics Number of siblings in household -0.765 5.54 -0.693 4.62 -0.661 5.52 Years of education (Father) -0.078 1.44 -0.087 1.62 -0.106 2.13 Years of education (Mother) -0.056 1.12 -0.064 1.22 -0.022 0.42 Age (Father) 0.061 2.83 0.055 2.34 0.042 1.87 Age (Mother) 0.055 2.31 0.057 2.39 0.026 1.02 ln (Gross weekly income) 0.216 0.82 0.322 1.18 -0.109 0.49 Lone parent 1.618 1.89 1.661 1.89 0.112 0.12 Working mother 0.006 0.02 -0.019 0.04 -0.729 2.49 Charitable donations (£'s, weekly) - - 0.040 3.80 0.022 2.62 Locational Characteristics Region (12) YES YES YES YES YES YES Urban 0.936 1.70 1.079 1.61 1.880 3.96 Rural 0.964 1.69 1.023 1.56 1.707 2.97 Constant -18.96 9.87 -19.57 9.93 -17.50 9.15 Log likelihood -5596 -5594 -5573 Rho 0.832 85.25 0.830 84.71 0.847 92.48 Sample (in 4055 households) 7482 7482 7482 Notes: Absolute t-statistics given in parentheses. The omitted categories are female, white, both parents in household, non-working mother, first born and living in a city. 24 TABLE 3: Household Fixed Effects Models of Child Allowances Determinants of Child Allowances Fixed Effects (1) Fixed Effects (2) β |t| β |t| Child Characteristics Age 0.051 2.92 0.076 3.82 Age squared 0.002 2.04 0.002 1.92 Male -0.084 2.19 -0.082 2.14 External income 0.024 0.91 0.020 0.58 External income squared -0.003 1.40 -0.002 1.32 Birth Order Second born - - 0.050 1.02 Third born - - 0.171 1.94 Fourth both - - 0.321 2.34 Fifth + born - - 0.582 2.88 Constant 0.150 2.39 -0.080 0.66 R-squared 0.060 0.063 Rho 0.796 0.795 Corr(u,xb) 0.112 0.061 Observations (household units) 4055 4055 25 Appendix 1: The Relationship between Allowances (A) and Child Income (YC) We strip down our model to the relevant bare-bone relationships: (( ), ) V fY Ab C = + + γ , U Y AV = P − + (1a) and Y v C = γ where we have taken parental income so large that we can set the marginal value of money equal at all ranges for the parents (all the trade-offs between the utility of the child and transfers is now in the function f), where services are unimportant, and where the child’s external income depends on the product of γ and some non-negative random variable v . We will use gγ and gν to denote the probability density functions of γ and v . In the first equation, b is a positive constant. If we take the value of independence that the parents assumes the child has equal to the expected value, the relation between A and YC follows from differentiating (10) for this case: 2 2 2 (( ), [ | ]) [| ] [ | ]( ) 1 * (( ), [ | ]) ( ) C C C C C C C C C C VY AbE Y dA E Y E Y Y Ab dY Y VY AbE Y Y Ab γ γ γ γ ⎛ ⎞ ∂ ++ ⎜ ⎟ ∂ ⎝ ⎠ ∂ ∂ ++ =− + ∂ ⎛ ⎞ ∂ ++ ⎜ ⎟ − ⎝ ⎠ ∂ ++ from which several items stand out immediately: unless changes in YC convey information about γ, then [| ] C C E Y Y ∂ γ ∂ will be 0 and / dA dYC will become negative. Only when [| ] C C E Y Y ∂ γ ∂ is sufficiently positive will there be a range for which / dA dYC is positive. Intuitively, we would think that [| ] C C E Y Y ∂ γ ∂ would have to be positive at YC =0 and that [| ] C C E Y Y ∂ γ ∂ becomes 0 at high levels of YC . A minimal set of circumstances under which this occurs is: g (0)>0, g (1)>0, g (0)=0, lim lim g (x+m)/g (x) 0 γγν νν x m →∞ →∞ → which are a set of regularity conditions on the p.d.f.’s of γ and v . Under these conditions, [| ] [ | 0] 0, [ | ] 1,lim 0 C C Y C E Y E E Y γ γ γ →∞ ∂ = ∞= = ∂ . Proofs of this are available on request, but the intuition is very basic: under these circumstances, when YC is near 0 then all the mass of v will correspond to γ being very close to 0, and when YC becomes very large then all the mass of v will correspond to γ being very close to 1. 26 This result implies that we will then indeed have a negative / dA dYC when YC becomes large whilst [ | ] E YC γ will be increasing in YC for some prior range. We now show two examples to illustrate the relations we may empirically find: a) ln( ( )) C f = ++ γ Y Ab In this case, the marginal utility of the child is higher with a higher value of independence and YC will indeed convey information about γ. Nevertheless, because 2 (( ), [ | ]) 0 [ | ]( ) C C C C VY AbE Y E Y Y Ab γ γ ∂ ++ = ∂ ∂ ++ , the information that YC conveys about γ is irrelevant and we would have / 1 dA dYC = − . b) suppose ln(( ) ) C f Y Ab γ = ++ and γ ∼ Uni[0,1] and 2 ln( ) [0, ] ν ∼ N σ . In this case we have [ | ]( ) 1 [| ] C C C CC dA E Y Y Ab dY Y E Y γ γ ∂ ++ =− + ∂ . We then have after some additional calculations: 2 1 1 1.5 0 1 0 0 ( /) ( ln / 2 ) [| ] [| ] ( ln / ) ( /) C C C C C C C gg Y d Ye Y E Y p Yd Y gg Y d γ ν σ γ ν γ γγ σ σ γ γγ γ σ σ γ γ Φ− − == = Φ− − ∫ ∫ ∫ where Φ(.) denotes the cumulative standard normal distribution. Now, 2 1.5 ( ) ( ln / 2 ) /1 / [ | ] ( ln / ) CC C C C C C Y A b Ye Y dA dY Y EY Y σ σ σ γ σσ + + Φ− − =− + ∂ ∂ Φ− − which displays an inverted u shape for some values of σ and b. A graphical example where σ =0.1 and b=0.15 is shown below. 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